THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING COMPREHENSIVE CAVITATION DAMAGE DATA FOR WATER AND VARIOUS LIQUID METALS INCLUDING CORRELATIONS WITH MATERIAL AND FLUID PROPERTIES ~:....' Ramo,. Gardia.''.';' "'..''a A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Nuclear Engineering 1966 IP-74.

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COMPREHENSIVE CAVITATION DAMAGE DATA FOR WATER AND VARIOUS LIQUID METALS INCLUDING CORRELATIONS WITH MATERIAL AND FLUID PROPERTIES by Ramon Garcia A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1966 Doctoral Committee: Professor Frederick G. Hammitt, Chairman Professor Richard K. Brown Associate Professor Julian R. Frederick Professor William Kerr Associate Professor Edward A. Martin Professor Clarence Ao Siebert

Doctoral Committee: Professor Frederick Go Hammitt, Chairman Professor Richard Ko Brown Associate Professor Julian R. Frederick Professor William Kerr Associate Professor Edward A. Martin Professor Clarence A. Siebert

ACKNOWLEDGMENTS The author would like to acknowledge the financial support of the National Science Foundation under Grant G-22529 which provided the bulk of the support for this work. Mechanical properties data supplied by Pratt & Whitney Aircraft (CANEL) and The University of Michigan Department of Chemical & Metallurgical Engineering is also gratefully appreciated. The guidance and assistance of Professor F. G. Hammitt during the term of this investigation is gratefully appreciated, Special thanks are also due Mr. Fazil A. Aydinmakine, now of the Turkish Navy, for the design of the experimental cavitation vessel and supporting calculations; Mr. Henry Leeper, Project Metallurgist, Pratt & Whitney Aircraft (CANEL), and Mr. Glenn Wood, Project Engineer, Pratt & Whitney Aircraft (CANEL), for their unusual cooperation, continuing interest, and many helpful suggestions to the project; Dro Clarence A. Siebert, Professor of Chemical & Metallurgical Engineering, for many helpful suggestions and for supplying several items of experimental apparatus to the project; Dr. Mo John Robinson, Lecturer in Nuclear Engineering, for many helpful suggestions and continuing interest in this project; Mr. Richard L. Crandall, Research Assistant, Computing Center, for much assistance in the proper use of the Least Mean Squares Regression Program used for data correlation and the proper ii

interpretation of results; Mr. Edward Rupke, Instrument Shop Supervisor, Mr. William Rekewitz, Instrument Shop Foreman, and Mr. John Love, Instrument Maker, for many helpful suggestions and prompt service in fabricating all of the test specimens and special hardware required; and Mr. Allen R. Schaedel, Research Assistant in the Department of Nuclear Engineering, for many helpful suggestions, stimulating conversation, and continuing interest in this project. iii

TABLE OF COTENTS Page ACKNOWLEDGMENTS O. e o o.. o............ ii LIST OF TABLES.... o..o.. o....... 0. o., ix LIST OF FIGURES...,..,... o. e o.. o. o xiii Chapter I. INTRODUCTION AND LITERATURE SURVEY......... A- Introduction o O o....,..... 1 B, Historical Background -.......... 4 C. Problem Statement o....e.. 0....... 10 II. EXPERIMENTAL EQUIPMENT.. o.......... 14 A. Facility Selection....o o....... 14 i. Introduction 2. Piezoelectric Effect 3. Electrostrictive -Effect 40 Magnetostrictive Effect 5o:Choice of Accelerated Cavitation Device B. Description of Overall System.......... 21 C. Ultrasonic Transducer Assembly......... 23 D. Test Specimens. 9. O o... o o.... 30 1o Effect of Density on Specimen Size 2. Standard Cavitation Test Specimen 3. Special Cavitation Test Specimens Eo High-Temperature Cavitation Vessel.. o.. 38 1o Design Philosophy and Criteria 2, Method of Fastening Transducer to Vessel F. Furnace Requirements o... o.. O... 48 G. Temperature Controller Requirements.... o.. 52 H, Accelerometer Assembly. G. o...... 54 1. Introduction 2. Accelerometer Description 3. Accelerometer Calibration 4. Summary and Conclusions iv

Chapter Page J. Special Hardware. 0 0........... 67 III. EXPERIMENTAL INVESTIGATIQ NS............... 77 A. Objectives of Experimental Program..... 77 B. Experimental Test Conditions........ 79 C. Cavitation Studies in Lead-Bismuth Alloy at 5000F and 15000~F 0 0 0 a 0 F....... 83 1. Experimental Procedure 2. Experimental Results at 500~F 3. Experimental Results at 1500~F 4. Discussion and Comparison of Results D. Cavitation Studies in Mercury at 700F and 500~F.. 105 1. Experimental Procedure 2. Experimental Results at 70~F 3. Experimental' Results at 500~F 4. Discussion and Comparison of Results 5. Comparison with Venturi Facility Mercury Results E. Cavitation Studies in Water at 700F... 127 1. Experimental Procedure 2. Experimental Results —Subsets One and Two 3. Experimental Results —Subset Three 4. Comparison with Venturi Facility Water Results F. Cavitation Studies in Lithium at 500~F and 1500~F.............. 151 1. Experimental Procedure 2. Experimental Results at 500~F 3. Experimental Results at 1500~F 4. Discussion and Comparison of Results 5: Temperature Depeendece of Cavitation Damage in Lithium 6. Oxygen Analyses G. Comparison of Mercury and Water Results at 700F. 179 Ho Comparison of Lead-Bismuth, Mercury, and Lithium Results at 500~F........... 184 J. Comparison of Lead-Bismuth and Lithium Results at 1500F,. o o 0....... 186 Ko Cavitation Studies of Bearing Materials... 188 1o Introduction 2. Cavitation Studies in Mercury at 500~F a. Experimental Procedure b. Experimental Results 3. Cavitation Studies in Mercury at 70~F (Graphitar) ao Experimental Procedure b. Experimental Results v

Chapter Page 4. Cavitation Studies in Water at 70~F (Single-Crystal Tungsten) a, Experimental Procedure b, Experimental Results 5. Effect of Teflon Coating on CavitationErosion Characteristics a. Experimental Procedure b. Experimental Results 6. Comparison of Cavitation Results in Bearing Program IVo MECHANICAL PROPERTIES DATA FOR THE TEST MATERIALS... 216 A. Introduction o o. oo o.,e 0 o 0 0. a 0 0 216 Bo Mechanical Properties Selection..... o... 217 1. Tensile Strength (TS) 2, Yield Strength (YS) 3. Engineering Strain Energy (ESE) 4. True Strain Energy Based on Elongation (TSEE) 50 True Strain Energy Based on Reduction in Area (TSER) 6. Hardness (H) 7. Elongation (ELON) 80 Reduction in Area (RA) 9o Elastic Modulus (E) 10. Hobbs' Approach C. Tables of Properties at 70~F, 500F, and 1500~F.o.o., 0 o 0 0 0o 0. o 0 223 V. FLUID PROPERTIES DATA FOR THE TEST FLUIDS.... 243 A, Introduction ao o. o. o o o.o o.. 243 B. Fluid Properties Selection.. o....o o.. 244 1o Acoustic Impedance Ratio (AI) 2, Density ( ) 3o Surface Tension ( ") 40 Net Positive Suction Head (NPSH) 5. Bulk Modulus (B) 6, Kinematic Viscosity ( ) C. Tables of Fluid Properties at 70~F, 500~F, and 1500 F o o o o o o oo. o o 251 VI. CORRELATIONS OF CAVITATION DAMAGE DATA WITH MECHANICAL AND FLUID PROPERTIES o. O O e o o... o. 254 Ao Introduction. o. o o o o o. o.. o. 254 vi

Chapter Page B. Preliminary Correlations............. 255 1 Lead-Bismuth Data 2o Bearing Program Data C. Lead-Bismuth Correlations. oo o o.. o o 261 1. General 2. Single Property Correlations 3o Multiple Property Correlations Do Mercury Correlations o.. o. o o. 0 o. o 268 lo General 2o Single Property Correlations 3o Multiple Property Correlations E Water Correlations —Subset One O O O O o 273 1 General 2o Single Property Correlations 3o Multiple Property Correlations Fo Water Correlations —Subsets Two and Three. 276 1o Single Property Correlations 2o Multiple Property Correlations Go Water Correlations~-All Water Data.. 0 280 1. Single Property Correlations 2o Multiple Property Correlations 3~ Summary Ho Lithium Correlations at 500"F o.. o 287 lo Single Property Correlations 2. Multiple Property Correlations J. Lithium Correlations at 1500~F O. o O, a' o 0 291 Ko Correlations of all Lithium Data. o o.. 292 Lo Summary of Single Fluid Correlations..... 292 Mo Comprehensive Correlations of Lead-Bismuth, Mercury, Water, and Lithium Data......... 294 1. General 2o Single Fluid Property Studies 3o Multiple Fluid Property Studies 4. Second-Order Interaction Correlation 5. Hobbs' Energy Concepts No Comparison with Venturi Facility Correlations o.. 309 Po Graphical Single Property Correlations o.O oo 311 VII. THERMODYNAMIC EFFECTS Oo o o o o a o o a o o 313 A. Introduction 0o o o.. o.... o o o 313 B. Calculation of Thermodynamic Parameters 0 oo.. 315 Co Final Predicting Equation O......... o 329 VIII o SUMMARY AND CONCLUSIONS.. o o.o o o. o o. o o 337 vii

Page APPENDICES........ 0.......... 0 *l. 346 A. Heat Transfer Calculations........... 346 B. Computer Regression Analysis of Cavitation Data. 353 C. Plots of Normalized Inverse Cavitation Damage Versus Single Mechanical Properties........ 358 REFERENCES.~ ~.~ ~ ~ ~......~ ~ ~ ~. o ~ ~ 389 SELECTED BIBLIOGRAPHY................. 398 viii

LIST OF TABLES Table Page 1. Amplitude Measurement Data............ o o )662 2. Specimen Material-Fluid-Temperature Combinations Investigated..... o.o.. o. o o o o. 78 3. Materials Tested in Bearing Program..... o.. 80 4. Specimen Dimensions.................... 84 5. Relation Between Weight Loss and MDP......... 91 6o Summary of Cavitation Results in Lead-Bismuth at 500~F. o 95 7. Summary of Cavitation Results in Lead-Bismuth at 1500~F. o 102 8. Comparison of Cavitation Results in Lead-Bismuth at 500 ~F and 15000F................... 104 9. Summary of Cavitation Results in Mercury at 70~F.... 109 10o Summary of Cavitation Results in Mercury at 5000F..... 115 11o Comparison of Cavitation Results in Mercury at 70~F and 500~F.....,.. o....., 120 12. Comparison of Cavitation Erosion Data in Mercury at 70~F - Venturi and Ultrasonic Facilities... o.... o o 125 13. Summary of Cavitation Results in Water at 70~F - Subsets One and Two. o o. ~. o..o 130 14. Summary of Cavitation Results in Water at 70~F - Subset Three o.,, o o.. e 9., o.. o 140 15. Comparison of Cavitation Erosion Data in Water at 70~F - Venturi and Ultrasonic Facilities (Subsets One and Two).................o o o o o 148 16o Comparison of Cavitation Erosion Data in Water at 70~F - Venturi and Ultrasonic Facilities (Subset Three).. o. 149 ix

Table Page 17. Summary of Cavitation Results in Lithium at 500~F.... 154 18. Summary of Cavitation Results in Lithium at 15000F.... 161 19. Comparison of Cavitation Results in Lithium at 5000F and 1500~F............... 166 20. Effect of Temperature on.Gavitation Damage - 304 Stainless Steel....... 0......... 172 21. Effect of Temperature on Cavitation Damage - T-111 and Cb-lZr(A) n..... o....... 175 22. Summary of Oxygen Determinations......... 180 23. Comparison of Cavitation Results in Mercury and Water at 700F...e. o...0.....0. 182 24o Summary of Cavitation Results in Lead-Bismuth, Mercury, and Lithium at 5000F........... o 0.. 185 25. Summary of Cavitation Results in Lead-Bismuth and Lithium at 1500~F.......... 187 ~.. ~'. ~ ~ ~ ~ ~ ~ ~ ~~ 260 Heat Treatment for BG-42 Cavitation Erosion Specimens.. 190 27. Heat Treatment for Blue Chip Tool Steel............ 191 28. Summary of Cavitation Results inMercury at 500~F (Bearing Program)..... -... 9......,.. 193 29. Summary of Cavitation Results at 70~F (Bearing Program).. 201 30. Comparison of Cavitation Results Obtained in Bearing Program.................. 213 31. Mechanical Properties Data at 700F from Pratt & Whitney Aircraft (CANEL)..... o.........,. 226 32. Mechanical Properties Data at 5000F from Pratt & Whitney Aircraft (CANEL).... 227 33. Mechanical Properties Data at 15000F from Pratt & Whitney Aircraft (CANEL)...... -.... -...... 228 34. Mechanical Properties Data at 70OF from University of Michigan Laboratories.................. 240 3,. Mechanical Properties Data for Bearing Materials..... 241 x

Table Page 36. Fluid Properties Data at Various Temperatures...... 252 37. Preliminary Correlation of Lead-Bismuth Data with Mechanical Properties Data at 5000F......... 257 38. Preliminary Correlation of Lead-Bismuth Data with Mechanical Properties Data at 15000F...... 259 39. Preliminary Correlation of Bearing Program Data with Hardness O O.... oo.........o...oo 260 40. Summary of Single Property Correlations - Lead-Bismuth Alloy................. 263 41o Summary of Best Correlations with Ten Properties Considered - Lead-Bismuth Alloy........... 265 42. Summary of Single Property Correlations - Mercury. o 0. 269 43. Summary of Best Correlations with Ten Properties Considered - Mercury 0 0 0 0 0 0 0 o 0 0 0 271 44o Summary of Single Property Correlations - Water - Subset One o o o o 0 0 0 0. 0 0 o o 0 o 275 45o Summary of Best Correlations with Ten Properties Considered - Water - Subset One.o OO o.o 277 46. Summary of Single Property Correlations - Water - Subsets Two and Three 0 0 0 0 0oo o. 0 o 279 47o Summary of Best Correlations with Ten Properties Considered - Water - Subsets Two and Three OOoo o 281 48. Summary of Single Property Correlations - All Water Data o 284 49. Summary of Best Correlations with Ten Properties Considered -All Water Data o. o o o o o 0 0 285 50o Summary of Single Property Correlations Lithium at 500 F o o o o o 288 51. Summary of Best Correlations with Ten Properties Considered - Lithium at 500~F o o o o 0 0 0o o 0 o 290 52o Summary of Statistics for Comprehensive Correlations (Single Fluid Property)............... o 302 xi

Tab e Page 53. Values of Thermodynamic Parameters for Various FluidTemperature Combinations.............. 318 54, Experimental Cavitation Data- Type 304 Stainless Steel.... * *.. *..... 323 xii

LIST OF FIGURES Figure Page 1. Block Diagram of the High-Temperature Ultrasonic Vibratory Facility.................. 22 2. Photograph of the High-Temperature Cavitation Facility o. 24 3. Exponential Horn and Ultrasonic Transducer Assembly... 26 4. Typical Waveform Showing Position of Nodes and Antinodes on Transducer Assembly o o o o...... 29 50 Effect of Density on Cavitation Test Specimen Size.. 31 6. Standard Cavitation Test Specimen......... 33 7o Special Plexiglas Cavitation Test Specimen and Mounting Stud o o.............. o o. oo o o o o 35 8. Special Cavitation Test Specimen for Cu, Cu-Zn, Cu-Ni, and Ni o o o o o o o o o o o o o o o o o 37 90 Special Single-Crystal Tungsten Cavitation Test Specimern o o.o.. o o o o. o o o o 39 10o High-Temperature Cavitation Vessel and Ultrasonic Transducer.,. oo.....o. o o o o o. oo. o o o. 44 11. High-Temperature Cavitation Vessel and Ultrasonic Transducer Assembly Mounted in Furnace......... 49 12. Schematic of Variac, Furnace, and Temperature Controller o o. o o o..... o o. o o.. 53 13. Calibration Curve for Accelerometer.o o o.oo o. o.. 65 14. Modified Ultrasonic Horn..o, o. o o o.. o,.. o. 69 15. Adaptor Stud o o......... o o o o. o o o 70 16 Ultrasonic Horn Adaptor.o o o o..... o o. 71 17. Stud for Modified Cavitation Specimen.......... 73 xiii

Figure Page 18. Modified Cavitation Specimen.............74 19. Assembly Drawing of Modified Ultrasonic Horn, Adaptor Stud, Ultrasonic Horn Adaptor, Specimen Stud, and Modified Cavitation Specimen........... 76 20. Photomicrograph of Type 316 Stainless Steel Specimen Tested in Lead-Bismuth Alloy at 1500~F (Interior of Specimen, Magnification 1000X).........,... 86 21. Photomicrograph of Type 316 Stainless Steel Specimen Tested in Lead-Bismuth Alloy at 15000F (SpecimenSurface, Magnification 500X).......... 87 22, Photomicrograph of Type 316 Stainless Steel Specimen Tested in Lead-Bismuth-Alloy at 1500F (Specimen Surface, Magnification 50OX) l.............. 88 23. Effect of Cavitation Test Duration on Weight Loss at 5000F in Lead-Bismuth Alloy............ 93 24. Effect of Cavitation Test Duration on MDP at 500~F in Lead-Bismuth Alloy i...........9.4.... 94 25. Specimens Subjected to Cavitation Damage in Lead-Bismuth Alloy at 500~F and 15000F......... 97 26. Effect of Cavitation Test Duration on Weight Loss at 15000F in Lead-Bismuth Alloy...,... o.. 100 27. Effect of Cavitation Test Durationon MDP at 1500~F in Lead-BismuthAlloy.'. 0. l'- ~ -..'. 0... 101.I 28. Effect of Temperature on Cavitation Resistance in Lead-Bismuth Alloy. a.............. 106 29. Effect of Cavitation Test Duration on Weight Loss at 700F in Mercury e.o.,.......... 110 30. Effect of Cavitation Test Duration on MDP at 700F in Mercury. e.. o e o. l e -.... 111 rcur.................. ~.... 31. Photographs of Specimens Subjected to Cavitation Damage in Mercury at 700F......... 113 32. Effect of Cavitation Test Duration on Weight Loss at 500~F in Mercury........... 116 33. Effect of Cavitat n Test Duration on MDP at 500~F in Mercury.............. 1...... 117 xiv

Figure Page 34. Photographs of Specimens Subjected to Cavitation Damage in Mercury at 500F ~F........... 0 o 119 35. Effect of Temperature on Cavitation Resistance in Mercury...... e.... o o,.... 123 36. Effect of Cavitation Test Duration on Weight Loss at 70~F in Water - Subset. One... e. o o.... 131 37o Effect of Cavitation Test Duration on MDP at 70~F in Water - Subset One.o o. o.... o..... 132 38. Effect of Cavitation Test Duration on Weight Loss at 70~F in Water -Subset Two.............. 133 39. Effect of Cavitation Test Duration on MDP at 70~F in Water - Subset.Two e.... o......... o - 134 40. Photographs of Specimens Subjected to Cavitation Damage in Water at 70F - Subset One.........- 137 41. Photographs of Specimens Subjected to Cavitation Damage in Water at 700F -Subset Two.,.. o.,... 139 42. Effect of Cavitation Test Duration on Weight Loss at 70 F inWater - Cu and Ni (Subset Three)..... 141 43. Effect of Cavitation Test Duration on MDP at 700F in Water -Cuand Ni (Subset Three).,0. o.o.... 142 44, Effect of Cavitation Test Duration on Weight Loss at 70~F in Water - Cu-Ni and Cu-Zn (Subset Three),.o,, 143 45. Effect of Cavitation Test Duration on MDP at 70~F in Water - Cu-Ni and Cu-Zn (Subset Three). 0 o... o 144 46. Photographs of Selected Specimens Subjected to Cavitation Damage in Water at 700F -Subset Three, o..o.a 0.0 146 47. Effect of Cavitation Test Duration on Weight Loss at 5000F in Lithium,.....a... b.... 155 480 Effect of Cavitation Test Duration on MDP at 500~F in Lithiume....-........... 157 49. Photographs of Specimens Subjected to Cavitation Damage in Lithium at 500~F 5.. o.,. 159 50. Effect of Caviti'oat Test Duration on Weight Loss at 1500~F in Lithium'.. o... o.... 162 xv

Figure Page 51. Effect of Cavitation Test Duration on MDP at 1500~F in Lithium. o... o 0........ 163 52. Photographs of Specimens Subjected to Cavitation Damage in Lithium at 1500~F................ 165 530 Effect of Temperature on Cavitation Damage in Water - Type 304 Stainless Steel Specimen........ 169 54. Effect of Temperature on Average Weight Loss Rate for 304 Stainless Steel o o. o o o. o.. 173 55. Effect of Temperature on Average MDP Rate for 304 Stainless Steel... o.. 0. 0.....174 56. Effect of Temperature on Average Weight Loss Rate for T-lll and Cb-lZr(A)..... o.. o........ 176 57. Effect of Temperature on Average MDP Rate for T-lll and Cb-lZr(A) o o e o o o o........... o 178 58~ Effect of Cavitation Test Duration on Weight Loss at 500~F in Mercury.0 0. o o. o... 0 o... 0 194 59o Effect of Cavitation Test Duration on MDP at 500~F in Mercury o 0 o o o o o e o o o 0. 0 0 o o 195 60. Specimens Subjected to Cavitation Damage in Mercury at 500~F o, 197 at 500 F 0 0 0 0 0 a o o o o o o o o o o o ~ ~ ~ o ~ 197 61. Effect of Cavitation Test Duration on Weight Loss of Graphitar at 70~F in Mercury o.oo o 0 o o oo 202 62. Effect of Cavitation Test Duration on MDP of Graphitar at 70~F in Mercury.0............ o o 203 63. Graphitar and Single-Crystal Tungsten Specimens Subjected to Cavitation Damage at 70~F.............. 205 64o Effect of Cavitation Test Duration on Weight Loss of Single-Crystal Tungsten at 700F in Water, o... o 208 65. Effect of Cavitation Test Duration on MDP of SingleCrystal Tungsten at 70"F in Water. o... o 209 66. True Stress-Strain Curve Showing Hobbs' Proof Resi1ience -Concept 0. 0 0 0 0 0 0 0.0 0 0 0 0 0 0 0 222 67. True Stress-Stra~in Curve Showing Hobbs' Ultimate Res;iience Concept 0 o o o 0 0o. o o o 9 O O O O O e o. o 224 xvi

Figure Page 68. Effect of Temperature on Mechanical Properties of Type 304 Stainless Steel........... 230 69. Effecti of Temperature on Mechanical Properties of Type 316 Stainless Steel..,................... 231 70. Effect of Temperature on Mechanical Properties of T-.lll.0. 0....0. 0.. 0 0.. 0..... 0. 232 71. Effect of Temperature on Mechanical Properties of T-222(A) 0........... *.. 0 233'72. Effect of Temperature on Mechanical Properties of Mo-l/2Ti0 0 0. 0 o' ~ o 0 * * 0 * o * o 234 73. Effect of Temperature onMechanical Properties of o-I2. -.... 23 Cb-lZr~ ~ 0 ~ ~~o 0 0 0 0 0 0 0 0 0 0 0 235 74. Effect of Temperature on.Mechanical Properties of ~Cb-lZr.236.C b- lZr (A) 0. 0 0. 0 0 0 0 * o o o 0 o 0 o ~ ~236 75. Effect of Temperature on Engineering Strain Energy of Stainless Steels and Refractory Alloys.....0... 238 76. Comparison of Predicted MDP Rate and Experimental MDP Rate - Lead-Bismuth Alloy...O o........ 267 77. Comparison of Predicted MDP Rate and Experimental MDP Rate -Mercury... 0. 0 0 o. 00....... 272 78. Comparison of Predicted MDP Rate and Experimental MDP Rate- Water -Subset One............... o 278 79. Comparison of Predicted MDP Rate and Experimental MDP Rate -Water - Subsets Two and Three.... o. o 282 80. Comparison of Predicted MDP Rate and Experimental MDP Rate- All Water Data.... o 0.... o. o.. 286 81. Comparison of Predicted MDP Rate and Experimental MDP Rate -All Lead-Bismuth, Mercury, Water, and Lithium Data (Acoustic Impedance.Ratio is the Fluid Coupling Parameter).. e 0 0. 0 0.o. o o 0 o o.. 304 82. Effect of Thermodynamic Parameter on Cavitation Damage - Liquid Metals,................ 325 83-. Effect of Thermodynamic Parameter on Cavitation Damage - Water.oo........ 0ex........... o 327 xvii

Figure Page 84. Effect of Temperature on the Thermodynamic Parameter - Liquid Metals and Water.o, o.. o. o 0.... 328 85. Effect of Mean Depth of Penetration on Mean Depth of Penetration Rate - Type 304 Stainless Steel in LeadBismuth Alloy at 1500 F 0 0. 0.. 0 o 342 86 Flange Cone................... o. 348 87. Schematic of Heat Transfer by Horn.......... 351 88. Normalized Inverse Cavitation Damage Versus Tensile Strength - Lead-Bismuth Alloy........ o o.o 359 890 Normalized Inverse Cavitation Damage Versus Yield Strength - Lead-Bismuth Alloy.. o.. o... 360 90. Normalized Inverse Cavitation Damage Versus Engineering Strain Energy - Lead-Bismuth Alloy..... * 361 91o Normalized Inverse Cavitation Damage Versus True Strain Energy - Lead-Bismuth Alloy o o.. o o o. 362 92. Normalized Inverse Cavitation Damage Versus Hardness - Lead-Bismuth Alloy o 0.. 0 0 0 0. o o... 363 93. Normalized Inverse Cavitation Damage Versus Ultimate Resilience - Lead-Bismuth Alloy o 0 o o 0.0 0 364 94. Normalized Inverse Cavitation Damage Versus Tensile Strength - Mercury e o o o......... 0 365 95o Normalized Inverse Cavitation Damage Versus Yield Strength - Mercury O 0 0 0 0 0 0.0... o o 366 96. Normalized Inverse Cavitation Damage Versus Engineering Strain Energy - Mercury o 0 o o 0... o o. 0 0 367 97o Normalized Inverse Cavitation Damage Versus True Strain Energy - Mercury.o. o o o o a a.0 o 368 98o Normalized Inverse Cavitation Damage Versus Hardness - Mercury.o.... e. o o.. o. o o e o e o o 3 369 99. Normalized Inverse Cavitation Damage Versus Ultimate Resilience - Mercury. e. o..o o e o. o, 0 0.o 370 100o Normalized Inverse Cavitation Damage Versus Tensile Strength - Water. o. o o o o.. o.. o o o 0.. 371 xviii

Figure Page 101o Normalized Inverse Cavitation Damage Versus Yield Strength -Water. o. e o o o o o o o o o 372 102. Normalized Inverse Cavitation Damage Versus Engineering Strain Energy - Water O. o.......... 373 103. Normalized Inverse Cavitation Damage Versus True Strain Energy - W ater..e o o.. o.. o.o o o 374 104. Normalized Inverse Cavitation Damage Versus Hardness - Water o. o o o.. o o 0. o 375 105. Normalized Inverse Cavitation Damage Versus Ultimate Resilience - Water. o o o...... 0 o o 0 376 106. Normalized Inverse Cavitation Damage Versus Tensile Strength - Lithium at 500~F........0 o o 377 107. Normalized Inverse Cavitation Damage Versus Yield Strength - Lithium at 500~F 0 0. o.0. 0 o o o 378 108. Normalized Inverse Cavitation Damage Versus Engineering Strain Energy - Lithium at 500~F........ 379 109. Normalized Inverse Cavitation Damage Versus True Strain Energy - Lithium at 500 F o.......... o o 0 380 110. Normalized Inverse Cavitation Damage Versus Hardness - Lithium at 500 F............. o o a 0 0 381 111. Normalized Inverse Cavitation Damage Versus Ultimate Resilience - Lithium at 500~F- 0 I a 0 00 O o 382 112. Normalized Inverse Cavitation Damage Versus Tensile Strength - Lithium at 1500~F.o e o o o 0 o. 383 113. Normalized Inverse Cavitation Damage Versus Yield Strength - Lithium at 1500~F o.... 0 0 0 0 0 384 114, Normalized Inverse Cavitation Damage Versus Engineering Strain Energy - Lithium at 1500~F...... o. o 385 115. Normalized Inverse Cavitation Damage Versus True Strain Energy - Lithium at 15000F.. e e o.. o 386 116. Normalized Inverse Cavitation Damage Versus Hardness - Lithium at 1500 ~F. O 0. o 0 0 o 0 0 o o 0 387 117. Normalized Inverse Cavitation Damage Versus Ultimate Resilience - Lithium at 1500~F. o o 0. O. o 0o. 388 xix

CHAPTER I INTRODUCTION AND LITERATURE SURVEY A. Introduction Cavitation can be described as a hydrodynamic phenomenon which relates to the formation and collapse of vapor bubbles in a liquid. In general terms, these bubbles form in regions where the local pressure is reduced below the vapor pressure at that temperature.and start to collapse as soon as the local pressure exceeds the vapor pressure. While this definition implies a distinction between phase transitions associated with reduction of pressure at constant ambient temperature, on the one hand, and addition of heat at constant pressure (i.e., boiling), on thee other, heat transfer effects may play an important role in many cases of cavitating liquids. Such effects are especially important in liquids near their boiling points in the undisturbed condition. From a purely physical-chemical point of view, of course, no distinction need be made between boiling and cavitation, at least insofar as the question of inception is concerned, and many of the basic physical ideas regarding inception, vapor mass transfer, and condensation apply equally in either case. The bubble collapse associated with cavitation can be considered as giving rise either to a shock wave which is propagated through the -1

-2fluid, or to a small high-velocity liquid jet, in either case terminating at the wall of the fluid container. The effects produced as a consequence of cavitation are twofold. First, for flow processes, it generally decreases the transferable energy and causes a loss in efficiency. Secondly, destruction (damage) of the material may take place when the shock wave or liquid jet terminates on structural material surfaces. Thus, it becomes necessary to investigate carefully those conditions resulting in cavitation and the damage suffered by various materials. Since the cavitation damage process is apparently very closely related to damage from droplet or particle impingement or conventional erosion, the damage data so obtained for various structural materials is also to some extent applicable to the resistance of these materials to these other forms of attack, so that the fields of droplet erosion in wet vapor streams (as in turbines or other two-phase flow passages), rain erosion of high-speed aircraft, micrometeorite bombardment of space vehicles, etc., are involved. For the past two hundred years the phenomenon of cavitation has been known, and the accompanying losses of component performance and material damage have been of considerable concern to the designers of fluid machinery since the turn of the century. In the earliest considerations of the cavitation phenomenon the primary fluid of importance Reference 1 includes many papers on the relations between these various forms of attack. Also ASTM Committee G-2 has recently been formed to attempt to relate these various phenomena and form applicable test standards,

-3was water, as this was the basic fluid used in fluid machinery until recent times. At the present, however, liquid metals, cryogenics, organics, and other fluids have come into prime consideration. a heat. transfer agents and as working fluids in thermodynamic cycles~ The successful pumping and handling of high-temperature liquid metals, wherein cavitation itself is a problem, is of considerable importance in the present and future space program, particularly from the viewpoint of power generation using nuclear heat sources and liquid metal Rankine cycle power conversion equipment. As has been recently 2 demonstrated, damaging cavitation attack can occur in bearings, close-: 3 4,5 clearance passages, etc., as well as pumps. Recent theoretical 6 studies emphasize, in addition, a form of microcavitation that may also occur in many high-performance bearing applications and even in components such as gear teeth, so that the pitting which is often found in such units may well be a result of a form of cavitation. The same problems are, of course, also important in the conventional nuclear power 3 plant program, which includes several existing and projected reactor systems using liquid metals as the coolant. Hence, the prediction of cavitation performance and damage in a variety of fluid-material environments at various temperatures becomes of.great importance. The high developmental costs for the component machinery and the difficult handling problems encountered with liquid metals make the full scale component testing and the materials-screening programs, which have been necessary in many cases, highly undesirable and very costly.

-4In the SNAP application the minimization of size and weight and the maximization of temperature are of over-riding importance, so that the fluid-handling equipment, which must utilize high velocity flow rates and minimum suppression heads, must be designed to operate under conditions approaching cavitation or actually in a cavitating regime. In addition, long unattended life is desired for many such units. Hence, it becomes necessary to know realistically under what conditions cavitationcan be anticipated, and the quantity and quality of damage to be expected for a given degree of cavitation, since it may not be possible or desirable to avoid the cavitating regime entirely by overconservative design, as has been the practice for conventional applications The objectives of the present study include the determination of the cavitation resistance of potentially useful alloys in water at room temperature and in liquid metals at elevated temperatures, and the determination of material-fluid parameters to correlate damage and allow its a priori prediction. B. Historical Background The possibility of the occurrence of cavitation due to pressure 7 changes in a flowing liquid was recognized by Euler as early as 1754 8 in his treatise on hydraulic turbines. Reynolds, in the last decade of the nineteenth century, produced and observed cavitation in a glass Acronym for System for Nuclear Auxiliary Power.

venturi tube at room temperature. These dates indicate the early sporadic interest in the problem. However, the major early analyses of 9 10 importance were those by Besant in 1859 and Rayleigh in 1917. The accompanying loss of component performance and the destructive action of cavitation were first noted in connection with a British destroyer's 11 propellers in 1895. Other early users of fluid handling machinery who 12 13 investigated cavitation were Barnaby, Parsons and Cook, Sir Charles 14 15 16 Parsons, Wagenbach, and Fottinger. Following the work of these early pioneers, numerous investigators have devoted major efforts to studying the details of this phenomenon over the past fifty years. In the 1930's the laboratory testing of various materials in order to determine their resistance to cavitation damage came into widespread use, and several different methods of testing were developed. These experimental facilities may be grouped into two categories: those that depend on inducing low pressures as a result of high velocities in flowing liquids or motion through a stationary liquid; and those that produce cavitation by means of local, periodic, accelerations in an otherwise stationary liquid. The first group includes devices such as venturi tubes, objects immersed in constant area sections of cavitation tunnels, and disks rotating in otherwise stationary liquid with throughholes to generate cavitation upon test specimens inserted in the disk, while the second depends on alternating pressure fields such as are produced by acoustic or other acceleration-producing devices. In addition to such equipment, other types of "impact" producing devices, such as liquid jets impinging on specimens, have also been used, since the

-6damage from such tests appears to be.very Simiilar to cavitation damage. Venturi sections, which are s imply convergent-divergent nozzles, or modifications thereof, were among the first flow devices used in the 16 study of.. cavitation damage under laboratory conditions. Fottinger in *17 1926 and Schroter in 1932 utilized such a device to produce cavitation, the extent and intensity of which could be controlled, and made to occur in a region where a test specimen could be inserted. Mousson (1937) and Lichtman et al (1958) also performed studies in such 20,21 nozzles. Most recently is the very extensive work of Hammitt' and 22 Robinson, who conducted studies both in water and mercury in a cavitating venturi. Since many machines operate under conditions of high velocity flow similar to that achieved in the venturi test sections, the venturi test is considered to be quite representative of field conditions. Cavitation damage tests have also been performed in large cavitation tunnels which operate on principles similar to a.wind tunnel. The cavitation is generally produced on a body of revolution or a hydrofoil placed in the fluid stream. Such devices have been described by 23 24 25 Robertson and Wright, while Knapp (1955)2 carried out cavitation damage experiments in such a tunnel. These tunnels are seldom used for damage tests because of the expense of operation, the relatively complicated procedures required in installing experiments, and the length of time they must operate to obtain measurable weight loss.o A device that has been used in recent years for studies of cavi-tation damage is a rotatin disk on which cavitation is induced in a

-7separated flow region. Basically, such devices consist of a disk with holes near the periphery with axis parallel to the disk axis, rotated at high speeds in a chamber filled with the test fluid in which the ambient pressure can be controlled. Several specimens can be mounted on the disk and subjected to the cavitation cloud which is produced downstream of the holes. Such devices have been used and described by Rasmussen 19 and by Lichtman et al. Very recently, a rotating disk assembly was utilized by Wood et al to obtain cavitation damage data in water and 28 by Kelly, Wood, et al to obtain data in liquid metals. Many investigators have used a variety of acoustic devices which produce cavitation by means of local, periodic, accelerations. The most common device of this type is the magnetostriction oscillator. The magnetostrictive effect.is exhibited by the ferromagnetic materials, which, under the influence of an alternating magnetic field, show a periodic change in length. The first magnetostriction oscillator used for cavi29 30 tation tests was developed by Gaines in 1932. Kerr and Schumb et' 31 al in 1937 published extensive results obtained with such a device. 32 33 34 35 Nowotny, Leith and Thompson, Rheingans, Plesset, and 36 Thiruvengadam et al also contributed valuable data and information accumulated over the years with this laboratory test device. Very recently, the vibratory apparatus has been used to test materials in 3,37,38,39 high-temperature liquid metals as sodium, and as part of this 4041 39,42 thesis investigation in lead-bismuth alloy,' mercury, and 43 lithium. -- Acoustic field generators comprise another type of laboratory device used to study effects of cavitation damage on materials. In this

-8case cavitation is produced by imposing a focused acoustic field in a liquid. The cavitation occurs in regions of maximum pressure amplitude. A very economical cavitation generator using barium titanate transducers to produce an acoustic field in a resonant container has been developed 44 by Ellis. The operating frequencies used with this device are 18 Kc./ sec. and 24 Kco/sec. Another type of acoustic field generator, operating at frequencies from 400 to 1000 Kco/seco has been used in experi19 ments by Lichtman et al. One other type of apparatus, namely impact testing devices, should also be mentioned along with the venturi test section, cavitation tunnel, rotating disk, magnetostriction oscillator, and acoustic field generator used in laboratory cavitation tests. Although the impact of water drops is not per se a cavitation process, the use of such impact tests was important in early examinations of the mechanism of cavitation damage since it was assumed that the processes were analogous.* In order to examine the question of whether the mechanism of cavitation 45 damage was associated with mechanical erosion, de Haller (1933) ran experiments in which small rods fastened to the periphery of a wheel rotating at a high rate of speed, were passed through a high speed water 46 jet. More recently, Hobbs used a similar device in which a high velocity liquid jet impinged on multiple test specimens mounted on a rotating disk. A similar device is now in use also at the Chatou laboratory of Electricite de France. According to present theory, this assumption appears justified.

-9Each of the above-mentioned. laboratory test devices has been used by many other investigators in the determination of the cavitation resistance of various materials as part of materials-screening programs currently being undertaken throughout the worldo Of these devices the venturi test sections and cavitation tunnels are considered to be quite representative of field conditions encountered in rotating machinery, However, damage appears only after very lengthy operation, and the result-ing costs are sometimes prohibitive. The rotating disk device and magnetostriction oscillator produce considerable damage in comparatively short periods of time and, hence, lend themselves nicely to materials-screening programs involving' a.variety of materials and several fluid conditions. Such apparatus is sometimes referred to as an "accelerated" cavitation test device due to the intense degree of cavitation produced and resulting extensive damage to test specimens. Corrosion is often present when cavitation occurs, and many investigators have studied the combined interaction of these two damag-.47,48,49 48 ing mechanisms Plesset proposed a pulsing technique using a magnetostriction oscillator, whereby a short period of cavitation is followed by a longer non-cavitating interval, and concluded that such a test produces more meaningful results in cases where corrosion is important. The accumulated non-cavitating time allows a more realistic opportunity for any corrosion mechanism to manifest itself on the test specimen. In a purely cavitating experiment of the accelerated type, the test time involved might be so short that the corrosion contribution,to the total damage mechanisnm would be negligible as compared to field

-10conditions, and, hence, the results misleading. Such pulsing apparatus can be used for both steady and pulsed cavitation studies. Hence, the effect of corrosion damage can be quantitatively determined. Co Problem Statement In a prototype system, the damage due to cavitation appears usually only after fairly lengthy operation under design conditions. Hence, it is clear that if a systematic study is to be made, involving a variety of materials and numerous plant conditions, it will be necessary to expend large amounts of time and money. An alternate approach, sacrificing direct applicability to some extent in the interests of economy, is to accelerate the cavitation losses by employing any one of the several laboratory techniques, previously discussed, which have been developed for this purpose. The most commonly-used method which is also employed in our own laboratory is a flowing tunnel system utilizing a venturi test section and a centrifugal pump to circulate the test fluid around a closed loop. This system has been described elsewhere. As mentioned previously, the venturi is reasonably similar to actual flow systems, but at the same time damage occurs only rather slowly. As an alternative to a flowing system, an acoustic vibratory device was chosen for this investigation. This accelerated acoustic system makes use of a 51 piezoelectric transducer and will be described in detail later. Damage is accumulated at a very rapid rate compared to the venturi system, and, hence, large numbers of potentially useful materials can be tested in a variety of fluid-temperature environments at an economical cost,

-.11In addition, this device makes it possible to conduct tests at elevated temperatures in liquid metals with relatively little trouble Comparable tests conducted in a flowing venturi system would involve a myriad of additional problems and prohibitive cost. In the past, the utility of accelerated acoustic cavitation damage results has been limited because no direct correlation with cavitation in a flowing system has been available. However, if such a correlation could be formulated, it might be possible to substitute relatively economical acoustic testing for tests in a tunnel facility. Our own laboratory has conducted cavitation tests in both water and mer20 21 22 cury in venturi facilities' for the past several years and has accumulated much useful data over this period of time. It is expected that the accelerated cavitation data obtained with the vibratory facility in this investigation can be compared with the tunnel results, so that a correlation can be obtained, allowing a more direct application of the accelerated test results. In addition to the cavitation testing program, it is essential to determine the applicable mechanical properties of the materials tested at the test temperatures so that a correlation between resistance to this form of two-phase attack and some combination of the mechanical properties can be obtained. Applicable mechanical properties certainly might include the ultimate tensile strength, yield strength, hardness, strain energy to failure, elongation, reduction in area, elastic modulus, etc. Since many fluid-temperature combinations are involved in this investigation, it is expected that any correlation of cavitation

-12data certainly will have to account for changes:in fluid properties. Applicable fluid properties for such a' comprehensive correlation might include density, surface tension, net positive suction head, bulk modulus, kinematic viscosity, specific heat,:thermal conductivity, heat of vaporization, thermal diffusivity, Prandtl Number, and vapor pressure. Thus, one would expect a complete correlation of cavitation damage data to involve both mechanical properties of the test materials and fluid properties at the applicable temperatures. Hence, the objectives of the present investigation are as follows: 1) Develop a practical laboratory device for obtaining cavitation damage data in a wide variety of fluids (including liquid metals') at tempe 1500.. metals) -at temperatures as high as 15000F under conditions of controlled purity utilizing an inert cover gas. 2) Utilizing the accelerated vibratory device developed for this program, determine the cavitation resistance of a wide variety of useful materials (involving a. considerable: range of mechanical properties) including stainless steels, carbon steel, tool steels, refractory alloys, aluminum, copper, nickel, brass, plastics, etc., in water at 70~F, in mercury at 70~F and 5000F, and in lead-bismuth alloy and lithium at 5000F and 15000F. 3) Obtain a comprehensive correlation of the cavitation damage data with applicable material and fluid properties utilizing a -,.-.. T Fluid "head" above vapor, i.e., NPSH = p - P, where p, Pv' and P are the local pressure, vapor pressure, and fluid density, respectively.

-13suitable computer program, so that one might be able to predict a priori the behavior of a new material under a given set of fluid-temperature conditions 4) Develop a relationship or correlation between the damage incurred in the flowing venturi device operated by this laboratory and the damage obtained in the accelerated vibratory facility studies.

CHAPTER II EXPERIMENTAL EQUIPMENT A. Facility Selection 1. Introduction As discussed previously, there are many types of accelerated cavitation research facilities available. These include the tunnel facility and its variations, the rotating disk device, and the several acoustic facilities. Early in the investigation by this laboratory, it was decided to develop an acoustic cavitation unit since the tunnel facility was already available and it was felt that the rotating disk device would involve excessive costs. It was further felt that it would be much more feasible to obtain data in liquid metals at elevated temperatures with an acoustic facility, as opposed to any alternative systems, Hence, an investigation of the various types of acoustic approaches was made, The types of transducers that would lend themselves nicely to 52,53 acoustic cavitation facilities are: a) Crystal oscillators -These utilize the piezoelectric effect, which is reversible. The range of frequencies used is very wide, the upper limit being about 10,000 Mc./sec. -14

-15b) Magnetostrictive' oscillators - These devices make use of the phenomenon of magnetostriction, which is also reversible, The upper frequency limit. is of the order of 100 Kc./sec. It should be noted that there are several other types of transducers available, such as electromagnetic transducers, electrostatic transducers, etc., but it was felt that only the two approaches mentioned above were suitable, considering the-experimental program which was proposed. 2o Piezoelectric Effect Crystal oscillators make use of one of two types of crystal for generating ultrasonic waves.o One type of crystal displays the piezoelectric effect and the other the electrostrictive effect. The piezoelectric effect, which was first discovered by the Curie brothers in 1880, occurs in crystals having axes of non-symmetry. Suppose a slab er disk of such a crystal is cut with its parallel surfaces lying normal to an axis of non-symmetry. On subjecting this slab to a mechanical stress, equal and opposite electric charges appear on the parallel surfaces. Provided that the crystal is not strained beyond the elastic limit, the magnitude of the charge density (or' dielectric polarization) is directly proportional to the applied stress. The converse effect was predicted by Lippman in 1881, and discovered' experimentally by the Curie brothers in the same year. When an electric field is applied in the direction of an axis of non-symmetry, the slab is mechanically strained, the amount of strain being proportional to the intensity of the applied ^' ~

-16field. From a consideration ofthe principle of'conservation of energy, the direct and converse piezoelectric effects may be shown to-be equal and opposite, i.e., the effect is reversible. It is the converse piezoelectric effect that is used in designing an ultrasonic transducer of this type for cavitation investigations. An alternating electric field is applied to the parallel surfaces of a piezoelectric crystal, and the resulting rapid variation of length of the crystal is transmitted along an exponential or stepped horn which is fitted with a suitable test specimen. The specimen then oscillates with a frequency equal to that of the applied electric field, and with anamplitude proportional to the magnitude of the applied field. These horns will bedescribed later. Crystals exhibiting the piezoelectric effect include quartz, Rochelle salt, tourmaline, and lithium sulphate. Each crystal has a natural frequency of vibration dependent on the dimension of the crystal. If the natural frequency corresponds to the applied frequency of the electric field, the amplitude of vibration of the crystal is a maximum. Unfortunately, many piezoelectric matric ials are: deliquescent: andcan only be used in controlled surroundings. 3. Electrostrictive Effect The electrostrictive effect occurs in all dielectrics and is a phenomenon analogous to magnetostriction, which will be described later. For most materials, the electrostrictive effect is negligible, but in certain dielectrics, called ferroelectrics, the effect is strongly pronounced. The application of an electric field in a given

-17direction produces a mechanical strain, the magnitude of which is proportional to the square of the applied field strength (as opposed to the piezoelectric effect where the strain is proportional to the applied field), and is thus independent of the sense of the fieldo Consequently a positive strain may occur for both positive and negative values of the exciting field. Electrostrictive materials can be made to exhibit the piezoelectric effect if they are properly polarized. This can be done permanently by heating the materials to a temperatur e above the Curie point (ioe., the temperature at which electrostriction disappears) and then allowing them to cool slowly in a strong electric field oriented in the direction in which one intends to apply the exciting field. Provided that the exciting field is small compared with the initial polarizing field, the strain will vary sinusoidally at the frequency of the sinusoidally varying exciting field. A polarized ferroelectric transducer appears to display the same effect as a piezoelectric transducer, and for this reason it is commonly referred to as being piezoelectric. At present, barium titanate and lead zirconate are the substances most widely used for electrostrictive applications. For the construction of this type of transducer, many small crystallites of ferroelectric material, together with suitable additives, are bonded together to form a ceramic of the required shape. Because these materials are polycrystalline, they have the advantage over naturally occurring piezoelectric crystals in that they are isotropic and do not have to be cut along specified axes. Such electrostrictive materials lend themselves nicely sto-the type of acoustic cavitation facility envisioned for this study.

-184, Magnetostrictive Effect Magnetostriction occurs i'th ferromagnetic materials and certain non-metals called ferrites.i The magnetostrictive effect was discovered by Joule in 1847, and the converse effect by Villari in 1868o When a rod or bar of ferromagnetic or ferrimagnetic material is subjected to a magnetic field, it experiences a change in length. Conversely, a mechanical stress applied to a rod or bar causes a change in intensity of magnetization. The magnetostrictive effect, which is analogous to the electrostrictive effect described above, is prominent for materials such as nickel, iron, and cobalt. Whether there is an increase or decrease in length depends entirely on the nature of the material and on the strength of the applied magnetic field, and this is independent of the direction of the field. For purposes of-cavitation investigation, an alternating magnetic field might be applied to a ferromagnetic material, the resulting rapid variation in length of the material constituting a standing wave generator. The ferromagnetic material may be coupled to an exponential or stepped horn which in turn would accommodate the test specimen. The standing wave would exist throughout the assembly. If the assembly is of a suitable length, e.g., equal to the wavelength of the sound wave propagated within it, then the amplitude of vibration at the tip of the assembly would be a maximum and give rise to a rapid variation of local pressure at the tip of the assembly, which, for purposes of cavitation investigations, is immersed in a liquid. If the pressure variation is such that the local pressure -is reduced below the vapor p essure of the liquid at the existing

-19temperature, then the phenomenon of cavitation occurs. The details of the design of such a transducer assembly will be discussed later. However, at this point, a decision must still be made as to which of the approaches described above is to be pursued. 5. Choice of Accelerated Cavitation Device The choice is one between the piezoelectric, electrostrictive, or magnetostrictive devices described above. Much work has been reported utilizing the magnetostrictive transducers, and hence it might be reasonable to adopt such a device on this basis. However, the power requirements and cooling problems can be somewhat severe, and perhaps the cost higher than the alternatives. Further, since a local vendor was available to help in the design of either the piezoelectric or electrostrictive-type transducers, it was felt that this approach should be adopted. The amplitude obtained with such generators is of the same order as that obtained with the magnetostrictive devices, and it is believed that the efficiency of energy conversion with the piezoelectric devices is greater than that obtained with the magnetostrictive generators. In summary, it was felt that a piezoelectric cavitation generator would be entirely suitable for the studies envisioned in that flexibility in the design permitted many changes, heat losses were kept at a minimum, crystal temperature did not exceed the Curie point with a feasible cooling arrangement, amplitude of vibration was sufficient, and cost was nominal. Pure lead zirconate (PbZrO3) is a non-ferroelectric, but if mixed with more than 10 mole % lead titanate (PbTi03), it acquires ferroelectric properties. Hence, in view of the previous

-20discussion, a polarized lead zirconate-titanate ceramic, which exhibits the piezoelectric effects was chosen as the crystal for the transducer assembly. This crystal has the following desirable properties: a) Satisfactory piezoelectric characteristics for the required modes of vibration, b) Homogeneous throughout. c) Capable of being worked to the desired shape and size. d) Variations of its properties with temperature are minimalo e) Internal friction is low. f) Chemically and physically stable. g) Retains its piezoelectric properties over the complete range of temperatures for which it. is to be used. h) Results in satisfactory matching with both the electrical circuit and the medium of propagation for efficient energy transfer. The ultrasonic transducer utilizing the piezoelectric crystal selected must satisfy-the following general requirements: a) It must be operable (ioeo, able to produce appreciable cavitation activity) in fluids ranging in density from 1-15 grams/cc. b) It must be capable of operating in fluids whose temperatures range from 70"F to 15000F. c) It must be so constructed that the amplitude of vibration can be accurately and conveniently measured. d) The stepped and/or exponential horns employed are to be removable and interlang~eable (i.e., easily replaced).

e) The exponential horn will be designed so as to accommodate the test specimens f) Provision is to be made for fastening the transducer to the fluid container without appreciably reducing the amplitude of vibration at the horn tip. B. Description of Overall System A general description and discussion of the major features of the University of Michigan high-temperature ultrasonic cavitation vibratory facility will be given here. Succeeding sections will describe the various components in detail. Figure 1 is a schematic block diagram of the high-temperature ultrasonic vibratory facility showing the audio oscillator, power amplifier, transducer-horn assembly, test specimen, oscilloscope, frequency counter, high-temperature furnace and cavitation vessel, and accelerometer. The signal supplied by the variable frecJency audio oscillator is amplified and applied to the piezoelectric crystals. The resultant periodic motion of the crystals effectively constitutes a standing wave generator with the amplitude of the standing wave being increased as it traverses the exponential horn assembly. The use of exponential horns as velocity transformers in this fashion was 54 first suggested by Mason. The movement of the horn tip, to which a test specimen has been attached, results in a rapid variation in local pressure, causing the periodic formation and collapse of an intense cavitation cloud. The final result is an accelerated erosion of the test specimens subjected to the collapsing bubble cloud. The materials of interest can be tested in a variety of fluids over a wide temperature

-22OSCILLOSCOPE AUDIO OSCILLATOR FREQUEN Y ACCELEROMETER COUNTERU TRANSDUCER ASSEMBLY 150 WATT ~150 WATT | \~ L PIEZOELECTRIC POWER ___ ____c RYSTALS AMPLIFIER VESSEL TOP / PLATE. o _~_o EXPONENTIAL 0 o 0 HORN TEST 0 __0 l SPECIMEN FURNACE ~ 1tTEST FLUID o0 POWER SUPPLY HIGH- TEMPERATURE CAVITATION VESSEL 1609 Fig. 1. —Block diagram of the high-temperature ultrasonic vibratory facility.

-23range. For studies at elevated temperatures the transducer-horn assembly is attached to the special cavitation vessel which is filled with the appropriate fluid. Figure 2 is a-photograph of the facility showing the audio oscillator, power amplifier, voltmeter, oscilloscope, timer, temperature controller, furnace, and the transducer-horn assembly installed in the high-temperature cavitation vessel, Thevvessel is inserted in the furnace, The line running to the vessel supplies argon as a cover gas for the fluid. The cavitation facility has been completely calibrated and operated at fluid temperatures in excess of 15000F at a frequency of approximately 20 Kc./sec. and double amplitude o fV 2 mils. It is capable of operation with a variety of fluids. C. UltrasoQnic Transducer Assembly As mentioned previously, the ultrasonic cavitation facility con-..... Fists of a variable frequency audio oscillator and power amplifier which supply a voltage of suitable magnitude and frequency directly to electrodes attached to the piezoelectric crystal (in this case lead zirconate-titanate). The applied voltage causes the crystal to alternately expand and contract its length by /V 0ol to 0.2 mils. In order to produce cavitation in various liquids, it is desirable to amplify this minute movement of the lead zirconate-titanate crystal. This can be done by attaching either a stepped or exponential horn assembly to the crystal transducer section. The horn acts as a velocity transformer, increasing the velocity of the standing waves propagated by the

-241767 Fig. 2. —Photograph of the high-temperature cavitation facility.

-25crystal. As a result, the maximum amplitude of the horn tip may be as great as 2 to 3 milso The amplification obtained with a stepped horn is a function of the ratio of the end diameters while the amplification obtained with an exponential horn is a function of the ratio of the end 53 areas. An exponential horn was chosen to minimize the stress problems within the horn assembly. With the stepped horn, stresses at the interface can cause the horn to fracture at this point. The general features of the ultrasonic transducer assembly are indicated in Figure 3o There are two lead zirconate-titanate crystal wafers in the driver so that both ends of the transducer can be grounded. If only one crystal had been used, one end of the transducer would have been at a voltage above groundo This represents an undesirable situation. The aluminum disk shown between the two crystal wafers is suitably bonded to each of the crystals and represents one of the electrodes (high volt- -. age)o An internal bolt, suitably insulated, contacts the steel counterweight, passes through both crystals and the separating aluminum disk, and terminates in the lower aluminum section. As a result, the steel counterweight, the upper surface of the top crystal wafer, and the lower surface of the lower crystal wafer are electrically the same point (ground). Hence, the second electrode is attached to the upper steel counterweight. The aluminum sleeve serves the purpose of making a firm attachment to the lower crystal. It is then possible to easily and quickly attach various exponential and stepped horns to this upper assembly without having to bond the crystal to a new horn surface each timeo The horn made for the transducer was exponential in form, as noted, and fabricated of type 303 stainless steelo

-26-.A' 518 - 20 i*.. STEEL COUNTERWEIGHT HEX. HEAD CAP SCREW. _ ALUMINUM SFACER LEAD ZIRCONATE- TITANATE CRYSTALS ALUMINUM SLEEVE 3/8-28 1/4- 28 TEST SPECIMEN 7,P."' 2II 1453 SECTION A- A' Fig. 3. —Exponential horn and ultrasonic transducer assembly.

-27The standing waves generated by the continual vibration of the crystal wafers are propagated throughout the length of the transducer assembly It is necessary to achieve a proper acoustic match between the various materials making up the assembly if efficient transfer of energy is to be realized. If one considers the reflection and transmission of plane waves at the interface of two materials, it can be shown that the reflection coefficient approaches zero and the transmission coefficient approaches unity as the acoustic impedances of the two media approach one another. The acoustic impedance is given by the product of the density of the medium and the velocity of sound propagated within ito In the case of aluminum and stainless steel, the velocity of sound in each is approximately the same, namely, f/ 16,000 feet/secondo However, the densities of the materials differ by about a factor of three, Thus, the acoustic impedance of the aluminum is 1o7 x 107kgo/mo2seco, while that of the stainless steel is 4~7 x.107 kgo/mo sec. Hence, at the interface of these two materials one would expect a transmission coefficient of approximately 0,75, or 75%, which indicates that the media are quite well matched and efficient transfer of energy is taking place across the interface, This is a very important consideration in the design of such a transducer in that poor selection of materials can result in large degree of reflection at the interface, and hence a very inefficient transducer, A final important consideration in the design of such a transducer is concerned with the dimensions of the upper driver section and the exponential horn assembly, Typically, the length of the upper

-28driver section and the exponential horn would each be equal to half the wavelength of the acoustic oscillation propagated in it. Figure 4 is a schematic of a typical waveform showing the position of the nodes and anti-nodes along the length of the transducer assemblyo It is clear that maximum amplitude is necessary at the tip of the horn assembly to which the test specimen is attached, Hence, the horn tip must correspond to an anti-nodal point of the standing wave propagated throughout the assembly. Further, it is clear also that if an attachment of the horn assembly is to be made to a stationary container of some type, this point of attachment must correspond as closely as possible to a nodal point of the standing wave, i.e., a point of zero amplitude. Due to symmetry, it is clear that the aluminum spacer electrode located between the two crystal wafers must be a point of zero amplitude, a nodal point. Many variations are possible here, but it is seen from Figure 4 that an anti-node will exist at the tip of the horn and a. nodeuwilli:.eist:at -' the mid-point of the horn assembly if both the horn assembly and the upper driver section are made equal to one-half wavelength of the standing wave propagated within the assembly. As mentioned previously, the velocity of sound in both aluminum and stainless steel is approximately equal, namely, /V 16,000 feet/second. Hence, it is possible to compute either the length of the transducer, given the applied frequency, or to compute the frequency, given the length. Of course, a convenient length, neither very small nor large, is desired. If a total length of 10 inches is chosen for the assembly, the required applied frequency is ^easily determined from the familiar relation:

LEAD ZIRCONATETITANATE CRYSTALS SOTEEL AH ALUMINUM SPACER ALUMINUM SLEEVE STAINLESS STEEL HORN SPECIMEN o i i i 0 111O I on' ANTINODE iNODE ANTINODE INODE i ANTINODE LI| | I I (TRANSDUCER SUPPORTED (POINT OF MAXIMUM 0 IN HIS REGION) AMPLITUDE) IAX/2 ~ /2~ 1454 Fig. 4. —Typical waveform showing position of nodes and antinodes on transducer assembly.

-30c = f\ where: c = velocity of sound-. f applied frequency = m wavelength of sound For the case above, the frequency determined in this fashion is found to be I/ 20 Kco/seco Such a frequency-can be easily supplied by a standard variable-frequency audio oscillator. The stainless steel horn is approximately 5 inches in length, while the upper driver assembly is about the same length. Hence, the transducer is referred to as a full wavelength transducer and the horn as a half wavelength horn. Figure 4 also shows schematically the velocity transformer action of the exponential horn, as the amplitude of the standing wave propagated within the assembly is increased due to the exponential variation in cross-sectional area. D. Test Specimens 1o Effect of Density on Specimen Size Since this study includes the testing of many different specimen materials, varying widely in density, and since it is necessary to maintain uniform weight of the specimens to obtain an approximately equal resonant frequency for all cases, the length of the various specimens will vary with the density of the material. Figure 5 is a curve of specimen length, A, versus density of specimen material. The required specimen weight is 9.4 + 0ol go The volume of the mounting hardware for a of

._ _ ~_ _ _ _ ________V]__.1 2.5'~~~ ~~~ ~~ ~~~ A - 2 Iw _ ___ _____ 0. _- _ _ _ _____ ____ _ _ _ _ _ _ _ _ _ _ i.5 I' ~ 0.5 1 2 3 4 5 10 15 20 DENSITY, G./CC. 1459 Figs 5. —Effect of density on cavitation test specimen size.

-32each specimen is constant, and this was determined by a weight measurement of the complete specimeno Hence, the required weight must be realized by suitable adjustment of the specimen face thickness A, which can be easily computed. 2o Standard Cavitation.Test Specimen Figure 3 clearly indicates the point of attachment of the test specimen at the tip of the ultrasonic transducer assembly. The details of the standard cavitation test specimen are shown in Figure 6..These specimens are screwed into the end of the horn and tightened with a special wrench which.does not in any way damage the specimen or remove material from it, as shown by repeated tests. The required dimensions "A" and "B" vary with the density of the material. The dimension "A" may be determined from Figure 5, while the length of the threaded hardware section (B -. A) is generally held constant at 3/8 in. 3o Special Cavitation Test Specimens A number of the materials tested in this program could not be machined in the form of the standard cavitation test specimen shown in Figure 6 due to very low density, brittle nature of some of the materials, unavailability of bar stock of the required material, and difficulty in machining and providing the material with a threaded length. In each case a special specimen was designed to overcome the problems encountered so as to achieve satisfactory operation. Plexiglas was one such material that required a special design for- the test specimen. _Durto the low density:of the Plexiglas

-3328 - UNF 0 o. | UNDERCUT m, O SHARP a | CORNERS K-.547~.001 NOTE DIMENSIONS "A" "B" 1455 VARY WITH SPECIMEN MATERIAL Fig. 6. —Standard cavitation test specimen.

(compared to the other materials tested) and its brittle nature, it was completely impractical to fabricate standard cavitation test specimens as shown in Figure 6. The low density would result in an unusually large "A" dimension (and hence appreciably change the resonant frequency of operation), 9 while the brittle nature of the material made it impossible to firmly affix a specimen to the ultrasonic horn without damage to the threaded portion. It is necessary that the specimen be firmly and tightly attached to the horn tip so that the ultrasonic energy is properly transmitted across the interface for efficient operation. Hence the design shown in Figure 7 consisting of a Plexiglas test specimen with internal thread and a separate stainless steel mounting stud was adopted and proved to be satisfactory. The mounting stud results in a firm attachment of the Plexiglas cylinder to the horn tip without damage to the Plexiglas internal threads since this connection need only be made once. The high density of the steel also allows the required specimen weight to be obtained without an unduly long specimen. Thus, this design overcomes all of the problems encountered with the standard cavitation test specimen Another material tested that posed similar problems to the Plexiglas was the materials graphitar, Graphitar is formed from carbon and graphite powders which are compacted under high unit pressures and then furnaced at temperatures up to 4500 F, and is of wide technological importance in connection with seals and bearings. It has a relatively low density and is brittle and porous. For these reasons the identical test specimen design adopted for the Plexiglas was also used for the

-35I/4 -28 1/4- 28 1 7/8 3/4 Fig. 7. —Special Plexiglas cavitation test specimen and.547mounting stud PLEXIGLAS CAVITATION STAINLESS STEEL SPECIMEN MOUNTING STUD mounting stud.

-36graphitar material and found to be completely satisfactory (Figure 7). It was desired to test in the vibratory facility the identical heat-treats of Cu, Cu-Zn, Cu-Ni and Ni that had been previously tested in the venturi loop facility. Since these materials were available only in sheet stock 1/16 in. thick, it was necessary to design a special specimen consisting of an adaptor of a suitable material and a disk of the desired test material. Means of attaching the disk to the adaptor had to be provided so that a firm bond would result. This is necessary so that the ultrasonic energy is efficiently transferred across the interface. Hence the design shown in Figure 8, consisting of a brass adaptor and a disk of the desired material, was adopted and proved to be satisfactory. The disk is fastened to the adaptor with soft solder. Various epoxies and cements were attempted as a bonding material initially, but the bond was immediately destroyed upon initiation of the test. The acoustic impedance of the soft solder is on the order of that of both the brass adaptor and disk materials, while the epoxies and cements possessed a very low acoustic impedance due to negligible elastic properties. The arrangement shown in Figure 8 results in a standard specimen weight of 9.4 + 0ol g., as desired. Finally, it was not convenient to fabricate a standard cavitation test specimen from single-crystal tungsten, which was also included in the cavitation testing program. Single-crystal tungsten is very difficult to machine using standard techniques, and due to the lack of a suitable grinder for forming the threaded portion of the specimen,'alternate designs were opnsideredo It was found feasible to produce a

-371/4 -28 BRASS ADAPTOR 5 8.58 UNDERCUT.14 DISC OF., I TEST MATERIAL.-~0.547:.001 SOFT SOLDER BOND 1776 Fig. 8. —Special cavitation test specimen for Cu, Cu-Zn, Cu-Ni, and Ni.

-38simple disk of single-crystal tungsten by-grinding, but it was still necessary to affix the disk firmly to the ultrasonic horn, Initially, an attempt was made to use epoxy resin to attach the tungsten disk to a stainless steel adaptor. However, as mentioned previously, little success was achieved with various epoxies and cements which were tried for this purpose due to negligible elastic properties and very low impact strength. As a result the epoxy bond.-immediately fractured at the start of the testo* Finally, the design shown in Figure 9 was found to be satisfactory. Here, a simple disk of single-crystal tungsten has been attached to a stainless steel adaptor with silver soldero The silver solder was found to form a very suitable bond between the tungsten and stainless steel, and resulted in satisfactory transmission of the acoustic energy across the interface. The diameter of the tungsten disk (1/2 in.) was slightly smaller than the diameter of the stainless steel adaptor (.547 in.) due to unavailability of single-crystal tungsten in a larger size at the time of the tests. Thus, all materials tested in this program were fabricated as per Figure 6, with the exception of the special circumstances and difficulties encountered with a few materials, as discussed above. E. High-Temperature Cavitation Vessel 1. Design Philosophy and Criteria Since one of the major objectives of the present experimental cavitation program is to obtain damage data at elevated temperatures At a later dat a suitable epoxy (Loctite Bonding Kit #2508:Loctite Corp.) for attaching specimen disks to adaptors was found and used for certain plastic materials where other methods of attachment

-39-/ 4 - 28,. ~1/4 28 I It /UNDERCUT STAINLESS STEEL. 5/8 ADAPTOR -/1/2 | O.547 oo~0.001 — -SILVER SOLDER BOND - 0.547 ~0.001 - 1761 Fig. 9. —Special single-crystal tungsten cavitation test specimen.

-40in liquid metals, it was necessary to give consideration to the design of a suitable high-temperature facility. Basically, such a facility would include a suitable closed vessel for containment of the test fluid, and for support of the transducer assembly, means for introduction and removal of the test fluid into and out of the cavitation vessel, means for controlling the oxide concentration in the test fluid where applicable, the necessary furnace for obtaining the desired temperature in the test vessel, and a suitable controller for maintaining the fluid temperature at the desired level within satisfactory limits. Clearly, various other auxiliary items such as "0" rings, snap rings, thermocouples, cover gas supply, valves, etc., would be necessary to complete the system. Detailed consideration will now be given to the design of the cavitation vessel, a furnace for obtaining the desired temperature level, and a suitable temperature controller for maintaining the test temperature at the desired level. The design of the high-temperature cavitation vessel will be considered first. The range of temperatures considered is from approximately room temperature to 1500~F. The room temperature tests are necessary for comparison with similar cavitation tests conducted in the venturi facilities operated by this laboratory. The 1500~F temperature level corresponds closely to typical operating temperatures encountered in SNAP reactor power plants utilizing Rankine cycles. The range of pressures considered in this design will extend from normal atmospheric "were not feasibleo For high-temperature applications the "Chemgrip-HT" (Chemplast, Inc o) is recommendedo

-41pressure to a maximum pressure of 50 psigo The high-pressure operation would be necessary in tests with fluids such as sodium at 1500~F due to the excessively large vapor pressure at this temperature. Thus the 50 psig maximum pressure figure was selected as certainly sufficient for such tests and also practical. Argon was chosen as a suitable inert cover gas, Operation with lithium, which is a very reactive liquid metal, will be assumed as a reference for the discussion that follows. Investigations with sodium or potassium could be conducted with almost no modifications to the procedure utilized for lithium, In tests with lead-bismuth, mercury, and water a much simpler procedure was used since maintenance of fluid purity is not nearly as difficult as with the alkali liquid metals. The problem of maintaining fluid purity for repetitive runs where numerous intermediate inspections and weighings are required is a difficult problem when the test fluid is an alkali liquid metal. The usual solutions that have been applied to this problem in the past include the utilization of a large dry-box which encloses the complete experimental apparatus, or an elaborate plumbing system which allows the liquid metal to be transferred to and from the experimental vessel by pressurization. The dry-box approach is very expensive and is complicated by the fact that a range of dry-box pressures would be required for suitable operation. The plumbing system would involve a need for several valves, system pressurization for fluid transferral, trace heaters for lines, hot traps, cold traps, etCo. for purification. Both of these approaches were unsuitable for the present investigation

-42because of these many problems and the fact that the financial resources were limited to a modest sum, Hence, we adopted the following procedure for the tests conducted in lithium, In order to minimize the formation of oxides when very reactive liquid metals are being used as the test fluid, the liquid metal was charged into the cavitation vessel in the form of a solid cylindrical ingot, properly sized to fit into the vessel and fill it, upon melting, to the desired level, The solid ingot, supplied by the manufacturer in an individual hermetically sealed container, was first placed in a clean stainless steel beaker which fit snugly into the cavitation vessel and provided for easy removal and disposal at the conclusion of a test. The loading operation was carried out at room temperature (where oxidation would be at a minimum rate) in a glove box under an argon atmosphere. The sealed vessel was then removed from the glove box and placed in the furnace where the liquid metal was brought to the required test temperatureo Each test was conducted with a new, fresh lithium ingot. This procedure eliminated the need for transferring the molten liquid metal to and from the experimental vessel while the test fluid was in the liquid state and eliminated the need for trace heaters, line heaters, hot traps, cold traps, valves, etc., from the system design. The need for an expensive pressurized dry-box arrangement was also eliminated, Such a procedure resulted in a very economical design and kept oxide contamination relatively uniform and at a minimum, since a fresh ingot was used for each test, Various procedures were developed to remove the ultrasonic transducer and specimen from the cavitation vessel at the

-43- - conclusion of the test in a very safe manner. These will be discussed later, Figure 10 is a schematic representation of the test vessel, showing the ultrasonic transducer assembly supported by the vessel top plate. The two "0" ring seals required, the position of the thermocouple, the argon gas inlet, and the cooling coil are also noted. The level of the liquid metal or other test fluid in the vessel can be measured with a suitable fast response thermocouple. The thermocouple will be attached to the top plate with an adjustable immersion packing gland,:The -adjustable packing gland makes it possible to measure the liquid metal level at any required submergence of the test specimen. For this design, a test specimen face submergence of one inch was chosen so that small differences in submergence between runs will not have a large effect,'When the liquid level reaches the thermocouple tip, there will be a step increase in the thermocouple reading because of the large difference between the film coefficient.for the argonthermocouple sheath interface and the liquid metal-thermocouple sheath interface. The film coefficient of heat transfer between the argon gas and the metal sheath of the thermocouple is much less than that between the liquid metal and the metal sheath of the thermocouple. Heat is always being conducted up the metal sheath of the thermocouple to the stainless steel top plate, and this heat must be supplied from the medium surrounding the thermocouple (argon gas or liquid metal). When the surrounding medium is argon gas, the temperature difference between the argon gas and the metal.sheath of the thermocouple is greater than

-44-'I Xzll o~~~~~~...c.....,./.px..._= 20 KC HIGH // /? \ VOLTAGE LINE'' LEAD ZIRCONATETITANATE CRYSTALS I I I I ULTRASONIC TRANSDUCER' HORN 3 /-14-'2 HEX HEAD BOLT I | -1:THERMOCOUPLE |' // CE ~COPPER COOLING COIL "O" RING..~~ OLDER LIQUID " LEVE TOP PLATE ",GON' q oL i. "'"' "O" R NOG~ INLET -TEST SPECIMEN TEST FLUID CAVITATION VESSEL. 1464 Fig. 10. —High-temperature cavitation vessel and ultrasonic transducer.

-45the temperature difference between the liquid metal and the metal sheath of the thermocouple when the surrounding medium is liquid metal. This is due to the lower film coefficient at the argon-thermocouple sheath interface. This thermocouple is also used for measurement of the temperature of the test fluid in the vicinity of the test specimen. Once the liquid metal has been introduced into the vessel and liquefied, the pressure and temperature can be adjusted to the desired operational conditions. Argon is supplied to the system from the side of the bottom flange (Figure 10). As indicated in Figure 10, the liquid metal is to be maintained at a maximum temperature of 1500~F only a few inches from the flangeplate assembly, and about 8 inches from the crystals, which must be maintained at a temperature not to exceed about 150-200~Fo Thus, special heat transfer, thermal stress, and sealing considerations arise. In general, the vessel wall and cone supporting the flange-plate assembly is made to minimum wall thickness, consistent with stress requirements, to minimize heat conduction to the flange-plate assembly. Heat is also unavoidably transferred to the flange-plate assembly by conduction through the horn and by convection and radiation in the argon cover gas. The heat is removed from the flange-plate assembly by a cooling coil, and the flange-plate assembly cross-section is thick enough so that temperature gradients in it are small. Hence, its temperature must be close to that of the cooling medium. This allows the use of conventional organic sealing materials such as rubber "0" rings, and assures that the allowable crystal temperature will not be exceeded.

-46The details of the construction are discussed more fully below. The cylindrical section of the vessel is made from type 316 stainless steel pipe. The top plate is fabricated of type 304 stainless steel, 3/4 ino thick. Since it will not come into direct contact with any of the test fluids and will not operate at excessively high temperature, this material is adequate. The substantial thickness was chosen to facilitate heat conduction to the cooling medium. The top plate is provided with an access hole for the thermocouple and a centrallylocated opening to accommodate the transducer horn. Figure 10 indicates the details of the top plate design. The section connecting the lower flange and the cylindrical vessel has been designed in the shape of a cone to minimize thermal stresses due to the large temperature gradients in this region. 2. Method of Fastening Transducer to Vessel The problem of attaching the horn at or near a nodal point to the top plate is quite unique in that a good seal is required between the plate and the horn, but at the same time the horn cannot be grasped in such a manner that the amplitude of vibration is reduced. To establish the seal, a rubber or teflon "0" ring with dimensions 1 1/4 in. x 1 1/2 in. x 1/8 in. is provided to slip around the transducer horn and to seat in the groove provided in the top plate. The horn is held in a proper axial position by fastening a snap ring around the horn directly below the top plate. This arrangement provides the required squeeze on the "0" ring. It has been shown experimentally that this arrangement

-47does provide a positive- seal and does not result in a decrease in horn amplitude because the "0" ring is soft enough not tow restrain the low amplitude, high frequency vibration at this point. A patent application has been filed for this arrangement under the title, "Seal Holder Device for Ultrasonic Vibratory Unit." Alternative approaches have involved a steel bellows attachment which is subject to fatigue failure, and the complete enclosing of the entire unit in a dry-box (which solution was beyond our financial capability)o The snap ring employed is of type 304 stainless steel. The arrangement has functioned over a total of 1000 hours and numerous assemblies and disassemblies without difficulty. The seal between the top plate and the upper flange section of the cavitation vessel is maintained by means of a rubber or teflon "0" ring of dimensions 7 1/2 in. x 7 3/4 ino which seats in agroove provided in the upper flange section, The cooling arrangement previously described allows the use of a soft seal at this point, thus obtaining more positive sealing than experience indicates might be obtained from gaskets suited to high-temperature service, A 1/2 in. OoD. Schedule 20 copper tubing cooling system is provided to remove the heat conducted to the top plate by means of the transducer horn assembly and the vessel proper. The copper tubing is seated in a groove provided in the top of the top plate and brazed into position to provide good thermal contact o Flexible tygon tubing from the inlet and outlet provide cooling water to and from the copper tub55 ingo Calculations have shown that the available tap water flow is sufficient to remove the hea)i transferred to the top plate.

-48The top plate is firmly attached to the cavitation vessel by means of six cap screws which are inserted into the top plate and terminate in the upper flange of the vessel proper, F. Furnace Requirements The furnace which was chosen for providing the heat to attain the test temperatures desired is fitted with an opening of suitable dimensions so that the vessel is easily accommodated. Since the heating chamber is of a length somewhat greater than the length of the vessel, it was decided to attach to the bottom of the cavitation vessel a heat conducting extension, to provide more area to receive radiant heat from the furnace windings and also more cooling area on shut-down. This conductive skirt, 7" long with 3 1/8" ID. and 4" OoD., was made of aluminum-bronze material, chosen because of its high thermal conductivity and excellent high-temperature properties and ability to withstand corrosion. Without such a skirt, an appreciable portion of the heaters making up the furnace would have been radiating heat across the vessel at each other. Such operation could cause burnout of the heaters, More important, though, in order to achieve reasonable heat-up times for the tests envisioned, it was necessary to provide as much thermal power as possible in the furnace. Hence, the conductive aluminum-bronze skirt was designed. It is shown in Figure 11, attached to the high-temperature cavitation vessel by means of set screws. Due to the operating temperatures of the system, the stress limitations of the materials used at these temperatures must be

-49LEAD ZIRCONATE-TITANATE CRYSTALS 20 KC HIGH ~, VOLTAGE LINE \O" RINGS'" I I ULTRASONIC TRANSDUCER HORN SNAP RING __ THERMOCOUPLE -V E SL \ / O /COOLING COIL VESSEL TOP PLATE ARGON INLET CAVITATION VESSEL FURNACE INSULATION ~ -TEST FLUID. CERAMIC FURNACE VESSEL HEATING ELEMENT ALUMINUM- BRONZE CONDUCTIVE SKIRT ____. _. u.____Z_ -FURNACE SUPPORT ~1 ~I~ I. 1463 Fig. ll. —High-temperature cavitation vessel and ultrasonic transducer assembly mounted in furnace.

-50considered. The short-term tensile strength of type 316 stainless steel drops from approximately 90,000 psi to approximately 20,000 psi when heated from 70'F to 1500~F, and becomes almost negligible at approximately 2000QF. Since the forging point of stainless. steel is 21002300~F, the system could conceivably operate up to approximately 2000~F for short periods of time at low pressures. However, for operation above about 1500~F, it might be wise to use more exotic materials, e.go, various refractory alloys, which have improved high-temperature -. properties The discontinuity stress values, i.e., stress at sharp corners, etc., should also be investigated, and are presented in reference 55, along with the stress calculations, assumptions, simplifications, and any necessary clarifying figures. Appendix A summarizes the major.55. assumptions and'results of the necessary heat-transfer calculations. Calculations indicated that the heating losses due to conduction in the cavitation vessel would be approximately 2800 Btu/hour, or about 800 watts. In order to achieve a heat-up time of one hour, which was deemed reasonable for a test at 15000F, it was then necessary to have at least a power input of 2000 watts. Many inquiries were made of -as 3. commercial vendors as to the feasibility of supplying a furnace of such a power rating which could also accommodate the cavitation vessel. In the meanwhile, it was found that a suitable furnace (Figure ll) existed in the Department of Chemical and Metallurgical Engineering at this University, and this was made available by Professor C. A. Siebert of that department for the experiments of this laboratory. The furnace was

-51in the shape of a cube, 16" on an edge._ The outer covering consisted of 1/16 in. sheet metal. The bulk of the sheet metal box was filled with suitable insulation, but centrally located in the enclosure was an alundum crucible about which were wound the heater coils. Alundum cement was then used to cover the coils. The dimensions of the furnace chamber formed by the crucible were 6 in. diameter x 12 in. length. The crucible was open at both ends. However, it rested in an upright position on a layer of firebrick positioned at the bottom of the sheet metal frame. A similar layer of firebrick was positioned at the top of the furnace and provided with an access hole 4 in. in diameter. The thickness of the top layer of firebrick was 1 1/4 in. This layer of firebrick was covered by a steel end plate 1/8 in. thick and fitted with a centrally-located access hole 5 1/2 in. in diameter. The 4 in. access hole in the firebrick closely approximates the diameter of the cavitation vessel. It was felt that heat losses would be greater if the 6 in. hole available in the crucible were not decreased in this manner. This end plate provides a suitable surface to support the cavitation vessel, i.e., the lower surface of the upper flange of the cavitation vessel is in direct contact with the carbon steel end plate and rests on it. The power rating of the furnace is 3000 watts at 220 volts, and hence is ample for the purposes of this investigation. Figure 11 shows the high-temperature cavitation vessel and ultrasonic transducer assembly mounted in the furnace. The furnace is supported in a simple Unistrut frame structure.

-52G. Temperature Controller Requirements A Foxboro automatic temperature controller was also provided by Professor Siebert from the Department of Chemical and Metallurgical Engineering for control of the furnace temperature. A thermocouple was embedded in the alundum cement surrounding the heating element, and is thus in close proximity to the heating element. This should reduce any cycling problems. The controller has an upper temperature limit of 25000F, which is considerably above the maximum temperature planned for the experiments. It is an ON-OFF type controller equipped with a standard mercury switch. When the process temperature is below the set point, the full 220 volts is applied to the windings of the furnace. When the process temperature exceeds the set point, the mercury switch opens, reducing the voltage to zero. Once the desired temperature is reached, it is possible to achieve somewhat finer control by reducing the voltage applied to the windings by means of a variac. Thus, perhaps only 100 volts is necessary to compensate for the heat losses once equilibrium has been reached. Figure 12 is a schematic indicating the relationship and connections necessary to achieve this fine control. The primary voltage supply, variac, furnace, thermocouple, and controller are shown. The thermocouple used for temperature control in this application is of chromel-alumel. The automatic temperature controller is driven by a small motor requiring a 220 volt supply.

-53() 220 VOLTS r l MERCURY SWITCH L_.\. ON CONTROLLER L. J PRIMARY VARIAC _|J. SECONDARY _ —' 0 - 220 V FURNACE THERMOCOUPLE H EATING ELEMENT CONTROLLER I I 1465 Fig. 12. —Schematic of variac, furnace, and temperature controller.

-.4 H. Accelerometer Assembly 1. Introduction. 36 48,56 It has been shown by several investigators that the amount of damage sustained by the test specimen is heavily dependent on the amplitude of the horn tip. to which the specimen is attached, and this is, of course, also to be expected on theoretical grounds. In fact, there exists a minimum threshold amplitude for a given facility below which no damage is suffered by the test specimen, either due to the complete lack of cavitation for this amplitude or the insufficient shock pressures generated by bubble collapse. Hence, it is clear that it will be necessary to determine the amplitude of the specimen with reasonable accuracy, and to maintain this amplitude within acceptable limits for the duration of a test. In addition, it is important that any given amplitude be reproducible for future investigations so that comparisons may be drawn between various specimen material-fluid-temperature combinations. The problem of amplitude measurement is made difficult since the amplitudes characteristic of the magnetostrictive and piezoelectric devices used for ultrasonic cavitation studies are in the range of 1 to 5 mils, while the frequency of operation is generally 36.,48.... 15 to 20 Kc./sec. Other investigators have utilized a "voice coil" arrangement, which surrounded the exponential section of the horn, to determine the amplitude of the device. During operation, a voltage is induced in the voice coil which, hopefully, is proportional to the amplitude at the horn tip by the cyclic change in inductance due to the variable area portion il th-e horn which is enclosed by the coil. One

-55difficulty which has been experienced with this and similar, arrangements is that it is..also sensitive to the electromagnetic radiation from the driving amplifier, etc., which then gives a very misleading output. The output from the voice coil may be displayed on an oscilloscope or fed to a vacuum tube voltmeter and/or frequency counter for analysis. This arrangement, as well as all others which seem feasible, requires that an absolute determination of the amplitude of the horn tip be made by direct observation in air (or conceivably in a transparent liquid) utilizing a suitable high-power microscope. Such a calibration would result in a.plot of absolute amplitude of the horn tip versus the voltage output from the voice coil, and would enable one to determine the amplitude easily in any fluid as long as the characteristics of the exponential horn-voice coil system were not changed by the conditions of the surrounding environment, which includes the horn and fluid temperature, fluid density,'viscosity, etc. This calibration is particularly necessary since it would be difficult to directly observe the motion of the horn tip during a test in water, and impossible during an investigation in an opaque fluid, eog., liquid metals at elevated temperatures, where the vessel would also be opaque. Hence, it is necessary to be able to easily measure some secondary quantity that is directly related to the absolute amplitude in a reproducible and reliable manner. In the case of our experiments, some of which have been conducted in liquid metals at temperatures up to 1500~F, it is not possible to utilize a voice coil arrangement, as described previously, because of the severe environment surrounding the exponential portion of the horn.

-56Thus, it was necessary to determine the amplitude in our investigations by some other method. Since the horn tip approximately describes simple harmonic motion, the vertical displacement measured from some suitable datum plane taken as the origin is given by' y = A sin J t (1) where: y = displacement at time, t A = maximum amplitude lJ ) 27 x frequency of vibration Thus, it is seen that the acceleration at the horn tip is proportional * to the amplitude at the horn tip. This suggests the use of a suitable commercially available accelerometer whose voltage output would be proportional to measured acceleration and, hence, amplitude, at a given frequency. Such an accelerometer could be mounted at some point along the transducer horn assembly where the temperature variation is very *The acceleration, being directly related to the acoustic pressi.on',(13 twice: -a- = -A 2 sin W t -:-y S 2 (2) When y Cmax. =A' a amaX -A Tsure t nduced in thae aflu ccedls een to be ha quantityip isproportionse la to the avitation phenomenon t the amplitude itself.usof ui commercially available accelerometer whose voltage output: would be pro-. portional to measured acceleration and, hence-, liude, ataa-pgiven frequency.. Such an accelerometer-could be''mounted at some point along the transducer horn assembly where: the temperature-vari tion is very to the cavitation phenomenon than the amplitude itself.

-57slight during the investigations. Hence, its operation would be unaffected by the severe environment existing at the horn tip. Nevertheless, for a fixed accelerometer position, it would be possible to determine a suitable calibration of absolute amplitude (as determined by direct visual microscopic observation in air) versus voltage output from the accelerometer. Such a calibration would be valid for operation of the transducer-horn assembly at elevated temperatures since the accelerometer responds to changes in acceleration only, assuming that the ratio between acceleration at the specimen face and at the accelerometer position remains constant even when the transducer is exposed to a severe temperature gradient. The approximate validity of this assumption seems intuitively reasonable. 2, Accelerometer Description The requirements of a suitable accelerometer for this application include an ability to operate at a frequency of 20 Kc./sec., which is the normal frequency of operation of our ultrasonic cavitation facility. In addition, the sensitivity of the accelerometer must be sufficiently large so that the output can be easily measured with an oscilloscope and/or vacuum tube voltmeter. The weight of the accelerometer should be a minimum so as to only slightly disturb the ultrasonic unit. The accelerometer chosen for this application was the Glennite accelerometer Model #CA260502, supplied by Gulton Industries, Inc., of Metuchen, New Jersey. This accelerometer has a sensitivity of 1.32 mv. /*r /g over a wide frequency range, a resonant frequency of 138 Kc./sec., a *g acceleration due to gravity, taken as 980 cmo/sec.2 at sea levelo

-58nominal frequency range extending from 3 cps to 20 Kco/sec., a nominal acceleration range from 0 to 2000 g, a transverse response of only 1.7%, and a weight of 1.3 grams. It is easily mounted to the transducer-horn assembly at a suitable location by means of a threaded stud. A consideration of equation (3) above shows that for a frequency of 20 Kc./sec., and an amplitude of only 0.1 mils, the maximum acceleration would be approximately 2000 g. Hence, the output from the accelerometer would be approximately 2.5 volts, which is easily measured. It should be noted that an acceleration of approximately 2000 g constiE tutes the upper limit of applicability of any accelerometer, due to mechanical limitations of the design. It was decided to mount the accelerometer at the top of the transducer assembly, as shown in Figure 1. Such a location resulted in easy access to the unit with respect to cable attachment, and the temperature at this location was shown to be less than 100~F, even when the test fluid was at 15000F. Although the acceleration at this location is considerably less than at the horn tip, it was felt that the sensitivity of the accelerometer was large enough to provide a suitable output voltage for measurement. In fact, the acceleration at the horn tip is so large (approximately 50,000 g*) that an accelerometer mounted in this vicinity would be immediately destroyed upon operation of the unit, even if operated in air rather than a high-temperature fluid. Since the transducer assembly had been fitted with a tapped hole (5/8-20) at its top when it was initially constructed, an aluminum adaptor was *Ibid, p. 57.

fabricated which attached to the top of the transducer assembly. The accelerometer was then firmly screwed into the aluminum adaptor with a torque wrench. Because of the high frequency of operation and the resultant low impedance of the accelerometer (approximately 20,000 ohms at 20 Kc./sec.), it is possible to feed the signal from the accelerometer directly to an oscilloscope or vacuum tube voltmeter, each of which has an input impedance of several megohms. As a result, in this application, a cathode follower or other similar impedance matching device is not necessary. 3. Accelerometer Calibration As previously noted, it is necessary to calibrate the accelerometer once it is mounted in a fixed position, i.e., determine the relationship between the voltage output from the accelerometer and the amplitude at the horn tip. The necessary calibration was performed in air at 70~F with the transducer-horn assembly mounted in the top plate. The complete assembly was supported so that the axis of the transducer was vertical, corresponding to normal operation of the unit. A Unitron Metallurgical Microscope fitted with an eyepiece which contained a uniformly graduated scale was employed for the absolute amplitude measurements. Previously, the graduated scale had been calibrated by observing a specimen of known dimensions at a magnification of 400. It was found that 8 divisions on the eyepiece scale corresponded to a length of 1 mil, the complete scale having a length of 100 divisions. Since 51 earlier visual amplitude measurements had established that the

-60amplitude of. vibration of the horn tip was in the range of l to 3 mils,. it was felt that the sensitivity obtained at a magnification of 400 would be sufficient for the measurements. The test specimen at the end of the horn was backlighted with a General Radio Company Type 1531-A Strobotac which was adjusted to a suitable frequency so that it was possible to observe the motion of the horn tip as it vibrated between the extremities of travel For a given test specimen, the voltage applied to the piezoelectric crystals was varied over awide range (at a fixed frequency of 20 Kc./sec., which corresponds to the resonant frequency of the transducer-horn assembly), and the peak-to-peak amplitude of vibration of the horn tip was observed under the microscope at a magnification of 400. By means of the calibrated eyepiece and stroboscope, it was possible to note easily the number of divisions corresponding to the specimen motion, and hence determine the absolute amplitude, knowing the calibration of the graduated scale, For each value of absolute amplitude observed, the output from the accelerometer was fed to a Ballantine Laboratories, Inc., Model 300-G Vacuum Tube Voltmeter with a scale range from 1 my, to 1000 volts RMS* Thus, it was possible to determine corresponding values of the absolute amplitude and voltage output from the accelerometer. The procedure was repeated for three test specimens, one each of stainless steel, aluminum, and a tantalum-base alloy, covering a density range from 2.77 g./cc. to 17.6 g./cc. All specimens weighed 9,4 + 0.1 grams. After many measurements were made, it was felt that Root-mean- square yo ltage.

-61the reproducibility of data was within a tolerance of 1 scale division on the calibrated eyepiece, or approximately 0.1 mils. Also, the visual measurement accuracy was estimated to be within a tolerance of 1 scale division, or approximately 0.1 mils. For various horn tip amplitudes the output from the accelerometer was also fed directly to a Tektronix, Inc., Type 502A Dual-Beam Oscilloscope for visual display and analysis. Hence, it was also possible to determine the frequency of vibration of the transducer-horn assembly by determining the frequency of the accelerometer voltage waveform, The results obtained in this investigation are presented in Table 1, which lists corresponding values of variac voltage (proportional to crystal voltage), accelerometer voltage output (RMS) as measured by the vacuum tube voltmeter, accelerometer voltage output (peakto-peak) as measured by the oscilloscope, and absolute amplitude (peak-to-peak) of the horn tip. It was found that the results were identical for each of the three specimens employed within the margin of experimental error. Note that the maximum amplitude measured was 3 mils (peak-to-peak), which corresponds to an acceleration of approximately 100,000 g (peak-to-peak) at the horn tip. Equation (3) was used for this computation. At this amplitude the peak-to-peak accelerometer output voltage was 16 volts, which corresponds to an acceleration of approximately 12,000 g (peak-to-peak) at the opposite end of the transducer-horn assembly where the accelerometer is mounted, This value of acceleration was computed assuming an accelerometer sensitivity of

-62TABLE 1 AMPLITUDE MEASUREMENT DATA Experimental Conditions: 1) Transducer-horn assembly mounted in vessel top plate and held in a vertical position by usual mounting device 2) Surrounding medium is air at 70~F 3) Microscope magnification = 400X 4) Eyepiece calibration: 8 divisions =.001" = 1 mil 5) Stroboscope frequency = 3300 flashes/minute 6) Frequency of vibration of transducer-horn assembly = 20.3 Kc./sec. 7) Test specimens were 304 stainless steel, 2024-T351 aluminum, and T-lll (Ta-base alloy); data applies to all materials. 8) Accelerometer mounted at top of transducer-horn assembly Accelerometer Voltage Output Variac Voltage VTVM(RMS)* CRO(P-P)* Amplitude(P-P) 60 V 0 V 0 V 0 mils 70 0.9 3.0 0.5 80 1.8 6.0 1.0 90 2.9 8.0 1.5 100 4.1 10.0 2.0 110 5.2 13.0 2.5 120 6,0 16.0 3.0 * Voltage measured by vacuum tube voltmeter, root-mean-square. Voltage measured by cathode-ray oscilloscope, peak-to-peak.

-631.32 mv./g, which represents a. careful calibration supplied by the manufacturer. This calibration is stated to be valid even at the very high values of acceleration involved in this investigation as long as the accelerometer-is not damaged, and the frequency of operation (20 Kc./ sec.)-is a factor of 3 or 4 below the resonant frequency of the accelerometer (138 Kc./sec.) so as to avoid accelerometer resonance effects. It is interesting to note that the acceleration (and hence amplitude) is approximately 8 times greater at the horn tip where the specimen is located than at the opposite end of the horn where the accelerometer is located. This is very reasonable since in an exponential assembly of this type, the amplitude of vibration varies inversely as the cross53,54 sectional areas of the ends of the exponential assembly. In our case, the cross-sectional area at the top of the transducer-horn assembly is approximately 9 times greater than the tip. cross-sectional area. Both ends of the horn assembly correspond to antinodal points of the standing waves propagated within the transducer. In Table 1, values of accelerometer voltage measured by the oscilloscope (peak-to-peak voltage) should be about 2.8 times as great as the values of accelerometer voltage measured by the vacuum tube voltmeter (RMS voltage), if the horn tip describes simple harmonic motion. The ratio of the corresponding voltage values varies from 2.5 to 3.3, which is reasonable, since the measurement error in reading the oscilloscope waveforms is at least 10%, and the motion of the horn tip is not exactly simple harmonic in nature. A plot of absolute amplitude of vibration of the horn tip in mils.(peak-to-peak) versus accelerometer voltage output (as measured by

-64an RMS vacuum tube voltmeter) is presented in Figure 13. Note that the relationship is nearly linear, which corresponds to equation (3). This calibration makes it possible to determine the amplitude of the horn tip during an investigation in any fluid environment by monitoring the output from the accelerometer mounted at the opposite end of the transducer-horn assembly. 4o Summary and Conclusions An accurate method for measuring the amplitude of vibration at the tip of an ultrasonic transducer assembly has been developed. The method consists of monitoring the voltage output from a Glennite accelerometer, Model #CA260502, mounted at the top of the transducer assembly where it is readily accessible. The absolute amplitude of vibration at the opposite end of the horn assembly to which test specimens are attached is desired. A calibration of absolute amplitude at the horn tip versus the voltage output from the accelerometer makes it possible to determine the desired amplitude during any investigation. The major features of this system are as follows: a) The accelerometer is able to operate at frequencies in the vicinity of 20 Kc./seCo b) The accelerometer has a sensitivity of 1.32 mv./g, which makes it ideal for amplitude measurements in the range 1-3 mils. c) The accelerometer is mounted at the top of the transducer-horn assembly where it is easily accessible and at a point where the temperature never exceeds 100~F, even when the test specimen is

-65~1) 6-5 Imw _ m a. -J! LbJ I I ACCELEROMETER VOLTAGE - VOLTS (RMS) Fig, 13, —Calibration curve for accelerometer.

-66immersed in a fluid at 15000F. Hence, the accelerometer is never exposed to a severe environment, thus insuring relatively trouble-free operation. d) The voltage output from the accelerometer is proportional to the acceleration to which it is subjected, and hence the amplitude at the point of mounting. Thus, the output is also proportional to the amplitude at the tip of the transducer, since the system is acoustically coupled. The major observations made during the investigation are as follows: a) The maximum amplitude measured at the horn tip was 3 mils (peakto-peak), which corresponded to an accelerometer voltage of 6 volts RMS. b) The relationship between absolute amplitude and accelerometer voltage is nearly linear (Figure 13). c) The ratio of peak-to-peak accelerometer voltage to EMS accelerometer voltage varies from 2.5 to 3.3 for this investigation. d) The calibration obtained is independent of test specimen density, over the complete range tested (/V 2.7 to 17.7 g/cc.). e) The oscilloscope waveforms of voltage output from the accelerometer confirm the frequency of vibration of the transducer-horn assembly,- namely 20 Kc./sec. -; f) The acceleration at the horn tip is approximately 100,000 g (peak-to-peak), i.e., ~50,000 g, whereas it is only about 12,000 g (p k+t'o-peak) at the point where the accelerometer is

mounted, as expected, due to the difference in cross-sectional area at the two locations. g) The absolute amplitude of vibration can be determined visually within a tolerance of + 0.1 mils. J. Special Hardware It was noted previously that the ultrasonic horn utilized in this investigation was of type 303 stainless steel. When tests are conducted at elevated temperature with cavitation specimens whose coefficient of thermal expansion is considerably less than that of type 303 stainless steel, improper operation may result if necessary precautions are not taken. The combination of the type 303 stainless steel ultrasonic horn and a stainless steel or carbon steel cavitation specimen does not result in any problem since the coefficients of thermal expansion are nearly identical. However, with the high coefficient of thermal expansion ultrasonic horn (type 303 stainless steel) and various low coefficient of thermal expansion cavitation specimens (T-lll, T-222, Mo-l/2Ti, and Cb-lZr) an axial gap may develop at the interface between the cavitation specimen and the ultrasonic horn at high temperature, particularly at 1500~F. Hence, for this type of test, special hardware is necessary to eliminate this effect as the gap would result in improper transmission of the acoustic energy across the interface and a reduced amplitude at the test specimen face. The cavitation results would be greatly in error. For the tests at 1500 F in lead-bismuth alloy and lithium special hardware was designed and fabricated. The design consists of five

-68separate items of hardware. Item (1) is'a modified ultrasonic horn fabricated of type 303 stainless steel. It'is shown in Figure 14. Its design is similar to the standard ultrasonic horn shown in Figure 3, except that it is about 1 1/4 inches shorter than the standard horn. Item (2) shown in Figure 15 is an adaptor stud made of the refractory alloy T-222(A). Any of the refractory materials used in this investigation, such.as T-222, Mo-1/2Ti, or Cb-lZr, would have been suitable for this stud as long as the coefficient of thermal expansion matched that of Item (3), shown in Figure 16. Item (3) consists of an ultrasonic horn adaptor, also fabricated of the refractory alloy T-222(A). This ultrasonic horn adaptor must be fabricated of material having a coefficient of thermal expansion nearly equal to that of the refractory materials to be tested. Fortunately, the T-.lll, T-222, Mo-1/2Ti, and Cb-lZr have nearly identical coefficients of thermal expansion. The stud in Figure 15 (Item 2) is used to attach the ultrasonic horn,adaptor shown in Figure 16 (Item 3) to the modified ultrasonic horn shown in Figure 14 (Item 1). The refractory cavitation test specimens are then attached to the tip of the assembly resulting from Items (1), (2), and (3). Such an arrangement eliminates any problems concerned with differential expansion, and results in intimate contact being maintained at the interface of the ultrasonic horn adaptor and the refractory cavitation specimen. Intimate contact is also achieved at the interface of the modified ultrasonic horn and the ultrasonic horn adaptor, since the connecting adaptor stud has a coefficient of thermal expansion equal to that of the....ultrasonic holn adaptor and less than that of the modified

-69ITEM 1: MODIFIED ULTRASONIC HORN MATERIAL: TYPE 303- STAINLESS STEEL 3/8 -24 - X - 22 HOLES e 1.491 ~ 5/8 I - 47:- 4.043.044 _ _ 32.220.0625: x.500 D I:' 9/16 COUNTERBOREI _____;: 1-655s4 TOLERANCES DECIMAL: ~.00I,FRACTIONAL: 1/32 1979 Fig. 14. —Modified ultrasonic horn.

-70-: ITEM "2: ADAPTOR STUD MATERIAL: T-222 (A) 3/8- 24 Fig. 15. —Adaptor stud.

-71ITEM 3: ULTRASONIC HORN ADAPTOR MATERIAL: T-222 (A) 3/8-24 TAP 1/4-28 TAP.0625 x.500 D X ~.655 ~ / PILOT 7/16 20o301~ I I I0 —-K 1 3/8 1/2' 1 I/8 ~ —.547"TlOLRANCES iCeIMAL::.001" FRACTIONAL: i 1/32" 1981 Fig. 16. —Ultrasonic horn adaptor.

-72horn. Thus, any differential expansion in this region would result in a tighter bond at this interface. The temperature existing at this interface during operation of the assembly is much lower than that existing at the interface of the cavitation test specimen and the ultrasonic horn adaptor. Hence, less expansion would be expected. The arrangement described above was used successfully to test the refractory specimens at 1500"F. At 5000F it was found that the differential expansion was so slight as to not affect the operation of the standard ultrasonic horn (Figure 3) with the refractory specimens attached directly to it. When testing types 304 and 316 stainless steel at 1500~F, the standard ultrasonic horn (Figure 3) was used, since the coefficients of thermal expansion of both the horn and the specimens were nearly identical. Since the special adaptor hardware described previously was used when testing the refractory specimens at 1500~F, it was felt that it would be instructive to experimentally compare the operation of the two systems. To do this, it was necessary to fabricate a modified cavitation specimen of type 304 stainless steel to be used in conjunction with the ultrasonic horn adaptor (Figure 16). The modified cavitation specimen is shown in Figure 18 as Item (5). It is attached to the ultrasonic horn adaptor by means of the modified cavitation specimen stud shown in Figure 17 as Item (4). This stud is made of Cb-lZr(A), but any of the other refractory materials previously mentioned would have been suitable for this item of hardware. With this arrangement at high temperature, the high thermal expansion coefficient cavitation specimen would expand

-73ITEM 4: STUD FOR MODIFIED CAVITATION SPECIMEN MATERIAL: Cb- IZr (A) Fig.. it i/4-28 — 1., /2 Fig. 17. —Stud for modified cavitation specimen. 1982

-74ITEM 5; MODIFIED CAVITATION SPECIMEN MATERIAL: TYPE 304 STAINLESS STEEL 1/4-28.125~.005.250:t1.005'.547 ~.001 ~ Fig. 18. —Modified cavitation specimen. 1983

-75more than the low coefficient stud or the low coefficient adaptor. Hence, an axial gap would not develop at the interface between the high coefficient cavitation specimens and the low coefficient adaptor. Of course, this arrangement is not necessary when testing the type 304 and type 316 stainless steel cavitation specimens as the standard ultrasonic horn (made of type 303 stainless steel) can then be utilized. However, both arrangements were employed to test stainless steel in lead-bismuth at 1500~F in order to compare the systems. The test results differed by 3%, thus verifying the proper operation of both systems. Items (1) through (5) are shown in an assembly drawing (Figure 19) which clearly indicates the order of assembly of the hardware, A patent application has been made to cover the special hardware assemblies described in this section.

-76-- -_ MODIFIED ULTRASONIC HORN (ITEM I) ADAPTOR STUD (ITEM 2) ULTRASONIC HORN ADAPTOR (ITEM 3) SPECIMEN STUD (ITEM 4) ^~ a MODIFIED CAVITATION SPECIMEN (ITEM 5) 1984 Fig. 19. —Assembly drawing of modified ultrasonic horn, adaptor stud, ultrasonic horn adaptor, specimen stud, and modified cavitation specimen.

CHAPTER III EXPERIMENTAL INVESTIGATIONS A. Objectives of Experimental Program Utilizing the high-temperature vibratory device developed for this program, it was desired to determine the cavitation resistance of a wide variety of potentially useful materials (involving a considerable range of mechanical properties) in a wide variety of fluids over a full temperature range in an attempt to learn more about the cavitation damage process as it isaffected by fluid and material properties. Materials included are stainless steels, carbon steel, refractory alloys, aluminum, copper, nickel, brass, plastics, etc., and the fluids to be used are water at 70~F, mercury at 70~F and 500~F, and lead-bismuth alloy and lithium at 5000F and 15000~F Table 2 summarizes the specimen material-fluid-temperature combinations which were studied in this investigation. The composition of the various refractory alloys is given along with the annealing temperatures and duration of anneal for the various Cu, Cu-Zn, Cu-Ni, and Ni materials tested. In addition, several potential bearing materials were tested to further widen the material property range. These were the tool steel alloy BG-42 (a modified 440-C stainless steel), Blue Chip Tool Steel -77

-78TABLE 2 SPECIMEN MATERIAL-FLUID-TEMPERATURE COMBINATIONS INVESTIGATED Fluid Pb-Bi & Li Water Mercury Mercury 5000F & Material 70~F 70~ F 500 ~F 1500 F 1100-0 Al (U-M) X....... 2024-T351 A1 (U-M) X. 6061-T651 A (U-M) X... 304 Stainless Steel (U-M) X X X X 316 Stainless Steel (U-M) X X X Hot-Rolled Carbon Steel (U-M) X X X T-lll (Ta-8W-2Hf) (P & W) X X X X T-222 (Ta-9.5W-2.5Hf-.05C) (P & W) X X T-222(A) (P & W)...... X Mo-1/2Ti (P & W) X X X X Cb-lZr (P & W) X X X X Cb-lZr(A) (P&W) X X X X Plexiglas (U-M) X X... Cu(60% cold-worked) (U-M) X........ Cu(900~F anneal, 1 hour) (U-M) X..... Cu(1500OF anneal, 1 hour) (U-M) X... * - Cu-Zn(60% cold-worked) (U-M) X...... Cu-Zn(850~F anneal, 1 hour) (U-M) X.... Cu-Zn(14000F anneal, 1 hour)(U-M) X... Cu-Ni(60% cold-worked) (U-M) X *.. Cu-Ni(1300~F anneal, 1 hour) (U-M) X... Cu-Ni(18000F anneal, 1 hour)(U-M) X Ni(75% cold-worked) (U-M) X..... Ni(1100OF anneal, 1 hour)(U-M) X..... Ni(16000F anneal, 1 hour)(U-M) X. 0 Notes: 1) "X" indicates test conducted for this specimen material-fluidtemperature combination. 2) The notations (U-M) and.(P & W) following the.specimen materials indicate the source of the material, namely, The University of Michigan andritt &.Whitney Aircraft (CANEL), respectively; whereas the notation (A) denotes an annealed condition of the material.

.79* (18-4-1 tool steel), Mo-1/2Ti, Cb-lZr(A), two grades of graphitar, single-crystal tungsten, and teflon-coated type 304 stainless steel. These were tested in mercury at various temperatures, and in water at 700F. The various materials tested in this program along with the fluid-temperature combinations involved are summarized in Table 3. B. Experimental Test Conditions Initially, each of the specimens was weighed on a precision balance to an accuracy of Oo01 mgo, and then attached to the tip of the stainless steel exponential horn, whereupon the entire unit was assembled. ~The tests in lead-bismuth alloy and lithium at 5000F and 1500~F and the tests in mercury at 700F and 5000F were conducted in the 316 stainless steel cavitation vessel previously described. The investigations in water at 70~F were conducted in a Plexiglas cavitation vessel whose inside dimensions were identical to those of the 316 stainless steel container. The Plexiglas vessel permits visual observation of the bubble cloud and continuous monitoring of the condition of the specimen surface during a test. At elevated temperatures the test fluid was maintained at the required temperature by the temperature controller, which allowed temperature variations of less than 5~F. The specimens were oscillated at approximately 20 Kc./sec. with the exception of the 1500~F tests where the resonant frequency *The 18-4-1 desi ation denotes a tool steel containing 18% tungsten, 47% chromium, and 1% vanadium.

-80TABLE 3 MATERIALS TESTED IN BEARING PROGRAM 70~F Meru0F Mercury 5350F Mercurrr Graphitar-Grade 50(U-M) Teflon-Coated 304 SS(U-M) BG-42 (Rc = 47)(TRW) Graphitar-Grade 80(U-M) BG-42 (Rc = 53)(TRW) BG-42 (Rc = 64)(TRW) Blue Chip Tool Steel (TRW) 700F Water Mo-1/2Ti (P & W) Single-Crystal Tungsten(U-M) Cb-lZr(A) (P &W) NOTE: The notations (TRW), (P & W), and (U-M) following the specimen materials indicate the source of the material, namely, Thompson-RamoWooldridge, Pratt & Whitney Aircraft (CANEL), and The University of Michigan, respectively; whereas the notation (A) denotes an annealed condition of the material. The grades of graphitar are designations of the United States Graphite Company.

-81was reduced to A) 18 Kc./seco by the reduction in sonic velocity in the high-temperature portion of the horn. The frequency, however, can be measured with an accuracy of + 0.002 Kc./sec. The submergence of the horn tip was held constant at 1 1/2 ~ 1/8 inches in all fluids, while the double amplitude at the specimen was maintained at 2 ~ 0.1 mils for all the tests, as determined by the precision accelerometer previously described 5 The argon cover gas was maintained over the test fluids at a pressure that was a function of the fluid-temperature combination being investigated. The value of argon cover gas pressure is chosen for a given fluid-temperature combination such that the suppression pressure, i.e., the difference between local pressure at the specimen face and vapor pressure of the fluid, is approximately constant for all investigations involving a variety of fluid-temperature combinations. The lead-bismuth tests at 500~F and 1500"F and the mercury tests at 700F were conducted at a slight overpressure (0,5 psig) to prevent inward leakage of oxygen, and the corresponding suppression pressure was used for the remainder of the tests. The mercury tests at 500~F then required an argon pressure of 2.4 psig, the lithium tests at 500~F required 11l psig, the lithium tests at 1500~F required 1.2 psig, and the water tests at 70~F an argon pressure of 1.5 psig. The variation is due to the different densities and vapor pressures of these fluids at the various test temperatures. While a constant suppression head (pressure/density) rather than pressure may have been desirable for considerations of fluid-dynamic modeling, the pressure capabilities of the

-82equipment were not adequate to allow this course to be pursued. Total test duration varied for the different materials and was always sufficient to obtain a good determination of damage rate, which, neglecting the very early portion of the test, was found to be essentially constant for most of the tests within the total accumulated damage obtained. Test duration was thus a function of the fluid and fluid temperature, and differed widely for the various materials. The appropriate test duration for each material-fluid-temperature combination will be discussed in more detail later. The tests were terminated when the complete face of the specimen was damaged, and an approximately uniform rate of damage established. Frequent inspections and weighings were made during the tests to monitor the condition of the specimen surface and establish the rate of weight loss. Heating time from 500~F to 1500~F for the lead-bismuth and lithium tests proved to be approximately 1 1/2 hours. Cooling time from 1500"F to 5000F is approximately five hours. Since the piezoelectric crystals must be maintained at a temperature below 150~F, the top plate of the cavitation vessel is cooled by circulating water as previously described. In addition, a fan in close proximity to the crystals provides additional cooling. The tests in each fluid generally required special handling procedures that were a function of the fluid-temperature combination. These will be described in the appropriate sections.

-83C. Cavitation Studies in Lead-Bismuth Alloy at 500~F and 1500~F 1. Experimental Procedure The seven materials tested in lead-bismuth alloy (70% lead30% bismuth) at 500~F and 1500~F were 304 stainless steel (U-M), 316 stainless steel (U-M), T-lll (P & W), T-222(A) (P & W), Mo-1/2Ti (P & W), Cb-lZr (P & W), and Cb-lZr(A) (P & W). Standard cavitation test specimens, as shown in Figure 6, were machined from available bar stock. The required dimensions "A" and "B" for the seven materials tested are listed in Table 4. These dimensions provide a standard specimen weight of 9.4 + 0ol go The vapor pressure of lead-bismuth at both 500 F and 1500~F is approximately zero. The argon cover gas pressure was maintained over the molten lead-bismuth throughout the tests at both 500 F and 1500~F at a slight overpressure of 0.5 psig to prevent in-leakage of oxygeno The corresponding suppression pressure, 15.3 psig, was then maintained constant for all the tests in all fluids. At 500 F the specimens were subjected to the cavitation environment for a total test period of 12 hours with the exception of the Cb-lZr(A) which showed gross erosion after 8 hours of testing. Preliminary tests had indicated that when this gross erosion was achieved, the damage rate starts to vary substantially from the relatively constant value obtained once damage had become fairly uniform. Hence, it is not Changes in atmospheric pressure from day to day have been assumed negligible,

-84TABLE 4 SPECIMEN DIMENSIONS Material "A"'"B" 304 Stainless Steel.250".625" 316 Stainless Steel.2501.625" Hot-Rolled Carbon Steel.250".625" T-111.085".460" T-222.085".460" T-222 (A).085".460" Mo-1/2Ti.1751". 550" Cb-lZr.220".595" Cb-lZr(A).220".595" 1100-0 Aluminum.820". 195" 2024-T351 Aluminum.820" 1.195" 6061-T651 Aluminum.820" 1.195" BG-42 (all heat-treats).250".625" Blue Chip Tool Steel.220".595"

-85desired to carry the tests to very heavy damage conditions. At 2 hour intervals the specimens were visually examined, photographed, and carefully weighed. Then the test was resumed. At each examination excess lead-bismuth adhering to the test specimen was removed by quickly heating the specimen with a propane torch to a temperature just above the melting point of the lead-bismuth (approximately 3500F). The excess fluid was then separated from. the test specimen by a quick blast of compressed air. The process was rapid enough so that only negligible oxidation occurred. For the tests at 15000F all transfers of the specimens to and from the high-temperature cavitation vessel were made at: a temperature of 5000F. Since the lead-bismuth is not grossly and rapidly affected by exposure to atmosphere, no special provisions as the use of pre-cast sealed ingots previously described for the lit hium were necessary. The fact that there was no substantial intergranular corrosion during the test is shown by the photomicrograph of Figure 20o The type 316 stainless steel specimen shown here was tested in lead-bismuth alloy at 15000F for 6 hours. The magnification is IOOOXo In Figures 21 and 22 photomicrographs of the surface of the same type 316 stainless steel specimen are shown at a magnification of 500Xo There is no evidence of corrosion at the surface but this may be due to surface cleaning by the cavitation process. The fact that the non-cavitated parts of the specimen were not corroded shows that corrosion in the absence of cavitation was negligible. The effects of corrosion in the vibratory type test 48 have — been previously examined by Plesseto After securing the

-86IN Fig. 20. —Photomicrograph of type 316 stainless steel specimen tested in lead-bismuth alloy at 1500~F (interior of specimen, magnification 100OX).

-871945 Fig. 21. —Photomicrograph of type 316 stainless steel specimen tested in lead-bismuth alloy at 1500~F (specimen surface, magnification 500X).

-88Fig. 22. —Photomicrograph of type 316 stainless steel specimen tested in lead-bismuth alloy at 15000F (specimen surface, magnification 500X).

-89ultrasonic transducer assembly to the top plate of the cavitation vessel and bolting the top plate in place, the temperature of the lead-bismuth alloy was increased to 1500~F by means of the automatic temperature cony aut.. troller. At the conclusion of the test the temperature was redued to 5000F again so that the specimen could safely be removed from the end of the exponential horn and visuailly exa mied nd:weighead. Aso, it: desired not to expose the test materi:als:.t0- heatmo phere at 1500~F where reaction rates would no doubt be considerably greater than at 500 0F.. The seven specimens tested for cavitation resistance at 1500~F were subjected, to the cavitation environment for arying lenths of time, the stainless steel being exposed for 5-6hours and the refractory alloys for a total of 10 hours. At appropriate intervals the specimens were visually examined, photographed,andcarefullyweighed Thenthe test resumed.- Excess lead-bismuth alloy was removed from the specimens using the procedure outlined earlier. It was not possible to examine the refractory materials as frequently as the stainless steels.because of numerous mechanical problems that were encountered with these materials. On several occasions the refractory specimens fractured during disassembly at the point where the threaded length joins the cylindrical button portion of the specimen, thus voiding the test. Hence, extreme care had to be exercised during assembly and disassembly, so that it was not desired to repeat this operation any more often than necessary. As a result, the refractory specimens we:re examined, photographed, and weighed after 4 hours of testj.ng, and again after a total of 10 hours in the cavitation environment.

-902o Experimental Results at 500~F The cavitation results obtained at 5000F in lead-bismuth alloy will be displayed as accumulative weight loss versus test duration, and also as accumulative mean depth of penetration (MDP) versus test duration. The mean depth of penetration, computed assuming that the weight loss is smeared uniformly over the cavitated specimen surface, is felt to be more physically meaningful than weight loss, since it is generally the total penetration of a particular component by cavitation erosion that would render it unfit for service. Of course, neither weight loss nor MDP is sensitive to damage distribution and form, i.e., damage may vary from isolated deep pits to relatively uniform wear, depending on material-fluid combination. Obviously, a "figure of merit" such as MDP takes into account the large variation in density that may occur within a set of test materials. The appropriate expression for computing the MDP of a given material is of the form: MDP (mils) CoW where W is the weight loss expressed in mg. and C is a constant for the given material. Values of the constant, C, for computing the MDP of all the materials tested, along with their densities, are presented in Table 5. Figure 23 is a plot of accumulative weight loss versus test duration for the seven materials tested, while Figure 24 is the corresponding plot of accumulative MDP versus test duration. The results presented in Table 6 are the slopes of these curves.

-91TABLE 5 RELATION BETWEEN WEIGHT LOSS AND MDP (MDP C.W).. - ostant Material _, -.;Density_, 1.* 1100-0 Aluminum 2.77 g./cc..0935 2024-T351 Aluminum 2,77.0935 6061-T651 Aluminum 2.77.0935 304 Stainless Steel 7.85.033 316 Stainless Steel 7.85.033 Hot-Rolled Carbon Steel 7.85.033 T- 111 17.66.0147 T-222 17.66.0147 T-222(A) 17.66.0147 Mo-1/2Ti 10.22.0253 Cb-lZr 8.72.0296 Cb-lZr(A) 8.72.0296 Plexiglas 1.23.210 Cu (60% cold-worked) 8.97.0288 Cu (9000F anneal, 1 hour) 9.04.0287 Cu (15000F anneal, 1 hour) 9.06.0286 Cu-Zn (60% cold-worked) 8.61.0300 Cu-Zn (850~F anneal, 1 hour) 8,62.0300 Cu-Zn (1400~F anneal, 1 hour) 8.62.0300 - ~ ~ - -.,. ~ ~- i~c~ ~' ~' - ~..~ ~.-~.....

-92TABLE 5 —Continued Constant Material Density _ - C* Cu-Ni (60% cold-worked) 9.05 g./cc..0287 Cu-Ni (13000F anneal, 1 hour) 9.05.0286 Cu-Ni (18000F anneal, l1hour) 9.02.0287 Ni (75% cold-worked) 8.97.0288 Ni (1100~F anneal, 1 hour) 9.00.0288 Ni (1600~F anneal, 1 hour) 9.00.0288 BG-42 (all heat-treats) 7.85.033 Blue Chip Tool Steel 8.70.0296 Graphitar-Grade 50 1.70.152 Graphitar-Grade 80 1.80.144 Single-Crystal Tungsten 19.30.0161 *Valid when MDP is expressed in mils and W is expressed in mg.:

-931000 - 0 304SS(UOFM) 0 E316SS(UOFM) 9 A CB -IZR (PPaw 0 M -1/2 TI (PaW) T- ll (Paw) 800- i CB-IZR(A)(PaW) / AT-222(A)(PaW) CB- IZR (A) 700 -; 600 CB-IZR Cr) o 500 T-ll400- T-222(A),. ~~~10 ^ l ^ ^304 SS 3 0 100- 2 316 SS 0 2 4 6 8 10 12: 14 TIME, HOURS 1602 Fig. 23. —Effect of cavitation test duration on weight loss at 5000F in lead-bismuth alloy.

-9420 0 304SS(UOFM) o 316SS(UOFM) 18- ACB-IZR(PaW) O Mo-1/2T, (PaW) * T-III(PAW) / CB-IZR(A) * CB-IZR(A)(P&W) 16 - T-222(A)(P&W) 14CB-IZR I- ^" / ^ 304SS 0 2 4 6 8 10 1211 TME.HOURS: 0 0 r ~316SS603 uLJ > 6 Fig. 24. —Effect of cavitation test duration on MDP at 5000F in lead-bismuth alloy.

-95TABLE 6 SUMMARY OF CAVITATION-RESULTS IN LEAD-BISMUTH AT 500OF Avg. Wt, Average Material 1. Loss Rate M D P;- Rate T-111. (P & W) 49.1 img./hr..72 mils/hr. T-222(A) (P & W) 51.6.76 Mo-1/2Ti (P & W) 30.7.78 316 SS (U-M) 26.6.88 304 SS- (U-M) 28-.2.93 Cb-lZr (P &. W) 55.1 1.63 Cb-IZr(A) (P & W) 1 19.5 3.54

-96On the basis of MDP it is clear that the alloy T-lll has exhibited the greatest resistance to cavitation damage in this experiment, although T-222(A), Mo-1/2Ti, 304 stainless steel, and 316 stainless steel are also quite cavitation resistant relative to the Cb-lZr and the Cb-lZr(A). The Cb-lZr(A) suffered gross damage after 8 hours of testing. The other materials were tested for a total of 12 hours. It is clear from Figures 23 and 24 that the rate of erosion for each individual material was approximately constant throughout the test, except for the very initial part. It is also significant that at 500~F the stainless steels tested fared almost as well as the refractory.alloys T-lll, T-222(A), and Mo-1/2Ti. Photographs of the test specimens before exposure and at the conclusion of the cavitation experiment are presented in Figure 25. The effect of the cavitation erosion action of the collapsing bubble field is quite apparent. Note the generally uniform dispersion of pitting over the entire surface except for a relatively undamaged thin rim around the outside. This eventually leads to a cupped specimen surface which affects the bubble cloud and damage rate. 3. Experimental Results at 1500~F The cavitation results obtained at 1500~F in lead-bismuth alloy are also presented as accumulative weight loss versus test duration and also as accumulative mean depth of penetration (MDP) versus test duration. The expressions given previously for MDP as a function of weight loss (Table 5) are, of course, applicable at 1500~F* also. *The damage measurements are, of course, made at room

-97BEFORE EXPOSURE 5000Fo 15000F. 304 Stainless Steel 304 Stainless Steel 304 Stainless Steel (U-M) 12 Hour Exposure 5 Hour Exposure 316 Stainless Steel 316 Stainless Steel 316 Stainless Steel (U-M) 12 Hour Exposure 6 Hour Exposure Mo-"Ti (P & W) Mo-<Ti (P & W) Mo-~Ti (P & W) 12 Hour Exposure 10 Hour Exposure T-lll (P &'W) T-lll (P &W):T-.ll (L" &w) (Ta-8W-2Hf) 12 Hour Exposure 10 Hour Exposure Fig. 25. —Specimens subjected to cavitation damage in lead- 1607 bismuth allov at 5000F and 1500~F.

-98BEFORE EXPOSURE 5000FO 15000F. T-222(A) (P & W) T-222(A) (P & W) T-222(A) (P & W) \Ta-9.5W-2.5Hf- 05C) 12 Hour Exposure 10 Hour Exposure Cb-lZr (P & W) Cb-lZr (P & W) Cb-lZr (P & W) 12 Hour Exposure 10 Hour Exposure Cb-lZr(A) (P & W) Cb-lZr(A) (P & W) Cb-lZr(A) (i & W) 8 Hour Exposure 10 Hour Exposure Fig. 25. —Specimens subjected to cavitation damage in lead- 1698 bismuth alloy at 5000~F and 1500~F.

-99Figure 26 is a plot of accumulative weight loss versus test duration for the seven materials tested, while Figure 27 is the corresponding plot of accumulative MDP versus test duration. The results presented in Table 7 are the slopes of these curves. On the basis of MDP the refractory alloy T-lll exhibited the greatest resistance to cavitation damage in this experiment. This was also true at 500~F. The T-222(A) and the Mo-1/2Ti were also quite cavitation-resistant relative to the other materials tested. The Cb-lZr and the 316 stainless steel rated behind the tantalum and molybdenum alloys, while both the Cb-lZr(A) and the 304 stainless steel exhibited little resistance to cavitation erosion at this temperature Both were grossly damaged, especially the 304 stainless steel after only 5 hours of testing. It is clear from Figures 26 and 27 that the rate of erosion for each individual material was approximately constant for all the materials tested except perhaps near the start of the test. This behavior was also noted at 5000F. There is, no question that the refractory alloys T-lll, T-222(A), Mo-1/2Ti, and Cb-lZr are far superior to the stainless steels with respect to resistance to cavitation erosion at 1500~F. Such materials are likely choices for components that are subject to cavitation damage in various types of turbomachinery, magnetohydrodynamic devices, etc., which are expected to operate at very high temperatures. Photographs of the test specimens before exposure and at the conclusion of the cavitation experiments at both 500~F and at 1500'F are temperature and expressfons*.for MDP presumed applicable at this temperature also.

-10020000,^1 0' 304SS(U OFM) 0: 316SS(UOFM) -ACB-IZR(PBW) O M-1/2 T (P8W) - T-Ill (PaW) CB-I ZR(A)(PaW) A T-222(A)(PaW) 1500' / - 304SS 0 / /CB- I ZR (A) - CB-IZR -J ~ ~ ~ ~ ~ ~ ~T-III -/^^^^^^fT- 222(A) 0 2 4 6 8 10 12 14 TIME, HOURS 1614 Fig. 26. —Effect of cavitation test duration on weight loss at 1500~F in lead-bismuth alloy.

-101. 80 O 304SS( UOF M) CBI1 SS OF M) I B- ZR (P aW) MO-/27, (pa / T111 (PaW) J CB- ZR(A)(Pal f 60 T-22(A)(P81W) -J ^ ^304 SS CB-l~a 40 ^ f / 7' 20 20~~~ ~~3/6S36 S m0-112 T, T-222(A) T' HOURS ^ ^ ^onon^^^^~161

-102TABLE 7 SUMMARY OFCAVITATION RESULTS IN LEAD-BISMUTH AT 1500 OF m - I -,.r,,* -, _, i. d, I Avg. Wt. Average Material...:Loss Rate MDP Rate T-1ll (P & W): 57.1 mg./hr..84 mils/hr. T-222(A) (P &W) 599.88 Mo-1/2Ti(P i& W) 42.6 1.08 C -.. Cb-Zr (P & W) 70.0 2.07 316 SS (U-M) 83.3 2.80 Cb-Zr(A) (P & W) 128.4 3.80 304 SS (U-M) 342.0 11,30

-103presented in Figure 25 (previously cited) for comparison. Detailed examination of the 303 stainless steel exponential horn, the 316 stainless steel container vessel, and the sides of the various test specimens, all of which are not subject to cavitation, but are submerged in the test fluid, indicates that corrosion effects in the absence of cavitation in these investigations at both 500~F and 1500'F were negligible. Also, the photomicrographs presented in Figures 20, 21, and 22 (previously discussed) do not show anyevidence of intergranular corrosi:on or corrosion at the surface of the specimen. Figure 20 does show slip lines in the grains near the surface, indicating the mechanical' nature of the attack. Hence, one might conclude that the damage suffered by the test specimens in these tests was due almost completely to the mechanical cavitation-erosion process,: and not to chemical corrosion. 4, Discussion and Comparison of Results Table 8 summarizes the cavitation data obtained at 500~F and at 1500 ~F. The seven materials tested have been rated on the basis of cavitation resistance as determined by MDP, with a rating of "1" indicating t:he most cavitation resistant material, while a rating of "7"1 would denote that material most susceptible to cavitation damage. The tantalum alloys, T-1ll and T-222(A), are the most resistant to cavitation at both 5000F and at 15000F. The Mo-1/2Ti ranks third at both temperatures. It is significant to note the poor performance of the stainless steels at 15000F after being only 25% less resistant to cavitation at 5000F than he T-lll and the T-222(A). In fact, at 15000F

-104TABLE 8 COMPARISON OF CAVITATION RESULTS IN LEAD-BISMUTH AT 5000F AND 1500~F 500~F 1500~F Material (Avg. MDP Rate) Rating (Avg. MDP Rate) Rating T-lll.72 mils/hr. 1.84 mils/hr. 1 T-222(A).76 2.88 2 Mo-1/2Ti.78 3 1.08 3 316 SS.88 4 2,80 5 304 SS.93 5 11.30 7 Cb-lZr 1.63 6 2.07 4 Cb- lZr(A) 3.54 7 3.80 6

-105the 304 stainless steel was damaged grossly after being subjected to the cavitation environment for only 5 hours. A similar comment applies to the Cb-lZr(A) at 5000F and 1500~F. Figure 25 displays photographs of the- specimens before exposure to cavitation and at the conclusion of the tests at 500~F and 1500~Fo:The differences in the amount of erosion attack on the various specimens and the effect of temperature are readily apparent. It is important to note that for each material tested the amount of damage sustained by the specimen at 15000F was greater than that sustained at 500~F for constant testing time. The effect of temperature on the cavitation results iin leadbismuth alloy is further displayed in Figure 28, which is a plot of average MDP rate versus temperature for the seven materials tested. The effect of temperature on the T-11l, T-222(A), and Mo-1/2Ti is almost negligible, while the effect on the stainless steels is quite dramatic, as evidenced by the slopes of the appropriate curves. Later it is noted that this is due primarily to the fact that the mechanical properties of the stainless steels over the range tested are strong functions of temperature, whereas those of the refractories are only slightly affected by it. At the same time the pertinent fluid properties for lead-bismuth alloy at 500~F and 15000F are nearly identical. D. Cavitation Studies in Mercury.at 70~F and 500F1. Experimental Procedure The eight materials tested in mercury at 500~F were 304 stainless steel (U-M), 316 stainless steel (U-M), hot-rolled carbon

,'.Ao T qpnmsTq-peiT UT aouvsTsal: UOJB:lTAB3O o U neev:a;;: Jo 0J Ja —— 8 Z'g8T 99T 311ln IV3dV l3 L oo0091 o o 0001 009 0..I -o II(V) Z 111-1 l 11 z/l o~ _ (V)uZI-83 / I SS1702. /: -0 - -'8 0 00-91 IV''fnOH/SIllW ~1I 6 ~ * -..0 1. -901

-107steel -(U-M), T-lll (P & W),: T-222(A).(P & W), Mo-I/2Ti (P &W), Cb-lZr (P & W), and Cb-lZr(A) (P-& W). Standard cavitation test specimens, as shown in Figure 6, were machined from available bar stock. The required dimensions "A" and "B" for the eight materials tested are listed in Table 4. These dimensions provide: a standard specimen weight of 9.4 + 0.1 g. The materials tested in mercury at 700F were identical to those tested at 5000F, and listed previously in Table 2, with the exception of T-222 which was substituted for T-2222(A) due.to a shortage of the annealed bar stock. In addition, Plexiglas was also tested at 70~F because of availability of cavitation data for this material from the 20 21,22 venturi tests.'' Standard cavitation test specimens of T-222 have the same dimensions as given previously for:-the annealed stock (Table 4). ~-:Due to the low density of- the; Plexiglas (compared to the other materials tested) and its brittle nature, as previously explained, it was completely impractical to fabricate standard cavitation test specimens as shown in Figure 6. Hence, the design previously discussed and shown in Figure 7, consisting of a Plexiglas test specimen with internal thread and a separate stainless steel mounting stud was adopted and proved to be satisfactory. The vapor pressure of mercury at 70~F is completely negligible in its effect on suppression pressure, while at 500~F it is 1.9 psia. -. ~' -...-~ ~ -:.. Thus, the argon cover gas pressure was maintained at a slight overpressure of 0.5 psig throughQut.he tests at 70F, and at a pressure of J 0! g 0 ~~.;:.-, * _.

-1082.4 psig for the tests at 5000F. This resulted in a suppression pressure of about 15.3 psia at both temperatures, as desired. At 70~F total test duration varied for the different materials, ranging from 8 to 12 hours, with the exception of the Plexiglas which was tested for only one hour due to mechanical problems. Very fine cracks began to develop within the Plexiglas cylinder after a test duration of approximately one hour which resulted in poor transmission of acoustic energy to the tip of the exponential horn. For all materials frequent inspections and weighings monitored the specimen surface. Prior to each weighing any excess mercury adhering to the specimen surface was removed by heating in a vacuum furnace (except for the Plexiglas) so as to eliminate oxidation of the specimen. At 500~F the total test duration also varied for the different materials, ranging from 8 to 12 hours, with frequent inspections and weighings monitoring the specimen surface. Prior to each weighing any excess mercury adhering to the specimen surface was removed using the same procedure employed for the 70~F tests. 2. Experimental Results at 70~F The cavitation results obtained at 70~F in mercury are displayed as accumulative weight loss and also accumulative mean depth of penetration (MDP) versus test duration, as for the lead-bismuth. Table 9 summarizes the cavitation results obtained in mercury at 70~F. Figure 29 is a plot of accumulative weight loss versus test duration, while Figure 30 is the corresponding plot of accumulative MDP versus test duration for thl. nilne materials tested.

-109TABLE 9 SUMMARY OF CAVITATION RESULTS IN MERCURY AT 709F Avg. Wt. Average Material. Loss Rate MDP Rate 304 SS (U-M) 9.82 mg./hr..32 mils/hr. 316 SS (U-M) 9.88.33 T-lll (P & W) 2371..35 T-222 (P & W) 28 92.43 Mo-1/2Ti (P & W) 22.58.57 Cb-IZr (P & W) 31.04.92 Carbon Steel (U-M) 31.17 1.03 Cb-lZr(A) (P & W) 54.22 1.61 Plexiglas (U-M) 19.00 3.99

-110-llO500 0-304 SS (U-M) -316 SS (U-M) A-CB- IZR(P&W) - Mo- I/2T, (PSW) *- T-III (PaW) -CB- I ZR (A) (P a W) A-T-222 (P&W ) 400 - CARBON STEEL (U- M) O- PLEXIGLAS(U-M) CARBON o, CB IZR(A) STEEL CB-IZR T- III 100 -- PLEXIGLAS 25- 1772 3 0._ 0 1 2 3 4 5 6 7 8 9 0 II 12 13 14 TIME, HOURS Fig. 29. —Effect of cavitation test duration on weight loss at 70~F in mercury.

. -11120 - 0-304 SS(U-M) O-316 SS(U-M) A-C- IZ.R (PaW) -Mo -/2 TI (PaW) *-T-lll(PaW) -CB- IZR(A)(PBW) A-T-222(PaW) 0-CARBON STEEL (U-M) c-PLEXIGLAS (U-M) 15 _J o] I CB-IZR(A) 10o>lo / / CARBON STEEL Cm ^PLEXIGLAS TIME, HOU222 32 / — ~~~~~~~304 SS:516'SS 1773 0 I 2 3 4-5 6 7 8 9 I0 lI 12 13 14 TIME,HOURS Fig. 30, —Effect of cavitation test duration on MDP at 70~F in mercury.

-i12The 304 stainless steel and 316 stainless steel, differing by only 3%, were the most resistant to cavitation at 700F based either on average weight loss rate or average MDP rate. These materials exhibited average MDP rates of 0.32 mils/hour and 0.33 mils/hour, respectively. The alloys T-lll and T-222 were 6% and 30% less resistant than the stainless steels, respectively, while the Mo-1/2Ti was 80% less resistant. The Cb-lZr, hot-rolled carbon steel, and Cb-lZr(A) all suffered heavy damage in the cavitation environment at 70~F. The MDP rates for these materials were approximately 3 times to 5 times greater than for the stainless steels and the T-lll. The Plexiglas suffered the most severe damage in terms of average MDP rate with a value of 3.99 mils/! hour. It is clear from Figures 29 and 30 that the rate of erosion for each individual material is approximately constant for all the materials tested for the duration of the test. Photographs of the test specimens at the conclusion of the cavitation experiment are presented in Figure 31. The materials.are - arranged in order of decreasing resistance to cavitation damage. Note the severe pitting of the Cb-lZr, hot-rolled carbon steel, Cb-lZr(A), and Plexiglas. In all cases the damage noted is relatively uniform over the specimen face as opposed to individual isolated, deep pitting which, as will be discussed later, was encountered with the low density fluids tested. This was also noted in the lead-bismuth tests at 500~F and 1500~F. It is felt that the approximately constant rate of erosion noted for all the materials tested in both mercury and lead-bismuth is due to this uniform damige^.pattern, and the fact that the area and

-113(1) 304 SS(U-M) (2) 316 SS(U-M) (3) T-111(P & W) 12 Hour Exposure 12 Hour Exposure 12 Hour Exposure (4) T-222(P & W) (5) Mo-1/2Ti(P & W) (6) Cb-lZr(P & W) 12 Hour Exposure 8 Hour Exposure 8 Hour Exposure (7) Carbon Steel(U-M) (8) Cb-lZr(A)(P & W) (9) Plexiglas(U-M) 12 Hour Exposure 8 Hour Exposure 1 Hour Exposure 304 SS(U-M) Before Exposure Fig. 31. —Photographs of specimens subjected to cavitation 1774

-114configuration (i.e., specimens remain approximately flat throughout the test duration) presented to the collapsing bubble cloud is approximately constant for the duration of the test. A photograph of a 304 stainless steel specimen before exposure is included in Figure 31, and serves to indicate a representative initial surface condition for all the specimens tested. Detailed examination of the 303 stainless steel exponential horn, the 316 stainless steel container vessel, and the sides of the various test specimens, all of which are not subject to cavitation, but are submerged in the test fluid, indicates that corrosion effects in the absence of cavitation in these investigations were negligible, as previously discussed for lead-bismuth. 3. Experimental Results at 500~F The cavitation results obtained at 500~F in mercury are displayed as accumulative weight loss versus test duration, and also as accumulative mean depth of penetration (MDP) versus test duration. Table 10 summarizes the cavitation results obtained in mercury at 500~F. -we -du Figure 32 is a plot of accumulative weight loss versus test duration, while Figure 33 is the corresponding plot of accumulative MDP versus test duration for the eight materials tested. On the basis of either average weight loss rate or average MDP rate it is clear that the T-lll is the most cavitation resistant of the materials tested, while the T-222(A) is about 7% less resistant. These materials exhibited average MDP-rates oQf 0.43 mils/hour and 0.46 mils hour, respectively. T b hob-rolled carbon steel, 316 stainless steel,

115-. TABLE. 10 SUMARY OF CAVITATION RESULTS IN MERCURY AT 500~F Avg. Wt. Average Material... Loss Rate MDP Rate T-lll (P &W) 29.48 mg./hr..43 mils/hr. T-222(A) (P &-W) 31 52.46 Carbon Steel (U-M) 18.60.61 316 SS (U-M) 19.01.63 304 SS (U-M) 20.83.69 Mo-1/2Ti (P & W) 43.16 1.09 Cb-lZr (P &W) 81.85 2.43 Cb-iZr(A) (P& W) 125.78 3.73

-116500 O0-304 SS (U-M) E-316 SS (U-M) A- CB-IZR(P W) 0- Mo- 1/2 T, (P SW) - T-11 (PaW) * -CB-IZR(A)(Paw) CB-IZR - T-222(A)(PaW) 0- CARBON 400'- STEEL(U-M) Mo T- 222 (A) CB- IZ R(A) 300 T-III uT 300 0 Fig. / /2-Efc X /cvtio tsdrin316 SS -J 200 0 / / CARBON STEEL 100 50 25 1768 0 1 2 3 4 5 6 7 8 9 10 II 12 13 14 TIME, HOURS Fig. 32. —Effect of cavitation test duration on weight loss at 500 ~F in mercury.

-117- - 20. -304 SS(U-M) 0-316 SS(U-M) A-CB -IZR (P aW) 0- T-III(P&W) E-CB-IZR(A)(P&W) A- T-222(A)(P&W) 0-CARBON STEEL (U-M) / 15 -IZR CB- IZR (A) / c0 Mo - 1/23 a- 10 CARBON STEEL _-J -304 SS 5 T' 222(A) 0 1 2 3 4 5 6 7 8 9 10 I "12 13 14 TIME, HOURS Fig. 33. —Effect of cavitation test duration on MDP at 500~F in mercury.

-118and 304 stainless steel rank third, fourth, and fifth, respectively, with average MDP rates of 061lmils/hour, 0.63 mils/hour, and 0.169 mils/ hour, respectively. Three refractory materials: Mo-l/2Ti, Cb-lZr, and Cb-lZr(A) were the least resistant to cavitation damage, with the Cb-lZr(A) suffering gross damage and ranking last among the materials tested. These three materials suffered damage ranging from 3 times to 8 times greater than that suffered by the tantalum-base alloys, T-lll and T-222(A) o It is clear from Figures 32 and 33 that the rate of erosion for each individual material is approximately constant for all the materials tested for the duration of the test. Photographs.of the test specimens at the conclusion of the cavitation experiment are presented in Figure 34. The materials are arranged in order of decreasing resistance to cavitation damage. Note the severe pitting of the Mo-1/2Ti,.Cb-lZr, and'.Cb-lZr(A) surfaces. In all cases the damage is again relatively uniform over the specimen face, as was the case for the 70~F tests. BDetailed examination of the exponential horn, container vessel, and the sides of the various: test specimens indicates again that corrosion effects in the absence of cavitation in these investigations were negligible. 4. Discussion and Comparison of Results Table 11 summarizes the cavitation data obtained in mercury at 70~F and 500~F. The eight materials tested at both temperatures have been rated on the basis of cavitation resistance as determined by MDP, with a rating of "1" *diiating the most cavitation resistant material,

-119(1) T-111(P & W) (2) T-222(A) (P & W) (3) Carbon Steel(U-M) 12 Hour Exposure 12 Hour Exposure 12 Hour Exposure (4) 316 SS(U-M) (5) 304 SS(U-M) (6) Mo-1/2Ti(P & W) 12 Hour Exposure 12 Hour Exposure 12 Hour Exposure (7) Cb-lZr(P & W) (8) Cb-lZr(A) (P & W) 304 SS(U-M) 8 Hour Exposure 8 Hour Exposure Before Exposure Fig. 34. —Photographs of specimens subjected to cavitation 1770 damage in mercury at 500~F.

-120TABLE 11 COMPARISON OF CAVITATION RESULTS IN MERCURY AT 70~F AND 500~F 700F 5000F Material Avg. MDP Rate Rating Avg. MDP Rate Rating 304 SS.32 mils/hr. 1.69 mils/hr. 5 316 SS.33 2.63 4 T-111.35 3.43 1 T-222*.43 4.46* 2 Mo-1/2Ti.57 5 1.09 6 Cb-lZr.92 6 2.43 7 Carbon Steel 1.03 7.61 3 Cb-lZr(A) 1.61 8 3.73 8 Plexiglas 3.99 9 *T-222(A) was tested at 500~F.

-121while a rating of "8" would denote that material most susceptible to cavitation damage. The most cavitation-resistant materials at 70~F were the stainless steels with the tantalum-base alloys ranking third and fourth. At 500F. the superior mechanical properties of the tantalumbbase, alloys at even a very moderate elevated temperature are already evident as the T-11l and T-222(A) rank first and second,.respectively. The hot-rolled carbon steel,.316 stainless steel, and 304 stainless steel rank third, fourth, and fifth, respectively, at 500~F. The Mo-1/2Ti, Cb-lZr, and Cb-lZr(A) all maintained the same relative position at both test temperatures. The hot-rolled carbon steel which had fared well at 5000F with a rating of "3" was damaged almost 70% more at 70~F. This apparently anomalous behavior is easily explained by the fact that-the mechanical properties of the hot-rolled carbon steel such as tensile strength and yield strength are greater at 5000F than at 70'F, which is attributed to "strain aging." As temperature is increased from room temperature, the strength properties pass through a maximum and then decrease. Very few materials possess this rather unique property. The engineering strain energy at 500~F is about 5% greater than at 700F. However, the true strain energy at 500~F is about 35% less than at 700F. It is further noted that with the exception of the hot-rolled carbon steel, all of the materials tested sustained greater damage at 5000F than at 700F. The stainless steels were damaged about 100% more and the T-lll about 23% more, while the damage rates for the Mo-1/2Ti, Cb-lZr, and Cb-lZr(A) were 2, times to 3 times greater at 500.~F than at

-12270"F. No direct comparison is possible in the case of the T-222 and, T-222(A), tested at 700F and 5000F, respectively, as the mechanical. properties of these materials differ. The effect of temperature on the cavitation results in mercury is further displayed in Figure 35, which is a plot of average. MDP rate versus temperature for the eight materials tested. The effect of tem-. perature on the T-lll and T-222 is almost negligible (at 500QF the. T-222(A) data point is plotted), while the -effect on all of the other materials is quite dramatic, as evidenced by the slopes of the appropriate curves.. The behavior of the hot-rolled carbon steel is once.again noted.'Later discussion shows -that the temperature-dependent behavior of the-cavitation resistance of these materials can be explained on the basis of the variation of mechanical properties with temperature. It is further shown that the mechanical properties of the tantalum-base alloys are weak functions of temperature, whereas those of the other materials vary considerably, even over the range from 700F to 500~F. 5. Comparison with Venturi Facility Mercury Results, It was noted earlier that the utility of acoustic cavitation damage results has been limited because no direct correlation with cavitation in a flowing system was available. However, if such a correlation could be formulated, it.might be possible to substitute relatively economical acoustic testing. for tests in a tunnel facility. This laboratory has conducted venturi cavitation tests in both.water and mercury for the past several years,''' and has accumulated much useful

-123O -304SS(U-M) E- 316 SS(U-M) A- CB- IZR (P a W) - Mo- 1/2 T, (PaW) T- T-III (P8W) -CB- IZR(A)(P8W) A-T- 222 OR T' 222 (A)(PW) 0-CARBON STEEL (U-M) CB- IZR(A)'-: 3 cn > | / / Mo- 1/2T, < L!/ CARBON STEEL l l1w^^^^ ^/ - IZR 03 T-II T- 222 OR T- 222 (A) 1775.... I I I.I. ) 0 0oo 200 300 - 400 500 600 700 TEMPERATURE, F Fig. 35. —Effect of temperature on cavitation resistance in mercury.

-124data over this period of timeO Now that data in mercury at 700F has been obtained with the ultrasonic (acoustic) facility, it is possible to qualitatively compare the data from both facilities for similar materials, Table 12 is a tabulation of the available data in mercury at 70~F for the two facilities. The wear in the venturi loop is given in terms of MDP after 50 hours of testing, whereas in the case of the acoustic facility, the average MDP rate is listed. The stainless steels tested in the venturi are similar to the 304 stainless steel and 316 stainless steel tested in the ultrasonic facility, but not identical. The composition of the T-lll is Ta-8W-2Hf, so that the corresponding specimens in both facilities are of the same composition. The composi- tion of the T-222 is Ta-9.5W-2.5Hf-.05C and differs slightly from the Ta-lOW tested in the venturi. The carbon steels tested are not identical but have similar carbon content and hardness-values. The remainder of the materials investigated in both facilities are nearly identical in composition. In both facilities the materials have been listed in order of decreasing cavitation resistance, or increasing susceptibility to cavitation-erosion attack.:The first five materials have identical rankings in each facility with the stainless steels being the most resistant to cavitation-erosion attack. The Cb-lZr, carbon steel, and Cb-IZr(A) occupy the next three-places in this qualitative ranking for both facilities, but their rankings do not agree in detail. In the case of the venturi tests t be'b-lZr ranks eighth, while it ranks sixth in

-125TABLE 12 COMPARISON OF CAVITATION EROSION DATA IN MERCURY AT 70~F - VENTURI AND ULTRASONIC FACILITIES Venturi Data Ultrasonic Data. iaterial.. -MDP at 50 Hours Material Avg. MDP Rate Stainless Steel.28x10-2 mils 304 SS.32 mils/hr. 316 SS.33 Ta-8W-2Hf.85x102 T-1lll.35 =2 Ta-lOW 1.7lx10 T-222.43 Mo-1/2Ti 2.10x102 Mo-1/2Ti.57 Carbon Steel 2.94x102 Cb-lZr.92 Cb-lZr(A) 5.87x10-2 CarboncSteel 1.03 Cb.-Zr 29.0 x102 Cb- Zr(A) 1.61 Plexiglas 225 xl102 Plexiglas 3.99.*M.DP at 25 hours.

-126the ultrasonic facility. The order of ranking of the carbon steel and Cb-lZr(A) is preserved in both facilities. It was- noted in the venturi investigations that the damage sustained by the Cb-lZr apparently indicated a thin multi-layer-like (laminated) structure. This could easily lead to greater damage and weight losses since large sections of the Cb-lZr outer layer were removed in some cases by the cavitation action as opposed to the normal minute pitting mechanism that would be expected. The unusual structure of the Cb-lZr tested in the venturi, apparently the result of improper heat-treat, probably accounts for the poor showing of this material in that facility. No such observation was made in the case of the acoustic facility. The Plexiglas was the'least resistant to cavitation damage by far in both facilities and attained ninth ranking. It is clear that with the exception of the Cb-lZr the qualitative rankings of the materials tested in the venturi and ultrasonic facilities agree verywello This agreement offers hope that a quantitative correlation could be developed that would couple the results of the two facilities. Such a correlation must await the generation of more complete data in both facilities for a variety of test fluids and temperatures It is interesting to note from Table 12 that the intensity of damage in the acoustic. facility is approximately 1000 times greater than that in the venturi loop, and also that the ratios of damage between various materials in the venturi facility is much greater, even though,the —rankings are almost identical.: This latter.phenomenon may involve A. ".~

-127the fact that corrosion is probably more important in the venturi tests since the exposure time is longer and the intensity of mechanical attack much less. However, the venturi test probably represents typical field conditions much more closely than the vibratory-type test. E. Cavitation Studies in Water at 70~F 1. Experimental Procedure The 24 materials tested in water at 70~F are listed in Table 2 (previously cited). The three grades of aluminum and the various heat-treats of Cu, Cu-Zn, Cu-Ni, and Ni were included in the vibratory cavitation program in water because extensive results from the venturi program are available for these materials in water. Standard cavitation test specimens, as;shown in Figure 6, were machined from available bar stock of the three grades of aluminum, carbon steel, stainless steels, and refractory alloys. The appropriate "A" and "B" dimensions are given in Table 4. It was desired to test in the vibratory facility the identical heat-treats of Cu, Cu-Zn, Cu-Ni, and Ni that had been previously tested in the venturi loop facility. Since these materials were available only in sheet stock 1/16 in. thick, it was necessary to design a special specimen consisting of an adaptor of a suitable material and a disk of the desired material. Means of attaching the disk to the adaptor had to be provided so that a firm bond would result. This is necessary so that the ultrasonic energy is efficiently transferred across the interface. Hence, the design previously, discussed and shown in Figure 8, consisting

-128of a.brass adaptor and a disk of the desired material, was adopted and proved to be satisfactory. The disk is fastened to the adaptor with soft solder. It was not desired to use a stronger higher temperature solder with these materials since their mechanical properties might be significantly altered by exposure to the higher temperatures required to make the joint. Various epoxies and cements were attempted as a bonding material, but the bond was immediately destroyed upon initiation of the test. The acoustic impedance of the soft solder is on the order of that of both the brass adaptor and disk materials, while the epoxies-and cements possessed a very low acoustic impedance due to negligible elastic properties, The arrangement shown in Figure 8 results in a standard specimen weight of 9.4 ~ 0.1 g. The Plexiglas specimens tested in water were fabricated as per Figure 7 (previously cited). The water tests were conducted in a Plexiglas cavitation vessel whose dimensions are identical to those of the 316 stainless steel container previously employed for the lead-bismuth and mercury testSo The Plexiglas vessel permits visual observation of the bubble cloud and continuous monitoring of the condition of the specimen surface during a testo All other equipment is identical to that previously used in the lead-bismuth and mercury investigations The vapor pressure of water at 70~F is approximately 0.4 psia. Thus, the argon cover gas pressure was maintained at 1.5 psig throughout the tests to provide the required suppression pressure of 15.3 psia. Total test durapio.pvaried for the different materials, ranging from 1 hour for the very soft 1100-0 aluminum to 36 hours for the

-129stainless steels and the refractory materials The Cu, Cu-Zn, Cu-Ni, and Ni specimens were tested for 6 hours. Frequent inspections and weighings monitored the specimen surface. 2. Experimental Results —Subsets One and Two The cavitation results obtained in water at 70~F are displayed as for the other fluids, and the appropriate expressions for computing the MDP of the aluminum, Cu, Cu-Zn, Cu-Ni, and Ni alloys are presented in Table 5. The 24 materials tested in water at 700F have been divided into three subsets for data display purposes. One subset consists of those materials that were also tested in mercury, lead-bismuth, and lithium; namely: 304 stainless steel, 316 stainless steel, T-lll, T-222, Mo-1/2Ti, hot-rolled carbon steel, Cb-lZr, and Cb-iZr(A)o The second subset consists of the three aluminum alloys and Plexiglas, while the third subset includes the 12 alloys of Cu, Cu-Zn, Cu-Ni, and Ni. The second and third subsets contain materials that have been tested only in water (with the exception of the Plexiglas that was tested in mercury at 70F) o Table 13 summarizes the cavitation results obtained in water at 70~F for the materials in the first two subsets. Figure 36 is a plot of accumulative weight loss versus test duration, while Figure 37 is the corresponding plot of accumulative MDP versus test duration for the eight materials contained in subset one. Figures 38 and 39 are the corresponding plots for subset two, which consists of the aluminum alloys and the Plexiglas o

-130TABLE 13 SUMMARY OF CAVITATION RESULTS IN WATER AT 70 F - SUBSETS ONE AND TWO Avg. Wt. Average Material LLoss Rate MDP Rate T-222 (P &W) 1.05 mg./hr..02 mils/hr. T-1ll (P &W) 4.33'.06 Mo-1/2Ti (P &W) 3.49.09 316 SS (U-M) 2.81.09 304 SS (U-) 3.04.10 Cb-lZr (P & W) 5.10.15 Cb-lZr(A) (P & W) 6.10.18 Carbon Steel (U-M) 7.08.23 2024-T351 A: (U-M) 6.13.57 6061-T651 Al (U-M) 7,73.72 Plexiglas (U-M) 6.60 1.39 1100-0 Al (U-M) 28.90 2.70

-131200 0- 304 SS(U-M) 8-CB-lZR(P8W) CARBON STEEL -316 SS(U-M) \ 180Q-Mo-1/2 Ti (P8w) -T-111I ( PaW) A-T-222(PBW) -CRB-IZR (A) U-CB-IZR(A)(P8W) 160 -CARBON STEEL(U-M) 160CB- ZR 140 120 U) U) 0 90 o 3 6 9 12 158 24 30 36 4' >I~TIME, HOURS Fig. 36. —Effect ofcavitation test duration on weight loss at F 700'60 50 40 30 20 — T-222 I01777 TIME, HOURS Fig. 36. —Effect of cavitation test duration on weight loss at 700F in water - subset one.

-1328 0-304 SS(U-M) A-CB-IZR ( Pw) 0-316 SS(U-M) 2 - Mo- 1/2 Ti(PaW) 7.2*-T-III(PaW) A-T-222 (PaW) *-CB-IZR(A)( P W) *-CARBON STEEL (U-M) 5.2 0 CARBON STEEL H L~J 4 > 3.6-- Mo-1/2 o 2.8 2.4 21.2 0.8 0.4.778 TIME, HOURS Fig. 37. —Effect of cavitation test duration on MDP at 700F in water - subset one. -

-133100 0-1100- 0 AL (U-M) A-2024-T351 AL(U-M) O-6061-T651 AL(U-M) 0-PLEXIGLAS(U-M) 75 CU3 0 3 50-6061-T651 AL W 45-J 40 25_ / 2024- T351 AL 5/ z C-PLEXIGLAS l79 1779 75^ ( 2 3 4 56 7 TIME, HOURS Fig. 38. —Effect of cavitation test duration on weight loss at 70~F in water - subset two.

-13410 0-1100-0 AL (U-M) A-2024-T351 AL(U-M) 9 -6061-T651 AL(U-M) O-PLEXIGLAS (U-M) 87a> 6061- T651 AL CPLEXIGLAS 1780 0 1 2 3 4 5 6 7 TIME, HOURS Fig. 37. —Effect of cavitation test duration on MDP at 70~F in water - subset two:

-135On the basis of either average weight loss rate or average MDP rate it is clear that the T-222 is the most cavitation resistant of the materials contained in subsets one and two.The T-lIl which ranked second suffered about 3 times more damage than the T-222, while the Mo-l/2Ti and 316 stainless steel were equally -damaged and ranked third and fourth. The 304 stainless steel in fifth place sustained 5 times more damage than the T-222.:The Cb-base alloys, Cb-lZr and Cb-1Zr(A), and the hot-rolled carbon steel ranked sixth through eighth, respectively, and suffered damage 7 to 12 times more severe than the T-222, based on average MDP rate..The aluminum alloys and the Plexiglas were the least resistant to cavitation-erosion attack among the materials in subsets one and two. Considering only the three aluminum alloys, the 2024-T351 alloy was the most resistant while the very soft -100-0 alloy sustained the greatest damage. An examination of Figures 36 and 37 indicates that the rate of erosion for the T-222, T-1ll, Mo-l/2Ti, 316 stainless steel, and 304 stainless steel is approximately constant for the duration of the test, while the rate of erosion for the Cb-lZr, Cb-lZr(A), and the hot-rolled carbon steel is approximately constant during-the early stages of the test and then begins to decrease as the accumulative weight loss and the accumulative MDP increase to larger values. oExamination of the specimens generally indicated that those materials showing a linear response rate exhibit a fairly uniform surface damage pattern, whereas those showing a non-linear response are characterized by surface damage consisting primarily of hea, 4iolated, deep pitting. This latter pattern

-136would result in a reduced surface area being presented to the collapsing bubble cloud since the area surrounding the very deep isolated pits has 59 been shown to produce relatively few cavitation bubbles. Hence, one would expect the erosion rate to decrease as the total weight loss or MDP increased, as clearly pointed out in a recent paper by Plesset and 59 Devine. Photographs of the test specimens in subset one at the conclusion of the cavitation experiment are presented in Figure 40. The materials are arranged in order of decreasing resistance to cavitation damage. Note the severe pitting of the Cb-lZr, Cb-lZr(A), and hotrolled carbon steel surfaces. It is clear from Figures 38 and 39 that the rate of erosion for the three aluminum alloys is approximately constant for the duration of the test in spite of the deep, isolated pitting of the type which in the previous materials corresponded to a non-linear damage rate, at least when MDP exceeds the order of 4 to 5 mils, i.eo, the influence of the non-uniform wear may not become significant until the volume loss roughly corresponding to this range of MDP has been reached. As previously indicated, the specimens tested in high density fluids maintained a constant MDP rate out to the order of 50-60 mils. However, their damage was extremely uniform. Thus, it may be that the rate remains essentially constant as long as a uniform damage pattern is maintained, and that the MDP for which uniform damage can be maintained is a function of the material-fluid combination. The possible reasons -fot fluid density effects pni damage characteristics ate:di~scus'sedli6ater.

-137(1) T-222(P & W) (2) T-111(P & W) (3) Mo-1/2Ti(P & W) 36 Hour Exposure 30 Hour Exposure 36 Hour Exposure (4) 316 SS(U-M) (5) 304 SS(U-M) (6) Cb-lZr(P & W) 36 Hour Exposure 30 Hour Exposure 32 Hour Exposure (7) Cb-IZr(A) (P & W) (8) Carbon Steel(U-M) 304 SS(U-M) 30 Hour Exposure 21 Hour Exposure Before Exposure Fig. 40. —Photographs of specimens subjected to cavitation 1781 damage in water at 70~F - subset one*

-138Photographs of the test specimens in subset two at the conclusion of the cavitation experiment are presented in Figure 41, A photograph of a 2024-T351 aluminum specimen before exposure is included for comparison. 3. Experimental Results —Subset Three Table 14 summarizes the cavitation results obtained in water at 70~F for the materials in subset three, namely the 12 Cu, Cu-Zn) Cu-Ni, and Ni alloys. The various heat-treats of a given material are grouped together for purposes of comparison. Figure 42 is a plot of accumulative weight loss versus test duration, while Figure 43 is the corresponding plot of accumulative MDP versus test duration for the 6 Cu and Ni alloys in subset three. Figures 44 and 45 are the corresponding plots for the 6 Cu-Zn and Cu-Ni alloys in subset three. On the basis of either average weight loss rate or average MDP rate the Cu-Zn (60% cold-worked) was the most cavitation resistant among the 12 materials contained in subset three with an average MDP rate of 0.38 mils/hour. The Ni (75% cold-worked) ranked second with an average MDP rate of 0,44 mils/hour, while the Cu-Ni (1800~F anneal, 1 hour) and Ni (1600~F anneal, 1 hour) were third and fourth with erosion rates of 0.47 mils/hour and 0.48 mils/hour, respectively. The three copper heattreats were the least resistant to cavitation damage in subset three with the Cu (900"F anneal, 1 hour) ranking last with an erosion rate of 1,02 mils/hour. This specimen suffered approximately 3 times as much damage as the most resistant material, Cu-Zn (60% cold-worked). Considering onTy the three copper specimens tested, the coldworked material was the most cavitation resistant while the high

-139(1) 2024-T351 Al(U-M) (2) 6061-T651 Al(U-M) (3) 1100-0 Al(U-M) 6 Hour Exposure 8 Hour Exposure 45 Minute Exposure Plexiglas(U-M) 2024-T351 Al(U-M) 30 Minute Exposure Before Exposure Fig. 41. —Photographs of specimens subjected to cavitation 1782 damage in-water at 70~F - subset two.

-140TABLE 14 SUMMARY OF CAVITATION RESULTS IN WATER AT 70 F - SUBSET THREE;, - R f - f -Ir I d - - — r I 1-~ I. I - Av..Wt.......^..Aveg:rage Material.; -Loss Rate - MD Rate Cu, cold-worked 32.83 mg/hr..95 mils/hr. Cu, 900'F anneal 35.37 1.02 Cu, 1500~F anneal 33.32.95 Cu-Ni, cold-worked 24.18.70 Cu-Ni, 13000F anneal 21.97.63 Cu-Ni, 1800~F anneal 16.25.47 Cu-Zn, cold-worked 12.74.38 Cu-Zn, 8500F anneal 23.88.72 Cu-Zn, 1400~F anneal 22.78.68 Ni, cold-worked: 15.27.44 Ni, 11000F anneal 20.25.58 Ni, 1600~F anneal 16.69.48

-141200 2 - Cu A- Cu -900F - Cu - 1500OF o- Ni 180 0 A - Ni - 1100 OF E- Ni - 1600~F 160- Cu- 900 F CuBCu-1500~F 140 oor^ XNi-1100 F /P 1783 0 40 1 2 34 5 6 7 20 TIME, HOURS Fig. 42. —Effect of cavitation test duration on weight loss at 700F in water - Cu and Ni (subset three). (D~ ~ ~~TIE OR <[ ~ Fg 2-Efc f aiaints uaio nwih:ls t 70"F inwater -Cu andNi sbe he)

-1420-Cu A-Cu-900 OF *-Cu-1500 F 4 0-Ni A-Ni-1100 F 0-Ni -1600 OF 4- Cu a Cu-1500~F 3.5Cu-9000.25 03 / Ni-110 0 / 1784 2.5 Ni -1600 II 2T 1.5 0.75 0.50r 1784 I 2 3 4 5 6 7 TIME, HOURS Fig. 43. —Effect of cavitation test duration on MDP at 700F in water - Cu and Ni (subset three).

-143200 -20 Cu-Zn A- Cu-Zn-850 F - Cu -Zn - 1400F 0 - Cu-Ni 180 0 A - Cu- Ni- 13000F - Cu -Ni-1800 F 160 Cu -Ni 140 r 0 - 1- - 2 3 - --.Cu- Ni- 1300~F 80 Cu-Ni -1800-F I o o 60 40 20 1785. —0'1'2 3 4 5 6 7 r'i~ME, HOURS Fig. 44, —Effect of. cavitation test duration on weight loss at 700F in water - Cu-Ni and Cu-Zn (subs'et three).

-144O *- Cu-Zn A - Cu -Zn- 850~ F * - Cu -Zn- 1400~ F O - Cu- Ni 4..5 A -- Cu- Ni- 1300~F | l - Cu- Ni - 1800~F uiCu-Ni f / 3.5 C- u-Zn-850~F C-.3^ tQ^: y4;/t, Cu - Ni-1300 F 2.5 I —^~~~~~~~ C Cu-Zn-1400' Cu- Ni - 1800'F water -Cu-Ni and Cu-Zn (subset three).n t Gil.5.25?786 Fig. 45. —Effect of cavitation test duration on MDP at 70~F in water - Cu-Ni and Cu-Zn (subset three)..

-145temperature heat-treat ranked second and the low-temperature heat-treat was lasto Identical rankings apply to the three Cu-Zn specimens and the -three Ni specimens. For Cu-Ni the high-temperature heat-treated specimen was the most cavitation resistant followed by the low-temperature heat-treated material and the cold-worked specimen in that order. An examination of Figures 42, 43, 44, and 45 indicates that the rate of erosion for the materials contained in subset three-ais generally not constant beyond about 2 mils MDP. This is presumed due to the pattern of the surface damage which is again characterized by heavy, isolated, deep pitting, even very early in the test. This preferential damage of the surface may be caused by non-uniformity of applicable mechanical properties. However, it is curious that for materials as stainless steel, the character of the damage in lead-bismuth or mercury is a uniform distribution, while in water it is composed of the previously discussed deep, isolated pitting, This lack of similarity in damage pattern may be due to the fact that the NPSH has not been modeled between tests, and similarity of "flow regime" would then not occur. One manifestation of the difference in flow regimes encountered is the occurrence of a star pattern of bubble cloud as opposed to the uniform 60 bubble cloud observed on other occasions.'No theoretical explanation for predicting these observed flow patterns yet exists. Typical photographs of the test specimens in subset three at the conclusion of the cavitation experiment are presented in Figure 46. Note the heavy, isolated deep pitting that has developed. In all of the te s,.bnnducted in water, only the hot-rolled carbon steel specimen showed definite visual indications of having

-146Cu(60% cold-worked) (U-M) Ni(75% cold-worked) (U-M) 6 Hour Exposure 6 Hour Exposure Cu-Ni(13000F anneal) (U-M) Cu-Zn(1400~F anneal) (U-M) 6 Hour Exposure 6 Hour Exposure Fig. 46. —Photographs of selected specimens subjected to cavi- 1787 tation damage in water at 70~F - subset three.

-147suffered corrosion damage. Hence, the results quoted for this material reflect damage caused both by the corrosion and erosion components. All other results can be attributed solely to the cavitation-erosion mechanism. 4. Comparison with Venturi Facility Water Results Cavitation data from the venturi facility operated by this laboratory was previously obtained for all of the materials that were tested in the ultrasonic facility in water. Hence, as was the case in mercury at 70~F, it is now possible to qualitatively compare the data from both facilities and hopefully be able to eventually arrive at a quantitative relationship coupling the results. Table 15 is a tabulation of the data available in water for the two facilities for the materials contained in subsets one and two. Table 16 is a similar tabulation for the materials contained in subset three, namely the Cu, Cu-Ni, Cu-Zn, and Ni alloys. The wear in the venturi loop is given in terms of MDP after 50 hours of testing, whereas in the case of the acoustic facility, the average MDP rate is listed. The stainless steels tested in the two facilities are comparable as are the T-lll and the Ta-8W-2Hf. The T-222 and the Ta-lOW are similar as are the carbon steels. The remainder of the materials investigated in both facilities are nearly identical in composition. In Table 15, the materials have been listed in order of decreasing cavitation resistance, or increasing susceptibility to cavitation erosion attack for both facilities, A certain amount of agreement is

-148TABLE 15 COMPARISON OF CAVITATION EROSION DATA IN WATER AT 70~F - VENTURI AND ULTRASONIC FACILITIES (SUBSETS ONE AND TWO) Venturi Data Ultrasonic Data Material MDP at 50 Hours Material Avg. MDP Rate Cb-lZr 3.50x103 mils T-222.02 mils/hr. Stainless Steel 5.27x103 T-lll.06 Mo-1/2Ti.09 -3 Ta-8W-2Hf 7.62x103 316 SS.09 Ta-lOW 11.11x103 304 SS.10 -3 Cb-lZr(A) 20.29x10 Cb-lZr.15 Plexiglas 67.25x103* Cb-lZr(A).18 Mo- 1/2Ti 99 72x10 3 Carbon Steel.23 Carbon Steel 769.2 x103 2024 Al.57 2024 Al 1618 xlO3 6061 Al.72 -3 6061 Al 1976 x10 Plexiglas 1.39 1100-0 Al 2451 x103 1100-0 Al 2.70 MDP at 4 hours.

-149TABLE 16 COMPARISON OF CAVITATION EROSION DATA IN WATER AT 70~F - VENTURI AND ULTIASONIC FACILITIES (SUBSET THREE) Material Venturi MDP at 50 Hourss Ultrasonic- MDP Rate Cu-Zn 39.77x103 mils (12).38 mils/hr. (1) Ni 14.85x103 (5).44 (2) Cu-Ni- 1800~F anneal 8.58x10-3 (2).47 (3) Ni-16000F anneal 4.04x103 (1).48 (4) Ni-1100L F anneal 14.63x10'3 (4).58 (5) Cu-Ni-1300~F anneal 13.29x10'3 (3).63 (6) Cu-Zn-1400~F anneal 25.09x103 (9).68 (7) Cu-Ni 19.23x10- (6).70 (8) Cu-Zn-8500F anneal 25.72x103 (10).72 (9) Cu 24.29x103 (8).95 (10) Cu-15000F anneal 27 62x103l (11).95 (11) Cu-900 F anneal 23.75x103 (7) 1.02 (12)

-150noted in Table 15. In.both facilities the stainless steels, the tantalum-base alloys, and the Cb-lZr are among the most cavitation resistant materials. But the rankings do not agree in detail. Among the least resistant materials, the carbon steel and the three aluminum alloys have identical rankings in both facilities. In was noted in the venturi investigations that the damage sustained by the Cb-lZr apparently indicated a thin laminated structure which could lead to erroneous results in this case. Note also the anomalous position of Plexiglas which is relatively much more resistant in the venturi than in the ultrasonic facility. Also note that the. damage rate is about 100 times as great in the ultrasonic facility (water tests) as compared to a factor of about 1000 in the mercury tests, but that the range of difference encountered in the venturi is about 10 times that in the ultrasonic facility (water tests) as compared to a factor of about 100 in the mercury tests. The reasons given in the discussion of the mercury'tests' are probably also applicable here. The results presented in Table 16 for the Cu, Cu-Ni, Cu-Zn, and Ni alloys agree only in a few respects. The rather general disagreement noted for this data subset cannot be fully explained at this time. However, it is noted that the damage rates for these materials differ by a much smaller factor than for those previously discussed (only about a factor of 3 for the ultrasonic tests and a factor of 10 for the venturi), so that an upsetting of the ranking order would involve much smaller errors in damage rates. For these materials it would be expected that corrosioiwq.ld play little part in either facility so

-151that this may have prevented.the range between materials from differing as widely as -in the other cases. F. Cavitation Studies in Lithium at 500-0F -and 1500 F 1. Experimental Procedure'The seven materials tested in lithium at 500QF and 1500 ~F were 304 stainless steel (U-M), 316.stainless steel (U-M), T-Ill (P & W), T-222(A) (P & W), Mo-1/2Ti. (P & W), Cb-lZr (P & W), and Cb-lZr(A) (P & W). Standard cavitation test specimens, as shown in Figure 6, were machined from available bar stock. The required dimensions "A" and'B" for the seven- materials are listed in Table 4. These dimensions provide a standard specimen weight of 9.4 0.1 g. The vapor pressure of lithium at 500~F is approximately zero, while at 15000F it is nearly 0.1 psia. As a result, the argon cover gas was maintained over the molten lithium throughout the tests at an overpressure of- 1I.1 psig for the 500~F tests and at 1.2 psig for the 1500~F tests, This resulted in the required suppression pressure of 15.3 psia. At 5000F, the test duration for each material was 10 hours with the exception of the Cb-lZr(A) which showed gross erosion after 6 hours of testing. At frequent intervals the specimens were visually examined, photographed, and carefully weighed. At 1500~F, total test duration was 10 hours in al:l cases with the exception of the T-lll which was exposed for 30 hours. Once again, frequent inspections and weighings were made. The lithium used in these investigations was obtained from the Lithium Corporation of AY ied, Inc. (Bessemer City, North Carolina) in

-152the form of individual /V 1/2 pound cylindrical ingots sized to fit into the cavitation vessel and fill it, upon melting, to the desired level, The ingots were packaged and hermetically sealed in individual tin cans, which were easily opened for charging the lithium into the experimental vesselo The solid ingot was first placed in a clean stainless steel beaker which fit snugly into the cavitation vessel and provided for easy removal and disposal at the conclusion of a test. The loading operation was carried out at room temperature (where oxidation would be at a minimum rate) in a glove box under an argon atmosphere. The sealed vessel was then removed from the glove box and placed in the furnace where the lithium was brought to the required test temperature of 500"F or 15000F. Each test was conducted with a new, fresh lithium ingot in a new, unused stainless steel beaker. This procedure eliminated the need for transferring the molten lithium to and from the experimental vessel and eliminated trace heaters, line heaters, hot traps, cold traps, valves, etc,, from the system design. This procedure resulted in a very economical design and kept oxide contamination relatively uniform and at a minimum, since a fresh ingot was used for each test. At the conclusion of each 500~F investigation, the vessel was removed from the furnace and quickly air-cooled to a temperature of about 3750F, which is slightly above the melting point of 362~F, and below the ignition temperature of 3920Fo With the lithium at 3750F, the vessel top plate was unbolted, and the ultrasonic transducer and specimen were quickly removed from the molten lithium while maintaining the argon cover gas over the test fluido The vessel was then covered

-153and the lithium allowed to solidify in the stainless steel beaker. The beaker and used ingot were then easily removed from the vessel and discarded. The next run made use of a new clean stainless steel beaker and a fresh lithium ingot. After solidification, any excess lithium adhering to the test specimen and the exponential horn was easily removed by dipping the end of the transducer into a large container of cold water placed outdoors. The reaction of lithium with water under these conditions was not very vigorous and resulted in complete removal of the excess lithium metal in a few minutes. The test specimen was then removed from the tip of the transducer and weighed. At the conclusion of a 1500~F test the cavitation vessel remained in the furnace until it had cooled to 500~F. Then it was removed and air-cooled until the lithium temperature reached the required 375~F at which point the specimen was removed. This complete procedure of ingot loading, unloading, and specimen retrieval was found to be completely safe and was carried out more than 50 times without incidento Personnel wore suitable protective clothing during the unloading and specimen retrieval operations. 2, Experimental Results at 500"F The cavitation results obtained at 5000F in lithium will be displayed as accumulative weight loss versus test duration, and also as accumulative mean depth of penetration (MDP) versus test duration. Table 17 summarizes the cavitation results obtained in lithium at 500~F. Figure 47 isa plot of accumulative weight loss versus test

-154TABLE 17 SUMMARY OF CAVITATION RESULTS IN LITHIUM AT 5000F Avg. Wt. Average Material. —. Loss Rate MDP Rate T-111 (P & W) 1.70 mg./hr. 0.03 mils/hr. T-222(A) (P & W) 2.48 0.04 Mo-1/2Ti (P & W) 4.61 0.12 Cb-lZr (P & W) 5.02 0.15 304 SS (U-M) 10.42 0.34 316 SS (U-M) 10.91 0.36 Cb-lZr(A) (P &W) 33.70 1.00

-155200 0 -304 SS (U-M) Q -316 SS (U-M) A-CB -IZR(P8 W) Q - Mo- /2Ti (Pa W ) - T- III (Pa W) - CB- IZR(A) (PBW) A- T- 222 (A) (Pa W) 150 CB-IZR (A) Cl)~~~~O~~~~ ~316 SS EI 0 / I00-! /-304 SS 100D C) <Q~ ~ /I~~~ ^/~ ~CB-IZR50 4030 20 I0~ L~T-III 1870 0 1 2 3 4.6 7 8 9 10 11 12 13 14 -TIME, HOURS Fig. 47. —Effect of cavitation test duration on weight loss at 500~F in lithium.

-156duration, while Figure 48 is the corresponding plot of accumulative MDP versus test duration for the seven materials tested. On the basis of either average weight loss rate or average MDP rate it is clear that the T-lll is the most cavitation resistant of the materials tested, while the T-222(A) is about 30% less resistant. These materials exhibited average MDP rates of 0.03 mils/hour and 0.04 mils/ hour, respectively. The refractory materials, Mo-l/2Ti and Cb-lZr, rank third and fourth, respectively, with average MDP rates of 0.12 mils/hour and 0.15 mils/hour, respectively~ The 304 stainless steel and 316 stainless steel were about equally resistant but suffered 11 times to 12 times the damage incurred by the T-lll. The Cb-lZr(A) was the least resistant to cavitation damage of the materials tested with an average MDP rate of 1.00 mils/hour, approximately 33 times greater than the rate of damage exhibited by the T-lllo It is clear from Figures 47 and 48 that the rate of erosion for each.individual material is approximately constant for most of the test. In some cases, the rate of damage is not constant in the early part of the test due to lack of temperature equilibrium of the ultrasonic transducer and the smooth surface of the specimen face which appears to prevent maintenance of a stable bubble cloud. In some cases the rate of damage decreases with increasing test duration. This is probably due to a decrease in the number of bubbles 59 generated by some types of roughened surfaces, as has been discussed in relation to the other fluids. Except for Cb-lZr and Mo-1/2Ti, the rates are fairly constant from about 1 to 4 mils MDP, which is reasonably consistent with the other' low density fluid tested, ioeo, water.

-1570- 304 SS(U-M) E- 316 SS (U-M) A- CB- I ZR (P8W) - Mo - /2 Ti (P W) - T-III (P8W) - CB-IZR(A)(PSW) A- T- 222 (A)(P8W) 4 CB-IZR (A) 316 SS - K / / T- 222 (A). I3 A 1 A 7 8 9 10 11 I.13304 SS J / [I / CB- I ZR T- 222 (A) 0 1 2 3 4 5 6 7 8 9 10 11 12.1314 TIME, HOURS Fig. 48. —Effect of cavitation test duration on MDP at 500~F in lithium.

-158The high-density fluids showed constant rates over a much greater MDP range, as was previously mentionedo Photographs of the test specimens at the conclusion of the cavitation experiment are presented in Figure 490 The materials are arranged in order of decreasing resistance to cavitation damage, Note the very heavy pitting suffered by the Cb-lZr(A), 304 stainless steel, and 316 stainless steelo As opposed to the other fluids, the damage is substantially con" centrated at the central portion of the specimen with a large outer rim nearly undamaged (a small undamaged outer rim has been noted for all fluids)o It is thought that the lack of damage in the outer annular 61,62 ring is due to "end effects" which create vortex action near the edge of the vibrating horno This results in higher pressures adjacent to the horn in this region and, hence, fewer bubbles That these conditions are apparently much more pronounced with the lowest density fluid (lithium) is believed due to the large suppression head (NPSH) values used for this fluid. The damage suffered by the other specimens is somewhat more uniform with the exception of the T-lllo However, the undamaged outer rim is present in all cases It has been noted in the cavitation tests with different fluids, all conducted at a constant suppression pressure (lead-bismuth, mercury, water, and lithium) that the heavier fluids give quite a uniform damage patterno The water patterns are intermediate between the heavy liquid metals and the lithium here observed in that for the lighter fluids the damage tends to become concentrated toward the center and less

-159(1) T-111(P & W) (2) T-222(A)(P & W) (3) Mo-1/2Ti(P & W) 10 Hour Exposure 10 Hour Exposure 10 Hour Exposure (4) Cb-lZr(P & W) (5) 304 SS(U-M) 10 Hour Exposure 10 Hour Exposure (6) 316 SS(U-M) (7) Cb-lZr(A) (P & W) 10 Hour Exposure 6 Hour Exposure Fig. 49. —Photographs of specimens subjected to cavitation 1906 damage in lithium at 500 ~F.

-160pronounced on the outer edge. As mentioned above, this may be due to the fact that NPSH is much greater for the lighter fluids than for the heavier, since suppression pressure was constant, i.e., the "flows" are not properly modeled (due, as already mentioned, to insufficient pressure. capability of the high-temperature cavitation vessel design) Detailed examination of the 303 stainless steel exponential horn, the 316 stainless steel beaker, and the sides of the various test specimens, all of which are not subject to cavitation, but are submerged in the test fluid, indicates that corrosion effects in the absence of cavitation in these investigations were negligible, as with all the other fluids tested, as would be expected for the short durations 63 involved. 3o Experimental Results at 1500 F The data obtained in lithium at 1500'F will be displayed as accumulative weight loss versus test duration and also as accumulative mean depth of penetration (MDP) versus test duration. Table 18 summarizes the cavitation results obtained in lithium at 1500~F. Only the 304 stainless steel, 316 stainless steel, T-lll, and Cb-lZr(A) were tested at this temperature. Figure 50 is a plot of accumulative weight loss versus test duration for the four materials tested, while Figure.51 is the corresponding plot of accumulative MDP versus test duration' On the basis of either weight loss or MDP the refractory alloy T-lll exhibited the greatest resistance to cavitation damage at 15000Fo This was also true at lO0Fo The refractory alloy Cb-lZr(A) which

-161TABLE 18 SUMMARY OF CAVITATION RESULTS IN LITHIUM AT 1500~F -. - ~.. g- 1 -3 _ I.... Avg. Wt. Average Material;Loss Rate MDP Rate T-lll (P & W) 0.26 mg./hr. 0.004 mils/hr. Cb-lZr(A) (P & W) 0.58 0.017 316 SS (U-M) 0.81 0.027 304 SS (U-M) 1.04 0.034

-1620- 304 SS(U-M) I i I I I l- 316 SS (U-M) - T-III (PBW) I- CB-I ZR (A)(PSW) 15 o r) 0 o 10 LW /316SS 1- 304 SS 8 CB- I ZR (A) T- III 2 1907 0 1 2 3 5 6 7 8 9 10 11 12 13 4 TIME, HOURS Fig. 50. —Effect of cavitation test duration on weight loss at 1500 ~F in lithium.

-1630.50-304 SS(U-M) I I I D - 316 SS(U-M) — T- III(P W) Ce — ZR (A)(P 8W) 0.4 c) 304 SS / _0.3 316 S 0.3 / / 6S I x ^ LiJ D 0.2 / C- IZR(A) 0.15 0.15 0. I. I I 1908 01 I 2 4 5 6 7 8 9 10 11 82 13 14 TIME, HOURS Fig. 51. —Effect of cavitation test duration on MDP at 1500~F in lithium.

.164suffered gross damage at 500~F and ranked last had an average MDP rate of only 0.017 mils/hour at 15000F and ranked secondo The two stainless steels were the least resistant of the four materials tested at 15000F, as expected from mechanical properties considerations. The 316 stainless steel sustained 7 times the damage rate of the T-lll (versus a factor of about 4 in the 1500~F lead-bismuth test), whereas the 304 stainless steel exhibited 9 times the damage rate (versus about a factor of 14 in the 1500~F lead-bismuth test), It is clear from Figures 50 and 51 that the rate of erosion for each individual material was approximately constant for all the materials tested during most of the testo Photographs of the test specimens at the conclusion of the cavitation experiment are presented in Figure 52. The materials are arranged in order of decreasing resistance to cavitation damage. Very little damage is apparent on any of the specimens Corrosion effects on the- non-cavitated surfaces -in the tests at 15000F were negligible, as was also the case for the 500~F tests, 40 Discussion and Comparison of Results Table 19 summarizes the cavitation data obtained in lithium at 5000F and 1500S Fo The seven materials tested at 500~F and four tested at 15000F have been rated on the basis of cavitation resistance as determined by MDP, with a rating of "1" indicating the most cavitation resistant material, while a rating of "7" at 500FF and "4" at 1500 F would denote that material most susceptible to cavitation damage at each; temperature o

-165(1) T-111(P & W) (2) Cb-lZr(A)(P & W) 10 Hour Exposure 10 Hour Exposure (3) 316 SS(U-M) (4) 304 SS(U-M) 10 Hour Exposure 10 Hour Exposure Fig. 52. —Photographs of specimens subjected to cavitation 1909 damage in lithium at 15000F.

-166TABLE 19 COMPARISON OF CAVITATION RESULTS'IN LITHIUM'.:.; AT 500~F AND 1500F 500 F 1.500 Material (Avg. MDP Rate)a Rating (Av.BDPRate) Rating T-1ll 0:.03 mils/hr. 1 0.004 mils/hr. 1.Cb-lZr 0,15.. 304 SS 0.34 5 0.034 4 316 SS 0.36 6 0.027 3 Cb-lZr(A) 1.00 7 0.017 2 - -:-. OF.f —.

-167The tantalum alloys, T-llland T-222(A), are the most resistant to cavitation damage at 500~F, while the T-lll is the most resistant at 15000F, T-222(A) not having- been tested at this temperature. The Cb-lZr(A) which:had a rating of "7" at 500~F ranked second among the four materials tested at 1500~F. The 304 and 316 stainless steel were among the. least resistant, materials at 500~F (although superior to Cb-lZr(A)), but ranked last at 1500~F. Thus, the expected superior performance of the refractories at the higher temperature, due to their less temperature-dependent mechanical properties, was verified. At both temperatures, the T.-lll was approximately 10 times more resistant than the stainless steels.. It is important to note that for each of the four materials -tested at both temperatures the amount of damage sustained by the specimen at 1500~F was much less than that sustained at 500~F for constant testing time. The exact opposite behavior was noted in the cavitation 64 42 tests conducted earlier in lead-bismuth alloy and mercury (and reported. earlier in this document) where the damage sustained by a given material at the higher temperature was greater than that measured at the lower temperature.. One.might. expect this latter behavior due to the reduced strength of.the materials at the elevated temperature. However, the variation of the fluid properties with temperature is also important and must be considered. A recent paper by Leith presents predictions of cavitation damage in a vibratory facility exposed to atmospheric pressure for liquid metals as a function of temperature for a material possessing constant mechanical properties, i.e., not a function of

-168temperature. Leith's interpretation of the previously available data is that the specific gravity, vapor pressure, viscosity, and surface tension are important fluid properties which affect the amount of damage sustained as a function of temperature. In the case of NaK, potassium, lithium, rubidium, cesium, and dium, Leith concludes that cavitation damage as a function of temperature reaches a maximum at a temperature 15%7 to 20% up the melting-boiling range, falling off below and above this maximum damage temperature. In the case of water, several investi32,33,66,67,68 gators' have reported that cavitation damage as a function of temperature reaches a maximum at'a temperature 50% up, the meltingboiling range (50~C or 122~F), falling off below and above this maximum damage temperature. Our own laboratory has investigated this effect in water, and the plot of cavitation damage versus temperature is presented in Figure 53. The maximum occurs at approximately 50~C, or 122~F The discrepancy in the position of the imaximum cavitation damage may be due to the following mechanism. Inthe case of the water, the dissolved air is an important factor, whereas in the liquid metals, the solubility of most common gases is nearly zero at all temperatures. At the low temperatures the dissolved air cushions the bubble collapse and, hence, the cavitation damage is reduced.- As the temperature is..increased, the dissolved air is driven off and this factor becomes unimportant. Then the effect of vapor pressure becomes predominant. The damage peaks and then begins to decrease due to the cushioning effect of -the vapor which does not have sufficient time to condense in the vibratory test. We feel that the cushioning effect of the dissolved air in the water test

-169-.20 304 STAINLESS STEEL IN TAP WATER.15 ~~~ o.1 z I-.10 -^\~~ TEMPERATURE, ~ F 1 1978.05 / TEMPERATURE, OF 1978 0 40 70 100 130 160 190 220 Fig. 53. —Effect of temperature on cavitation damage on water - type 304 stainless steel specimen.

-170results in the maximum damage occurring at a temperature further up the melting-boiling range, as opposed to the liquid metal tests where this mechanism is negligible. The mechanical properties of several refractory alloys, such as T-1ll, T-222(A), Mo-1/2Ti, and Cb-lZr, tested in our investigations are very weak functions of temperature, and Leith's analysis would apply more closely to these than to the stainless steels. It is our present feeling that the trend in the lithium results can be explained primarily on the basis of cavitation "thermodynamic effects," as follows. At 1500~F the vapor pressure of lithium is many times greater than at 5000F. When the cavitation bubbles collapse at the higher temperature, the heat of condensation from the condensing vapor trapped within the bubble must be conducted into the surrounding fluid. If this does not occur rapidly enough, then the uncondensed vapor serves to cushion the bubble collapse with a resultant decrease in collapse pressures and reduced damage to the test specimens. This effect was not operative in the lead-bismuth tests since the vapor pressure was essentially nil even at 1500~F. 5. Temperature Dependence of Cavitation Damage in Lithium As previously mentioned, the damage suffered by all materials tested at 1500~F in lithium was less than the corresponding damage measured at 5000F. To obtain further information on this somewhat surprising result, the temperature dependence of cavitation damage in our vibratory rig in lithium for a few selected materials over the range

-171from 500~F to 1500~F was investigated. The 304 stainless steel, T-lll, and Cb-lZr(A) were chosen for this purpose. The mechanical properties of the 304 stainless steel vary greatly over this temperature range, and the predictions of Leith would not be expected to apply without introducing corrections for this effect. The mechanical properties of the refractory materials, T-lll and Cb-lZr(A), are weak functions of temperature, so that their behavior should more clearly illustrate the effects'of fluid property changes over this temperature range. Cavitation damage data for 304 stainless steel was obtained at 4000F, 500~F, 7000F, 900~F, 1100OF, 13000F, and 1500~F using the experimental procedure previously discussed. Total test duration at each temperature was 10 hours. Table 20 summarizes the data obtained. Figure 54 is a plot of average weight loss rate versus test temperature, while Figure 55 is the corresponding plot of average MDP rate versus test temperature. The damage rate reaches a maximum at approximately 500~F and decreases thereafter, presumably due to the thermodynamic effects men-................ -65 tioned previously. The shape of the curve is similar to Leith's plot of cavitation damage versus percent of the melt-boil range of lithium. Leith's prediction for lithium is shown in Figure 55 as a dashed curve. The difference between Leith's curve and the experimental data between 500~F and 15000F is in the wrong direction to be explained by his assumption of constant mechanical properties for the test materials. Similar experimental data was obtained for T-lll and Cb-lZr(A) at 500"F, 10000F, and 15000F, Total test duration at each temperature was 10 hours. Table 21 summarizes the data obtained, while Figures 56

-172TABLE 20 EFFECT OF TEMPERATURE ON CAVITATION DAMAGE304 STAINLESS STEEL Temperature- Avg. Wt. Loss Rate Avg. M P -Rate 400 F 7.23 mg./hr. 0.24 mils/hr. 500 10.42 0.34: 700 5.39 0.18 900 2.88 0.10 1100 1,50 0.05 1300 1.21 0.04 1500 1.04 0.03

-17315 304 STAINLESS STEEL SPECIMEN TEST DURATION: 10 HOURS IO L10 W 9 8 cn U) 0 7 6 5 4 3 1 - 1874 0 400 500 700 900 1100 1300 1500 TEMPERATURE,OF Fig. 54. —Effect of temperature on average weight loss rate for 304 stainless steel.

-1740.40 304 STAINLESS STEEL SPECIMEN TEST DURATION: 10 HOURS 0.30/'\ \ ~LEITH'S PREDICTION I \ \, 0.200.04- O^ ^ 0.021875 0 400 500 700 900 1100 1300 1500 TEMPERATURE,.F Fig. 55. —Effect of temperature on average MDP rate for 304 stainless steel.

-j75qTABLE 21 EFFECT OF TEMPERATURE ON CAVITATION DAMAGE - T-111 AND Cb-1Zr(A) Material Temperature Avg. Wt. Loss Rate Avg. MDP Rate T-ll 500"F 1.70 mg./hr. 0.025 mils/hr. 1000 0.61 0.009 1500 0.26 0.004 Cb-IZr(A) 5000F 33.70 mg./hr. 1.00 mils/hr. 1000 8.10 0O24 1500 0.58 0.02

-17640 0- CB - I ZR(A) (P aW) ^-T- 111 (PAW) 30 - r.. 20 (3 ()20 10 8 - 1876 4- \ o0' 500 1000 o1500 TEMPERATURE, F Fig. 56. —Effect of temperature on average weight loss rate for T-lll and Cb-lZr(A).

-177and 57 are plots of average weight loss rate versus temperature and average MDP rate versus temperature, respectively, for the T-lll and Cb-lZr(A). Leith's prediction for lithium is also shown in Figure 57 as a dashed curve. The T-lll damage rate decreases by a factor of 7 from 500"F to 1500~F, while the Cb-lZr(A) damage rate decreases by a factor of approximately 60 over the same temperature range. A very large decrease in damage in sodium tests in a similar facility over the 37 38 same temperature range is reported by Hydronatics,' although in their tests stainless steel appeared very much superior to the refractories at 15000F. This is, of course, inconsistent with the mechanical properties of these materials (see Chapter IV). 6. Oxygen Analyses Five lithium ingots were sent to the General Atomic Division of General Dynamics Corp. in San Diego, California, for an analysis of Li20 in lithium. Each sample was irradiated, along with an oxygen standard, for 10 seconds in a 14 Mev neutron flux of approximately 108 2 neutrons/cm. -second, and counted for nitrogen-16 induced activity on a single-channel pulse-height analyzer, using a pair of 3" x 3" NaI(Tl) scintillation crystals. The oxygen concentration was determined by comparing the intensity of the 6.13 Mev gamma-ray photopeak of N16 from the sample with that from the oxygen standard. Oxygen forms N16 by interaction with 14 Mev neutrons via the 016(n, p)N16 reaction. Four of the ingots sent for analysis had been used in cavitation tests at various temperatures, while the fifth was an unopened can of lithium (hermetically sealed) as received from the Lithium Corporation

* (V):zl-qo puv 1T11-. OJ a94B ac 9Za9sAB uo aJniz9daia o jo oeJa —-Lg *Ti 0'3nliV83dV^Yl 091 0001 009 0 LL8T O' 0.. 0~' \ \'. I\ \ \ 0 I\ \ I r \ \ |1 I \ \ -09' o O0' N~ -a3Ud 5 1.. \. -',. \\ \.. I (MBd) -111 —V \ \I / (Md) i(v)-uZ~- -0', \./: ~. -ELI~xx -/

-179of America, A sample core was removed by General Atomic from each ingot supplied (cut from the bottom of the ingot) and analyzed. The results of the activation analysis are summarized in Table 22. The plus-orminus values represent one standard deviation determined from counting statistics only,. The very high oxygen concentration reported for the unopened lithium ingot is quite surprising. Conceivably, it may be due to poor packaging techniques prior to the analysis, rather than a high oxygen content in the lithium as supplied. The oxygen content reported for the ingots which had been used in cavitation tests was greater than the saturation concentration of Li20 in lithium at the highest temperature experienced by the ingot. This might suggest that excess Li2Owas formed and became entrained in the lithium. Hence, the analysis would detect both oxygen dissolved in the lithium as Li20 and also the oxygen present in the entrained Li20. Alternatively, the high oxygen concentration in the used samples may result from absorption of oxygen by the solid lithium before shipping to General Dynamics, since'the solid lithium ingots were exposed to the atmosphere during this period. Since corrosion effects in the lithium cavitation tests for the 63 short durations involved are apparently negligible, it is felt that the damage rate is only slightly affected by the oxide level. Hence, no further efforts have been made to resolve the above anomalies. G. Comparison of Mercury and Water Results at 70~F It is interesting to compare the results obtained in mercury and water at the same test temperature of 70~F in an effort to determine

-180TABLE 22 SUMMARY OF OXYGEN DETERMINATIONS - ~,''. -. t''.. ~.'''..Samp le Description': Oxygen Content #1 Blank —unopened can as received from Lithium Corporation of America 1000 + 58 PPM #2 Ingot used in test at 500~F 3850 + 186 PPM #3 Ingot used in test at 10000F 3000 + 110 PPM #4 Ingot used in Test at 15000F 805 + 110 PPM #5 Ingot used in test at 500~F 2840 + 100 PPM

-181fluid effects on cavitation damage. Table 23 summarizes the cavitation data obtained in mercury and water at 70~F. The nine materials tested in both fluids have been rated on the basis of cavitation resistance as determined by the average MDP rate, with a rating of "1" indicating the most cavitation resistant material, while a rating of "9" would denote that material most susceptible to cavitation damage. The following comments apply to the comparison: 1) There are several differences in the comparative ratings of the materials in the two fluids. In mercury the stainless steels and the tantalum-base alloys were the most resistant to cavitation damage at this temperature and only differed in this respect by about 25%. In the case of the water the tantalum-base alloys were the most resistant among the materials tested, while the stainless steels suffered damage 2 times to 5 times greater than the T-lll and T-222. The Mo-1/2Ti ranked third in water and fifth in mercury. However, the first five rankings were occupied by the same materials in both fluids. The Cb-lZr, carbon steel, Cb-lZr(A), and Plexiglas suffered the most damage and had nearly identical rankings in both fluids. 2) For any given material the damage suffered in mercury was 3 times to 20 times more severe than in water. Note that the comparison is on the basis of equal static suppression pressures rather than head. The stainless steels, in particular, suffered about 3 times as much damage in mercury as in water. 3) The stainless steels were the most cavitation resistant materials in mercury, while fe tantalum-base alloys, T-lll and T-222, were

-182TABLE 23 COMPARISON OF CAVITATION RESULTS IN MERCURY AND WATER AT 70 0F — ~ c'9..............- i * i l' III-;' i, IllCl I I i I-!' l Mercury W__.Water: Maeia A Rain A MDP aterial Avo Rte Rating,.- -aterial'. -.t. 304 SS o32 mils/hr.o.10 mils/hr. 5 316 SS.33 2.09 4 T-111.35 3.06 2 T-222 043 4.02 1 Mo-1/2Ti - 057 5.09 3 Cb-lZr 92 6.15 6 Carbon Steel. 1.03 7 o23 8 Cb-lZr(A) 1 61 8.18 7 Plexiglas 3099 9 1.39 9

-183far superior in water. The Plexiglas was the least resistant in both fluids, as opposed to the venturi tests where it was quite resistant in water but poor in mercury. This may indicate that materials which rely to some extent on a superior yield deflection range for their protection (as rubberized coatings and also Plexiglas in the present tests) are suitable in relatively low intensity cavitation fields but fail under more intense attack. This observation is eonsistent with much field experience. It is felt that the primary cause of the greater damage suffered by all the materials in mercury as opposed to water is its much greater density. The pressure generated by bubble collapse would be proportion-'al to the fluid density if the suppression heads seen by the bubbles were the same, since then collapse velocities would be the same. This may be approximately true in the present case since the major contribution to t-he suppression head at the start of collapse is the dynamic head caused by the horn motion. This portion would be the same for all tests, assuming horn Lmotion to be unaffected by the test fluid, although the static heads differ by the density ratio since constant static suppression pressure was maintained. A more definite conclusion in this regard will have to await the accumulation of more complete cavitation erosion data in a variety of fluids. In the venturi results previously presented, it is noted that the stainless steels were the most resistant in mercury at 700F, as is the case.in the ultrasonic facility. In water the venturi results show "the Cb-lZr to be. the m t es-istant, followed by the stainless steels.

184H. Comparison of Lead-Bismuth, Mercury, and Lithium Results at 500~F It is interesting to compare the results obtained in lead-' 64 42 43 bismuth, mercury, and lithium at the same test temperature of 500'F in a further effort to determine fluid effects on cavitation damage Table 24 summarizes the cavitation results obtained at 5000F for the various materials tested in- the three fluids in terms of average MDP rate The following comments apply to the comparison: 1) The tantalum-base alloys, T-lll and T-222(A), are the most resistant in all the fluids, while the Cb-lZr(A) is the least resistant, In fact, the order of ranking of the various materials based on ability to resist cavitation damage is quite similar for all three fluids, with only minor deviations being noted. Particularly, the stainless steels rank quite low in lithium after being only 20% to 45% less resistant than the best refractories tested in lead-bismuth and mercury. 2) The damage suffered by a given material in lead-bismuth and mercury was of the same order of magnitude for all materials. This is not surprising considering the similarit the the fluid properties. However, the amount of damage sustained in lithium was less than that measured in mercury or lead-bismuth by a factor ranging from 2 to 30. The density of lead-bismuth and mercury is about 25 times that of lithium. In order to fully determine the effect of various fluid properties on cavitation damage, it will be necessary to conduct computer correlations involving tdtihechanical properties of the test materials and fluid properties of the test liquid,

-185TABLE 24 SUMIRY OF CAVITATION' RESULTS IN LEAD-BISMUTH, MERCURY, AND LITHIUM AT 500~F - _. ____Average MDP Rate Material Lithium Mercury Lead-Bismuth Water - 700F T-llt 0.03 mils/hr. 0.43 mils/hr. 0.72 mils/hr. 0.06 mils/hr. T-222(A) 0.04 0.46 0.76 0.02* Mo-1/2Ti 0.12.1.09 0.78 0.09 Cb-lZr 0.15 2.43 1.63 0.15 304 SS 0.34 0.69 0.93 0. 10 316 SS 0.36 0.63 0.88 0.09 Cb- Zr(A) 1.00 3.73 3.54 0.18.Carbon Steel.. 0o61. 0.23 -T-222 was tested. in water at 700F.

-186Table 24 also includes the cavitation data obtained in water at 70~F. Water at 70~F and lithium at 500~F have the same order of magnitude values of density and vapor pressure. Hence, comparison of the cavitation damage data obtained in the two cases may prove to be instructive. Generally, the damage obtained in lithium at 500~F is somewhat greater than that obtained in water at 700F (T-lll is the exception), even though the density of lithium is less by a factor of twoo Of course, the effect of temperature on material properties must also be considered This would be negligible for the refractory materials, but would be important for the stainless steels. The data indicates that this is, indeed, the case, as the damage values in the two fluids for the stainless steels are most divergent. J, Comparison of Lead-Bismuth and Lithium Results at 1500~F The cavitation results obtained in lead-bismuth alloy and lithium at the same test temperature of 1500~F are summarized in Table 25 for purposes of comparison. Only four materials were tested in lithium at 15000F. The following comments apply to the comparison: 1) The tantalum-base alloys, T-111 and T-222(A), are the most resistant in lead-bismuth alloy, while the T-1ll is the most resistant in lithium (T-222(A) was not tested in lithium at 15000F). The 304 stainless steel was the least resistant in both fluids, 2) The damage suffered by a given material in lead-bismuth alloy was 100 to 400 times more severe than the damage sustained in lithium. This is undoubtedly di not only to the much greater density of the

-187TA BLE 25 SUMMARY OF CAVITATION RESULTS IN LEAD-BISMUTH AND LITHIUM AT 1500OF-...... Average MDP Rate Material.... Lithium Lead-Bismuth T-ll. 0o. 0004 mils/hr, 0.84 mils/hr. T-22.2(A).... 0 88 Mo-1/2Ti -- 1.08 Cb-lZr-. — 2,07 304 SS 0.034 11.30 316 SS 0.027 2.80 Cb-IZr(A) 0.017 3.80

-188lead-bismuth test fluid but also to thermodynamic effects which are very important in lithium at 1500~F, but negligible in lead-bismuth at this temperature Again, further analysis is necessary to fully determine the effect of various fluid properties on cavitation damage. K. Cavitation Studies of Bearing Materials 1o Introduction As mentioned previously, it has been shown both experimen2 2, tally and theoretically' that damaging cavitation may well occur in many high-performance bearing applications. This problem is at present of considerable importance to the designers of the mercury space power2 plant components. The objective of this portion of the present study is the determination of the cavitation-erosion characteristics of several selected bearing materials in mercury at 500F, since this information is of considerable present technological value as well as increasing the scope of the general information gathered in this laboratory relating cavitation damage resistance to material and fluid properties. It was necessary to conduct some of the investigations at reduced temperature, and in one case to utilize water as the test fluid, due to various mechanical and compatibility considerations which are discussed fully latero The materials examined include three heat-treated specimens of the tool steel alloy BG-42 (a modified 440-C stainless steel), Blue Chip Tool Steel (18-4-1 tool steel), Mo-l/2Ti, Cb-lZr(A), two grades of graphitar, single-crystal tungsten, and teflon-coated type 304

-189stainless steel. Table 3 (previously cited) summarizes the materialfluid-temperature combinations which were studied. 2. Cavitation Studies in Mercury at 5000F a. Experimental Procedure The six materials tested in mercury at 5000F were BG-42 (TRW) in three heat-treated conditions, Blue Chip Tool Steel (TRW), Mo-1/2Ti (P & W), and Cb-IZr(A) (P &-W). The BG-42 in the "as-received" condition was subjected to the heat-treat schedule specified in Table 26 so as to obtain specimens of three distinct hardness ranges, as noted. In Table 27 the heat-treat schedule for the "as-received" Blue Chip Tool Steel is specified. This results in specimens with a hardness of approximately 64 Rc (Rockwell "C") Prior to any heat treating, standard cavitation test specimens, as shown in Figure 6, were machined from available bar stock.. The required dimensions "A" and "B" for the six materials are listed in Table 4. These dimensions provide a standard specimen weight of 9.4 + 0.1 g. The argon cover gas over the mercury was maintained at 2.4 psig throughout the 5000F investigations, resulting in the required suppression pressure of 15.3 psia. Total test duration varied for the different materials, ranging from 8 to 12 hours, with frequent inspections and weighings monitoring the specimen surface. Some specimens were not inspected and weighed as frequently as others due to their brittle nature and the possibility of damaging or breaking the test button during assembly and disassembly. Prior to each weighing any excess mercury

-190TABLE 26 HEAT TREATMENT FOR BG-42.CAVITATION EROSION SPECIMENS The following process shall be performed:. 1o In a salt bath preheat the part thoroughly at 1400~F to 1450~F. 2o Transfer the part to a salt bath at 2075 to 2100~Fo Soak at temperature for 1/2 hour per inch of thickness (20 minutes minimum), 3o.. Oil quench to room temperature, 4. Temper at 300 to 4000F for one houro. 5o.Refrigerate at minus 100~F + 100F for 1/2.hour. 60 After allowing the specimen to warm to room temperature, double temper in a neutral salt bath (preferably chloride) for 2.- 2 hours at one of the following temperatures: Desired Final,Hardness, Rc Temper Temperature, ~F 44-46 1150-1180 53-55 1060-1090 62-64 975-1000 7. Air cool.to room temperature in still air after each temper. -- - C - -... ~. -'.

-191TABLE 27 HEAT TREATMENT FOR BLJE CHIP TOOL STEEL (AMS 5626, T-l, 18-4-1) ~ T r — __ For a hardness level of Rockwell C 61-64: 1. In a protective compound, salt, or atmosphere, preheat the specimen slowly over a two hour period to 15000F - 16000F. 2. Soak at 15000F - 1600:F for one hour and then transfer the part to a controlled atmosphere furnace or salt bath at 2325~F - 2350 ~F. 3. Soak at 2325~F - 2350~F for 2 - 5 minutes, the exact time being dependent on the size of the part. This soaking time should never be overdone. 4. Remove and cool in still air to room temperature. 5. Draw at 1025~F - 1050~F for 2 1/2 hours, then allow to cool slowly to room temperature. 6. Re-draw at 7000F - 750FF for two hours, then allow to cool slowly to room temperature.

-192adhering to the specimen surface was removed by heating in a vacuum furnace so as to eliminate oxidation of the specimen. b. Experimental Results The cavitation results obtained at 5000F in mercury will be displayed as accumulative weight loss versus test duration, and also as accumulative mean depth of penetration (MDP) versus test duration. The appropriate expressions for computing the MDP of all the materials tested are presented in Table 5. Table 28 summarizes the cavitation results obtained in mercury at 500~F. Figure 58 is a plot of accumulative weight loss-versus test duration, while Figure 59 is the corresponding plot of accumulative MDP versus test duration for the six materials tested. On the basis of either average weight loss rate or average MDP rate it is clear that the three BG-42 materials and the Blue Chip Tool Steel are.far superior to the Mo-1/2Ti and the Cb-lZr(A). The BG-42 with a hardness of 64 Rc is the most resistant tocavitation based on average weight loss rate while the Blue Chip Tool Steel with identical hardness is about 15% less resistant. Based on average MDP rate these materials exhibit identical resistance to cavitation damage. These two materials are about 10 times more resistant than the tantalum-base alloy, T-lll, which was found to be the most resistant in mercury at 500~F among the materials previously tested. The BG-42 specimens with hardnesses of 53 Rc and 47 Rc ranked third and fourth, respectively, among the six materials tested. The Mo-1/2Ti and Cb-lZr(A) specimens were both much more seveaely damaged, and exhibited average weight loss

-193TABLE 28 SUMMARY OF CAVITATION RESULTS IN MERCURY AT 500~F (BEARING PROGRAM) Material Avg. Wt. Loss Rate Avg. MDP Rate BG-42 (Rc = 64) (TRW) 1.20 mg./hr,.04 mils/hr. Blue Chip Tool Steel (TRW) 1.43.04 BG-42 (Rc =-53) (TRW) 3.08.10 BG-42 (Rc =-47) (TRW) 5.88.19 Mo-1/2Ti (P & W) 43.16 1.09 Cb-IZr(A) (P & W) 125.78 3.73

-194500 5001,. 0|i( BG-42 (Rc47) (TRW) _ / 8 -BG-42 (Rc 53) (TRW) Ol BG-42 (Rc=64) (TRW) 450 7 Mo-12Ti (Paw) / BLUE CHIP TOOL STEEL (TRW) _ P Cb-I Zr (A) (PaW) 400 ~ ~-+ -_ + Cb-I Zr (A) 350 M- TI (I) c001 300 250.-J 200 2 4 68~- 1 11 150 100 TIME - HOURS 1754 Fig. 58. —Effect of cavitation test duration on weight loss at 500F in mercury.

-19520 ^~~~ ~~20 0r'~~~ 0- BG-42 (Rc 47)(TRW) 1 - BG-42 (Rc=53) (TRW) E] - BG-42 (Rc:64)(TRW) Q - Mo-2Ti (P W) 18 * - BLUE CHIP TOOL STEEL (TRW) 17 - Cb-IZr (A) (PaW) 17 16 1 5 ~ - ~ - - -/~ - - ~ +- - ~. 14 o3 13 Cb-IZr (A) 1 2 / / Mo-T 0J I 0 0 9 7 5 __ X-+ X 4C / /vE r BG-42 (Rc=53) BLUE CHIP TOOL STEEL BG-42 (Rc= 47), -BG-42 (RC= 64) IIo 0 2 4 6 8 10 12 14 TIME- HOURS 1755 Fig. 59. —Effect of cavitation test duration on MDP at 500~F in mercury.

-196rates of 43.16 mg.o/hour and 125.78 mg./hour, respectively. It is interesting to note that the hardest of the BG-42 specimens exhibited the greatest resistance to cavitation damage, while the softest showed least resistance. It is clear from Figures 58 and 59 that the rate of erosion for each individual material is approximately constant for all the materials tested for the duration of the test. Photographs of the test specimens at the conclusion of the cavitation experiment are presented in Figure 60. Note the severe pitting of the Mo-1/2Ti and the Cb-lZr(A) surfaces. However, as was previously mentioned for the heavy liquid metal tests, the damage is spread uniformly over the surface. We feel that this results in the uniform.damage rates up to the order of 10-15 mils MDP. Very little damage is noted in the case of the BG-42 (Rc = 64) and the Blue Chip Tool Steel. A photograph of the Cb-lZr(A) specimen before exposure indicates a representative surface condition for all the specimens tested, Detailed examination of the stainless steel exponential horn, container vessel, and the sides of the various test specimens, all of which are not subject to cavitation, but are submerged in the test fluid, indicates that corrosion effects in the absence of cavitation in these investigations were negligible. Hance, it seems probable that the damage suffered by the test specimens was due almost completely to the cavitation erosion process and not to chemical corrosion by the mercury test fluid.

-197(1) BG-42(R = 64) (2) Blue Chip Tool (3) BG-42(R = 53) ^C ~Steel(R = 64) 12 Hour Exposure 12 Hour Exposure 12 Hour Exposure (4) BG-42(R = 47) (5) Mo-1/2Ti (6) Cb-lZr(A) c 12 Hour Exposure 12 Hour Exposure 8 Hour Exposure Cb-lZr(A) Prior to Exposure Fig. 60. —Specimens subjected to cavitation damage in mercury 1756 at 500 ~F.

-1983o Cavitation Studies in Mercury at 70~F (Graphitar) ao Experimental Procedure The initial intention was to conduct all of the cavitationerosion tests of these bearing-type materials at 500~F in mercury, but a variety of mechanical and compatibility problems made this impossible in the case of the graphitar and the single-crystal tungsten. The graphi-:: tar materials conceivably could have been tested at 5000F, but it was judged that the changes in mechanical properties from 700F to 5000F were negligible for this material. Further, testing at 700F would enable a direct comparison (from a temperature standpoint) with the singlecrystal tungsten which had to be tested in water at 70~F, as will be discussed later. Graphitar is formed from carbon and graphite powders which are compacted under high unit pressures and then furnaced at temperatures up to 45000F. A variety of grades are available from The United States Graphite Company and other vendors, and differ in hardness, density, compressive strength, and other mechanical properties. The two grades investigated here are denoted as grades 50 and 80, and were chosen to provide a substantial variation in mechanical properties within the useful range for this material Applicable mechanical properties are presented in Chapter IV. Due to the low density of the graphitar (compared to the other materials tested) and its brittle, porous nature, it was completely impractical to fabricate standard cavitation test specimens as shown in Figure 6. The low denaity "would result in an unusually large "A"

-199dimension (thus giving the assembly an improper length for resonance) to obtain the required weight, while the brittle, porous nature of the material made it impossible to firmly affix a specimen to the ultrasonic horn without damage to the threaded portion. It is necessary that the specimen be firmly and tightly attached to the horn tip so that the ultrasonic energy is properly transmitted across the interface for efficient operation. Hence the design shown in Figure 7 (also used for Plexiglas), consisting of a graphitar test specimen with internal thread and a separate stainless steel mounting stud was adopted and proved to be satisfactory, The mounting stud results in a firm attachment of the graphitar cylinder to the horn tip without damage to the graphitar internal threads. This design overcomes all of the problems encountered with the standard cavitation test specimen. The experimental procedure employed for the testing of the graphitar specimens in mercury at 700F closely parallels that used for the 500~F tests discussed previously. However, for the 70~F tests the argon cover gas-pressure was maintained at 0.5 psig throughout the investigations to again provide the same pressure above vapor pressure at the specimen surface. Total test duration for both grades of graphitar was 10 hours, with two specimens of each being runo Frequent inspections and weighings were conducted to monitor the specimen surface. Since the graphitar is very porous and absorbs mercury during the cavitation test, it was necessary to drive off the absorbed mercury by heating in a vacuum furnace before weighing. The vacuum is necessary to ~eliminate oxidation of Be specimen material.

-200b. Experimental Results The cavitation results obtained at 70~F for graphitar will be.displayed as accumulative weight loss versus test duration, and also as accumulative mean depth of penetration (MDP) versus test duration. Table 29 summarizes the cavitation results obtained in mercury at 700Fo Figure 61 is a plot of accumulative weight loss versus test duration, while Figure 62 is the corresponding plot of accumulative MDP: versus test duration for the two grades of graphitar tested. The response of the graphitar to cavitation-erosion damage was non-linear for the initial part of the test out to about 50 mils MDP, as opposed to all the other materials, but a constant rate portion of the curve does exist from approximately 50 mils MDP out to about 100 mils total MDP. However, due to the rapid rate of damage obtained, no data points were obtained below about 25 mils MDPo Hence, there may well have been a constant rate portion of the curve in the 1-3 mil MDP range used to rate many other materials which exhibited non-linear tendencies for higher values of MDPo On the basis of either average weight loss rate or average MDP rate the grade 80 variety of graphitar appears to be superior to the grade 50. However, both grades suffered a total MDP which was on the order of 100 times as great as that of the Blue Chip Tool Steel and BG-42 specimens tested at 5000Fo In fact, the maximum penetration, as opposed to mean penetration, of both grades of graphitar was approximately 1/4 in. (250 mils). - Since the graphitar does not melt at any temperature and begins to sublime at approximately 6000~F, it is felt that the mechanical

-201TABLE 29 SUMMARY OF CAVITATION RESULTS AT 70~F (BEARING PROGRAM) Material Avg. Wt. Loss Rate Avg. MDP Rate *Graphitar-Grade 50 (U-M) 71.60 mg./hr. 10.90 mils/hr. *Graphitar-Grade 80 (U-M) 55.30 7.95 **Single-Crystal Tungsten (U-M) 1.55.025 *Tested in Mercury. **Tested in Water.

-2021000 - GRAPHITAR (U-M) 0- -GRADE 80 900 - GRADE 50 800 --- - + + 700 600 + - _T_ GRADE 50 500 ~WJTM — HOUR GRADE 80 < 400 +-~ —~- ~- ~~" ~ I_ I < 300 200 100 0 2 4 6 8 10 12 14 TIME- HOURS 1758 Fig. 61. —Effect of cavitation test duration on weight loss of graphitar at 700F in mercury.

-203200 190- GRAPHITAR (U-M) 0 - -GRADE 80 180 A8 - GRADE 50 170 160 150 + + 140 () 130 120 o 110 J 100 +I + - < 90- GRADE 50 0 30 70 / 60 40 20 10, I I I I,I,,' I 0 2 4 6 8 10 12 14 TIME- HOURS 1759 Fig. 62. —Effect of cavitation test duration on MDP of graphitar at 700F in mercury.

-204properties of the two grades tested here would not be significantly affected had the tests been conducted at 500~Fo Hence, it is assumed that the data presented in Table 29 for graphitar is approximately applicable at 500~F alsoo Photographs of the test specimens at the conclusion of the cavitation experiment (10 hours duration) are presented in Figure 63. A photograph of a typical graphitar cylinder before exposure is included for comparison. Note the very severe damage suffered by both grades of graphitar 4. Cavitation Studies in Water at 70~F (Single-Crystal Tungsten) a. Experimental Procedure It was intended to test the single-crystal tungsten in mercury at 500~Fo However, because of the very great difficulty encountered in machining a standard cavitation test specimen from this material, and due to the lack of a suitable grinder for forming the threaded portion of the specimen, alternate designs were consideredo It was found feasible to produce a simple disk of single-crystal tungsten by grinding, but it was still necessary to affix the disk firmly to the ultrasonic horn, Initially, an attempt was made to use epoxy resin to attach the tungsten disk to a stainless steel adaptor. However, the epoxy had little elasticity and very low strength in shock so that it was immediately fractured at the start of the test, Various other cements provided similar results. Finally, the design shown in Figure 9 was found to be satisfactory. Here a simple disk. of single-crystal

-205Graphitar Graphitar Graphitar Grade 80 Grade 50 Before Exposure 10 Hour Exposure 10 Hour Exposure Single Crystal Tungsten 50 Hour Exposure Fig. 63. —Graphitar and single-crystal tungsten specimens sub- 1760 jected to cavitation damage at 700F.

-206tungsten has been attached to a stainless steel adaptor with silver solder. The use of a high-temperature solder of this type was considered feasible with tungsten with.its very low temperature sensitiityo. The silver solder was found to form a very suitabie bond tSv I ek, as.. - t. b... between the tungsten and stainless -s1teel.and resulted insatisfactory transmissionof the ultrasonic energy acr0os the interface. The diameter of the tungsten disk (1/2 ino) was slightly smaller than the diameter of the stainless steel adaptor ( ~547 ino) due to unavailability of tungsten in a larger size at the time of the testso However, it was felt that errors from this slight dimensional change would not be significant within the overall experimental errors, The silver solder proved to be satisfactory in all respects with the exception of its compatibility with mercuryo Even during a relatively short test in mercury and in spite of the small surface of solder exposed (merely the edge of the- bond), the bond was destroyed. Hence, it was necessary to test the tungstenn inwater. Due to pressure limitations of the equipment, a test in water at 500~F was not possible. Since the properties of tungsten are not significantly temperature dependent in this range, it was decided that a test in water at 70~F would suffice to at least obtain some realistic idea of the cavitation resistance of the material, The single-crystal tungsten used in these investigations was obtained from Cleveland Tungsten, Inc. Due to the previously mentioned fabrication difficulties and lack of ample stock, only one specimen of tungsten was tested. The tests were conducted at the same frequency, amplitude, and submergence

-207used in the other tests. The argon cover gas pressure was maintained at 1.5 psig to obtain the same pressure above vapor pressure at the specimen surface. The total test duration was 50 hours, with inspections and weighings being conducted at l0-hour intervals. b. Experimental Results Table 29 summarizes the results obtained with the singlecrystal tungsten. Figure 64 is a plot of accumulative weight loss versus test duration, while Figure 65 is the corresponding plot of accumulative MDP versus test duration for the single-crystal tungsten tested. The response of the single-crystal tungsten to cavitation-erosion attack is nearly linear for the duration of the test, at least over the range of about 0.5 to 1.5 mils MDP. Hence, the characteristics of the damage rate curve are similar to those of other materials tested. Clearly, the tungsten tested in water was damaged only slightly compared to the graphitar tested in mercury at the same temperature. In fact, the amount of damage incurred by the tungsten is on the order of that suffered by the Blue Chip Tool Steel and the three BG-42 specimens tested in mercury at 500~F. Before any true comparison can be made between these materials, it is necessary to correct the tungsten results obtained in water at 700F in an appropriate manner so as to reflect the expected additional damage that the tungsten would have suffered in mercury at 70~F and 5000F. Cavitation-erosion data obtained for type 304 stainless steel in water at 700F and in mercury at 70"F and 5000F will be used for this purpose. Hence, if one assumes that the tungsten and the stainless steel bot* suffer the same % increase in damage when

-208100 95 - SINGLE CRYSTAL TUNGSTEN (U-M) 90 85 8075 (370-'65 (n 6055 5 50+ + _ 45 4 40,35 0t 30 25 20 15 100 10 20 30 40 50 60 70 TIME- HOURS 1762 Fig. 64. —Effect of cavitation test duration on weight loss of single-crystal tungsten at 70~F in water.

-2092.0 1.9 - SINGLE CRYSTAL TUNGSTEN (U-M) 1.8 1.7 1.6 1.5 ++ / 1.4 (n 1.3 1.2 w 1.0 +.9.8 <. 7.6.5 ++.4.3.2 0 10 20 30 40 50 60 70 TIME - HOURS 1763 Fig. 65. —Effect of cavitation test duration on MDP of singlecrystal tungsten at 70~F in water.

-210-M changing the test fluid from water to mercury at 70~F, and when increasing the mercury temperature from 70~F to 5000F, then it is possible to compute projected damage rates for the single-crystal tungsten on the basis of the 304 stainless steel data available~ Hence, one might compute the expected rate of damage for single-crystal tungsten in mercury at 70~F as follows: 3040F0SgS W =Og70~F Hg W70~F Hg W70~F H 0 X 304 SS70F H20 2 304 SS70' 0 W70~F Hg = (.025 mils/hro) X.32 mils/hr. 0.08 mils/hr. -10 mils/hro where W and 304 SS denote the corresponding MDP rates for tungsten and type 304 stainless steel, respectively. In a similar manner one can estimate the expected rate of damage for the single-crystal tungsten in mercury at 5000F as follows: 304 SS500oF Hg 500 F Hg W70~F H 0 304 SS70F 20 W500~F Hg (.025 mils/hro) X 6 m 0173 mils/hr. ~00:10 mils/hr. It is felt that the estimate at 500~F is probably conservative, since the mechanical properties of the single-crystal tungsten are only slightly affected by the increase in temperature from 70"F to 500~F as compared with the stainless'steelo It is believed that the effects of the change in mercury properties between 700F and 500~F are probably

-211small and are in a direction to reduce damage ("thermodynamic effects") if the mechanical properties of the material were constant. Then.the MDP rate:of 0.08 mils/hour may be more applicable for a test of single-crystal tungsten in mercury at 5000F. Presently, mechanical properties data for the single-crystal tungsten at the two temperatures in question are not available, and this matter will remain in some doubt until such data is- obtained. A photograph of the single-crystal tungsten cavitation specimen at the conclusion of the 50-hour test is included in Figure 63 (previously cited). Very little damage is apparent. The outer dark ring noted in the photograph is not part of the tungsten specimen, but represents a space between the edge of the specimen and the cardboard holder used for photography. However, the lighter ring within this does represent the typical relatively undamaged area around the outside of the specimen. 5. Effect of Teflon Coattng on CavitationErosion Characteristiscs a. Experimental Procedure Several type 304 stainless steel standard cavitation test specimens were coated with liquid teflon obtained from DuPont, Inc., in an attempt to determine its effectiveness as a protective coating against cavitation-erosion attack, since various coatings of this type have sometimes proven effective in water tests. The stainless steel specimens were sand-blasted so as to roughen the surface, and then the liqu-id teflon was applied with an insecticide sprayer to a thickness of

-2122.5 mils. The cavitation tests were conducted in mercury at a temperature of 3500F, which was believed to be about the upper limit of applicability for teflon, at a frequency of apptoximately 20 Kc,/sec. and double amplitude of approximately 2 milso b. Experimental Results Initially, a teflon-coated 304 stainless steel specimen was soaked in mercury at 3500F for 15 hours with no cavitation present to determine whether the teflon coating would adhere to the stainless steel surface in this environment. Visual examination indicated no damage or loss of teflon, and precision weighing confirmed this conclusion. Several teflon-coated 304 stainless steel specimens were then subjected to cavitation in mercury at 350~F. The rate of weight loss was essentially the same as that obtained with uncoated 304 stainless steel tested at 500~F in mercury (agreement within- 2F2). In fact, after only 5 minutes of testing, it was found that the teflon coating had been completely removed. Since the teflon coating remained intact upon exposure to the 350~F non-cavitation environment (i.e., did not "soak off"), it appears that the teflon coating was ineffective as a protective measure in the presence of cavitation in mercury at 3500F. 6, Comparison of Cavitation Results in.Bearing Program Although it was not possible to test all of the materials in mercury at 500 F, it is possible to compare all of the results as corrected to 5000F,mercury, as previously discussed. Table.30 summarizes all of the cavitation data obtained in the bearing program investigation.

-213TABLE 30 COMPARISON OF CAVITATION RESULTS OBTAINED IN BEARING PROGRAM (BASED ON 500~"F MERCURY OPERATION) Material Avg. Wt. Loss Rate Avg MDP Rate BG-42 (R = 64) (TRW) 1.20 mg./hr..04 mils/hr. Blue Chip Tool Steel (TRW) 1.43.04 *Single-Crystal Tungsten (U-M) 4.96.08 BG-42 (Rc = 53) (TRW) 3.08.10 BG-42 (Rc = 47) (TRW) 5.88.19 Mo- 1/2Ti (P & W) 43.16 1.09 Cb- lZr(A) (P & W) 125.78 3.73 *Graphitar-Grade 80 (U-M) 55.30 7.95 *Graphitar-Grade 50 (U-M) 71.60 10.90 *These values estimated from data obtained at 70'F.

-214The values given for graphitar anrd single-crystal tungsten are projected values based on assumptions previously discussed. All of the values for the other specimens were actually obtained in mercury at 500~F and previously presented in Table 28. It is clear from Table 30 that the BG-42 (Rc= 64) and the Blue Chip Tool Steel are the most resistant to cavitation in mercury at 500~F. The single-crystal tungsten with the estimated MDP rate of 0o08 mils/hour ranks third and the BG-42 (Rc = 53) fourth. The BG-42.(Rc 47) is about 90% less resistant than the BG-42 (Rc = 53). The Mo-l/2Ti and Cb-lZr(A) were both much more heavily damaged and suffered average MDP rates of 1.09 mils/hour and 3.73 mils/hour, respectively. The graphitars were both very grossly damaged, exhibiting by far the least resistance to cavitation attack of the materials tested. It is interesting to note that the Blue Chip Tool Steel, all three specimens of BG-42 (varying hardness), and the single-crystal tungsten were all more resistant to cavitation attack in mercury at 500~F than the refractory alloy, T-lll, which was the most resistant in mercury at 500~F among the materials previously tested. Presumably, Table 30 could serve as a materials guide for the designer of bearings, serving to indicate those materials which exhibit the greatest resistance to cavitation-erosion attack among those tested in mercury at 500~F. However, it is believed that final check tests in a flowing facility similar to the University of Michigan mercury tunnel or more preferably in a close-clearance space similar to bearing geometry, would be desirable.

-215Although it has been indicated that considerable difficulty was encountered in fabricating the single-crystal tungsten, it is believed that these difficulties could be overcome with further- experimentation so that a test in mercury at 500~F could be accomplished. Since the only specimen of this material which was tested ranked among the best materials, such a continued effort would be desirable to obtain the performance of other closely related materials. While the teflon coating was unsuccessful, it is known that other coating materials and perhaps more suitable bonding procedures have provided useful materials for cavitation resistance in water in the past. Presumably similar materials could be developed also for fluids, other than water, such as mercury.

CHAPTER IV MECHANICAL PROPERTIES DATA FOR THE TEST MATERIALS Ao Introduction In order to obtain a meaningful correlation between the cavitation resistance of the various materials tested, their mechanical properties, and suitable fluid coupling parameters, it is absolutely essential that the applicable mechanical properties be measured at the test temperatures using tensile bars machined from the same bar stock as were the cavitation specimens. Otherwise the variations between material lots due to differences in heat-treat, cold work, etc., are too large to allow useful results. Accordingly, all the cavitation test specimens, tensile bars, and special hot hardness specimens for each individual material were machined from the same piece of bar stock. In the case of the Cu, Cu-Ni, Cu-Zn, and Ni alloys it was desired to use the precise 22 materials that had been tested in the venturi, and these were available only in sheet stock. From this sheet stock flat tensile specimens were fabricated and tested. It was found that handbook values or those supplied by vendors were not sufficiently accurate to be of use in this context even for relatively standard materials. It has been the experience of this laboratory that supposedly identical materials taken from -216

-217different heats may have variations in applicable mechanical properties as great as 50%. Among the properties which may be important are tensile strength (TS), yield strength (YS), engineering strain energy (ESE), true strain energy (TSE), hardness (H), el ongation(ELON), reduction in area (RA), and elastic modulus (E). Each of these mechanical properties will be examined with respect to motivation and experimental evidence pointing to their selectionas possible test material correlating parameters. B. Mechanical Properties Selection The mechanical properties of the test materials which were selected as possible correlating parameters for the experimentallydetermined cavitation damage data are listed above. Qualitative motivation and experimental evidence supporting their selection as possible material correlating parameters follow. It is, of course, desired to find a relation between cavitation damage rate and the conventional (measurable) mechanical and fluid properties so that cavitation damage might be predicted in advance. 1. Tensile Strength (TS) Several investigators have attempted to correlate the cavitation damage resistance of various materials with the tensile strength. 18 32 70 Among these were Mousson, Nowotny, and Plesset and Ellis. In each case some success was achieved. If one were to generate the engineering 71 stress-strain curve for a material (based on the original gauge length "and cross-sectional arena of the tensile specimen), the maximum stress

-218experienced by the test specimen as determined from this curve is known as the ultimate tensile strength. Hence, it seems intuitively reasonable to include this quantity among the possible material mechanical properties.,to be used as correlating parameters. 2. Yield Strength (YS) 18 Mousson also attempted a correlation with the yield strength on a limited number of materials. In the case of the engineering stress-strain curve the yield strength is approximately equal to the stress beyond which the material passes from the elastic range to the plastic range. If the cavitation damage mechanism is similar to fatigue failure, then the yield strength should be an important correlating parameter, since the endurance limit (or fatigue strength) is usually an approximately fixed proportion of the yield strength rather than ultimate tensile strength. 3. Engineering Strain Energy (ESE) Both Shalnev and Thiruvengadam7374 have postulated the use of strain energy concepts with respect to cavitation damage correlations and have reported limited success in their use. The engineering 71 strain energy (strain energy to failure) is based on the "approximate" or engineering stress-strain curve and is equal to the area under this curve. This area is a measure of the work or energy per unit volume that must be delivered to a tensile specimen in order to completely fracture it, Hence, it appears that it might be a reasonable correlating parameter.

-2194. True Strain Energy Based on Elongation (TSEE) In an attempt to take into account the elongation and reduction in cross-sectional area experienced by the tensile bar during a test, factors which are neglected in the generation of the approximate, or engineering stress-strain curve, two commonly-used approximations for "true strain energy" will be considered. These are based on approxima-..1-: 71. tions of the true stress-strain curve. The first value of true strain energy takes into account elongation of the test specimen incomputing the strain, but assumes that necking of the specimen does not occur. 5. True Strain Energy Based on Reduction in Area (TSER) The second value of true strain energy considered takes into account elongation of the test specimen in computing the strain and also necking of the specimen, i.e., reduction in area after plastic deformation begins, in computing the true breaking stress. Hence, higher values for the breaking stress and strain are obtained in this manner than was the case with the engineering strain energy, since a greater account is taken of the ductility of the material. This may or may not more closely represent the cavitation case which is characterized by very high rates of loading, leading in some cases to apparently brittle fractures. The true strain energy values used in our correlations are only approximations since it is difficult to obtain true stress-strain data beyond the elastic range during a tensile test (except for the values at rupture).

2.206. Hardness (H) Hardness has been shown to be an important factor in cavitation damage resistance correlations by many investigators. In general, materials with high hardness values are more resistant to cavitation 34 damage than softer materials. Rheingans showed that the order of resistance generally follows the order of hardness in a series of tests 18 of cast stainless steels using a magnetostriction oscillator, Mousson obtained a similar successful correlation with hardness on materials 70 tested in a venturi apparatus. Plesset and Ellis conducted experiments on a number of different materials and found hardness to be reasonably successful as a correlating parameter. Hence, hardness has been included among the mechanical properties to be used as possible correlating parameters in our investigations. 7. Elongation (ELON). Since the value of elongation for a particular material is important in determining the true strain energy, it was included in the mechanical properties listo 8. Reduction in Area (RA) Since the value of reduction in area for a particular material is important in determining the true strain energy, it was included in the mechanical properties listo 9, Elastic Modulus (E) 70. Plesset and Ellis investigated the use of elastic modulus as. a correlating parameter for cavitation damage on a number of

-221materials ranging from very soft aluminum to stellite and tungsten. Moderate success was achieved. Early correlations in our own laboratory 22 with the venturi data showed elastic modulus to be prominent in the correlating equations. This may not be surprising since it is closely related to sonic velocity and acoustic impedance, both of which appear in basic equations involving the stress from an impinging droplet or jet. 10. Hobbs' Approach 67 Hobbs suggested the use of still other quantities to correlate cavitation damage. Figure 66 is a schematic diagram of a typical true stress-strain curve for some material. Hobbs found that the area under the true stress-strain curve within the elastic region (crosshatched in Figure 66) correlated well with some of his data. If one postulates that when this amount of energy is delivered to the test specimen (work done on the specimen), i.e., once the yield point is reached, the collapsing bubbles begin to remove material from the cavitation specimen, then such a quantity is a reasonable correlating parameter. This quantity, which Hobbs refers to as the "proof resilience" (PR), will be examined in our work also. It is seen that it is equal to: Hobbs' Proof Resilience (PR) = 1/2 (Sield /E) where: Syield yield strength (YS) of the material E = elastic modulus of the material

-222FRACTURE'W W S yield. / \ | (HOBBS PROOF RESILIENCE (PR)2 \1/2 ((yield)(Syield)= 1/2(Syield /E) 8yield SyiIeld/E TRUE STRAIN 192 Fig. 66. —iruei, stress-strain curve showing Hobbs' proof resilience concept.

-223Hobbs found still further that a better correlating parameter for his data was a quantity that he calls the "ultimate resilience" (UR) Figure 67 is another schematic diagram of a typical true stressstrain curve. The cross-hatched area in this figure corresponds to Hobbs' ultimate resilience. Since the process of cavitation represents highly transient loading, Hooke's Law may be valid to fracture as no elongation or reduction in cross-sectional area of the specimen occurs (i.e., brittle fracture occurs). Thus, during the cavitation process, the stress-strain relationship might well be linear up to the point of failure, as suggested in Figure 67. This quantity will also be examined in our worke Hobbs' ultimate resilience can be computed as: Hobbs' Ultimate Resilience (UR) 1/2 (Sultimate2/E) where: Sultimate true ultimate stress (true breaking stress) of the material E = elastic modulus of the material The above mechanical properties were chosen as material correlating parameters for the cavitation damage data obtained in leadbismuth, mercury, water, and lithium. C. Tables of Properties at 70~F, 500~F and 1500~F The mechanical properties data for the stainless steels and refractory materials were determined at 70~F, 500~F, and 1500~F at Pratt & Whitney Aircraft (CANEL) under the supervision of Mr. Henry P. Leeper, Project Metallurgist. Earlier, Pratt & Whitney Aircraft (CANEL)

-224Sultimote - - - - -- FRACTURE - X\ \ \^ (oultimao ultime t)e I.'C 8ultimate ultimate/E 1913 TRUE STRAIN Fig. 67. —True stress-strain curve showing Hobb's ultimate resilience concept.

-225had supplied generous portions of all of the refractory materials tested in this program, whereas the stainless steels used were supplied by this laboratory. The results of the mechanical properties determination pro75 gram were supplied to this laboratory by private communication and have become an integral part of our cavitation analysis and correlation effort. The data supplied by Pratt & Whitney Aircraft (CANEL) at 700F, 500~F, and 1500~F is tabulated in Tables 31, 32, and 33, respectively. Three values for strain energy to failure are listed: i.e., "engineering strain energy" (ESE) which is based on the "approximate" or engineering stress-strain curve and is equal to the area under this curve, and two values for "true strain energy" (TSE), which are based on approximations of the true stress-strain curve. The first value of true strain energy listed takes into account elongation of the test specimen in computing the strain (denoted by TSEE), while the second value takes into account necking of the specimen (i.e., reduction in area after plastic deformation begins), and the resulting higher values for the local true breaking stress and strain in the actual failure region (denoted by TSER), as previously discussed. The large discrepancies in some cases, as for highly ductile materials, between these differentlydefined strain energy values indicate the difficulties and uncertainties incurred in using this parameter. If it occurs that the engineering strain energy (ESE) proves to be a better correlating parameter than the true strain energy based on reduction in area (TSER), the t his may indicate that brittle rather than ductile failures are typical of

TABLE 31 MECHANICAL PROPERTIES DATA AT 70~F FROM PRATT &' ITNEY AIRCRAFT (CANEL) Engo. Tensile Yield Strain True DPH Elonga- Area Elastic Strength Strength Energy Strain Energy Hardness tion Reduction Modulus Material psi p si pi psi' psi 1. Klg. % psi 304 -S 94,500 64,700 57,300 41,3000 4237 63.8 77.9 29.0x10 316 -S 87,200 63,600 48,850 38,200 49,500 227 57.8 80.3 29.0x106 T-lll 131,600 124,900 16,750 16,000 68,600 308 14.8 80.4 28.0x0l6 T-222 154,200 154,200 15,250 16,050 70,350 338 10o6 55.6 28.0x10 a T-222(A) 108,900 91,100 23,950 22,180 52,350 288 231o 61.1 28.0x106 Mo-1/2Ti 165,800 150,400 21,300 14,570 11,600 295 9.3 7.9 45.0x10 Cb-lZr 59,200 59,000 6,650 6,300 29,600 151.14o3 88.4 15.0x10 Cb-lZr(A) 36,300 19,200 13,200 7,050 12,110 99 41.9 91.4 15.0x106

TABLE 32 MECHANICAL PROPERTIES DATA AT 500~F FROM PRATT & WHITNEY AIRCRAFT (CANEL) Eng. Tensile Yield Strain True DPH Elonga- Area Elastic Strength Strength Energy Strain Energy Hardness tion Reduction Modulus Material psi psi i si psi 1 Kg. % % psi 304 S$.92,500 56,700 16,150 18,200 37,200 154 30.8 72.9 26.0x106 316 SS 72,400 - 52,300 18,050 17,700 38,000 203 30.4 78.2 26.0x106 T-111 101,800 100,800 15,100 10,700 50,900 218 13.8 86.2 27.0x106 T.411 -Jo.00 50o900 218 13.8. 86.2 2~.. - T-222 133,800 133,800 12,850 12,900 67 800 286 10,9 71.5 27.0x106 T-222(A) 92,300 63,400 20,650 33,800 42,200 209 23.6 66.9 27.x106 Mo-1/2Ti 84,100 79,700 11,000 44,400 207 15.0 75.9 43.0x106 Cb-lZr 54,700 54,700 6,450 5,185 27,700 133 12.7 88.7 14.5x106 Cb-lZr(A) 25,000 11,600 8,100 3,780 7,890 71 35.9 92.2 14.5x106

TABLE 33 MECHANICAL PROPERTIES DATA AT 15000F FROM PRATT & WHITNEY AIRCRAFT (CANEL) Eng Tensile Yield Strain True DPH Elonga- Area Elastic Strength Strength Energy Strain Energy Hardness tion Reduction Modulus Material psi_ psi_ psi __s 11 Kg psi I_ 3041s 21,900 18,400 4,600 1,640 2,410 66 19.7 30.5 18.0x106 3163 S24,201 21,400 7,300 4,160 6,600 74 31.7 55.0 18.0x10 T-111 87,301 67,300 15,100 13,400 45,850 161 18.4 79.5 26,0x106 T-222 120,719- 119,700 16,950 11,960 65,500 257 10.8 75.5 26.0xI6 T-222(A) 85,500 41,800 16,950 14,030 38,500 140 22.1 72.9 26.0x106 Mo-l/2Ti 70,000- 61,600 7,950 7,200 32,500 148 13.5 80.4 340x106 Cb-lZr 47,600 47,100 5,650 3,460 19,500 106 11.6 84.1 13.5x106 Cb-lZr(A) 28,000 9,700 6,700 2,200 7,050 67 26.5 9101 13o5x106

-229cavitation damage. The remaining values listed in Tables 31, 32, and 33 are rather commonly reported metallurgical properties which have already -been discussed. The hardness values listed were measured with a diamond pyramid indenter and 1.1 Kg. load. Figures 68, 69, 70, 71, 72, 73, and 74 present plots of ultimate tensile strength, 0.2% yield strength, and hardness of the type 304 stainless steel, type 316 stainless steel, T-lll, T-222(A), Mo-1/2Ti, Cb-lZr, and Cb-lZr(A), respectively, as a function of temperature. The following observations regarding these mechanical properties are noted: 1) For 304 stainless steel the ultimate tensile strength and the 0.2% yield strength are nearly constant from room temperature to 5000F. Then they rapidly deteriorate as the temperature increases to 15000F. The hardness decreases in a relatively uniform manner over the temperature range investigated. 2) For 316 stainless steel the ultimate tensile strength, 0.2% yield strength, and the hardness all decrease in a fairly uniform fashion as-the temperature is increased. 3) For T-lll, the ultimate tensile strength and the 0.2% yield strength decrease from room temperature to 500~F, but are relatively constant thereafter. The same comment applies to the variation of the hardness. 4) For T-222(A) the variation of the mechanical properties as shown in Figure 71 is similar to that of the T-lll. The changes from 500~F to 1500~F are quite small. 5) For Mo-1l/2Ti comwaen1d similar to (3) and (4) above apply.

140,,,,,,,,, 280 100\ -200 ULTIMATE TENSILE STRENGTH HARDNESS ( IX X - 1 I 0 0 50 i,0 o 0 0.2% YIELD STRENGTH'Q 0 500 1000 1500 2000 TEMPERATURE, F 617 Fig. 68. —Effect of temperature on mechanical properties of type 304 stainless steel.

1401~F~{, I I,, I I I,I I I 280 100 - 200'Q ULTIMATE TENSILE O 0 STRENGTH7 ^ rHARDNESS VC) 0.2% YIELD STRENGTH: Q- 50 0 X i ii, 1 1 I I I I I I I I I I I I, 0 500 1000 1500 2000 TEMPERATURE F 1618 Fig. 69. —Effect of temperature on mechanical properties of type 316 stainless steel.

140 1-I ~,,,,,,350 300 ULTIMATE TENSILE STRENGTH 0o' HARDNESS ] x 0.2% YIELD STRENGTH l <. I50 /-F~ -2; ~100 I 0 0 0 L,., I,,,,,,,,,, i i i,, 0 0 500 1000 1500 2000 1oi9 TEMPERATURE, OF Fig. 70. —Effect of temperature on mechanical properties of T-lll.'' ^~~~~~~~~~~~~~~~~~~~~~~~~~~

140, I I ~ I,,,, 3550 -_^~~~~~~~~~ -~~~~300 <~- ^^ ^-ULTIMATE TENSILE STRENGTH,.~.. ^^^^^^ ^HARDNESS 0 0.2 % YIELD STRENGTH 11 0 0 I - LCL 0 500 1000 1500 2000 TEMPERATURE,~F 1620 Fig. 71. —Effect of temperature on mechanical properties of T-222(A).

~~~~~~~~721 0,,,||, 1 E3 5 0 210 300 150 HARDNESS 200 ULTIMATE TENSILE STRENGTH i 0. 75 I.2 % YIELD STRENGTH. ~500 1000 1500 2000 ~~~~~~~~~~~~~~~0 L~~~~~1621 TEMPERATURE,F Fig. 72. —Effect of temperature on mechanical properties of Mo-1/2Ti.

o-60 / — ULTIMATE TENSILE STRENGTH 50 -150 ^" ^^^^ ^0.2% YIELD STRENGTH 40 O ~ 0 o - HARDNESS 30 - CO) - -75 I " 0 - 1010 0 500 1000 1500 2000 TEMPERATURE, F 167? Fig. 73. —Effect of temperature on mechanical properties of Cb-lZr.

701 ] r I 11140 60 40 HARDNESS ( _ 00 (J)9~n~~~ ~50 I0 20 m I~ / I- m -- ULTIMATE TENSILE STRENGTH 10 0.2% YIELD STRENGTH 0 I I, I I I I I I 1. I I I I. 0 0 500 1000 1500 2000 TEMPERATUREF iF2 Fig. 74. —Effect of temperature on mechanical properties of Cb-lZr(A).

-237 - 6) For Cb-lZr the variation of the mechanical properties shown in Figure 73 is a very weak function of temperature. 7) For Cb-lZr(A) there is a decrease in the ultimate tensile strength, 0.2% yield strength, and hardness as the temperature is increased from 70~F'to 500~F. Thereafter, the properties are a very weak function of the temperature. 8) At room temperature the tensile strength and yield strength of the stainless steels are about 50% less than the corresponding properties for the T-lll, T-222(A), and Mo-l/2Ti. 9) At 5000F the tensile strength and yield strength of the stainless steels are roughly comparable with the corresponding properties of the T-lll, T-222(A), and Mo-1/2Ti. 10) At 15000F the tensile strength and yield strength of the T-lll, T-222(A), and Mo-1/2Ti are on the order of 4 times greater than the corresponding properties of the stainless steels. The strain energy to failure (ESE) was determined by computing the area under the engineering stress-strain curve which was supplied by Pratt & Whitney Aircraft (CANEL). The effect of temperature on the strain energy of the seven materials tested is shown in Figure 75. Again, it is apparent that the strain energy of the stainless steels decreases rapidly with increasing temperature, while the strain energy of the T-lll, T-222(A), and Mo-1/2Ti is not greatly affected by temperature. Although the strain energy of the Cb-lZr and the Cb-lZr(A) is somewhat insensitive to temperature also, the absolute magnitude of the

70 60 50 r~;\ ~ —304 SS o r \~ ~31 6SS (f) >_ 30^ M -Mo-L/2Ti rT- 222(A) ( Lij_ T- 11i 0^ 2~ cl~~~~~~~ I 0 ~ ~ ~ ~ ~ IZ CB 500 CB-IZR 0 1000 1500 0.0 Lo-,4 TEMPERATURE, Fig. 75, —Effect of temperature on engineering strain energy of stainless steels and refractory alloys.

-239quantity does not compare with that of the other refractory alloys at any temperature. The mechanical properties data for the aluminum alloys, carbon steel, Plexiglas, and the Cu, Cu-Ni, Cu-Zn, and Ni materials were determined at room temperature in the Department of Chemical and Metallurgical Engineering laboratories at The University of Michigan and are presented in Table 34. The mechanical properties for carbon steel were also determined at 5000F and so noted in Table 34. Available mechanical properties data for the bearing materials are presented in Table 35. The three BG-42 materials and the Blue Chip Tool Steel were tested at 500~F (stress-strain curve generated and hardness measured) in the Department of Chemical and Metallurgical Engineering laboratories. Hardness data was obtained for all of the bearing materials investigated and is also presented in Table 35. Examination of the data in Tables 31 through 35 indicates that several of the mechanical properties such as tensile strength, yield strength, strain energy, and hardness decrease in value for a given material as the temperature is increased. Such trends are indicative of the behavior of the cavitation resistance as a function of temperature in some cases, as has been previously discussed. Undoubtedly, it should be possible to correlate the cavitation resistance of the materials tested with the applicable mechanical and fluid properties data at the The hot-rolled carbon steel used in these investigations had a carbon content of 0.05%, silicon content less than 0.05%, and a hardness of Rockwell "B" = 42.

TABLE -34 MECHANICAL PROPERTIES DATA AT 70"F FROM UNIVERSITY OF MICHIGAN LABORATORIES Eng Tensile Yield Strain True DPH Elonga- Area Elastic Strength Strength Energy Strain Energy Hardness tion [Reduction Modulus Material' psi_ psi _ psI _ psi 1.1 Kg, % _ ^ __ psi 1100-0 Al 12,250 7,600 4,950 4,320 22,600 27 44.5 85.5 10.0x10 2024 Al 72,000 57,900 13,300 13,600 31,050 171 20.0 34.5 10.0x10 606*Al 45,300 40,000 25,800 9,840 38,620 127 19.4 56.7 10.0x106 Carb9n Steel ~(7Or).45-,3- - 41,600 18,440 30,530 111,000 193 46.3 76.1 29.0x106 Carbon.Steel I (500OF) 62,510 -18,400 19,225 20,900 66,650 125 37.2 63,6 28,0x106 Plexiglas: 10,445' 1,600 320 320 320 9 4.0 0.0 0.4x0 Cu 53,400 49,500 3,100 11,800 11,800 133 6.2 19.8 17.0x106 Cu-900'F 31,500 9,500 13,900 26,900 26,900 51 51.3 48.5 170x06 Cu-1500 OF 30,700 5,000 6,100 11,800 11,800 41 32.5 33.2 17.0x106 Cu-Zn 93,900 82,000 4,700 55,400 55,400 197 5.3 40.7 160x106 Cu-Zn"850'F 47,600 20,000 28,600 57,000 57,000 71 62.6 60.9 16.0x106 Cu-Zn-14000F 40,400 11,000 15,300 33,000 33,000 48 58.9 51.7 16O0x106 Cu-Ni 87,300 77,000 6,100 13,200 13,200 197 4.5 15.4 22.0x106 Cu-Ni-13000F 57,900 20,000 3,100 36,200 36,200 96 349 43.5 22.0x106.910 369200:100 9 34.9 4305 22,01 Cu-Ni-18000F 53,300 18,000 16,300 21,800 21,800 77 34.4 34.4 22.0x106 Ni 93,10 82,000 3,200 8,300 8,300 206 3.9 10,2 30.0x106 Ni-11000F 50,500 13,000 18,300 48,300 48,300 67 43.8 51.6 30.0x106 Ni-16000F 48,700 7,000 16,100 40,500 40,500 59 41.8 49.7 30.0106

TABLE 35 MECHANICAL PROPERTIES DATA FOR BEARING MATERIALS Tensile Yield Strain True Elonga- Area Elastic StrenStre Strength Energy Strain Energy tion Reduction Modulus Material ps _ps p. psi_ pi _____ Hardness 2psi 7- 2,50 (789*).25.3 O' Ox'O BG-42(Rc=64) 318,000 273,000 4,840 6,650 7,250 64 R(789) 2.2 2.5 30.x10 BG-4 Rc==53) 251,000 234,000 2,940 3,300 7,940 53R (562*) 1.6 3.2 30.0x106 C~~~~~~~~~~~~~~~~~~ BG-42( 47) 184,000 154,000 3,120 3,810 4,910 47 R(471) 2.3 2.8 30.0x106 Blue Chip Tool Steel 340,000 302,000 6,840 7,300 7,800 64 R (789*) 2.6 2.5 30.0x106 Single-Crystal" Tungsten 32 R (317*) GraphitarGrade 80 20,000** 54 Rh(80^) GraphitarGrade 50 35,000*** 70 Rh(100) *DPH (1.1 Kg. Load). *Average Shore Sclerocope -Hardness. Compressive Strength.

-242test temperatures. However, the conventional mechanical properties as here described are measured under semi-static conditions and, hence, may not be fully applicable to the high loading rates typical of cavitation failure. Applicable fluid properties will now be examinedo

CHAPTER V FLUID PROPERTIES DATA FOR TE TEST FLUIDS A. Introduction In order to obtain a meaningful correlation between the cavitation resistance of the various materials tested, their mechanical properties, and suitable fluid coupling parameters, it is important to choose applicable fluid properties for this purpose. Since the dynamics of bubble formation and collapse are controlled by the physical properties of the fluid, it is necessary to account for variations in fluid properties, as the tests were conducted in four different fluids at several test temperatures. Both Plesset and Hammitt and Smith7 have conducted comprehensive reviews of the dynamics of bubble formation and collapse. The various fluid properties that enter into the appropriate differential equations (and solutions for bubble collapse pressure) describing the growth and collapse of a bubble under different sets of assumptions include the fluid density, surface tension, vapor pressure, net positive suction head, bulk modulus, and kinematic viscosity. In 69,76,7'8' addition, if heat transfer effects become important in describing the formation and collapse of bubbles, then various thermal properties such as the specific heat, thermal conductivity, heat of -243

-244vaporization, thermal diffusivity, and Prandtl Number of the test fluid must be considered. Initially, the computer correlations of cavitation damage data with applicable mechanical and fluid properties for this study were conducted under the assumption that thermodynamic effects in the formation and collapse of bubbles were negligible. The validity of this assump79 tion has been explored in detail by Florschuetz and Chao, but it is generally true if the fluid temperatures involved are considerably below the ordinary fluid boiling point, ioe,, the vapor pressure of the fluid is small. This was not exactly true in all of our investigations. As a result, the thermodynamic effects will be examined separately in a later section At this point the fluid properties that have been examined in the computer correlations include the ratio of the acoustic impedances of the test fluid and specimen material, fluid density, surface tension, net positive suction head, compressibility or bulk modulus, and kinematic viscosity. Each of these fluid properties will be examined with respect to theoretical and experimental evidence pointing to their selection as fluid coupling parameters. B. Fluid Properties Selection The fluid properties which were selected as coupling parameters for the computer correlations of the experimentally-determined cavitation damage data are listed above, Again, it is emphasized that thermodynamic~ effects have been neglected in these correlations, From a

-245theoretical point of view all of these fluid properties have appeared in differential equations describing the formation and collapse of a bubble and the resultant pressure loading on adjacent surfaces, under different sets of assumptions. Hence, it is reasonable to choose such properties as fluid coupling parameters. Detailed comments regarding each of these properties follow. 1. Acoustic Impedance Ratio (AI) 52 The acoustic impedance ratio is defined as: R AI - Acoustic Impedance of Test Fluid R1 Acoustic Impedance of Test Specimen R (Qc) A= FLUID C)MATERIAL where: AI = acoustic impedance ratio Q = density c = velocity of sound in medium R1 acoustic impedance of test fluid R2 = acoustic impedance of test specimen The velocity of sound, c, can be expressed as: c = (E/ )1/2 (for a solid) c = (B/ )1/2 (for a liquid) where: E = elastic modulus (for a solid) B = bulk modulus (for a liquid)

-246Thus:. (B ) P)1/2 ( FLUDID. AI = 1/2 (E ): SOLID' Physically, the acoustic impedance ratio is related to the ratio of reflected to transmitted energy as liquid shock waves or jets impinge on the solid test material. The transmission coefficient, 0C t, which is defined as the fraction of acoustic energy incident upon an interface of two materials possessing dissimilar acoustic impedances that is 52 transmitted across the interface, can be expressed as: 4 RR 4(R/R2) (R1+R2) (R1/R2) + 2(R1/R2) + where in our case R1 and R are the acoustic impedances of test fluid and test material, respectively It is seen that as R1 — R2, t -> l, and we have 100% transmission. Further, if a liquid jet is assumed to be the damaging mechanism in cavitation, then according to the most 77 simplified "water-hammer" analysis, R1/R2 enters into the expression for the transient pressure generated on the surface by jet impact, i.e., A 1 -v IPimpact 1 + R2/R1 where: aPimpact = pressure increase on surface due to impact P -= density of fluid Cl — ~ velocity of sound in fluid

-247v = velocity of liquid jet R1 acoustic impedance of fluid R acoustic impedance of test specimen In the case of our experiment there are several reasons why one might select the acoustic impedance ratio as a suitable coupling parameter for the comprehensive cavitation damage correlations. First, acoustic energy in the form of sound waves is transmitted along the exponential horn assembly to which the test specimen is attached. This acoustic energy is then propagated from horn to test specimen and from test specimen into the test fluid, but the amount of energy passing these two interfaces and into the fluid is determined by the acoustic impedances of the horn, test specimen, and fluid. Presumably, the formation of a bubble cloud at the specimen face is strongly dependent on the energy being transmitted into the fluid. Secondly, the bubble collapse gives rise to a shock wave or liquid jet that is propagated through the fluid. In order for damage to occur at the specimen surface, this energy in the form of the shock wave or liquid jet must be transmitted across the liquid-solid interface. Hence, one might expect the amount of damage to the test specimen to be a function of the amount of energy transmitted across this interface and actually reaching and being absorbed in the specimen. Here again, the ratio of acoustic 80 impedances or the transmission coefficient is the determining factor.80 Finally, the ratio is involved in the relation for pressure-loading of the surface in the case of jet impact, as previously stated. Because of its possible involvement- in all these ways the ratio of acoustic

-248impedances between liquid and specimen was chosen as a possible fluid coupling parameter. It is further postulated that the greater the acoustic impedance ratio, the greater the amount of damage sustained by the test specimen. This is reasonable since as (R1/R2) — 19( t~l, and we have complete transmission of the acoustic energy from transducer tip to fluid, and complete transmission of energy represented by shock waves or liquid jets from fluid to specimen surface, causing maximum damage, In addition, the pressure generated by the impacting jet is also maximized for a given fluid condition. 2. Density ( ) The density of the fluid may be a suitable coupling parameter since one would expect the pressure exerted on the specimen surface to be approximately proportional to the density for fixed NPSH, compressibility, kinematic viscosity, etCo Hence, one would expect the damage 81 to increase as the density was increased. Wilson and Graham conducted cavitation tests on silver in a variety of fluids and showed experimentally that this was, indeed, the case, as is also indicated in the present study by comparison of the different fluids usedo 3o Surface Tension (0 ) The expected effect of surface tension on cavitation damage, based on the conclusions from dynamics of transient cavities, would be an increase: in damage as the surface tension is increased, since collapse pressures would be higher with greater surface tension. This 32 behavior was reported experimentally by Nowotnyo However, recent

-249numerical calculations show that the effect of surface tension in this 82,83 regard should be quite negligible On the other hand, for a given kinematic situation, high surface tension would inhibit bubble nucleation and thus tend to reduce the bubble population. This, presumably, would result in a reduction of cavitation damage. 4o Net Positive Suction Head (NPSH) The net positive suction head, NPSH, is defined as: P ~ Pv NPSH - P PL where: p 8 local pressure of fluid p = vapor pressure of fluid = density of fluid It is commonly used as a similarity parameter in turbomachinery design where cavitation is a factor, ioe., to a first approximation, if geometry and NPSH are maintained constant, the cavitating flow regime should 32 remain constant. It was shown by Nowotny that damage was decreased as the vapor pressure increased for tests where p in the above relation was held constant, since the collapsing pressure differential was reduced for a given fluid and, in addition, perhaps the additional vapor served to cushion the collapsing bubbles, as is discussed later under thermodynamic effects. As mentioned previously, the damage rate would be expected to increase as the density increased if the NPSH were held constanto In general, the damage should be inversely related to the NPSH. In our experiments the local static pressure, p, was varied by varying

-250the argon cover gas. pressure so that the difference between local static pressure and vapor pressure, p - Pv, was maintained constant. Then; NPSH i lI/ for the tests of this study based on steady-state pressureo However, the transient head caused by the vibration of the horn would be the same for all fluids, assuming the fluid density and temperature do not affect the vibrating behavior of the horn (of courses this is not precisely true). Since the transient contribution to the NPSH is probably predominant, these tests may well be closer to a constant NPSH condition than a constant pressure suppression conditiono If so, the collapse velocities would be similar for all fluids, and the imposed pressures on the surface would be proportional to the fluid density, so that damage should increase with increased fluid density, as it dido Clearly, more sophisticated and detailed analysis on this point is required to understand che complex relationships involvedo 5. Bulk Modulus (B) The bulk modulus is the inverse of the compressibility0 It should be an important coupling parameter, since it strongly affects the pressure exerted on the specimen surface, as shown by numerical analy82,83,84 ses8 Hence, one would expect the damage to increase as the bulk modulus increased (compressibility decreased). This behavior was reported from experiments by Wilson and Gaham81 reported from experiments by Wilson and Graham.

-2516 Kinematic Viscosity ( V ) The kinematic viscosity, 2, is defined as: where - -- = dynamic viscosity of fluid P - density of fluid 82,83 Since bubble collapse pressures are theoretically greater in fluids of low kinematic viscosity (although the effect is quite small for fluids in the conventional viscosity range), one would expect cavitation damage to be inversely related to this parameter. Since kinematic viscosity is directly involved rather than viscosity, it is chosen at this 81 point. Wilson and Graham reported this effect from their experiments. It is felt that each of the six quantities discussed above merits consideration as a fluid coupling parameter for the comprehensive lead-bismuth, mercury, water, and lithium correlations to be discussed. C, Tables of Fluid Properties at 70"F, 5000F. and 1500~F Fluid properties data for water, mercury, lead-bismuth alloy, and lithium at the appropriate test temperatures are listed in Table 36. The data was taken from references 65, 85, and 86. The properties include the six coupling parameters that have been discussed previously and which will be used in the comprehensive computer correlations of the cavitation damage data and also the thermal properties which determine the importance of heat transfer effects These will be described later e

TABLE 36 FLUID PROPERTIES DATA AT VARIOUS TEMPERATURES (Taken from V'ferences 65, 85, and 86) V_.Fluid Water Mercury. Mercury Pb-Bi Pb-Bi Li Li Fluid Propert 70OF 70 OF 5000F 500~F 1500 OF 500 OF 1500 F Acoustic Impedance (Al) 6 66 66 (lbm ft.2sec.) 0 o.299x106 4.03x10 385x10 3.08x10 2.86x10 O. 149x10 0 137x106 Density (p ) (g.I/cc.) 1.0 13.55 12.98 10.38 9.64 0.50 0.46 Surface Tension (C") ) (dynes/cmo) 72.8 465.0 419.0 397.0 367.0 386.0 308.0-. Net Positive Suction Head (NPSH) (feet) 365 ~ 2.7 2.8 3.5 3.8 73.0 79.4 Bulk Modulus (B) 6 (psi) 0.31x106 4.11x106 3.94x106 3.16x10 2.92x106 0.160x106 0. 14x610 Kinematic Viscosity(v) ) (ft.2/hour) 0.039 0.0044 0.0030 0.0064 0.0047 0.035 0.017 Specific Heat(C ) (cal./g?0C) lo.00 0.033 0.032 -0.035 0o,035 1.00 1.00 Thermal Conductivity(k) (cal./sec.cm.o C) 1.41x10' 0.021 0.030 0.025 0.022 0.090 0.090

TABLE 36 —Caontinued F l::Fuid Water Mercury Mercury Pb-Bi Pb-Bi Li Li Fluid Property 7.0.F 700F 500~F _:500~F_ 1500~F 500~F - 1500~F Heat of Vaporization (HV) (cal./g.) 585 69.9.7 6.7 204 204 4680 4680 Vapor Pressure (pv) (psi) 0.36 < 0.001 1.93 0.01 < 0.001 < 0.001 0.1 Thermal Diffusivity (K) (ft 2/hr.) 0.0053 0.169 0.3333 0,457 0.522 0.700 0.771 Prandtl Number (Pr) (Dimensionless) 7.31 0.026 0.009 0.014 0.009 0.050 0.022 (D -~ -~~~....10

CHAPTER VI CORRELATIONS OF CAVITATION DAMAGE DATA WITH MECHANICAL AND FLUID PROPERTIES A. Introduction In order to fully investigate the dependence of cavitation resistance on the mechanical properties of the test materials and on the fluid properties, and to obtain a better understanding of the damage mechanisms involved, it is desirable to subject the experimentallydetermined cavitation data and the appropriate mechanical and fluid properties data to a least mean squares fit by means of a suitable digital computer program. For these studies the University of Michigan IBM 7090 digital computer facility has been utilized along with a very sophisticated least mean squares stepwise regression program which was 87 88 first proposed by Westervelt and later revised by Crandallo This'42,43,64 program has been described previously However, for the sake of completeness the detailed explanation is included in Appendix Bo Before the results of the computer correlations are described, it is instructive to obtain a qualitative feel for those mechanical properties that might best give some clue as to the cavitation resistance of a particular material.The lead-bismuth data obtained at 500~F -254

-255and 1500 F and the data obtained in the bearing program have been examined on a preliminary basis and the results are described below. B. Preliminary Correlations 1. Lead-Bismuth Data A preliminary correlation of the lead-bismuth data obtained at 5000F and 1500~F with the ultimate tensile strength, 0.2% yield strength, hardness, and the engineering strain energy was attempted initially. The data at each temperature was analyzed individually. On the basis of the mechanical properties values listed in Tables 32 and 33, it is possible to arrive at several ratings of the materials tested at each temperature. An ultimate tensile strength rating would be obtained by assigning that material with the greatest ultimate tensile strength a value of 1",' while'"7" would denote that material with the smallest value of this property. In a similar manner the materials can be rated on the basis of the 0:.2%.yield strength, the hardness, and the engineering strain energy. In each case a rating of "1" would be assigned to that material having the greatest value of the particular property involved, "7" denoting the material with the smallest value It is intuitively obvious that those materials having greatest tensile strength, yield strength, hardness, and engineering strain energy probably will be the most cavitation-resistant also.. Based on the four mechanical properties listed above, each material now has four ratings. If one now assumes a weighting factor of unity appropriate for each of these properties, it is possible to obtain a final rating for each of

-256the materials, namely, the sum of the four ratings already determinedo0 Then the materials can be rated on. the basis of the sum of the four individual ratings, The end result is an arrangement of the 7 materials tested with a rating of "1" denoting that material which will probably be most cavitation resistant, predicted on the basis of- the mechanical properties listed above. The rating of "7" denotes that material which should be most susceptible to cavitation erosion. It is then possible' ~ ~:...... ~ ~~... *:.... t. * ~ ~.. to compare the final rating of the materials with the rating based on the actual cavitation data obtained in the experiment At 500F the individual ratings of the materials based on mechanical properties, the final rating, and the rating based on the average MDP rate exhibited by the specimens are all summarized in Table 37o It is interesting to note that the experimental rating (based on MDP) agrees almost exactly with the rating based on the mechanical properties data. So, incidentally, does a ranking of hardnesses (which has often been used as a basis for rating cavitation resistance). However, none of the other properties taken Singly are successful in this regardo All these results are applicable at 500~Fo Although the treatment is very qualitative and may appear naive, it is merely an attempt to generate some feeling for the problem at hand. It does show that, in general, a ranking by either strength or energy properties alone will not sufficeo Hardness is a hybrid property in this sense, being neither a pure strength or energy property. A qualitative correlation was also attempted at 1500OF in the same manner as was indicated at 5000Fo The results are summarized in

TABLE -.37 PRELIMINARY CORRELATION OF LE-BISMUTH DATA WITH MECHANICAL PROPERTIES DAAAT5000F UTS o0.2%'YS ESE Hardness Final MP Material _RatinggRatin_ _Rattin ating_ Total _Rating Ratin T-il(P W) 1 1 4 - 1 7 1 1 T-1(A) (P &W) 3 3 1 2 9 2 2 Mo-l/2Ti(P&W) 4 2 5 3 14 3 3 316SS(U-M) 5 6 2 4 17 5 4' 304SS(<U-M) 2 4 3 5 3 5 Cb- Zr(P&W) 6 5 7 6 24 6 6 Cb-lZr(A) (P:&W) 7 7 6 7 27 7 7

-258Table 380 The experimental rating agrees very well with either the final rating based on the mechanical properties data or the hardness rating, as before. Again, only hardness as a single property is reasonably successful in this regard. 2. Bearing Program Data The only mechanical properties data available for all of the materials tested in the bearing program consists of values for the hardness, However, the complete list of properties used for all the materials and derivable from the stress-strain curve and hardness measurements are available for the various BG-42 materials and the.Blue Chip Tool Steel (Table 35). Only fragmentary data is available for both grades of graphitar tested (Table 35). It is useful to attempt to obtain a qualitative correlation (similar to that presented above for the lead-bismuth data) between the cavitation data obtained in the bearing program and the corresponding hardness data. In Table 39 the materials tested in this study are rated according to their cavitation resistance based on average MDP rate, with the BG-42 (Rc = 64) and the Blue Chip Tool Steel being the most resistant and each having a rating of "1." The graphitar-grade 50 was;:damaged the most and has a rating of "9~" The hardness values for all the materials are also listed along with a rating based on hardness, The material with the greatest value of hardness is given a rating of "1," while the softest is given a rating of "90" There is quite good agreement between the MDP rating and the hardness rating. Only in minor instances is there di.sagerenepat, It appears that the cavitation

TABLE 38 PRELIMINARY CORRELATION OF LEAD-BISMUTH DATA WITH MECHANICAL PROPERTIES DATA AT 1500~F UTS 0.2% YS ESE Hardness Final MDP Material Rating Ra Rating Rating Rating _ Total Rating Rating T-lll (P & W) 1 1 2 1 5 1 1 T-222(A) (P & W) 2 4 1 3 10 2 2 Mo-1/2Ti (P & W) 3 2 3 2 10 2 3 316 SS (U-M) 6 5 4 5 20 5 5 304 SS (U-M) 7 6 7 7 27 7 7 Cb-lZr (P & W) 4 3 6 4 17 4 4 Cb-lZr(A) (P & W) 5 7 5 6 23 6 6

-260TABLE 39 PRELIMINARY CORRELATION OF BEARING PROGRAM DATA WITH HARDNESS - -: P'.. - Hardness ESE Material: _ ___ Rating Hardness Rating Rating BG-42 (R 64) (TRW) 1 64 Rc(789*) 1 4 Blue Chip Tool Steel (TRW) 1 64 Rc(789*) 1 3 BG-42 (Rc =53) (TRW) 4 53 Rc(562*) 3 6 Single-Crystal Tungsten (U-M) 3 32 Rc(317*) 5 BG-42-(R = 47) (TRW) 5 47 R (471*) 4 5 Mo-1/2Ti (P & W) 6 7 R(295*) 6 1 Cb- Zr(A) (P & W) 7 81 Rf( 99*) 7 2 Graphitar-Grade 80 (U-M) 8 54 Rh(80*) 9 Graphitar-Grade 50 (U-M) 9 70 Rh( 100 ) 8 *DPH (1.1 Kgo Load) eAverage Shore Scleroscope Hardness.

-261res istance. of these materials correlates quite. well with hardness on- a qualitative basis.. Of course, hardness has been selected by many past investigators as the best measure off the ability of a material to resist. cavitation-erosion attack... A ranking according to engineering strain energy is also included in.Table 39. It is noted that this parameter is low for all the bearing materials as compared to conventional materials, although their cavitation resistance- is very high.: The graphitar-grade. 50 and' graphitar-grade 80 have average compressive strengths- of. 35,000 psi.and 20,000 psi, respectively. However, the grade 80 appears to be the most cavitation resistant of the two, despite having the lower compressive strength, and also the lower hardness. Obviously, a complete correlation of cavitation data with the applicable mechanical properties data demands full knowledge of the appropriate properties and a suitable digital computer program for analysis~. Those materials. tested in. the bearing program for whih complete mechanical properties data is available (all grades of BG-42 and Blue Chip Tool Steel) will be- included in the computer correlations to be described at. this time. C. Lead-Bismuth Correlations 1. General The cavitation data obtained at 500O~F and 1500'~F in leadbismuth alloy was all submittedt to the least mean squares regression program previously discussed in an attempt to obtain a ~first-olrder

-262interaction correlation that would be applicable at both temperatures and, hence, have the greatest generality allowed by the limited data. Ten mechanical and fluid properties were taken to be the independent variables with the average MDP rate being the dependent variableo The mechanical properties allowed in the analysis were the tensile strength, 71 yield strength, engineering strain energy, true strain energy (two values were considered, as explained before, one taking into account the 71 elongation of the test specimen, and the other the reduction in area), hardness, percentage elongation, percentage reduction in area, modulus of elasticity, and'ratio of the acoustic impedances of the test fluid 42 and specimen materialo These properties were selected since previous investigators had attempted correlations with them and/or because many of the properties have been involved in hypothesized damage mechanisms, as previously explained. 2o Single Property Correlations Initially, an attempt was made to correlate the damage data with each mechanical property individually in order to determine the relative importance of each alone with respect to predicting the observed cavitation damage. Table 40 summarizes the results of this effort. The 10 properties considered, the statistically best predicting equations generated by the program for each property, the coefficient of determination (CD) for the analysis, and the average absolute percent The coefficient of determination is a statistical quantity that can be interpreted as the proportion of the total variation in the dependent variable that is explained by the predicting equation~ Its values range from O (no prediction) to loO0 (perfect prediction)o

TABLE 40 SUMMARY OF SINGLE PROPERTY CORRELATIONS - EAD-BISMUTH ALLOY Property____. i, ________________Predicting Equation CD*_,____t AAPDt 1. True Strain Energy (TSER) (Based on Reduction in Area) Avg. MDP Rate 0.233 + 2.57x10 (TSER)Y 0.986 0.1 2. True Strain Energy (TSEE) (Based on Elongation) Avg. MDP Rate = 1.106 + 4.08x100(TSEEI3 0.964 13.8 3. Reduction in Area (RA) Avg. MDP Rate 0.937 + 2.89xlO5(RA)3 0.907 37.9 4. Engineering Strain Energy,(ESE) Avg. MDP Rate i 0.324 + 8.77x1011(ESE)3 0.878 5.7 5. Tensile Strength (TS) Avg. MDP Rate 0.675 + 7.41x1O(TS)3 0.847 2.4 6. Hiardness (H) (PH -1.1 Kg. Load) Avg. MDP Rate 0.451 +1.72x10 () 0.794 2.9 7.Yield Strength (YS) Avg.MDP Rate -4.139 + 2.14x102(YS)l13 0.632 28.3 8. Acoustic Impedance Ratio (Al) Avg. MDP Rate =-2.321 + 12.22(AI) 0.546 40.9 9. Elastic Modulus (E) Avg. MP Rate = -0.999 + 6.9 (E) 0.520 47.2 3 -3 10. Elongation (ELON) Avg. MDP Rate = 2.771 - 2.38x0l(ELON) 0.434 88.5 Coefficient of Determination. Average Absolute Deviation.

-264deviation (AAPD) for the analysis are noted. The predicting equations are arranged in order of decreasing statistical significance:based on the coefficient of determinationo It is seen that true strain energy based either on the reduction in area or elongation is quite successful as a single correlating parameter for all of the lead-bismuth data. The tensile strength, hardness, and engineering strain energy, although having much lower values of coefficient of determination, are also successful in this regard, based on the average absolute percent deviation. The other mechanical properties listed do not suitably account for the experimental data on an. individual basis. It is further noted that the average MDP rate is inversely.proportional to powers of true strain energy, engineering strain energy, tensile strength, and hardness in this analysis. Hence, one might conclude that the cavitation resistance of a group of materials in lead-bismuth alloy could at least be qualitatively predicted on the basis of these mechanical properties. 3o Multiple Property Correlations Further attempts at complete correlations of the experimental data were conducted in which all ten mechanical properties noted previously, each raised to any of ten integer or reciprocal integer exponents, were possible terms in the predicting equation. Hence, a total of 100-terms plus a pure constant were considered by the program, Table 41 summarizes the statistically best predicting equations obtained *The percent deviations between the experimental and predicted values of MDP rate are algebraically summed, oThe average algebraic per~cent deviation is then ee,^aslgebraic sum divided by the number of data pointso

-265TABLE 41 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - LEAD-BISMUTH ALLOY (1) Avg. MDP Rate = 0.713 + 3.12x104(TSER)-1 - 6.55x10O4(TS)1 + 2,97x1021(E)-3 Coefficient of Determination - 0.996 Average Absolute % Deviation - 0.4% (2) Avg. MDP Rate = 0.233 + 2o57x104(TSER)-I Coefficient of Determination = 0.986 Average Absolute % Deviation = 0.1% (3) Avg. MDP Rate = 0.682 + 3.24x101 (TSEE)-3 + I109x109(TS)-2 Coefficient of Determination 0 0.986 Average Absolute % Deviation - 0.8%

-266under these conditions. The coefficient of determination and average absolute percent deviation are noted for each of the correlations presented. Note that all three equations contain terms involving the true strain energy based either on elongation or reduction in areao The tensile strength is also prominent in two of the equationso These mechanical properties all enter the predicting equations in an inverse manner, as was the case with the single property correlationso The equation with the highest coefficient of determination involves a combination of true strain energy, tensile strength, and elastic modulus, each entering in an inverse relationship, In the analysis of the lead-bismuth data allowing all ten mechanical properties, the end result is a series of 15 predicting equations or correlations, each with a different statistical accuracy Obviously, the equation with the greatest statistical accuracy would result in the best fit between the predicted and experimental data. However, for the data submitted for analysis here, namely, the experimental cavitation information obtained at 5000F and 15000F in leadbismuth alloy and the corresponding mechanical properties, it was found that the coefficient of determination for all the correlations was never less than 0o98, indicating extremely good agreement between the predicting equation values and the experimental data. Figure 76 is a plot of the predicted values of average MDP rate based on Equation (1) in Table 41 versus the corresponding experimental points. Deviation from the 45~ line noted on the plot is a measure of.the-error inherent in the coprelationo The excellent agreement between the predicted values and experimental points is notedo

-26720 AVG. MDP RATE 1 K + K(TSER)- + K3(TS)- + K4(E)-3 COEFFICIENT OF DETERMINATION = 0.996 AVERAGE ABSOLUTE % DEVIATION 5 0.4% 15 nI0O W.. 04 ~~~~U7J ^^~~~~~~~~1788 O 2 3 4 5 10 14 EXPERIMENTAL MDP RATE, MILS/HOUR Fig. 76. —Comparison of Predicted MDP rate and experimental MDP rate - lead-bismuth alloy. MDP rate - lead-bismuth alloy.

-268Do Mercury Correlations 1o General The cavitation data obtained at 700F and 500~F in mercury was also submitted to the least mean squares regression program in an attempt to obtain a first-order interaction correlation that would be applicable at both temperatures. The independent variables were the same as those discussed previously-for the lead-bismuth correlations. 2. Single Property Correlations Initially, an attempt was made to correlate the damage data with each mechanical property individually. Table 42 summarizes the results of this efforto The ten properties considered, the statistically best predicting equation generated by the program for each property, the coefficient of determination for the analysis, and the average absolute percent deviation for the analysis are noted. The predicting equations are arranged in order of decreasing statistical significance based on the coefficient of determination. It is seen that true strain energy based on elongation and hardness are quite successful as single correlating parameters for all of the mercury data, although the best correlations are significantly worse statistically in terms of either coefficient of determination or percent deviation than those obtained with the lead-bismuth data. Tensile strength, yield strength, and *Note that true strain energy based on reduction in area was a more successful parameter in the lead-bismuth correlations but is quite unsuccessful for the mercury tests.:The reason for this disagreement is not knowno

TABLE 42 SUMMARY OF SINGLE PROPERTY CORRELATIONS -MERCURY..... -...: "''. i L "..' ].Z ~"~....' Property_".. _Predicting Equation CD* AAPD* 1. True Strain Energy (TSEE) (Based on Elongation) Avg. MDP Rate m 0.338 + 4.90x10 (TSEE) 0.965 8.5 2. Hardness (H) (DPH - 1.1 Kg. Load) Avg. MDP Rate 0.242 + 1.76x104(H)2 0.921 15.8 3. "Tensile Strength (TS) Avg MDP Rate -0.385 + 9.59x104(TS)-1 0,909 14.9 4. Yield Strength (YS) Avg. MDP Rate = 0.178 + 3.82x104(YS)"1 0.863 26.5 5. Elastic Modulus (E) Avg. MDP Rate 0.269 + 6.16x1021(E)3 0.831 18.5 6. True Strain Energy (TSER) (Based on Reduction in Area) Avg MDP Rate 0.657 + 1.40x1012(TSER) 0.824 35.1 7. Engineering Strain Energy (ESE) Avg. MDP Rate = -0.179 + 1.58x104(ESE)1 0.752 22.3 ~''a' + 4"91 (AI) 0.735 8. Acoustic Impedance Ratio (AI) Avg. MDP Rate -0.186 + 4.91(AI) 0.735 34.2 9. Reduction in Area (RA) Avg. MDP Rate -0.237 + 2.52x106(RA) 0.684 49.0 10. Elongation (ELON) Avg. MDP Rate = 1.091 - 1.96x10 (ELON)3 0.538 64.3 Coefficient of Determination. *Average Absolute % Deviation.

-270elastic modulus are somewhat less successful in this regard. The other mechanical properties listed do not suitably account for the experimental data on an individual basis. It is further noted that the average MDP rate is inversely proportional to some power of true strain energy, hardness, tensile strength, yield strength, and elastic modulus in this analysis. Hence, one might conclude that the cavitation resistance of a group of materials in mercury could at least be qualitatively predicted on the basis of these mechanical properties. 3. Multiple Property Correlations Complete correlations in which all ten mechanical properties were allowed to enter the predicting equation were also conducted with the mercury data. Table 43 summarizes the statistically best predicting equations obtained under these conditions, The coefficient of determination and average absolute percent deviation are noted for each of the correlations presented, Note that all three equations contain terms involving the true strain energy based on elongation, whereas, as previously mentioned, the true strain energy based on reduction in area was prominent in the lead-bismuth:correlationso The hardness and tensile strength are also prominent. All of these properties are inversely proportional to the average MDP'rate and, hence, proportional to cavitation resistance. The statistically best correlation includes the true strain energy based on elongation and the hardness, Figure 77 is a plot of the predicted values of average MDP rate based on Equation (1) in Table 43 versus the corresponding experimental data points. The excel.net.:agreement of the predicted values and experimental points is noted,

-271TABLE 43 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - MERCURY (1) - -.:. -. 3 Avg. MDP Rate = -0.577 + 1.39x1011(TSEE)-3 16.49(H)1/2 Coefficient of Determination = 0.966 Average Absolute % Deviation = 10.1% (2) Avg. MDP Rate = 0.338 + 4,90xl07(TSEE)'2 Coefficient of Determination = 0.965 Average Absolute % Deviation = 8.5%.(3) Avg. MDP Rate: 0.232 + 1.41x1011(TSEE))- + 2.89x104(TS)Coefficient of Determination = 0.961 Average Absolute % Deviation 13.1%

-2726.0 AVG. MDP RATE = K1 + K2(TSEE)-3 + K3(H) / COEFFICIENT OF DETERMINATION = 0.966 AVERAGE ABSOLUTE % DEVIATION = 10.1% 4.5 ~ 3.0 / t,_ In / CL I. 0.9 1789 1 I I. / I I 0 / 0.9-:: 0.3 0 0.3 0.6 0.9 1.2 1.5 2.1 3.0 3.6 4.2 EXPERIMENTAL MDP RATE, MILS/HOUR Fig. 77. —Comparison of predicted MDP rate and experimental MDP rate - mercury.

-273The materials tested in led-bismuth alloy,and mercury were i.dent ical with.the exception of the. carbon steel.nd Plexiglas which were tested in -mercury only. Single property correlations for each of the fluids indicate that a different form of true strainenergy is successful as a correlating parameter, each raised to a different exponent. Hardness and tensile strength are. also relatively successful in this regard for both fluids. Ten property correlations for each of the fluids.show that a form of strain energy and also tensile strength appear in the predicting equations- for each fluid. In general, it is seen for both fluids that mechanical properties that successfully correlate the experimental data individually are also prominent in the full ten property predicting equations, as expected. E. Water Correlations Subset One. General The cavitation data obtained at 70F in water was analyzed in a manner similar to that employed for the lead-bismuth and mercury data.. Since many more materials were tested in water than in the liquid metals, the materials were divided into three subsets for data analysis, as mentioned previously. Subset one consisted of those materials which were also tested i-n the liquid metals, -whereas subsets two and three were tested in water only. Separate correlations of the cavitation data in subset one, subsets two and three combined, and the full water data set were carried out, Hence, the effects of different fluids on the correlations can be determined by examining the individual correlations

-274for the lead-bismuth data, mercury data, and subset one of the water datao The materials tested in all three cases were identical. Further, by comparing the correlations of subset one and the full water data set and by examining the correlation of subsets two and three combined, it is possible to determine any significant differences that may exist fin correlating parameters for the various subsets of water data, 2. Single Property Correlations Subset one was first correlated in terms of single properties. Table 44 summarizes the results of this effort. The ten properties considered, the statistically best predicting equation generated by the program for each property, the coefficient of determination for the analysis, and the average absolute percent deviation for the analysis are notedo It is seen that tensile strength, hardness, and yield strength are successful as single correlating parameters for subset one, each appearing in an inverse relationship. Note the extremely low average absolute percent deviation obtained in the tensile strength correlationo The acoustic impedance ratio is partially successful in this regardo The single property correlations of lead-bismuth and mercury data also indicated that tensile strength and hardness were successful correlating parameters However, the prominence of some form of true strain energy in the lead-bismuth and mercury cases has been reduced considerably in the correlations of the subset one water data, It might also be noted here that the damage obtained in lead-bismuth alloy and mercury was very uniform, as noted previously, whereas the damage

TABLE 44 SUMMARY OF SINGLE PROPERTY CORRELATIONS - WATER - SUBSET ONE Property,..CD, AAPD** Property _ _ Predicting Equation _CD* AA 1. Tensile Strength (TS) Avg, MDP Rate - 0.006 + 8.38xlO3(TS) 1 0.953 0.2 2. Hardness (H) DPH - 1.1 Kg. Load) Avg. MDP Rate 0o.184 - 4.26x109(H)3 0.934 4.8 3. Yield Strength (YS) Avg. MDP Rate = 0.011 + 27.95(YS) 12 0.922 9.0 4. True Strain Energy (TSER) (Based on Reduction in Area) Avg. MDP Rate = 0.108 + 7.50x1017(TSER)3 0.901 15.6 2 5. Acoustic Impedance Ratio (AI) Avg. MDP Rate 0.038 + 54.55(AI) 0.897 10.8 6, Elongation (ELON) Avg. MDP Rate = 0.147 - 5.62(ELON) 2 0.865 17.3 7. True Strain Energy (TSEE) (Based on Elongation) Avg. MDP Rate = 0.115 + 1.26x1010(TSEE)3 0.860 16.8 8. Reduction in Area (RA) Avg. MD Rate = 0.087 + 7.13xl0'6(RA) 0.857 18.3 9. Elastic Modulus (E) Avg. MDP Rate = 0.041 + 1.80x106(E)-1 0.810 3.2 10. Engineering Strain Energy (ESE) Avg. MDP Rate = 0.089 + 4.21x102(ESE) 0.782 4.9 *Coefficient of Determination. **Average Absolute % Deviation.

-276obtained in water on the materials in subset one was somewhat more selective and was characterized by some individual, discrete craters. 3. Multiple Property Correlations Full ten property correlations of the subset one data are summarized in Table 45 where only the statistically best predicting equations obtained are listedo We note that each predicting equation involves only a single mechanical property, namely, tensile strength, hardness, and acoustic impedance ratio, each of which was successful in the single property correlations. In fact, the predicting equation involving the tensile strength is identical to that obtained in the single property analysis. Full ten property correlations of the lead-bismuth and mercury data also showed a strong dependence on tensile strength and hardness. Figure 78 is a plot of the predicted values of average MDP rate based on Equation (1) in Table 45 versus the corresponding experimental data points and serves to indicate the extent of agreement obtained. F. Water Correlations —Subsets Two and Three 1o Single Property Correlations The materials contained in subsets two and three (Plexiglas, aluminum, Cu, Cu-Ni, Cu-Zn, and Ni) were tested in water only. Single property correlations of the two subsets combined are summarized in Table 46. Hardness, reduction in area, and tensile strength are most suitable for correlation purposes, whereas the other properties listed are-less successful in this regard. Tensile strength and hardness were

-277-. TABLE 45 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - WATER - SUBSET ONE.,, I 1 1 1.. I' 11. r I I'. 3. (1) Avg. MDP Rate = 0.006 + 8.38x103(TS)-1 Coefficient of Determination'0.953 Average Absolute % Deviation =0.2% (2) Avg. MDP Rate = 1.83(H)/ Coefficient of Determination 0.904 Average Absolute % Deviation 14.9% (3) Avg. MDP Rate = 72.98(AI)2 Coefficient of Determination = 0.873 Average Absolute % Deviation = 28.9%

-278-.40 AVG. MDP RATE = K1 + K2(TS)1 COEFFICIENT OF DETERMINATION = 0.953 AVERAGE ABSOLUTE % DEVIATION " 0.2%.35.30 a: nr.25 O ^.20-..15 10:: 0^^.04.02.02y^/~~~~~~~~~ ~1790 I II. 1 0.02.04.10.15.20.28 EXPERIMENTAL MDP RATE, MILS/HOUR Fig. 78. —Comparison of predicted MDP rate and experimental MDP rate - water - subset one.

TABLE 46 SUMMARY OF SINGLE PROPERTY CORRELATIONS - WATER - SUBSETS TWO AND THREE PropertyV g Eg Predicting Eq u ation CDA 1. Hardness (H) Avg. MDP Rate 1,038- 3.96x104lO(H)3 (DPH - I.1 Kg. Load) -1.02x10 (H) + 5.35x10(H) 0.966 6.1 2. Iduction in Area (RA) Avg. MDP Rate 1.3r a3 +4.54x106(RA)3 - 0.1 18(RA)^.0.950 8.0 3. "Tnsile Strength (TS) Avg. MDP Rate = -0.413 + 2.50x110(TS1/2 0.910 5.4 4. Acoustic Impedance Ratio (AI) Avg.MD Rate = 1.505- 3.31x102(AI)"1 0.794 15,4 5. Elastic Modulus (E) Avg. MDP Rate.-0.021 - 1.89x106(E) 1 + 3,83x103(E)K12 0.775 19.5 6. Yield Strength (YS) Avg. MDP Rate 0.198+15.80(Y 13 0.768 17.6 7. True Strain Energy(TSER) (Based on Reduction in Area) Avg. MDP Rate 1.031 - 1.80x1010(TSER) 0.737 21.2 8. True Strain Energy (TSEE) (Based on Elongation) Avg. MDP Rate ~ 0.447 + 6.91(TSEE)1'3 0.737 21.9 9.Engineering Strain Energy (ESE) Avg. MDP Rate 0.641 + 13.80(ES)12 0.731 22.4 10. Elongation (ELON) Avg.M3PPRate 0.723 + 3.86x10O (ELON) 0.709 24.7 *Coefficient of Determination. Average Absolute % Deviation.

-280also successful in the subset one single property correlations, as well as in the corresponding lead-bismuth and mercury analyses, although they did not appear in the same functional relation for the different cases. Note that for water. subsets. two and three the correlation with any of the forms of strain energy is very pooro 2. Multiple Property Correlations Full ten. property correlations of subsets two and three combined are presented in Table. 47. All three expressions listed have very high coefficients of determination and very low average absolute percent deviations, indicating excellent agreement between the experimental and predicted values. Hardness, tensile strength, and yield strength are prominent in these expressions. As.noted previously, hardness and tensile strength were also successful as single correlating parameters. Hence, it appears that tensile strength and hardness are the most successful correlating parameters both for the subset one'water data and also the combined data in subsets two -and three. Figure 79 is a plot of predicted values of average MDP rate based on Equation (1) in Table 47 versus the corresponding experimental data points and serves to indicate the extent of agreement obtained. In this case the agreement is excellent. Go Water Correlations-'All Water Data C. 1. Single Property Correlations' Finally, the complete set of water data was subjected to the regression analysis.:The sipgle property correlations'are summarized in

-281- TABLE 47 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - WATER - SUBSETS TWO AND THREE () Avg. MDP Rate = 0.392 - 12.0(YS)-1/3 - 3.82x107(TSEE)3 + 3.61xlO (TS) Coefficient of Determination = 0.991 Average Absolute %Deviation = 2.7% (2) Avg. MDP Rate - -0.822 + 6.22xlO2(TS)1/2 11.45(H)12 Coefficient of Determination = 0.985 Average Absolute % Deviation = 1.1%.(3) Avg. MDP Rate -0.163 - 3.41x103(YS)1 + 3.62x104(TS)- 1 Coefficient of Determination = 0.984 Average Absolute % Deviation = 3 -1

-2824.0 AVG. MDP RATE =K K + K(YS) 1/3 + K3(TSEE)3 + K4(TS)-1 COEFFICIENT OF DETERMINATION = 0.991 AVERAGE ABSOLUTE % DEVIATION - 2.7% 3.0 IU) -J LJ 2.0 0- I'..../ 0 _'.5 -08 0.8 A 0.4 0.2 / 1791 I I, I, I, I.... 0.2 0.4 1.0 1.5 2.0 2.8 EXPERIMENTAL MDP RATE, MILS/HOUR Fig. 79. —Comparison of predicted MDP rate and experimental MDP rate - water - subsets two and three.

-283Table 48. It is seen that the hardness, tensile strength, and yielt strength are the mos.t successful as. correlating.parametersiamong the ten properties, as expected. However, only hardness is reasonably successful from a statistical point of view, and then only with a 5 term relation. For the other properties, variations between experimental and predicted values are 40% and greater. This points up the general conclusion that precise correlations between the conventional mechanical properties and large varied sets of cavitation damage data do not apparently exist. 2. Multiple Property Correlations The statistically.best ten property correlations' of the water data are summarized in Table 49. Only Equation (1),: involving a combination of tensile strength,. hardness, and.: reduction in area,: satisfactorily predicts the experimental data. Figure 80 is a plot of the predicted values of average MDP rate based on Equation:(l)- in Table 49 versus the corresponding experimental data points and indicates the extent of agreement obtained.: 3. Summary In summary, it is seen: that the mechanical properties of hardness, tensile strength, and yield strength adequately predict the experimental water data on a single property basis. This is true either for subset one, subs:ets two and -three combined, or the full water data set. In addition, the elastic modulus is successful as a single correlating paramet:er for subset one.. T-hese same properties are the most prominent in the ten pr erty water correlations. However, for all

TABLE 48 SUMMARY OF SINGLE PROPERTY CORRELATIONS - ALL WATER DATA' Property Predicting Equation CD* AAPD** 1. Hardness (H) Avg. MDP Rate = -023 + 1.30x104 ()2 (DPH - 1.1 Kg. Load) +53.63(H) 6.17x102(H) - 8.00x104((H)3 0.946 18.7 2. Tensile Strength (TS) Avg. MDP Rate = -0.619 + 2.69x102(TS) 1/2 0.851 40.7 3. Yield Strength (YS) Avg. MDP Rate =-0.193 + 22.4(YS) -/3 0.708 62.1 4,.-*~ ~ ~ ~ ~ ~ - ~~ -2,A' 0.0 1 4. Acoustic Impedance Ratio (AI) Avg. MDP Rate = 1.491 -3.99xO1 (AI) 0.708 70.8''4.2.. 5. Elastic Modulus (E) Avg.MDPRate 1.832 -2.79x10 (E) 0.695 62.5 6. True Strain Energy (TSEE) 1/ (Based on Elongation) Avg. MDP Rate = 0.053+ 10.70(TSEE) 0.627 92.6 7. Engineering Strain Energy (ESE) Avg. MDP Rate = 0.084 + 10.39(ESE)1/3 0.624 91.2 8. True Strain Energy (TSER) (Based on Reduction in Area) Avg. MDP Rate = 0.295 +7.95(TSER)-1 0.587 110.9 9. Reduction in Area (RA) Avg. MDP Rate = 0.829 - 1.51(RA)-1/ 0.549 124.6 A~~~~~~~~' ~.. 12.. 10. Elongation (ELON) Avg. MDP Rate = 0.557 + 3.28(ELON)2 0.538 120.9 Coefficient of Determination. *Average Absolute % Deviation.

-285TABLE 49 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - ALL WATER DATA (1) Avg. MDP Rate = -0.068 + 3.07x108(TS)-2 - 8.32x10-7(RA)3 - 2.03xlO(H)3- + 1.49x102(TS)1/2 Coefficient of Determination = 0.976 Average Absolute % Deviation = 0.5% (2) Avg. MDP Rate =-2.224 + 19.93(H)-/3 2.22x10(YS)-1/2 Coefficient of Determination 0.864 Average Absolute % Deviation = 28.5% (3) Avg.MDP Rate = -0.619 + 2o69x02(TS)1/2 Coefficient of Determination = 0.851 Average Absolute % Deviation = 40.7%

-2864.0 AVG. MDP RATE = K1 + K2(TS)2 + K (RA) +K4 (H) + K (TS)-1/2 COEFFICIENT OF DETERMINATION - 0.976 AVERAGE ABSOLUTE %DEVIATION = 0.5% 3.0 QL I 2.0 cr m 1.5 1.0 CL i,.4 -.2 6 0 1792 0.2.4 1.0 1.5 2.0 2.8 EXPEf1MENTAL MDP RATE, MILS/HOUR Fig. 80. —Comparison of predicted MDP rate and experimental M)P rate - all water data.

-287case:s different functional forms. of- the properties- are required for good correlation. In: the case of lead-bismuth,. tensile strength and hardness were a-lso success.fu as sing prop., also.successful as -single.. property correlating parameters, but the true strain energy was more successful in_ this respect. A similar comment applies to the single. property mercury correlations. In general, it. is concluded that those properties most successfu: as single correlating parameters.in. a given. fluid are the most prominent in the ten property correlations, as one would expect. H... Lithium Correlations at. 500.~F 1.- S'ingle..Property Correlations As a first step in -the analysis, an attempt was. made to correlate the.damage data obtained at 500.F with each mechanical property individually to determine the relative importance of each alone with respect to predicting. the observed cavitation damageo. Table 50 summarizes the results of this effort. The ten properties considered, the statistically best predicting equations generated by the program for each property, the coefficient of determination (CD) for the analysis, and the average absolute percent deviation (AAPD) for the analysis are noted.. The predicting equations are. arranged in order of decreasing statistical significance based on the coefficient of determination. It is seen. that the elongation, yield strength, true strain energy based on reduction in area (TSER), hardness, and tensile strength are quite successful as single correlating parameters. The other mechanical

TABLE 50 SUMMARY OF SINGLE PROPZRTY CORRELATIONS - LITHIUM AT 5000F Property.. __ Predicting Equation CD AAPD 1. Elongation (ELON) Avg. MDP Rate = 0.409 - 2.91xlO 3(ELON)2 +9.34x10 5(ELON)3 0.992 14.1 2 1 Yield Strength (YS) Avg. MDP Rate -0.899 + 43.40(YS)1 0.959 3.2 3 True Strain Energy (TSER) (Based on Reduction in Area) Avg. MDP Rate -0.494+ 1.32xl(TSER) 0.929 31.7 4. Hardness (H) (DPH - 1.1 Kg. Load) Avg. MDP Rate ~0.114 + 3.17x105(H)"3 0.924 37.3 I 00 5. Tensile Strength (TS) Avg. MDP Rate 0.143 + 1.34x1013(TS)3 0.920 40.3 6. True Strain Energy (TSEE) (Based on Elongation) Avg. MDP Rate - 0.129 + 4.17x1010(TSEE)3 0.839 44.2 7. Acoustic Impedance Ratio (Al) Avg, MDP Rate = 0.028 - 6.36x102 (AI)2 0.705 33.1 8. Elastic Modulus (E) Avg. MDP Rate = 0.035 + 1.139x1014(E)2 0.647 73.9 9. Reduction in Area (BA) Avg. MDP Rate = -0.244 + 1.OlxlO0(RA)3 0.612 25.1 10. Engineering Strain Energy (ESE) Avg. MDP Rate = 0.055 + 2.74x10(ESE)- 0.520 87.3 Coefficient of Determination. Average Absolute %Deviation.

-289 - properties listed do not suitably account for the experimental data on an individual basis. Surprisingly, the worst correlation among the ten properties, in terms of either coefficient of determination or average absolute percent deviation, is attained with the engineering strain energy. It is further noted that. the average MDP rate is inversely proportional to powers of yield strengtlh, true strain energy based on reduction in area, hardness, and tensile strength. The dependence of average MDP rate on elongation is no.t as easily determined, since two terms in the predicting equation are functions of elongation, each contributing to the average MDP rate in an, opposite manner. One might conelude that the cavitation resistance of a group of materials in lithium at 5000iF could at least be qualitatively predicted on the basis of these five mechanical propertieso.. 2. MulJltiple Property Correlations Further attempts at complete: correlations of the experimental data were conducted in which all ten mechanical properties noted previously, each raised to ten exponents, were possible terms in the predicting. equation. Hence, a total -of' 100 terms plus' a pure constant were considered by the program o Table 51 summarizes the statistically best predicting equations obtained under these conditions, The coefficient of determination and average absolute percent deviation are noted for each of the correlations presented. Note that each equation contains only one mechanical property. In fact, the equations containing the. yield strength and tie Hardness are identical to those obtained in

-290TABLE 51 SUMMARY OF BEST CORRELATIONS WITH TEN PROPERTIES CONSIDERED - LITHIUM AT 500 ~F: -..(1 ~.~" -- ~' ~'- ^:''~ A:i''~ - ~-~:, -I'.~ "... (1) Avg. MDP Rater — 0.899 + 43.40(YS)1/3 Coefficient of Determination 0.959 Average Absolute % Deviation = 3.2% (2).. Avg. MDP Rate = -0.039 + 8.21x1O3(TSER)"1 Coefficient of Determination 0.928 Average Absolute % Deviation = 40,6% 5 -:. -... Avg. MDP Rate 0.114 + 3.17xlO1 (H)'3 Coefficient of Determination: 0.924 Average Absolute % Deviation = 37.3% ~ ~ ~.I I ).''. I.. ~.i!t.''i ~ i~ ~' i.''. i... i'

-291the single property correlations. The true strain energy based on reduction in area enters to the power (-1) in the ten property correlations, while it was present to the power (-1/2) in the single property correlations, However, a comparison between Tables 50 and 51 shows that the correlation to the (-1/2) power was slightly better. The selection of correlating equations which are less suitable than others available is a result of the random selection of the variables by the computer program and the fact that only a small number of random selections were possible within a feasible limitation on machine time~ Of course, the mechanical properties involved in the ten property correlations are those that were also quite successful in predicting cavitation damage individually, as expected. J. Lithium Correlations at 1500~F Although there are only four experimental points available in lithium at 1500 F, both single and multiple property correlations were carried out on this small body of data. In all of the single property correlations and the multiple property correlations, the same predicting equation was generated by the computer program, namely: Avg. MDP Rate 0 0.0225 Coefficient of Determination = 0.880 Average Absolute Percent Deviation = 21.9% Thus the predicting equation consisted of only a constant term in all cases. This is a direct result of the lack of a suitable number of data points for a correlation,

— 292K. Correlationsof all Lithium Data' The combined lithium data obtained at 5009F and 1500~F was also submitted to the least mean squares regression analysis. One would not expect particularly good predicting equations in this case since only mechanical properties are allowed as independent variables. In fact, it is questionable if a suitable correlation could be obtained even if such fluid properties as the density, surface tension, net positive suction head, bulk modulus, and kinematic viscosity were introduced as independent variables. Thermodynamic effects are apparently quite important in lithium at 1500~F. Hence, a suitable correlation must involve fluid properties of lithium such as specific heat, thermal conductivity, heat of vaporization, thermal diffusivity, Prandt Number, and vapor pressure. The results of such a study will be presented later. Nevertheless, single property correlations and full ten property correlations of the combined lithium data as a function of mechanical properties only were investigated. It was found in both cases that no suitable predicting equations existed for the combined data, as expected. L. Summary of Single.Fluid Correlations Thus far, the only property included in the regression analysis that is a function of the fluid has been the ratio of acoustic impedances of the. test fluid and specimen, material.. This, quantity.did not: successfully correlate the lead-bismuth, mercury, or lithium data and. did:-not appear in the ten prQperty correlations, In the case of the

-293water data the acoustic impedance ratio was more successful as a correlating parameter. It is noted at this point that whereas energy properties were quite important in the correlation of the data from the tests with high density liquid metals (lead-bismuth alloy and mercury), they are much less significant in the water and lithium tests. On the other hand, the strength properties (including hardness in this category) are predominant in the water and lithium tests, The same observations apply to the venturi tests, although the role of energy terms was not as great for the liquid metal (mercury) venturi tests as for the vibratory liquid 22 metal tests. Theoretical arguments have been advanced in the past to show 58 that a correlation would involve both energy and strength terms. This argument is reinforced by consideration of the limiting case of a very strong but brittle material, As a hypothetical example, suppose a cavitating flow regime with such a material where the implosions were not capable of imposing stresses on the surface in excess of the "fatigue strength." Then no damage would result, even though the strain energy were very low as it often is for such materials, Data obtained with tool steels and stellite are consistent with this viewpoint. It would be expected that this limiting condition would apply more closely to the water and lithium tests (relatively low density fluids) than to the heavy liquid metal tests, since the stresses imposed are probably roughly proportional to fluid density. Thus this argument is consistent with the present experimental data obtained with these different fluids.

-294M. Comprehensive Correlations of Lead-Bismuth, Mercury, Water, and Lithium Data 1o General The major objective of the computer analyses described thus far is to deduce a single comprehensive predicting equation that would suitably explain the lead-bismuth, mercury, water, and lithium data. Such an-equation would, of necessity, include at least one fluid coupling parameter to account for the variations in fluid properties for the four fluids considered and the corresponding test temperatures, since it has already been shown that the cavitation resistance of all the materials tested, and their relative rankings, depend on the fluid. The combined lead-bismuth, mercury, water, and lithium data was submitted to the regression program in an attempt to arrive at the required correlation of all experimental data in terms of mechanical and fluid properties, The mechanical properties allowed in these correlations were the same as previously employed: tensile strength, yield strength, engi. neering strain energy, true strain energy (two values based on elongation and reduction in area), hardness, elongation, reduction in area, and elastic modulus. In addition, each of the six fluid coupling parameters discussed previously, namely, acoustic impedance ratio, density, surface tension, net positive suction head, bulk modulus, and kinematic viscosity, was combined separately with the group of nine mechanical properties. Hence, six comprehensive correlations were attempted, allowing a total of nine mechanical and one fluid property in each. It _was. hoped that such a procedure would indicate those fluid properties

-295that were most successful as coupling parameters. The values of the fluid coupling parameters used in these correlations were listed previously in Table 36. In addition, all of the cavitation data obtained in leadbismuth, mercury, water, and lithium was correlated in terms of five mechanical properties and five fluid properties. The five mechanical properties chosen for this purpose were the tensile strength, true strain energy based on elongation, true strain energy based on reduction in area, elastic modulus, and hardness. The fluid properties included were the ratio of acoustic impedances of the test fluid and specimen material, fluid density, surface tension, bulk modulus, and kinematic viscosity. Such a correlation indicated those fluid properties which were most successful as coupling parameters. 2. Single Fluid Property Studies A summary of the results of the six comprehensive correlations (lead-bismuth, mercury, water, and lithium) involving nine mechanical properties and one fluid property follows. 1) Acoustic Impedance Ratio (AI) When the acoustic impedance ratio is used as the fluid coupling parameter and combined with the nine mechanical properties allowed to enter the predicting equation, the statistically best correlation obtained is~ Avgo MDP Rate = 8.97 - 3.10x102(TSER) 1/3 + 450x104lO(TSER)1 0o159(TSER) 1/3 - l20x10 (TSEE)-1/2 + 1/o37 12 (ESE)-1/2 + 1,71(AI)^ - 7.40x10 (ESE)

-296- 3o49xi09(TSER) -3 + 322x102(TS)1/2 + 8.88x103(TSEE)'+ 2.32x10(ESE)1/3 Coefficient of Determination 0 0.980 Average Absolute % Deviation = 2.7% Although the equation may appear formidable at first glance, it should be noted that 8 of the 11 terms present involve some form of the strain energy. If the allowable exponents were not restricted to positive and negative integers and their reciprocals, the many strain energy terms, of which all three types are included, could undoubtedly be combined and reduced considerably. The appearance of the tensile strength in an inverse relationship is not surprising since it was successful as a single correlating parameter in each of the four fluids. Th' acoustic impedance ratio is also included, and it is noted that the damage rate increases as the acoustic impedance ratio increases, as postulated in Chapter V, section Bo One might conclude that the acoustic impedance ratio is successful as a fluid coupling parameter in these experiments. 2) Density ( ) The density was next combined with the other nine mechanical properties allowed to enter the predicting equation, and the statistically best correlation obtained is: Avg, MDP Rate = 2.44 - 1062(P )1/3 + 4.82x102(E)1/3 + 2o07x103(TSEE) 1 - l99xl013(E)-2 + 4.26x104(TSER)- - 7 35x102(H) 1/2 - 5.48xlO2(TSER)-1/2 + 236x108(TS)-2

-297Coefficient of Determination.= 0969 Average Absolute % Deviation 907% Three of the terms present in the equation involve the true strain energy and two terms are functions of the elastic modulus' The tensile strength and hardness are also present, each indicating that a decrease in damage rate would be expected with increasing tensile strength or hardness. The density also appears as the fluid coupling parameter; and despite the negative exponent, increasing density would result in increased damage, since the coefficient of the term is negative This is consistent with the observations in our own laboratory, 921,22,58 both in the venturi212258 and vibratory facilities, and has, of 81 course, been postulated by other investigators, as well as being theoretically anticipated through consideration of bubble dynamics or jet impingement equations, However, there is another density effect as will be developed later, in its effect upon NPSH, which in turn affects the configuration of the cavitation flow fieldo The fact that density enters to the (-1/3) power is interesting, since yield strength has also been often involved to this power (Tables 40, 46, 47, 48, 50, and 51) According to the simplest bubble collapse or jet impingement calculations, the stress imposed upon the surface is proportional to the density and, hence, it would not be surprising if strength and density entered all relations for volume loss in the same way, Assuming this proportionality between density and stress, it then would follow that volume removed is very roughly of course inversely related to the cube root of imposed stress0

-2983) Surface Tension (') In a similar manner the surface tension was investigated as a possible fluid coupling parameter, and the statistically best predicting equation is: Avrg MDP Rate 0.982 - 6.38(RA)L3 + 2.50x106 (-)2 -1/2 4 -l - 1.28(ELON)-1 + 2.36x10 (TSER) + 4.53x10(ESE)- + 14.87(TSEE) 1/3 13 -2 -1.28x013(E) 2 Coefficient of Determination = 0.923 Average Absolute % Deviation =. 2.4% Again, three of the terms involve various forms of the strain energy. The surface tension enters with an exponent of 2, whereas in the previous relations the acoustic impedance ratio and density were each raised to the 1/3 power. The correlation indicates that increasing surface tension results in increased damage. This was reported by 32 Nowotny as a result of his experiments, although his relation between MDP rate and surface tension is nearly linear, rather than squared. However, no variation of MDP rate with surface tension is predicted by numerical analyses of bubble collapse. However, the simplified models used may in some way neglect the mechanism here involved. 4) Net Positive Suction Head (NPSH) Since the local pressure was varied in our experiments so as to maintain the difference between local pressure and vapor pressure constant, the static net positive suction head is inversely proportional ^ A.@

-299to the density, but the dynamic NPSH applied by the horn is more closely constant, as already discussed. The correlation was.carried out using the static NPSH values, and the statistically best predicting equation obtained is: Avg. MDP Rate - -1.17x102 + 5.60x10"3(E)12 + 1.l0xlo (TSEE)'2' 3.68x102 (RA) +.88x10(TSER) + 5.81xl04(E) 3+ 2.-76xl0(TS) -2.48x10 (NPSH) -45.21TSEE)' - 5.12xl2(TSER) 1/-3 5.17x105(E)-/2 i 5,2x 0... TSE Coefficient of Determination 0..962 Average Absolute % Deviation 5 5.0% Two terms are functions of each of the forms of true strain energy used, while three additional terms involve the elastic modulus. The tensile strength appears in an inverse relationship, as expected, and the net positive suction head is present in a linear manner, but with negative coefficient. Hence, increasing net positive suction head results in:a decrease in cavitation damage. However, this probably is merely the same effect as that previously discussed in relation to density, since these tests were conducted so that NPSH is always ( 1/. 5) Bulk Modulus (B) The statistically best predicting equation obtained when bulk modulus is introduced as the fluid coupling parameter is: Avg. MDP Rate = 0.665 - 1.66xlO (TS)- 2 - 2.59x1016(B)3 4+ 5o:x.16(TSEE) 2 + -113x104(H) 2

-3006 7 -2 5 -3 + 3.49x1l0 (TS-ER). 4. 53xl05 (H) +.99x1013(TS) 3 + 9.02xl06(E) Coefficient of Determination = 0.-975 Average Absolute. % Deviation = 5.1% The true strain energy, hardness, and tensile strength are each entered in the equation twice, while the bulk modulus is present with both a negative exponent and negative coefficient. Hence, as the bulk modulus is increased (compressibility decreased), the damage would 82,83 increase, as expected theoretically, and as often observed in field practice where damaging cavitation with petroleum pumps is virtually unknown as compared to water pumps. This trend has also been reported 81 in a previous laboratory investigation using a vibratory facility. 6) Kinematic Viscosity () ) The final fluid coupling parameter investigated was the kinematic viscosity, V. The statistically best predicting equation obtained in this case was: Avg. MDP Rate= - 0.294 + 6.91x102(E)-1/3 -1.-30xlO2(TSER)-1/3 + 3.13x-104(H) -3+ 25.40(TSEE)/3 + 3.76x104(TSER) -1 5.95x10-3(RA)1/2 - 6.30x102( ))2 + 0.243(ELON)1/3 - 2.54x1 O1(E) -2 + 2.04x105 (9) Coefficient of Determination. =-0.963 Average Absolute % Deviation. = Z.2% The true strain ene2gy is involved in three terms while the elastic modulus appears in two.'The hardness is also prominent in a

-301strong. inverse relationship. The kinematic viscosity, 9, appears in two terms, such that increasing kinematic viscosity results in a decrease in cavitation damage, as postulated. A summary of the statistics applicable to the six comprehensive damage correlations discussed above are presented in Table 52. The fluid coupling parameters considered ar-e listed in an order determined by the coefficient of determination of the corresponding predicting equation. It is seen. that the acoustic impedance ratio results in the predicting equation with highest coefficient of determination. However, all fluid properties considered as coupling parameters were quite successful iin this regard.It should be emphasized that the acoustic impedance ratio involves both the density and bulk modulus of the fluid, and, hence, to some extent may also cover effects normally ascribed to mechanisms associated with these properties. All predicting equations had..a value of coefficient of determination greater than. 0.960, except when the surface tension was employed as the coupling parameter. In addition, the average absolute percent deviation was less than 10% in all cases. As a result,.it is difficult to make any recommendations as to an optimum fluid coupling parameter. All fluid properties considered in this study seem to be successful, and this is not surprising when it is considered that for a liquid the fluid properties can all be expressed as smooth functions of temperature alone and, hence, are smooth functions of each other. The resulting predicting equations show a strong dependence on strain energy, hardness, tensile strength, and'elastic modulus. In fa, he six predicting equations described above

-302TABLE 52 SUMMARY OF STATISTICS FOR COMPREHENSIVE DAMAGE CORRELATIONS (SINGLE FLUID PROPERTY) Fluid Coupling Parameter CD* - AAPD* 1. Acoustic Impedance Ratio (AI) 0 980 2.7 2. Bulk Modulus (B) 0.975 5.1 3. Density (?) 0.969 9.7 4. Kinematic Viscosity (y) 0.963 2.2 5. Net Positive Suction Head (NPSH) 0.962 5.0 6. Surface Tension (CO) 0.923 2.4 Coefficient of Determination. *Average Absolute % Deviation.

-303contained terms involving some form of strain energy 23 times (TSER-12, TSEE-8, and ESE-3), elastic modulus 9 times, tensile strength 5 times, hardness 4 times, reduction in area 3 times, and elongation 2 times. Of course, a coupling parameter was present in each equation, although it was by no means forced into the equation, since the program uses a repeated choice and then testing for suitability of the selected terms. It will be recalled that strain energy, tensile strength, and hardness were the most successful properties in the single property correlations of lead-bismuth, mercury, water, and lithium separately (elongation and yield strength were also successful in the lithium correlations). These mechanical properties along with the elastic modulus are also the most prominent in the comprehensive lead-bismuth, mercury, water, and lithium correlations. The fact that all the forms of strain energy are sometimes involved and that their relative involvement depends on fluid, temperature, material, etc., may indicate that different modes of material failure are involved, depending upon the various test parameters, since it would be expected that:TSER would most closely represent resistance to ductile failure, while TSEE or ESE would be most closely involved with brittle failure. Figure 81 is a plot of the predicted values of average MDP rate, computed using the comprehensive predicting equation with acoustic impedance ratio as the coupling parameter, versus the corresponding experimental data points, and indicates the extent of agreement afforded by this analysis.

-30420 AVG. MDP RATE = K1 + K2(TSER)/3 +K3 (TSER) + K4(TSER)1/3 + K5(TSEE)-/2 + K6(AI)/3 + K (ESE)-/2 + K (TSER)3 + K (TS)-1/2 + K (TSEE)1 + Kl (ESE)1/3 COEFFICIENT OF DETERMINATION = 0.980 AVERAGE ABSOLUTE % DEVIATION = 2.7% 15 1 - U) 2101793'' 2:3 4 4 10 14 EXPERIMENTAL MDP RATE, MILS/HOUR QL CL5 0o 2 3 4 5 10 14 EXPERIMENTAL MDP RATE,MILS/HOUR Fig. 81. —Cotparison of predicted MDP rate and experimental MDP rate - all lead-bismuth, mercury, water, and lithium data (acoustic impedance ratio is the fluid coupling parameter).

-3053 Multiple Fluid Property Studies The previous comprehensive computer correlations have shown that all of the fluid properties considered as coupling parameters were quite successful when considered individually. In order to better determine the most significant fluid coupling parameters for our correlations, five such properties were included in a comprehensive correlation of all the cavitation data The fluid properties considered were the ratio of acoustic impedances of the test fluid and specimen material, fluid density, surface tension, bulk modulus, and kinematic viscosity. The number of mechanical properties was reduced to five for.this study and included the tensile strength, true strain energy based on elongation, true strain energy based on reduction in area, elastic modulus, and hardness. Under these conditions the statistically best correlation obtained is.. Avg, MDP Rate — 2.32 1.74(C ) -4.86x105(TSER)~2: +40 60(TSEE) -1/3 + 5.42x102(TS)-1/2 + 4.25xlO (AI) Coefficient of Determination = 0.711 Average Absolute % Deviation-= 49..5% It is seen that both the density and the ratio of acoustic impedances appear in the predicting equation. The degree of statistical fit afforded by this equation is not nearly as good as that obtained in the previous comprehensive correlations. In the 15 correlations obtained when one allows five mechanical and five fluid propertie tQ enter the predicting equation, it was found

-306that the fluid density and bulk modulus appeared in these equations seven times each, while the ratio of acoustic impedances and the kinematic viscosity each appeared two times. The surface tension did not appear in any of the correlations, and this is consistent with theoretical expectations, as previously discussed. If this analysis is carried out after omitting the 4 data points obtained in lithium at 1500~F (these points are obviously influenced by thermodynamic effects), then under these conditions the statistically best correlation obtained is: Avg. MDP Rate - 10.45- 2.82x102(TSER)-/3 O.ll(TSER)1/ 3 4 -l 1/3 -1 *+ 5.13x10 (TSER) + 2.98(AI) + 54.68(H) - 3.95x109(TSER)- - 3.38xlO 2.(TSEE) 1/3 3.23'10 4(B)/2 Coefficient of Determination = 0.965 Average Absolute; % Deviation = 1.1% It is seen that the bulk modulus enters the predicting equation as the fluid coupling parameter. This equation is far superior statistically to that obtained above when the lithium data at 1500~F was retained in the full data set. 4o Second-Order Interaction Correlation As previously mentioned, the least mean squares regression computer program used for these studies includes the option of a secondorder interaction correlation, i.e., cross-products of the independent variables are allowed to appear in the predicting equation. This, of course, increases greatly-the number of possible terms that may appear

-307in the predicting, equation as compared to a first-order interaction: correlation involving the same me chanical: and fluid properties. Inn this preliminary study the five mechanical and five fluid properties previously employed in the multiple fluid property correlations were retained for the second-order interaction study. Clearly, large amounts of computer time will be necessary if one is to complete a detailed analysis of the cavitation data under these conditions. The preliminary correlations, consuming considerable computer time, did not indicate any particular combinations or products of independent variables appearing consistently in the many predicting equations generated in this study. 5. Hobbs' Energy Concepts Hobbs' proof resilience and ultimate resilience concepts were previously discussed. In order to determine if either would be prominent in explaining our own cavitation data) a comprehensive correlation was carried out in which all the mechanical properties previously mentioned.were allowed to appear in the predicting equation with the exception of the engineering strain energy (ESE) which was replaced first by Hobbs' proof resilience (PR) and then by Hobbs' ultimate re silience. (UR) In. both cases the fluid density was also included as the fluid coupling parameter..as. this fluid property had been very prominent in the multiple fluid property correlations..Under these conditions it was found that Hobbs' proof resilience did not appear in any of the correlations generated in the study. However, Hobbs' ultimate resilience wasvery successful as a correlating parameter as it appearedn every equation generated. The

-308statistically best correlation obtained in this case was: Avg. MDP Rate -=0.510 + 6.045(UR) /2 -0.47l(P)2 Coefficient of Determination = 0.658' Average Absolute % Deviation = 54.5% Although it is not statistically impressive, the equation is very compact and involves only one mechanical property and one fluid property. Further, it is seen that damage decreases with increasing ultimate energy, and increases with increasing density, as expected. When the data obtained at 1500~F in lithium is removed from the total data set because of the thermodynamic effects previously mentioned, Hobbs' proof resilience still did not appear in any of the predicting equations generated by the program. However, in the analysis involving Hobbs' ultimate resilience without the 1500~F lithium data, the statistically best correlation obtained in this case was: Avg. MDP Rate = 0.193 + 8.243(UR) 12 0.536( ) Coefficient of Determination = 0.762 Average Absolute.% Deviation = 26_7% It is seen that the dependence on density has been reduced from an exponent of (-2) to (-1). The coefficient of determination has been increased considerably and the average absolute percent deviation has been significantly reduced. The equation is of a very simple form in that only two properties are involved, one material and one fluid property.) The dependence on ultimate resilience is the same regardless of the inclusion or exclusf^n'of the 1500~F lithium data. Note also that

-309the coefficients of the terms involving the ultimate resilience and the density are not much different in the two cases. Such a simple equation as this, suitably accounting for the complete body of cavitation data (with the exception of the 1500~F lithium data), would be of value to the designer of components susceptible to cavitation damage. N Comparison with Veturi Facility Correlations 22 Previously, computer correlations of cavitation damage data generated in this laboratory's mercury and water venturi facilities were carried out and reported. It was found that no good correlation existed between any single mechanical property and the cavitation damage in the mercury tests. However, true breaking stress exhibits the best fit. The ten property correlation of the mercury data showed that a combination of true breaking stress and tensile strength was significant. In the case of the corresponding ultrasonic investigations described above, true strain energy (based on elongation), hardness, and tensile strength were successful in the single property correlations. These same properties dominated the ten property correlations. In the single property correlations of the full set of water data obtained in the venturi facility, it was found that the acoustic impedance ratio and the elastic modulus resulted in the best fit statistical expressions. The corresponding ultrasonic studies showed the hardness and tensile strength to be the most suitable. Single property correlations of the subset of water data involving materials also tested in mercury was also carried out for the

-310venturi facility. These materials correspond to subset one of the acoustic results. It was found that elastic modulus and reduction in area result in good fits individually. Subset one of the water data in the ultrasonic facility was correlated well in terms of tensile strength, hardness, yield strength, or elastic modulus. Here, there is some agreement among the two facilities. The analysis of the remainder of the venturi data (i.e., those materials tested in water only) on a single property basis shows that the correlation with elastic modulus and acoustic impedance ratio again is very good. This was also true with the full set of water data. These materials correspond to subsets two and three of the acoustic water data where hardness, tensile strength, and reduction in area were successful as single correlating parameters. The multiple property correlation of the full set of venturi water data and the two subsets individually resulted in predicting equations where the acoustic impedance ratio, elastic modulus, tensile strength, and true breaking stress were the most prominent properties. The corresponding ultrasonic studies showed the tensile strength, hardness, and yield strength to be the predominant terms. Correlations of the combined water and mercury venturi damage results are not yet available for comparison with the corresponding ultrasonic analysis. In general, it is seen that the venturi results are best correlated in terms of tensile strength, elastic modulus, true breaking stress, and acoustic impedance ratio. The ultrasonic results correlate

-311best in: terms of tensile strength, elastic nmodulusj hardness,-and.strain energy. However, the functional relations inolving any of the terms are generally not the same between the two facilities' or for s-ubsets within- the same facilityo:There is no explanation at.this.time as to the differences that exist. Undoubtedly, they are due:to differences in the damaging mechanism itself in the two facilities. - P.o Graphical Single Property Correlations For the sake of completeness it was decided to graphically investigate the ability of the tensile strengthyield strength, engineering strain energy, true strain energy (based on reduction in area), hardness, and ultimate resilience to correlate cavitation damage individually in each of the fluids tested. These mechanical properties were chosen since they had been the most successful in earlier computer correlations.. The lithium data obtained at 5000F and 1500~F was treated separately due to the thermodynamic effects that are important in lithium at 1500~F. Thus, for lead-bismuth, mercury, water, lithium at 500~F, and lithium at 1500~F, the experimentally-determined cavitation data was normalized to the data obtained for type 304 stainless steel. In leadbismuth the data was normalized to the type 304 stainless steel data obtained at 5000F, while in mercury the data was normalized to the- type 304 stainless steel data point obtained at 700~F Plots of normalized inverse cavitation damage versus each of the six mechanical properties listed above were made., Tje best straight line was drawn through the

-312data points. The specimen materials have been categorized as refractory alloys, ferrous metals, Plexiglas, and a group including aluminum, copper, nickel, Cu-Ni, and Cu-Zn. Thus, it is possible to distinguish from the plots the types of materials whose cavitation resistance (proportional to normalized inverse cavitation damage) may be adequately correlated in terms of a single mechanical property. The 30 plots prepared for this study are included in Appendix C as Figures 88 through 117.

CHAPTER VII THERMODYNAMIC EFFECTS A. Introduction The cavitation results obtained in lithium (Chapter III) indicated that the amount of damage sustained by a given material at 1500~F was cons.iderably less than that sustained at 500~F for constant testing time. The exact opposite behavior was noted in the cavitation tests conducted in lead-bismuth alloy and. mercury as part of this overall investigation. In these two.fluids-the damage sustained by a given material at the higher temperature.was greater than that measured at the lower temperature. OOne.might expect this latter behavior due to the reduced strength of the materials at the elevated temperature. However, the variation of the fluid properties with temperature is- also important 65 and must be considered. A recent paper by Leith presents predictions of cavitation damage in a vibratory facility exposed to atmospheric pressure for liquid metals as a function of temperature for a material possessing constant mechanical properties, i.e., not a function of temperature.. Leith's interpretation of the previously available data indicates that the specific gravity, vapor pressure, viscosity, and surface tension are important fluid properties which affect the amount of damage -313

-314sustained as a function of temperature. In the case of NaK, potassium, lithium, rubidium, cesium, and sodium, Leith concludes that cavitation damage as a function of temperature reaches a maximum at a temperature 15% to 20% up the melting-boiling range, falling off below and above this maximum damage temperature. It is our present feeling that the trend in the lithium results can be explained primarily on the basis of cavitation "thermodynamic effects," as follows. At 1500~F the vapor pressure of lithium is many times greater than at 5000F. When the cavitation bubbles collapse at the higher temperature, the heat of condensation from the condensing vapor trapped within the bubble must be conducted into the surrounding fluid. Since the vapor pressure is much higher at the higher temperature, there is more vapor present within a given bubble and, hence, more heat must be conducted into the surrounding fluid. If this does not occur rapidly enough (during the vibratory half-cycle corresponding to horn insertion), then the temperature and pressure of the uncondensed vapor are raised, thus arresting the bubble collapse. This uncondensed vapor serves to cushion the bubble collapse with a resultant decrease in collapse pressures and reduced damage to the test specimens. Such thermodynamic effects have been studied in great detail by 65,69,76,77,78,79,82,.83,84,89 through 96 many investigators. These studies generally have resulted in the derivation of some "thermodynamic parameter" which could be used to characterize cavitation bubble collapse in a given fluid-temperature environment as being controlled either by liquid inertia~efctts or the heat transfer effects discussed

-315- above.,'-Of course, in some cases sboth effects would influence bubble collapse. A simple model for bubble formation and collapse will now be examined. B. Calculation of Thermodynamic Parameters Very qualitatively, if the local pressure is.reduced below the vapor pressure in a:fluid, the phenomenon of cavitation occurs. The vapor bubbles that are formed when the local pressure is reduced below the vapor pressure depend upon the surrounding liquid for the required heat of vaporization. The heat- of vaporization is drawn from a thin 76,'78,79,84,91 through 95 liquid film adjacent to the cavity. The basic heat balance between the heat required for vaporization that occurs during cavitation and the heat drawn from a thin liquid film adjacent to the cavity is simply stated as: e vL L L(' T) where: v = vapor density, lbm./ft. Vv = vapor volume in bubble, ft. L = latent heat of vaporization, Btu/lbm. e L liquid dens ity bm.o/ft3 VL - liquid volume of film surrounding bubble from which heat can be drawn within the allowed time, ft'3 CL = specific heat of the liquid, Btu/lbm.~F A T = temperature drop in liquid film due to vaporization, ~F

-316The ratio: of vapor-volume formed to liquid volume.supplying the neces-. sary heat of.vaporization is: Vv PL CL L VL F L Ja where J = Jakob Number. a Generally, for a spherical bubble, the liquid volume, VL, is expressed as: VL = Ah where: A = liquid film area (vapor-liquid interface) h = average thickness of cooled liquid film The ratio of vapor volume to liquid volume has been called the thermodynamic parameter, B, by several investigators. It seems more physically meaningful to speak in terms of the ratio of the vapor volume formed to the liquid volume supplying the necessary heat of vaporization 78 per decrease in net positive suction head, A H. Thus, Hammitt7 defined the thermodynamic parameter, B, as follows,.although various 69,79,91,92 other related definitions are to be found in the literature:' pL C L T Ja B = PLL A a eL. H..H where: H decrease in net positive suction head corresponding to a - decrease' A; T in liquid temperature

-317 - This is the form of the thermodynamic parameter that will be: initially considered in this analys is. Since: H eL we have: B:A:T B= e'L2 LCL. —.T B.. From the Clausius-Clapeyron'equation, we can express p/ T B ( ) 0L T. -jT T T Tspeci hu, the herxpessioynamic fr bcparamet, B, abomes has 500F and 1500F, and sodium at and 1500F ence,and B car be tabcomputed for a giousen fluluid-temperature-comb-natiQn, know mbing the liquited density apor ensitheat of vaporization,, and specific heat of the liquid. The thermodynamic parameter:, B, above has been evaluat-ed for water:at 55~F, -'950F, 120-~F,- 150~F, and I8'O~F".for mercury at 70~F and 5Q0~F, lithium at'500~F and 1500~Flead-bismuth at 500~F and 1500~F- and.sodium at..500~F" and 1500~F. Values of.i..., v and B' aretabulated in'Table(53-Efor these, various. fluid-temperature~ combinations.. computed from the ideal gas law.

TABLE 53 VALUES OF THERMODYNAMIC PARAMETERS FOR VARIOUS FLUID-TEMPERATURE COMBINATIONS Fluid& 2L 2 Temperature Ibm,/ft.3 lbm./ft.3 B Ja JaC Beff. Water -550F 62.5 6,98xl0~4 4.69x103 4.69x103 2.20x1107 1.60x100 174.0 Water - 950F 62.2 2.48x10" 413.0 413.0 1.71x10 1.60x100 1.35 -3 4 10 Water -1200F 61.7 4,92x10 111.1 111.1 1.24x10 1.57x10 0.10 -2~~L 10 Water -1500F 61.1 1.03x102 27.4 27.4 729.0 1.54x100 0.006 -2 10 Water - 1800F 60.5 1.99x10 7.7 7.7 60.0 1.51x10 0.0005 -7 1 12.08x 25 Mercury- 700F 845.0 5.56x107 3.28x102 3.28x10'2 1.08x1025 1.58x107 2.72x10 2 Mercury -5000F 808.0 3.80x102 114x10 1.14x10 1.30x10 4.06x10 644.0 10 14 14 29 9.20x105 2.02x1026 Lithium -5000F 31.2 1.96x10 4.41x104 4.41x10 1.94x10 9.20x10 2.02x -44 Lithium- 15000F 28.7 3.76x10 206.0 206.0 4.25x104 7.56x105 48.9 -13 24 24 4~9 6i4 Lead-Bismuth —500'F 648.0 1.63x10"13 5.04x10 5.04x104 2.54x10 2.15x10 1.73x104 -6 9 9 19 6 Lead-Bismuth —15000F 600.0 8.44x10 3.30x109 3.30x109 1.09x10 1.65x106 8.49x10'5 - 88 17 Sodium - 5000F 55.3 7.54x107 5.42x108 5.42x10 2.94x107 6.88x10 1.12x10'5 Sodium - 100^ 490 161x0" 2.4 204.16 9. 4 Sodium - 15000F 49.0 1.61x102 2.04 2.04 4.16 9.54x10 0.1

-319The formulation of the thermodynamic parameter, B, above neglected the rate of bubble formation. and bubble collapse. Hence, the very effect we are most interested in investigating, i.e., the rate of 79 heat transfer, has not been taken into account. Florschuetz and Chao, in a very comprehensive paper dealing with the mechanics of vapor bubble growth and collapse, show that the effective thermodynamic parameter, Beff which does take into account heat transfer effects, can be expressed as: eLKL 2- / \ *TI- 1 //2.. _ Beff. C1/2 e 2L ) A 1/ where: - J = Jakob Number (dimensionless) a C = C-number (dimeasionless) KL = thermal diffusivityof the liquid, ft.2/hr., L/ PL L kL = thermal conductivity of the liquid, Btu/hr.ft.~F RO = equilibrium bubble radius, ft. The Jakob Number, Ja can be expressed as: a J sB NPSH where B is the thermodynamic parameter introduced previously which does not take account of the heat transfer effects. As a result, Bff can be expressed in terms of B, as; B eff -B2 (NPSH)3/2 eff~~~~.,

-32079 Florschuetz and Chao show that for low Beff bubble growth and collapse.is heat transfer. controlled, whereas for highBeff. it.. is liquid.pse w.reasi. - for~h.,. inertia'controlled. The Jakob Number, Ja, has been computed for..the various fluidtemperature combinations listed in Table 53 for a constant NPSH of 1 foot., The values are tabulated in Table 53. The value of 1 foot was selected arbitrarily, but it is reasonable to conclude that the effective NPSH controlling bubble formation and collapse in our experiments was constant, since it is the dynamicNPSH caused by the rapid insertion and withdrawal of the ultrasonic horn that is applicable. This is approximately constant for all the fluid-temperature combinations investigated. The C-number was also computed, assuming an equilibrium bubble radius of 1 cm. This value was also arbitrarily chosen, but it is reasonable to assume that the bubble radius was constant for all the cases considered since the dynamic NPSH was constant in all cases. Values of C and Beff computed under these assumptions are tabulated in Table 53. Since, as they are used herein, only ratios of these quantities are required, the use of arbitrary constants for Ro and NPSH is permissible. The values of C and Bff. for other values of Ro and NPSH-can be obtained easily from Table 53 by suitable ratios, if so desired. In the case of the liquid metals it is seen that Beff is a minimum for sodium atl1500~F. The value for lithium at 1500~F is also quite small. As the:value of Beff is decreased, this would indicate a greater ratio of vapor volume formed to liquid volume supplying the necessary heat for a gvea'drop in NPSH. Low values of thermal

-321diffusivity, indicating that the fluidis apoor therma conductor would further reduce the value of Beff. Hence. it is clearly seen that as Beff is reduced,. the heat transfer effects become important, i.e., more vapor is available for condensation ard/or the heat of condesation cannot be conducted into the surrounding fluid sufficiently rapidly in the horn half-cycle available for bubble collapse because of poor thermal conductivity. Thus:, in this case, the uncondensed vapor serves to cushion the bubble collapse "as its temperature and pressure are raised by the heat not conducted to the surrounding fluid. In the case of mercury at 70~F, lithium at 500F,:and lead-bismuth at 5000F and 15000F, the values of Bef are very large. In these cases bubble collapse was not heat transfer controlled, as demonstrated by the cavitation damage results. Rather, it is controlled by^iquid inertia.effects. Bubble collapse in mercury at 500~F appears to be influenced by both factors, as will be seen later. The values of Beff for water are all quite low. However, even at 550F the vapor density of water is appreciable. It appears that heat transfer effects may be important in bubble collapse in water at all the temperatures considered, especially at the highest temperature of 180~F?, which is very near the boiling point Sodium at 1500~F is also near the boiling point, and the value of Beff is very small, as expected, In the comprehensive analysis of Florschuetz and 79. Chao in water, it is concluded that -for values of Bef less than 0.05, heat transfer- effects contr-ol bubble collapse, whereas for Be ff greater than 10, the liquid inertia is controlling For intermediate ialues of Beff both eff tsare important. Applying these criteria to

"322our water data, it is seen from Table 53 that the bubble collapse at 55~F and 95~F appears to be controlled by the liquid inertia, while at 150~F and 180~F the heat transfer effects are controlling. At 120~F both effects are apparently important. It would be instructive to determine in a more quantitative manner those fluid-temperature combinations considered in this investigation that are influenced by heat transfer effects in bubble collapse. In Table 54 is listed the experimental data obtained for type 304 stainless steel in the various fluids at several temperatures in terms of MDP rate. Data for type 316 stainless steel tested in sodium was taken from references 37 and 380 The data obtained in each individual fluid was normalized to a given data point in that fluid. Hence, the water data was normalized to the data point obtained at 1200F, the mercury data to 70~F, the lithium data to 500 F, the lead-bismuth data to 5000F, and the sodium data to 500~Fo The resulting normalized MDP rates are also included in Table 54. This data was next corrected for differences in temperature which would change the mechanical properties of the test material and, hence, influence cavitation damage. The correction -I1/2 applied was proportional to (UR) 2, where UR denotes Hobbs' ultimate resilience, which was previously discussed. The form of the correction was taken from a predicting equation discussed in Chapter VI, which suitably accounted for the complete body of cavitation data. The temperature corrections are noted in Table 54, and also the corrected normalized MIDP rates, which are computed by simply multiplying the normalized MDP rate by the temperature correction factor. It is noted that in

TABLE 54 EXPERMENTAL CAVITATION DATATYPE:304 STAINLESS STEEL......'~:;-' ~Material Fluid & -Norm. Temperature Corr. Norm. Temperature M MDP Rate MDP Rate Correction MDP Rate eff~. Water - 550F 0.06 mils/hr, 0.43 1.0 0.43 174.0 Water - 950F 0.11:0.79 1.0 0.79 1.35 Water 120OF 0.14 1. 1.Q 1.0. 0.10 Water - 150~F 0.08 0.57 1.0 0.57 0.006 Water - 180OF 0.001 0.007 1.0 0.007 0.0005 Mercury -700F 0.32 1.0 1.0.0 2.7 2x1021 Mercury - 500~F 0.69 2.2 0.81 1.78 644.0 Lithium - 500OF 0.34 1.0 1.0 1 0 2.02x1026 Lithium - 1500~F 0.034 0.1 0.129 0.0129 48.9 Lead-Bismuth-~5000F 0.93 1 1.0 1.0 1.0 1.73x046 Lead-Bismuth —1500~F 11.30 12.2 0.129 1.57 8.49x1015 Sodium - 500~F 0.53* 1.0 1.0 1,0 1.121015 Sodium - 15000F 0.00033* 0.0006 0.126 0.000076 O0.01 Type 316 stainless steel tested by Hydronautics, Inc. (References 37 and 38). *Taken fromTable 53.

-324the case of mercury and lead-bismuth the corrected normalized MDP rate is greater at 1500.~F than at 500~F. This could be due to the decreased fluid viscosity at the higher temperature. If all effects were precisely accounted for, the corrected normalized MDP rates would be identical at both temperatures. In the case of the lithium and the sodium the corrected normalized MDP rate is much smaller at 1500~F than at 500~F. This is unquestionably due to the heat transfer effects previously discussed that are in a direction to reduce cavitation damage at the higher temperature. In Figure 82 the Log Corrected Normalized.MDP Rate is plotted versus Log Beff. for the liquid metals. The water data is not included on this plot due to the additional complicating factor of dissolved gas which affects cavitation damage in water, but is a negligible effect in liquid metals, as previously discussed, since their solubility for any of the common gases is negligible. Any value of corrected normalized MDP rate greater than 1.0 in Tabie 54 was plotted as a value of 1.0 in Figure 82. This is due to the fact that there is no known physical mechanism that could account for values greater than 1.0 other than data scatter and the minor effect of fluid viscosity or surface tension men82 83 tioned previously. Numerical calculations show that these effects are apparently quite negligible. Of course, the mechanical property -1/2 temperature correction applied to the data, (UR) 1, is only approximate, and this could result in the discrepancy. The data in Table 54 indicates that bubble collapse only in lithium and sodium at 15000F, of -the several cases considere4, is subject to heat transfer effects. The

LIQUID METALS w I Pb-Bi (1500 F) - HOg (500F / Li(500~ F) Pb-Bi O(500 F) 0. Na 500F)~ Hg (O* F o _ __I_ _ _ _ _ _ INERTIA CONTROLLED COLLAPSE 0.z -2 -~ w Li (1500 F) wI -3-8(~)__________ ________ ___~_______ _____ 0 HEA TRANSFER CONTROLLED COLLAPSE -1 No (1500 F) -5 ^ LOG B^ 2193 -3~$~3 6 12 ~ 1824 30 36 42 48 54 Fig. 82. —Effect of thermodynamic parameter on cavitation damage - liquid metals.

-326situation with respect to mercury at 500~F is not nearly as clear, although the corrected normalized cavitation data for mercury at 70~F and 5000F would seem to indicate that heat transfer effects are negligible at 500~F. In the case of the other fluid-temperature combinations, bubble collapse is controlled by liquid inertia only. In Figure 82 a dashed vertical line has been arbitrarily placed on the curve, passing through a value of Beff= 1000. It is in this range of Beff that heat transfer effects apparently become important in bubble collapse in liquid metals. In Figure 83 the corrected normalized MDP rate is plotted versus Log Beff for the water data. The reduced values of corrected normalized MDP rate noted at 55~F and 950F are most probably due to effects of 66 dissolved gas, increasing at low temperature due to increased solubility, which serve to cushion the bubble collapse. The dissolved gas is reduced substantially as the temperature is increased. Its proportionate effect is also reduced as the vapor pressure increases with temperatureo The reduced damage rate noted at 150~F and 180~F in water is presumably due to the heat transfer effects previously discussed. The dashed curve in Figure 83 serves to indicate the probable behavior of the damage rate as a function of Beff if the effect of dissolved gas were negligible. In Figure 84 Log Bef. is plotted versus the fluid temperature for each of the 5 fluids considered. Again, an arbitrary dashed horizontal line is drawn corresponding to a value of Beff 1000. Gener-ally- values of Beff. greatl than 1000 would denote fluid-temperature

1.4 I..1 ~WATER NO DISSOLVED GAS PRESENT, 20 F 1.0./... a. t// - 29 0 / / Fv 4'/.50 ___.5-~damage -,water. u M~. ~ LOG B_____2194 0 / -4 3 -2 o 2 34 5 Fig. 83. —Effect of thermodynamic parameter on cavitation damage - water.

60I I I I 50 - 40 30 L I1 LE AD-BISMUTH 30 ZO ^^ eSODIUM' LITHIUM 20 ER o 1. ^^^^^NETIA CONTROL D I.LAPSE MERCURY 10 W TER HEAT TRANSFER CONTROLLED COLLAPSE TEMPERATURE OF 21 0 500 1000 1500 Fig. 84. —Effect of temperature on the thermodynamic parameter - liquid metals and water.

-329combinations where bubble collapse is liquid inertia controlled. Values of Beff below 1000 would denote fluid-temperature combinations where bubble collapse is heat transfer controlled. Of course, there is an intermediate range of values of Beff where both effects are operative. Figures 82, 83, and 84 could be used by the designers of equipment which is susceptible to cavitation damage in order to approximate the change in damage corresponding to a change in operating conditions from one temperature to another in a given fluid if NPSH and degree of cavitation were maintained constant. C. Final Predicting Equation Comprehensive computer correlations of experimentally-determined cavitation damage data with applicable mechanical and fluid properties were discussed in Chapter VI. The cavitation damage data used in these correlations was raw experimental data. There are at least two corrections that should be applied to certain sections of the complete data set involving four different fluids and a variety of test materials. The "thermodynamic effects" were discussed in detail, and it was seen that for certain fluid-temperature combinations this mechanism results in a reduction in cavitation damage. Clearly, the damage data obtained in lithium at 1500~F was significantly reduced because of these "thermodynamic effects." The same comment applies to the water data obtained at 700F, although in this case the effect is believed primarily due to dissolved gas effects. These thermodynamic effects were not operable in the other fluid-temperature combinations considered in this study. The

-330correction for "thermodynamic effects" that should be applied to the,. lithium data at 15000F is merely the ratio of the corrected normalized MDP rates for lithium at 500~F and 1500~F listed in Table 54. This. ratio is 1/0.0129 - 77.5. In the case of the water. data at 700F the appropriate correction factor is not so easily obtained because of the complicating factor of dissolved gas -,previously discussed. However, part of the error. can be accounted for by correcting the data to the maximum point observed in Figure 83 (V 120~F). This ratio is 14/11 = 1.27. Hence, the lithium data at 1500~F and the'water data at 70~F should be increased by the appropriate factors to take account of the reduced damage due to "thermodynamic effects." The second correction that should be applied to the cavitation damage data is concerned with the large variation in static net positive suction head (NPSH) between the various fluids. The suppression pressure was maintained constant at 15.3 psia throughout all the tests in all the fluids at all temperatures. It was not possible to maintain constant NPSH in these tests due to the pressure limitations of the experimental equipment. Hence, static NPSH varied by about a factor of 30 between mercury and lithium. As previously discussed, the dynamic portion of the NPSH due to the vibrating horn is approximately constant for all the fluid-temperature combinations. Since this quantity is large compared to the static portion, it controls bubble collapse and no correction is required on this account. However, the static NPSH controls the bubble regime (size of bubble cloud and bubble population) - and, hence, it also influences the amount of damage. Variations in

-331static NPSH obviously lead, then, to improper modeling between fluids. It was noted that the surfaces of the-.specimens tested in mercury and lead-bismuth (minimum NPSH) were almost completely and uniformly covered with damage, while the specimens tested in water and lithium (maximum NPSH) were only selectively damaged. Particularly, in the case of the lithium the damage was concentrated in a small region near the center of the specimen. It is believed that the difference in these damage patterns is due to improper flow modeling and the fact that a bubble cloud does not cover the entire face of the specimen in the case of the water and lithium tests. From experimental observations it is estimated that on the average the damaged area noted for a specimen tested in water was approximately 1/2 the damaged area noted for the same material tested in mercury. This variation is attributed to the variation in static NPSH. Thence, an appropriate correction factor is deduced from this data for all of the fluids. Adopting the mercury test fluid as the standard (correction factor = 1.0), one may compute the correction factor for water in the following manner: (NPSH) n H20 (NPSH) = 2 = Ratio of damaged areas (NPS — Hg i.e., it is postulated that the NPSH ratio between the two fluids, raised to an appropriate power, is inversely proportional to the corresponding ratio of damaged areas noted in the two fluids, and to the ratio of bubble populations. Then, we have: [(35.3) /(2.60) 2

-332Solving for n, we find that n = 0.266. We further postulate that this constant is approximately applicable for.all of the fluids tested-. Thus, the correction factor for lithiumis easily computed as: (NPSH)Li] _0.266 (NPSH) [(7006)/(2.6j0) x = 2.41 The correction factor for lead-bismuth is: (NPSH). r Pb-Bi Hgj (NPSH) H 0.266 (3.40)/(2.60) = X= 1.075 Thus, the cavitation damage data obtained in water, lithium, and leadbismuth should be increased by the appropriate factors to take.account of the variation in bubble population due to the variation in static NPSH. Both the correction for "thermodynamic effects" and the correction for variation in static NPSH were applied to the complete body of cavitation data. This corrected data was then submitted.to a-final computer correlation where only Hobbs' ultimate resilience and the fluid density were allowed as material and fluid correlating parameters,respectively. The ultimate resiIience and density were chosen since a combination of these two properties had previously correlated the uncorrected data very satis!ictqrily, whereas simple combinations of other

-333mechanical and fluid. properties were non-existent in this respect. In the present correlation the allowable exponents were +.1j, 2, -1~/2, ~3, and.+1/3, as was the case with all of the previous correlations-. Hence, a total of 10 exponents per independent variable were allowed and only 2 independent variables. Thus, a total of 20 possible terms Could enter the predicting equation under these circumstances. The statisticallybest predicting equation generated in this case was as follows: Avg. MDP Rate = 0.142 + 8.918(UR)-1/2 Coefficient of Determination = 0.780 Average Absolute % Deviation. 51.3% Note that this equation is a function of the ultimate resilience only, while the fluid density does not appear. This is undoubtedly due.to the fact that the correction for variation in static NPSH that was applied to the full data set is a function of the fluid density only, since the suppression pressure was held constant in all cases. Hence, the individual effects of density and NPSH cannot be separated in these experiments Additional tests under different conditions, e.g., variable suppression pressure and constant density, or constant NPSH and variable density, would be required in order to assess the separate contribution of each of these effects to the damage mechanism. However, this present correction for NPSH would indicate a dependence on the density only to the extent of ( ) 266 whereas previously the density had entered as ( )-2 (all data and no corrections of any kind applied) and as (P )1 (lithium.data at 1500~F excluded from the full data set and no corrections of any kind appli'').:,

-334When only the correction for'.thermodynamiceffects" is applied to the full data set~, the statistically-best predicting equation generated in this case-was as afollows:-.: Avg..MDP Rate 40.284 + 7.254(UR)L2 0_.331( )2 Av- g,... 84..Coefficient of Determination:. 0.744. Average Absolute % Deviation' = 49.5% Here both the ultimate resilience and the density enter into the predicting equation. In all cases studied the ultimate resilience enters to the power (-1/2), whereas the dependenceon density varies. When neither the correction for "thermodynamic effects" nor the correction for variation in static NPSH is applied to the full data set, the statisticallybbest predicting equation obtained was as follows: Avg."IMDP Rate-= 0.510 + 6.045(UR) 1/2 0.471(f )-2 Coefficient of Determination' = 0.658 Average Absolute % Deviation = 54.5% This was precisely the predicting equation obtained in Chapter VI when a *. *..*-'. multiple mechanical and fluid properties correlation was carried out on the full body of cavitation data, and serves as a check on the overall......,............ procedur.e.The various correlations are somewhat consistent in that the dependence on the ultimate resilience is identical and the dependence on density is either to the power (-1) or (-2) in all cases considered. In summary, if the designer of equipment susceptible to cavitatiton damage were to make ue. of these results in choosing appropriate

-335cavitation-resistant materials for use in a given fluid-temperature environment, the recommended equation for computing the relative expected damage rate is as follows: 1) Avg. MDP Rate C1C2[0.142 + 8.918(UR)-1/2] where: Ci - correction for "thermodynamic effects" (O0C1 1) C2 correction for variation in NPSH (O C2 1) C1 is precisely the corrected normalized MDP rate, previously discussed, and plotted in Figures 82 and 83 as a function of the thermodynamic parameter, Beff. Figure 82 is valid for tests in liquid metals and Figure 83 for tests in water. Hence, one must first compute the value of Beff for the fluid-temperature combination of interest and then determine the corresponding value of C1 (corrected normalized MDP rate) from Figure 82 or 83. Figure 84 could be used for determining Beff if the fluid-temperature combination of interest to the designer is displayed. Hence, C1, is easily determined. Note that Figures 82 and 83 are plots of Log Corrected Normalized MDP Rate versus Log Beff. and that the correction for "thermodynamic effects," C1, is equal to the corrected normalized MDP rate, not log corrected normalized MDP rate. C2 can be easily expressed as: C2 = 1.29(NPSH) -0266 where NPSH corresponds to the net positive suction head (expressed in feet) for the fluid-temperature combination of interest. Thus, both C1 and C2 result in a reduction of the relative expected damage rate, except when C1 - C2 I.

-336If the tests are to be conducted at constant NPSH, then the recommended equation for computing the relative expected damage rate is as follows:. 2) Avg. MDP Rate =C1[0.284 + 7.254(UR) /2 0.331( ) 2] where C1 is determined from Figures 82 or 83, as before. In all cases the ultimate resilience (UR) is expressed in units of in.lbf./in.3, or psi, while the density is expressed in units of g./cc.

CHAPTER VIII SUMMARY AND CONCLUSIONS Ultrasonic-induced cavitation studies have been conducted in lead-bismuth alloy at 500~F and 1500~F, in mercury at 70~F and 500~F, in water at 700F, and in lithium at 500~F and 1500"F for a wide variety of materials including refractory alloys, steels, aluminum, brasses, copper, nickel, tool steels, plastics, etc. The detailed results for the various fluid-material-temperature combinations are listed in the appropriate sections of the report. Various salient features include the following: 1) The ultrasonic cavitation facility which was developed as part of this dissertation is capable of operation at temperatures up to 15000F in fluids including reactive liquid metals, and provides a sealed, inert atmosphere for these tests at pressures up to about 50 psig. 2) The tantalum-base alloys, T-lll and T-222(A), were the most cavitation resistant of the materials tested in lead-bismuth alloy at 500~F and 1500~F, in mercury at 500~F, in water at 70~F, and in lithium at 500~F and 1500~F. Thus, the superiority of these refractory alloys at elevated temperature has been -337 -

-338demonstrated. The stainless steels were the most resistant in mercury at 700F. In the bearing program the tool steel alloys BG-42 (Rc = 64) and Blue Chip Tool Steel were the most resistant. The cavitation resistance of these alloys correlated well with hardness. These tool steels were.approximately ten times more resistant than the T-Ill and.T-222 in mercury at 5000F. 3) The refractory alloy,.Cb-IZr(A), was the least resistant of the.. -,t e. e in.. — --.!,:',' materials tested in lead-bismuth alloy, mercury, and lithium at 500~F. Type 304 stainless steel was the least resistant in lead-bismuth alloy and lithium at 15000F, while Plexiglas (tested only at room temperature) was least resistant in mercury at 700F,, and type 1100-0 aluminum least resistant in water at 700F. In the bearing program the two grades of graphitar tested were found to be the least resistant of the materials used. 4) As would be expected, all -materials'tested in lead-bismuth sustained greater damage at 1500~F than at 500~F. All materials tested in mercury sustained greater damage at 5000F thanat 70~F with the exception of the hot-rolled carbon steel. This can be explained by the superior mechanical properties of this material at the higher temperature. In lithium the damage suffered by all materials tested at 150QF was much less than that at 5000F. This is believed due to thermoddyamic effects which are very important in lithium at iS00~F." This effect was not operative in the lead-bismuth, tests since the vapor pressure was nearly zero even at 1500~F.

-3395) For the tests at 500~F, wherein the applied static pressure above vapor pressure was held constant for the different tests, the amount of damage sustained by a given material in lithium was less than that measured in mercury or lead-bismuth by a factor ranging from 2 to 30. The large variation in this ratio indicates that coupling parameters between fluid and materials are necessary to obtain a comprehensive correlation. The amount of damage sustained in lithium at 500~F and in water at 70~F was of the same order of magnitude. Damage rates with mercury were 3 to 20 times greater than for water at the same temperature (700F)o No corresponding direct comparison was possible in the 22 venturi tests, although generally damage with mercury was greater. The damage noted in lead-bismuth and mercury at 500~F was about the same. 6) Plexiglas was relatively less cavitation resistant in mercury than in water, and in fact there are numerous substantial differences in rankings between materials in different fluids at the same temperature. Thus, clearly, any equation to predict cavitation damage must consider fluid as well as material properties in such a way as to achieve a coupling between the two. The acoustic impedance ratio between fluid and test specimen could serve in this capacity. These observations are consistent with previous venturi test results from this laboratory. 7) Detailed examination of the wetted but non-cavitated parts of the equipment and test specimens indicates that corrosion

-340-.effects in thea.bsence of cavitation were insignificant in these investigations.: Photomicrographs have not indicated, intergranu-.lar corrosion in.any; of the- tests... 8). In.general.1 -the damage. rate was approximately constant through1 -8). -"'. * out the tests. for the liquid; metal tests and for most of the water:tests. However, in -.some of the water tests,.the damage rate decreased markedly during the test. -.t is felt that this.is a result-of the very deep;,. isolated pitting encountered in these tests. -.Generally, water-and lithium tests differed from the heavy liquid metal tests in that quite uniform and relatively fine: damage was encountered:.in the heavy liquid metal tests -as opposed to the water and lithium tests on the- same materials. This -difference may be a result of the improper modeling of the fluid flow regime between the two. fluids, as indicated by the large difference in static NPSH between tests. It is indicated that -the -volume.toss rate remains approximately.constant as long as the damage covers the surface uniformly. This condition persis-ts to d.iffer'ent accumulated MDP: for different -material-fluid combinations. It.persisted to the order of at -least 50-100 mils accumulated. DP for the heavy liquid metal tests (lead-bismuth and mercury).- but in some cases only to /V 3 mils MDP for the.water and.lithium tests. nIn. these tests.a useful. constant rate persisted between about 1 and 3 mils accumulated MDP, and this rate could be used to rank the materials.:.-Since..the. initial -.rate is less than'the constant

-341rate achieved, this constant rate is a maximum "plateau" rate. After the plateau portion of the rate curve, there is usually a continuous decrease of damage rate. In this respect, the water tests and the data recently reported by Hobbs7 and Plesset and 59 Devine, using a similar facility, are in close agreement. As was observed in one of the present lead-bismuth tests carried to very high total MDP, the volume loss rate increased again from a minimum which followed a first maximum. The test was concluded before it was possible to determine whether or not a second maximum would occur. This plot of MDP rate versus MDP for two type 304 stainless steel specimens tested in lead-bismuth alloy at 1500~F is shown in Figure 85. This type of rate curve has also 99 been noted in the venturi tests, and a recent theoretical 100 study based on the statistics of the fatigue process shows that all of the experimentally observed damage rate curves can be justified assuming a fatigue mechanism. They can also be justified on the basis of the-feedback between flow regime and 101 accumulated damage. The difference in extent of the "plateau" rate between heavy liquid metals on the one hand and water and lithium on the other is thought to be due to the lack of proper flow modeling due to a large variation in NPSH. 9) Direct comparison of venturi and vibratory results from this laboratory shows that the rankings of materials for cavitation damage are quite similar, and- particularly so for the mercury tests, but that the relative ratios between different materials

16 co 15 +-_ —-: 14 / + \ BI /I\\ a 12 4 z I Q. 9 -~_ I__ 174/.7 / z 6 - y p+ 3 + z If6 LJ / s' 1 CAVITATION IN Pb-Bi AT 1500~F 4 I l/ I:: I SPECIMEN No. 3 - 304 SS /^~~~~ JJ ____________ ________SPECIMEN No.5 - 304 SS 2''1, I. I 1748 0 5 10 15 20 25 30 35 40 45 50 55 60 MEAN DEPTH OF PENETRATION -MILS Fig. 85. —Effect of mean depth of penetration on mean depth of penetration rate - type 304 stainless steel in lead-bismuth alloy at 1500 F.

-343are much greater in the venturi facility. The damage rates in the vibratory tests are of the order of 103 times those in the venturi, so that corrosive effects are much less important in the vibratory tests. This factor may be responsible for the much larger range between materials in the venturi test as well as some of the discrepancies in ranking of some materials from these two facilities. To investigate the possible influence of corrosion in the liquid metal tests, a further step would be the use of the pulsing technique pioneered by Plesset. Computer correlations of the cavitation damage data with applicable mechanical and fluid properties indicate the following important conclusions: 1) There is no single material mechanical property which can be used to correlate the damage with good precision, even if coupling parameters to account for fluid property changes are included in the correlation. However, the "ultimate resilience" 67 suggested by Hobbs seems best in this respect, as discussed below. 2) In general, the best correlations include one or more energytype mechanical properties, one or more strength-type properties, and one or more fluid coupling parameters if the fluid properties are varied in the data set. 3) The energy-type properties are more predominant in the tests with the high-density liquid metals, while the strength-type

-344properties predominate. for the water and lithium tests. This is consistent with theoretical expectations.. -.. ~4) In- the comprehensive' correlations involving data obtained in all four fluids at various temperatures, the fluid density and bulk modulus were the most significant fluid coupling parameters. 5):It was:f-ound that a- predicting equation involving only Hobbs' ultimate resilience parameter and —the.-.f luid density partially accounted for"all the cavitation damage data obtained in the four fluids at the various temperatures...This suggests that Hobbs' parameter may be quite significant in predicting cavitat ion damage. 6) Thermodynamic effects are very important in lithium at 1500~F, reducing the damage by an order of magnitude for the vibratorytype test conducted. This requires that fluid thermal properties such as the specific heat, heat of vaporization, thermal conductivity, and thermal diffusivity, be introduced into the comprehensive computer correlations. 7) No relatively simple single comprehensive correlating equation applies well to all the data. If sufficient terms are allowed, of course, any degree of'fit-can be obtained. This lack of a single simple correlating equation may indicate that all important mechanisms in cavitation damage may not have been considered. For example, it may not be possible to explain cavitation damage in terms of properties which are determined under semi-static conditgeons, as are the conventional mechanical and

-345fluid properties. Also, the contribution of corrosion in the presence of cavitation may be important in some cases, even though it is negligible in the absence of cavitation. 8) For the designer of equipment susceptible to cavitation damage, the recommended equation for computing the relative expected damage rate of potentially useful cavitation-resistant materials for use in a given fluid-temperature environment is as follows: -1/2 Avg. MDP Rate = C-C2[0.142 + 8.918(UR) ] where C1 and C2 are corrections for "thermodynamic effects" and for variation in NPSH, respectively (C1 and C2 are both. 1), and are easily determined. If the designer is dealing with a constant NPSH condition, the recommended equation for computing the relative expected damage rate is as follows: Avg. MDP Rate = C1 [0.284 + 7.254(UR)1/2 - 0.331( )2]

APPENDIX A 55 - HEAT TRANSFER CALCULATIONS:It' is essential that- the:crystal temperature be kept below the critical value known as the Curie point. For the lead zirconatetitanate crystals used, this is about 1500F, Heat could be transferred to the crystals from the test fluid by two distinct conductive paths. These are: 1) From the test fluid to the cylindrical vessel walls, thence to the flange cone, flange, top plate, transducer horn, and crystals. 2) From the test fluid to the transducer horn tip, thence to the remainder.of the transducer horn and the crystals. In order to maintain the crystal temperature below the Curie point, it is necessary to provide some means of cooling the top plate. Calculations have been made to indicate the extent of cooling which is required. As discussed in the report, 1/2 in. copper tubing is seated in a groove provided in the top of the top plate and brazed into position. Tap.water can be continuously circulated through this tubing. The problem is now one of computing-the heat flux reaching the top plate by means of the two paths noted above to see if such cooling is adequate. We consider the two paths for heat flow separately. -346

-347- A. Heat Transferred From the Test Fluid to the Top Plate Via the Cylindrical Vessel Walls. F lange Cone, and: Flange It is first necessary to determine the temperature distribution within the flange cone section before the heat flux conducted to the top plate can be computed. Refer to Figures. 10 and 86, which clearly indicate the sections of the cavitation vessel involved and the necessary dimensions. The flange cone section is in the shape of an annular disk, and the differential equation relating the temperature as a function of position is Bessel's equation. For the required boundary conditions the worst conditions (i.e., those which will give maximum heat transfer from the cylindrical vessel to the top plate) will be assumed. Major assumptions and simplifications are listed below: 1) A steady-state condition prevails. 2) The material of which the disk is composed is homogeneous and isotropic. 3) There are no heat sources within the disk. itself. 4) The natural convective heat transfer from the exposed surface at any point is proportional to the difference in temperature between the disk and its surroundings. This is a conservative *assumption compared to the usual relation that natural convection heat flux is proportional to (A T)4/3..5) The thermal conductivity, k, and heat transfer coefficient, h, are not functions of temperature. 6) The temperature of the surrounding medium is uniform.

-3482000o 200 F FLANGE CONE (TOP VIEW) 1486 Fig. 86. —Flange cone.

-3497) There prevails a condition of symmetry of heat flow about the center. 8)- The temperature at the base of the cone is assumed to be 2000~F (actual maximum fluid temperature to be used is only 1500~F, so this too is highly conservative). 9) The temperature at the top of the cone is assumed to be 200~F. 10) No heat loss from the inner surface of the cone was assumed, thus introducing an additional safety factor. 11) Since the wall thickness is relatively small compared to the other dimensions, we can consider the system two-dimensional. The details of the heat transfer calculation can be found in reference 55. However, the major results and procedures will be summarized here. The appropriate heat balance for the flange cone section results in a differential equation (Bessel's equation) relating the temperature of the flange cone as a function of position. The solution is thus well known. After applying the appropriate boundary conditions, the arbitrary constants are evaluated. Hence, the solution for flange cone temperature as a function of position is determined. It is then possible to compute the heat flux into the flange cone from the cylindrical vessel walls by conduction. It is found that heat is being transferred to the flange cone from the vessel walls by conduction at a rate of 2860 Btu/hour. Of this amount, 60 Btu/hour are lost to the atmosphere by the flange cone due to convection and radiation. Hence, 2800 Btu/hour are transferred from the flange cone to the top plate.

-350B. Heat Transferred from the Test Fluid to the Top Plate Via the Transducer Horn It is first necessary to determine the temperature distribution within the transducer horn before the heat flux conducted to the top plate via this path can be computed. Refer to Figure 87, which schematically indicates the transducer horn. After determining the temperature distribution in the transducer horn, it will be possible to compute the heat flux transferred from the tip of the horn to the base of the horn. As a conservative measure, it will be assumed that this heat flux reaches the top plate. Again, the appropriate heat balance for the system yields the required differential equation, giving the temperature of the horn as a function of position. The general solution is determined, the proper boundary conditions are applied, and the temperature distribution is computed. Then, it is possible to determine the heat transferred from the tip of the horn to the base section, which is found to be 109 Btu/hour. This is only a fraction of the heat flux conducted to the top plate via the cylindrical vessel walls, flange cone, and flange (2800.Btu/hour). C. Total Heat to be Dissipated from Vessel The heat reaching the top plate, i.e., the conductive heat flux from the vessel walls and from the transducer horn, is to be removed by means of a copper cooling coil through which cold water will be circulated. In the steady-state, the heat removed by the cold water will equal the heat reaching the top plate. Thus, the total amount of heat

-351I__.oo1.500' ~qxA A+ d (qxA)dx HORN h / -- dx - qcPdx I I al ~LIQUID.. xt LEVEL L^J~~~ ~ qxA SAMPLE Fig. 87. —Schematic of heat transfer by horn. 1487

-352to be removed by the cooling water is 2800 Btu/hour + 109 Btu/hour = 2909 Btu/hour = 48.5 Btu/min. (A/850 watts). The copper tubing provided to remove this heat is 1/2 in. O.D. x.430 in. I.D. #20 (.035 in. wall) tubing. Considering the normal pressure supplied in the city water mains, a flow rate of approximately 1 gpm would be achieved in this tubing. This would result in a steady-state water outlet temperature of 6~F above the inlet temperature. Such a facility should be able to easily remove the heat conducted to the top plate. All the stress calculations pertinent to the design of the hightemperature cavitation vessel are contained in reference 55. *The electrical input to the crystals is about 200 watts, and, hence, not of great importance compared to the heat flow from the hightemperature fluid.

APPENDIX B COMPUTER REGRESSION ANALYSIS OF CAVITATION DATA87,88 A least mean squares stepwise regression computer program was used to correlate the cavitation damage data with mechanical properties. Using the first-order interaction form of the program, the problem at hand can be simply stated as follows: it is required to determine the appropriate coefficients and exponents in a predicting equation of the form: Ya x c + d 4 Y= Co+C1X1 +C2X2 +C3X3 +C4X4 d + +Cn where CO, C1, C2, C3, C4,.o, C are constant coefficients; a, b, c, d,.o.o...., q are constant exponents; the X's are the independent variables, in this case the mechanical properties of the materials and the fluid properties; and Y is the dependent variable, the average MDP rate. The independent variables are allowed to appear in the predicting equation any number of times, each time raised to a different value of exponent and multiplied by an appropriate coefficient. The program allows great latitude on the possible exponents for the independent variables. The form of the program used in this investigation allows any or all of the independent variables to be raised to the following exponents: 1, + 2, + 1/2, + 3, + 1/3. -353

-354A predicting equation of the type noted above would be obtained by allowing only a "first-order interaction" of the possible terms, i.e., terms involving products of the independent variables would not be allowed. The program, however, does allow the option of a "second-order interaction," i.e., allows terms involving products of different independent variables. The choice must be made by the individual programmer. In the present analysis (permitting only first-order interaction) the allowable mechanical properties (independent variables) were taken to be the tensile strength, yield strength, engineering strain 71 71 energy, true strain energy, hardness, percentage elongation, percentage reduction in area, and modulus of elasticity. In addition the 42 ratio of acoustic impedances of test fluid and specimen material was also included among the independent variables for all the correlations involving only a single fluid. In the comprehensive correlations involving all four fluids one fluid property was included among the independent variables for all the correlations as a fluid coupling parameter to explain differences in cavitation resistance of a given material in different fluids. The fluid coupling parameters that were investigated included the ratio of acoustic impedances of test fluid and specimen material, density of fluid, surface tension, net positive suction head (NPSH), bulk modulus, and kinematic viscosity. Additional comprehensive correlations involved a combination of five mechanical properties and five fluid properties. Hence, in a given correlation there were 10 independent variables and 10 possible exponents for each

-355independent variable. As a result a total of 100 terms are possible candidates.for inclusion in the predicting equation plus a pure constant. From a physical point of view, it is hoped that a good statistical correlation will be possible with a minimum number of terms so that the predicting equation may hopefully be justified on physical grounds. This possibility would be unlikely if more than 5 or 6 terms were needed for the correlation. A brief outline will be given here of the mechanics of the program. The interested reader is referred to the literature previously cited for the details. The major features of the program are as follows: 1) Of the 100 possible terms that are candidates for inclusion in the predicting equation, the program randomly selects a subset of 40 terms to be analyzed. 2) A correlation coefficient is computed for each of the 40 terms. The correlation coefficient is a measure of the ability of each term to individually explain the experimental data, i.e., predict the average MDP rate. 3) The term with the greatest correlation coefficient is then included in the predicting equation, which at this point is of the form: a Y = CO + C1Xl where CO and C1 are constants to be determined. 4) The constants CO and C1 are computed using the least mean squares criterion.

-3565) The initial 40 terms are then' sorted into 2 subsets,, those that, are included in the predicting equation at. this point, and those that are not. 6) An importance factor is computed for each term now in the equation. The importance factor is a measure of the total contribu-tion made by each term in expltaining.the' experimental data. 7) The importance factors of the terms in the equation are compared to a minimum level of importance set by the user. A typical range of values is 1% to 5%. 8) Terms having an importance factor less than the minimum level are deleted from the equation. 9) A potential importance factor is computed for each term not in the equation. The potential importance factor is a measure of the ability of each term not in the equation to explain the presently existing variance between the experimental data and the predicted data. 10) The potential importance factors of the terms not in the equation are compared to a minimum level of importance set by the user. A typical range of-values is.1% to 5%. 11) Terms not in the equation having a potential importance factor greater than the minimum leveL are entered into the equation. This procedure is used to examine the subset of 40 terms chosen randomly and is terminated either when all qualified terms have been entered into the equation or when certain statistical criteria (such as the coefficient of deteimi#ation and standard error in the dependent

-357variable) set by the user have been satisfied. Whenever a new term is entered into the equation, the least mean squares criterion is used to compute a new set of coefficients. For a given problem it is possible to analyze several subsets of 40 terms, each chosen randomly from the set of 100 possible terms available. Such a procedure is advisable in that it increases the probability that the most significant terms contained in the initial set of 100 terms-will enter the predicting equation~. The output from the program includes the terms in the predicting equation along with the appropriate exponents and coefficients, predicted MDP rates based on the correlation, experimental MDP rates, percent deviations, standard error in the dependent variable, coefficient of determination for the analysis, average absolute percent deviation for the analysis, etc. As a result, it is possible to show graphically the statistical accuracy of the predicting equation by plotting the predicted MDP values versus the experimental points and noting the deviation from a 45~ line which would signify a perfect fit.

APPENDIX C PLOTS OF NORMALIZED INVERSE CAVITATION DAMAGE VERSUS S- SINGLE. MECHANICAL PROPERTIES —.LEAD-BISMUTH. ALLOY, MERCURY, WATER, LITHIUM AT 500~F, AND LITHIUM-AT 1500~F Lead-Bismuth Alloy: Figures 88 through 93 Mercury: Figures 94 through 99. Water: Figures 100 through 105 Lithium at 5009F: EFigures. 106 through 111 Lithium at 15000F: Figures 1.1:2 through 117. -358

-3592.0 o ~ o REFRACTORY ALLOYS 1 FERROUS METALS 1.8 1.6 m 1.4 0 1 1.0 N oy i _.4.20 1920 CO 0 20 40 60 80 100 120 140 TENSILE STRENGTH, PSI x 10 Fig. 88. —Normalized inverse cavitation damage versus tensile strength - lead-bismuth alloy.

-3602.0 0 REFRACTORY ALLOYS * FERROUS METALS 1.8 1.6 1.4 0L2.4 0 0.I I I0..8. *~~...... Q'''t.8 00 20 60 80 100 120 140 YIE'LD STRENGTH, PSIxl O Fig. 89. —Normalized inverse cavitation damage versus yield strength - lead-bismuth alloy.

-3612.0 0 REFRACTORY ALLOYS *( FERROUS METALS 1.8...... 1.6...... i4 ____. _____ —, >Q ~ ~ ~, 0 UJ / 1.2 C,) z. /,.0.6 0 I 1 / I 1. 28.. 0 4 12 ENGINEERING STRAIN ENERGY, PSI x 10 Fig. 90. —Normalized inverse cavitation damage versus engineering strain energy - lead-bismuth alloy.

-3622.0 o REFRACTORY ALLOYS * FERROUS METALS 1.8 1.6_. 4 1.4 11.2 ~ i 10-0s 4 0 - 01 I.0,J 0.6 __ _ PIx 0.4 1923 00 O -20 ~~ 30 40 50 60 TRUE STRAIN ENERGY, PSIx O 10 Fig. 91. —Normalized inverse cavitation damage versus true strain energy - lead-bismuth alloy.

-3632.0 0 REFRACTORY ALLOYS B FERROUS METALS 1.8 1.6 c1 1.4 o 0 1.2 I0 )... C)' zLJ z / ~~~0,6.4.2 1924 0 40 [0 ~ 120 160 200 240 280 HARDNESS, DPH (I.I KG. LOAD) Fig. 92. —Normalized inverse cavitation damage versus hardness - lead-bismuth alloy.

-3642.0 REFRACTORY ALLOYS' FERROUS METALS 1.8 1,6 4 I I * 0 1.0 W' 1 Co Z_ 0 8 / N Fig. 93. —-Normalized inverse cavitation damage versus ultimate resilience - lead-bismuth alloy. resilience - lead-bismuth alloy.

-365 — 10. i-.. 0 REFRACTORY ALLOYS @ FERROUS METALS 8 PLEXIGLAS 9 8 7' 6 0 IN I I1 Z; ___1~~~~~II___ II 0 JT^^ O lit' 0 - TENS LE STRENGTH PSI xl03 |: 0 50 100 150 200 250 300 350 Fig. 94. —Normalized inverse cavitation damage versus tensile strength - mercury.

-36610 ~~~~~~~ o REFRACTORY ALLOYS ( FERROUS METALS 1 J PLEXIGLAS 7 Lu CD 6 o 5: u. 4 O 0 N 2 -4 0 e 3 _Z _.. - _ I~fi^^p *___________ _ _YIELD STRENGTH, PSI x 10_ 0 50 100 150 200 250 300 350 Fig. 95. —Normalized inverse cavitation damage versus yield strength - mercury.

-367- 10 0 REFRACTORY ALLOYS * FERROUS METALS 0 PLEXIGLAS 9 7C$ C: 4C,I9. -.~-~.. ~ ~ - ~.. --'-~., 6.: - - _. g strain — erg — me z 0 e. 10 20 0 40 50 6' 70

-36810 o REFRACTORY ALLOYS * FERROUS MET-ALS 8 No I0 4 I-.. 0 LUi 0.. O 3 4 -i~ I r: TRUE STRAIN ENERGY, PSI xlO^ * 1928 0 20 40 60 80 100 120 140 Fig. 97. —Normalized inverse cavitation damage versus true strain energy - mercury.

-369 — 10,.,'' - 0 REFRACTORY ALLOYS 0 FERROUS METALS 83 PLEXIGLAS 9 ~.. 6t.z I f-t 4 I. 2 0&1: i e mercury,, 3 Z _ mercury...

-37010 I 0 REFRACTORY ALLOYS 0 FERROUS METALS E PLEXIGLAS 8 -*~ -* —l 7 k i.... hi F / 4 0 3 0 00 300 I.I PI ___ r0 300'600 900 1200 1500 1800 1 2100 Fig. 99. —Normalized inverse cavitation damage versus ultimate resilience - mercury. resilience - muercury.....

icD 1.4 1~.4 i Q j0 REFRACTORY ALLOYS tj *( FERROUS METALS i H. " El PLEXIGLAS 1,* AI, Cu, Ni, Cu-Ni, Cu-Zn rt r (D I o NI CD CD 0 o 20 40 *" C D" I!I.6 >'>' _ _ _ _ CD ^J^ TENSILE STRENGTH, PSI x 103O ~' 0 20 40 60 80 100 120 140 160 180 200 oD

1.4.,, 0 REFRACTORY ALLOYS * FERROUS METALS E PLEXIGLAS 2 Al, Cu, Ni, Cu-Ni, Cu-Zn ________ 0 0: |. | l YE.P x 13ll W 0" LO -' ~ ~,~ ^ ~t~ent~ ~ ~a~e~ -,.hi.6/ z,: O 4 hJ.4s- -- water N ~ 2 */ ^: YIELD STRENGTH, PSi x IO 0 2'0 40 60 80 100 120 140 160 180 200 Fig. 101. —Normalized inverse cavitation damage versus yield strength - water.

1.4 O REFRACTORY ALLOYS * FERROUS METALS iE PLEXIGLAS AI,Cu, Ni, Cu-Ni, Cu-Zn 1.2 ~~~~ __~ Z. 1.0o - Q _. ~_ /_____ W' I f. 1.2 -: O' ~.... 9'.4~ ~ 0 I0 20 30 40 50 60 70 80 g 90 I00 Fig. 102. —Normalized inverse cavitaton damge versus engineering strain energy - water.

1.4. 0 REFRACTORY ALLOYS * FERROUS METALS E] PLEXIGLAS ~ Al, Cu, Ni, Cu-Ni, Cu-Zn 1.2 ~.....' -.. "I.. w Fi "... —Normalized inverse cavitation damage versu true 1.0 0____ I},6 2- 4 60 8 1 1 4 6 18 200 ^' F 13 -o invrs tio da ve19u Fig. s03. —Normalized inverse cavitation damage versus true strain energy - water.

J, 1.4 O REFRACTORY ALLOYS * FERROUS METALS X PLEXIGLAS * Al, Cu, Ni, Cu-Ni, Cu-Zn ________________ 1.2....... 01.-.~.~ 4~ ^.. ~. ~ - ~...'~.... - z > w'... 0 EI.24 -41934 i^ l ~~ I I HARDNESS, DPH (I.I KG. LOAD) O0 40 s0 120 160 200 2840 2)0 320 360 401 Fig. 104. —Noorm alized inverse cavitation damage versus hardness- water.

'1.4 0 REFRACTORY ALLOYS FERROUS METALS e PLEXIGLAS Al, Cu, Ni, Cu-Ni, Cu-Zn.>, reilience3 -4 w40 W Z 1-o 0 12.'.6..'''.-% /, ^"^^ ULTIMATE RESILIENCE, PSI 60 120 240 300 360 420 480 540 600 Fig. 105. —Normalized inverse cavitation damage versus ultimate resilience - water.

-37720 O REFRACTORY ALLOYS 0 FERROUS METALS 18 16..~ 14 -z o. w 10 II 0 60 4 c /n id: s0 2) 40 6)gh 80 lt10 a 2 00 ~ 140 T- TENSILE STRENGTH, PSI x 10 Fig. 106. —Normalized inverse cavitation damage versus tensile strength - lithium at 5000F.

~JoOOg:IninEq^T - qL~u9.is plT;' SnsJLL A;DSVMuIp -UOT4 LLTASnAU 2paZ l'l UOV — -E0 U':SL ~01 X Id'HIO9N3.M18 a'31A 3 ~^10 Ot1 _1 __ 001 08_ 09 O8C Oa 0o ~6~1 /;C:! 9 o ~^ N.. m ______ I II i >.... ~ - - ~~~~~,,',......,,,' *.. 81 S'lV. 3W SnnO 3J 0 SAO''V A:IO.LDVt:I3 0

-37920 0 REFRACTORY ALLOYS * FERROUS METALS 18... -- ~ 16 u J 14 0 2< 0~,w /IO.... > /' /e N 4S ^ ___ 60 _____ * ~ 1937 0 4 8 12 16 20 24 28 ENGINEERING STRAIN ENERGY, PSI x 10 Fig. 108. —Normalized inverse cavitation damage versus engineering strain energy - lithium at 5000F.

-38020 1 0 REFRACTORY ALLOYS * FERROUS METALS 18 ~ ~~~~~ 16.... w 0 I - z A "( 14' - SD6_____ 0U S N E, e - l a - = 4_________T_

-38120 1 O REFRACTORY ALLOYS * FERROUS METALS 18 ~ "~ ~.. Is u.I 1 W m 10 I I I A 20 O I ~ ~ ~ ~ ~........ Z 0 HARDNESS, DPH (1.1 K0. LOAD) Fig. 110. —Normalized inverse cavitation damage versus hardness - lithium at 5000F.

-38220 0 REFRACTORY ALLOYS * FERROUS METALS 18 ~~~~~~~ I 16 LLX 14 4 I - I0- /. (0 I2 -J 2 _ _ _ _ _ _ _ _ _ _ _ _.' ULTIMATE RESILIENCE, PSI 1964 0.'40 80 120 160 200 240 280 Fig. lll. —Normalized inverse cavitation damage versus ultimate resilience - lithium at 500~F.

-38310 0 REFRACTORY ALLOYS B FERROUS METALS 9 < 7 6 i / z I I 0 1',4 o 3 -J / 1940 O 2 0 40 60 80 I1oO 1I 0 TENSILE STRENGTH, PSI x 103 Fig. 112. —Normalized inverse cavitation damage versus tensile strength- lithium at 15000F.

-384I0 0 REFRACTORY ALLOYS * FERROUS METALS 4 2 l^ (0 t/ 30 0 0 YIELD STRENGTH_ PSI x _03 Fig. 113. —Normalized inverse cavitation damage versus yield strength - lithium at 15000F.

'aoOOIT 1e mTrlUTTI - bAgau UTI u S guT -:laUTuaO snsalA aSmvep UOTeTA3O asIaAUT pazTT ST1o N — -7Tl *TAI o01 X Id'A9O3N3'NiVlS:'NIa33Ni9N3a 8 _'t 0' 91 01 - Z I 8 tP' Oo L'1 | 1 91961 ________________________________I_________________ I 1'zI 1 1 /^2 /<T X 7 ^ 1 D'*' ~/~ ^~~r fTI m / m SIV1L3W sno0H3-* ~ 0V ] _______ _ ______ 0,,. ~ -.,,....~~~~~~~~~~0

-38610 I 0 REFRACTORY ALLOYS 0 FERROUS METALS 9 4 I0' ~ 40 6 7 0 0 / S.. I- VX 4 0~0 10 )- 20 30)- -- 40: 50 60 70 TRUE STRAIN ENERGY, PSI x lO0 Fig. 115. —Normalized inverse cavitation damage versus true strain energy - lithium at 15000F. strain energy - lithium at 1500~F.

-3870 FERROUS METALS 9 ~~~ S 7 4 Z /. 2 0 I 4 I i i eFig. 116. —Normalizedierse cavtation amage versus Fig. hardne6. —Normaized inverse cavtation damage versus hardness- lithium at 1500~F.

-38810 O REFRACTORY ALLOYS * FERROUS METALS 9 8 I w 440 0 740 8o 120 160 200 _ _ 280 6. 5 i. Co resilience - lithium at 1500 (F. >L 0.

REFERENCES 1. Royal Society Discussion on Deformation of Solids Due. to Liquid Impact, May 27, 1965; Londion,' England. 2.o Decker, 0., "Cavitation Erosion Experience in Liquid Mercury Lubricated Journal Bearings," First Annual Mercury Svmposium, November, 1965, Atoinics International, C:aoga Park, California, p. 14. 3. Shoudy, Ao Ao and Allis, R. J., "Materials Selection for Fast'React~or Applications, " Proc.o of Michigan- NS Fast Reactor Topical Meeting, April, 1965, Detroit-Michigan. 4. Wood, G.., Kulp, Ro S. and Altieri, J. V. "CavitationDamage Investigations in Mixed-Flow Liquid Metal Pumps," Cavitation in Fluid Machinery ASME, November, 1965, pp. 196-214. 5. Smith, P. G., DeVan, J. -H. and Grindell, A, G.,'"Cavitation Damage to Centrifugal Pump Impellers During Operation with Liquid Metals and iMolten Salt at 1050-14000F-'" Journal of Basic:Engineering,. Trans. ASME, September, -1963, pp. 329-337. 6. Hunt, J, B,, "Cavitation in Thin Films of Lubricant," The Engineer, January 29, 1965, ppo 22-23., 7. Euler, Leonhard, "Theorie plus complete des machines qui sont mises mouvement par la reaction de l'eau" (More Complete Theory of Machines:Driven by Hydraulic R:eactioon), Historie de l'Academie Royale des Sciences et Belles: ettres, Classe de Philosophie Experimentale, Germany, 1754.o 8. Reynolds, 0., "Experiments -Showing the Boiling of:Water in an Open Tube at Ordinary Temperatures," British Assoco Adv. Sci, Report, 18940 1-'.... 9. oBesant, W., A Treatise on Hydrodynamics, Cambridge University Press, Cambridge, England, -1859. - 10.. Rayleigh, Lord, "On the Pressure Developed in a-Liquid During the Collapse of a Spherical Cavity"-' Phil. Mag., Vol. 34, 1917, pp. - 94-98..... 11. Thornycroft, J., and Barnaby, S. W,, "Torpedo Boat Destroyers," Proc.. -Inst. Civil Engineers. Vol. o 122, 1895, p. 51. - -389

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-391- 24. WrightE. A., "Some. Interniational Aspects of Ship Model Research," David Taylor Model Basin Re.port.l20, Apri!, 1-958. 25. Knapp, R. T., "Recent Investigations of the Mechanics of Cavitation - and Cavitation Damage, "-Tratns. ASM, Vol, 77, No. 7,- Oictober, 1955, pp 1045-1054.-.-: —26. Rasmussen, R. EoH,. "S ome -.Experiments —.on Cavitation Erosion in Water Mixed with Air, Cavitation in H-drodynamics- Procwi National Phys. Lab. Symposium, 0Paper No, 2 0, H M_. Statio nery Office, London, England:1956. - April., 1966. 28i- - Kelly, R. W., Woodf, GC M., Marmnan, H. V. and Milich, J.: J., "Rotating Disk Approach for Cavitation Damage Studies in High Temperature Liquid Metal," ASME Paper No. 63-AHWT-26, March, 1963. 29. Gaines, N., "A Maggetostrict-ion Oscillator Producing Intense Audible Sound and. Some: Effects Obtained," Phy.sicss Vo:1. 3 No. 5,.1932, pp. 209-22-9., -- 30. Kerr, S. Logan, "Determination of the Relative Resistance to Cavitation Erosion by the Vibratory Method" Trans. E V. ol. 59, July, 1937, pp. 373-397. - 31 Schumb, W.C., Peters, H. and Milligan, L. H., "New Method for - Studying oavitation Erosion of Metals," Metals:and Allos, Vol. 8,May., 1937, ppe 126-132.. ~;.; -. 32. Nowotniy, H.,':estruction of Materials by Cavitation," VDI-Verlag,. BerlGine, Goermany, 1942. o-Rerinted: by Edwards:Broth ers Inc., Ann Arbor, Mich-igan, 1946. English Translation available -as ORA -Internal Report No. 03424-15-I, Department of Nuclear Engineering, T. he -University of Michigan, 1962. 33.0 Leith, W. CS and Thompson, A. Lloyd, "Some Corrosion Effects in: Accelerated Cavitation Damage," ASME Paper No. 59-A-52, November, ~ ~ ^.1 95 9.....:'....... 340. Rheingans, W.eJ., "Accelerated C avitation Research," Trans. ASME Vol. 72., No. 5, July, 1950, pp. 705-719. 35. Plesset, M. S.," Ont.Ctathodic Protection in Cavitation Damage," Journal of Basic Engineering, Trans. ASME, Series D, Vol. 82, No. 4, 1960,:pp. 808-820.'

-39236. Thiruvengadam, A. and Preiser, H. S., "On Testing Materials for Cavitation Damage Resistance," Hydronautics,- Inc., Technical Report No. 233-3, December, 1963. 37. Thiruvengadam, A., Preiser, H. S. and Rudy, S. L., "Cavitation Damage in Liquid Metals," Technical Progress Report 467-2 (NASA CR-54391) For the Period January 1, 1965, to March 31, 1965,.Hydronautics, Inc., April.28, 1965. 38. Thiruvengadam, A.. Preiser, H. S. and Rudy, S. L., "Cavitation Damage in Liquid Metals," Technical Progress Report.467-3 (NASA CR-54459) For the Period April 1, 1965, to May 31, 1965, Hydronautics, Inc., June 30, 1965. 39. Young, S. G. and Johnston, J. R.,'-'Accelerated Cavitation Damage of Steels and Super-Alloys in Sodium and Mercury," presented at ASTM Annual Meeting, Symposium on Erosion by Cavitation or Impingement, Atlantic City, New Jersey, June,; 1966; to be published by ASTM. 40. Garcia, R. and Hammitt, F. G., "Ultrasonic-Induced Cavitation in Liquid Metals at 1500~F," Internal Report No. 05031-1-I, Department of Nuclear Engineering, The University of Michigan, February, 1965; also Transactions of the American Nuclear Society, Vol. 8, No. 1, June, 1965, pp. 18-19. 41. Garcia, R, and Hammitt, F. G., "Ultrasonic-Induced Cavitation Studies in Lead-Bismuth Alloy, 500-15000F," Corrosion, Vol. 22, No. 6, June, 1966, pp. 157-167. 42. Garcia, R., Nystrom, Ro E. and Hammitt, F. G., "Ultrasonic-Induced Cavitation Studies in Mercury and Water," ORA Technical Report No. 05031-3-T, Department of Nuclear Engineering, The University of Michigan, December, 1965. See also "Comprehensive Cavitation Damage Data for Water, Mercury and Lead-Bismuth Alloy Including Correlations with Material and Fluid Properties," presented at ASTM - Annual Meeting,? Symposium on Erosion by Cavitation or Impingement, Atlantic City, New Jersey, June, 1966; to be published by ASTM. 43. Garcia, R. and Hammitt, F. G.,. "Ultrasonic-Induced Cavitation Studies in Lithium at Elevated Temperatures," ORA Technical Report No. 05031-5-T, Department of Nuclear Engineering, The University of Michigan, May, 1966. 44. Ellis, A. T., "Production of Accelerated Cavitation Damage by an Acoustic Field in a Cylindrical Cavity," Journal of the Acoustical Society of America, Vol.. 27, No. 5, September, 1955, pp. 913-921. 45. de Haller, P., "Untersuchungen uber die durch Kavitation Hervorgerufenen Korrosionen," Schweiz. Bauztg., Vol. 101, 1933, pp. 243-246, 260-244.,f';

-393- 46. Hobbs, Jo M., "Problems of Predicting Cavitation Erosion-from Accelerated Tests, ASME Paper No. -61-HYD-19, 1961.. 47. Petracchi, G., "Investigations of Cavitation Corrosion," La Metallurgia Italiana, Vol. 41, No. 1, 1949, pp. 1-6. See also Engineering Digest, Vol. 10, No. 9, September, 1949, po 314. 48. Plesset, M. S., "The Pulsation Method for Generating Cavitation Damage," Journal of Basic Engineering, Trans. ASME, Vol. 85, Series D, No. 3, 1963, pp. 360-364. See also "'Pulsing Technique for Studying Cavitation Erosion of Metals," Corrosion, Vol. 18, No. 5, May, 1962, pp. 181-188. 49. Wheeler, W. H., "Indentation of Metals by Cavitation," Journal of Basic Engineering Trans ASME, March, 1960, pp. 184-194. 50. Hammitt, F. G., "Cavitation:Damage and Performance Research Facilities,' Symposium on Cavitation Research Facilities and Techniques, pp. 175-184, ASME Fluids Engineering Division, May, 1964. See also ORA Technical Report No. 03424-12-T, Department of Nuclear Engineering, The University of Michigan, November, 1963. 51. Garcia,9 R. and Hanmitt, F. G.,o "Ultrasonic-Indvced Cavitation Studies," ORA Technical Report No, 05031-1-T, Department of Nuclear Engineering, The University of Michigan, October, 1964. 52. Blitz, J., Fundamentals of Ultrasonics,'Butterworth & Co., Ltd., London, England, 1963. 53. Frederick, J. R., Ultrasonic Engineering, John Wiley & Sons, Inc., New York, 1965.' 54. Mason, W, P., "Internal Friction and Fatigue in Metals at Large Strain Amplitudes," Journal of the Acoustical Society of America, Vol. 28, No. 6, November, 1956, pp. 1207-1218. 55. Aydinmakine, F, A., "High-Temperature Vibratory Cavitation Damage Research Facility of the University of Michigan," Term Paper Submitted for the-Course Mechanical Engineering 600, May 15, 1964, University of Michigan, Ann Arbor, Michigan. 56. Kerr, S. Logan and Leith, W. C., "A Review of Cavitation Damage by the Vibratory Method at the Dominion Engineering Works, Limited," Dominion Engineering Works, Limited, Technical Report, 1955. 57. Garcia, R. and Hammitt, F. G., "Amplitude Determination of an Ultrasonic Transducer by Means of an Accelerometer Assembly," Internal Report No. 05031-7-I, Department of Nuclear Engineering, The University of Michigan, December, 1965.

-39458~.H "io D etu-S 58. Hammitt,- F G.,."Damage to Solids Caused by Cavitation," to be published Proc, Royal Society; presented at Royal Society Discussion on Deformation of Solids Due to Liquid Impact, May 27, 1965, London, England. 59. Plesset, M. S. and Devine, R. E., "Effect of Exposure Time on Cavitation Damage," ASME Paper No. 65-WA/FE-23; to be published Journal of Basic Engineering Trans. ASME, 60. 0lson H. G., "High Speed Photographic Studies of UltrasonicallyInduced Cavitation and Detailed Examination of Damage to Selected Materials," Ph.D. Thesis and ORA Technical Report No. 07738-2-T, Department of Nuclear Engineering, The University of Michigan, August, 1966.. - 610 Jackson, F. J. and Nyborg, W. L., "Sonically-Induced Microstreaming Near a Plane Boundary..I. The Sonic Generator and Associated Acoustic Field,"' The Journal of the Acoustical Society of America,.Vo l. 32, No..10, October, 1960, pp. 1243-1250. 62. Jackson, F. J., "Sonically-Induced Microstreaming Near a Plane Boundary. II. Acoustic Streaming Field," The Journal of the;Acoustical Society of. America,- Vol. 32, No.. 11,.November, 1960, pp. 1387-1395.: ~. -. 63. Crofford, W. N., Kovacina, T. A. and Miller, R. R., "Isothermal Study of Concentration and Transport of Radioactive Stainless Steel Components in Liquid Lithium," NRL Report 5572, U.S. Dept. of Commerce, Dec. 29, 1960. 64. Garcia, R. and Hammitt, F. G., "Ultrasonic-induced Cavitation Studies in Lead-Bismuth Alloy at Elevated Temperatures," ORA Technical Report No. 05031-2-T, Department of Nuclear Engineering, The University of Michigan, June, 1965. See also "UltrasonicInduced Cavitation Studies in Lead-Bismuth Alloy at Elevated Temperatures," Internal Report No. 05031-4-I, Department of Nuclear Engineering, The University of Michigan, September, 1965. 65. Leith, W. C., "Prediction of Cavitation Damage in the Alkali Liquid Metals," to be published in ASTM Proceedings,. 1965. 66. Devine, R. Eo and Plesset, M. S,, "Temperature Effects in Cavitation Damage," Report.No. 85-27, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, April, 1964. 67. Hobbs, J. M., "Experience with. a 20-Kc, Cavitation Erosion Test,. Paper #120 presented at 1966 Annual ASTM Meeting, Symposium on Erosion by Cavitation or Impingement, Atlantic City, New Jersey, June, 1966.

-39568. Kemppainen, D. J. and Hammitt, F:. G,, "Effect of Temperature on' Cavitation Damage," ORA Internal Report No. 05031-10-I, Department of Nuclear Engineering, The University of Michigan, July, 1966. 69. Stahl, H. A. and Stepanoff, A. J., "Thermodynamic Aspects of Cavitation in Centrifugal Pumps," Trans ASME, Vol. 78, 1956, pp. 1691-1693. - 70. Plesset, M. S. and Ellis, A. T., "On the Mechanism of Cavitation Damage," Trans. ASME, Vol.: 77, No. 7, October, 1955, pp. 1055-1064. * g.. S.;b.r.-.9.5: p 71. Harrison, Curtis:A., Robinson, M. John, Siebert, Clarence A., Hammitt, Frederick G. aand Lawrence,; Joe, "Complete Mechanical Properties Specifications for Materials as Used in Venturi Cavitation Damage Tests," Internal Report No. 03424-29-I, Department of Nuclear Engineering, The University of Michigan, August, 1965. 72. Shalnev,-.K., "The Energetics Parameter and Scale Effect in Cavitation Erosion," Akademiya nauk SSSR, Izvestiya Otdeleniye teknicheskikh nauk. Mekhanika i mashinomostroyeniye, No. 5, 1961, pp. 3-10. 73. Thiruvengadam, A., "A Unified Theory of Cavitation Damage," Journal of Basic Engineering, Trans. ASME, Vol. 85, Series D, No. 3, September, 1963, pp. 365-376.' 74. Thiruvengadam, A., "Prediction of Cavitation Damage," Ph.D. Thesis, Dept. of Hydraulic Eng., Indian Institute of Science, Bangalore, India, 1961. 75. Personal Communication from Henry P. Leeper, Project Metallurgist, Pratt & Whitney Aircraft (CANEL), to F. G. Hammitt; February 26, 1965, and May 13, 1965. 76. Plesset, M. S., "Bubble Dynamics," Report No. 85-23, Division of Engineering and Applied Science, -California Institute of Technology, February, 1963. 77.' Hammitt, F. G. and Smith, W., "Bubble Dynamics," Department of Nuclear Engineering, The University of Michigan, October, 1962, to be published....'' b.'..e's i''.. 78. Hammitt., F G.,'Liquid-Metal Cavitation —Problems and Desired Research," ASME Paper No. 60-HYD-13,. March, 1960.....po 79. Florschuetz, L. W. and Chao- B. T., "On the Mechanics of Vapor Bubble Collapse —A Theoretical -and Experimental Investigation," Report ME-TN-1069-2 Department of Mechanical and Industrial.Engineering, The University of Illinois, Urbana, Illinois, October, - 1963.

-39680. Hoff, G., Langbein, G. and Rieger, H., "Investigations of Material-:Destruction Due to Liquid Impact," Dornier-System Technical Report, translated..from the German... 81.' Wilson, R., W.:and Graham, R1., "Cavitation of Metal Surfaces in Contact with Lubricants, "'Conference on Lubrication and Wear, The Inst'itution'of~ Mechanical Engineers, London, England, October, 1957.. 82. Ivany, R.D., "Collapse of a. avitation Bubble in.Viscous, Compressible Liquid —Numerical and Experimental Analyses," Ph.D. Thesis, Department of Nuclear Engineering, The University of.Michigan, April, 1965; Also:available as OA,.._.Technical! Report No.:03424-15-T., ~..The University of. Michigan-. -:. 83..Ivany, R. D. and Hammitt,F..G ca... vavitation Bubble Collapse in Viscous Compressible Liquids —Numerical Analyses," ASM Paper No. 65-FE-16; to be published Journal of Basic Engineering, Trans. ASME. 84. Hickling, Robert and Plesset, Milton S., ~"Collapse and Rebound of a Spherical Bubble in Water," The Physics of Fluids, Vol. 7, No. 1, January, 1964, pp. 7-14. 85. Liquid Metals Handbook, Richard N. Lyon, Editor-in-Chief, Second Edition, June, 1952. 86, -International Critical Tables, Compiled by Clarence J. West and Callie Hull,. McGraw-Hill Book Company, New York, 1933. -87.. Weste'rvelt, Franklin H., "Automatic System Simulation Programming," Ph.D. Thesis, College of Engineering, The University of Michigan, November, 1960. 88. Crandall, Richard L., "The Mathematical and Logical Procedures of the Stepwise Regression Program with Learning," University of Michigan Computing Center Internal Report, 1965. 89. Rohsenow, W. M., Editor, Developments in Heat Transfer, The MIT Press, Cambridge, Massachusetts, 1964. 90. Proceedings of the Conference on Selected Technology for the Petroleum Industry., NASA Lewis Research Center.Cleveland, Ohio, December 8-9, 1965. 91. Collier,-.J. G., "The Boiling of Sodium and its Significance to the Safety of Fast Reactors," Internal Document,.. Chemical Engineering Division, A.E.R.E. Harwell,. January, 1966.

-39792. Simpson, H.C. and Silver, R. S., "Theory of One-Dimensional, TwoPhase Homogeneous Non-Equilibrium Flow," Symposium on Two-Phase Fluid Flow, Institution of Mechanical Engineers, London, February 7, 1962... - 93. Plesset, M. S. and Zwick, S. A., "The Growth of Vapor Bubbles in Superheated Liquids," Journal.,of Applied Physics, Vol. 25, No. 4, April, 1954, pp. 493-500. 94. Plesset, MN.,S., "The Dynamics of Cavitation Bubbles," Journal of Applied Mechanics, September,1 1949, pp. 277-282... -... f..,... 95. Private Communication from Robert S Ruggeri-, NASA Lewis Research Center, Cleveland, Ohio-, May 10-,-1966, File: No..2751. 96.. Hollander, A., "Thermodynamic Aspects of Cavitation in Centrifugal Pumps," American Rocket Society Journal, October, 1962, pp. 15941595. 97. Sears,. Francisr W., Mechanics, Wave Motion, and Heat, AddisonWesley Publishing Co., Inc., Reading, Massachusetts, 1958, pp. 602-604. 98. Van Wylen, Gordon J. and Sonntag, Richard E., Fundamentals of Classical Thermodynamics, John Wiley & Sons,, Inc., New York, 1965, pp. 331-332. 99. Hammitt, F. G., Robinson, M. John, Siebert, C...A. and Aydinmakine, F. A., "Cavitation Damage Correlations for Various Fluid-Material Combinations," ORA Technical Report No. 03424-14-T, Department of Nuclear Engineering, The University of Michigan, October, 1964. 100. Heymann, F. J., "On the Time Dependence of the Erosion Rate Due to Impingement or Cavitation," Paper #136 presented at. 1966 Annual ASTM Meeting, Symposium on Erosion by Cavitation or Impingement, Atlantic- City,. New Jersey, June, - 1966. 101. Hammitt, F. G., Discussion of Paper #136, ASTM Symposium on Erosion by Cavitation or Impingement, June, 1966, entitled "On the Time Dependence of the Erosion Rate Due to Impingement or Cavitation," by F. J. Heymann.

SELECTED BIBLIOGRAPHY (RELATED BACKGROUND MATERIAL) 1. Albers, Vernon M., Underwater Acoustics Handbook —Volume II, Pennsylvania State University Press,' 1965. 2. Blitz, J., Fundamentals of Ultrasonics, Butterworth & Co., Ltd., London, England, 1963. 3. Blitz, J., Elements of Acoustics, Butterworth & Co., Ltd., London, England, 1964. 4. Cady, Walter G., Piezoelectricity, Volumes One and Two, Dover Publicat-ions, Inc., New York, 1964. 5. Coleman, B. D,, Gurtin, M. E., Herrera, I., Truesdell, R. and Truesdell, C., Wave Propagation in Dissipative Materials, SpringerVerlag, Inc., New York, 1965. 6. Crandall, I. B., Theory of Vibrating Systems and Sound, D. Van Nostrand Co., New York, 1926. 7. El'piner, Isaak E., Ultrasound: Physical. Chemical, and Biological Effects, Translated from the Russian by K. L. Sinclair, Consultants Bureau, New York, 1964. 8. Frederick, Julian R., Ultrasonic Engineering, John Wiley & Sons, Inc., New York, 1965. 9, Hueter, T. F. and Bolt, R. H., Sonics, John Wiley & Sons, Inc., New York, 1955. 10. Kinsler, L. E. and Frey, A. R., Fundamentals of Acoustics, John Wiley & Sons, Inc., New York, 1950. 11. Krasil'nikov, V. A., Sound and Ultrasound Waves in Air, Water, and Solid Bodies, Jerusalem, Israel Program for Scientific Translations, Available from Office of Technical Services, U.S. Dept. of Commerce, 1963. 12. Mason, W. P., Physical Acoustics, Principles and Methods, Volume I, Part B, Academic Press, New York, 1964. 13. Mason, W. P., Piezoelectric Crystals and Their Applications to Ultrasonics, D. Van Nostrand Co., New York, 1950. -398

-39914. Sharman, R. V., Vibrations and Waves, Butterworth & Co., Ltd., London, England, 1963.