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TECHNICAL REPORT 233-5
MECHANICAL PROPERTIES OF METALSAND THEIR CAVITATION
DAMAGE RESISTANCE
By
A. Thiruvengadama nd
Sophia WaringJune 1964
Prepared Under
Office of Naval ResearchDepartment of the Navy
Contract No. Nonr 3755(OO)(FBM)
Iof c I) ¥ s
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TABLE OF CONTENTS
Page
SUMMARY 1 . . . . . . . . .. . . . . . . . . . . . .
INTRODUCTION ............................................... 1
MECHANISM OF CAVITATION DAMAGE............................... 3EI1E.TAL FACILITY AND TECHNIQUE ........................... 5
RESULTS AND DISCUSSION....................................... 6
Metals Tested and Their Mechanical Properties... 6
Cavitation Damage Resistance............................ 9
L~imiItations............................................. 11
Intensity of' Cavitation Damage......................... 11
CONCLUSIONS.................................................. 12
ACKNOWLEDGMENTS............................................ 13
REFER:ENC:ES........................................ 14
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LIST OF FIGURES
Figure 1 - Definition Sketch for Deformation Due to Cavitation
Bubble Collapse
Figure 2 - Schematic Representation of the Response of Metals
to Repeated Straining
Figure 3 - Hypothetical Distribution of Strains Caused by the
Collapse of Bubbles in a Cavity Cloud
Figure 4 - Schematic Fatigue Dlagram Showing Three Regions
Figure 5 - Deflnit!on Sketch of the Magnetostriction Device
Figure 6 - Correlation Between Estimated Strain Energy and
the Reciprocal of Rate of Volume Loss
Figure 7 - Engineering Stress-Strain Diagrams for Six Metals
Figure 8 - True Stress Strain Diagrams for Six Metals
Figure 9 - Effect of Amplitude on Darnage Rate for ElevenMetals
Figure 10 - Correlation Between Strain F .ergy and Reciprocalof Rate of Volume Loss
Figure 11 - Correlation Between Ultimate Strength andReciprocal of Rate of Volume Loss
Figure 12 - Correlation Between Yield Strength and Reciprocalof Rate of Volume Loss
Figure 13 - Correlation Between Brine]l Hardness and Reciprocalof Rate of Volume Loss
Figure 14 - Correlation Between Modulus of Elasticity andReciprocal of Rate of Volume Loss
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Figure 15 Correlation Between Ultimate Elongation andReciprocal of Rate of Volume Loss
Figure 16 Relationship Between Strain Energy and Reciprocalof Rate of Volume Loss at Various Amplitudes
Figure 17 - Relationship Between Amplitude and Output Intensity
ix
I.
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NOTATION
S Estimated strain energye ..
T Ultimate tensile strength
E Ultimate elongation
Y Yield strength
S ' True strain energye
n Strain hardering factor
Tf' True fracture strength
E f Elongation at fractu:e
Intensity of cavitation damage
r Rate of volume loss
A Area of erosione
S Strain enprgye
ro Corelatioon factor
a Ampi tud-
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SUMMARY
Detailed investigations with a magnetostriction apparatus
were carried out to determine the cavitation damage resistance of
eleven metals in distilled water at 80 OF. The cavitation damage
resistance is defined as the reciprocal of the rate of volume loss
for a given metal. Among the mechanical properties investigated
(ultimate tensile strength, yield strength, ultimate elongation,
Brinell hardness, modulus of elasticity and strain-energy), the
most significant property which characterizes the energy absorbing
capacity of the metals, under the repeated, indenting loads due
to the energy of cavitation bubble collapse in the steady state
zone, was found to be the fracture strain energy of the metals.
The strain energy is defined as the area of the stress-strain
diagram up to fracture. The correlation between the strain en-
ergy and the reciprocal of the rate of volume loss leads directly
to the estimation of the intensity of cavitation damage; this
intensity varies as the square of the displacement amplitude of
the specimen. All these conclusions are limited to the steady
state zone of damage.
4I NTRODUCTI ON
Since the work of Parsons (1) in 1919 and Fottlnger (2) In
1926, there have been many attempts to 'characterize the cavit, ation
damage resistance of materials by a single, commo,± mechanical
property. Although Honegger (3), in 1927, did not find any cor-
, relation between hardness and erosion resista.nce, Gardner (4),
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in 1932, found that the hardness of a metal was the principal
property in determining the resistance to erosion. Many more ref-
erences may be cited to bring out similar controversies with re-
gard to other mechanical properties such as yield strength, ulti-
mate tensile strength, ultimate elongation and modulus of elasticity.
One can get a clear picture of the magnitude of the conflicts in
this area from some of the excellent review articles in the tech-
nical literature (5,6,7).
These controversies are a result of an inadequate under-
standing of the mechanism of cavitation damage. Recent advances
in this direction have made it possible to rationalize some of the
conflicts, and to propose a mechanical property that most signifi-
cantly characterizes the cavitation damage resistance of metals
tn the absence of corrosion. It is the purpose of this paper to
develop the logic behind such an argjment, and to present recent
substantiating experimental evidence,
One of the basic parameters involved in the testing of ma-
terials fcr cavitation damage resistance is the test duration. The
rate of loss of material depends upon the test duration itself
even though every other t'-st paraimeter is maintained precisely con-
stant Recent analysis showed that there exist four zones of dam-
age with respect to testing time, They are
1, 1ncubation Zone
2. Accumulation Zone
3, Attenuation Zone
4. Steady State Zone
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A detailed discussion of these zones appears elsewhere (14).
All the results and conclusions presented herein are limited to
the steady state zone of damage in which the rate of damage does
not change with time.
MECHANISM OF CAVITATION DAMAGE
It ,i now generally established that the bubble collapse
energy produces indentations on the metal as shown in Figure 1.
The indentations may be produced on the material either by the
impingement of Jets or by shock waves. The evidence in support
of these methods of dent formation is abundant in the litera-
ture (8,9,10,11,12). In the absence of corrosion, it is quite
reasonable to proceed on the assumption that these dents, formed
by mechanical means, are the main cause of fracture and loss of
metal.
Wh n such repeated, indenting forces or blows act upon a
metallic surface, one of the following events may occur depending
upon the intensity of impact:
(i) There may not be any permanent deformatlon;
(ii) The metal nay deform after a certain number of
repetitive blows;
(iii) A permanent deformation may develop at the onset
of the first blow; and
(iv) The metal may 'splash' and 'wash-out' on the first
blow itself or after a certain number of repetitions./: I,
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These possibilities can be readily understood from Figure 2
which shows schematically the variation of the internal friction
of metals with strain amplitude in the case of' repeated loadings.
In the case of cavitation damage, it is reasonabie to assume, for
the sake of the present argument, that the energy of collopse for
a given frequency, amplitude, and liquid varies in a statistical
manner as shown by the hypcthetical distribution in Figure 3. As
the strain amplitude is increased, the mean strain may increase,
the mean number of bubbles possessing adequate energy of collapse
to produce this strain may increase, or both of these possibilities
may occur. In any case, the response of a metal to a given strain
can be qualitatively explained by an equivalent indentation fatigue
diagram as shown in Figure 4. Accordingly, the response of a metal
to a cavitation damage test is dependent upon the order of magni-
tude of the strain. In Figure 4 three regions have been designated
to point out the possible material respo.nses to indentation events
I discussed previously. Photographs of the metallic surfaces which
exhibited the response of each region are also shown.
With the above physical picture In mind, let us pose the
question: What Is the characteristic property of a metal that
controls the ro]-d volume as a result of this mechanical process?
Obviously this property is the energy absorbing capacity per unit
volume of the motal up to fracture when subjected to the repeated
overlapping indentations. At the present state of knowledge, there
is no way to detezrn,1ne thl3 quantity exactly. For this reason,
several investigators have tried to correlate this quantity with
most of' the commonly krnowr mecnan.c l properties of metals.
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Our superficial intuition initially suggests that the hard-
ness of the surface may be of utmost importance. However, when
the physical meaning of hardness is examined critically, we find
that indentation hardness is essentially a measure of the yield
stress of the material (13). It does not represent the full mea-
sure of the energy required for fracture because it neglects the
elongation of the material up to its ultimate stength. Similar
arguments can be advanced against other mechanical properties such
as yield stress, ultimate stress and others. An earlier attempt
to correlate the area of the stress-strain diagram up to fracture
and the cavitation damage rate proved to be encouraging (12). The
present investigation is an extension of this attempt in a more
detailed manner and confirms the earlier results.
EXPERIMENTAL FACILITY AND TECHNIQUE
The HYDRONAUTICS, Incorporated Magnetostriction Apparatus
was used for these investigations. The details of the equipment
and the experimental procedure are outilned in Reference 14. A
double cylinder velocity transformer replaced the exponential
horn. In Figure 5 are shown the essential test parameters of the
magnetostriction apparatus. Simple flat specimens were tested in
distilled water at 270 C (approximately).
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RESULTS AND DISCUSSION
Metals Tested and Their Mechanical Properties
The following metals were tested.
Group 1.
(1) 1100-0 Aluminum
(ii) Cast Iron
(I1) Molybdenum
(iv) 410 Stainless Steel
(v) 3o4-L Stainless Steel
Group 2.
(I) 1100-F Aluminum
(ii) 2024-T4 Aluminum
(ill) 1020 Mild Steel
(iv) Tobin Bronze
(v) Monei
(vi) 316 Stainless Steel
For the materials listed under Group 1, the mechanical prop-
erties were obtained from the literature. The typical values in
the references varied over a ran-e as shown in Table 1. These
values are available only for the common propertle3 such as yield
strength, ultimate strength, ultimate elongation, Brinell hard-
ness and modulus of elasticity. Even typical stress-strain dia-
grams are a rarity in the literature for these metals. Further,
it should be realized that these properties vary from heat to
heat for the. same material. However, a preliminary attempt was
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made to correlate the cavitation damage resistance with these me-
chanical properties. For this purpose, the strain energy was
roughly estimated from the following relationship
Es e" (T + Y) [1
wherei*
S is the estimated strain energy,e
T is the ultimate tensile strength,
E is the ultimate elongation, and
Y is the yield strength.
This relationship was used since the values of T, Y and E were
readily available and gives an approximate value of the area of
the stress-strain diagram, assuming it to be a trapezoid. Among
the properties considered in this preliminary analysis, the
best correlation was obtained with this estimated strain energy
as shown in Figure 6. Since T, Y and E vary over a wide range,
the estimated value of the strain energy also varies over a
range; this range is shown in Figure 6 by a solid line for each
material, while the mean value is shown by a solid circle. This
analysis revealed the need for additional test data.
The second group of six metals was selected for actual tests
and detailed analysis. The engineering stress-strain diagrams
were obtained from the same bar stock of material from which the
cavitation test specimens were machined. The stress-strln
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diagrams for these six materials are given in Figure 7. These
data were obtained according to the Federal Test Method Standard
TT-, No. 151a with half an inch diameter tensile specimens of two
inch gauge length (15). The true stress-strain diagrams for the
six metals are shown In Figure 8. The strain energy was computed
by the following three methods:
1. Area of the true stress-strain diagram given by the
relationship
S =( i Tf f [2]Se 1 + nf
where
S ' is t 1 .e true strain energy,e
n Is the strain hardening factor,
T f is the true fracture strength, and
Cf Is the elongation at fracture.
2. Area of the engineering stress-strain diagram ob-
tained by direct measurement.
3. An approximate estimation according to Equation [I].
The reason for employing these three methods is to determine
the perceitage deviation among the three strain energy values.
The mechanical profAert1ec of the second group of six metals,
obtained by actual tests, are listed in Table 2. However, the
Brinell hardness values shown In this table are typical values
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reported in the literature. It can be seen that the strain energy
values computed by the above three methods agree closely, within
*10 percent, with the true strain energy as the standard.
Cavitation Damage Resistance
All of these metals were tested for their cavitation damage
resistance according to the procedures outlined in detail in
Reference 14. Essentially, the procedure is to test each of the
metals under a given set of experimental conditions through the
four zones of damage, namely, incubation zone, accumulation zone,
attenuation zone and steady state zone. It is of interest to
note that all the metals which were tested exhibited these zones.
The specimen that had reached the steady state zone was used to
obtain the relationship between the rate of volume loss and the
displacement amplitude as shown in Figure 9. The reciprocal of
the rate of volume loss is defined as the cavitation damage re-
sistance of a material. The cavitation damage resistance at a
given amplitude (2 x 10-3cm) in the steady state zone was plotted
against the various mechanical properties of the metals as shown
in Figures 10 through 15. The mechanical properties considered
here ere strain energy, ultimate tensile strength, yield strength,
Brinell hardness, ultimate elongation and modulus of elasticity.
Both groups of metals have been included for this correlation.
The values of inear correlation factor for each of the above me-
chanical propertleE are tabulated below.
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Mechanical Property Correlation Factor
"train Energy 0.91
Ultimate Strength 0.79
Yield Strength 0.65"
Brinell Hardness 0.51
Modulus of Elasticity 0.49
Ultimate Elongation 0.48
The correlation factor, r',for two variables, x and y, is
calculated from the following formula:
nE - E E
r xy x y
rc -x2 E )2] [ Ey2 y12]
where
n is the number of points in an x, y plane.
This is based on ten sample points since the yield strength
for cast Iron Is not available.
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This analysis clearly shows that the most significant linear
correlation is obtained with the strain energy of the material.
It follows from this result that the energy absorbing capacity
of a metal characterizing the cavitation damage resistance is
largely determined by the strain energy.
Limitations
1. This analysis is confined to six common properties
of metals. It is not implied that there is no other property
more significant than strain energy.
2. This analysis is limited to the steady state zone.
In the earlier zones, the interaction of the strain hardening
exponent and the surface roughness will have to be taken into
account.
3. No superposition of a corrosive environment is
considered in this analysis. The Interaction of a corrosive
environment on the fatigue properties of metals is important.
Intensity of Cavitation Damage
One of the immediate uses of th..s correlation .- to estImate
the intensity of cavitation damage as a function of *J!.sp1ement
amplitude. The intensity has been defnned a1 the oer absorbed
per unit area of the material (16) and is gl% rn by
r.SA [3I
if i
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where
I is the intensity of cavitation,
r is the rate of volume loss,
A is the area of erosion, ande
S is the strain energy.e
It can be seen that the intensity of cavitation damage for a
given amplitude is given by the reciproc-al of the slope of the
line in Figure 10 divided by the area of erosion. The best fit
lines by the least square method for each amplitude are shown in
Figure 16. The Intensity, thus computed, varies as the square
of the amplitude for the experimental conditions in the steady
state zone (Figure 17).
CONCLUSIONS
The following conclusions are drawn as a result of' these
investigations
1. Among the mechanical properties Investigated to
characterize the energy ,bsorblng capacity of metals under the
repeated Indentations produced by cavitation damage, the most
significant correlation Is obtained with the strain energy of the
metal, where the strain erergy Is defined as the area of the
stress-strain diagram up to fracture In a simple tensile test.
This conclusion Is limited to the steady state zone of damage
In a non-':orroslve environment.
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2. The above relationship leads directly to the esti-
mation of the intensity of cavitation damage. According to this
estimate the intensity varies as the square of the displacement
amplitude In the steady state zone under the present experimental
conditions.
ACKNOWLEDGMENTS
This Investigation was supported by the Office of Naval
Research, Department of the Navy, Contract No. Nonr 3755(OO)(FBM)
NR 062-293. Many useful discussions with Mr. H. S. Preiser during
the course of this work are gratefully acknowledged.
N
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REFEREN C ES
1. Parsons, C. A. and Cook, S. S., "Investigationz into theCauses of Corrosion or Erosion of Propellers," Engineering,Volume 107, pp. 515-519, 1919.
2. F5ettinger, H., "Untersuchungen ueber Kavitation undKorrosion bei Turbinen, Turbo-pumpes und Propellers inHydraulisobe Probleme," (Berlin) V.D.I. Verlag, pp. 14-64,1926.
3. ionegger, E., Concerning Erosion Experiments, Brown BoveriReview, 14, pp. 74-95, 1927.
4. Gardner, 0., "The Erosion of Steam Turbine Blades," Engineer,Lond., Vol. 153, pp. 146-2C5, 1932.
5. Nowotny, H., "Werstoff Zerstoorung durk Kavitation," V.D.I.Verlag, Gimbh, Berlin, 1942, English Translation as ORAReport No. 03424-15-I, Nuclear Engineering Department,University of Michigan, 1962.
6. Godfrey, D. J., "Cavitation Erosion" - A Review of PresertKnowledge, Report Prepared for the Inter-Services Metallurgl-cal Research Council Corrosion and Electro-depositionCommittee, Ministry of Supply (England) September, 1957.
7. Eisenberg, Phillip, "Cavitation Damage," HYDRONAUTICS,Incorpcrated Technical Report 233-1, December 1963.
8. Boetcher, H. M., "Failures of Metals Due to Cavitation UnderExperimental Conditions," Trans. ASME, Vol. 58, pp. 355-360,1936.
9. Wheeler, W. H., '"Mechanism of Cavltatlon Erosion," Proc.Symposium on Cavitation in Hydrcdynamvs, National Phys sLaborato-y, Paper No. 21, H.M.S.O. (London) Publieation 1956.
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10. Naude, C. F., and Ellis, A. T., "On the Mechanism ofCavitation Damage by Nonhemispherical Cavities Collapsingin Contact with a Solid Boundary," ASME Paper No. 61 -
Hyd - 8, January 30, 1961.
11. Bowden, F. P., and Brunton, J. H., "The Deformation of Solidsby Liquid Impact at Supersonic Speeds," Proc. Roy. Soc. A.,Vol. 263, pp. 433-450, October 10, 1961.
12. Thiruvengadam, A., "A Unified Theory of Cavitation Damage,"Trans. ASME, Vol. 85, pp. 365-377, September 1963.
13. Tabor, D., "The Physical Meaning of Indentation and ScratchHardness," British Journal of Applied Physics, Vol. 7,pp. 159-166, May 1956.
14. Thiruvengadam, A., and Prelser, H. S., "On Testing Materialsfor Cavitation Damage Resistance," HYDRONAUTICS, IncorporatedTechnical Report 233-3, December 1963.
15. Metals; Test Methods, Supplement A Fed. Test Method Std.No. 151, July 19, 1956, Notice 1, May 6, 1959.
16. Thiruvengadam, A., "A Comparative Evaluation of CavitationDamage Test Devices," HYDRONAUTICS, Incorporated TechnicalReport 233-2, November 1963 (See a! o Symposium -n CavitationResearch Facilities and TechnIques, A2ME, May I964,pp. 157-164.)
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MODULUS OF ELASTICITY- DYNES - (i
CMFIGURE 14 -CORRELATION BETWEEN MODULUS OF ELASTICITY AND RECIPROCAL
OF RATE OF VOLUME LOSS
HYDRONAUTICS, INCORPORATED
800
304-L STAINLESS STEEL 41
700 10316 STAINLESS STEEL
o 600x
w MONELO FREQUENCY; 14KCS, .AMPLITUDE: 2.0 X ,0"kMu) LIQUID: DISTILLED WATER9 500 @ 27"C
410 STAINLESS STEEL@ SPECIMEN DIAMETER: 1.59CMw CORRELATION FACTOR, 0.48
-J0
4000w iO20 MILD STEEL
i 00 TOBIN BRONZE
0.300
200 0MOLYBDENUM
0 ALUMINUM 202 4 T- 4
100
0 CAST IRON
______ _ M ALUMINUMALUMINUM 1100-F 1100-0
0 0 20 30 40 50
PERCENTAGE OF ELONGATION IN TWO INCHES
FIGURE 15-CORRELATION BETWEEN ULTIMATE ELONGATION AND RECIPROCALOF RATE OF VOLUME LOSS
HYDRONAUITICS, INCORPORATED
3000LIQUID' DISTILLED WATERFREQUENCY: 14 KCSSPEC IMEN DIAMETER:
b~1,59 CM
UP2500
0
2 2000-J0
IL0w~
S1500
0
1. 5 x Io3 CM
oc 1000Itl
500
0 100 200 300 400 500- YNE! 7STRAIN ENERGY---- x 10
FIGURE 16-RELATIONSHIP BETWEEN STRAIN ENERGY AND RECIPROCAL OFRATE OF VOLUME LOSS AT VARIOUS AMPLITUDES
HYDRONAUTICS, INCORPORATED
LIQUJID; DISTILLED WATER @771___ -FREQUENCY 4 KCS
x
2 a 5I 789100 2 4AMPLITUDE-CM X 10- 3
FIGUIRE 17-EFFECT OF DISPLACEMENT AMPLITUDE ON OUTPUT INTENSITY
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