fatigue - initiation of small cracks 1981

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S . J . Hudak, Jr.1Structural Behavior of Materials Department,Westinghouse R&D Center,

Pittsburgh, Pa. 15235

Small Crack Behavior and thePrediction of Fatigue LifeIt is becoming increasingly evident that an understanding of incipient microcrackingan d growth of small cracks is essential to the development of improved predictionsof the fatigue life of structures. Information on the threshold and kin etic propertiesof small cracks is reviewed and critically discussed. It is shown that the use ofconventional fracture mechanics concepts tocharacterize small cracks results inbehavior which differs from that of large cracks this difference is du e to abreakdown of underlying continuum mechanics assumptions. Methods to incorporate sm all crack behavior in fatigue life predictions are also considered. Inthese predictions, the importance of separately treating crack in it iation and crackgrowth and of accounting for small crack behavior and plasticity effects (particularly for notched members) is demonstrated.

IntroductionThe concept that fatigue is not a sudden event, but ratherone which occurs by a progression of damaging events, wasadvanced nearly 60 years ago [1,2]. Nevertheless, dueprimarily toexpediency in testing, most of the fatigue datawhich have been generated over the years have used cycles-to-failure as the measure of fatigue resistance. Mechanisticstudies have provided some information on the developmentof crystallographic slip, incipient microcracking and earlygrowth of small cracks, however, except for a few notablestudies [3,32], most of this information has been in the formof qualitative descriptions. More recently, with the advent offracture m echanics, much effort has been devoted to the studyof fatigue crack growth. However, in compliance with underlying continuum mechanics assumptions, most of thesedata have been generated using relatively large crack sizes.Thus, there currently exists a lack of systematic, quantitativeinformation on the initiation and growth of small cracks.The need to understand incipient m icrocracking and growthof small cracks is becoming increasingly recognized and recentefforts to systematically examine these phenomena have beenincreasing. Such understanding is essential to developingmaterials with improved resistance to fatigue, to selecting theproper material for a given application, and, perhaps mostimportantly, to formulating improved methods of predictingfatigue lives of structures by combining crack initiation and

crack growth concepts. With respect to the latter, elucidatingthe nature of small cracks is fundamental to resolving thefollowing issues, both old and new:1) Formulating an improved definition of crack initiation.2) Determining the relation between the smooth bar en-

Currently, Senior Research Scientist, Department of Materials Sciences,Southwest Research Institute, San Antonio, Texas 78284.Contr ibuted by the Materials Division for publication in the JOURNAL O FENGINEERING MATERIALS AND T E C H N O L O G Y . Manuscript received by theMaterial Division, June 1980.

durance limit, Aa e, and threshold stress intensity for fatiguecrack growth, AKlh.3) Resolving apparent size effects and the discrepancybetween the elastic stress concentration factor, K,, and thefatigue reduction factor, Kf.4) Explaining nonpropagating cracks at notches.5) Properly combining crack initiation and crack growth topredict the total fatigue life, particularly for notched members.The purpose of the present paper is to review and interpretinformation on the initiation and early growth of smallcracks. Whenever possible, this information is discussed interms of the above issues. First, microstructural features ofcrack initiation are treated briefly. With this as background,subsequent treatment will focus on aspects of small crackbehavior which differ from large crack behavior and on thecomplex problem of incorporating small crack behavior andplasticity effects into the prediction of cracking from notches.

Microstructural Aspects of Crack Initiation and EarlyGrowth

The progressive nature of fatigue damage is clearlyillustrated by Hunter andFricke's systematic microscopicstudies of smooth specimens subjected to completely reversedbending [3-6]. The development of slip, incipient cracking andgrowth of microcracks was monitored using plasticreplication techniques and etching. Figure 1 shows the onsetof various microscopic events observed during the testing ofan unalloyed aluminum of 99.5 percent purity [3]. Theseresults, expressed in the form of S-N curves, show that slipcan occcur very early in the fatigue life and that it subsequently increases in intensity and amount until a saturationlevel is achieved. In this relatively soft material, incipientcracking is difficult to resolve because of extensive surfaceroughening developed by slip. Relatively large cracks areobserved subsequent to slip saturation and these finally causethe specimens to fail.2 6 / V o l . 103, JA NUA RY 1981 Transac t ions o f the ASME

Copyright 1981 by ASME

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5500

CyclesFig. 1 Relation between various stages of progressive fatigue damagein a pure aluminum (D D1 S-0) sheet (reference^])

Hunter and Fricke also examined structural aluminumalloys and found them to exhibit somewhat differentmicroscopic damage than did pure aluminum. Figure 2 givesS-N type relations corresponding to the first observation ofcracking (typically, crack depths of 0.0025 mm or less) and tofailure in a 6061-T6 aluminum alloy [5]. Although slip mayhave preceded incipient cracking, it was not resolvable, indicating that it was much less extensive than that which occurred inpure aluminum.Forsyth proposed that the mechanism of crack initiationand growth occurs by two physically different processes,designated Stage I and Stage II, which proceed as follows[7-9]. Stage I cracking results from dislocation motion alongthe slip plane and is determined by the magnitude of theresolved shear stress on the slip plane. Thus, cracks formpreferentially on those planes which are closely aligned andwhich areoriented in themaximum shear stress directions. Inmany materials, cyclic loading then causes intrusions andextrusions to form in the slip band s [10]. These microscopicnotches provide the nucleation sites for crack initiation. StageI cracks generally continue growing along the slip plane andexhibit fracture surfaces which are primarily featureless. Inpolycrystalline metals, theStage I cracks generally extend foronly a fewgrain diameters before crack propagation changesto Stage II.Stage II cracks grow on planes which are normal to themaximum principal tensile stress operating on the compon ent.Their fracture features generally involve microscopicstriations, each of which corresponds to a loading cycle; thusthey are often distinguishable from Stage I cracks.The above slip initiated mechanism is capable of occurringin many systems, however, often it is superseded by othermechanisms when more favorable crack nucleation sites areavailable. Recall, for example, that the 6061-T6 aluminumalloy examined by Hunter and Fricke initiated microcrackswith little or noprior slip deformation (Fig. 2). More recently,Morris et.a l. used scanning electron microscopy toshow thatcrack initiation in2219-T851 aluminum alloy occurs at brittleintermetallic inclusions at or near the specimen surface (11).Microcracks initiated either at the matrix-inclusion interfaceor in the inclusions themselves andpropagated asnon-crystal-lographic, Stage II cracks. Pearson found similar results intwo other comercial aluminum alloys [12]. Yokobori and hiscollaborators found that non-metallic inclusions were thepreferred crack initiation sites at the surface of a mild steel[13] and a tempered martensitic steel [14]. Initiation alsooccurred, although much less frequently, along prioraustenite grain boundaries, at packets of martensite plateletsand at precipitates along packets of martensite platelets.

35000

3000U

25000

~ 20000

15000 -

10000

-

_-

1 T

First Crack

1 I

\ p

1

1 cW\o

1

! 1

-Fa i lu re

-

-

10 10 10 10 10

225200175

150125 !

100

; 75

10 910 10Cycles

F ig . 2 Relation between the first observable crack (0.0025 mm depth)and failure in a 6061-T6 aluminum alloy (reference [5])

Grain boundaries are also known to serve as primaryinitiation sites under environmental and/or creep conditionswhere selective attack occurs because of chemical segregationfollowed byenhanced oxidation at theboundaries [15].Thus, in commercial alloys, there exist many opportunitiesfor Stage I cracking from slip band formation tobe precludedby direct Stage II cracking from more favorable nucleationsites. Furthermore, even in the absence of these favorablesites, it has not been demonstrated that Stage I cracks formunder themultiaxial stress states which exist at notches wherefatigue cracks inevitably form in engineering structures. Thissummary of microstructural aspects of crack initiation andearly growth serves to emphasize the importance of notchessince even in the case of fatigue of smooth specimens thecracks are shown to initiate at the "metallurgical notches"formed by intrusions or extrusions or present as inclusions.Unique Character of Small Cracks

A number of recent studies have demonstrated that smallcracks behave differently than large cracksor at least thisappears to be the case when small cracks are analyzed usingconventional fracture mechanics concepts. For purposes ofdiscussion, it is convenient to separate the unique characteristics of small cracks into the following two categories: 1)threshold stress or stress intensity considerations, includingthe relation between thesmooth bar endurance limit, Aae, andthe threshold stress intensity for fatigue crack growth, AA',/,,and 2) kinetics of small crack growth, particularly comparingthem to kinetics of large crack growth. Each of thesecategories is treated separately in this section. This information is then used in the following section on the morecomplex problem of the effect of small cracks on the fatiguelife of notched members.

Threshold Stress and Stress Intensity. Traditionally, theproblem of fatigue has been approached by empiricallydetermining the nominal stress range (or amplitude) whichcould be applied to either a smooth or a notched specimenwithout causing failure for an indefinite num ber of cycles. Insmooth specimens, this stress range is termed the endurancelimit, ACT,,, and is operationally defined in terms of a givennumber of applied cycles, typically ranging from 107 to 109cycles. More recently, the application of fracture mechanicsto fatigue has led to the empirical establishment, in crackedmembers, of a threshold stress intensity below which nodetectible crack propagation occurs, AKlh. Here anoperational definition, based on the AA' correspon ding to arate of 10~10 m/cyc le, has recently been established [16].From its inception, the AKth concept has caused aphilosophical conflict with that of the smooth bar endurancelimit. Measurement of a AAT,,, establishes a regime of cracksizes and applied stress ranges for which further crack ex-J ou rna l of Engineer ing Mater ia ls and Techno logy J AN U AR Y 1981, Vol . 103 /27



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tension does not occu r. For the case of a wide plate containinga central , through-crack of length "2a," or an edge-crack oflength " a , " this regime is defined byA(rfwa


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a, mm1.0 10.0

0J i o ta

^ 1 1^ \ ^ A K - A t r ^ T r a

^ A K A a V T T l a t y ~ " % k .

0=0.24- mm

EXPERIMENTAL RESULTSG40. l l STEEL R - - IPREDICTION

1 l

1

1 A I T . = constant

1

1

2 ~-

"

\ ^

0.10a, inF i g . 4 Comparison of experimental and predicted values of thefatigu e thresho ld stress as a function of crack size (reference [19])

Log AK, MN m u nits0.2 0. 4 0. 6 0.8 1.0 1.2 1.4 1.610

10 -

n - 5

1 0 ^ h

-7

1 1 17 1 I

Long Through Section Cracks>0 . 254 mmlO. 01 in) L on g^

/// /7 ^ /

//

, / , ,

'/ ~~':

J/ // '/ /A

// Short Surface Cracks/ 0. 006 m m - 0 . 5 mm(0. 00025 in. -0 .0 2 in. ) ":Deep

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-6

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3. 0 3. 2 3. 4 3. 6 3. 8 4. 0 4. 2 4. 4 4. 6Log AK, lb in. unitsFig . 5 Fatig ue crack growth kinetics for long and short cracks in a BSL65 aluminum alloy (reference [12])

U sami has recently suggested that the physical interpretation of equation (5) is that AKlh corresponds to aconstant fatigue plastic zone size [21].Kinetics of Small Crack Growth. Several studies have beenmade of the crack growth kinetics of small fatigue cracksusing either linear elastic or elastic plastic fracture mechanicsto describe the mechanical "driving forc e."Pearson (12) examined the initiation and subsequentgrowth of short cracks (0.006 mm < a < 0.25 mm) inaluminum alloys BS L65 (490 MN/m 2 yield strength) andDTD 5050 (540 MN/m 2 yield strength). Smooth taperedspecimens were loaded under linear-elastic conditions usingcantilever bending. Resulting crack growth rate data wereanalyzed using linear-elastic fracture mechanics and are givenin Figs. 5 and 6 where they are compared with data for largecracks (a > 0.25 mm). Pearson concluded from these results

-3

-A

- 5

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-7

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-

Log AK, MN m units0.6 0. 8 1.0 1.2 1.4 1.6

i i i i ' I -

/" Long Through Section Cracks y>0 . 254 mrnlO. 01 in. ) Long /

-y 1-7

/r /- /,/ ,

// // // /A :/ / Short Surface Cracks/ 0 . 012 m m - 0 . 5 mmf 10. 0005 in. -0 . 0 2 in. )deep

.-

i i i i i i

_ 10

-4

10 ' 7

1 0 -8 -

- 6

10 3. 0 3. 2 3. 4 3. 6 3. 8 4. 0 4. 2 4. 4 4. 6Log AK, lb in unitsF i g . 6 Fatig ue crack growth kinetics for long and short cracks in aDTD 5050 aluminum alloy (reference [12])

A K , M P a ^ / m50 IOO 20 0 4O0

-

*J*

D r> a ' . ''. J

Otf* *A 9SB*** 0 0

0

00

0

0*90?

SOrG40. l l STEEL P . - - I

SHORT CRACKS a s I mmo AO" = 60 KSI !4l4MPa)o A O " . 4 9 K S I ( 3 3 8 M P a )A A O " - 4 8 K S I ( 3 3 I M P a )o A C T " 4 1 KS I ( 2 8 3 M P a )o i l - 3 5 K SI ( 2 4 I M P a) LONG CRACKS

A K = A c y f a f (a )I

-

-

IOOAK KS I y i n "F i g . 7 Long and short fatigue crack growth kinetics in a G40.11 steel(reference [19])

Journal of Engineering Materials and Technology J AN U AR Y 1981, Vol . 103 /29wnloaded From: http://materialstechnology.asmedigitalcollection.asme.org/ on 07/30/2013 Terms of Use: http://asme.org/terms
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id

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SHORT CRACKS a S 1 mmo A C . 6 0 K S I ( 4 1 4 M P a )o A 0 " 4 9 KS I ( 3 3 8 M P a )a i f f . 4 8 K S I ( 3 3 1 M P o)o A C T - 4 1 K S I ( 2 8 3 M P a )o A C T . 3 5 K S I ( 2 4 1 M P o ) LONG CRACKS

K = Aa y i 7 - (a + f 0 ) f ( a )

1

-

_

A J . m - M N / m 20 . 0 0 1 . 0 1

e,- E

10 100AK KSI y in "F i g . 8 Long and short fatigue crack growth kinetics in a G40.11 steelanalyzed using / 0 (reference [19])

that microcrack growth kinetics are faster than macrocrackgrowth kinetics.4Similar results were obtained by El Haddad et.al. on a CSAG40.11 steel at R = - 1 using sheet specimens containingsmall edge cracks (19). These results are com pared with longcrack data on the same material and, again, show themicrocrack kinetics to be faster, as shown in Fig. 7. H owever,it is interesting to note that a reanalysis of these data usingequation (3) and the material constant l0 which was discussedin the previous section provided an improved correlationbetween the small and large crack data as shown in Fig. 8. Thesame value of l0 which was determined from small crackthreshold considera tions, equation (4) and Fig. 4, was used inthis reanalysis of the kinetic data. The utility of this simpleapproach to model effects which are presumably related to thebreakdown of continuum mechanics is remarkable, eventhough it is not physically un derstood.The remainder of the relevant data on the kinetics of smallcrack growth were obtained using specimens which wereplastically strained, thus elastic-plastic fracture mechanicsanalyses were required to interpret the results. Apart fromproviding a means of correlating small crack data from thesespecimens, these elastic-plastic methods are significant in thatthey are relevant to the important problem of the behavior ofsmall cracks at notches. Here, elastic-plastic fracturemechanics considerations are necessary since cracks are often

A P P R O X A 9 0 0 . 0 4B D 0 . 0 2* A 0.012* O 0.009# 0 .005

O P E N S Y M B O L S a < 0 . 0 0 7 i n .( O . I 7 7 8 m m )

- 4 v -

I 10 I0 2 I 0 3A J , i n . - l b / i n . 2F i g . 9 Large and small fatigue crack growth kinetics obtained underplastic loading and analyzed in terms of AJ (reference [22])

A J m - M N / m zo .o i

A 5 3 3 B S TE ELDATA FROM 10 TES TS, IS CRACKS

SCATTERBAND FROMLARGE SPECIMENS

4 It should be noted, however, th at equatio ns 2 thru 4 in reference [12] for thestress intensity solutions for various crack configurations are incorrect. I t isunclear whether these errors are included in the data of Figs. 5 and 6.

l b / i n 2F i g . 10 Large and small fatigue crack growth kinetics obtained underplastic loading and analyzed using AJ an d l0 (reference [20])

completely imbedded in the notch plastic zonea problemwhich is discussed in the next section.Dowling measured th e initiation and growth of small cracksin axialiy loaded smooth specimens of A533B steel subjectedto completely-reversed, strain cycling [22]. Cracks wereinitiated at about 10 percent of the specimens' fatigue life;subsequent crack growth from 0.08 mm cracks to failure ofthe 0.76 cm-diameter specimens was monitored using plasticreplication techniques. Growth rate data were analyzed usingA/, based on J integral concepts, which was previously3 0 / V o l . 103, JAN UARY 1981 Transac t ions o f the ASME

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A K ff , MPov'm0.2 0.3 0.4 0.5

AK ,. ksiVTrlF i g . 11 Fatigue crack growth kinetics of microcracks (25-100 pm)analyzed in terms of the effective stress intensity range, AK e )( , basedon measured crack opening loads (reference [28])

successfully applied to growth of large cracks under elastic-plastic conditions [23]. Values of AJ were determined fromthe measured cyclic stress-strain response of the mater ialusing an approximate / -analysis for the surface cracked,cylindrical specimen.The resulting crack growth kinetics expressed interms of AJare given in Fig. 9. Mo st of the data for the various appliedstrain ranges correlate well with each other and with largespecimen, i.e., large crack data. Note, however, that datacorresponding to crack lengths of less than about 0.18 mmconsistently exhibit faster kinetics. A subsequent reanalysis ofthese data [20], using El H a d d a d ' s l0 correction is shown inFig. 10. Again , as in the case of the previously discussedlinear-elastic results, this simple correction results in asignificant improvement in the correlation between small andlarge crack data.

Ki tagawa, et al. [18] have conducted similar experimentsusing low cycle fatigue specimens subjected to plasticstraining under both tension and bending . Al though, in thisstudy, a plastic stain intensity factor, AKep was utilized toaccount for plasticity effects. The value of AKtp was computed by simply substituting the plastic strain range, Aep, forACT in the l inear elastic stress intensity expression to giveAK [p=At p^ -w a (6)

w h e r e Aep is g iven byAe p=y(Ao)" (7)

Equat ion (7) represents the materials ' cyclic stress-strainresponse and thus is a measured proper ty . However , an inconsistency exists in the above approach since the form ofequat ion (6) is based on l inear-elastic assumptions whileequat ion (7) is in the realm of cyclic plasticity. N evertheless,Ki tagawa, et al. claim that this approach eliminates thedependence of the cracking kinetics on applied stress level andload ing mode ( that is, rotating versus in-plane bending).

-Tneroetical Stress to Form Crackat Notch R oot =A o e /K (

Complete Fracture

No Cracks Formed

Non-propagating CracksFormed at Notch Root

250

200

150

100

50

07 9

K tFatigue limit based on stress to initiate crack at notch rooto PlateD Round BarFatigue limit based on complete fracture Plate= Round bar

F i g . 12 Fatigue threshold stress versus K, for plate and cylindricalmild steel notched specimens tested under completely reversed tension-compression loading (reference [33])

U nfor tunately , resu l ts analyzed in this manner cannot becompared with large crack data.Crack closure considerations have thus far not beenment ioned . However , th is phenomenon is known to accompany fatigue crack growth of large cracks [24] and hasbeen proposed as a major factor in determining load ratioeffects, particularly at low growth rates {da/dN < 10~5mm/cycle) where it appears to become increasingly importantdu e to the ever decreasing magnitude of the applied stressintensity range [25-27]. It follows that crack closure should beim p o r t an t in microcrack propagat ion in the thresholdreg imeperhaps, more so than in the case of large cracks.Recent data of Morris and Buck tend to support this view[28]. They measured the growth of very small , surfacemicrocracks in miniature flexural specimens of aluminumalloy 2219-T851 using the scanning electron microscope. Sincecrack growth measurements were made on thegrain size level,

specifically from 25 to 100 txm, all cracks were in the sub-cont inuum reg ime. It was found that crack growth rates fromseveral different specimens could only be correlated whencrack closure was accounted for by using the effective stressintensity range, AKef!, as shown in Fig. 11. Crack openingdisp lacement measurements at the t ips of growing cracks weremeasured and used to estimate closure stresses and AKiff. Anat tempt wasm ad e to account for the non-cont inuum aspectsof the problem by incorporat ing a model for the crack-tipplastic zone which depends on grain size and the relativeposition of a crack in a grain. Admittedly much more effort isneeded to develop the mechanics of the non-cont inuum.Nevertheless, these results indicate the importance of crackclosure in determining the growth of very small cracks in theth reshold reg ime.B e hav ior of Smal l C r a c k s at N o t c h e s

Preceding sections discussed the microprocesses which giverise to crack init iation and defined the threshold and kineticcharacteristics of smal l cracks . Thechallenge which remains isto apply this information in such a m an n er to improve ourability topredict the total fatigue life of s t ructures .The importance of notches inproviding a preferred site forinit iation of cracks was indicated in previous discussion.Virtually all engineering structures contain notches in oneform or another . Moreover , themater ial at thenotch root willnearly always undergo plastic deformation. Thus, improvedmethods having general uti l i ty for predicting fatigue livesJournal of Engineering Materials and Technology JANUARY 1981, V o l . 103 / 31



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should contain both small crack characteristics and plasticityconsiderations. Both of these aspects are discussed in thissection.Nonpropagating Cracks and Related Effects. The fact thatcracks can init iate at notches, grow for some distance, andeventually become nonpropagating was first suggested byPhillips, et al. [29]. This interesting aspect of fatigue ofnotched members was subsequently confirmed by Frost andco -wo rk er s wh o , t h ro u g h ex t en s iv e m eta l l o g rap h icexaminations, showed that cracks could remain unchanged

for millions of cycles after having initiated and grown asmicrocracks [30-34], Conditions of notch geometry, nominalstress range and mean stress corresponding to no crackinitiation, nonpropagating cracks and complete failure weredefined. Figure 12 provides a typical summa ry of such information in terms of the long life fatigue strength of notchedmild steel specimens as a function of the elastic stress concentration factor, K, . The key points i l lustrated by these dataare as follows:1) the existence of a lower limiting alternating stress, ACT,,,,required for complete specimen failure, which is independento f # , .2) the existence of a critical value of K, above whichnonpropagating cracks can occur .3) the alternating stress required to predict the initiation of

cracking in a notched m embe r is given by Ao e IK,.These facts serve to clarify some long misunde rstood behaviorin fatigue of notched members. For example, much effort hasbeen expended to experimentally determine values of thefatigue strength reduction factor, K f, which is defined by

smooth bar endurance limit, ACT.K f = (8)notch bar endurance limitFurthermore, much discussion has centered on the fact thatKf < K t, this difference becoming larger as K, increases.Many hypotheses have been proposed to rationalize thisdifference and equations have been developed to predict Kffrom K, , most of these relying on an empirically determinedsize factor which has been thought of as being related to theminimum distance over which a stress gradient can exist in ag iven m ater ial .However, this apparent discrepancy between K, an d Kf isclearly unde rstand able in terms of the data of Fig. 12 and thethree points cited above [34]. Specifically, this difference isdue to the fact that Kf is defined in terms of specimen failureand no account is take n for the fact that n on-prop agatingcracks occur. When fatigue strength of notched members ismeasured in terms of actual crack init iation, this propertybecomes predictable from a knowledge of ACT,, and K t. Th u s ,the apparent differences between K, and Kf stem from notseparately treating crack init iation and crack propagation.

Final comments on the reason for the occurrence ofnonpropagating cracks are in order. A relatively simplepossible explanation is provided by the previously discussedthreshold conditions for small cracks. As il lustrated in Fig. 3,small cracks are capable of growing below the AKlh valuedefined by large cracks. Thus, once init iated, a small crackwill propagate for some distance until the combination of i tssize and local stress associated with the notch field causes it toarrest at the long crack AKth value.It follows that the horizontal l ine of Fig. 12, whichcorresponds to the lower l imiting stress required for completespecimen failure, is defined by ACT,,, as previously given inequation (2)

Notch Root Radius, mm

0. 90. S

S 2 0. 70. 60. 5

, ^ I 0.40 . 30 . 20. 1

0 *

Failure Defined as a Crack Length of 5 mm \A No In i t ia t ion a t 2x 10 Cycles Pre-existing Fatigue Crack.

ACT, , AK (2)/ ( a ) V i r aIn a ddition, since the lower curve of Fig. 13 is given by Aa lh =

10 10 J 10Notch Root Radius, in.Fig. 13 Effect of notch root radius on the fraction of the total fatiguelife spent in ini tiatin g a crack (reference [35])

Aae/Kt, the point of divergence of these two curves, that is,the critical K, for the occurrence of non-propagating cracks isgiven by AoJ(a)yJira (9)T h u s , nonpropag at ing cracks are expected w hen

K,>K,(NVC) (10)Equations (9) and (10) define the notch geometries for whichnonpropagating cracks are expected to occur in a givenmaterial , that is, for specific properties, Aa e and AKlh. Theseequations are not hampered by non-continuum effects sincethey are based on equation (2) and the long crack AK ,h value.However, equations (9) and (10) will only provide reasonablepredictions when the non-propagating crack lies outside of thenotch plastic zone since equation (2) implicidly assumes thatlinear elastic conditions prevail .

Incorporating Small Crack Effects in Fatigue LifePredictions. Previous discussions have established that acomplete treatment of fatigue must include considerations ofboth crack init iation and crack propagation. Thus, i t isessential to delineate these features in any theoretical orexperimental study of fatigue, regardless of whether theprimary goal is mechanistic understanding or engineeringpredictabili ty. This concept is formally expresed by thefollowing simple relation:N f = Ni+Np (11)

where Nf = cycles to failureN; = cycles to initiate a crackNp = cycles to propaga te the crackFor notched members, the relative contributions of crackinitiation and crack propagation to the total fatigue life willdepend on the K, or more precisely on the notch root radius,

p. The latter is of fundamental importance since i t controlsthe notch stress-strain gradient and thereby the notch plasticzone. The variation of the ratio of init iation life to total l ife(Nj/Nf) with p is i l lustrated by the data of Allery andBirkbeck [35] in Fig. 13. For small p values, Nj/Nf is alsosmall indicating that the total fatigue life is dominated bycrack propagation. In contrast at large p values, Nj/Nf islarge indicating that the total fatigue life is spent in initiating acrack at the notc h. In addition, for a given p value, therelative contributions of crack init iation and crackp ro p ag a t io n wi l l d ep en d o n t h e ap p l i ed s t r es s32 /Vo l . 103, JANUARY 1981 Transactions of the ASME



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C R AC K T i P P L AS T I C I T Y

/ N O T C H P L AS T I C I T Y BO U N D AR Y

AK, MPa yirT60 80 100

H U H I T T r T T T T f r r n T i T r n r r r T T i T ^ ^F i g . 14 Grow th of a sma ll crack at a notch and associate d elast ic andplast ic s tress-strain f ields (reference [43])

rangeinitiation being relatively more important at low stressranges corresponding to the long life regime.The practical implication of the above two factors is thatthe relative importance of crack initiation and crackpropagation will depend on the geometry of the structure aswell as the loading history. This fact needs to be recognizedfor proper selection of both a design philosophy and amaterial. The latter is affected by the above concept sincegood resistance to fatigue crack propagation cannotnecessarily be taken to imply good resistance to crackinitiation, and vice versa.Although equation (11) is conceptually simple, its application is often difficult primarily because of the followingtwo factors: 1) the breakdown of continuum concepts forsmall cracks, and 2) the effect of local plasticity on crackgrowth from the notch. This latter complexity is schematicallyillustrated in Fig. 14. Here, a crack of length, /, is growingfrom a notch of depth, D, and roots radius, p. The notch iscontained in a large body which nominally behaves elasticallywhen acted upon by an applied stress a. Associated with thenotch are two distinct stress-strain fields, the larger is elasticwhile the smaller is plastic.Again, referring to Fig. 14, the initiation life can be obtained using the local strain approach which is thoroughlydescribed in the literaturefor example, see references [36]and [37]. This method accounts for local plastic deformationat the notch, local means stresses, as well as alterations inmaterial properties due to cyclic loading. Furthermore, itsutility has been dem onstrated for variable amplitude loading.In the other extreme, when / is large compared to p, crackpropagation can be treated in a straightforward manner usingfracture mechanicsfor example, see references [38] and[ 3 9 ] . In fact, since linear-elastic stress intensity factorsolutions are available for cracks eminating from notches( 4 0 ) , crack propagation can be computed for / values withinthe elastic notch field. However, it should be noted that thefracture mechanics treatment of crack propagation is not aswell established for variable amplitude loading [41] as is thelocal strain treatment of crack initiation under variableamplitude loading.

The remaining crack propagation life, namely, thatassociated with / values of less than the notch plastic zone andwith / values on the order of microstructural features of thematerial, is exceedingly more difficult to treat.O ne approach is to avoid the small crack and plasticityproblems by operationally defining growth in this regime tobe included as part of crack "initiation." Dowling hasrecently proposed procedures for applying this approach and

HoxlO"5)

-(2xl0~5]

EE 2x10-- ( I x i c r 5 )

I 0 - - ( 4 x l 0 "6 )

( 2 x l 0 -6 )

CENTRAL CRACKCIRCULAR HOLE, P/t -0136CIRCULAR HOL E, p/b '0 -22 7ELLIPTICAL H0LE,/>U9mmACT-269 MPa (39KSI1R IS 40.11 STEEL

I I20 40 50 60 70 80 90 100AK, KSI v / i i T

F i g . 15 Fat igue c rack growth k inet ics o f smal l c racks eman at ing f romvarious notch geometries (reference [20])

has demonstrated limited success in predicting the fatiguelives of notched members [42].An alternative approach is to attempt to account for smallcrack and plasticity problems through appropriate analysis,thereby directly computing the small crack growth contribution. Hammouda and Miller [43] have outlined one suchapproach but its utility has not been tested. Recently, ElHaddad, et al. have demonstrated some success at handlingthe problems using this general approach [20]. The smallcrack problem was treated by using the previously discussed l0correction of equation (4). Notch plasticity was treated usingNeuber's rule to estimate the local plastic notch field and anapproximate /-integral analysis to define AJ. This analysiswas applied to experimental data on two steels for growth ofsmall cracks from notched specimens having various notchroot radii and subjected to various applied stress levels.Typical results are shown in Fig. 15 in terms of crack grow thrate simply expressed as a function of elastically calculatedstress intensity range . G rowth ra te kinetics for cracks near thenotch were faster than those for large through-cracks. Theoverall trend in the small crack kinetics also appeared to bedependent on the local notch geom etry. Subsequent reanalysisof these and other results, in terms of AJ as outlined above,resulted in a reasonable correlation of data from a variety ofnotch geometries and applied load levels as shown in Fig. 16.

The initial success of the above approach warrants itsfurther study and development. The approach is physicallyappealing since it explicitly handles the two major problemsassociated with the growth of small cracks from notches,namely the unique behavior of small cracks and local notchplasticity.Summary and Conclusions

1. When analyzed using conventional fracture mechanicstechniques, small fatigue cracks behave differently than dolarge fatigue cracks (for example, see 2. and 3. below). The

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yEAJ , M P a y m50 100 200

ELASTIC LONGCRACK SCATTERBAND

ELLIPT ICAL NOTCH K ) _ 5- A C T - 5 5 KSI ( 379 M P a)- A C T - 4 5 K SI ( 31 0 M P a)l A 0 - - 3 9 KSI ( 269 M P a)I A O - - 3 3 . 5 KSI (231 MPa)ELLIPT ICAL N O T C H j j - 4 . 8m mK( 2* A C T - 39 KSI C" 7,9 mm

K,-3CIRCULAR NOTCH ACT. 45 KSICIRCULAR N O T C H C - 4 . 8 m m

K( - 3. ACT.56 KSI (386 MPa) ACT-39 KSI (26 9 MPa) ACT-33.5 KSI (231 MP a)CIRCULAR NOTCH S * . 0 ; 2 0

ACT- 70 KSI (48 3 MPa) ACT. 60 KSI (414 MPa)

0 4 0 . 1 1 STEEL R - - IC= Notch Depth

ICT1

I0"K) 100y i A J . KSI,/in

Fig. 16 Fatigue crack growth kinetics of small cracks emanating fromvarious notch geom etries and analyzed using AJ and /0 (reference [20])

primary reason for this difference is thebreakdown of underlying continuum mechanics assumptions.2. Small cracks can grow at crack sizes and applied stresslevels which are below those predicted from large crack AKlhdata.3. Small cracks grow at faster rates than those predictedfrom large crack da/dN- Mf data.4. The unique behavior of small cracks can be accountedfor in analysis by adding aconstant length, l0, to the physicalcrack size. The term /0 is a material property which can bedetermined from o ther measurable prope rties as follows

* - - L [ ^ ] iK L Aff e JAlthough no physical interpretation of l0 currently exists, this

approach provides reasonable predictions of small crackthreshold and kinetic behavior (namely, 2. and 3. , respectively).5. In order for fatigue life predictions to be of generalutility they must separately treat crack initiation andcrackgrowth and include both small crack behavior and plasticityconsiderationsparticularly at notches where fatigue failuresinevitably originate in engineering structures.Acknowledgments

I wish toacknowledge the many enlightening discussions,on various subjects contained in this work, with N. E.Dowling of the Westinghouse R&D Center.

The work wassupported by theWestinghouse TechnicalO perations Division - Turbine Development.

References1 U p t o n , G. B., The Structure and Properties of the More CommonMaterials of Construction, J. Wiley, N.Y., 1st Ed. , 1916, p. 112.2 M oor e , H. F. , andVer, T., "A Study of Slip L ines, Strain L ines, andCracks in Metals U nder Repeated Stre ss," Bulletin No. 208, Engr . Exp.Sta t ion, U niv. of Illinois, June 3, 1930.3 Hunte r , M. S., and Fr icke , W. G., Jr., "Meta l lographic Aspec ts of

Fatigue Behavior ofA l u m i n u m , " Proc. ASTM, Vol. 54, 1954, pp. 717-736.4 Hunte r , M. S., andFr icke , W. G., Jr. , "Effec t ofAlloy Content on theMeta l lographic Changes Accompanying Fa t igu e ," Proc. ASTM, Vol. 55,1955,pp . 942 - 953 .5 Hunte r , M. S., andFr icke , W. G., Jr. , "Fa t igue Crack Propaga t ion inAlum inum Al loys , " P r o c M S r M , Vo l . 56 , 1 956, pp . 1 03 8 -1 050.6 Hunte r , M. S., and Fr icke , W. G., Jr., " C r a c k ing of Notch FatigueSpec imens," Proc. ASTM, Vol. 57,1957, pp. 643-652 .7 Forsyth, P. J. E., "A TwoStage Process of Fat igue Crack Growth,"Proc. of the Crack Propagation Symp. , Cranfield, England, Vol. 1, 1961.8 Forsyth, P. J. E., "Fa t igue Damage and Crack Growth in AluminumAlloys, "Acta Met., Vol. 11 , 1963 , pp. 703-715.9 McEvily , A. J., Jr. and Boettner, R. D. , "O n Fa t igue Crack Propaga t ionin FCC Meta ls ," Acta Met., Vol. 11 , 1963, pp. 725-743 .10 W. A. Wood, "Recent O bserva t ions in Fatigue Failure in M e ta l s , "ASTM S TP 237, 1958, pp. 110-11 9.11 Morris, W. L., Buck, O., and M a r c us , H. L., "Fatigue Crack Initiationand Ear ly Propaga t ion in Al 2 2 1 9 - T851 , " Met. Trans ., Vol. 7A, 1976, pp.1161-1165.12 Pearson, S., "Ini t ia t ion of fatigue Cracks in Commerc ia l AluminumAlloys and theSubsequent Propaga t ion of Very Shor t Cracks," Engr. Fract.Mech., Vol. 7, 1975, pp. 235 -247.13 Yokobor i , T. , Sawaki , Y., S hono , S., andKumagai , A., "Ini t ia t ion andPropaga t ion of Fat igue Cracks in U nnotched Spec imens of High StrengthEutec toid S tee l , " Repor ts ofthe Research Institute for Strength and Fracture ofMater ia ls , Toho ku U niv. , Vol . 12 , No. 2, Dec. 1976, pp. 29-54.14 Yokobor i , T. , Kuribayashi , H., Kawagishi , M., and Takeuchi , N.,"Studies on theP r opa ga t ion of Fat igue Crack inTempered-Mar tensit ic HighStrength Steel by Plastic-Replication Method and Scanning ElectronM ic r osc ope , " Rep. Res. Inst. Strength and Frac ture of Mater ia ls , TohokuU niv. , Vol . 7, 1971 , pp. 1-23.15 Sidney, D., and Coffin, L. F., Jr., "L ow-Cycle Fa t igue DamageMechanisms atHigh Tempera ture ," ASTM STP 675,1979, pp. 528-554.16 Hudak, S. J., Jr., Saxena, A., Bucci, R. J., and Malcolm, R. C ,"Deve lopment of Standard Methods of Testing and Analyzing Fatigue CrackGrowth Rate Da ta , " Repor t AFML -TR-78-40, Air Force MaterialsLabora tory, May 1978.17 Kitagawa, H., and Takahashi , S., "Applicabi l i ty of Fracture Mechanics

to Very Small Cracks orthe Cracks inthe Ear ly S tag e ," Proc. 2nd Intnl. Conf.on Mech. Beh. ofMatls., 1976, pp. 6 2 7 - 6 3 1 .18 Kitagawa, H., Ta ka ha sh i , S., Suh, C. M., and Miyashi ta , S., " Q u a n titative Analysis ofFatigue ProcessM icrocracks and Slip Lines Un der CyclicL oadin g," ASTM ST P 675, 1979, pp. 420-449.19 El Ha dda d , M. H., Smith, K. N., and Toppe r , T. H., "Fa t igue CrackPropaga t ion of S hor t C r a c ks , " AS M E JO U RNAL OF ENGINEERING MATERIALSAN D TECHNOLOGY, Vol. 101, 1979, p. 42.20 El Ha dda d , M. H., Dowling, N. E., and Topper , T. H., " J - I n t e g r a lApplica t ions forShor t Fa t igue Cracks atNotc he s , " Int. J. of Fracture, Vol. 16,No. l ,Feb. 1980, pp. 15-30.2 1 U sa m i , S., Fatigue of Engr. Materials and Structures, Vol. 1, No. 4 ,1978, p p . 471-481 .22 Dowling, N. E., "Crack Growth Dur ing Low Cycle Fa t igue of SmoothAxia l Spec imens," ASTM STP 637,1978, pp. 9 7 - 1 2 1 .23 Dowling, N. E., "Geometry Ef fec ts and the J - Integra l Approach toElast ic -P las t ic Fa t igue Crack Grow th," ASTM STP 60 1 ,1976 , pp. 19-32 .24 Elber, W., "The Significance ofCrack Closure ," ASTM STP 486 , 1971 ,p. 230.

25 Schmidt, R. A., and Par is , P. C, " Thr e sho ld for Fatigue CrackP r opa ga t ion and Effects of L oa d R a t io and Frequency," ASTM STP 536,1973, p. 79.26 Kikukawa, M., J o n o , M., and Ta na ka , K., "Fa t igue Crack ClosureBehavior of Low Stress Intensity Le vel," Proc. of 2nd Int. Conf. onMechani cal Behavior of Materials, Boston, 1976.27 Ta ira , S., Ta na ka , K., andHosh ina , M., "Grain Size Effect on CrackNuclea t ion and Growth in Long-Life Fa t igue of Low-Carbon S tee l , " ASTMSTP 675, 1979, pp. 135-173.28 Mo rr is , W. L., and Buck, O . , "E nvironmen ta l Ef fec ts onFatigue CrackInit iatio n," Rockwell International Science Center Report SC5050.1FR,Thousa nd O a ks , Calif., Feb. 1979.29 Fenner, A. J., O w e n , N.B., and Phillips, C. E., "Th e Fa t igue Crack as aStress-Raise r ," Engineering, Vol. 171 , 1951 , pp. 637-638.30 Frost, N. E., " C r a c k F o r m a t ion and Stress Concentration Effects inDirect Stress FatigueNo. 1," The Engineer, Vol. 200, 1955, pp. 464-467, pp.501-503 .

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31 Frost , N. E., andDugdale , D. S., "Fatigue Tests on Notched Mild SteeiPlates With Measurement of Fat igue Cracks ," J. Mech. and Phys. of SolidsVol. 5, 1957, pp. 182 -192.32 Frost , N. E., "A Relation Between theCrit ical Alternating PropagationStress and Crack Length for Mild Steels," Proc. Instn. Mech. Engrs., Vo l 173No . 35, 1959, pp. 811-82 7.33 Frost , N. E. , "Notch Effects and the Critical Alternating Stress Requiredto P ropagate a Crack in an Alumiunum Alloy Subjected toFat igue Loading ,"J. Mech. Engr. Sci., Vol. 2, N o. 2, 1960, pp. 109-1 19.34 Frost , N. E. , Marsh , K. J., and P o o k , L. P., Metal Fatigue, ClarendonPress, O xford, 1974, pp. 166-173.35 Allery, M. B. P., andBirkbeck, G., "Effect of Notch Root Radius on theInitiation and Propagat ion of Fat igue Cracks ," Engr. Fract. Mech., Vol 41972, pp . 325-331 .36 Morrow, J., "Cyclic Plast ic Strain Energy and Fatigue of M et a l s , "ASTM STP 3 78, 1965, pp. 45-87.

37 Landgraf, R. W., and L aPoin te , R. N., "Cyclic Stress-Strain ConceptsApplied to Component Fat igue L i fe P red ict ions ," SAE Paper No. 740280,Autom otive Engineering Congress, Detroit , 1974.38 Clark, W. G., Jr., "Fracture Mechanics in Fat igue," ExperimentalMechanics, 1974, pp. 1-8.39 Hoeppner , D. W., andKrupp, W. E., "Predict ion of Component Life byApplication of Fatigue Crack Growth Knowledge," Engr. Fract. Mech., Vol. 6,1974, p p . 4 7 -7 0 .40 Newman, J. C, Jr., "An Improved Method of Collocation for the StressAnalysis of Cracked Plates with Various Shaped Boundaries," NASA TN D-6376 ,1971 .41 Fatigue Crack Growth Under Spectrum Loads , ASTM STP 595, 1976.42 Dowling, N. E., "Fat igue at Notches and the Local Strain and FractureMechanics Approa ches ," ASTM STP 677 , 1979 , pp . 247-273.4 3 H am m o u d a , M. M., and Miller, K. J., "Elastic-Plast ic FractureMechanics Analysis of Notches," ASTM STP 668, 1979, pp. 703-719.

1979 JE M T Best Pap er Aw ard to A. D . WilsonThis simply ti t led "Best Paper Award" was inaugurated by the Materials DivisionExecutive Committee in the second year of publication of this section of ASME Tran s

actions, the JO URNAL OF ENGINEERING MATERIALS AND TECHNOLO GY. In honoring the authorsdeemed tohave contributed themost prestigious paper of a given volum e or calendar year, itwas hoped tha t the fact of the award would attract the best possible papers to th is Journal .Tha t this objective has been attained isobvious from the list of previous recipients.1974 - K. D. Ives, A. K. Shoemaker , andF . R. McC artney , U S Steel L aborator ies .1975 - K. Masubuchi , T. Mu rak i , and J. J. Bryan , MIT1976 - R. Ku m i , H. O kabayashi , and M. Am ano, Ish ikawaj ima-Harimi L td . , Yokahama1977 - R. O. Ritchie, MIT (work atU . Cal . , Berkeley and U niv . of Cam b r id g e , U K)1978 - C. F. Shih and D. Lee, General Electric Corporate Research and DevelopmentThis year the 1979 Best Paper Award goes to A. D. Wilson, Senior Research Engineer,L ukens Steel Com pany. His paper entitled "The Influence of Inclusions on the Toughnessand Fatigue Properties of A516-70 Steel" appears in the July 1979 issue of JEMT. P resen tation of the Award Certificate was m ad e at the Annual Materials Division Dinner heldduring the ASME 1980 Winter Annual Meeting inChicago , November 16 - 21 .Two other authors whose papers were selected by the Associate Editors of J E M T asdeserving commendation are: W. H. Bamford, Westinghouse Nuclear Energy Systems"Ap p l i ca t i o n of Corrosion Fat igue Crack Growth Rate Data to Integrity Analyses ofNuclear Reactor Vessels"; and M. S. Weschler, Iowa State U niversity, "The Influence ofImpurity-Defect Interactions onRadiat ion Hardening and Embri t t lement . ' 'The Edi tors of J E M T are proud to announce th is award and prouder sti l l to remind ourauthors and readers that again, as inprevious years, the high caliber of the publication madeselection difficult.

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