THE UNIVERSITY OF MICHIGAN College of Engineering Department of Mechanical Enginee ring Cavitation and Multiphase Flow Laboratory Report No. 03371-1-T IMPACT AND CAVITATION EROSION AND MATERIAL MECHANICAL PROPERTIES (Submitted for Journal Public ation) by F. 0. Hammitt Financial Support Provided by:. NSF Grant GK 13081

ABSTRACT The mechanisms of mechanical cavitation and liquid impingement damage are reviewed. In the light of available experimental and photographic evidence it is concluded that the predominant mechanisms in real flow situations of mechanical cavitation damage and liquid impingement damage are very probably the same, i. e. liquid jet impingement in both cases. Numerical data relating to the microjet diameter and velocity in the cavitation case is presented. A comprehensive data set involving only metallic materials, but with tests conducted in several types of cavitation facilities as well as liquid impact facilities, is used to obtain a relatively simple best fit correlation'in terms of conventional mechanical properties of materials. It is concluded that no very precise correlation of this type with general applicability even for metallic materials is possible, and that a standard error of estimate factor for a new material is of the order of 2. 5.

TABLE OF CONTEN\TS Page ABSTRACT.i LIST OF FIGURES....i LIST OF TABLES..iv I. INTRODUCTION..1 II. MECHANICAL DAMAGING MECHANISMS IN CAVITATION AND LIQUID IMPINGEMENT............1 A. Bubble Collapse Contours1 B. Non-Photographic Experimental Evidence of Damaging Bubble Collapse Mode.. 3 III. CORRELATION OF DAMAGE RATES WITH MECHANICAL MATERIAL PROPERTIES.............6 A. General Considerations......6 B. Mechanical Property Correlations.7 IV. CONCLUSIONS.9 V. BIBLIOGRAPHY..1 FIGURES..13 TABLES. 2

LIST OF FIGURES Figure Page 1. Cavitation Bubble Near Venturi Splitter. 13 2. Cavitation Craters on Cadmium-Plated Stainless Steel..16 3. Cavitation Craters on Plexiglas. a *17 4. Water Droplet Impact Crater on Plexiglas...18 5. Non-Symmetric Cavitation Craters on Plexiglas..19 6. Correlation of I/MDPR with Ultimate Resilience.'20 7. Correlation of I/MDPR with UR x Hardness. 21 2 8. Correlation of 1/MDPR with UR x F.22

LIST OF TABLES

IMPACT AND CAVITATION EROSION AND MATERIAL MECHANICAL PROPERTIES I. INTRODUCTION The detailed mechanisms whereby cavitation or liquid impingement cause damage to even the strongest of materials are undoubtedly extremely complex. In the case of either phenomenon, mechanical effects are apparently usually predominant, although in both cases corrosive effects are also more or less important. While either phenomenon as encountered in the field may often include both significant corrosive and mechanical influences, the combined phenomena in the present state of the art seems too complex for useful basic study. Hence, most laboratory investigations of cavitation or liquid impingement have been conducted with mate rial- fluid combinations and'Intensities suchbthat mechanical effects predominate. The present paper concerns only the basic mechanisms involved in mechanical attack from either cavitation or liquid impingement. In addition, the correlation of volume loss rates from cavitation or liquid impingement with material mechanical properties is discussed along with the statistical merit of various correlations. II. MECHANICAL DAMAGING MECHANISMS IN CAVITATION AND LIQUID IMPINGEMENT. A. Bubble Collapse Contours As is well-known to cavitation researchers, it has been usually assumed from the time of Rayleigh's original bubble collapse analysis ()until recent years that mechanical cavitation damage results from the imposition of essentially spherical shock waves promulgated through the liquid from the site of bubble collapse onto

2 studies have shown, even when the real fluid properties of corn(2, 3) pressibility and viscosity are considered'.In addition,it is to be expected on theoretical grounds that the bubble centroid will move appreciably toward an adjacent surface during collapse (4' 5) so that the shock wave attenuation to be expected if the bubble cen(2, 3) ter were stationary is reduced. However, the probable importance of this mode of collapse and damage in real flow situations is greatly reduced in the author's opinion by the fact that it requires a very large ratio, about 103to 10 43)between initial and final bubble radius to generate shock wave pressures of the magnitude necessary to explain observed pitting in strong materials. Recent experimental evidence, some of which is briefly reviewed below, indicates the improbability of such collapse radius ratios in real flow situations, as well as the likelihood of the production of damage in many situations by a liquid microjet which forms as a result of the asymmetric nature of bubble collapse in real situations. In those cases where cavitation damage is the result of microjet impingement it is clearly closely analogous to liquid drop or jet impact damage, except perhaps for the effect of scale, i. e.,the drop or jet has a diameter which is probably many times greater than that of the microjet in cavitation. It is then probable that the microjet velocity must be greate r than that in the impact experiments if damage to equally hard materials, as is observed, is to occur. The collapse of a cavitation bubble through the radius ratio necessary to produce the observed pitting requires that a high degree of spherical symmetry exist. It has been shown theoretically~ that a spherical collapse is unstable even if asymmetric influences are minimal. In an actual flow situation involving cavitation damage, very strong asymnmetries are caused by the proximity of a wall

3 through more than a small radius ratio is unlikely before a microjet develops. This has been shown experimentally to be the case by various previous investigators( 8,9,10, etc.) Fig. 1 shows recent frames from a high-speed motion picture sequence obtained in our laboratory showing a spark-generated bubble in a water venturi collapsing adjacent to a knife-edge of aluminum, which is oriented parallel to the flow. It is clear that the effective radius decreases by a factor of about 10 before a microjet is formed. This then impacts the soft aluminum at about 100 m/s, which is sufficient to cause a crater. The bubble centroid moves appreciably toward the wall during this sequence. After the impact the bubble "rebounds' to an appreciable fraction of its initial size. It is possible to locate the single crater formed by such a single microjet impact. In this experiment, where the important parameters are under very close control, it is thus possible to produce a crater with a single bubble implosion. Actual flow experiments(11' e.g.) with random 4 cavitation fields normally showing a ratio of 10 to 10 between bubbles observed to collapse adjacent to surface and individual craters actually formed. The fact that such a large ratio is found for a random cavitation field, but that for carefully controlled collapse a unity ratio can be obtained (Fig. 1) is indicative of a very great sensitivity of damaging potential to precise bubble collapse parameters. Such a high level of sensitivity seems much more likely if the bubble collapses in the microjet mode rather than with spherical symmetry, since bubble orientation then becomes a variable parameter, in adubble size, position, and gas content. B. Non-Photographic Experimental Evidence of Damaging Bubble Co_ ll ae ModeAs mentnioned above, Fig. 1 shows a spark-generated

4 produced directly beneath the spark electrodes, presumably bythe shock waves radiated from the growing bubble. Thus this experiment also shows that the shock wave mechanism, at least for a growing bubble, can produce damage, and in fact provides a method for studying either shock or jet produced damage. In flowing fields, however, it seems unlikely for the reasons already discussed that bubble collapse can proceed in such a manner that shock wave damage wvill be a predominant mechanism. There'is at present no direct proof of this statement, but some experimental evidence in its support from our laboratory is shown in Figs. 2 and 3. Fig. 2 shows craters produced by cavitating water on a cadmium-plated stainless steel cylinder placed across the diffuser of a cavitating venturi. The cadmium thickness'is 0. 6 microns (0. 6 x 103 MM) and the full crater diameters are about 0. 1 mm. The cadmium-plate is completely removed from the central region (about 1/2 the full diameter) so that the under-lying stainless steel is exposed. This region is surrounded by an annular area from which the cadmium is partly removed. This damage disposition suggests the impact of a microjet which accelerates radially after impact (a common observation for the impact of actual liquid jets (2 ), and washes away the cadmium plate. However, we found in experiments where hard steel balls were shot at the surface (about 100 m/s) that a spherical shock front as thus provided would merely press the cadmium down into the surface rather than remove it. Presumably the cavitation craters were produced by a microjet of diameter less than that of the central region. If the diameter of the jet were about 1/2 that of the central region, the jet diameter would be about 0. 02 mm (20 microns). The diameter of the microjet shown in Fig. 1 is about 60 microns, but this spark-generated bubble is lar

5 estimates probably cover the actual range of microjet diameters in typical flow cases. Fig. 3 shows a cavitation crater produced in plexiglas in the cavitating water venturi. This crater has an overall diameter of about 12 microns, with a central impact region of about 4 micron diameter. Assuming that the jet which produced this crater had a diameter no more than that of the central region, the microjet diameter would be about 4 microns,9 i. e., of the same general order of magnitude obtained from the previously discussed estimates. The plexiglas crater shown in Fig. 3 is very similar to damage observed in plexiglas from the impact of large-scale droplets or jets. Fig. 4 shows such a crater of about 0. 8 mm diameter. As'is typical for plexiglas, there is a central relatively undamaged area directly under the droplet impact and the droplet diameter is about that of this region. Since this material is stronger in compression than tension, failure does not occur in the region of impact where the stress is compressive, but in a region at a considerably larger diameter where tensile stresses predominate. The very strong similarity in form between the very small cavitation pit and the much larger droplet impact pit in the plexiglas is evident, thus indicating the strong likelihood that the cavitation pit was formed by microjet impingement rather than shock wave imposition. Since the impact reg ion of the cavitation pit is indeed damaged, whereas it is not damaged inli:he case of the droplet impact (about 300 mis), the cavitation microjet impact velocity must be somewhat greater than this value in this case. Another segment of the experimental evidence from this laboratory favoring the theory of microjet rather than shock wave cavitation damage is the fact that the craters from individual

6 non-symmetrical craters are observed in the plexiglas tests (Fig. 5). This type of crater could easily be formed with a nonperpendicular jet impact. In fact this has been observed with larger drop impacts on plexiglas (12). However, it seems intuitively unlikely that such craters could be formed by the imposition of spherical shock waves, the local sound velocity being much greater than the flow velocities in the vicinity of the crater. III. CORRELATION OF DAMAGE RATES WITH MECHANICAL MATERIAL PROPERTIES A. General Considerations Many papers have been published over the last 30 to 40 years on the relationship between cavitation or liquid impingement damage and material mechanical properties. However, no good correlation, valid over a broad range of materials or test parameters has emerged. This lack of a precise correlation with mechanical properties of materials is no doubt due to many factors among which can be included, a) Corrosion effects are always present to some extent; b) Most mechanical properties are measured under semi-static conditions, but failure under cavitation or liquid impingement occurs in a few microseconds; c) Cavitation or impingement attack does not closely resemble any of the laboratory-induced failures used to measure various mechanical properties. d) The modes of failure under cavitation or impingement differ drastically between even metallic materials, and even for the same material depending upon the intensity of attack.

7 obtain an idea of the possible precision and generality of such fits. As explained in the following we have recently completed such an attempt. B. Mechanical Property Correlations Since it seems likely that the basic mechanical damaging processes in cavitation are very similar to those in droplet or jet impingement, we have used a data set which includes vibratory cavitation tests (with both vibrating specimen and stationary specimen) from our own laboratory, venturi cavitation tests (3 f rom the Indian Institute of Science, Bangalore, India, and rotating arm and disc impact tests from Dornier Systems (14) adEetiied France (15) In all cases the material mechanical properties are well known, and in many cases identical materials were used which were cut from the same piece of stock. Common materials linking all data sets existed, and the volume loss rates per unit exposed area (MDPR) were normalized to those common materials. In all cases the maximum volume loss rates were used. The resulting 33 normalized MDPR values (6 and all pertinent mechanical properties are listed in Table 1. The last two items, Stellite 6-B and a tool steel,were not considered in the correlation since their properties differ very substantially from those of the other materials and therefore they appear to be special cases. It is recognized that for any such data set it would be possible to generate a good correlating function in terms of any selected mechanical property or group of properties if sufficient degrees of freedom in the fitting function were used, i. e., a power series with a large number of terms might be used. However, since the physical model behind such a polynomial fit would be weak, it is not likely that the resulting correlation would fit new

8 volume loss rate would be inversely proportional to the energy required to remove a unit volume from the mater ial. Thus it was desired to find the best material property which could be derived from the conventional mechanical properties and would have units of energy per unit volume. Our own past experience in this regard (7, as well as suggestions of other investigators, 11) led us to assume that the mechanical energy property to be investigated would be a combination of ultimate resilience UR =(ultimate tensile stegh2/2(elastic modulus~, as suggested by Hobbs, (18) and strain energy to failure SE (1,ec), which is the total area under conventional stress-strain curve. Ultimate resilience is the area under the stress-strain curve if failure were entirely elastic, i. e., if brittle failure occurred. Observation of damage surfaces leads to the conclusion that this may be the case. We thus attempted a least mean square regression analysis fit of the type MDPR -C 0+C IUR +C2SE(1 Eq. (1) was investigated by computer, with the following results: a) The correlation coefficient with SE alone was very poor compared to that with UR. b) The correlation coefficient with UR and SE together was only slightly better than that with UR alone. Since in addition SE is much more difficult to evaluate for many materials of interest than is UR, SE was henceforth dropped from the correlation. c) The best fit value for C0 was close to zero, so that - - -', I,,, T_ _ - -0

9 d) If UJR is raised to an arbitrary exponent in the remaining relation, the best value for this exponent is very close to unity. It thus appears that the physics of the model, which assumes a first power energy relation, is essentially correct. Results (a), (16). (b), and (c) above were previously reported As a result of our own work above, we recommended the simple relation, eq. (2), that reciprocal maximum volume loss rate is proportional to ultimate resilience 1 MDPR - CR(' However, the fit is by no means precise. The correlation coefficient obtained was 0. 811 and the standard error of estimate, taken as a factor of the actual value, 2. 52. Other papers appearing at approximately the same time or subsequently have suggested that improved correlations can be obtained in terms of UR x (Brinell hardness) 1) or UR x (elastic 2 (20) modulus). We have investigated these suggested correlations for our own data set, and the results are shown in Table 2. The correlation coefficients are of the same order of magnitude but appreciably less than those for the simple UR relation, eq. (2), and the standard error of estimate factors considerably greater. Pig. 6, 7, and 8 show the actual data, standard deviation cone, and best fit line, IV. CONCLUSIONS From this investigation we conclude the following: a)Temchnclcmpnn f aiain aaei

10 close to solid objects. The asymmetries are the result of the proximity of the object to be damaged, pressure gradients, velocity gradients, etc. Thus cavitation damage and droplet or jet impingement damage is basically very similar. b) A precise correlation between cavitation and impingement damage rates and conventional material mechanical properties which will have general applicability to a broad range of materials, even if only metallic materials are considered, is not possible, for a standard deviation less than a factor of about 2. 52. Certainly, individual mateidals, such as Stellite 6-B can differ from the prediction by a much larger factor (~'l0 for Stellite). c) The best such correlation is in terms of the first power of ultimate resilience. Slight improvements may be possible in terms of more complex functions, but the improvement is not great.

V. BIBLIOGRAPHY 1. Lord Rayleigh, "'On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity", Phil. Mag., 34, 94-98, 1917. 2. R. Hickling and M. S. Plesset, "'Collapse and Rebound of a Spherical Cavity in Water"', The Physics of Fluids, -7, 1, 6-19, 1964. 3. R. D. Ivany and F. G. Hammitt, "'Cavitation Bubble Collapse in Viscous, Compressible Liquids -- Numerical Analysis'' Trans. ASME, J. of Basic Engr., D, 87, 4, 977-985, 1965. 4. A. Shima, "'The Behavior of a Spherical Bubble in the Vicinity of a Solid Wall"', Trans. ASME, D, 90, 1, 75-89, 1968.5. 0. A. Khoroshev, "'Influence of a Wall on the Collapse of Cavitation Bubbles"', Inzhenero- fizicheskiy Zhurnal, 6, 1, 5 9- 65, 1963. 6. M. S. Plesset and T. P. Mitchell, "'On the Stability of the Spherical Shape of a Vapor Cavity in a Liquid'', Quarterly Appl. Math., 13, 419-430, 1956. 7. T. B. Benjamin and A. T. Ellis, "'The Collapse of Cavitation Bubbles and the Pressures Thereby Produced Against Solid Boundaries",, Phil. Trans. Roy. Soc., A, 2609 1110, 221-240, 1966.8. S. P. Kozirev, "'On Cumulative Collapse of Cavitation Cavities"', Trans. ASME, 3. Basic Engr., D, 90, 1,1 116-124, 1968, 9. 5. P. Kozirev, "'Collapse of Cavities Formed by Electrical Discharge in Liquid"', Soy. Phys. -Doklady, 13, 11, 1168-1170, May 1969, (English trans.) 10. R. D. Ivany, F. 0. Hammitt, and T. M. Mitchell, "'Cavitation Bubble Collapse Observations in a Venturi", Trans. ASME,

12 11. M. J. Robinson, F. G. Hammitt, "Detailed Damage Characteristics in a Cavitating Venturi", Trans. ASME, J. Basic Engr., D, 89, 161-173, 1967. 12. A. A. Fyall, "Single Impact Studies with Liquids and Solids", Proc. 2nd Meersburg Conf. on Rain Erosion and Allied Phenomena, August,1967, edited A. A. Fyall and R. B. King, RAE, Farnborough, England. 13. R. C. Syamala Rao, N. S. Lakshmana Rao, K. Seetharamiah, "Cavitation Erosion Studies with Venturi and Rotating Disc in Water", ASME Paper 69-WA/FE-3, to be published Trans. ASME, J. Basic Engr. 14. G. Hoff, G. Langbein, H. Rieger, "Investigation of the AngleTime Dependence of Rain Erosion", Prog. Report No. 62269-7002050, Dornier Systems GmbH, March, 1968. 15. R. Canavelis, "Comparison of the Resistance of Different Materials with a Jet Impact Test Rig", HC/061-230-9, Electricite de France, Chatou, France, November,1967. 16. F. G. Hammitt, Y. C. Huang, C. L. K]ing, T. M. Mitchell, L. P. Solomon, "A Statistically Verified Model for Correlating Volume Loss Due to Cavitation or Liquid Impingement", ASTM Symposium on Characterization and Determination of Erosion Resistance, June, 1969, to be published ASTM STP. 17. R. Garcia, F. G. Hammitt, "Cavitation Damage and Correlations with Materials and Fluid Properties", Trans. ASME, J. Basic Engr., D, 89, 4, 753-763, 1967. 18. J. M. Hobbs, "Experience with a 20-kc Cavitation Erosion Test", ASTM STP No. 408, 159-179, 1967. 19. A. Thiruvengadam, "A Unified Theory of Cavitation Danmage", Trans. ASME, J. Basic Engr., D, 85, 3, 365-376, 1963. 20. F. J. Heymann, "Erosion by Cavitation, Liquid Impingement, and Solid Impingement", Engr. Report E-1460, Westinghouse Elec. Corporation, Dev. Engr. Dept., Lester, Pa., March 1968.

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16 Rk.-f~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 2443 Figure 2. Craters Produced by Cavitating Water on 0. 6 [im Cadm-rniumn-Platedp Stainless Steel. Mag.nification 18 x

17 Figure 3. Crater Produced by Cavitating Water in a Venturi on Plexiglas, Magnification 4, 000 x.

co Figure 4. Water Droplet Impact Crater on Plexiglas, Magnification 100 x. (After A. Fyall, RAE, Farnborough, England).

19 Water in a Venturi on Plexiglas, Magnification 4, 000 x.

9 _ Tool Steel Stellite 6B 1/MDPR = I g 1/MDPR = 13.6hr/mil 55. 5 hr/mil 8 UM Vibratory Cavitation / Facility ~~~~~~~~/ ~~UM Vibratory Cavitation * Facility with Stationary Specimen 0 RAE - Dornier Rotating Arm 6X~~~~ 0 ~~~~~~Facility / 0 ~~~~~/ / A~~~~ /\ Venturi Facility 5 L/ X Rotating Wheel Impact Facility / Best Fit Line 24F / o 0~~~~~~~~~~ 0 / 0 2933 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 UR (psi) Figure 6. Best Fit Correlation and Standard Deviation Cone for 1/MDPR vs. Ultimate Resilience for 33 Materials.

Tool Steel Stellite 6B 1/MDPR - 1/MDPR = 13. 6hr/mil 55.5 hr/mil 8 7 / Best Fit Line UM Vibratory Cavitation I Facility ~/ /~ OUM Vibratory Cavitation 6-// Facility with Stationary ~~~~~~~~~~7/ /Specimen RAE - Dornier Rotating Arm Facility 5 _ / I 0 f~~~~~~~~~~~~~A //Venturi Facility /~~~ 7/ X Rotating Wheel Impact E ~~~4 P~0/ / Facility I ~~~~~~~~~~~~~0 0 / O / 2 / / I/7 c?7 2934 0 105 2x 105 3 x 10s 4 x I 0 UR'HARD (psi'BHN) Figure 7. Best Fit Correlation and Standard Deviation Cone for 1/MDPR vs. UR x BHN for 33 Materials.

Tool Steel 4 Stellite 6B I/MDPR =13. 6 hr/mul 1 /MDPR 55.5 hr/mul 8/ UM Vibratory Cavitation 0 Facility UM Vibratory Cavitation 7 ~ ~ ~ ~ I0 Facility with Stationary / ~~~~~~~~~~~~~~Specimen 0 0~~~~~~~~~~~~~ RAE- Dornier Rotating 6 /0Arm Facility / B~~~~~~~~~e st Fit Line A Venturi Facility X Rotating Wheel Impact 5 /Facility / ~~0 4 I0 0 0 0~~~~~~~~~~~~ 2 / x 0 A.-~~~~~~~~~~~~~~~~~~~~~23 0~~~~~ 010172 x10'7 3 x 0'r 4 x 10'7 UR E2(Puis) Figure 8. Best Fit Correlation, and Standard Deviation Cone for 1/MDPR vs. UJR x E for 33 Materials.

___________________ ~~TABLE I. Mechanical Properties of Materials in Data Set YS TS __ Y _ EL HARD MDPR UR SE N~ S BS1433 ~COPPER O. 300E 05 0.360E 05 0.180E 08 0.180E 00 0.900E 02 0.647E 01 0.360E 02 0.648E 04 1.000 1.0 STAINLESS STEE L 31 6 _ O.~3-10E.05 0. 8_13E 05 — 0. 260E -08 0.690E 00 0.748E 02 0. 301E 00 0.127E 03 0.561E 05 3.5-31 8.657NIC(LE 270 0.800E 04 -0.488E 05 O. 277E 08 0.610E 00 0.249E 02 0. 128E 01 0.430E 02- 0-.298E 05 1.194 459 AL 6061 0. 407E 05 0.475E 05 0.910E 07 0.220E 00 0.600E 02 0.436E 01 0.124E 03 0.104E 05 3.444 1.3 ST AINL USS STEEL 304 0.647E 05 0.945E 05 0.290E 08 0.638E 00 0.237E 03 0.330E 00 0.154E 03 0.603E 05 4.277 9.0 BRONZE #1 0.2 43 E 05 0.452E 05 0.128E 08 0.230E 00 0.189E 03 0.189E 01 0.798E 02 0.104E 05 2.217 1.0 BRONZE # 2 O.70E 5.11-2-E 06 0A 8 0.205E 00 0.304E 03 0.63 00 0.2E03.2E5 i~. BRONZE # 3 0:880E 05 0.119E 06 _0.lI72E 08 0.150E 00 0.225E 03 0.220E 00 0.411E 03 0:178E 05 11.410 2.5 BRONZE #4.l0 5 ~~ 05.TT00EW 012E 03 ~TTE0.2E0.6E0.1.6 BRUNZE #D5 0.105E 05 0.189E 05 0.558E 07 0.130E 00 0.974E 02 0.330E 01 0.320E Q2 0.246E 04 0.889 0.9 0. 162E 05 0.193E 05 0.711E 07 0.300E-01 0.152E 03 0. 257E 01I 0.262E 02 0.579E 03 0.728 0.8 STAINLESS STEEL #1 0.115E 06 0.157E 06 _0.2b3E 08 0.220E 00 0.290E 03 0.25?E 00 0.470E 03 0.346E 05 13.050 5.3 STAINLrESS STEEL #2- U- - Y.8 6E 06-~WEU 0.2-57E 08 0.750E-01 0.418E 03 0. 2 7 E 0 EY011 -05 19.189 2.179q- STAINLESS STEEL #3 0.104E 06 0.1266 06 0.2 5 1E 08 0.195E 00 0.2646 03 0. 4306E 00 0.319E 03 0.247E 05 8.865 3.0 COPPER ~~~~~~~~0.2 82 E 05 0.333E 05 0.160E 08 0.543E 00 0.968E 02 0. 67Th 1 0 f 6.34ThE 0-2 0.181 05 — 0.96 3 29 B RAS S (6 5- 3 5 0.489E 05 0.605E 05 0. 157E 08 0.393E 00 0.146E 03 0. 170E 01 0.117E 03 0.238E 05 3.238 3.6 -M[LD STLEL 1020 0.891h 05 0.965E 05 0. 300E 08 0.259E 00 0.227E 03 0.808E 00 0.155E 03 0.250E 05- 4.311 3.5 STAINLESS STEEL 3034 0. 4106E 05 0.9946 05 0.290E 08 0.1686 00 0.3156 03 0.332E 00 0.1706 03 0.1676 05 4.732 2.7 ASTM B144(5SAE-6601 0.750-5O7 225ET7053-0.140E 08 0.173E -00 0.174E 03 017F01t273 ~~..0 MAGNESIJ4 0.241E 05 0.392E 05 0.6506 07 0.255E 00 0.885E 02 0.434E 01 0.118E 03 0.1006 05 3.283 1.4 ALUMINUM 3003-0 — 060E0 0.56E~ 00~.41E 00 0.512E 02 0.304E 02 0.140E 02.6-0E 0a40 3-90 137 COPPER 0.300E 05 0.360E 05 0.1806 08 0.1806 00 0.9006 02 0.647E 01 0.3606 02 0.648E 04 1.000 1.0 CR-130STFEEL 0.290E 05 0.780E 05 0.N2?)0E 08 0.280E 00 0.255E 03 0. 465 E 0 1 0.105E 03 0.218E 05 2.914 330 AL ALLOY 0.4 5 06 05. 5 6 0E 0 5 0.lOOE 08 0.lOOE 00 0.114E 03 0.802E 01 0.1576 03 0.560E 04 4.356 086 ALUMINUM - - ~~~~~~0.150E 0 5 9.iOEO-EO.9007NYT0. 5 0 0 E-0l 0-.-270GE 02 0.5 2 01-4-26 0O2 0.8010.9~.2 COPPER 0.142E 05 0.310E_ 05 0.170E_08 0.500E 00 0.600E 02 0. 824E 01 0.2836_02 0.155E 05 0.785 2.9I\ PHOSPHOR BRONZE 0.394E 05 O.416E 05 0. 150E 08 0.1106 00 0.9506 02 0.440E 01 0.5776 02 0.458E 04 1.602.0 B RA SS 0. 157E 05, 0.260E 05. 160E 08 0.530E 00 0.150E 03 0.200E 01 0.2116 02 0.138E 05 0.587 2.7 MILD STEEL 0.484E 05 0.650E 05 0.280E 08 0.600E-01 0.9506 02 0.236E 01 0.754E 02 0.390E 04 2.096 062 STAINLESS ST E EL 0.3 546E 05 0.9 30E 05 0. 280E 08 0. 570E 00 0. 170E 03 0.653E 00 0.1546 03 0.530E 05 4.290 818 -STAINLESS STEEL 31-6 0.160.1E0.6E8 0600~74ET.160.127E 0-3-~ 0.5 61 E6 05 3.1 865 NICKLE 270 U.800E 04 0.4886 05 0. 277E 08 0.610E 00 0.249E 02 0. 126E 01 0.4306 02 0.2986 05 1.194 459 AL 6061 0.407E 05 0.475E 05 0.910E 07 0.220E 00 0.6006 02 0.4366 01 0.124E 03 0146 5 3.4 44.1 STELLITE 6-B 0. 710E 05 0. 138E 06 0. 304E 08 0. 210E 00 0. 322E 03 0. 180E -01 0. 313E 03 0. 290E 05 8. 728 4.7 TOOL STEEL #1 0. 540E 05 0. 11OE 06 0. 275E 08 0. 175E-01 0. 235E 03 0. 730E -01 0. 220E 03 0. 193E 04 6. 111 0.29 YS Yield Strength (psi) - - - MDPR =Maximum Mean Depth of Penetration Rate lrnfIstfhr-F __________________________ ~~(All values are corrected to U. M. vibratory aclity) TB =Tensile Strengthn(psi) Y = Elastic, Modulus ~(psi) ---— kiae-cilec S 2 p - - SE S~~~~~~~~~~train~ nergyto Tailure-=TS xE (psiV - EL = Elongation (% NUR =Ultimate Resilience normalized to BS 1433 Copper HARD = Brinell Hardness NSE =Strain Energy normalized to BS 1433 Copper 293

24 TABLE 2 Correlating Relation Correlation Standard Error of Coefficient Estimate Factor = C (UR) 0. 811 2. 52 MDPR C (URxBHN) 0. 716 2. 57 C (URxE 2 0.684 2. 86 C UR 0.811 2.57 (b 0. 9985) " - C (SEW 0. 498 3. 30 C (Hardness) 0. 742 2. 75