03 p- a. - IWr A'ASMYSIS OF P1OB.L:E'EA PA.TA FOa cAVITAT: oN PITS PrToject 03424 Ienternal Repori: 2 sWritgten by: zT-TFa, J. Wal.s Approved: F. GP~. H&Wlilll-.

T<rttee virt.ints.s s-eel:-ear czmples, ^ith iur ac.s pitted faom et-,s.to a cait iation:,.eXd, e-rer testead with a profilometer to daterm:iae:,e prof"'.-;s -of the'?i:s. T.'These tests were conceirved.ad supervised by 1Mr. V, F. Czraer. They wree conducted uinsv equipment very kindly loaned by Micrometrical Mfg.'o c Ana Arbor, with the a.sistance of their Mr. Charles Cood, A prof iimteter is3 a mechaa'ical-el3ectric instrt'ment- whi.h p- tvid- S v -ermanae.i t mEagn ifi.eed chart record of tl.:e helgh't, skap-e, and spac;-l oaf uS-aac i.reguar.:ties.:Th pit pro 1es? were traced by tUsinLg &a ) 00ta1 vh - diaetAc inUromnd sttylus wxiich is capable o' detsectitg surface irreular iti: e of less thaaaa millionth of an inch. For our purposes, t.-e tns-tri.ent wans l:tinitcd ti: f.ose;its t hich were either large enough ocr the I mil d:aa.ete:r otyl-s to't: into o were shallow tenoughL to accorCodate the he irpheAIca s tyl<s tip. To triate.'y, all pxis eteeed were very stalo-C: an-d mot of the pits greater tPat 1/2 n.il in diaertei yielded raaingtfuI treraces. The prof ilomwtee traciag wtere cowTpard -ithb high wagl.ificatiton 2hotographs of t'he surfaces tested to aid'in making an esimte of the overl.' smapes of the pite involved. In rmst ea~ses, only 2 or 3 oweeps'ae traced ecross each pit and the photographic i1nformation veas very helpful. XII A ~llsi.ts ltottdure The proficorder charts traced ap'roxiatealy 50 n's but ia na^any cases tihe informEtion was not useful due to stall pit sizes, inadequate profile informationj etc. However, 14 p.its are found whose traoinrs asrseli able in^ormation. Bach of these pits was elosely investigated avD i-s overali shape and volume loss estimated. The 14 pits selected showed a surprising similarity and several generalities could be made.

A typical pit may be considered. to c)nsist of two parts - a "pit" and a "ridge." A vertically exaggerated sketch of a "typical" pit is given below;: I JD _ | d s B j Id -. -"..ES. Surface Level __ ___ Surface Level The follouing quantitiesl are dafined D a Average pit diemeter id Avr.re rag ie eideh B H MCesmum pit depeth hm = Maximum ridge height HMv = Average pit depth iav = Avelrage ridge height The quantities (D, d, HM, HBa, hL, ha^) were estirmated and tabulated for each of the 14 pits used.' It should be noted that the pit diameter, D, differs from the appaw:&ent average pit diameter (Dp) as seen visually or photographically. D, the observed diameter, is measured from ridge peak to ridge peak.

!It. Observations A. All pits abserved were very shallow; Hm L (l/13)D. B. Ridges account for a large amount of the volume los at the pite....Be3tweea 10-50%. C. Average pit depth x 2/3 x Maximum pit depth; Hay: (2/3)E. D. Many pits are circular and many are heart-shaped. E. The ridges generally extend only 1/2 way around the holes. F. For a given surface area, the ridges occur on the sme sides of the pits; about 90% of the observed ridges occur on the dowistrean side of the pits; the 10% which occur on the upstrea oaide are relatively small ridges. G. Pit shapes appear to be relatively uniform, whereas ridge shapes appear to be quite random. H. Photographs provide the best method for estimating the average pit diameters but are useless for estimating pit depths or ridge heights. Often, what appears to be a deep pit photographically turns out to be very shallow, and tice versa.

4, 1V. Calcu aloions Volusme of piJ t x E Ha Hl/ 1/13 D; Hav 2/3 m Volume of pit ~ (2/3)(1/13 D)(_2) Volume of pit' rD **** Where D is the average pit diameter (Average ridge thickness, d w 0.56 D) ( * ) (Maximum ridge height, b1m 0.54 Hm ) Conclusions from profilometer <~(~~~~ ) charts (Average ridge height, h -: 1/3 h ) Ridge volume, VR = Circumference x Average cross-sectional area s 1/2 Since ridges only extend about half way aro.tnd. VR (T7rD x (0.56 D x 1/3 x O..54x D/13) x 1/2 Volume of ridge. 7T D2Dp 260 Dp 5/4 D (From profilometer traces) ff'D3 V-R ^208 Total we. loss per pit. Vptt VDdge D3(/78 - 1/208) Total wt. loss per pit s 0.008 7rD3 V pa f 6 -.6) 0.375 Ridges ac8 of ) Ridges account for 3/8 of the pit volu-e loss.

O In terms of the apparent pit diameter, Dp.... Volume loss per pit z 0.008 VD3 - 0.008 r (4/5 Dp)3 For n pits occurring on a surface: 3 ( 3 Total wt. loss ox 0.008-r(4/5) (Dp) where /~ density of the metal. Presently, only the pits on the polished surfaces of the metal samples have been measured, counted, etc. However, teight is also lost from the nonpolished surface areas which project into the cavitating region. One possible solution would be to assume the weight loss (per unit area) from both surfaces to be equal. Unfortunately, this appears to be a poor assumption since the polished surfaces themselves exhibit great variations in the pitting tendency along the various regions of a given suriace. We have no assurance that the pitting rate of an unpolished surface is similar to that of a polished surface on the same specimen. The polished surface constitutes only 15% of the total area exposed to cavitation. A much better, but less comprehensive Assumption would be that the rates of pitting of the two surfaces are directly proportional to each other. For example, if the xfeight loss from the polished surface'is doubled, the weight loss from the sides would also be doubled. For n pits occurring on the polished surface..... Total weight loss of the sample = k (Dp)3 Where(Dp)t is the apparent diameter of the ith pit k is a constant for a given material and cavitation field.

It would be nearly impossible to tabulate the average D for each n ~ pit over the entire polished surface of a sample and computei (Dp)i, since in most cases there are hundreds of pits and each is unique. The following method of analysis is suggested: Consider the spectrum of pits to be separated into 3 major divisions...."Small"pits, "Large" pits, and "Very Large" pits iith the following definitions: (0.3 mils < Small pits < 1.5 mils ) ( ) (1.5 mils - Large pits - 3.0 mils ) (?.) (3.0 mils < Very Large pits < 10 mils)'.he pits smaller than 0.3 mils are considered negligible for the consideration of weight loww, although there usually are thousands of them. No pits larger than 10 mils have been observed to the present. (Dp)i CA C2A + + 3C Where A Number of small pits B Number of large pits C m Number of very large pits C1, C2, and C are unvarying constants for a given material and represent the average Dp of the regions involved. From photographic evidence (See Appendix pp 1- 12 ).... C1 s 0.455 02 11.5 C3 " 238 The equation becomes.... n 238 5f(Dp)i 0.455 A + 11.5 B + 238 C i:M p

7. If a given region contains less than %-P 10 pits, the statistics of 3 the mnethod become poor and no(Dp)i for that region should be calculated term-rise. Etale A: Consider a typical surface with the following data: 20 Large pits 150 Small pits 1-6.5 mil )it 1-7.0 mil pit E (Dp)i3 (0.455)(150) + 11.5(20) + (6.5)3 + (7.0)3 = 68.3 + 2304275 +343 a 916.3 In the ezsWgle above, which may be considered typical.....the two "very large"' pits acconmted for 68% of the weight loss; the "large" pits represent 25%; and the "small" pits only 7% of the total. All of the pits less than 0.3 mils in diameter can be shown to have a negligible effect. Assuming a (Dp) 3 of -6 x 104 mils3 for this region, over 300,000 pits would be needed to cause a 10% change in the weight loss. Exat le B: Consider a sample with the following data: (230 Small pits 67 Large pits 20 Very Large pits ni E (Dp)i3 = 0.455(230) + 11.5(67) + 238(20) - 104 + 771 +4760 " 5635

In this case the eight distribution was: 84.4% Very Large pits 13.7% Large pits 1.9% Small pits Again, the pits smaller than 0.3 mils are negligible with regard to wxeight loss -- Oer 1 million pits in this region wmould be needed to alter the total weight loss by 7%. The general equation for the total weight loss of a sample is: n W = k2 (Dp)i3 - k(0.455 A + 11.5 B + 238 C) The only unknown in this equation is k, which may be estimated in three different ways: 1. Comparison with direct weighing results 2. Observation of pitting behavior on the sample sides 3. Comparison with radioactive test results (Standard solution, etc.) As a first approximation of k, the assumption of equal pitting rates on both surfaces may be used. w /ox 0.008 7(4/5)3 (Dp) i x (1/0.15) /0 p W 0.086/0 (Dp)i3 - 0.086 x 7.86 /cm (Dp mils3 x l -) x (Dp)i l03; xn ch~W = 1.11 x 10'8 (0.455 A + 11.5 B + 238 c) gtaas The weight loss predicted by this equation is probably low. A large part of the pitting occurs on the edges of the samples. This pitting is such

that the pit count at the edge would underrate the weight loss8 At many places on the edge, the area is so heavily pitted that the entire edge is wornj doma......Also in many instances the corners are battered to the extent that the depths of the pits are very large compared to that of the typical shallow pit for which this correlation ams derived. For any degree of accuracy, one of the three methods of estimating k (listed on page 8) should be used. V. SsummaEE From profilometer traces and photographic evidence, the geometry of a typical cavitation pit has been postulated and several methods of estimating the sample weight loss suggested. With our present information, only a rough approx:tmation can be made. Three methods of improving the weight loss equation are listed: Comparison with direct weighing results, observation of the pitting behavior at the sample sides, and comparison with radioactive test results. All of these methods should probably be attempted. The profilometer data was very limited and more profilometer traces are recomsended. These should include mora sweeps across each pit and an expanded horizontal scale. Also, a recheck of the same pits after additional cavitation would be desirable to yield infonation on the development and growth of pits.

10. APPINDIX

Estimation of C1 e n __~m1 I ~we" Size range, mils mobobia"WA 0.3-0.4 0*4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0*8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1t2-1.3 1.3-1.4 1.4-1.5 n,= of pies 100 79 61 48 37 30 25 20 16 12 9 6 fn: 443 3 S.a!sv3 n(DP)av3 0.0430 4.300 0,0911 7.200 0.1663 10.20 0.2750 13.20 0.422 15.60 0.613 18.40 0.857 21.40 1.160 23.20 1.52 24.32 1.95 23.40 2.46 22.14 3.04 -18.24 3 (D)av3 = + 201.6 - 201.6 443 2 c,, (Dp)3V - (Dp)av3 0.4' 2E n(Pp)3 S. ~ 55 ttil8 55 milel ) ROOT M1 COEBg ~ 0.77 mil C1 P 0.455 UiS3

Estimation of C2 and C3 Size range, rails n # o pits 1.5-2.0 100 2.0-2.5 88 2.5-3. 70 n a 258' p)a 3 (DPp)av3 5.36 500.4 11.40 1003.0 20.80 1457 ~n(Dp) E 2960.4 (Dp)av3 _A C0;P C2 s ll.5.,,a.0. OT * EAO T CUBS = 2960.4 = 11.5 258 Dp! 2.25 mils Estimation of C3: In the Calculation of C1 and C2 the root mean cube DP was found to be slightly lees than the aterage diameter. We will assume the same behavior to exist in this regions For estimation of C3.... Dr - ^ ~av 3 mile + 10 mile 2 = 6.5 mils Assume:.(Dp)av3 r (6.2 mils)3 = 238 C3 = 238..... B T M M AN CUBE D 6.2 tmls. p

1.0 0.9 0.8 0.7 a E cc -0.6,) 0.5 w -J m 0.4 N.J N 0.3 0.2 0.2 0.1 N, 0.1 0.2 0.3 0.4 0.5 DISTANCE FROM THROAT EXIT (inches) Figure 10. Normalized Observed Bubble Radius vs Distance from Throat Exit, 73 Bubbles

DS t*' \ -l v v E 0.. 0 0 0. 00.11 *V 0 Ofl l* * e * * l 0 V: **'* * -1200r.~~ ~ -0 0 0 0 80 * to 0.3W0 * * * * p~=0.010t ~ a. -1200 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 TIME MICROSECONDS FROM FIRST MAXIMUM RADIUS Figure 11. Normalized Observed Bubble Radius vs Time from the First Observed Maximum Radius, 73 Bubbles.. 6 0.2. Po=0.010 tm 0.2-~ CALCULATED CURVE Po = 0.001 atm -1200 -I000 -800 -600 -400 -200 0 200 400 600 800 I000 TIME MICROSECONDS FROM FIRST MAXIMUM RADIUS Figure 11. Normalized Observed Bubble Radius vs Time from the First Observed Maximum Radius, 73 Bubbles

80 I: I I I I.............. A El 304 SS (2SAMPLES) esem4 72-:{ Sa* 0- 316 SS 0-~i Ta-8W-2Hf Cbi Zr 64'304 SS 604 SS 5 HOUR EXPOSURE 304 SS 4 HOUR EXPOSURE O.. LU -.:: 5 0 0 24 304 SS 2 HOUR EXPOSURE Tta.8W-2Hf BEFO~RE EXPOSUREf~ 16 SS:304 SS BEFOSRE EXPOSURE Ta 8W2H f 12 HOUR EXPOSURE 0 OI ts _ ~ ~ ~ ~ ~ ~ ~ ~ ~~A............I..,.., 0 2 4 10 12 14 1583 FIGURE 1. CAVITATION IN LEAD-BISMUTH AT 15000 F