Correlation of cavitation erosion behavior with mechanical properties of metals

Wear,

140 (1990)

63-82

Correlation of cavitation properties of metals

erosion behavior with mechanical

R. H. Richman and W. P. McNaughton Daedalus

Associates

Inc., Mountain

V&w, CA 94043 (U.S.A.)

(Received

May 10, 1989; revised September 22, 1989; accepted February 19, 1990)

Abstract Good correlations are presented between material removal rates and cyclic deformation parameters, a strong indication that damage in cavitation erosion is a fatigue process. The predominant property in cavitation erosion resistance is shown to be the fatigue strength coefficient q which accounts for most of the differences among materials. Correlations are further improved by incorporating the cyclic strain-hardening exponent n’ in a combined parameter ur’n’. This combined parameter also correlates well with the stacking fault energy, a primary dete rminant of deformation modes in many of the materials used in past experiments.

1. Introduction Although cavitation erosion in hydraulic systems is a long-standing problem, the damage mechanism (or mechanisms) that culminates in material loss is still poorly understood. It is largely for this reason that it is not yet possible to specify the materials properties that will ensure good resistance to cavitation collapse. Hence the choice of resistant alloys and coatings is based primarily on previous experience. Over the years, may attempts have been made to find a material property or combination of properties that correlate with measured cavitation erosion rates: hardness, tensile strength, strain energy, ultimate resilience ((ultimate tensile strength)2/2(elastic modulus)), ductility, etc. Most of these trials have been reviewed by Hammitt [ 11. Good correlations are obtained only within narrow classes of materials of similar structure (see for example refs. 2 and 3 for recent work). A consensus has developed that material removal in cavitation erosion, in common with liquid droplet erosion and with solid particle erosion (in the low velocity, normal impact regime), is not a consequence of single impulses or impacts; rather, damage accumulates for thousands of impacts before a particle is dislodged [ 41. In fact, several investigators have attributed the failure mode specihcally to fatigue [ 5-71, and evidence of material removal by fatigue can be deduced from other experiments [3, 8-121. Our aim in this paper is to demonstrate that strain-based material properties derived from cyclic deformation experiments correlate well with cavitation erosion behavior.

0043-1648/90/$3.50

0 Elsevier

Sequoia/Printed

in The Netherlands

2. Scope of analysis If erosion damage accumulates by fatigue, there should be a clear relationship between cavitation erosion behavior and cyclic deformation parameters. However, any correlation between cyclic properties and cavitation erosion behavior must not be confined to unalloyed metals alone. As has been pointed out from time to time and most recently by Sundararajan [ 131, the various mechanical and thermophysical properties of pure metals are not independent of one another. To isolate the material property or properties that really dominate cavitation erosion rates, information about alloys must be included. 2. I. Cyclic deformation parameters It is now generally agreed that the steady state cyclic deformation resistance of metals and alloys is well described by the cyclic stress-strain curve [ 14, 15). This relation is obtained by connecting the tips of stable hysteresis loops for companion specimens, each tested at a different strain amplitude, as illustrated schematically in Fig. 1. As shown by Morrow [ 141, the relation between stress amplitude og and plastic strain amplitude AeP/2 can be expressed by a power function of the same form as is commonly used for the monotonic curve:

where K’ and n’ are the cyclic strength coefficient and the cyclic strainhardening exponent respectively. A related property that provides more meaningful comparison with monotonic properties is the cyclic yield strength a,’ which can be calculated for any desired plastic strain level from eqn. ci).

Fig. 1. Construction of the cyclic stress-strain

curve, and comparison with monotonic behavior.

65

The relationship between total strain and the number of cycles to failure (i.e. the failure criterion) was shown by Manson and Hirschberg [ 161 to be the sum of elastic and plastic strain resistance:

where the various coefficients and exponents are defined in Fig. 2. Here four strain-based material properties are illustrated: q’, the fatigue strength coefficient; Q’, the fatigue ductility coefficient; b, the fatigue strength exponent; c, the fatigue ductility exponent. Furthermore, Morrow [14] has shown through an energy argument that the exponents b and c are related to the cyclic strain-hardening exponent n’ by n’=

b

-

C

Thus, in instances where a cyclic stress-strain curve is not separately determined, it is still possible to obtain a value for n' from the strain-life curve. Ideally we would wish to examine all the strain-based material properties (Cf’, +‘, b, c and rY’) for correlation to cavitation erosion parameters. It is unfortunate that strain-based cyclic deformation experiments have not been reported for many of the materials in the cavitation erosion databases, as will be seen. However, the historical use of stress (or load) to characterize fatigue properties (applied stress-number of cycles to failure (S-N) curves) means that many more materials have been tested for stress resistance than for strain resistance. If the logarithm of true stress amplitudes is plotted against log(2Nf), instead of the usual engineering stress VS. log N,, Fig. 3 results. The relation between true stress amplitude ga and reversals 2N, to failure is given by

Reversals to Failure (log scale) 2. Relationships

of fatigue life to elastic,

plastic

and total strain amplitudes.

MORTAL LIFE RANGE 4 ai t LOG 2Nf Fig. 3. Schematic stress-life relation.

(4) where af’, the fatigue strength coefficient, and b, the fatigue strength exponent, are the same as previously defined for strain cycling. Therefore, by extrapolating only from the high cycle regime of S-i? curves where plasticity effects are minimal, it is possible to obtain reasonable estimates of CQand b from stressbased tests reported in the Literature. The use of cyclic deformation parameters derived from constant-amplitude tests conducted at low to moderate strain rates is not intended to impIy that these conditions are characteristic of cavitation erosion. It is well known that void collapse imposes high strain rate spectrum loads on solid surfaces. Nevertheless, it is equally well known that damage accumulation in random loading is closely related to, and calculated from, constant-amplitude deformation [ 171. Furthermore, cyclic stress-strain behavior of ahuninum alloys, cu+ j3 brass, copper and heat-treated AISI 4340 steel, measured over the range of strain rates from 0.003 to 0.3 s-l, showed no strain rate dependence [ 181. Significant effects might occur at higher strain rates; however, for the initial identification of critical materials properties in cavitation erosion behavior, it seems reasonable to rely on the much Iarger amount of information available from conventional fatigue experiments. 2.2. Cavitation erosion parameters Two sets of measurements were chosen for exploration of correlation between fatigue and cavitation erosion, the work by Feller and Kharrazi [19) and the compilation presented as Table 9-4 by Knapp, et al. [ZO1. They were by no means the only possible choices. They did, however, seem to satisfy most conveniently two important criteria: they encompass a wide range of materials, including alloys, and all members of each group were measured by the same methods under the same conditions.

The investigation by Feller and Kharrazi covered ten unalloyed metals and 11 alloys; three of the alloys were tested in two different heat treatment conditions. Cavitation erosion was determined by weight loss. Table 1 lists the incubation time and maximum cavitation erosion rate for each material. The Vickers microhardnesses and yield strengths given by Feller and Kharrazi are also included. The incubation time was taken as the intercept on the abscissa of an extrapolation of the weight loss curve. The maximum erosion rates were taken from plotted curves of cavitation erosion rate ZIS.exposure time in the published paper (Fig. 3-7 in ref. 19). The data given by Knapp et al. (adapted from the work of Garcia et al. 1211) for 14 materials, some in more than one heat ~eatment condition, are listed in Table 2 along with mechanical properties from Table 9-5 in ref. 20. (MDP) gives the volume loss per specimen face area. Tables 3 and 4 list the available cyclic deformation parameters for the materials used by Feller and Kharrazi and by Knqp et al. respectively. References to the sources of the fatigue properties are given in the tables. In several instances the listed fatigue properties were not provided directly by the cited references (e.g. for cobalt); the methods by which they were deduced are discussed later. The cyclic deformation properties in Tables 3 and 4 were compared, f?rst one at a time and then in combination, with the cavitation erosion parameters. Monoto~c or “standard” properties in Tables 1 and 2 were also examined for correlation to cavitation erosion behavior. Correlations were sought by the stepwise procedure of multiple regression f47]. Significant variables were determined by testing the coefficients with the Student’s t test. If a coefficient had a probability greater than 0.10 of being zero, the variable was deleted. All the correlation coefficients in what follows were tested for validity at the 99.9% level, except where otherwise noted.

3. Correlations between mechanical properties and cavitation erosion rates

For each of the cavitation erosion databases it is possible to find correlation with some of the “standard” mechanical properties. Whereas correlation between incubation time and microhardness is almost non-existent, the yield strengths given by Feller and Kharrazi [ 191 are roughly correlated with incubation times, as shown by Fig. 4. The dispersion of the data at yield strengths greater than 100 MPa should be particularly noted. The line in Pig. 4 was obtained by a simple least-squares fit of the logarithm of the incubation time against the logarithm of the yield strength; the correlation coefficient r of the relationship shown is 0.860. Similar trials were conducted for the logarithms of the MDP results from Knapp et al. [ZO) against the log~t~s of hardness, yield strength, ultimate

1

21 22 23

18 19 20

17

16

15

14

1 2 3 4 5 6 7 8 9 10 I1 12 13

Mczk?+ial

cbronze> X155CrvMo12 1 (1.5wt.96C-1 lwt.%Cr steel) GXCrNiMoCu 256 (duplex stainless steel) XfjCrNiCuNb 174 (17-A PH stainless steel) GXCrNiio 18 10 (type 316 stainless steel) Hastelloy B-2 Hastelloy C-4 MnStX120Mnl2 (JSadfieId steel) Haynes 25 Haynes 6B Haynes 6B (heat treated)

W GG25 (cast iron) 41CrMoS4 (4140) GCuAl 9NiFe

MO

Al zn Cu Ni Fe Cr co

Mg

desigMltia

Material

Summary of results from Feller and Kharrazi 119)

TABLE

2595 4367 4160

2166 2304 2280

3100

2680

2633

300 160 320 540 720 580 1500 1620 1560 4868 3220 I780 1820

Vickm-s mimohardness (HYVZOO)

490 599 599

352 1242

393

247

700

561

780

715 270

2.9 1.04 0.95 2.5 18 84 429 138 154 380 (estimated)

0.2% yield strength (MPal

966 1554 1560

.rect?ssicm

Frn he’)

1.6-1.7 0.4 0.37-0.38

3.1 2 2.2

2.7

210 220 282 330

2.7

3.6

5.1

200

102

8.9 6.1

120 438 900 56 12 32 1.4 2.6 6.4 1.5

(x10:’

1.0 1.2 4.5 8.1 36 102 340 360 380 738 32 38 70

rats

(min)

Ak.ximwr~

Incubation time

g

69 TABLE 2 Summary

of results from Table 9-4 of Knapp et al. [20]

Material

T- 111 tantalum alloy Mo-4 wt.%Ti AISI 316 stainless steel AK1 304 stainless steel Nb-lwt.%Zr annealed Carbon steel Al 2024-T351 Al 6061-T651 Al 1100-O Cu, cold worked Cu, 482 “C annealed Cu, 816 “C annealed Cu-Ni, 982 “C annealed Cu-Zn, 760 “C annealed Ni, 871 “C annealed Ni, cold worked

0.1% yield stress (Mw4

Ultimate stress NW

Diamond

861 454 439 446 132 287 399 276 52.4 341 65.5 34.5 124 75.8 48.3

907 1037 601 652 250 312 496 312 84.5 368 217 212 368 279 336 642

308 295 227 237 99 193 171 127 27 133 51 41 77 48 59 206

565

pyramid

hardness W’P)

Average MDP rate (pm h-9

1.52 2.29 2.29 2.54 4.57 5.84 14.48 18.29 68.58 24.13 25.91 24.13 11.94 17.27 12.19 11.18

tensile strength and ultimate resilience. The best correlation is with hardness (r= -0.813) (Fig. 5) and the worst is with ultimate resilience (r= -0.693). Again, there is a good deal of dispersion even in the best correlation. 3.2. Cyclic deformation properties The single properly that contributes most to correlation with cavitation erosion behavior is the fatigue strength coefficient a,‘. By itself it accounts for most of the variability of the data for incubation time (Pig. 6) and MDP (Fig. 7). The corresponding correlation coefficients for least-squares fit are 0.965 and -0.953 respectively. In Fig. 6 the relationship between log Us and the logarithm of the incubation time is shown as a second-order regression, since a curve fits the results better than a straight line does, i.e. the correlation coefficient is higher. Moreover, in Fig. 6 there is an obvious point (for iron) that is further removed from the relationship than any of the others. If we were arbitrarily to leave that datum out of the least-squares calculation, the correlation coefficient would improve to 0.980. In the above instance, and in two others later in the section, one “outlier” is left out of the analysis when the quality of the correlation is significantly improved by the omission. We do not know why these points do not fit the proposed relationships, nor do we suggest that such outliers be eliminated. Correlations from which one entry has been omitted are presented mainly for comparison. Analysis of these outliers might provide useful insights. All the other main factor variables except the cyclic yield strength wY’ failed the significance test for correlation with cavitation erosion parameters

TAE%LE 3 Cyclic defecation

parameters

Material

for the Feller

Cyclic Yidd

n’

and Kharrazi

database

%

-b

-c

References

114 166 387 564

0.083 1.643

0.074 0.096 0.152 0.141

0.157 0.669

1.342 0.799

0.670 0.597

0.155 0.52 1.12

0.147 0.127 0.107 0.22 0.082 0.087 0.011 0.089 0.08 0.129

0.711

122, 231 r241 [23, 251 [24, 261 [14, 271 1241 I281 w1 130, 311 [30, 321 L301 1331 (341 118, 261 [351 (36, 371 1381 1391

’ $Pa)

stress W’a)

Mg Al ZSI

89.5 63

0.47 0.144

cu

137

Ni Fe Cr co MO W Cast iron fmatrix) AISI 4140 Al-bronze 1.5wt.%G1 lwt.%Cr 25wt.%Cr_6wt.%Ni2.5wt.%Mo 17-4 HP AISI 316 stainless steel HasteUoy B-2 Hastelloy C-4 Hadfield steel Haynes 25 Haynes 6B Haynes 6B (heat treated)

250 158

0.263 0.15 0.220 0.208

255 359

0.38 0.18

524 540 340

0.15 0.16 0.26

1046 683 2040 2370 2186 3517 1041 1340 1350

0.181

2447

1.111

505

0.336

1964 1999

0.127

0.121

0.384

875

0.278 0.37

2255 2400

1.16

0.11 0.130

0.503

0.483

0.58 0.096

0.535

0.62 0.457 0.047 0.58 0.62

0.089

f40-421 143, 441

(incubation time, maximum recession rate or MDP rate). Correlation of incubation time against uY’ is relatively poor (co~elation coefficient of 0.759 at the 99% level); however, there is good correlation between maximum recession rate and uY’, with a correlation coefficient of - 0.9 16. It is customary in stepwise multiple regression to sum all the significant main factor variables and all the signticant two-factor interactions. This was not done with rv’ because there were far fewer known values for uY’ than for cr,‘, particularly for the alloys. Incorporation of ay’ into the regressions would thus have truncated the databases severely. In addition, uY’ does not participate in the two-factor ~provement of the correlations, as will be seen below. Description by af’ of the maximum recession rates from Feller and Kharrazi [ 191 is less successful than for incubation time. The relationship shown in Fig. 8 has a correlation coefficient of -0.906, which is still quite significant. The dispersion at the lower right of Fig. 8, however, should be noted.

71 TABLE 4 Cyclic

deformation

for Table 9-4 of Knapp et al.

parameters

Material

n’

T-111 Mo+vt.%Ti AISI 316 stainless steel AISI 304 stainless steel Nblwt.%Zr, annealed Carbon steel AI 2024-T351 Al 6061-T651 Al 1100-O Cu, cold worked Cu, 482 “C annealed Cu, 816 “C annealed Cu-Ni, 982 “C annealed Cu-Zn, 760 “C annealed Ni, 871 “C annealed Ni, cold worked

0.287 0.24 0.336 0.379 0.3 0.287 0.134 0.126 0.144 0.158

> 2350 > 2373 1999 2231 999 870 779 631 166 456

0.15 0.204 0.254 0.220

564 713 443 1046

0.2

1.0

10.0

100.0

Yield Strength, Fig. 4. Correlation vibratory apparatus

between [ 191.

4’

-b

-C

0.096 0.127 0.101 0.44 0.163 0.410 0.922 1.643 0.548

0.132 0.082 0.121 0.143 0.12 0.119 0.089 0.098 0.096 0.098

0.457 0.384 0.378 0.46 0.414 0.664 0.777 0.669 0.619

0.141 0.101 0.087 0.147

0.535 0.495 0.455 0.670

0.483 0.440 1.342

R43jhmces

1301 130, 321 WI

1241 1451 (241 1241

[241 (241 I391 114,271 [461 K-1 [241

1000.0

MPa

yield

strength

and incubation

the

for cavitation

erosion

in a

Substantial improvement in the description of material removal rates is accomplished by incorporating the cyclic strain-hardening exponent n’ as a multiplier on a[. The relationship between maximum cavitation erosion rate [ 191 and the product q’n’ is shown in Fig. 9, which can be compared directly with Fig. 8 for goodness of fit. Two values for copper are plotted in that figure, a situation that arises in two experimental levels for n’ reported in the literature. The higher value of 0.263 comes from the Ford Motor Co. analysis [24] of the tabulation by Nachtigall [48]; Saxena and Antolovich [26] measured even higher values. In contrast, a lower value of 0.15 for n’

G

Hardness, DPH

I

Fig. 5. Correlation between diamond pyramid hardness and MDP by cavitation erosion

: D 1000.0

.-z E

_

100.0

I

z 'F E .: z E

_._ 50.0

100.0

1000.0

Fatigue

Strength

l.OE4

Coefficient,

af’,

MPa

Fig. 6. Correlation between fatigue strength coefficient CT,’and erosion in a vibratory apparatus.

i

Fatigue

Strength

Coefficient,

[lQ] for cavitation

of’, MPa

&. 7. c orrelation between fatigue strength coefficient q and MDP [20] by cavitation erosion in a vibratory apparatus.

73

Fatigue

Strength

Coefficient,

Fig. 8. Correlation between by cavitation erosion.

fatigue

uf’, MPo

strength

coefficient

cr,’ and maximum

recession

rate

[19]

recession

rate [19]

316

“f’

Fig. 9. Correlation between by cavitation erosion.

.

”

,

MPo

the combined

parameter

q’n

and maximum

of copper is given by Morrow [ 141 and by Feltner and Laird [ 271 and corroborated indirectly by Feltner and Beardmore (491. If we use the lower value, the resulting correlation is extraordinarily good: log {maximum recession rate (pm h-l)} = 4.635 - 1.494 log (crf’n’)

(5)

with a correlation coefficient of -0.989. In other words, for this particular data set, 98% of the variability in maximum cavitation erosion rate is explained by eqn. (5). The two-factor interaction between gY’ and n’ resulted in only a marginal improvement of the correlation for maximum recession rate, from - 0.916 to - 0.927. Since this slight improvement was accompanied by an increased dispersion of the residuals, correlations involving a,’ were not examined further.

Since the MDP is also a measure of cavitation erosion rate, application of q’n’ to Table 9-4 of ref. 20 also results in an improved relationship, as illustrated in Fig. 10. The correlation coefficient calculated with all the plotted points is -0.977. The line drawn in Fig. 10 is described by log {MDP (pm h-‘)}=3.366-

1.063 log (q’n’)

(6)

If the one outher (in this case the point for nickel) is deleted, the correlation coefficient becomes -0.987. It should be noted that the lower value of n’ for copper, 0.15, has been used in these correlations. Unlike the cases involving material removal rates, the relationship between of’ and incubation time in cavitation erosion is not improved by incorporating the cyclic strain-hardening exponent. Application of the combined parameter to the Feller and Kharrazi incubation times leads to Fig. 11, with a correlation coefficient of 0.936 with all the results, or 0.964 after the outlier (for iron) is deleted. In other words, the previous correlation with a,’ alone is somewhat diminished by the incorporation of the cyclic strain-hardening exponent. This distinction between correlations with and without n’ suggests that incubation

D’f

l

n’, MPo

Fig. 10. Correlation between the combined parameter ~‘Tz’ and MDP [20] by cavitation erosion.

“5 lo*

100.0

1cloo.o

c_rf . n’, MPo

Fig. 11. Correlation between the combined parameter q’s cavitation erosion.

and incubation time [ 191 for

75

time depends primarily upon cyclic stress resistance, whereas material removal rates depend to a significant degree upon cyclic strain resistance. 4. Discussion 4.1. Cyclic deformaticm properties In some instances the citations for the cyclic properties given in Tables 3 and 4 do not refer specifically to the metal or alloy under which the entry is made. In the case of chromium, for example, we were unable to discover any reports of fatigue properties. However, Northwood et al. [29] conducted high temperature stress-controlled fatigue tests of a Cr-2wt.%Ta-0.5wt.%Si-O. lwt.%Ti alloy. Results for 900 “C tests were analyzed for a,’ and b, and af’ was then adjusted upward by the ratio of ultimate strength at room temperature to the ultimate strength at 900 “C. As it turned out, the yield strength at room temperature given by Feller and Kharrazi [ 191 for chromium matched almost exactly the proportional limit stress at room temperature given by Northwood et al. [ 291,and so no further adjustment was made. Cyclic properties of the alloys T-111 (tantalum base) and Nb-lwt.%Zr (niobium base) were arrived at similarly, in that a*’ of the unalloyed metal was adjusted upward by the ratio of the ultimate strength of the alloy to that of the metal. In contrast, the cyclic properties entered for Hastelloy C-4 (nickel base) in Table 3 are actually those of Hastelloy X [40, 411 with some further adjustment based on a study of Nimonic 115 [42]. Owing to the unusually high resistance of cobalt and its alloys to cavitation erosion, it was thought desirable to obtain good estimates of all the cyclic deformation parameters of cobalt. Although stress-based fatigue tests on cobalt were reported by Ferro et al. [ 301, from which uf’ and b were extracted, no strain-based fatigue tests were discovered for cobalt or the cobalt-based alloys in Table 3. However, Chalant and Remy [ 311 conducted cyclic deformation experiments with f.c.c. Co-Ni alloys, one of which, Co-33wt.%Ni, has the same stacking fault energy (SPE) as cobalt. Moreover, the ai value determined for Co-33wt.%Ni is identical with that determined for cobalt from the results of Ferro et al. Hence the properties of cobalt reported in Table 3 are mostly those of Co-33wt.%Ni. The cyclic deformation properties of Co-33wt.%Ni have wider utility than just their correspondence to cobalt. Adler et al. [44] show that the extraordinary strain-hardening behavior of Hatield manganese steel (Fe-l 2 .Swt.%Mn-1 . l&t.%C-0.2wt.%Si) is attributable to pervasive mechanical twinning, that the twinned volume fraction as a function of plastic strain is almost identical with that for Co-33wt.%Ni and that the monotonic work-hardening rate of the Hadileld steel is slightly higher than that of Co-33wt.%Ni. These qualities, coupled with the true stress-true strain curves provided by Raghavan et aZ. [43] and Adler et al. [44] facilitated reasonable, if conservative, estimates of pertinent cyclic deformation properties for Hatield steel (Table 3).

Finally, the properties of aluminum bronze were derived from measurements of cyclic strain-hardening exponent on Alloy 365, which is a twophase (cy+ p) brass [ 181, combined with extrapolations of the properties of &-Al alloys to 9.4 wt.% Al [26]. This estimate of n’ is corroborated by the corresponding effects brought about by variation in the volume percentage of martensite in dual-phase steels [35]. 4.2. Relationship of the fatigue strength coeficient to monotonic properties It is generally assumed [ 14, 50, 511 that Us’ is about equal to gf, the true fracture strength in a monotonic tension test. This assumption is based largely upon fatigue studies of steel. For that matter, there is also a connection between af’ and a, (the engineering ultimate strength) since V~is linearly related to 0; of medium carbon quenched-and-tempered steels, as shown in Fig. 12. However, the connection between a, or a, and cavitation erosion behavior is only fair, with correlation coefficients in the range 0.80-0.85. While it is true for steels that af’ = V~up to true fracture strengths of about 2000 MPa, as illustrated by the linear relationship in Fig. 13, at higher Upthe relation probably becomes concave upward, i.e. uf’ increases faster than 1.7~Moreover, the austenitic stainless steels are seen in Fig. 13 to comprise a separate population, almost parallel to the quenched-and-tempered steels but displaced to higher values of uf’. In other words, uf’ does vary regularly with u, in the 300-series stainless steels; however, the commonly held belief that oj’ = uf is certainly not true for this class of alloys, and not for some others. Nevertheless, it should be possible to estimate af’ from

500

: 500

1000

Tensile

1500

2000

Strength,

2500

ou,

MPo

3000

2

-500

True

1000

1500

Fracture

2000

Strength,

2500

3000

mf, MPo

Fig. 12. Variation in true fracture strength CQwith tensile strength a, for medium carbon quenched-and-tempered steels. Fig. 13. Relationships between true fracture strength ar and fatigue strength coefficient c~’ for low alloy quenched-and-tempered steels and austenitic stainless steels; two populations are evident.

77

monotonic tension tests via master curves of the sort in Fig. 13, once the cyclic behavior of the alloy class is known with certainty. The reason that ultimate (engineering) strength does not correlate simply with cavitation erosion behavior can be seen most clearly, in terms of o,‘, in Fig. 14. Each of the three classes of alloys portrayed in Fig. 14 (quenchedand-tempered steels, nickel-base alloys and austenitic stainless steels) constitutes a separate population. Within each class, correlation of cr, to Us’, and thus to cavitation erosion resistance, is well defined. The property that unifies the relationship between strength and cavitation erosion behavior is Eifl, which is mediated by cyclic strain hardening. 4.3. The role of sta.ckimg fault energy A number of investigators have deduced that the materials most highly resistant to cavitation erosion are those that deform by ilne-scale mechanical . . hvmnmg under the loads imposed by void collapse [4,52,53]. The propensity for strain-induced phase transformation has also been associated with cavitation erosion resistance 1541. In either case, the SFE should be a key microscopic property in acco~t~g for material behavior. Accordingly we have sought relationships among SFEs (measured by weak beam, dark field imaging of extended dislocation nodes by transmission electron microscopy) [55-571 and cyclic deformation parameters. Table 5 is a compilation of properties for some of the materials of interest here and for which SFR can be measured, e.g. austenitic stainless steels and a few other metals and alloys. The SFE of Hadfield steel with 13 wt.% Mn was actually measured by X-ray line broadening (591, which gives consistently higher values than does the weak beam, dark field imaging method. Therefore the SFE given by Schramm and Reed [59] was adjusted

-K

4400

-

3600

”

2800

-

.

+J 6 p .‘;;; 0”

4 ?

6 is

5

.g 9

2000

l

4 1200-7,

l /;

/’ AA / .A* ,.<

*. Jrn

1 -+ cn

?’ .i’

i

i#

l l

l,&ih ./ 8.

0 OMSteels A Ni Boss Alloys n Aus Stainless Stl.

’ 400 400

ma

Tensile

1200

1600

Strength,

2000

24w

2800

uU, MPA

Fig. 14. Relationships between tensile strength 0; and fatigue strength coefficient a( for low alloy quenched-and-tempered steels, nickel-base alloys and austenitic stainless steels.

78 TABLE 5 Stacking fault energies and mechanical properties of selected metals and alloys Materi4d

SFE

Type 310 stainless steel Type 316 stainless steel Type 304 stainless steel Type 301 stainless steel Nitronic 40 stainless steel Hadtield steel Co-33wt.%Ni cu

Cyclic p?-ope?-ties

Value (mJ rne2)

Refwences

40 25 15 9 33 17” 15 55

]55, 561 ]551 ]551 ]551 ]571 ]591 (311 ]601

0,. Wa)

&a)

221 228 255 276 393 375 80 30

1660 1999 2231 2476 3474 2400 2370 564

n’

Refmes

0.281 0.336 0.379 0.440 0.552 0.37 0.38 0.15

[24] [39] [24] [58] [58] This work [31] [14, 24, 271

“Adjusted value, see text.

t Nitronic .

t

0

0

40

4 10

Stacking-Fault

20

30 Energy,

40

50

mJ

50

m

-2

Fig. 15. Correlation between the combined parameter ur’n’ and SFJXfor selected metals and alloys.

downward by the ratio of SFEs determined for Nitronic 40 by the same two methods [57]. Good correlation (r= -0.967) was obtained between SFE and the corresponding q’, as long as Nitronic 40 was excluded. Various manipulations of q’ to normalize the effects of solid solution strengthening among the various metals and alloys neither improved nor diminished the correlation significantly. By far the best correlation (r = - 0.990) was obtained for SF’E ~1s.q’n’, again excluding Nitronic 40, as shown in Fig. 15. The failme to account for Nitronic 40 strongly suggests either that the SFE is not always the main determinant of cyclic deformation behavior in these materials or that the measurement of SFE for Nitronic 40 is wrong. In any case, the fact that q’n’ correlates very well both with SFE and with cavitation erosion rates does lend further support for the thesis that cavitation erosion is a cyclic deformation process controlled by microscopic materials properties.

79

5. Conclusions (1) The cavitation erosion process is described by cyclic deformation parameters, i.e. it is a fatigue process. (2) The predominant determinant of cavitation erosion resistance as measured either by incubation time or by material removal rates is the fatigue strength coefficient a,‘. This property by itself explains 96% of the variability in the incubation times measured by Feller and Kharrazi [ 171. oi’ can be thought of as an index of cyclic stress resistance. (3) Material removal rates in cavitation erosion (either maximum recession rate or MDP) correlate very welI with the product cq’n’, in which n’ is the cyclic strain-hardening exponent. n’ can be ~ou~t of as an index of cyclic strain resistance. (4) The inability of monotonic mechanical properties to account for cavitation erosion behavior stems from the fact that 0,’ is strongly mediated by cyclic strain hardening, and thus q’ is not simply related to any of the monotonic measures of strength. (5) The role of mechanical twinning, and to a lesser extent of straininduced phase transformation, in conferring resistance to cavitation erosion is corroborated by excellent inverse correlation between SFE and q’n’.

This work was performed under Contract RP2426-13 to the Electric Power Research Institute (EPRI); C. W. Sullivan was the EPRXproject manager. The authors are grateful for that support. Special thanks are owed to Dr. J. Stringer of EPRI who contributed substantially to the planning and guidance of this project, and to Dr. R. W. Landgraf, formerly of Ford Motor Company, for provision of some of the cyclic deformation properties and particularly for many enlightening discussions about fatigue over the years. References 1 F. G. Hammitt, Cavitation and MuUi@xrse Flozo Phaamema, McGraw-Hi& New York, 1980. 2 C. J. Heathcock, B. E. Protheroe and A. Ball, Cavitation erosion of stainIess steeIs, Wear, 81 (1982) 311-327. 3 S. Vaidya and C. M. Preece, Cavitation erosion of age-hardened ahuniuumalloys, Metall. Trans. A, 9 (1978) 299307. 4 C. M. Preece and I. L. H. Hansson, A metallurgical approach to cavitation erosion, in R. M. Iatanision and R. J. Courtel (eds.), Advances in the Mechadcs and Physics of Su?rfaces, Vol. 1, Harwood Academic, New York, 1981, pp. 199-253. 5 F. ErdmannJesnitzer and H. Louis, Studies on cavitation damages, in A. Thiruvendagam AsTMSpec. Tech. PubL 567, 1974, (ed.), Erosion, Wear, and In-teqfbceswith Cm pp. 171-195. 6 Y.-K. Zhou and F. G. Hammitt, Vibratory cavitation erosion in aqueous solutions, Wear, 87 (1983) 163-171.

80 7 I<. S. Zhou and H. Herman, Cavitation erosion of titanium and Ti-6Al--4V: effects of nitriding, Weur, 80 (1982) 101-113. 8 C. J. Heathcock, B. E. Protheroe and A. Ball, The influence of microstructure on the cavitation erosion of materials, in P. Hassen, V. Gerold and G. Kostorz (eds.), Proc. 5th Int. Conf on the Strength of Metals and Alloys, Pergamon, Oxford, 1979, pp. 219-224. 9 C. M. Preece and J. H. Brunton, A comparison of liquid impact erosion and cavitation erosion, Wear, 60 (1980) 269-284. 10 V. Riddei, I’. Pacer and K. K. Appeldoorn, Cavitation erosion and rolling contact fatigue, Wear, 27 (1974) 99-108. 11 B. Vyas and C. M. Preccc, Cavitation-induced deformation of aluminum, in A. Thiruvengadam (cd.), Erosion, Wear, and Interfaces with Corrosion, ASTMSpec. Tech. Publ. 567, 1974, pp. 77-101. 12 P. S. Follansbec, G. B. Sinclair and J. C. Wiiiams, Modelling of low velocity particulate erosion in ductile materials by spherical particles, Wear, 74 (1981-1982) 107-122. 13 G. Sundararajan, On the correlation of erosion and wear resistance of pure metals with their mechanical and thermophysical properties, Ser. Metall., 19 (1985) 347-352. 14 J. D. Morrow, Cyclic plastic strain energy and the fatigue of metals, in Intend Friction, Damping, and Cyclic Plasticity, ASTM Spec. Tech. Publ. 378, 1965, pp. 45-84. 15 R. W. Landgraf, J. D. Morrow and T. Endo, Determination of the cyclic stress-strain curve, J. Muter., 4 (1969) 176-188. 16 S. S. Manson and M. H. Hirschberg, Fatigue behavior in strain cycling in the low- and intermediate-cycle range, in J. J. Burke and V. Weiss (eds.), Fatigue-An Interdisciplinary Approach, Proc. 10th Sagamore Army Research Conf , Syracuse University Press, Syracuse, NY, 1964, pp. 133-178. 17 R. M. Wet&, (ed.), Fatigue Under Complex Loading: Analyses and Experiments, Society of Automotive Engineers, Warrendale, PA, 1977. 18 D. K. Benson and J. R. Hancock, The effect of strain rate on the cyclic response of metals, Metall. Trans., 5 (1974) 1711-1715. 19 H. G. Feller and Y. Kharrazi, Cavitation erosion of metals and alloys, Wear, 93 (1984) 249-260. 20 R. T. Knapp, J. W. Daily and F. G. Hamrnitt, Cavitation, McGraw-Hill, New York, 1970. 21 R. Garcia, F. G. Hammitt and R. E. Nystrom, Comprehensive cavitation damage for water and various liquid metals including correlations with material and fluid properties, in Erosion by Cavitation or Impingement, ASTM Spec. Tech. Publ. 408, 1967, pp. 239-279. 22 B. Tomkins, Fatigue crack propagation - an analysis, Philos. Mag., 18 (1968) 1041-1066. 23 R. D. McCammon and H. M. Rosenberg, The fatigue and ultimate tensile strengths of metals between 4.2 and 293 “K, Proc. R. Sot., London, 242 (1957) 203-211. 24 F. A. Conle, R. W. Landgraf and F. D. Richards, Materials Data Book: Monotonic and Cyclic Properties of Engineering Materials, Ford Motor Co., Dearborn, MI, 1987. 25 D. M. Fcgredo, S/N curve variations of polycrystalline zinc due to temperature and grain size, Metull. Truns., 3 (1972) 1943-1949. 26 A. Saxena and S. D. Antolovich, Low cycle fatigue, fatigue crack propagation and substructures in a series of polycrystalline Cn-Al alloys, Metall. Trans. A, 6 (1975) 1809-1828. 27 C. E. Feltner and C. Laud, Cyclic stress-strain response of f.c.c. metals and alloys I, Phenomenological experiments, Acta Metall., I5 (1967) 1621-1632. 28 C. Roller and T. Seeger, Mater-iuls Data for Cyclic Loading, Part A, Unalloyed Steels, Elsevicr, Amsterdam, 1987. 29 J. E. Northwood, M. B. Shaw and R. S. Smith, An evaluation of a chromium-base alloy for high-temperature service, J. Less-Common Met., 14 (1968) 157-166. 30 A. Fcrro, P. Mazzeti and G. Montalenti, On the effect of the crystalline structure on fatigue: comparison between body-centred metals (Ta, Nb, MO and W) and face-centred and hexagonal metals, Philos. Mag., 12 (1965) 867-875. 31 G. Chalant and L. Remy, The slip character and low cycle fatigue behavior: the influence of f.c.c. twinning and strain-induced f.c.c. h.c.p. martensitic transformation, Acta Metall., 2X (1980) 75-88.

81 32 P.

Beardmore and P. H. Thornton, The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum, Metall. pans., I (1970) 775-779. 33 M. R. Mitchell, A unified predictive technique for the fatigue resistance of cast ferrousbased metals and high hardness wrought steels, in Fatigue Resistance Testing and Forecasting, Publ. SP-448, Society Automotive Engineers, Warrendale, PA, 1979. 34 P. N. Thielen, M. E. Fine and R. A. Foumelle, Cyclic stress strain relations and straincontrolled fatigue of 4140 steel, Acta Metall., 24 (1976) l-10. 35 S. R. Mediratta, V. Ramaswamy and P. Rama Rao, On the estimation of the cyclic plastic strain energy of dual-phase steels, ht. J. Fatigue, 10 (1988) 13-19. 36 H. W. Hayden and S. Floreen, The fatigue behavior of ilne grained two-phase alloys, Metall. Trans., 4 (1973) 561-568. 37 J. E. Truman and K. R. Pirt, Properties of a duplex (austenitic-ferritic) stainless steel and effects of thermal history, in R. A. Lula (ed.), Duplex Stainkxs Steels, American Society for Metals, Metals Park, OH, 1983, pp. 113-142. 38 Westinghouse Electric Corporation, Corrosion fatigue of steam turbine blading alloys in operational environments, Research Project 912-I Final Rep. CS-2932, September 1984 (Electric Power Research Institute, Palo Alto, CA). 39 C. BolIer and T. Seeger, Materials Data for Cyclic Loading, Part C, High-Ah Steels, Elsevier, Amsterdam, 1987. 40 R. W. Smith, M. H. Hirschberg and S. S. Manson, Fatigue behavior of materials under strain cycling in low and Intermediate Iife range, NRSA Tech. Note TN D-1574, 1963 (National Aeronautics and Space Admlnstration). 41 J. S. Huang and R. M. PelIoux, Low cycle fatigue crack propagation in Hastelloy-X at 25 and 760 “C, Metall. Trans. A, 11 (1980) 899-904. 42 L. G. Reitzmeier and J. K. Tien, The cyclic stress-strain behavior of nickel-base superalloys, I, Polycrystals, Acta MetalL, 36 (1988) 275-282. 43 K. S. Raghavan, A. S. Sastri and M. J. Marcinkowski, Nature of the work-hardening behavior in HadEeld’s manganese steel, ?‘?-a%%Metall. Sot. AIME, 245 (1969) 1569-1575. 44 P. H. Adler, G. B. Olson and W. S. Owen, Strain hardening of Hadfield manganese steel, Metall. Trans. A, 17 (1986) 1725-1737. 45 D. W. Chung and N. S. Stoloff, Fatigue behavior of niobium-hydrogen alloys, MetaZL Trans. A, 9 (1978) 1387-1399. 46 H.-R. Sinning, High cycle fatigue of spinodaIly decomposed alloys, Acta MetalL, 30 (1982) 1019-1026. 47 N. Draper and H. Smith, Applied Regression Analysis, Wiley, New York 2nd edn., 1981. 48 A. J. NachtigaIl, Strain cycling fatigue behavior of ten structural metals tested in liquid helium (4 IQ, in liquid nitrogen (78 K), and in ambient air (300 K), NASA Tech. Note TN D-7532, 1974 (National Aeronautics and Space Administration). 49 C. E. Feltner and P. Beardmore, Strengthening mechanisms in fatigue, in Acheivement of High Fatigue Resistance in Metals and Alloys, ASTM Spec. Tech. Publ. 467, 1970, pp. 77-112. 50 R. W. Landgraf, The resistance of metals to cyclic deformation, in Achievm of High Fatigue Resistance in Metals and Alloys, ASTM Spec. Tech. PubL 467, 1970, pp. 3-36. 51 J. C. Grosskreutz, Strengthening and fracture in fatigue (approaches for achieving high fatigue strength), Metall. Trans., 3 (1972) 1255-1262. 52 D. A. Woodford, Cavitation-erosion-induced phase transformation in alloys, Metall. Trans., 3 (1972) 1137-1145. 53 S. Vaidya, S. Mahajan and C. M. Preece, The role of twinning in the cavitation erosion of cobalt single crystals, MetalL Trans. A, II (1980) 1139-1150. 54 A. Akhtar, A. S. Rao and D. Kung, Cavitation erosion of stainless steel, nickel and cobalt alloy weld overlay materials, in R. D. Sisson, Jr. (ed.), Coatings and Bimetallics for Aggressive Environments, American Society for Metals, Metals Park, OH, 1985, pp. 125-142. 55 C. G. Rhodes and A. W. Thompson, The composition dependence of stacking fault energy in austenitic stainless steels, MetaU. Trans. A, 8 (1977) 1901-1906.

82

56 C. C. Bampton, I. P. Jones and M. H. Loretto, Stacking fault energy measurements in some austenitic stainless steels, Acta MetaL!., 26 (1978) 39-51. 57 R. E. Stoltz and J. B. Vander Sande, The effect of nitrogen on stacking fault energy of Fe-Ni-Cr-Mn steels, Metall. !lYans. A, 11 (1980) 1033-1037. 58 D. Hennessy, G. Steckel and C. AlWetter, Phase transformation of stainless steel during fatigue, Metall. 7hzns. A, 7 (1976) 415-424. 59 R. E. Schramm and R. P. Reed, Stacking fault energies of seven commercial austenitic stainless steels, Met&. Tru?r.s.A, 6 (1975) 1345-1351. 60 P. C. J. Gallagher, The infIuence of alloying, temperature, and related effects on the stacking fault energy, Metall. Trans., 1 (1970) 2429-2461.