Introduction
IN A recent series of publications by Thiruvengadam and collaborators [1-5],1 emphasis has been placed on the changes in the rate of cavitation damage with the duration of the exposure time. The cavitation damage process is divided by these writers
into four zones which are described as follows: Zone 1the in-cubation or no-weight-loss zone; zone 2the accumulation zone;
zone 3the attenuation zone;
and zone 4the steady-state
zone. Typical graphs which are presumed to show these zones are reproduced in Figs. 1 and 2. These figures are reproduced from reference [3] ; they have also been published in reference [5]. The important "zone" of cavitation damage is considered in these papers to be zone 4, which is taken to be the region of theoretical1 Numbers in brackets designate References at end of paper. Contributed by the Fluids Engineering Division and presented at the Winter Annual Meeting, Chicago, Ill., November 7-11, 1965, of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received at ASME Headquarters July 19, 1965.
Paper No. 65
WA/FE-23.0
.
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= .1, 1Effect of Exposure Time on
Cavitititin
Damage
It has been proposed in some recent publications that the cavitation damage rate decreases
markedly in solids after long exposure to cavitation. It has also been proposed that this low rate of cavitation damage is the one with physical significance for the solid. These observations have been made with specimens oscillated sinusoidally in liquids
by means of magnetostrictive devices. In the observations described here, it is shown by
means of photographs of the cavitation cloud over such specimens that the reduced damage rate results from the very sparse bubble cloud which is formed over the deeply
damaged surface. The change in the damage rate therefore has hydrodynamic origin and is not related to a change in the properties of the solid. X-ray analyses show also that the extent of the plastic deformation of a solid with very light damage is the same
as for a solid with very heavy damage.
significance. The cavitation damage in these experiments was
produced by oscillating a specimen immersed in water at an ampli-tude of the order of 10-3 in. at a frequency of approximately 14 X 103 cycles/sec. The accelerations of the specimen are produced by means of a magnetostrictive oscillator.
Cavitation Damage Measurements
We have measured cavitation damage which Ii as been generated
in a similar way with a magnetostrictive oscillator. Our equip-ment, indicated schematically in Fig. 3, has been described in de-tail [6, 7] and does not require further description here. We undertook to make measurements similar to those made in
'refer-ences [1-5]. We chose as the test material 4340 steel. All the specimens were made from the same stock, which was annealed and had a Brinell hardness number of 173 (3000 kg scale). It was useful to use annealed specimens since our observations included X-ray analyses. Our measurements were made both with
fiat-faced and with dished specimens, Fig. 4. The cumulative weight loss is shown as a function of time of exposure in Fig. 5, and the
rate of cavitation damage is shown in Figs. 6 and 7. The data
10 2 3 4 5 6 7 8 9 102 2 3 4 5 6 7 8 9103
TIME,M1NUTES
Fig. 1 Rate of cavitation weight loss with "zones of cavitation" as described by Thiruvengadam and Preiser [3, 5]
Maim
2 3 4 5 6 7 8.9 104
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IFREQUENCY
16 KCS I DIAMETER OF IISPECIMEN
0.625 INCH ARC1711,Et7r-M. S. PLESSET Professor of Engineering Science. Mem. ASMER. E. DEVINE Research Engineer, Engineering Science Department. California Institute of Technology, Pasadena, Calif. 2.0 1.6 0 c en-v) 0 0.8 C'. 0 I-< Cr 0.4
DRIVING COIL DISPLACEMENT PICKUP COIL TEST LIQUID 1.4 1.2 1.0 C E I G tr.; cr, 0.8 0
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VTVM SPECIMENFlg.3 Block diagram of magnetostrictive oscillator and associated equip-ment as used in cavitation damage experiequip-ments at C. I. T.
d 4 MATERIAL, CAST-IRON LIQUID: WATER AT 80° F DOUBLE AMPLITUDE: 1.75 z 10-3 INCH FREQUENCY: 15 (CS DIAMETER OF SPECIMEN' 0.625 INCH 0
J
0 0which are given in these latter figures have a general trend similar
to that shown by Thiruvengadam and his coauthors. We find Fig. 4(a) Photograph of flat specimen before exposure to cavitation
that the so-called zone 2 has a much more nearly constant rate of weight loss tha,n indicated by Thiruvengadam. This region
corre-sponds to the "linear" portion in Fig. 5. It is our observation that this region of damage has a more nearly constant rate of
weight loss and has a more extended duration when the face of the specimen has been carefully prepared to have a smooth, plane
sur-face. The so-called zone 4 in our measurements does not show a
precisely constant rate. It is very clear that the damage rate
has fa,llen to an appreciably lower value than that characteristic of the line,ar region.
It should be emphasized that, in this zone 4, the region of re-duced cavitation weight loss rate, the specimen has undergone ex-tensive damage. After this exposure time, the face of the speci-men has deep, ragged pits which extend inward of the order of 30
to 50 thousandths of an inch, being separated by clistancas of
this same order of magnitude, and have widths again of this
mag-nitude; see Fig. 8. It is most difficult to accept the view which has been advanced that this region of damage, which appears
after very long exposure times, has a fundamental significance for the response of the solid to the cavitation. It was shown some
time ago [8] that the plastic deformation produced in a solid by
cavitation sets in almost immediately upon exposure and, after a Fig. 4(b) Photograph of dished specimen before exposure to cavitation
692 / DECEMBER 1966 Transactions of the ASME
20 40 60 80 100 120 14
TIME, MINUTES
Fig. 2 Rate of cavitation weight loss as given by Thiruvengadam and Praiser [3,5]
AUDIO
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0 DISHED SPECIMENS FLAT SPECIMENS
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35 40 45 50 55 60CAVITATION DAMAGE TIME, HOURS
Rg. 7 Continuation of Fig. 6, which gives rate of cavitation weight loss for long exposure times
Fig. 8 Photograph of 4340 steel after long exposure to cavitation. Sped. men is In zone 4.
plications for the behavior of the solid have been developed.
It has also been proposed that a test procedure using zone 4 should be adopted. Presumably, these ideas have contributed to a
mis-understanding [3] of the role of corrosion in cavitation damage
[7].
Photographic Observations of the Cavitation Cloud
The faces of the specimens used for the damage studies were of
two kinds. One kind had flat faces exposed to the cavitation cloud, and the other kind had "dished" faces for which the flat surfaces were surrounded at the perimeter by a wall approxi-mately 0.030 in. high and 0.020 in. thick. Both kinds of
speci-mens showed the same general behavior.
Pictures were taken of the cavitation cloud with an exposure
time of 2 microsec, which is short compared with the 70 microsec period with which the specimens were oscillated by the magneto-strictive driver. The short exposure was obtained by means of a pulse which fired an FX 2 flash lamp. The pulse was phased with the 14 kcisec magnetostrictive driving voltage so as to
photograph the bubble cloud at its maximum over the specimen
face. Fig. 9 shows the maximum bubble cloud over a dished 350
4340 STEEL IN DISTILLED WATER AT 25°C
0 DISHED SPECIMENS FLAT SPECIMENS 300 6 -b o
±0
AO 250 £0 Agie 200Ai.
Co 0 XAi
AgAl
0 150 A a A 100 6 50 5 10 15 20 25CAVITATION DAMAGE TIME, HOURS
Fig. 5 Cumulative cavitation weight loss in milligrams as a function of cavitation exposure time in hours for 4340 steel, Brinell hardness number
173
0 5 10 15 20 25 30
CAVITATION DAMAGE TIME, HOURS
Fig. 6 Rate of cavitation damage weight loss in milligrams per hour as a function of cavitation damage time in hours for 4340 steel
relatively short time of the order of seconds or minutes,
establishes a region of cold work which is rather shallow. In theobservations of [8], it was found that this depth of plastic
de-formation was of the order of only 50/2.2 Therefore, it is to be expected that the behavior found in a heavily damaged surface does not reflect any basic property of the solid when exposed to
cavitation. Rather, it is to be expected that the effect is an in-cidental, superficial one related to the particular hydrodynamic
behavior of an extremely rough specimen as it is oscillated by the magnetostrictive device. That this is indeed the case may be
shown by photographic study of the cavitation cloud and by
X-ray analyses of the damaged solid. The misinterpretation of the
meaning of the change in damage rate with exposure time by the authors of references [1-5] has led them to several erroneous sug-gestions and conclusions. As has been indicated, theoretical
Fig. 9 Photograph of maximum cavitation cloud over dished 4340 speci-men before appreciable exposure to cavitation damage (zone 1).
Photo-graphic exposure time, 2 microsec.
Fig. 10 Photograph of maximum cavitation cloud over dished 4340 speci-men in linear weight loss region (zone 2). Photographic exposure time,
2 microsec.
specimen before visible damage has developed; this bubble cloud occurs in the so-called zone 1. Fig. 10 shows the maximum bubble
cloud over a dished specimen when the cavitation damage is
taking place in the region of linear weight loss; this region is the so-called zone 2 of Thiruvengadam, et al. There is no essential difference between the bubble cloud in these two regions. Fig. 11 shows the maximum bubble cloud over a dished specimen which
has been heavily damaged; this is the so-called zone 4, or the "steady-state" zone. It is very evident that the bubble cloud is considerably reduced in intensity as a consequence of hydrody-namic damping effects over the deeply damaged surface. It is
apparent that the reduced rate of weight loss is a result of the
re-duced density of the bubble cloud. Figs. 12, 13, and 14 show that flat-faced specimens have the same behavior as the dished speci-mens.
The hydrodynamic effect on the bubble cloud of the deeply pitted face may be shown very clearly in other ways. After a specimen had reached the so-called zone 4, one half of the face was smoothed off, and the remaining half was left unchanged as
t41.
491
Fig. 11 Photograph of maximum cavitation cloud over dished 4340 speci-men after long exposure to cavitation (zone 4). Photographic exposure time, 2 microsec.
Fig. 12 Photograph of maximum cavitation cloud over flat 4340 speci-men before appreciable exposure to cavitation damage (zone 1).
Photo-graphic exposure time, 2 microsec.
shown in Fig. 15. Fig. 16 is a flash photograph of the cavitation cloud over the face of such a specimen; it shows the great differ-ence in the cavitation cloud for the surface in these two con-ditions. The effect of holes in a surface on the cavitation clbud also may be illustrated by making small holes in an undamaged
flat surface as illustrated in Fig. 17. These holes were made
electrolytically with a bundle of fine wires; the holes are
approxi-mately 0.19 in. din, 0.050 in. deep, and approxiapproxi-mately 0.015 in. apart. Fig. 17 shows the maximum bubble cloud over the speci-men face as the specispeci-men is oscillated sinusoidally by the magneto-strictive oscillator. The bubble cloud is clearly very sparse com-pared with that over a specimen with smoother surface.
X-Ray Analysis of Cavitation Damage
Laue X-ray diffraction patterns were obtained from 4340 steel specimens before exposure to cavitation and after exposure to cavitation for various times. The X-ray beam was circular in
cross section with a diameter of 0.030 in. and was well collimated.
The X-ray line used was the Cobalt K. line, which has a
Fig. 13 Photograph of maximum cavitation cloud over flat 4340 speci-men in linear weight loss region (zone 2). Photographic exposure time,
2 microsec.
Fig. 14 Photograph of maximum cavitation cloud over flat 4340 specimen after long exposure to cavitation (zone 4). Photographic exposure time, 2 microsec.
length of 1.790 Angstroms. The beam was directed normally on
the face of the specimen, and the back-reflected diffraction pat-tern was recorded on photographic film The maximum depth
of penetration of these X-rays into the specimen material is about
25k; the important contribution to the diffraction pattern comes
from the first 10g below the specimen surface.
Fig. 18(b) shows the diffraction pattern of a 4340 specimen
be-fore exposure to any cavitation; the sharp spots are indicative of
a well-defined crystal structure. The progressive smearing of the
spots into a continuous ring upon exposure to cavitation is
illus-trated in the series of patterns shown in Fig. 19, and the distortion
of the structure is thereby demonstrated. Loss in definition of
the spots is already evident in Fig. 19(a), which corresponds to
only 10 sec exposure to cavitation. It is evident that the plastic
deformation of the crystal structure begins immediately upon
ex-posure to cavitation. The plastic deformation sets in before the
surface shows damage which is evident from optical examination.
Plastic deformation of the depth available to examination by the
X-rays appears to be fairly complete in 5 min and is clearly com-plete in 30 min to 1 hr of exposure to the cavitation. The depth
Fig. 15 Flat-faced 4340 specimen with one-half of the face ground and polished smooth; the remaining half of the face has been left as it was after long exposure to cavitation (zone 4)
Fig. 16 Photograph of maximum cavitation cloud over the specimen with the face as shown in Fig. 15. Photographic exposure time, 2 microsec.
of penetration of the plastic deformation after 1 hr exposure to cavitation may be found by removal of surface layers by means
of electrolytic polishing until the crystal pattern is restored. The X-ray patterns after successive removals of surface layers are shown in Figs. 20(a, b, and c). It is evident that the removal of
31g from the damaged surface does not restore the sharp spot
pat-tern completely. It is, however, restored completely after 46g
has been removed.
A question of concern remains as to whether the depth of
plas-tic deformation changes with the duration of the cavitation
ex-posure. More particularly, we wish to determine whether periods of exposure to cavitation that are longer than 1 hr give a different depth of plastic deformation. Fig. 21 shows that the sharp spot
pattern is restored for a specimen which has been exposed to
cavi-tation for 2 hr when 41g of the surface has been peeled away. A more detailed series is shown in Figs. 22(ad), which give the
results of the X-ray analysis for a specimen exposed to cavitation
for 10 hr. As Fig. 22(d) shows, the sharp spot pattern is
rees-tablished when 48g is removed from the surface. Similar results
Fig. 17 Photograph of maximum cavitation cloud over undamaged speci-men with cylindrical holes. Holes are approximately 0.019 in. die and 0.050 in. deep. Photographic flash duration, 2 microsee.
X-RAY
BEAMS COLLIMATING
TUBE
-so-CIRCULAR FILM WITH HOLE IN CENTER 696 y DECEMBER 1966 BACK DIFFRACTED X-RAY BEAMS No, SPECIMEN
LIGHT TIGHT ENVELOPE
EP
Fig. 18(a) Diagram of arrangement for obtaining X-ray diffraction pattern
Fig. 19(a) X-ray Lou. diffraction pattern of specimen after 10-see expo-sure to cavitation
Fig. 19(b) X-ray Laue diffraction pattern of the specimen after 1-min ex-posure to cavitation
Fig. 18(b) X-ray Laue diffraction pattern from an undamaged 4340
speci-men. The well-defined spots show regular crystal structure of material. Fig. 19(c) X-ray Laue diffraction pattern after 5-min exposure to cavitation Transactions of the ASME
L.
Rg. 19(d) X-ray Laue diffraction pattern after 15-min exposure to cavita- Fig. 20(a) X-ray Laue diffraction pattern for specimen exposed to
cavita-tion lion damage for 1 hr; six microns (A) of surface have been peeled off by
electrolytic polishing
Rg. 19(e) X-ray Laue diffraction pattern after 30-min exposure to cavita-tion
,\
I
/
..._.,"
Fig. 20(b) X-ray Laue diffraction pattern for specimen exposed to cavita-tion damage for 1 hr; 31i of surface have been peeled off by electrolytic polishing
r '
,
Fig. 20(c) X-ray Laue diffraction pattern for specimen exposed to cavita-tion damage for 1 hr; 46As of surface have been peeled off by electrolytic Fig. 19(1) X-ray Laue diffraction pattern after 1-hr exposure to cavitation polishing
Ls,
Fig. 21 X-ray Laue diffraction pattern for specimen exposed to cavitation
for 2 hr; 41u have been removed by electrolytic polishing Fig. 22(c) X-ray Laue diffraction pattern for specimen exposed toi cavita-tion for 10 hr; 32u have been removed by electrolytic polishing I
.4-Fig. 22(a) X-ray Lace diffraction pattern for specimen exposed to cavita- Fig. 22(d) X-ray Laue diffraction pattern For specimen exposed to
cavita-tion for 10 hr lion for 10 hr; 48u have been removed by electrolytic polishing
J
1
Fig. 22(b) X-ray Laue diffraction pattern for specimen exposed to cavita- Fig. 23(a) X-ray Laue diffraction pattern for specimen exposed to
cavita-tion for 10 hr; 6/4 have been removed by electrolytic polishing tion for 18 hr
Fig. 23(b) X-ray Laue diffraction pattern for specimen exposed to cavita-tion damage for 18 hr; 33m have been removed from surface by electro-lytic polishing
men exposed to cavitation for 18 hr. The sharp spot pattern of
the undistorted crystal structure is obtained after removal of 471.1,
from the surface. It is also of interest to observe that, before
any of the damaged surface has been removed, the plastic deforma-tion does not appear to vary over a range of exposure times from
30 min to 18 hr. This behavior is shown in Figs. 19(e), 19(f), 22(a), and 23(a).
Conclusion
X-ray diffraction patterns show that plastic deformation of the
structure of a solid exposed to cavitation begins essentially
im-mediately upon exposure to cavitation. When cavitation damage
has been well established, the depth of the deformation of the structure does not change even after appreciable surface erosion has taken place. The decrease in cavitation damage rate after
long exposures which has been discussed by some investigators, who used specimens oscillating in the cavitating liquid, is shown
to be an incidental hydrodynamic effect. Photographic
exami-nation of the bubble cloud over a severely damaged specimen oscillating in a cavitating liquid demonstrates that the cavitation
cloud is much more sparse than it is over a more uniform specimen.
Acknowledgments
The authors wish to thank Prof. Pol Duwez for advice and sug-gestions regarding the X-ray analysis procedure. They are also indebted to Frank Youngkin for his valuable assistance in ob-taining the X-ray diffraction patterns.
The program was supported by the Office of Naval Research.
References
1 A. Thiruvengadam, "A Comparative Evaluation of Cavitation
Damage Test Devices," Tech. Rep. 233-2. Hy dronautics, Inc., November, 1963.
2 A. Thiruvengadam and H. S. Preiser, "On Testing Materials for Cavitation Damage Resistance," Tech. Rep. 233-3, Hydronautics, Inc., December, 1963.
3 Sophia Waring, H. S. Preiser, and A. Thiruvengadam, "On
the Role of Corrosion in Cavitation Damage," Tech. Rep. 233-4, Hydronautics, Inc., February, 1964.
4 A. Thiruvengadam and Sophia Waring, "Mechanical Properties of Metals and Their Cavitation Damage Resistance," Tech. Rep. 233-5, Hydronautics, Inc., June, 1964.
5 A. Thiruvengadam and H. S. Preiser, "On Testing Materials for Cavitation Damage Resistance," Journal of Ship Research, vol. 8, no. 3, 1964, pp. 39-56.
Fig. 23(c) X-ray Laue diffraction pattern for specimen exposed to cavita-tion damage for 18 hr; 47AL have been removed from surface by electro-lytic polishing
6 M. S. Plesset, "On Cathodic Protection in Cavitation Damage,"
JOURNAL OF BASIC ENGINEERING, TRANS. ASME, Series D, vol. 82,
1960, pp. 808-820.
7 M. S. Plesset, "The Pulsation Method for Generating Cavitation
Damage," JOURNAL OF BASIC ENGINEERING, TRANS. ASME, Series
D, vol. 85, 1963, PP. 360-364.
8 M. S. Plesset and A. T. Ellis, "On the Mechanism of Cavitation Damage," TRANS. ASME, vol. 77, 1955, pp. 1055-3064.
DISCUSSION
Phillip Eisenberg3
The authors deserve commendation for their experimental
technique and excellent photographs of cavitation clouds in the various "zones" of cavitation damage. These photographs
pro-vide useful information concerning the flow variations in the mag-netostriction oscillator as the roughnesses of test specimens change. However, the conclusions drawn by the authors as a
basis for criticism of the results of Thiruvengadam, et al., indicate
a misunderstanding of the latters' reported findings.
It is the
purpose here to discuss the authors' conclusions and criticisms in
terms of both the damage mechanisms and the hydrodynamic
interactions. It should be emphasized at the outset that never
has it been contended that there are changes in the properties of
the solid in the various zones of damage nor that these zones, and
in particular the "steady state" zone, have a fundamental
sig-nificance for the metallurgical response of the solid to damaging
cavitation pressures.
It is
difficult to comprehend how theauthors gained such interpretations from the publications cited by them. What is of importance is the demonstrated existence of the so-called steady zone, at least for all materials tested to
date, and the unique ordering of the cavitation damage resistance of materials in this zone. The absence, within experimental accuracy, of time dependence and the very nearly constant rate of damage in this zone have made possible the most successful
correlation of damage rate with measurable material properties so far achieved. Furthermore, results have emerged which prove
to be extremely useful in engineering applications where extensive damage is encountered.°
That the existence of the various zones are, in part, associated with hydrodynamic effects was early postulated in the work at
3 President, Hydronautics Inc., Laurel, Md. Mem. ASME. Phillip Eisenberg, Berman S. Preiser, and A. Thiruvengadam, "On the Mechnnisms of Cavitation Damage and Methods of Protection,"
Society of Naval Architects and Marine Engineers, Paper No. 6,
HYDRONAUTICS, and experiments to demonstrate the effect of artificial roughness carried out. In this respect, the hydrody-namic interaction is hardly an "incidental, superficial" effect. The damage intensity is intimately associated with the
hydrody-namic pressure, of course, and, as constantly pointed out in
Thiruvengadam's work, the correlations which have been found relate only to the damage in a given environment. Since it is not
yet possible to describe the pressure "intensity," various en-vironments can so far be compared or characterized only in terms of the material behavior. These correlations have made it possible to compare the damage rates in different types of damage
producing equipment. In this connection, it is clear that the existence of a steady zone is not a characteristic of the magnetostric-tion oscillator alone as the authors imply. According to the authors' interpretations, the various zones in which extensive
damage appears must be a result of the "inefficient piston" action of a rough specimen which results in production of a sparse
cavitation cloud and consequent reduction in damage rate. The
question therefore arises: is the effect a peculiarity of the mag-netostriction oscillator, wherein the cavitation cloud is produced
by the specimen itself, or is it independent of the manner in
which a cavitating region is applied to the specimen face? This question was asked by A. Thiruvengadam and his collaborators and it was postulated that the effects observed were associated with the influence of rough surfaces in reducing the cavitation collapse pressures. To confirm these ideas of the hydrodynamic influences and to examine whether the steady-state zone is a
peculiarity of the equipment or of the material, experiments were
first carried out with preroughened specimens. It was shown that preroughening indeed tends to eliminate the peaks in the rate versus time curves but that the buildup and approach to a steady zone still occurs.4 Even preroughening by the severe test of drilling many deep holes showed the buildup and steady
zone without, in some cases, eliminating the peak. That the effect
is not restricted to the magnetostriction oscillator was proved by
examination of many data from tests in rotating disk devices and
venturi tubes wherein the production of the cavitation cloud is independent of the specimen. The same pattern of behavior was found, of course, and tends to confirm the hypothesis that the
reduction in damage rate is associated with reduction in collapse
pressures of cavitation bubbles in the vicinity of rough surfaces.
The sparser cloud in the zones of heavy damage in the mag-netostriction oscillator may or may not be a more significant reason for the lower damage rate. In a sparse cloud, the collapse
pressure produced by a single isolated bubble even near a rough surface may be much greater than that of a single bubble in a
dense cloud. In the latter case, the interaction with the very
great number of bubbles close by will greatly reduce its collapse
pressure, not to mention the strong influence of a smooth surface in reducing collapse pressures. Until this question is answered, it appears just as likely that the decrease in damage rate in the later
zones is associated with the interactions of collapsing bubbles
with rough surfaces (as would be concluded from the rotating disk
and venturi tests) as with the existence of sparser clouds. Again, the hydrodynamic effects are hardly incidental; on the contrary,
they are crucial.
It is clear that in the steady-state zone a kind of equilibrium has been established. The critical questions to be asked in
con-nection with the significance of this zone are: (i) do changes take place in the surface roughness of a given material which result in a change in the hydrodynamic "input" intensity with time so
that the damage rate is only fortuitously approximately
con-stant? and (ii) in this zone, are the roughnesses of different ma-terials sufficiently different so that the input intensities are
dif-ferent for the various materials even in the same device? Critical
attention should be addressed to these questions to further ex-amine the significance of the steady state zone; it cannot be
dis-missed on the basis of the evidence and interpretations presented by Professor Plesset and Devine. Dr. Thiruvengadam has found
that at the start of the so-called "attenuation zone" (the peak in
the curve of damage rate versus time), the average depth of
erosion is, within about 10 percent, the same for all of the
ma-terials he has tested (actually, the difference is less for mos't of the materials). Greater differences in average depth of eroSion (as high as 50 percent in one or two cases) have been found for ma,
teriaLs in the steady-state zone. It is, of course, difficult rto esti-mate whether such differences will result in significant differences in collapse pressures since the details of surface shape also play a role. Nevertheless, that the damage rates in this zone remain
very nearly constant indicates that the roughness patterns
re-main sufficiently similar as damage proceeds to re-maintaini about the same input hydrodynamic intensity. Furthermore, that the damage rate in the steady zone varies as the square of the ampli-tude (in the magnetostriction oscillator) to a high degree, of
ac-curacy for all materials tested indicates either that the, input
energy is not unduly dependent upon the roughness or, 'again,
that the roughness patterns remain sufficiently constant as damage progresses. While these arguments do not settle the
question of unique correlation between different materials, since
the various materials do, in fact, have somewhat different degrees
of roughness, they do identify the questions to be examined be-fore the correlation with strain energy can be finally accepted as the most significant single correlation factor, as would be indi-cated by the results to date. Furthermore, a great deal of work must be done before the progress of cavitation damage in the earlier zones can be described and an understanding reached of
why crossovers in order of merit appear in these earlier zones.
Now, the foregoing is still not the whole story as far as the be-havior of the cavitation cloud in the steady zone is concerned. If the damage becomes very massive (i.e., if very deep isolated craters occur), the production of the cavitation (in the magneto-striction oscillator) may be hampered. In fact, Dr.
Thirtrven-gadam has found that cavitation may almost cease and/or that the damage rate may become almost undetectable. This is con-sidered to be a result either of deaeration of the liquid in the dome created within the undamaged rim or even in the deep crevices themselves, or that air has accumulated within the dome or crevices, thus either preventing damaging pressures or
cushion-ing what cavitation does occur. Evidence to date indicate S the former since the experiment can be continued successfully if fresh
water samples are substituted. This phenomenon is easily de-tected by the change in sound intensity and frequency as well as
by weight loss. Professors Plesset and Devine evidently antici-pated the possibility of entrapped air when they decided to run their experiments with the specimen facing upward. They do not comment on the possibility that a part of the explanation for the sparsity of the cloud may have been a result of deaeration.
With regard to the authors' observation that the damage rate
is also constant in the "accumulation zone" in their
experi-ments, it should be noted that the material they used is one that
exhibits "strain softening," unlike most of the materials that have been examined. Strain-hardening materials do not exhibit this
behavior. That the damage rate in the "steady zone" is not
exactly constant in their experiments may be attributed to the
very small weight losses that this material suffers under the small
amplitude used by the authors. Large experimental errors Can be expected in determining damage rates where the weight losses per unit time are almost an order of magnitude less than has been the case in most of the experiments on which the conclusions con-cerning the steady-state zone have been based.
As for the authors' remarks that the ideas concerning SI he
steady-state zone have contributed to a misunderstanding of the role of corrosion in cavitation damage, no reason is given and is
dearly unsubstantiated in view of the above discussion.
In summary, the authors' have made very nice experiments, which do not contradict any previous results, and which, prop-erly interpreted, will hopefully be pursued toward constructive
contributions to an understanding of and ability to predict cavitation damage phenomena.
F. G. Hammitt' and R. Garcia'
The authors are to be congratulated on this very careful in-vestigation of damage rate effects, and the very ingenious tech-niques which they have used. We believe that it is very clearly
shown here that rate effects for the magnetostriction type of test, and probably for most other cavitation damage tests, are pri-marily due to changes in the flow geometry caused by the
already-incurred damage. If one makes this assumption, then it becomes logical to consider plotting damage rate against accumulative
damage. If it is further assumed that all materials damage in
the same fashion (which is certainly not true, but might serve as
a rough approximation), then the plots of volume-loss-rate versus
accumulative-volume-loss should have the same shape, but
dif-ferent amplitudes, for all material-fluid combinations (neglecting
Professor, Department of Nuclear Engineering, University of
Michigan, Ann Arbor, Mich. Mem. ASME.
Doctoral Candidate, Dept. of Nuclear Engineering, University of Michigan. Volume loss Rate
err
ce 16 x 15 14 1 13 11I
M 7z6
2 5
4 12 8 2 0corrosion) tested in a given facility, with given test-operational
parameters.
This leads, under the foregoing limitations, to the assumption of a "characteristic damage curve" for a given facility, which would apply to all fluid-material combinations tested therein. All test results could then be reduced to a single curve, plotted using suitable dimensionless damage rate and time. The
nondi-mensional volume loss rate on such a plot would be the same for
all fluid-material combinations tested to the same dimensionless
time. Fig. 24 shows typical curves and the required derivation. Note that a scale constant, k, alone then denotes the cavitation
damage resistance of a given material-fluid combination.
With regard to actual test results in our vibratory facility, we have found that below about 10 mils total MDP, (volume loss considered as smeared over specimen face), ignoring the very
early part of the test, an approximately constant rate period
exists over the complete test duration. We feel that this rate can best be used to relate different materials. This is essentially con-sistent with the data from the present paper. If the rate is
con-CHARACTERISTIC DAMAGE CURVE FOR GIVES FACILITY
'
t
-1d1/.1 where time
- volume loss
and I.. signifies material-fluid combination. Suppose a set of dimensionless time,E and rate of volume change,
dir/dr
such that Atr-o_z is the same for all material-fluid Combinations. for a given type of test.
dv-Then let
WE - Etat
the particular'material-f uid combination.
and
Then
l'o-Lr
'54 -- - dfIG for all material-fluid combinations. Hence k, alone characterizes cavitation damage resistance for a particular material-fluid combination. N Fig. 24 ' CAVITATION IN Pb-BI AT 1500°F SPECIMEN No.3 - 304 SS SPECIMEN No 5 - 304 $S 10 15 20 25 30 35 40 45MEAN DEPTH OF PENETRATION:- MILS
Fig. 25
where k is a constant which depends on
1740
55
stant throughout the test, the "characteristic damage curve," of
course, degenerates into a horizontal straight line.
We have, however, carried one series of tests to total MDP of the order of 1/16 in. This was for stainless steel in Pb-Bi at 1500 deg F. In this test, where damage was accrued very rapidly,
we found no constant rate at high total damage, but, rather that
after passing through a minimum, the damage rate again
in-creased. In Fig. 25, data for 2 separate specimens are shown.
With such a large amount of damage the "flow geometry" has,
of course, changed very significantly (specimens have become severely dished, as well as deeply pitted) and the geometry is
continuing to change so that in our opinion it is not reasonable to expect constant rate of damage for such a case. The total damage
in the tests of the present paper is much less than that from our Pb-Bi test (order of about 20 mils MDP). This is also true of the
tests reported by the Hydronautics group.
In these Pb-Bi tests, we did not observe a continued
attenua-tion in damage rate, due to a lack of bubbles caused by the
roughened surface. Perhaps this is due to the fact that we do not obtain in these tests the deep pits reported by the present paper,
but rather a somewhat finer wear (Fig. 26) with the dishing, edge break-off, and so on.
F. J. Heymann'?
The authors' contribution reflects the increasing attention that is being paid to the nonuniformity of erosion rate as a function of time, and to the causes and significance of this observed.
be-havior. Awareness of this behavior is of course not new; Kerr [9],8 in 1937 recognized that cavitation erosion rate changes
with time and he presented two relative resistance scales for
materials, one based on a period of "initial erosion" and one on a period following that Many authors have discussed the
"incu-bation" or "delay" period before major material loss occurs. Plesset [10] in 1959 described a loss rate versus time pattern
very much like that discussed in the present paper, and at least hinted, even at that time, at the conclusions which the authors
7 Senior Engineer, Development Engineering Department, Westing-house Electric Corp., Lester, Pa. Mem. ASME.
8 Numbersinbrackets designate References at end of paper.
Fig. 26
2.0
1.0
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Fig. 27 Examples of computed erosion rate-time curves
5.0 4.0 '5 310 2 e 1.0 3.0 HOURS (STELLITE 6) (TOOL STEEL, 610 VPN) 20 40 60 80 100 120 140 160 180 HOURS
Fig. 28 Experimental rate-time curves (constructed from cumulative
loss-time curves in Parsons Journal, Christmas, 1964)
702 / DECEMBER 1966 Transactions of the ASME
7 3 1.6 1.4 ne (STELUTE 6) 1.2 S SPEC. NO. 5-3 0 1.0 0.8 8 0.6 0.4
Fin. 29, Experimental erosion rate-time curves from Westinghouse
rteam arvisioniests
(TITANIUM MST 821) SPEC. NO. T1-1
10 20 30 40 50 60 70 80 90
TIME - HOURS
planning and interpretation of material tests, for the
extrapola-tion of test data to predicting field behavior, and for a fuller
understanding of the mechanisms and variables involved in the
whole erosion process. The increased concern with this aspect is
indicated by the work of the authors, as well as that of A. Thiru-vengadam and his associates, and indeed by the disagreement
which still exists. It is interesting to note that in Great Britain several independent researchers, working with droplet impact as
well as with cavitation devices, have come to conclusions similar
to those of the authors: in assigning primary significance to the
period of maximum erosion rate, in relating the "attenuation
zone" to the effects of gross surface damage, and in questioning
the general existence of a final "steady-state zone." (J. M. Hobbs
at National Engineering Laboratory and D. Pearson of Central Electricity Generating Board, as stated in private
communica-tions to the writer and in papers to be published.)
The authors of this paper have given a very convincing
ex-planation for the "attenuation zone" in vibratory cavitation testing; in droplet impact testing the usual explanation (first
proposed by Honegger [11]) is the cushioning effect of liquid trapped in the pockets and crevices of the eroded surface.
It
had occurred to the writer, however, that a behavior somewhat
similar to that described by Thiruvengadam could be analytically
predicted on the basis of nothing more than the assumption that material removal occurs by a fatigue mechanism. This analysis regards both the original surface, and the surfaces exposed as a
result of erosion, as composed of elementary particles whose
life-times (when subjected to an erosion environment) can be de-scribed by an appropriate statistical distribution function (much as the lifetimes of a large collection of fatigue specimens, tested under the same stress conditions, can be described statistically).
This rather simplified conceptual model has been mathematically
formulated and computer programmed, using normal
distribu-tions. The input parameters are the mean (M.') and the
stan-dard deviation (crf) assumed for the original surface element life-times, and a corresponding pair of values (M9) and (as), assumed
valid for all subsequently exposed surfaces. Some characteristic results are shown in Fig. 27. The rate-time curves, as can be
expected, generally exhibit an "incubation period" followed by a peak at about the mean lifetime of the original surface elements,
followed by a dampened series of fluctuations tending toward a final steady state value. Fluctuations such as shown here can, in fact, be found in reported test results. An example is shown
by Fig. 28, which represents two rate-time curves computed from cumulative loss curves found in reference [12].
The results obtained in the erosion test facility at the
Westing-house Steam Division (a moisture carrying -steam jet impinge-ment device) exhibit no incubation or accumulation zones; the erosion rate seems to decrease rapidly from a high initial value,
sometimes leading to a steady state value and sometimes merely tending toward one. But here, too, fluctuations have sometimes been observed, as exemplified by Fig. 29. A similar analytic curve can be generated by the somewhat artificial device of mak-ing the "mean" lifetime of the original surface equal to zero. This is shown in Fig. 30.
Fluctuations which appear quite prominently in rate-time
curves are not nearly as evident if the same data are plotted as cumulative erosion versus timewhich is, of course, the form in which raw erosion data are obtained. Therefore it seems con-ceivable that in many cases such fluctuations would have been
"smoothed out" of the data, or lost entirely through the test points being too far apart in time.
The foregoing is, admittedly, an over-simplified analysis, and
in no way is it meant to suggest that the surface geometry effects
described by the authors, and other mechanisms, do not play an important or perhaps major role. This work is to be continued to elaborate the analysis and to incorporate some of these other effects and mechanisms, and it is hoped to report on that more fully at a later date. For this projected work, the contribution
made by the authors today will be most valuable.
.0 2.0 3.0
TIP SCALE
Fig. 30 Computed erosion rate-time curve
have presented today. Honegger's [11] results for
impinge-ment erosion, published in 1927, show a generally similar rate-time
pattern.
What is new, it seems to the writer, is the realization that this time dependence is not merely a peculiarity to be noted in pass-ing, but rather an important aspect of which more thorough in-vestigation and understanding is required for the meaningful
0.2 0 0 I I 10 20 30 40 50 TIME - HOURS 60 70 80
References
9 S. L. Kerr, "Determination of the Relative Resistance to
Cavitation Erosion by the Vibratory Method," Ta&xs. ASME, vol. 59,1937, pp. 373-397.
10 M. S. Plesset, Discussion to "Some Corrosion Effects in Ac-celerated Cavitation Damage," by W. C. Leith and A. L. Thompson, JotraNAL or Besic ENGINEERING, TRANS. ASME, Series D, vol. 82. 1960, pp. 804-805.
11 E. Honegger, "Tests on Erosion Caused by Jets," The Brown Boveri Review, vol. 14, no. 4, April, 1927, pp. 95-104.
12 R. P. Kent, "Some Aspects of Metallurgical Research and
Development Applied to Large Steam Turbines," Parsons Journal, vol. 10, no. 59, Christmas, 1964, pp. 285-295.
W. C. Leith9
The authors have employed some excellent experimental
tech-niques to study the change in the rate of accelerated cavitation damage with exposure time. Their conclusion, that the decrease in cavitation damage rate after long exposures is due to an
inci-dental hydrodynamic effect, appears to agree with recent work of
Hobbs in Scotland and Pearson in England which will be
pub-lished in the Proceedingsofthe Royal Society at the Symposium: Deformation of Solids by the Impact of Liquids.
Additional data on this controversy is scheduled for discus-sion at the ASTM Symposium on Erodiscus-sion by Cavitation or
Im-pingement in June, 1966, when Hobbs, Heymann, and Thiruven-gadam will present papers related to the significance of the cavitation damage rate.
A. Thiruvengadam10
The writer is pleased to note the growing interest among
competent investigators on the effect of testing time on the rate
of cavitation damage particularly because this is one of the basic
parameters in any experimental investigation on this subject. In the past, it has been the general practice among most of the
investigators to select some arbitrary testing time anywhere from
a few minutes to two hours and then to attempt to correlate the loss of material after this preselected time interval with other parameters such as material properties, liquid properties, and other hydrodynamic parameters. Given a relationship such as shown in Fig. 1 (which is more typical of results conducted on 9 H. G. Acres & Company Limited, Niagara Falls, Ontario, Canada. Mem. ASME.
lo senior Research Scientist, Hydronautics, Inc., Laurel, Md.
Assoc. Mem. ASME.
0.35 0.30 025 0.20 .0.15 0.10 0 200 400 600 800 1000 1200 1400
several metals in several liquids)," the question comIes up as to
whether such attempts are logical.
It has been the writer's contention that it would Make more sense to select some time interval at which the testing time has
no effect and then to study the correlations with other parameters
at least till we understand the interrelation between the various
"zones."
The result that the decrease in cavitation damage rate is due to
the interaction of the surface roughness on the hydro4namics of bubble collapse confirms our own earlier conclusion', reference
[2] of the original paper. The second conclusion that a 'the depth
of deformation of the structure does not change even after ap-preciable surface erosion has taken place" does not ',contradict
any of our results.
In light of these facts, none of our results reported in references
[1-5] of this paper are proven erroneous by the conclusions of these authors. The unsubstantiated remarks of these authors about our investigations characterizing them as
"misinterpreta-tions" and "misunderstandings" are, we believe, due to their own lack of understanding of our results.
Authors' Closure
We address ourselves first to the lengthy discussion of our paper
by Mr. Eisenberg since it presents again some of the problems
which are connected with a precise understanding of the technical
content of the views of the Hydronautics group on cavitation
damage.
We must accept Mr. Eisenberg's statement that they have
"never contended that there are changes in the propertiles of the solid in the various zones of damage," and we shall not ascribe such a contention to them. Our objective in this studyNvas not a minute examination of the conjectures in other studies. Rather, our objective was to examine experimentally the! two as-pects of cavitation damage in the various "zones": first, the
response of the solid, and second, the hydrodynamic environ-ment, in order to make available some factual material. We do ascribe to the Hydronauties group the notion that the I'steady state zone" is the region of theoretical significance although we may have somewhat overstated their position by implying that
11 P. Eisenberg, H. S. Praiser, and A. Thiruvengadam, ;:20n the
Mechanisms of Cavitation Damage and Methods of Protection," Paper No. 6, The Society of Naval Architects and Marine
Engi-neers, Winter Annual Meeting, New York, November, 19651
1600 1800 2000 2200 ' '2400
MATERIAL 304-1. STAINLESS STEEL
LIQUID WATER AT 804F DOUBLE , AMPLITUDE. L85 a 10- INCH FREQUENCY 16 (CS , DIAMETER OF SPECIMEN'0 625 INCH . . . . . . . . .
704 / DECEMBER 1966 Transaction's of the ASME
TIME. MINUTES p.
it is their view that this region has a fundamental significance for the response of the solid to cavitation. We have been led to
this idea, in part at least, by the numerous publications from
Hydronautics on this subject.
The Hydtonautics workers maintain that "the very nearly
constant rate of damage in this zone has made possible the most successful correlation of damage rate with measurable material properties so far achieved." We believe that our observations
give decisive information regarding any possibility of fundamental
features in this zone. Beyond that we should like to point out that in our experience the damage rate does not remain "very nearly constant" in this zone. We find that the scatter in dam-age rate values is greater there on a percentdam-age basis than it is in the flat region about the peak damage rate. In addition, the
steady state zone does not remain even roughly steady if exposure to cavitation is continued. We find that the damage rate in
water begins to rise again in the same way as has been found by Hammitt and Garcia (Fig. 25) in liquid metals. The discussion
by Heymann also gives extensive data which shows this rise in
water. This rise in damage rate beyond "zone 4" is a most
per-tinent observation in view of the postulate presented by Mr.
Eisenberg that the drop in damage rate from zone 3 to zone 4 is
to be "associated with the influence of rough surfaces in reducing
the cavitation collapse pressures." The rise in damage rate
beyond "zone 4" to a "zone 5" takes place even though the sur-face of the specimen continues to be at least as rough as before.
This rise in damage rate presumably is the result of a crude dish-ing of the specimen which eventually takes place.
Rather than describing the view that a rough surface reduces cavitation collapse pressures as a "hypothesis" we would con-sider it to be an untenable assumption. We should like to point
out once more that within experimental accuracy our X-ray measurements show that the depth and degree of plastic
deforma-tion of the solid exposed to cavitadeforma-tion is the same for a lightly
damaged, smooth surface as it is for a heavily damaged extremely
rough surface. We have great difficulty in following the line of
Mr. Eisenberg's reasoning in his speculations on the mechanisms
involved in the variation in damage rate. He states that "the reduction in damage rate is associated with reduction of cavitation collapse pressures of cavitation bubbles in the vicinity of rough
sur-faces . . . In a sparse cloud, the collapse pressure produced by a single isolated bubble even near a rough surface may be much
greater than that of a single bubble in a dense cloud. In the
latter case, the interaction with a very great number of bubbles
close by will greatly reduce its collapse pressure, riot to mention the strong influence of a smooth surface in reducing collapse pres-sures." (italics ours).
We may turn from consideration of Mr. Eisenberg's generalities
to some of the specific errors in his discussion. He mentions their concern with deaeration and entrapped air and states that
Reprinted from the December 1966 Journal of Basic Engineering
presumably for this reason we ran our experiments with the speci-men facing upward. Our damage experiments were run with the
specimen facing downward. We did, however, take photographs of the bubble cloud both with the specimen facing upward and
with the specimen facing downward. The bubble clouds
ex-hibited the same features in both experimental arrangements. We did not comment on the possibility that the sparsity of the cloud may have been the result of deaeration or of entrapped air
since we did not encounter either of these effects.
Mr. Eisenberg's statement that the material we used, 4340 steel, is "strain softening" is incorrect. This material is a strain hardening material as any competent metallurgist can readily
verify.
Mr. Eisenberg is concerned also that the lack of constancy we
find in the "steady zone" arises from the "very small weight losses
that this material suffers under the small amplitude used by the authors." As stated in the introductory section of our paper,
we operated at an amplitude of 10-3 in. which is a double ampli-tude of 2 X 10-8 in. Fig. 1 of our paper is from Thiruvengadam
and Preiser (references [3 and 5] of our paper) and gives their
double amplitude as 1.25 X 10-3 in. It would be expected that for comparable materials their weight losses would be less than
ours. The order of magnitude that Mr. Eisenberg is missing may possibly be the factor of 10 in the ordinate scale of their
curve (see Fig. 1). The weight loss that their curve gives at the
end of zone 3 is about 0.5 mg/min. X (1/10) which turns out to be
3 mg/hr. Our corresponding value (see Fig. 7) is about 5 mg/hr. We now turn to the other discussions of the paper. We have
already mentioned the interesting findings of Professor Hammitt
and Dr. Garcia, on the behavior of cavitation erosion in liquid metals. We agree with their view that rate effects in magneto-strictive tests, and very likely for other types of tests, are due
primarily to changes in the flow geometry caused by the already-incurred damage. With regard to their characteristic damage
curve concept, we shall look forward to a presentation of greater length than was available to them here.
We also appreciate the information presented by Dr. Heymann
regarding the change with time of the rate of weight loss. His remarks concerning a similar behavior with droplet impact damage
is most interesting. Dr. Leith points out that an opportunity will be available to learn more regarding these exposure time
ef-fects at the ASTM Symposium of June, 1966. Perhaps on this same occasion we may have the opportunity of getting a full
presentation of Dr. Heymann's statistical model of the time
varia-tion of erosion. This approach is, so far as we are aware, an entirely new theoretical view of the problem and, therefore, is of great interest to all workers concerned with cavitation and
droplet erosion.
In conclusion, we wish to thank the discussers for their
