Influence of microstructure onnear- threshold fatigue-crack propagationin ultra-high strength steelR. O. Ritchie

Fatigue crack propagation behaviour of an ultra-highstrength, silicon-modified AISI 4340 alloy steel (300-M) has been investigated in moist air over anextremely wide range of growth rates from 10-8 to10-1mm/cycle. Particular emphasis has been devotedto the influence of microstructure on fatigue-fracturebehaviour near the threshold stress intensity, Mo'

below which crack growth cannot be detected. Byvarying microstructure through quench and temperingand isothermal transformations, the threshold stressintensity and near-threshold crack-propagation ratesare observed to be influenced by mean stress (loadratio), material strength, grain size, and impuritysegregation. The threshold I!1Ko for crack propagationis found to be inversely related to the strength of thesteel, and a relationship between I!1Ko and cyclic yieldstress is observed. It is shown how near-thresholdcrack -growth resistance can be improved by (i) cyclicsoftening, (ii) coarsening the prior austenite grain size,and (iii) controlling impurity segregation to grainboundaries. These effects are contrasted with crack-propagation behaviour at higher growth rates. A semi-quantitative model is developed to rationalize near-threshold fatigue crack growth behaviour, based onthe environmental influence of hydrogen, evolved fromcrack tip surface reactions with water vapour in moistair.Paper No. MS 613. Contribution to 'Fatigue 1977' Conferenceheld at the University of Cambridge on 28-30 March 1977.Robert O. Ritchie, MA, PhD, MIM, is in the Department ofMechanical Engineering, Massachusetts Institute of Tech-nology. .

In many engineering applications where design against cyclicloading is a prime consideration, the principal factorcontrolling the lifetime of a particular component is often therate at which fatigue cracks can grow from pre-existingdefects. Accordingly, over the past 10-15 years, a largevolume of data has been generated on fatigue crackpropagation behaviour at growth rates in excess of10-6 mm/cycle. Although this information is useful for moststructural engineedng 'applications (determining safeinspection intervals in aircraft, for example), in situationswhere structural and machinery components are subject toextreme high-frequency, low-amplitude loadings for

368 Metal Science August/September 1977

1010-1012 cycles, a need exists for an assessment of fatiguecrack propagation behaviour at growth rates below 10-6mm/ cycle. This area has received comparatively littleattention in the literature, and consequently there is bothlittle understanding of the growth mechanisms at very lowpropagation rates and a substantial lack of reliableengineering data. Such information, particularly a knowledgeof a threshold stress intensity below which cracks cannotpropagate, has been shown to be essential in the analysis ofsuch problems as cracking in turbine rotor shafts 1 andacoustic fatigue of welds in gas ducts in magnox reactors.1, 2The application of linear elastic fracture mechanics and

related small-scale crack-tip plasticity has provided the basisfor describing the phenomenon of fatigue-crack pro-pagation.3 Many investigators have confirmed that thecrack-growth rate per cycle (da/dN) is primarily controlledby the alternating stress intensity (1!1K), through anexpression4 of the form:

da / dN = CDJ(m . . . . . . . . . . . . . . . . . . (1)

where C and m are scaling constants, and M is given by thedifference between the maximum and minimum stressintensities for each cycle, i.e. M=Kmax - K min' Thisexpression adequately describes behaviour for the mid-rangeof growth rates, typically 10-5-10-3 mm/cycle, and can beused here with confidence to predict propagation rates inservice components to provide a rational basis for designagainst failure by fatigue. At higher growth rates, however,when Kmax approaches KIC' the fracture toughness, eqn. (1)often underestimates the propagation rate, whereas at lowergrowth rates it is found to be conservative as M approachesa threshold stress intensity I!1Ko' below which crackpropagation cannot be detected.5-21Recent studies have shown that this sigmoidal variation of

growth rate with M can be characterized in terms ofdifferent primary fracture mechanisms (Fig. 1). For the mid-range of growth rates (Regime B), failure generally occurs insteels by a transgranular ductile striation mechanism22,23and there is little influence of microstructure and mean stress(characterized by the load ratio, R = Kmin/KmaJ on crackgrowth.24-26 At higher growth rates (Regime C), when Kmaxapproaches KIc' growth rates become extremely sensitive toboth microstructure and mean stress due to a departure fromstriation growth to include static fracture modes, such ascleavage and intergranular and fibrous fracture.24-26 At low(near-threshold) growth rates (Regime A), there is similarly astrong influence of microstructure12,14,lS,17,18 and meanstress7-11,13-21 on growth rates, together with an increasedsensitivity to stress history6 and environmental effects.14-16,19,27 Explanations for this behaviour, however, remain asubject .of some controversy, involving conflicting viewsbased on crack closure9-11 and environmental factors.14-16

Z"0--o"0

Regime A

NON -CONTINUUMMECHANISMS

large influence of:

i microstructurei i mean stressiii environment

threshold

Regime B

CONTINUUM MECHANISM(striation growth)

Little influence of:

i microstructureii mean stressiii dilute environmentiv thickness

log ~K

Ritchie Influence of microstructure 369

IIKe·1final: failure

I

Regime C, ,STATIC MODE ME.CHANISMS(cleavage, intergranular and

fibrous)

large influence ,of:

i microstructurei i mean stressiii thickness

little influence of:iv environment

Primary fracture mechanisms in steels associated with sigmoidal variation of fatigue crack propagation rate (da/dN) with·alternating stress intensity (~K).

Paris and co-workers,9-11,13 for example, have suggestedthat the mean stress dependence on I!J.Ko and near-thresholdgrowth rates is a direct result of crack closure, i.e. contact ofthe crack surfaces due to residual tensile strains above theminimum load of the fatigue cycle.28 This was originallyproposed without experimental verification,9-11 although, in·a later study, 13 closure was detected using surface strain-gauge measurements. However, there is now evidence toshow that closure may only be significant in surface (plane-stress) regions,29, 30 and furthermore is reduced by thepresence of an environment31-33 (as opposed to vacuum) andat low stress intensities.34 Since threshold measurementsinvolve low stress intensities, where plane-strain conditionsalmost invariably exist, it is unlikely that crack closure canprovide a useful explanation for the effect of mean stress onnear-threshold .growth rates. The influence of theenvironment on crack growth constitutes an alternativeexplanation, based on results which show (i) slowerpropagation rates and higher threshold values measured invacuo compared to air;14-16, 19,27and (ii) little or no effect ofmean stress for tests in vacuo.1S, 16 A later section of thispaper will examine how this can be modelled for near-threshold fatigue-crack growth in ultra-high strength steels toencompass both microstructure and mean stress effects.Growth mechanisms in this region have been termed'microstructurally sensitive',14-16 but it is still not clear whichmicrostructures provide the best resistance to near-thresholdgrowth. From limited data in the literature, it is probable that

material strength and the scale of the microstructure areimportant variables. Higher threshold values have beenobserved in lower-strength steels by decreasing the yieldstrength,12, 17 and lower near-threshold growth ratesmeasured in the same steels17 and titanium alloys14 byincreasing the grain size.The present paper summarizes the results of an investiga-

tion to characterize microstructural influences on near-threshold fatigue-crack propagation in an ultra-high strengthsteel, 300-M (composition shown in Table I). Experimentswere designed to systematically examine effects of strength, 18grain size,20 and impurity segregation, 21in the hope that theresults may provide some basis for the design of alloys moreresistant to very high cycle fatigue· failure.

EXPERIMENTAL MEASUREMENT OFNEAR-THRESHOLD GROWTHIdeally, the threshold stress intensity, I!J.Ko' represents thestress intensity where the growth rate is infinitely small,although, for practical measurement purposes, it is moreuseful to define Mo in terms of a maximum growth rate,calculated from the accuracy of the crack monitoringtechnique and the number of cycles imposed.16 In the presentinvestigation, crack lengths were continuously measuredusing the electrical potential technique,3S and the thresholdMo was computed from the highest stress intensity at whichno growth occurred within 107 cycles. Since the crackmonitoring technique is at least accurate to O· 1 mm, this

Metal Science August/September 1977

370 Ritchie Influence of microstructure

Table I Composition of aircraft-quality (vacuum-arc remelted) 300-M low-alloy steel (wt.-%)

C

0·42

Si

1·59

Mn

0·76

P

0·007

S

0·002

Cr

0·76

Mo

0·41

Ni

1·76

v0·10

Table II Ambient temperature mechanical properties of 300-M 'steel

Code 0·2% offset yield stress UTS, Elongation Kw Prior austeniteMonoton'ic, Cyclic, (%of grain size,MPa MPa MPa 1in. gauge) MPaml12 Jlm

TI00 1497 2107 2338 12·4 35·5 20T300 1737 1486 2006 11·9 65·1 20T470 1497 1198 1683 12·1 68·9 20T650 1074 861 1186 18·1 1851 20

1522T650SC 1070 858 1179 14·9 79·6 20IS0250 1497 1502 1862 14·5 88·5 20A1200 1657 1571 1986 6·3 80·3 160

1 Invalid KIC result, estimated using equivalent energy procedure at maximum load.212 Invalid KIC result, estimated using JIC procedure at crack initiation. 21

corresponds to a maximum growth rate of 10-8 mm/cycle.,To minimize residual stress effects, thresholds wereapproached using a successive load reduction followed bycrack -growth procedure. Measurements of crack -growthrate were taken, at each load level, over increments of1-1· 5 mm, after which the load was reduced, by less than10%, and the same procedure followed. The increments overwhich measurements of growth rate were taken representdistances exceeding 100-1000 times the maximum plasticzone size generated at the previous (higher) load level, and soany initial retardation in growth rate caused by change inload was negligible. Following ~Ko measurement, the loadwas increased in steps and a similar procedure adopted.Higher growth-rate tests were performed under continuousconstant cyclic loading to yield an extremely wide range ofpropagation-rate data from 10-8 to 10-1 mm/cycle. Testswere conducted at a cyclic frequency of 50 Hz, under plane-strain conditions, in a controlled atmosphere of humid air atconstant temperature (23°C) and constant relative humidity(45%). Full experimental details are given elsewhere.18, 21

'RESULTSEffect of material strengthTo assess the influence of strength at constant grain size, 1-Tcompact tension specimens (12·7 mm thick) were oil-quenched from 870°C to yield a prior austenite grain size of20 Jim, and tempered for 1h at 100, 300, 470, and 650°C(these treatments are hereafter referred to as TI00, T300,T470, and T650, respectively). Further specimens wereaustenitizedat 870°C, isothermally held at 250°C (20 degCbelow Ms)' and tempered at 300°C to produce a structure(referred to as IS0250) with identical monotonic yieldstrength to the T 100 and T470 conditions. The IS0250structure was selected in view of its high retained austenitecontent (12%), which is known to change hardening andstress corrosion cracking characteristics. 18 Ambienttemperature mechanical properties of the structures areincluded in Table II, and fatigue crack propagation results inFigs. 2-4. It is apparent from these plots that the influenceof microstructure and load ratio R is maximized at low andhigh stress intensities (i.e. in Regimes A and C of Fig. 1).For ··th~ mid.:range of growth· rates, represented by the

linear portion (Regime B) of the growth-rate curves, there is

Metal Science August/September 1977,

little variation in propagation rate between differentmicrostructures at both load ratios. Growth-rate curves tendtowards a common line of slope (i.e. exponent min eqn. (1))of 2·5 at R=0·05 and 2·7 at R=0·70. Transgranularductile striation growth (Fig. 5(a)) was observed to be themechanism of failure for all structures in this range,consistent with a lack of microstructural and load-ratiosensitivity on growth-rate behaviour.24-26 Considering thewide variation of tensile strength (2-fold) and toughness (6-fold) shown by the structures tested, fatigue-crack growth inRegime B appears independent of such mechanicalproperties.At higher stress intensities, growth-rate curves display an

acceleration in propagation rate as Kmax approaches KIC(Regime C). Marked effects of microstructure and load ratiocan now be seen (Figs. 2-4), with resistance to crack growthdecreasing as the toughness is reduced. Fractography offailures in this region confirmed the presenc~ of static modes,as shown in Fig. 5. Areas of microvoid coalescence werepresent in all structures (e.g. Fig. 5(b) and (c)), withadditional intergranular cracking in the T470 condition, andintergranular and cleavage cracking in TI00 (Fig. 5(b)).The largest influence of microstructure and load ratio can

be seen at low stress intensities in Regime A, where growthrates are < 10-6 mm/ cycle. Close to the threshold Mo'

measured propagation rates become less than 'a latticespacing per cycle, indicating that crack growth is notoccurring uniformly over the entire crack front. Consideringfirst results for quenched and tempered material at R =0·05(Fig. 2), it is apparent that tempering temperature exerts astrong influence on threshold values and on near-thresholdcrack-propagation rates. At ~K = 9 MPa mt, for example,the growth rate in the T100 condition is over two orders ofmagnitude greater than in the T650 condition. As thetempering temperature is raised, the thresholdMo increasesfrom 3·0 to 8·5 MPa mt, concurrent with a two-foldreduction in tensile strength. At R =O·70 (Fig. 3), the sametrend of increasing M 0 with decreased strength is stillapparent but the effect is drastically reduced: Mo increasesfrom 2·3 to 3·7 MPa mt for the same reduction in strength.The variations of threshold ~Ko with monotonic yieldstrength and ultimate tensile strength (UTS), plotted in Figs.6 and 7, respectively, indicate a general trend of an inverse

Ritchie Influence of microstructure 371

6

300-M alloy steel

6 8 10 20ALTERNATING STRESS INTENSITY ~K, MPa m1/2

-310

Q1

U>0-u

-6C10 '- •.Z"0

d"0

80

80

60

60

40

40

1 lattice spacing Icycle

tlK, lbf x 103 in2. in1/210 208

2·983·085·108·50

. ~Ko,MPa m1/2

UTS,MPa

2338200616831186

100°C300°C470°C650°C

temper(1 h)

o

•A

2

Z"0 -3"";"10"0

60

40

40

K1c' ~Ko'MPa m1/2 MPa m1/2

35-5 2-2865-1 2·3068·9 2·46(185) 3·68

20

K = 65 MPa m1/2Ic+

I K =69 MPa m1/2~ +Ic

III.c.

UTS,MPa2338200616831186

20~K, MPa m1/2

temper(1 h)

100°C300°C470°C650°C

o

•

6 8 10ALTERNATING STRESS INTENSITY

4

300 - M alloy steel

2

Q1 102U>0-u--EE"10-3z~o"0

w"' 0-4I- 1<{a:::II-

~ -5~ 10<!)

~u<{ -6510

Austenitized at S70°C, oil-quenched and tempered. Environment: air at 23°C, 45% relative humidity. R=O·05.2 Fatigue crack propagation results for 300-M, quenched and tempered between 100 and 650°C, showing influence ofmaterial strength at R=0·05. .

3 -2 1/2tlK, lbf x 10 in . in

6 8 10

Austenitized at S70°C, oil-quenched and tempered. Environment: air at 23°C, 45% relative humidity. R=O· 70.

3 Fatigue crack propagation results for 300-M, quenched and tempered between 100 and 650° C, showing influence ofmaterial strength atR=0·70.

Metal Science August/September 1977

372 Ritchie Influence of microstructure

t t threshold .1Ko

4. 6 8 10 20

ALTERNATING STRESS INTENSITY .1K, MPa m1/2

300-M alloy steel

R=0'70

-6 -10 ~d"U

80

60

60

2·4.4

2·4.5

40

3·085·10

1/2.1Ko ,MPa mR=0·05 R=0'70

3·50 2·4.5

1737

14.97

temper y"leld,(1h) MPa

300°C 14.97

heattreatment

isothermal250°C

quenched

quenched

.1K, lbf x 103 in2. in1/28 106

heat treatment

isothermal 250°C, 300°C temperquenched and tempered at 300°Cquenched and tempered at 470°Co

•°

R=0·05

•R=0'70

2

~ -2~ 10~EE•..

-3z 10"U0-"U

w164I-

<{0:::

II-

30 -s0::: 10~~u<{0:::

-6u10

w:::>~~ -7LL 10

Austenitized at 870oe. Environment: air at 23°e, 45% relative humidity.

4 Fatigue crack propagation results for 300-M, isothermally transformed at 250°C (150250), compared with T300 and T470structures at R =0 ·05 and O·70.

dependence ofMo on material strength. However, far bettercorrelation with Mo is obtained using UTS rather than yieldstress. This suggests that strain hardening may be important.The flow stresses within the cyclic plastic zone generatedahead of a growing fatigue crack, however, are governed bycyclic rather than monotonic strain hardening effects.Accordingly, cyclic stress/strain tests were performed toassess cyclic yield strengths; a comparison of cyclic andmonotonic stress/strain curves is shown in Fig. 8. Allstructures can be seen to cyclically soften with the exceptionof the T 100 condition which cyclically hardens, and theIS0250 condition which shows neither significant hardeningnor softening.* Utilizing these data, a better correlation canbe obtained between threshold I1Ko and material strength(now plotted as the 0·2% offset cyclic yield stress) as shownin Fig. 9. As cyclic strength is increased, either because ofhigh initial monotonic strength or by cyclic hardening, thethreshold for fatigue-crack propagation is reduced, to alimiting value of Mo= 3 MPa m2 at a yield of 1600 MPa forR =0·05, and 2·3 MPa mt at a yield of 1200 MPa atR =0· 70. At greater yield strengths, no further reduction inM0 can be measured in this steel. It is now reasonable to

* Cyclic softening in quenched and tempered steels is generallyattributed to a rearrangement of dislocation substructure and areduction in dislocation density with alternating loading. Cyclichardening has been attributed to dynamic strain agei,ng, and ischaracteristic of untempered and lightly tempered steels having highdislocation densities.36 The lack of softening in the 180250condition results from an offsetting effect of transformation-inducedhardening of retained austenite to martensite with cyclic strain.18

surmise why the three structures with identical monotonicyield strengths (i.e., TI00, T470, and IS0250) show widelydiffering values of Mo. The TI00 condition has the smallestthreshold because this structure is the hardest, due to cyclichardening. The T470 condition, on the other hand, is thesoftest condition after cyclic softening, and consequently hasthe largest threshold.Fracture morphology of near-threshold failure consisted

of a flat, ductile transgranular mode with isolated segmentsof intergranular separation (Fig. 10). Close to the threshold,the proportion of intergranular facets was small « 1%),increasing to a maximum at around 11K = 6-10 MPa mt andthen gradually diminishing at higher stress intensities (Fig.10(b)-(d». The contribution from intergranular fracture wasalso found to vary with tempering temperature. Significantamounts of intergranular facets were observed in the TI00and T470 conditions, typically 15% at 11K = 7 MPa mt,compared to a maximum of 8% in the T300 condition, andnone at all in the T650 structure.

Effect of grain sizeTo assess the influence of prior austenite grain size on near-threshold fatigue-crack growth, specimens were austenitizedat 870 and 1200°C, oil-quenched and tempered at 300°C(referred to as T300 and A 1200 structures, respectively).The higher austenitizing temperature results in a larger prioraustenite grain size (160 ~m), yet the strength propertiesremain largely unaffected. Mechanical properties are listed inTable II. The fatigue results at R = 0·05 and O·70 (Fig. 11)indicate that growth rates are similar in both structures overthe mid-range of growth rates, and begin to differ at high and

Metal Science August/September 1977

Ritchie Influence of microstructure 373

o~<l

Eo~<I

•...•~4 x

3408

o2300

300

R=0'056

T470

8300-M alloy steel

--+-- ~Ko at R=0'05--0-- ~Ko at R=0·70

R=0'05

300-M alloy steel-- t.Ko at R= 0·05--0-- t.Ko at R=0'70

UTS, lbf x 103 in-2

250

, 3 -2YIELD STRESS, Ibt x 10 in

200 250150

o1000

o1100

8

o~<I

g4o --'""'0__ ISO 250.~ •....- ••.._ T100 A1200. T300~ R=0'70 ••..-_..... •~ - ....g----o--o __ 2

2

o~<l

:34-o -0__ •:r: ---_(.f) R= 0.70----- ...~ 2 0----0---(0- _

I-

1500 2000ULTIMATE TENSI LE STRESS, (Ju' MPa

7 Influence of UTS on threshold for fatigue-crack growth(~Ko).

A120 structure, particularly at R =0·05, although thethreshold is unchanged. Near-threshold fracture surfaceswere much rougher in the coarser structure, showing afaceted, ductile transgranular mode with segments of in-tergranular fracture.

1500YIELD STRESS, cry, MPa

6 Influence of monotonic yield strength (Oy) on thresholdfor fatigue-crack growth (~Ko).

Effect of impurity segregationThe influence of impurity segregation was examined bycomparing fatigue-crack propagation behaviour in un-embrittled and temper-embrittled structures. Specimenswere austenitized at 870°C, oil-quenched, and tempered at650°C. One half of the material was then oil-quenched aftertempering; the other half was taken through a step-coolingprocedure21 of holding for progressively longer times atdecreasing temperatures through the temper embrittlementrange. The resulting structures are hereafter referred to as

low stress intensities. At high stress intensities, the A1200structure shows superior resistance to crack propagationbecause of increased toughness. At -low stress intensities,growth rates are somewhat lower in the coarser-grained

Arrow indicates general direction of crack propagation.

5 Mechanisms of growth at medium and high growth rates(R=0·05): (a) ductile striation growth in T300 conditionat ~K=20-M-P-amt; (b) intergranular, cleavage, andfibrous fracture at high growth rates in T100 condition at~K=30MPa mt; (c) fibrous fracture in T300 condition at~K=60MPa mt.

Metal Science August/September 1977

374 Ritchie Influence of microstructure

cyclic

monotonic

cyclic

monotonic

'cyclic

470°C temper 650°C temper

8 Monotonic and cyclic stress/strain curves for 300-M steel.

unembrittled (T650) and embrittled (T650SC), respectively.The step-cooling procedure results in a severe loss oftoughness (--50%) without change in strength (Table II),concurrent with a change in fracture mode from microvoidcoalescence to intergranular. Using Auger spectrosqopy,this

embrittlement was attributed to the co-segregation ofalloying elements (Ni and Mn) and impurity elements (PandSi) to prior austenite grain boundaries.21The effect of the impu"rfty--segre-gatlon on fatigue-crack

propagation in moist air is shown in Fig. 12 for load ratios of

150

3 -2CYCLIC YIELD STRESS, lbf x 10 in

200 250 300

8300-M alloy steel

8

__ ~__ quenched and tempered

R=0-05 • 0 isothermally transformed6

o~<J

N

I.~mo

o-J04I<.f)Wa::::I~

2

'0, ." ',R=0'70

..•.•..-0 o~ ~ --0-,

4 x

o~<J

2

o220020001000

o800 1500

CYCLIC YIELD STRESS, 0";, MPa9 Influence of cyclic yield strength (Oy'), measured by 0·2% offset, on threshold for fatigue-crack growth L:~Ko)

Metal Science August/September 1977

Ritchie Influence of microstructure 375

Arrow (top left) indicates general direction of crack propagation.

10 Mechanisms of growth at low growth rafes, showing ductile transgranular mechanism with segments of intergram..ilarfracture (I), in T470 condition at R=O·05. (a) and (b) at threshold, ~K=5·2 MPa m-!; (c) ~K=7·6 MPa m-! ; (d)~K=11 MPa m.-!.

R =0·05 and O·70. It is clear that prior temper embrittle-ment results in an increase in crack-growth rates at both loadratios, particularly at low stress intensities. At growth ratesgreater than ,....,10-5 mm/cycle, the embrittled structure(T650SC) shows only marginally higher growth rates, andthere is little influence of load ratio on crack-propagationbehaviour in either structure. No major differences wereobserved in fatigue-fracture mechanisms in this region, withboth structures exhibiting a transgranular ductile striationmode, similar to Fig. 5(a). At near-threshold growth rates< 10-6 mm/cycle, however, propagation rates in theembrittled structure become over an order of magnitudehigher than in the unembrittled structure, and the value ofthe threshold Mo is significantly reduced from 8·5 to6·2 MPamt at R=0·05, and from 3·7 to 2·7 MPamt atR =0· 70. It is also noticeable that growth rates areincreasingly sensitive to load ratio as the threshold isapproached. Significant amounts of intergranular fracturewere present in embrittled samples (Fig. 13(b»; theproportion of which varied with stress intensity. Near I1Kothe fraction of intergranular fracture was,....,5%, increasing to,....,20% at M=10MPamt (at R=0·05), and thendecreasing to zero above 11K = 15MPa mt. No evidence ofintergranular separation could be detected at any stressintensity in unembritt!ed material (Fig. 13(a».

DISCUSSIONThe present results have confirmed that microstructure andload ratio effects on fatigue-crack propagation in steelsoccur primarily at high and low growth rates. The mid-rangeof growth rates, where the crack growth rate curve is linear,has been associated with a ductile striation mechanism ofgrowth, with the exponent m in eqn. (1) found to lie between2·5 and 2· 7. This is consistent with most metallurgicap7 andmechanical models38-40 of 'ductile' fatigue-crack growth,which predict an exponent of ,....,2.Such models also predictlittle influence of load ratio and microstructure on growthrates, and this is clearly verified by the present results in thisregion. Where the mechanism of failure is by ductilestriations, fatigue-crack growth appears to be controlled bythe amount of crack opening each cycle, dependent upon theelastic modulus.At high growth rates (Regime C), the present results show

(i) an acceleration in growth rate, (ii) increased values of theexponent m, (iii) large microstructure effects, and (iv) amarked influence of load ratio. This behaviour has beenpreviously characterized in terms of the occurrence of staticfracture modes,24-26 and such mechanisms have beenobserved in this region in the present study (Fig. 5). Themicrostructural influences on growth rate arise here becausesuch static fracture mechanisms are sensitive to material in-

Metal Science August/September 1977

376 Ritchie Influence of microstructure

806040

1 lattice spacing I cycle

prior austenite grain size

20 fJm (870°C), 160 fJm (12000C)

20INTENSITY ~K, MPa m1/2

10STRESS

6 8ALTERNATING

~ threshold

4

~K, lbf X 103 in2.in1/2

4. 6 8 10 20 40 60 80

300-M alloy steelR=0·05 ......

austenitizingR

~Ko'temperature MPa m1/2

• 870°C 0-05 3·08 ° R=0'70

° 870°C 0'70 2·30 °12000C 0·05 3·00 °A

6 12000C 0·70 2'39

o ~~o ~

o~

10-12

<lI -2U 10>-~EE -3:i' 10~d"'0

w104~«

0:::-

I~~ -so 100:::~~U« -60::: 10uw::>~~

-710

1082

Austenitized, oil-quenched, tempered at 300°C. Environment: air at 23°C, 45% relative humidity. R=0·05 and O· 70.11 Fatigue crack propagation results for 300-M, austenitized at 870°C (T3QO) and at f200°C (A1200), showing influence of

grain size.

-6 -10 ~

d"0

80

80

60

60

40

40

1 lat tice spacing I cycle -----~

~K, lbf x 103 in2. inl/210 208

threshold ~Ko

~Ko,MPa m 1/2

8·503·686·172·65

6

R

0·050'700-050·70

6 8 10 20

ALTERNATING STRESS INTE NSITY ~K, MPa m1/2

coolingrate

oil quenchoi I quenchstep-cooledstep-cooled

300-M alloy steel

temper(1 h)

650°C650°C650°C650°C

2

<lI

~102~EE

z -3~ 10d A"'0

6

W •~« °0:::

I~~00:::~~u«0:::uw::>S2~

10-7«LL

108

2

Austenitized at 870°C, oil-au~.n_ched and te..!!'p_e!edil.!.~§.o_oC.Environment: air at 23°C, 45% relative humidity. R=0·05 and O· 70.12 Fatigue crack propagation results for 300-M, oil-quenched (T650) and step-cooled (T650SC) after tempering at 650°C;

showing influence of impurity-induced embrittlement.

Metal Science August/September 1977

Ritchie Influence of microstructure 377

o present study• Paris et al. (1972)•• Buccietal. (1972)o Pook (1972)f:::,. Priddle and Jerram (1972)• Cooke etal. (1973-75)v Beeversetal. (1975)T Masounave and Bailon (1975\

14 Summary of results showing variation of threshold forfatigue-crack growth (~Ko) at R=O with yield strengthfor steels. Solid lines from threshold model (eqn. (11)).

within a single grain. Cooke et al.l6 have shown that bytesting a similar steel in vacuo the intergranular fracturelargely disappears. Furthermore, the lack of intergranularcracking in the T650 condition is consistent with the factthat this condition is far less sensitive to hydrogenembrittlement.l4 The observation that the overall proportionof grain-boundary facets changes with temperingtemperature suggests a further influence of the grain-boundary strength, which would depend on any impuritysegregation there. For example, the largest. fraction of inter-granular separation during fatigue-crack growth can be seenin structures where impurity segregation is likely to haveoccurred during heat-treatment (i.e. T100, T470, andT650SC). All three structures were observed to fail at leastpartly by intergranular cracking in monotonic K1C tests. WithT650SC, such fracture was directly identified with thesegregation of P and Si (temper embrittlement). For theT 100 structure, as-quenched embrittlement is a possibilityresulting from the segregation of, say, P in the austenitephase, either prior to, or during quenching after austenitiza-tion.42-44Finally, the T470 structure involves tempering at atemperature within the tempered martensite embrittlement45range for 300-M where impurity separation to grainboundaries is again a strong possibility. There is apparentlya close interrelationship here between the sensitivity of thematerial to the environment (i.e. hydrogen embrittlementfrom moisture in air) and any impurity segregation to grainboundaries, which determines the amount of intergranularseparation observed during near-threshold fatigue-crackgrowth in steels. The most significant finding of this study isthe dependence of near-threshold fatigue crack propagationrates and the value of the threshold I1Ko on materialstrength, since no such dependence has been observed athigher growth rates.46Examination of the literature (Fig. 14)indicates that this trend of increasing I1Ko with decreasingstrength clearly exists for steels. Kitagawa et al.12 andMasounave and Bailonl7 have observed similar effects inmuch lower strength steels. The present work has shown thatsuch a relationship exists for ultra-high strength steels,provided that cycliC strength IS considered rather than the

12N

~10 0-:NI.~

8C"'lox

6 Bo

4 &"0

2 'Y.,0

<l

o2000

250

o

o

500 1000 1500YIELD STRENGTH, MPa

-- eqn.(11)

o 8 ~ ~o

~ 6o<5 4I

~ 2~2= 0o

3 -2STRESS, lbf x10 in

SE 1/.0-:-.:: 100 150 200

~ 12 • ~~ ~ p.=1500A0' 10 ~ ~& ~

homogeneities, which control the toughness. An influenceof load ratio is observed because cleavage and intergranularcracking are largely tensile-stress-control1ed fracture modesand fibrous fracture is dependent on the hydrostaticcomponent of stress. Increasing the load ratio raises Kmaxwith respect to M, and therefore leads to an increased con-tribution from such mechanisms. Thus, the onset of anacceleration in growth rate in Region C is essentially afunction of the toughness, brought about as Kmax approachesK1C'

At low growth rates, less than 10-6 mm/cycle in RegionA, fatigue-crack growth similarly becomes markedlysensitive to load ratio and microstructure. It is tempting torelate this again to a fracture mechanism change,24 i.e. theoccurrence of intergranular cracking at low values of 11K(Figs. 10 and 13). However, the lack of such features in theT650 condition (which shows the largest load ratio effect)suggests that this is an oversimplification. It is believed thatthe occurrence of intergranular cracking in this region is dueto the influence of water vapour in air environment, causinghydrogen to diffuse to and embrittle prior austenite grainboundaries, particularly when the plasticity is confined

Arrow indicates general direction of crack propagation.

13 Morphology of fatigue fracture at near-threshold crack-growth rates at ~K=9·5MPa m1- (R=O·05) in 300-Msteel: (a) ductile transgranular mechanism inunembrittled material (T650); (b) segments of in-'tergranular fracture tl) in temper-embrittled material(T650SC).

Metal Science August/September 1977

378 Ritchie Influence of microstructure

monotonic yield stress. Consequently, cyclic softening mustbe regarded as beneficial in improving near-threshold crack-growth resistance. Coarsening the prior austenite grain sizehas also been observed to improve near-threshold crack-growth resistance although no change in the threshold stressintensity was detected. Results in low-strength steels17indicate both a decrease in crack -growth rate and anincrease in Mo with larger grain sizes. However, in such,steels, there is a reduction in yield strength on coarseninggrain size which is not observed in lightly tempered ultra-high strength steels. Finally, the build-up of residualimpurities in grain bbundaries (temper embrittlement) hasbeen shown to worsen markedly the crack-propagationresistance at near-threshold rates, whereas little effect can bedetected at intermediate growth rates.-- It is clear from the present results - that all the micro-structural effects observed principally affect near-thresholdfatigue crack propagation behaviour at growth rates<""10-6 mm/cycle, and are far less important at higherpropagation rates in the intermediate range. Furthermore,within this regime, growth rates become extremely sensitiveto the load ratio, particular in the lower strength conditions(Fig. 9). It is possible to rationalize these results in terms ofthe influence of the moist air environment on fatigue-crackgrowth. It is generally accepted that the primary mechanismof environmental attack during fatigue-crack growth of high-strength steels in the presence of water vapour is hydrogenembrittlement. 47 With this in mind, a semi-quantitativemode118,21 is developed relating the contribution to fatigue-crack propagation from the environmental effect ofhydrogen, evolved from crack tip surface reactions withmoist air. This environmental effect can occur under fatigueloading at stress intensities less than the threshold forhydrogen-assisted cracking under monotonic loading (KTHor K1SCC) because fresh- surface at the crack tip, wherehydrogen can enter the lattice, is continually renewed bycyclic stressing.

MODEL FOR FATIGUE CRACK GROWTHTHRESHOLD IN STEELSFollowing Weiss and Lal,48 a model for fatigue-crackpropagation is considered based on the assumption that thecrack advance per cycle (da/dN) represents the distanceahead of the crack tip where the nominal stress exceeds acertain critical fracture stress (a F)' such that

da _ LloN(nF + l)/nF(~~ _d!\T - a . f p*/2. . . . . . . . (2)Iv OF W

where a is the crack length, ~a N the applied stress amplitude,j{a/w) a dimensionless correction factor for the finite widthof specimens, nF the cyclic strain hardening exponent in thestress range to which the critically stressed region issubjected, and P* the Neuber microsupport constant,representing the effective radius of a sharp crack. For near-threshold fatigue-crack growth, the maximum cyclic stressdecreases towards the elastic limit, hence nF must approachunity. Thus, it follows that

da t::J(2 p* "dN = rroj; - 2 (3)

where'

AK2 = rra. ~a~. f(~)For crack growth, the local tensile stress (ayy) must exceedaF over a distance larger than P*, and thus, at the threshold,

Metal Sciel"ce August/September 1977

Weiss and Lal48 suggest da/dN=p*, viz.

AKo =J% rrp* . aF : (4)

In moist air, however, cyclic stressing will lead to theproduction of chemically reactive surface at the crack tip,where atomic hydrogen can be evolved from water vapourby reactions49 of the typeFe + H2 0 ~ FeOH+ + H+ + 2e2H+ + 2e ~ 2H

The stress gradient ahead of the crack tip then drivesadsorbed hydrogen atoms into the lattice where theyaccumulate in the region of highest dilatation, the point ofmaximum hydrostatic tension, resulting in a reduction of thecohesive strength. 50If this reduction in cohesive strength dueto hydrogen is taken as ~a H' the expression for the thresholdin the presence of moist air becomes

Following Oriani and Josephic,51 it is assumed that ~aH isproportional to the local concentration of hydrogen at thepoint of highest triaxial tension (Cfj), and that this con-centration at equilibrium can be obtained from

a.VLlOH = QCH = QCo exp -- (6)

RoTwhere Co is the equilibrium concentration of hy~rogen in theunstressed lattice, a an unknown constant, V the partialmolar volume of hydrogen in iron (2 cm3/moI), 6 the hydro-static tension, Ro the gas constant, and T the absolutetemperature. Combining eqns. (5) and (6), it follows that

AKo=~. [aF-acoexp(~~~]. .... (7)

'The hydrostatic tension (6) is defined as the mean of thethree principal stresses ahead of the crack tip (axx, ayy, azz)'and can be approximated under conditions of plastic flowusing Hill's slip-line field equations for plane strain, i.e.

a = ~ (axx + ayy + azz) = al uy In [(I + ~) +~] (8)

where ay is the yield strength, x the distance ahead of thecrack tip, p the crack-tip radius, and al a coefficient (> 1)allowing for an increase in plastic constraint due to workhardening. Rewriting eqn. (8) iri terms of the plasticconstraint factor (ayymax/ay) ahead of the crack tip,41 itfollows that 6 can be approximated by

_ _ (max I)O-Q! 0yy /oY-2 ~Oy+2Q2K (9)

where ayymax/ay~ 1 + aiK/ay),** K is the stress intensity, a2an empirical constant =2 in-I/2, and at is taken to be equalto 2. Combining eqns. (7) and (9) and putting K =Kmax=M/I-R, where R = Kmin/Kmax' we have

AKo"'~ x

{OF - QCo exp [ V (Oy + 2Q2 f:J( q\l} (lO)

RoT I~R)J

** This expression for the plastic constraint factor was firstobserved by Hahn and Rosenfield52 for mild steel, but recentstudies53 have shown that it is also valid for high-strength low-alloysteels such as 4340.

Ritchie Influence of microstructure 379

Rearranging eqn. (10), assuming (V a2I1Ko)/(RoT(1-R) issmall, gives'

da ~2 p*dN 1T(aF- ~aI)2 2 (14)

predicts higher propagation rates .in impurity-embrittledstructures at all stress intensities, as has been experimentallyshown (Fig. 12). However, at near-threshold growth rates,larger effects of impurity-induced embrittlement are likelydue to reduced cohesion from both impurities and hydrogenatoms. For example, the presence of an impurity atom in agrain boundary could raise the local H concentration,due to an attractive interaction between impurity and Hatoms.S6 Furthermore, there is a possibility that, atchemically active sites (e.g. grain boundaries) on freshlyexposed surface at the crack tip, where H is initiallyadsorbed from the environment, the presence of impurityatoms in embrittled structures could raise the H concentra-tion by retarding the recombination of atomic H.sS Theseeffects are consistent with the observations that the influenceof prior' temper embrittlement on fatigue-crack growthincreases as the propagation rate is decreased (Fig. 12).It can be seen, therefore, that the influences of micro-

structure and load ratio observed on near-threshold fatigue-crack growth of high-strength steels in moist air can beusefully rationalized in terms of a model incorporating thecontribution to crack propagation from the environmentaleffect of H. This microstructural and mean stressdependence should, however, disappear at higher(intermediate) growth rates, when H permeation ahead of thecrack tip can no longer keep pace with the crack velocity. t

t Microstructural and load ratio effects can reappear at higher crack-propagation rates, owing to the occurrence of static modes offracture during striation growth. IS, 25, 26

maximum triaxiality. If crack closure effects are' considered,however, some influence of load ratio might be expected evenin vacuo. There is a further possibility that P* may be some-what related to the yield strength, through changes in thedislocation density, for example. In this instance the value ofMo would be sensitive to material strength in the absence ofhydrogen effects. However, data showing the dependence ofI1Ko on yield strength for tests in vacuo are not available atthis .time.The effect of prior austenite grain size is not so clear.

However, it is possible to rationalize the observation of lowergrowth rates in coarser-grained steel in terms of thediffusion of hydrogen atoms; to grain boundaries. Tien etal.s4 have postulated that the transport of H atoms from thecrack surface into the metal occurs, not by H diffusion, butthrough the motion of dislocations ('dislocation sweep-in').Thus the concentration of H atoms reaching a grainboundary will be greatest when the maximum plastic zonesize is of the order of the grain size.ss In coarser-grainedstructures the plastic zone size remains small compared tothe grain diameter until much higher stress intensities (in thepresent study M", 90MPa m 1/2 in the A 1200 structure,when maximum plastic zone size equals grain size), resultingin a reduced environmental influence.Finally, the presence of impurity elements in grain

boundaries can be considered to reduce the fracture strengthby an amount (1101)' dependent on the reduction (l1y) ingrain boundary surface energy (Yo) due to the solute, S6 Le.

( ~r)1/2a F - ~a I ~ a c 1 - r0 . . '. . . . . . • . . ( 13)

where °c is the theoretical cohesive strength. Mbdification ofeqn. (3) to allow for this lowered cohesion due to impurities,i.e.

Mo 0< J% rrp* :( (X~F.~:~~exp, (Ba~) .. 11 + (1 -R) . B . exp (Bay)J

... (11)

B' =V3/2n' V/RoT. 2a2" .:AtB=8xl0-4 (MPa)-I, and

where B= V/RoT, andam bient temperature,B'=5 x 10-2 (MPa ml/2)-I.Evaluation of the remaining parameters in eqn. (11) is

complex. The constant a from eqn. (8) is unknown at thistime, requiring experimental measurement. Furthermore, thesignificance of OF and P* at the threshold is also uncertain. OFrepresents the critical fracture stress in the absence ofenvironmental influence, and it has been suggested47 that, atthe threshold, this stress approach~s the theoretical cohesivestrength (oc~ 1/10 elastic modulus) acting across a distanceahead of the crack tip of P* '" so' where So is the cube root ofthe defect-free volume. For the present steel, assumingaverage dislocation densities at the crack tip between 1012and 1010 cm-2, So (and hence P*) should be of the order of100-1000 A. finally, the magnitude of Co will depend onwhether the hydrogen is internal (from charging experi-ments) or external as hydrogen gas or from moisture. For anexternal gas, Co is the hydrogen concentration in theunstressed lattice in equilibrium with a hydrogen gaspressure of PH2'which according to Sievert's LawS 1 is givenbyh - {3S P 1/2Co - L H

2•••••••••••••••• (12)

where SL is Sievert's parameter for H in a-Fe= 1·26 x 109atom H/atom Fe (torr)-l/2 and p is a multiplicative factor(~1), which allows for the fact that the hydrogen solubility inthe grain boundaries, where the fractures often occur, may. be considerably larger than in the normal lattice. Again themagnitude of Co remains unclear because of the uncertaintyin the value of p. However, the concept of hydrogen-assistedfracture during fatigue-crack propagation and the form ofeqn. (11) can provide a useful 'rationalization of fatigue-threshold behaviour in high-strength steels. Firstly, anyincrease in the hydrostatic tension (6) will markedly increasethe. local concentration of hydrogen and hence lower thethreshold (eqn. (7». This is achieved by (i) raising the yieldstress, and (ii) increasing Kmax or the load ratio R (eqn. (10».Both effects have been experimentally' observed in thepresent investigation (Fig. 9). Furthermore, at high yieldstrengths, the 0y term in the expression for a (eqn. (9»dominates the Kmax term, suggesting a smaller load ratioeffect than at low strengths where the °y and Kmax terms aremore comparable. This again is experimentally observed inthat the influence of load ratio on I1Ko increases as thestrength decreases (Fig. 9). Moreover, since the effect of loadratio (i.e. Kmax) arises from the environmental contribution,in the absence of an environment (Le. PH2oc Co = 0) the valueof Mo should be less affected by the load ratio. This isentirely consistent with existing near-threshold data for low-alloy steels,16 where the influence of load ratio on I1Ko'measured in air, was found to disappear when tests wereperformed in a vacuum. Thus, the effect of strength and loadratio on fatigue-threshold behaviour in moist air can bethought of in terms of an enhanced environmental influencearising from an increase in the hydrostatic tension.Additionally, increasing the load ratio will raise themagnitude of Kmax which in turn leads to a larger plasticstress gradient ahead of the crack tip. This provides a greaterdriving force for the transport of hydrogen into the region of

Meta'i Science August/September 1977

380 Ritchie Influence of microstructure

This has been experimentally observed for ,the mid-range ofgrowth rates.Utilizing the model to predict threshold behaviour

quantitatively requires principally' the assigning of values totwo parameters in eqn. (11), namely P*, which has beengiven some physical significance in terms of the defect-freevolume,48 and (a Co), which must be fitted empirically.Considering threshold data for steels ranging in strengthfrom 200 to 2000 MPa, best fit was obtained with(aCo)=3·5 x 103 MPa. Using this value, with aF equated tothe theoretical strength, the variation of ~Ko with yieldstrength from eqn. (11) is shown by the solid lines in Fig. 14.It can be seen that the exp~rimentally observed trend iscorrectly reproduced with all threshold values for steels lyingwithin the curves for P* = 300 and 1500 A, which isreasonable considering the approximate nature of theestimate for a (eqn. (9». The values ,ofP* are somewhat large,but still of the same order as those discussed by Weiss andLal48 for the threshold range. Further verification of thismodel must await more extensive data on near-thresholdfatigue-crack propagation, particularly in hydrogen-containing and inert atmospheres.

CONCLUSIONSFrom a study of fatigue-crack propagation in 300-M ultra-high strength steel tested in humid air, the followingconclusions can be made:

1. For the mid-range of growth rates (Regime B, Fig. 1),variations in microstructure and mean stress (load ratio) donot lead to significant changes in the crack-propagation rate.The exponent m in eqn. (l) was found to be between 2·5 and2·7, consistent with the ductile striation mechanism ofgrowth observed.2. At high growth rates (Regime C, Fig. 1), crack-

propagation rates become sensitive to microstructure andload ratio consistent with the occurrence of 'static' fracturemodes during striation growth. Optimum fatigue-crackingresistance in this region is achieved with high-toughnessmaterials.3. At low growth rates (Regime A, Fig. 1), significant

effects of load ratio and microstructure on the crack-propagation rates are observed; the maximum sensitivity toload ratio occurring in lower-strength material, and themaximum sensitivity to microstructure occurring at low loadratios.4. Increased near-threshold crack -growth rates and a

decrease in the threshold for crack propagation (~Ko) areseen as the load ratio (R) is increased, the value of ~Ko beinginversely related to R.5. Decreased near-threshold crack-growth rates are seen

as the strength of the steel is reduced, the value of ~Ko beinginversely related to the cyclic yield strength. Cyclic softening(and the use of low-strength steels) can thus be regarded asbe~eficial in improving resistance to very high cycle, lowgrowth rate « 10-6 mm/ cycle) fatigue-crack propagation.6. Decreased near-threshold crack -growth rates are seen

as the prior austenite grain size is increased, the value ofMoremaining unchanged. Thus coarsening the microstructureappears beneficial to near-threshold crack -propagationresistance.7. Increased near-threshold crack -growth rates and

significantly lower thresholds are observed in steel previouslysubjected to impurity-induced embrittlement during heat-treatment.8. A model for the threshold (~Ko) for fatigue-crack

propagation in steels in the presence of a moist airenvironment is developed based on a critical stress criterionfor growth modified by the effect of hydrogen from the

Metal Science August/September 1977

environment. The model is seen to rationalize the· experi-mentally observed trends of microstructure and load ratio onnear-threshold growth rates and the value of ~Ko'

ACKNOWLEDGEMENTSThe research was conducted under the auspices of the USEnergy Research and Development Administration throughthe Materials and Molecular Division of the LawrenceBerkeley Laboratory. The author acknowledges the awardby the Miller Institute for Basic Research in Science of aUniversity Miller Research Fellowship, and thanksProfessors E. R. Parker and V. F. Zackay for their supportand encouragement.

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'Mechanics and mechanisms of crack growth', Cambridge,April 1973, p. 264. (British Steel Corporation, SpecialSteels Div., Rotherham, 1974).

2. M. HEATON: Proc. lnst. Physics/Metals Soc. Conf. 'Mechanicsand physics of fracture', Cambridge, Jan. 1975, p.4/1.

3. H. H. JOHNSON and P. C. PARIS: Eng. Fracture Mech., 1968, 1,3.4. P. C. PARIS and F. ERDOGAN: J. Basic Eng. (Trans. ASME, n),

1963, 85, 528.5. N. E. FROST, L. P. POOK, and K. DENTON: Eng. Fracture Mech.,

1971,3, 109.6. M. KLESNIL and P. LUKAs: ibid., 1972,4, 77.7. M. KLESNIL and P. LUKAS: Mater. Sci. Eng., 1972,9,231.8. L. P. POOK: ASTM STP 513, 1972, 106.9. R. J. BUCCI, P. C. PARIS, R. W. HERTZBERG, R. A. SCHMIDT, and A. F.

ANDERSON: ibid., p. 125.10. P. C. PARIS, R. J. BUCCI, E. T. WESSEL, W. G. CLARK, and T. R.

MAGER: ibid., p. 141.11. R. J. BUCCI, W. G. CLARK, and P. C. PARIS: ibid., p. 177.12. H. KITAGAWA, H. NISHITANI, and J. MATSUMOTO: Proc. 3rd lnt.

Congr. Fracture, Munich, 1973, Paper V-444/ A.13. R. A. SCHMIDT and P. C. PARIS: ASTM STP 536,1973,79.14. J. L. ROBINSON and c. J. BEEVERS: Metal Sci. J., 1973, 7, 153.15. P. E. IRVING and c. J. BEEVERS: Metall. Trans., 1974, 5, 391.16. R. J. COOKE, P. E. IRVING, G. S. BOOTH, and c. J. BEEVERS: Eng.

Fracture Mech., 1975, 7, 69.17. J. MASOUNAVE and J.-P. BAILON: Scr. Metall., 1976, 10, 165.18. R. O. RITCHIE:J. Eng. Mater. Technol. (Trans. ASME, H), 1977,

99, in press (Lawrence Berkeley Lab. Rep. LBL-5496, Oct.1976).

19. A. J. McEVILY and J. GROEGER: 'Fracture 1977', Proc. 4th lnt.Conf. Fracture, Waterloo, Canada, June 1977, vol. 2.

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951.25. R. O. RITCHIE and J. F. KNOTT: Acta Met., 1973,21,639.26. R. O. RITCHIE and J. F. KNOTT: Mater. Sci. Eng., 1974, 14, 7.27. J. A. FEENEY, J. C. McMILLAN, and R. P. WEI: Metall. Trans., 1970,

1, 1741.28. W. ELBER: ASTM STP 486,1971,230.29. T. c. LINDLEY and c. E. RICHARDS: Mater. Sci. Eng., 1976, 14,

281.30. F. J. PITANIAK, A. F. GRANDT, L. T. MONTULLI, and P. F.

PACKMAN: Eng. Fracture Mech., 1974, 6, 663.31. P. E. IRVING, J. L. ROBINSON, and c. J. BEEVERS: Internat. J.

Fracture, 1973,9, 105.32. O. BUCK, J. D. FRANDSEN, and H. L. MARCUS: Eng. Fracture

Mech., 1975, 7, 167.33. P. E. IRVING, J. L. ROBINSON, and c. J. BEEVERS: ibid., 1975, 7,

619.34. T. T. SHIH and R. P. WEI: ibid., 1974, 6, 19.35. R. O. RITCHIE, G. G. GARRETT, and J. F. KNOTT: Int. J. Fract. Mech.,

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37. R. M. N. PELLOUX: Eng. Fracture Mech., 1970, 1,697.38. H. w. LIU: J. Basic Eng. (Trans. ASME, n), 1963,85, 116.39. s. D. ANTOLOVICH, A. SAXENA, and G. R. CHANANI: Eng.

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271.42. B. J. SCHULZ and c. J. McMAHON Jr: ASTM STP 499, 1972, 104.43. G. CLARK, R. O. RITCHIE, and J. F. KNOTT: Nature Phys. Sci.,

1972, 239, 104.44. H. OHTANI and c. J. McMAHON Jr: Acta Met., 1975,23,377.45. J. M. CAPUS: Rev. Met., 1959,56, 181.46. J: BARSOM, E. J. IMHOF, and s. T. ROLFE: Eng. Fracture Mech.,

1970, 2, 301.47. R. P. WEI and J. D. LANDES: Mats. Res. Standards, 1969,9,25.

Ritchie Influence of microstructure 381

48. V. WEISS and D. N. LAL: Metall. Trans., 1974,5, 1946.49. T. MISAWA: Corrosion Sci., 1973, 13,659.50. A. R. TROIANO: Trans. ASM, 1960,52,54.51. R. A. ORIANI and P. H. JOSEPHIC: Acta Met., 1974,22, 1065.52. G. T. HAHN and A. R. ROSENFIELD: Trans. ASM, 1966,59,909.53. A. T. SANTHANAM: Proc. 2nd Int. Conf. Mech. Behaviour

Materials, Boston, Aug. 1976, p. 1022.54. J. K. TIEN, R. J. RICHARDS, O. BUCK, and H. L. MARCUS: Scr.

Metall., 1975, 9, 1097.55. J. D. FRANDSEN and H. L. MARCUS: 'Effect of hydrogen on

behaviour of materials' (ed. A. W. Thompson and I. M.Bernstein), 233.1975: (Met. Soc. AIME).

56. c. J. McMAHON Jr, C. L. BRIANT, and s. K. BANERJI: 'Fracture 1977',Proe. 4th Int. Conf. Fracture, Waterloo, Canada, June 1977(ed. D. M. R. Taplin), vol. 1, p. 363 (Univ. Waterloo Press).

© THE METALS SOCIETY 1977

TEXTURE AND THE PROPERTIESOF MATERIALS

Proceedings of the 4th International Conference on Texture organized by ActivityGroup Committee I of The Metals Society and held at St Catharine's College andthe Department of Metallurgy and Materials Science, Cambridge, on 2-4 July1975.

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