Fatigue crack initiation and stage-I propagation in polycrystalline materials. II: Modelling

IntJ Fatigue 13 No 2 (1991) pp 110-116

Fatigue crack tiation and stage-I propagation in polycrystalline materials. II: Modelling j . w . Provan and Z.H. Zhai

Based on the discussion of the micromechanisms involved with fatigue crack initiation presented in part I, an analytic model of stage-I fatigue crack initiation and the subsequent stage-II crack propagation based on a plastic strain intensity factor, ~lKp, is proposed. In this model, the stage-I crack initiation process is simplified as a straight line on a log-log plot of da/dN against ~Kp. An inflection point that divides the crack growth into the initiation and propagation categories is introduced as the plastic crack propagation threshold, ~Kpth, whose value is determined by [(~J)E]~t/h2, where ~J is the range of the J-integral and E is the Young's modulus. Following this, the integration of the crack growth rate as a function of the plastic strain intensity factor yields a fatigue crack initiation life estimate whose error is less than 5%. For comparison, the experimental data presented in this paper are also discussed on the basis of the parameters ~K and ~K~ff that have been proposed by other researchers. Key words: microcracks; crack initiation; crack propagation As discussed in part I, the life of components that are subjected to fatigue loading situations comprises fatigue crack initiation, Ni, and propagation, Np. While the crack initiation portion contributes more than 90% at low stress or strain levels (see Buck et al 1 and Field et a12), no generally accepted description of crack initiation has been developed. This lack of information prompted both the investigation discussed in this series of papers and the previously reported studies by the present authors. 3'4 To start the development of the modelling portion of the investigation, a brief review of shortcrack propagation is necessary.

cases, with the incorporation of ~J, this analysis is reasonably successful. However, it was subsequently found by Lankford et al 8 that although this AiK0formulation correlated well with the short-crack propagation results in air environments, it did not improve the description of experiments involving inert environments. The closure effect has been described by McEvily9 as follows. At applied stresses below certain levels, the crack front remains closed and that portion of the ~tK value that is not used to propagate a crack is deducted from the full value so as to obtain a corrected form of the stress intensity factor, that is

Short-crack propagation Since data for short cracks do not precisely fit d a / d N against ~IK curves, efforts have been made to find other expressions for the driving forces involved. Even though it does not answer all of the anomalies of short cracks, the observation that their tip plastic zone sizes are relatively large has led to an implementation by Dowling 5 of an elastoplastic fracture mechanics (EPFM)J-integral formulation that does indeed bring the short-crack data closer to the long-crack data. To account further for the highly localized plastic strain effect, E1 Haddad et al 6"7 proposed a modified ~tK approach. In this empirical model an initial crack length is added to the actual crack length, that is ~o

= O ~ [ ~ ( a + a o ) ] '/2

(1)

where Q is the usual geometric factor and a0 is the empirical crack length given by a 0 = "iT l(AKth/AO'e)2

(2)

In equation (2), ~l/(th is the threshold stress intensity factor and A~e is the fatigue limit stress of the material. In some

110

AK~rf = (1

-1 P°/PRmax~-1~iK

(3)

where R is the stress ratio, P0 the crack opening load, and P,~x the maximum applied load. The closure analyses of long through-thickness cracks by Ohta et al 1° and Minakawa and McEvily11 show that at the crack threshold the ratio of the crack opening load and the maximum applied load, Po/P . . . . approaches unity. As ~IK increases, the ratio decreases. At high ~dqvalues, the ratio ranges from 0.15 to 0.35. Furthermore, the closure effect for both small through-thickness cracks and surface cracks under bending was analytically and experimentally investigated by Newman. .2 The results indicate that an effective stress intensity factor AiKe, may be obtained by multiplying the centre crack tension (CCT) stress intensity factor by 0.7. Lankford et al s showed that the ratio Po/Pm~x for long cracks is a linear function of the crack length, while the ratio for short cracks is a constant 0.6 for the stress intensity range involved. The experimental data, however, were not improved by applying a AIKorfanalysis to the short cracks studied.

0142-1123/91/020110-07 (~) 1991 Butterworth-Heinemann Ltd Int J Fatigue March 1991

In summary, the existing models describing short-crack propagation are as yet not convincing. While continuous testing of these parameters carries on, other driving forces should be investigated.

(when its strain softening had just begun) is an example of early persistent slip bands (PSBs), although they did not serve as the fatal-crack initiation sites. The submicrocracks that eventually led to the main cracks were formed on PSBs towards the end of the strain-hardening process for specimen h (Fig. l(a)) and shortly after the saturation state for the other three specimens. Strain hardening or softening is the first step of fatigue damage. During this step, the drastic change of dislocation pattern forms the PSBs and opens up the weakest linkages in the grain boundaries. This is the stage of submicrocrack initiation discussed in part I. Figures 4 and 5 of part I illustrate the evolution of the main cracks. Despite the plastic strain level, for a fatigue life of less than or equal to 1.2 × 10s, all the cracks started at grain boundaries. This is not surprising for specimens 2 and 21 since they are in the low-cycle/high-strain fatigue regime; but with both a low plastic strain of 0.05% and a much higher hardness than specimen k, specimen 22 also had the fatal crack initiate at grain boundaries. On the other hand, specimen h is a good example for PSB crack initiation. Although it has the same plastic strain level as 22, its better annealed condition led to a longer fatigue life. As mentioned before, the PSBs formed early in the fatigue damage process and led to the formation of the submicrocrack in this specimen at 0.4% of its life compared to 2% in the other three grain boundary

Experimental observations Hardening or softening processes With reference to part I, the strain hardening or softening processes were all completed within 2% of the fatigue life for three of the specimens, while the softest specimen, h, attained a stable loop after only 0.4% of its life. The cyclic and monotonic stress-strain levels and specimen fatigue lives are listed in Table 1. It is seen from Table 1 that even with a large variation in plastic strain the saturated stresses of specimens 2 and 22 are similar, which implies that the two plastic strain amplitudes chosen for the experiment are in the plateau or quasi-plateau region for polycrystalline copper, as discussed by Kuokkala and Kettunen. 13

SEM observations Scanning electron microscopy (SEM) studies of the replicas revealed that the slip lines were formed during the hardening or softening process. Figure l(b) for specimen 2 at 50 cycles

Table 1. Stress and strain amplitudes and the fatigue lives of various specimens Specimen number

1 t2 h

Plastic strain amplitude, ½Aep (%) O.15 O.15 0.05 0.05

Stress amplitude ½&~ (MPa)

Total strain amplitude,

½~e, (%)

Monotonic

Cyclic

Monotonic

Cyclic

230 128 161 46

186 178 166 112

3.48 2.57 1.82 0.92

3.12 2.99 1.79 1.37

Fatigue life (cycles)

1 . 9 8 × 104

2.13 x 10 `= 1.22 × 105 2 . 5 8 x 105

Fig. 1 Early formations of PSBs during the tests Int J Fatigue March 1991

111

crack initiation cases. While the coalescence of submicrocracks to form a microcrack in the other three specimens occurred in less than 10% of their total lives, it took specimen h more than 30% of its total life to complete this process. The microcrack initiation and propagation in these tests are as described in part I. Figures 4(a) and 5(a) of part I illustrate submicrocracks at crack initiation sites. The surface crack lengths, 2a, arc 4 ~m and 5 txm, respectively. Figures 4(b) and 5(c), again of part I, illustrate initiated microcracks. As can be seen in Fig. 5(b) of part I, the microcrack crossed the grain boundary prior to traversing the grain itself, which implies that the grain boundaries are not necessarily crack inhibitors. These figures of part I provide strong evidence for the submicrocrack and subsequent microcrack propagation coalescence mechanism proposed in part I.

I0 0 0 0 0

I

I

I

!

I000 /

o

#

r,,

IOO

e,'

=,

/

,al:

/l

o

=o

Submicrocrack and microcrack growth rates

Number of Cycles, N IOOOOO 200000 300000

z~

l

.-,ill

L)

The crack lengths were carefully measured from photographs taken of the replicas at each step. The resulting number of cycles are plotted against half the surface crack length in Fig. 2. Since the crack length characteristics are not clearly illustrated by this method, they were transformed to a logarithmic scale as presented in Fig. 3. Owing to the nucleation feature described previously, the submicrocrack and microcrack lengths often remained at the same level for a number of cycles, especially in the case of specimen h. In calculating the crack growth rates, an average was taken.

IO

o :I

09 w,-

"5

"I-

I

A companion E647 test TM

0.1

As part of the investigation reported in this series of papers, oxygen-free high-conductivity (OFHC) copper was also tested in strict accordance with the ASTM E647 standard test procedure for determining both the technical crack propagation threshold and the characteristics of the region-II fatigue response of this material. Where appropriate, reference will be made to the results of this test series throughout the remainder of this paper.

Analysis

O

O upper scale ~r lower scale i

IOO00

I

20000

i

30000

Number of Cycles, N Fig. 3 Half the surface crack lengths (log scale) p l o t t e d as a f u n c t i o n o f t h e n u m b e r of cycles

IO-S

i IO-7

The AK calculations As illustrated in Fig. 4, the growth rates were first correlated with a conventional stress intensity factor, AK, developed by Hayashi and Abe 14 and Hartranft and Sih, is namely:

~. IO'e =. 3=

Number of Cycles, N 0 1.8

200 000

I00 0 0 0

!

250.000

2

(.9

LEGEND n • z~ •

1.5 o a¢

g

--

specimen I o

specimen t l

specimen/2 specimen ,4

0.I I I0 I00 Stress Intensity Factor, AK (MPo,Jm) Fig. 4 Crack growth rate plotted against the stress intensity range AK 0.01

o

~, 0.5

0

0

I0000 Number

20000

25000

of Cycles, N

Fig. 2 Half the surface crack lengths plotted as a f u n c t i o n o f the n u m b e r o f cycles

112

,1

io-IO

O upper scole lower scole

1.0

,o-, AK = 1.2(2 A~/X/-~)V~a

(4)

where a is half the surface crack length and, conservatively, the factor of 1.2 describes the stress concentration along the crack circumference. All four curves in Fig. 4 have one thing

Int J Fatigue March 1991

in common: the deep valley that typifies the subthreshold micromechanism discussed in part I. For comparison, two crack growth curves obtained from implementations of the ASTM E647 standard are included in Fig. 4. One is from the companion series of E647 tests carried out at R = 0.1 by the authors on the O F H C copper used throughout this investigation, while the other is from the work of Usami, 16 who studied 99.97% pure copper, annealed to a 25 MPa, 0.2% yield stress, at a stress ratio of R = 0. The da/dN against RK curves in Fig. 4 are not only far removed from the LEFM curves but are also very far from each other, and, as a result, are not suitable as a description of the Ip crack initiation region of the crack growth curve presented in Fig. 6.

The AJ approach Based on aspects that were discussed in the introduction and since this study involves the transition from low-cycle to highcycle fatigue, the AJ integral was next reviewed as being an appropriate driving force. For a semicircular surface crack, the AJ integral may be expressed, as shown by Suresh and Ritchie, 17 in the approximate form: AJ --- 3.2(AWe) a + 5.0(AWp)a

(5)

where a equals half of the surface crack length and AW= and AWp are the elastic and plastic energies, respectively. The values of AWe and AWp are determined from their respective areas under the hysteresis loops obtained during the tests. Crack growth rates plotted against [(AJ)E] 1/2 are shown in Fig. 5. Despite the acknowledged errors in the derivation of Equation (5), the crack growth data plotted against [(AJ)E] 1/2, on the whole, are better than those depicted in Fig. 4. Even though they do not overlap, they are much closer to the LEFM curve and have some common characteristics. The first of these is the location of the submicrocrack threshold in the submicrocrack-microcrack initiation curves. We interpret this as the location where the submicrocrack

I0 -7

LEGEND t I specimen specimen/I specimen 12 specimen

13 • A •

U

E

El

"0

P =

£ o

,

/

iO-s

I

..J

DI

o

d /

i0-~o

The second of these common characteristics is the location, in terms of [(8J)E] 1/2, of the inflection point in the curves. This value, which is interpreted as the energy crack propagation threshold, [(AJ)E]~, is being proposed in the light of this investigation as a material property that distinguishes an initiating crack from one that is propagating. In other words, this characteristic identifies both the termination of the combined submicrocrack and the microcrack propagation microfatigue processes and the point where the region Ip gives way to a region-II response. For the O F H C under review in this investigation, the value of [(AJ)E]~,~ determined from Fig. 5 is [(AJ) E]~,/~ = 7.3 MPa V~m

d , y~ I

I0

(MPov~} Fig. 5 Crack growth rate plotted against [(AJ) E] 1/2 Int J Fatigue March 1991

(7)

a value that will be used in the next section first to determine

al, the crack size at the end of the initiation processes, and then to give estimates for mi and Np. As a comment, from the companion E647 test results, this number compares with the standard crack propagation threshold value of AKth = 4.9 MPa V~m for the O F H C copper. Having accepted the definition [(AJ) E]~/~ of the threshold, it may be substituted into a rearranged form of Equation (4) in order to obtain a non-arbitrary interpretation of the crack size that distinguishes an initiating crack from one that is propagating. Hence, it follows that ai = 0.54S([(AJ) E]~,/~/A(r) 2

(8)

This relation will prove to be crucial in the next section for the determination of the values of both Ni and Np. The final characteristic that may be noted is that the regionII crack propagation curve obtained in this manner becomes similar to that determined by a strict implementation of the E647 Standard. While a certain amount of success can be attributed to the AJ integral crack driving force, the curves in Fig. 5 are still not of a nature that leads to a description of the Ip portion of the crack growth curve. For this reason, yet another driving force is reviewed.

AKp = YQ(2 Aep E)V~a

0.1

(6)

AKp

In any fatigue analysis, an accurate estimation of fatigue life, both initiation, Ni, and propagation, Np, are required. Under the AJ control highlighted in the previous subsection, it appears impossible to accomplish this task since, while the crack initiation threshold is established, the crack growth curves prior to this inflection point are significantly different. On the basis, however, that the AJ crack driving force brought the curves of Fig. 5 closer, simply because it had the plastic strain energy separated and emphasized, and recalling again the importance of plastic deformation in the fatigue damage process, a new plastic strain intensity factor or submicrocrack and microcrack driving force, designated as RKp, is proposed. It takes the form for both low- and highcycle fatigue of

I

/

0 I1:

[(AJ)E]~t/~ = 1.8 mPa V~m.

The plastic strain intensity factor,

Z

~0 10-s

micromechanisms change to those characteristic of the microcrack initiation process discussed in part I. For this material, this is determined from Fig. 5 as occurring at

IOO

(9)

where Q is the conventional geometry factor, a is half of the surface crack length, Aep is the plastic strain amplitude, and E is the Young's modulus. Furthermore, in Equation (9), Y

113

is a coefficient reflecting the microstructural properties, which is defined as

y

=

(,~y/,,y0)2

(10)

where % is the current cyclic yield strength of the material measured during the actual test and %o is the standard cyclic yield strength of the material in a heat-treated state. See Table 1 of part I. This model further proposes that the crack growth rate da/dN be a function of the plastic strain intensity factor, AKp, and that the da/dN curve also have three distinguishing regions as indicated in Fig. 6. The crack propagation regions II and III are the same as in the linear elastic fracture mechanics (LEFM) analyses, while region Ip is now another straight line whose slope is lower than that of region II. Even though the crack growth pattern in this region is complicated, the straight line simplification for region Ip that is proposed in this model is based on grounds which will be presently elucidated. The transition between the region Ip and the region II is defined as the plastic crack propagation threshold, Ml'pth, below which submicrocrack and microcrack initiation and nucleation occurs and above which crack growth compatible with the LEFM analysis occurs. One of the advantages of this model is that under &Kp control the crack growth rate at all strain levels but with different grain sizes falls under the same line in the region I v. This is of particular importance in the high-cycle fatigue situation where specimens and components spend most of their fatigue lives. A second advantage is that a qualitative prediction of the fatigue crack initiation life may now be possible. Once the critical crack lengths are calculated from the energy crack propagation threshold, [(AJ) E]pth, 1/2 the crack initiation lives may be easily and accurately obtained by an integration of this function.

As discussed in part I the higher stress concentration field at the inner crack tip serves as a driving force for the submicrocracks to expand into the material. This process continues until a certain depth where the stress concentration factors along the crack circumference become uniform and surface crack growth resumes. This cycling lasts until these submicrocracks coalesce. If the applied strain is high, the coalescence of the submicrocracks occurs rather quickly, appearing on the curve of da/dN against ~lKp as an early crack propagation region. If the strain is low, however, the coalescence progress may be significantly lower. Figure 7 is the first application of this idea, where the plastic strain intensity factor ~iKp is calculated from Equation (9). Both the submicrocrack and microcrack initiation parts, introduced in part I, that pertain to all four curves now fall on one straight line given by

da/dN = B(~Kp) v = 6.92 x 10 l°(~kKp)l.377.

(11)

This describes the region Ip of Fig. 6 for this material. As a final comment, it should be mentioned that the cracks illustrated for specimens el and h are not the fatal cracks but the main cracks. As a result, the data for the region-III crack growth for these two specimens were not attained. The difference between the main- and the fatal-crack growth behaviours does not, however, become apparent until the AKpth threshold has been surpassed. The former develops like the latter during the submicrocrack and microcrack propagation regions but after the fatal crack passes the threshold, the speed of the fatal crack increases to such an extent that the non-fatal cracks become dormant.

Ni and Np The crack initiation lives, Ni, are obtained by an integration of Equation (11) from a zero crack length to a crack length

!

Region

Ip

Region T[

10-v

Region 11-1" "G

o v

Z

E

o

Z

"o

d

El • & •

LEGEND specimen I specimen lm specimen specimen

/

P I

~2

10-8

O '10

o

O

0C

=. )= o

2 J¢: U

L9

o

jd iO-e

J¢

P

(J

II

iO-mo

0.1 Plastic Strain Intensity Factor, ~Kp (log) Fig. 6 The proposed model for microcrack initiation a n d ' p r o p a g a t i o n based on the plastic strain intensity factor ~Kp

114

I

I0

I00

AKp (MPaV-~) Fig. 7 Crack growth rate plotted against plastic strain intensity factor ~Kp

Int J Fatigue March 1991

When a0 and ~(0 were calculated as in Equation (2) and Equation (1), the results were, as expected, far removed from the LEFM curve. However, following the principle that the AJ integral controls the two thresholds, a modification was made, and ao was calculated for each specimen using the relation

obtained from Equation (8) and the [(AJ)E]~/~ value of 7.3 MPa V'-mm. Noting that Q is itself a function of the submicrocrack and microcrack sizes, the integration takes the specific form:

ai

r',- f

N, = Jo da =

(AKp) -~ da

ao =

= C 'o'(Qv~) -~ da

(12)

1

~

]-~

2

(14)

where AK~h= 4.9 MPa V~m is the LEFM crack propagation threshold determined from the companion E647 test, and all the other parameters are as defined in Equation (5). The halfcrack length, a, in Equation (5) is then replaced by a + ao to obtain a modified [(AJ)El 1/2. The crack growth rate plotted against the modified [(AJ)E] 1/2 thus obtained is shown in Fig. 8 where the full curve indicates the LEFM result.

where

C = =[(~-Y-12AepE]

AK,h [(3.0AW= + 5.0AWp)E] '/z

(13)

~L\%o/

By considering Q and a to be constant over small extensions in either the submicrocrack or microcrack sizes, it is possible to change this integration into a summation, thereby making the evaluation of N i a simple procedure. The region-II propagation lives, /Vp, were obtained by integrating the corresponding equations from a crack length of ai tO a crack length of af corresponding to [(SJ)E] 1/2 being 22 MPa Vmm as reported by Usami 16 and obtained in the companion E647 test. The total fatigue lives, N, were then obtained by summing the submicrocrack and microcrack initiation lives, and the propagation lives. The 'integrated--(Pred.)' lives for the specimens for both regions Ip and II are listed in Table 2. Also presented are the 'experimental--(Exp.)' estimates of both the initiation and propagation lives calculated on the basis of the value of ai determined during the course of the replica/fractographic technique given in part I. Although further research is required to confirm the comparison between the two methods, the preliminary findings illustrated in Table 2 are encouraging. Indeed, while acknowledging that the predicted values are obtained from empirically generated material coefficients and that the experimentally measured values are determined from a non-standard replica/fractographic procedure, the disparity between the predicted and experimental initiation and propagation lives of all specimens is below 5%. Finally, this table illustrates that three of the specimens have crack initiation lives of more than 80% of the total lives, with the initiation lives increasing as the fatigue lives increase.

l

l

i

,

i,,,

I

!

!

l

,

,l,,|

,

,

,

!

l,,!

n 10-7

I:] • A •

0

z

LEGEND specimen / specimen /I specimen /2 specimen

lO-S

D/

0 "10

J~

8

10-9

0

o

i0-~0

Comparison

0.1

To compare this new model with the other parameters that have been proposed by other researchers and have been discussed earlier in this paper the data were plotted for the effective AJ integral with corrected crack lengths a = a + ao.

I I0 Effective ~/AJ.E (MPoV-~)

I00

Fig. 8 Crack growth plotted against the modified effective [(AJ)E] 1/2, and the ASTM E647 determination of the LEFM curve

Table 2. Predicted and experimental crack initiation and propagation lives Specimen No

2 21 22 h

Crack length at initiation (izm)

59 70 191 247

Int J Fatigue March 1991

Total life (cycles)

Crack initiation life (cycles) Pred. ( x l 0 4)

Exp. ( x l 0 4)

1.40 1.77 10.55 23.22

1.40 1.70 10.3 22.5

Error (%)

0 4.1 2.4 3.2

Pred. ( x l 0 4)

Exp. ( x l 0 4)

1.99 2.23 12.7 26.6

1.98 2.13 12.2 25.8

Proportion of initiation in total life Error (%)

(%)

0.1 4.7 4.1 3.1

70.7 79.8 84.4 87.2

115

Physical Damage, ASTM STP 811 (American Society for Testing and Materials, 1983) pp 71-94

Conclusions 1)

2)

3)

An empirical model for fatigue crack initiation based on an effective plastic strain energy AKp has been proposed and verified by replica/fractographic observations, the differences between the predicted and experimentally determined crack initiation lives being less than 5%. In this model, the crack initiation region, Ip, is simplified as a straight line on the log-log scales of the da/dN against AKp curve. The transition from Ip to II is defined by the plastic crack propagation threshold, AKpth, and an initiation crack size, ai, has been defined on this basis. The microcrack initiation and propagation mechanisms are mainly the result of surface deterioration as a result of free irreversible dislocation sliding. The submicrocrack and microcrack processes require the formation and coalescence of submicrocracks prior to the crack propagation threshold. The microcracks initiated experience two thresholds in their propagation life, namely: i) a submicroscopic threshold, ~rC,a~, and ii) a microscopic or plastic crack propagation threshold,

3.

Provan, J.W. 'The micromechanics of fatigue crack initiation' in Modelling Problems in Crack Tip Mechanics Ed. J.T. Pindera (Martinus Nijhoff, The Hague, 1984) pp 131-154

4.

Provan, J.W. and Zhai, Z.H. 'A review of fatigue crack initiation' in Time Dependent Fracture Ed. A. Krausz, (Martinus Nijhoff, The Hague, 1984) pp 201-212

5.

Dowling N.E. 'Crack growth during low cycle fatigue of smooth axial specimens' Cyclic Stress-Strain and Plastic Deformation Aspects of Fatigue Crack Growth, ASTM STP 637 (American Society for Testing and Materials, 1977) pp 97-121

6.

El Haddad, M.H. Smith, K.N. and Topper, T.H. J Eng Mater Techno/, Trans ASME Set H 101 (1979) pp 42-46

7.

El Haddad, M.H., Dowling, N.E., Topper, T.H. and Smith, K.N. Int J Fract 16 (1980) pp 15-30

8.

I ankford, J., Davidson, D.L. and Chan, K.S. Metal/Trans A 15A (1984) pp 1579-1588

9.

McEvily, A.J. 'On the quantitative analysis of fatigue crack propagation' Fatigue Mechanisms: Advancement in Quantitative Measurement of Physical Damage, ASTM STP 811 (American Society for Testing and Materials, 1983) pp 283-312

10.

Ohta, A., Kosurge, M. and Sasaki, E. Eng Fract Mech 9 3 (1977) pp 655-662

11.

Minakawa, K. and McEvily, A.J. 'On near-threshold fatigue crack growth in steels and aluminum alloys' Proc of First /nt Conf on Fatigue Thresholds Ed J. Backland (EMAS, Granary Press, Crawley, UK, 1981) Vol 1 p 373 Newman, J.C. Jr. 'A nonlinear fracture mechanics approach to the growth of small cracks' Behaviour of Short Cracks in Airframe Components, AGARD Conf Proc No 328, 55th Meeting of AGAKD Structures and Materials Pane/, Toronto, Canada, 1982 (Nato, Reuilly sur Seine, 1983) pp 6-1-6-26

z~kKpth ;

4)

5)

the latter also being the transition between the shortcrack growth (Ip) and the long-crack growth (II) regimes. In both cases, the AJ integral is the more appropriate driving force and controlling measurement. For the material under discussion the value of [(AJ)E]sth for the subthreshold is 1.8 MPa Vmm and for the plastic crack .propagation threshold it is [(AJ) E]~/~ = 7.3 MPa Vm. The initiation crack size, ai, for the O F H C copper investigated in this study and determined on the basis of [(AJ)E]~,~/~ ranges from 59 ~m to 247 ~m; values that are borne out by the replica/fractographic investigation, details of which are given in part I. The crack initiation sites are grain boundaries and grain boundaries interacting with PSBs for fatigue lives of less than 1.2 x 105, and the initiation sites are on PSBs for fatigue lives greater than 2.6 × 105. The total crack initiation lives ranged from 70% to 87% in the sequence of increasing total fatigue life.

12.

13. 14. 15.

Hartranft, R.T. and Sih, G.C. 'Alternating method applied to edge and surface crack problems' Mechanics of Fracture 1: Methods of Analysis of Crack Problems Ed G.C. Sih (Noordhoff, The Netherlands, 1973) pp 179-238

16.

Usami, S. 'Applications of threshold cyclic-plastic-zonesize criterion to some fatigue limit problems' Proc of First /nt Conf on Fatigue Thresholds Ed J. Backland (EMAS, Granary Press, Crawley, UK, 1981) Vol 1 pp 205-238 Suresh, S. and Ritchie, R.O. Int Met Rev 29 6 (1984) pp 883-898

17. 18

References 1.

2.

116

Buck, O., Morris, W.L. and James, M.R. 'Remaining life prediction in the microcrack initiation regime' Fracture and Failure: Analyses, Mechanisms and Applications Eds P.P. Tung et al (American Society for Metals, Metals Park, OH, 1981) pp 55-64 Field, J.L., Behnaz, F. and Pangbom, R.N. 'Characterization of microplasticity developed during fatigue' Fatigue Mechanisms: Advances in Quantitative Measurement of

Kuokkala, V.T. and Kettunen, P. Acta Metal/33 11 (1985) pp 2041-2047 Hayashi, K. and Abe, H. Int J Fract 16 3 (1980) pp 275-285

1990 Annual Book of ASTM Standards (American Society for Testing and Materials, 1990) Vol 03.01 pp 648-668

Authors J.W. Provan and Z.H. Zhai are with the Mechanical Engineering Department, McGill University, Montreal, Quebec, Canada.

Int J F a t i g u e M a r c h 1991