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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

HYRONAUTICS, Incorporated

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-


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,

YDRONAUTICS, Incorporated

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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.


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


-7,-

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

IYDRONAUTICS, Incorporated

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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


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.


~-11-

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


-12-

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.

IIYDRONAUTICS, Incorporated

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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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HYDRONAUTICS, Inc orporated

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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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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


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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