THE UNIVERSITY OF MICHIGAN Department of Mechanical Engineering Cavitation and Multiphase Flow Laboratory Report No: UMICH 320711 —-I ( I ) VIBRATORY CAVITATION DAMAGE AT STANDARD CONDITIONS (!I ) COMPUTER OUTPUT ANALYSIS Submitted by: Moharnmed AKBI Undergraduate Research Student To: Profe ssor F.G. HAMMITT as a Report for M. E. 490 (Directed Undergraduate Research) Supported by Aerojet Liquid Rocket Company and Internal University of Michigan (Work Study and SEP) Funds. April 6, 1978

TABLE OF CONTENTS PART ( I) I ABSTRACT II ACKNOWLEGMENT III WORK ITEM PERFORMED IV NEWV REDUCED DATA V RESULTS AND CONCLUSION VI APPENDIX DART I II ) I INTRODUC TION II ANALYTICAL PROCEDURE III RESULTS AND COMPUTER OUTPUT IV APPENDIX

tI]_L.IV,

I ABSTRACT in vibratory cavitation, the forces causing the cavities to form and collapse are due to a continuous series of high amplitude, high-frequency pressure pulsations in the liquid. The compressiondecompression phenomena causes the cavities to occur. There are two important data to record for each material tested: Incubation Period (IP) and Mean Depth of Penetration Rate (MDPR). They are related in the following equation (where n and C are constants): (IP)n = C/DPRmax (1) A computer program was used to give us the best-fit line and the best-fit values of n and C for each material. II ACKNOWLEDGEM-ENT Aside from the author, many tests were run by Charles Muller AcX 4^e CeOm^r r v armo -rirn c\ id pIctf U ee re- e Ci_ 0y T r F. )0oe 3J, NiEDZtELSKt lII xWORK ITEMS PERFORMED Three different materials were tested under standard conditions ( 1.0 mils, 800F, 1 Bar in sea water) to find a correlation between them. Also Al 1100-0 and Ti 6A1-4V specimens sent by Aerojet were tested under the same conditions in order to have a basis for comparison. Table III summarizes the work performed in the first part of our tests and Table I summarizes tests done using Aerojet specimens only. Table II gives an average value for the Incubation Period and the MDPR for each material. Further discussion onr this matter will be done in part V of this report. fR.C. le.4 piedIek-i r.,Co^plr AAC^. A's Pr7rS -, c ^,p4e~- cj r^p,'kcS ", Rer-N0. uMict l4-7+ - 1S- I,April It7

IV NEW REDUCED DATA So far two important data were found using some measurement and calculations: 1. The Incubation Period: Intercept of the abcissa of a curve of cumulative weight loss vs. test duration with the tangent drawn from the first maximum slope. 2. MDPR: Mean depth of penetration rate based on total surface area (diameter 5/8") The new redured data that are now introduced are namely: 1. The "0.1 mil" incubation period. This corresponds to the time at which there is a substantial MDPR (small and finite). For our case we used 0.1 mil as a point where time is recorded. This was introduced because of its simplicity and practicality (it lends itself to easy comparison). 2. Incubation Scale Factor k (= f) where T is the time at which we have maximum cavitation (or inflection point) and IP is incubation period. Values of k for different materials are tabulated (Table III). This new parameter k was introduced because it helps predict when maximum erosion rate is going to occur so that it can be avoided. V RESULTS AND CONCLUSION 1. Al 1100-0 Three Al 1100-0 specimens sent by Aerojet were run at standard conditions. University of Michigan specimens behave about the same way as Aerojet specimens do. The IP for Aerojet specimens was lower (about 20,) than that of the U of M ones; however the averaged values of IP for both U of I.'s and Aerojet's were very close (6.35 min and 6.85 min). The MIDPR data for Aerojet's show a behavior

almost identical to U of M's ) each MDPR vs. Test duration curve has two characteristic peaks. The MDPRma, (averaged values) as given in Table II, show 6.7 mils/hr for U of M and 5.9 mils/hr for Aerojet- a difference of 12%. 2. Ti 6A1-4V Two Ti specimens, supplied by Aerojet, were run at standard conditions. Their results were very close to our previous tests using U of M Ti specimens. The average value for IP was 128.5 min for Aerojet's and 133 min for U of M's. The MDPRmax was 102.4 mils/1000 hours and 112 mils/1000 hours for Aerojet's and U of M's respectively. Altogether, U of M test specimens and Aerojet cannot be discriminated because there is no systematic difference between the materials. The small difference in IP and MDPRma values are due to experimental errors only. 3. Incubation Scale Factor (k) K varies between 1.5 for small mechanical intensities to 2.5 for higher ones. K seems to be independent of the material tested but there is a slight increase of k as the intensity increases. Both U of M test specimens and Aerojet's present similar k's. So the predictability for maximum erosion rate occurrence is the same for U of M's and Aerojet's. Further analysis of the problem of cavitation damage of Ti 6A1-4V, Al 1100-0, and SS 17-4 is done using the profocorder results and computer program results and plots.

VI APPENDIX ~BLE I: Aerojet specimens at standard conditions in sea water ~BLE II: Corrparison between Aerojet and U of M specimens iBLE III: Incubation Scale Factor results g: Cavitation Erosion Apparatus 2 Photo of instruments used in cavitation erosion study 3: Picture of U of M specimens 4 In i t 5,! A erojet ".TA and PLOTS for AL100-0 Aerojet specimens I" i" Ti 6A1-4v " "

TABLE It 1 ncubotiiol- M. D. P. R. max _MATERiAL _-_ P.riod (min) (m it.o/ioos.) t6_____ | 7. 2 12A 6 / 6_ /tl ~!00 -— o C l -i0o I W'6.5 3.2 6-O YT 6L-h-4-V. _A, IL;J/:3 ) 160 ///O 34-/-"' 150 8-4. 9 /1 I, -A 7Ti AL-4V - 40 / A erojet 5pec c mI e n t. arclC d coldt i o' i s itn.\ Sax \ta"Ier

TAiBLE. C comparison between i4e. et and UofM pecmen) SDA TA Incu a taoI M. 0. P. R. W Period (men) (mils/0ooohrs) MATERIAL 6.33^^ 1 t; ^^ Al,too -.^ ^&5 r /^9/3 -r / /.//33. I //^ ^ T; 6AL-4V.^ 7^8.5 ^''02,4 Note: {3<> ^^^AVERtAG~ED VA L)UES Aerojet

TABLE, Zr J 0;M StSCiDEN S.._______________ W ______...,...... -AL /0oo - O - 8 - lo,n; 1 7^ S7 1 3.5 1 I, #9 il.o m; 4 7;. 5 180 _uD iz- sc i e. s0 - - _.I c 1 1.0 mJ | o /5, 2.-/4 # e -Zo 1/;l,3, /6o 2.13 # 4 l-5 7/ 6o 50 1 5 - 5.S. 1-7-4 Wl.5 o 66 tl /o 3/5 3 1,2 2 0.55,;/ / 1/0 /9' /.; $.$. i C3 6: -8 J,( 63 - 05? 6O'S5$mllI. 420 i 630 /5 o /<7.3, o~ 60^^ / 1 o3 5648 8 1 o.63,,. 2/ 0 26-2 /.2 #5- 1O ml.O 1 5 / 85 1 -.16 #f// 7*o iv/ /o6 /656 /5' 4 14 1 lo ml 90 56 /.73 AerojoeT SPECIMENS (Ti*17-A N^C4 NCr EcA ______________ MFLectiOP pOeNT J __a AL I Ol 0 w 16-A | 1.Q mnlI 7. 2 14 5,. Io * 17-A lo r;l 6.5 11.5 1. 76 - Th AL-4v. 7,- ( A!ro -m;!'300 1.64- 7 -,-A 6.,' 4 \'60 15 62

20 kHz..... 250 Watt Power Supply Ultrasonic Transducer-Horn Thermocouple Vessel Top Plate Cooling Coil'Argon Inlet 3/16" il r i / ~-I~~~~~t~-F "-'\ IrTST SPEC M N I$- "'CA^ ^C ^ i t =1 sCavitation _.....~ hVessel C —Furnace \ - -— T~est Fluid. /1 |; — 1Ceramic Furnace l l 2" n, -7"' ^l Vessel 5-7/8" i ) 0 _ -Heating Element Furnace Support --- 15-7/8" 1 6 15 Ti-. 1''ibrstory ac' i Cc'rat'on'- zcr:v. SS3,v/t2e

Figure 2. Photograph of the High-Temperature Ultrasonic Cavitation Facility 1. A rA pli v-et t. Vibrow h-4j kil 3. Pr ensure- c9-3c4-. 4eq f\K' vet+ 5.61g. c, tV brI Z, A pa r- fat. t 9. 14QA TreFcm^g Cate

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DATA AND CURVES OF CUIM. WEIGHT LOSS VS. EXPOSURE TIME AND MDPR VS. EXPOSURE TIME

MATERIAL DAMAGE SHEET HORN: -L:v. _ MATERLAL: AL c(. AMPLITUDE:.0 0.. NUMBER:. /6 - WATER: ___c.C_. - _. APPROX. DATE: - 2/-2 / 77 TEMPERATURE:..F___ DENSITY: O. 0 7 S!'< /rr PRESSURE: -' _z AREA: O.. 2-4 z TORQUE: __ ___ _ _. M.D. P. FACTOR: PRE-RUN: _........ -: - COMMENTS:;J r - DATA.........., —--- [- — r- - - -- ------- ----- - - - ~- ~ —- —' -- - - = TIME CUMULATIVE WEIGHT CUM. WT. M.D. P. M. D. P. R. INTERVAL I TIME LOSS LOSS (/. -.,(M \) _*.i. /.' % 3',G', S'_ _ ____ ___I 3.40!. ~5o.3 ____/8 -' i,-~_z.'.....,.... 3 __ 9 3___ 3..2':. 4 _,,9 1.25 8622 _ ___3 //, lo o,./ 3 /. 3,36 3 I S 22S /o5 _. /8GS 7,P3 i. 3~0..os. 22.'o.45" 4.2.752___ 5....27o..' 3 36 5..f..! io4 22s..3;...., A2! ~.,.... 10....,. 2.,, _.0I. /,*,2. _ _,__\_ _ _ _ \ _ _ S.............. _________

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I INTRODUCTION The two most important parameters that we measure in our tests for each material are the Incubation Period(IP) and the Mean Depth of Penetration rate(MDPR). The IP is found from the cumulative weight loss vs. exposure time curves. Then we find MDPR (volume loss per exposed area) using the material densities. A relationship between IP and MDPRmaX was found from experimental data and it seems that the two quantities are related to the following equation: TPlan MDPRmax2 IIP23 MDPmaxl This equation can be simplified into: (IP)n = C/(MDPRma) (1) Various attempts were made to draw the iP vs. MDPRmax curves manually but were inaccurate and therefore a computer program was written to calculate the best-line fit as well as n and C. U ANALYTICAL PROCEDURE If we take the logarithm base 10 of both sides of(1) and simplify: n log IP = log C + log 1/MDPRmax Or, by rearranging the equation; log 1/MDPRmax = n log IP - log C (2) If we want to draw the curve log( 1/MDPmax ) vs log IP then (2) has the equation of a standard line: y=mx+b where m is the slope and b corresponds to the log of the proportional constant. In order to find m and C, the following equations

were used n n n / iL xiYi- Xi yi/ n i'l i=l i=l n n is Xi2 -f^ Xi /n 0(| ~ yi + m(!i xi)/n) C 10 i= i=l i These two numbers are the ones that are most important in the ODPH and incubation period analysis. In addition to a proportional constant for the best-fit line, a constant can be found for each pair of data points using the calculated slope according to the original equation C - (xim)(yi) or C = (Incubation Period)m (MDPi) By finding the proportional constant for each pair of data points, an analysis can be made of all the proportional constants obtained for a set. The average proportional constant is calculated by 1 n C = - ~ Ci N ill The proportional constant mean deviation is found by 1 n MD =- -. Ci -':C N i=l The proportional constant standard deviation is defined by ( - Ci)2 SD = ( N - 1) The proportional constant root mean square is calculated by ( v i / i=

III. Results and Computer Output The computer output enabled us to get the values of n (exponent) and c (constant y-intercept) for each material tested. 1 * Then best-fit lines of (MD ) vs. IP (Tan intercept and MD PR ( MPR) vs. IP (0.1 mil) were plotted for each material. In previous experiments, values of n were computed manually and found to be close to unit (1) which means that the MDPR is inversely proportional to the first degree of IP (see relation (1)). This calculated result was confirmed using the computer program. The exponent n varies between 0.901 and 1.32 for the material tested, thus the best-fit lines make approximately a 45~ angle with the horizontal axis. The small deviations are due to experimental errors only. Note that n is independent of the material tested. The constant C varies over a broad range of values (i.e. 12920 to 64429). Since the C's indicate only the position of the lines (y - intercept) and not their behavior, they do not influence our results. In summary the plots made by the machine verify relation (1) better than manual plots.

IV APPENDIX ~) MDPR and INCUBATION DATA ANALYSIS For A LIIOO 0 SS17 4 (CAST, WROUGHT ) TITANIUM 6A L 4V 2) PLOTS OF (1/MDPR) VS. INCUBATION PERIODS For ALIIOO 0 SS17 4 (CAST, WROUGHT ) TITANIUM 6AL 4V

,) Mb1>PR c\ad IhNC uAl'lON IA-T A t LYSI S

.:DPI[ AND l;Cu.Alil DATA AVALYSTIs A.*LUl.lii, LJh l' j- J ) A4, i s) - L i L U; 1' J Ja,. 7 Il A. I 1?LiCEPT INCUBATIN DATA.1i u DT1LA P;OO. TIO[AL INCBT LOG (I1SCBrTI) PALZA LCG n)P)..sTAN. 7.500 0.875061 70 -o.UuJ -3.0013 5306.5G55 7.50)0 0.875061 701J. jj3 -J.8'6213 52512.9 14 4.000 0.002 060 12450.000 -4.0 5170 4 9 7 0.503 7.230 0.857333 61836. jj -3.7 140)9 4443U.012 6.500 0. 12913 56O4 J.00 -.7 51279 36580.969 E OF LINE (EXPONENT,N) = 0.9988479 PROPORTIONALITY' CONSIANT= 4o 8 35. 262 TISTICAL AIALYSIS CF hOPOhTIUL CONSTANT HIEATIC MEAN = 47269.773 DEVIATION = 5408. 242 DARD D EVIATICN = 6886.898 iEAN SQUARE = 47669.434 MUr PROPORTIONAL CCNSTANT = 53096.555 iUM' PR.i OPOCRTI ONAL CCNSTIANW'' = J6580. 969 * * * * * 3 * * * * * e * ** * * * *. * * * * t *

L DPP AND I CUBATIOJ DATA ANALYSIS AL J L'i INU 1 0-0 0. 1 ilL I;CUB3ATIGN DATA:iD)P D lA PEOP TIoNAL II.CBT LOG (IN CETN).. tr LoJ (iDPR) CO STANT 2.500 3 339790i 7J9t. uj0 -3.ot1013 1 33 1 33'J414 3.500 0. 54408 701^.) 0 -.oob213 20118.727 1.533 3. 176091 1245J. JJ -4.0v5170 17506.766 2.900 0.46238 618 u.0 -3.791409 15140.453 3.2030 3.505153 564. J3J -3.751279 14995.082 )E OF LINE (EXPONENT,N) =. 8406835 PROPORTIONALITY CONSTANT = 16537.699 LTISTICAL ANAL YSIS OF PiROPORTiOi AL CON:STANT'HMATIC EEAN - 16618.273 DEVIATION = 1755.563 iDARD DEVIATION = 7232. 516 MEAN SQUAiE = 16735.336;MU PROPOKTIONAL CONS~ANT = 20118. 727.MUM PROPORTIONAL CONSTANT = 14995.082 ^ ^ ^ 3(c~ i~c^ ^ a{~3(c~ y 4;* ^ ^ ^ ^ *lq95.08

Tir'c T N T SLxEPT ItCUBAT.CN DATA iiOt' LJATA Pi'UO PCTIONAL I C3T LOG (INCTN) i DP J L)G (A. DPIP) CONSTANT')3 1.850 133J -. 1173 14508 1i - 1 73 3622.625 D5.000., 875061 125.400 -J.. 0 )29 7 1 278.594 j.000 1l. 698c97 214.500 -2.3J14 28 14659.637 5.000 2.0^1 189 174. 000 -z.24J549 2497. 543 3. 30 2.041392 10o. OJ -2. JOO 3 16 13.043 3.000 1.7993 0 19. ) -. 29o665 17368.023 3.0 0 2 3 79 181 138 o J -2. 141763 2 380.613 5.000 0.698970 1i00.000 -3.255273 102:34.844 J.000 2. 146128 9.9 3 -0.995635 2356 893 E OF LINE (EXPONENT,N) = 1.079674 PROPORTIONALITY CONSTANT = 12919.656 TISTICAL ANALYSIS OF PiOP2OiTION1 L CONSTANT HMATIC'lEAN = 15345.734 DEVIATIION = 583. 594 DAHD DEVIATI:N = 8875. 461 MEAN SQUASE - 16800.738 M.UM PROPORTIONAL CCNS-ArNT = 26497.543:'U PROPORTIONAL CONS' ANT = 2056.893 ^ ^ ^ ^ L E t= ]9 ~bC s^ <: 4 ^JD a;: c:;f * *: ^ ^ ^ ^ * ^P 9

tv'.- Nt T ~, &.C D \? 1ii >,N. I'- [' C J L' i 1. AT I SI Ti AILLJ2 LL L 1i7-4- Pi'. -1.L INCUBATION C ATA "O[?t DOA^A p <O PO TIC A.;CUT2 LC (INCP TN),i tPD ) COIS'A Li 3.300 2,.041392 1Jo. u, -3. 1 176 3 477672. 143 3.000 2.0791 12540T0 -.0 297 4 43. 97 J.30 1.30 1.0309) 214 5JJ -2.0 1 426 49756 117 5.000 2.24 038 174.i00 -..J40549 1067 3.03 5. j i L. 1 -0 1 3 & i_ J J v b 7j 5 3 2 5. 3000 2. 1136 8 1 3JO -l. 0J30 4Jd.57.323 0.000 2.141 1928!9.000 -.26665 92030.000 3. )00 2.J791 1 138.o00 -2. 141763 53217.289. 000 1 301029 1800. T0 -3. 55273 74536. 50 E OF LINE (EXPONEN,N) = 1.2429361 PROPORTICNALITY CFONSTaT = oi 944. 71 TI STICAL ANiALYSIS CF P OPTCON STANT THATIC MEAN = o5107. 7 1 DEVIATION = 19519.016 DARD DEVIATION = 25134.406 NEAN SQUARE = 68651.438 MUM PROPOT fi 1 C C CC IC, s. N 1 = 6 A 8 31.3 U[JM PROPORTIONAL CC NSXANT = 106783.063 tIUM PROPOETIONAL CC NT ANT = 47762.148 * t * * * * * ** * * e 4 v M * * + * B * * *

* D)Pc AND l:I_2,,"ION JAT'RA ANA LYSI S -; I "'; ~. > J ~- 1 i. i', ^ (Ci' ) _, 1,.;- A T i X l- A.,; 1. E? L; C X v A T t T) ti LJ a _, a. w_-' A T T V 7[ T z IT:CBT LOG (INC tF N) *'i OG [2i) CNS ANT 7'3Q.00 i.84,5098 133.oJO -~. 1763 i/03.2'J 75. J33 1.6756 1 12.4 J. 0 297 36 65.1* 1 j 50.000 1.698b70 214.0J4 -2.4 1423 3t,823.104?E OF LINE (EX:PONENT,N) = i. 3153229 PROPOTON ALITY CONSTANT = 36852. 121 TI STI$ CAL ANALYSIS OF P LPOU rOT CI O A L CON S ANT rHMATIC iEAN = 6852. 500 DEVIATION = 124.507;DARD DEVIATION = 47322.473 MEAN SQUARE = 36852.793:-MIU PROPORTIONAL CCNSTANT = 37039.293 l UM PROPORTIONAL CONSTANT = 36695. 109 c * * * * * * $t C** * 4 t Y * * * * * * * $

~:Pi) Ai'[) ihCuLATiU? uATA ANILYSLS 3. i,':ii. S;-7 i..- L, P li.qi INCUEAriON DATA:iP< DJ:A PIi"ORTICI, AL 7I:8 C U E ts $ T i k 1 >* Ll a < R i, J~ i t; * i`Sl........... 3; C r.0 l- T I C L I CBT L ( i C:... i) i L G (i ) C N STAT i <). 0 0 O41'g,4.5 0.000 2.041392 1;CJ.,QO -=.:i]763 E42433.945!3. J33 2. t79131 1 25. 4 ) -. JB3297 42735.25 3 30.000 2.079181 3. 3 U -2. 14 763 47223.70;.3 30 1.90309 3 21. D0 -.3 14 2 4 46 1.:113 OF LINE (EXPONENT,!) - 1.2183223 PROPORTIONALITY CCONST: T = 44225.285.TISTICAL ANALYSIS CF ri;iOPGT' O;AL CONSTANT H"ATITC II EAN - 44265.734 DEVIATION = 1656.155 DARD DEVIATION = 38456. 297 MEAN SQUARE = 44306.516.iUM PROPORTIO NAL CONSiTAiLT = 47233 703 MUt PROPORTIONAL COI4S8jALT = 42483.945 * * * * * * * * * * * * 4 4 * 4 4 * 4 * * * * 4 * *

YDPR AND 1i: I+ui;{i,.,Ti DATA Ai:LYSiS J.' T _\''. - 3, _, tIr' A - \ *T -I _i: J " | 077 T"C.........,L * Li L.S S.I A. - 1; i_ NCUD3ATICN DATA.i'DiiP AIA; PROPO r ONAL INC5T - LCG (7INI_) * L D -) CON ANT rn, 3~99 ) O 2, 3 7 1'i.) 7 - <_ 73 8 J J J _31 2 7 5. 33. 1 3 13 9 J,J. - 2 J. 27 1 9.J 5.,00 2.211S9 17..J, -z.:43549 3oi,:4.76u 3.300 2.341392 1),.,JO.-2.OJ3,, 21'39.121 3.000 1. 7939 1 9o J -. o:) 5 22 395. 02 3.330 2. 1T4123 1 2:.J -j. j 93635 28 59.:84 2 OF LINE (EXPO'EENT,N) = 1.1465826 PROPORTIONALITY CCNSA ANT = 14265.379 TIST ICAL ANALYSIS CF PiOPOLTI NAL CONSTANT HEATIC MEAN - 19040).234 DEVIATION = 953. 410 DARD DEVIATION = 35610. 625 MEAN SQUAiE = 2129.047 MUM PROPORTION:AL CCONSTAN' = 3 141. 766 IMUM P ROPO TI ON' L CONSTANT = 2859.884 * * * * * * * * * * g * * * *

A.s. P, A U; L a J:PL AN I CUTL, DAA< i ( A Ai) LYSI ST7INLESS o3iZZ^ 17L Dii (Ak ICGII ) I. C. I L TNCU BATr ON D _ DATA ikLDLA2A >OOT ECiONAL INCUT LOG(INC;rTN) riu: i < L G( ID) CONSTANT )O.D30 1.30 1029 l dO.Ju'_.:5527 O2602.S 13 5. 3 0 2.2 430J8 174..j.J -.24 549 679 3. 93 5.00 O 2.! 1. t 3 0 J 3-. J J 7 3 982 5 29 i,93O 2. 146 12 19o JJ -L. 2 o t 05 75514. 00 )E OF LINE (EXPO NENT,N) = 1.2027998 PROPORTIONALITY CONSTANT = 64429.512 iTIST ICAL ANALYSIS CF P O ORTIONAL CONSTANT iHMATIC MEAN = o7044.936 I DEVIATION = 14107.508 LDARD DElVIATION = 4 57.512'MEAN SQUARHE = 69256.500:IUM PROPORTIONAL CCNSTANT = t 6790.938 MUM PROPORTIONAL CONtSTANT = 39782.590 r^ e ^ 84s at Ib: a3C r 4T: 9: 4:4: iC^ C ^ 3L G CC FL 3

L. A I J i L- 4- INCUBATICO DATA: JiKp DATA PbOPORTIONAL T.....', -.- L.- _A P':O -?q-., I OI. AL INCBT L0C (ILC.T:') 1J'iO: LOG 1(DPR) C0'NJ3TA': t.. C t'. 3. 30J 2. G23249 7. j1 ) -j. o'26351 233. 416 I,003 O. 1 94.:9740 -. 6651 971o. 62'5.)33 1.977723 t/. jJ - 1.u 9339 3751.55 3, $ 0 3. ( 7 7 1 7 72 2, _ 3 3 4 t,4 7 5 1 O. O5.000 1.977723 10JO -.3423 706o.762 1iJ.JO 2. 322219 42. JJ -.o25312 5720.039 O O00 1.954242 7. 1 0 -1.o 98231 4 25.715'5. 30 1.875061 127. 3 J -2. 1 3804 6688.723 )5.00 2. 02119 158.2 0 -. 1920O 11347.75 0 30.000 1.954242 82.04J -1.914025 5108. 145 )0.000 3.477121 _. )i -0.591065 5 674.285 0. 300 3.322219 3.910 -v.592177 4389.223 10.000 2.681241.860 -0.7o7898 1960.724 3. 30 0. 477 1 2 1 300. JJ3 -3.0 0J 0 2 7 41.931 (0.000 1.95 44242 4 i.)j30 - i.61 783 2552.830'E OF LINE (EXPONENTN) = 0.9181247 S PROPORTIONALIT'Y CCNST;, T = 4721.000 TISTICAL A NALYSIS CF PL 2OPOTIO 1AL CONSTA NT'HATIC MEAN = 5412.895 DEVIATION = 20 7. 908 DARD DEVIATION = 2151.750 MEAN SQUARE = 6342. 74 rUM PROPORTICNAL CCNSTANT = 11347.750 MU^M PROPOiTICNAL CONSTANT = 1696. 724 * * * * C * * V * * V 4; V * * * 0 * * *e * * *

T I)^ iIi T -4V' TT I': C I J3 A,I A.'1: L_, iT - I.. A L slTC3~ fG (3 CI:' 3 i ) J L. R - T; S iICUBATioN DATA:!D~:: sA'A PROPO[,TIONAL ilCBT L~ (INCBT):)if' LU-; DPR) CONSTANT. J. 0'2.954.43 7.,J - 2.3651 144. ) 5,0;5.Y)0 2. 45444 4.2JJ 1 u2532 11976. 523 )0. 00 2.000000 7'. i JI - i. o23 1960.3023. JO 2. 14123 127. 313 -2. 1j38034 27735,6539,3O.00 2. i14123 15-5. 0 -. 199206 j34513.1 8;J. 3 2. 176 91 2.. J -1. i 025 1929 5.539 i. 000 3.255273 3.900 -0.5910 65 13757. 875,. 300 2.954243 3. bj -J.767896 9712.523 8.000 0.903090 1000.000 -3.000000 9641.770 0. 309 2. 518514 4 1. 3J -1.612783 22770.664 0.000 2.204120 111.340 -,.0 b651 28094. 52. J33 2. 176091 87.,J9 -1. 949393 20673.793 5.000 1.977723 10Do.00 -.033423 15441.172:i OF LINE (EXPO4NENT, ) = 1.0897665 PROPO RTI N ALITY COIL TANiT = 17552. 609 TISTICAL ANALYSIS CF PhUOOR1TO1NAL CONSTANT HiMATIC MEAN = 18960. 73 DEVIATION = 620.879 DARD DEVIATION = 24318.191 MEAN SQUARE = 20364.378 H1U.M PROPORTIONAL CCNJTANT = 34513. 184 MUM PROPORTIONAL CCNSTANT = 9641.770 c; ^ * * ^ 3 3t *C* $ $Sc: * 3E * ^ 9t 7 0 $

z)_PLo s

0. 0010 / U)|* ALUMINUM 1100-0 C. ICt[: CTAN INTERCEPT3 o N=.999 Co C=4721 CD I I+ I2 0. 00001 1 10 100 INCUBATION PERIOD CMIN3

0. 00100 ALUMINUM 1100-0 CO zcr CO. 1 MILD JZ: N=. 841 cD C- 17553 CD o /I F - ++ \ +/+ co 0.00010- / E 0. 00001 1 10 100 INCUBAT I ON PER I OD CMI N) a his line soS dghuor A;*oA u5inp -he lower mBy po'vt+, chic ^o i"^*ncp n^s tAisK'tt'^ r* DF'at dr.&cr

0O 100 0.100 STAINLESS STEEL 17-4 PH rr. C TAN INTERCEPT ZE o | N=1.08 o o C= 12920 0. 010 / I —-I 0, 001 - 2: x O 0 0. 0001-" -0 -- - --- I 1 10 100 1000 INCUBATION PERIOD CM IN

0. 100[ () ~STAINLESS STEEL 17-4 PH YCO( CO. 1 MIL) 32 Co No N-1.24 Do C=-61944 o0. 0100- ++ CO) / -I a /01 LL /+ 0~ 0001 - I / 0 _ v —I 0. 0001.'...." —— I-..,. 1 10 100 1000 INCUBATION PERIOD CM IN

0O 100 f) |STAINLESS STEEL 17-4 PH r C(CAST / _J / _.r CTAN INTERCEPT) Co r 0a 001 DJ 0. 0001 1 10 100 1000 INCUBATION PERIOD CMINJ

0. 100 [|^.STAINLESS STEEL 17-4 PH ~. [CAST) rI:( CO.1 MIL) Co N= 1.22 Co0. 010o C= 44225 cr gO / J / O 00010 a0 rO 0EZ 0. 00011 10 100 1000 INCUBATION PERIOD CMIN]

0. 100 Cr) STAINLESS STEEL 17-4 PH ^~L C CWROU6HT) II: ~ CTAN INTERCEPT) CD C) NN=1,147 CDO.0100 C= 14265 + \ ^~~~~~~~+ co) It 00.001 Q I >1 v-H 0, 0001 1 10 100 1000 INCUBATION PERIOD CMIND

0. 100 STAINLESS STEEL 17-4 PH CY C WROUGHT) IZ CO. 1 MIL)::| N=1. 203 o.0100 o C=64429 + CO \: 0, 0001u0.00010 1 10 100 1000 INCUBATION PERIOD CMIN]

CNIWN UOI3d NOIIV8nONI 00001 0001 001 01 I 1000'0 /+ -TO0 T'0 000' I +./ - +y Cld33J31NI NV1I A1-gV9 NnINVII Cn 000'I

1. 000 CO |TITANIUM 6AL-4V = | CO.1 MIL) + l —~ + / o0.100- N=1. 09 Co C- 17553 )O_ 0.100 cL/ C- 0010 + K: / Q_' 0. 0001 i -- 1 10 100 1000 10000 INCUBATION PERIOD CMIND

1.000 Co TITANIUM 6AL-4V CO, 1 MIL) + """ ~~~~~~+/ cDO. 100 N=1.09 CD C=17553 f) + Os 01 0 ~2001 + D z: / 0.0001- I 1 10 100 1000 10000 INCUBATION PERIOD CMINJ

UNIVERSITY OF MICHIGAN 3 9015 02493 7735