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Review 245

Near-threshold fatigue-crack propagation in steelsby R. O. Ritchie

LIST OF SYMBOLS

R. O. Ritchie, MA; PhD, MIM, CEng, is in the Depart-ment of Mechanical Engineering, MassachusettsInstitute of Technology, Cambridge, Mass., USA.

== effective alternating stressintensity taking into account crackclosure

== threshold stress intensity for nocrack growth

== exponent in Paris power law,equation (1)

== number of cycles

== load or stress ratio (Kmin/Kmax)

== gas can stant

== absolute -temperature

== partial molar volume of hydrogenin iron (2 em 3 mol-1)

== constant relating reduction in co-hesi ve strength to local hydrogenconcentration CH

== Neuber's effective crack-tip radius

== limiting microstructural dimensionat threshold

== hydrostatic stress

== critical local fracture stress atthreshold

== ultimate tensile strength (UTS)

== monotonic yield strength

== cyclic yield strength

== alternating stress

== fatigue limit or endurance strength

== reduction in cohesive strength dueto hydrogen

== alternating threshold stress for nocrack growth

E == elastic modulus

== stress intensities at final failure(fracture toughness)

Kmax, Kmin == maximum and minimum stressintensities during cycle

~K == alternating stress intensity(Kmax - Kmin)

N

R

RoT

In many safety-critical engineering applications,where design against fatigue is based on the so-called defect-tolerant approach, the prime con-sideration in dictating the lifetime of a componentis taken as the time or number of cycles topropagate a subcritical crack from an assumed

p'

p*

== local concentration of hydrogen atpoint of maximum dilatation

== equilibrium concentration of hydro-gen in unstressed lattice

== cyclic crack-tip opening displace-ment

== crack length

== constant characteristic of material/material condition in expressionfor M, equation (3)

== fatigue- crack propagation rate percycle

== constant in Paris power law forfatigue- crack growth, equation (1)

== constants dependent upon materialand temperature in expression for~Ko' equation (13)

== constant in expression for ~Ko inabsence of environment, equation(10)

The characteristics of fatigue-crack pro-pagation in metals and alloys have been thesubject of several extensive reviews inrecent years, but in very few instances havethe details of ultralow growth rate, near-threshold fatigue-crack propagation beensimilarly discussed. In this review theeffects are examined of various mechanical,microstructural, and environmental factorswhich influence fatigue-crack propagation insteels at growth rates less than 10-6 mmlcycle, where the alternating stress intensity~K approaches the so -called thresholdstress intensity ~Ko' below which crackgrowth cannot be experimentally detected.The marked influences of load ratio,material strength, and miGrostructure onsuch near-:threshold growth are analysed indetail and rationalized in terms of possibleenvironmental contributions and crack-closure concepts. These effects are con-trasted with crack-propagation behaviour inother engineering materials and at highergrowth rates.

A

B,B'

c

~COD

a

da/dN

International Metals Reviews, 1979 Nos. 5 and 6 205

206 Ritchie: Fatigue-crack propagation in steels

initial defect size (often taken as the largest un-detected flaw) to critical size where final failureoccurs either catastrophically or at the limit load.The widespread adoption of this approach over thelast dec"ade for design against cyclic loading hasspurred a multitude of investigators to charac-terize the rate of growth of· fatigue cracks in themajority of engineering materials as a function ofsuch variables as microstructure, mean stress,environment, frequency, and so forth. The majorityof these data, however, have been generated forgrowth rates typically in excess of 10-6 mm/cycle.Although this information is vital for many struc-tural engineering applications (i.e. determiningsafe non-destructive inspection intervals in air-craft), in recent years there has been a rapidlyincreasing need for fatigue -crack propagationdata pertaining to extremely low growth rates(less than 10-6 mm/cycle) where the alternatingstress intensity ~K approaches a so-called thres-hold value ~Ko' below which cracks remaindormant or grow at undectable rates. The reasonsfor this are several. First, there are fundamentalaspects in that this topic represents a compara-tively unexplored area of fatigue research com-pared to the vast amount of information on fatigue-crack propagation at higher growth rates.Essentially, little is known from a mechanicsor metallurgical point of view about micro-mechanisms of crack propagation at near-threshold growth rates, and furthermore, thereis still a substantial lack of reliable engineeringdata. Secondly, there is the practical concern ofstructural and materials engineers to designcomponents which can withstand extremely highfrequency, low-amplitude loadings for lifetimes inthe range 1010-1012 cycles. A high-speed rotoroperating at 3000 rev min-1 in a steam turbine,for example, may be expected to see 1010 cyclesof stress over a typical lifetime of 20 years.Should fatigue-crack propagation be occurring atthe seemingly insignificant near-threshold growthrate of 3 x 10-9 mm/cycle, this would still repre-sent a total growth of 30 mm during the life ofthe rotor, which could clearly result in catastrophicfailure. In fact, a knowledge of low growth rate,fatigue -c~ack propagation data and, in particular,information regarding the existence of a thresholdstress intensity, has been shown to be essential inthe analysis of such problems as cracking in tur-bine blade s, 1 turbine shafts, 2,3 and al te rnatorrotors, 3 and acoustic fatigue of welds in gascircuitry in nuclear-reactor systems.2-4

There now exist results in the literature onnear-threshold fatigue-crack growth for a widerange of materials, including ferritic, 5-20 mar-tensitic,5,19-29 and austenitic, 19,30-32 ~teels,titani um5, 33,34 and titani urn all oys, 34:-41 andseveral alurniniurn,5,19,22,41-43 copper,5,44 andnickel, 1,5 alloys. It is apparent from such datathat near -threshold crack-growth rates and thevalue of the threshold ~Ko are particularlysensitive to several mechanical and microstruc-tural variables, namely, mean stress or load

International Metals Reviews, 1979 Nos. 5 and 6

ratio,5,28,31-44 prior stress history,9,19 cracksize,45 cyclic frequency, 22,32,42 mono-tonic11, 16, 18,24 and cyclic 26,27, 43,44 strength,grain size, 16,18,26,27,29,33,36 and grain-boundarycomposition.25 However, the influence of environ-mental factors on near-threshold crack growthhas remained somewhat of a controversy. Al-though it is well documented that fatigue-crackpropagation at rates exceeding 10-5 mm/cycleis generally accelerated in the presence of anenvironment compared to inert conditions, initialstudies by Paris and co-workers, in low-strengthsteels6,7 and titanium alloys35 in air, water,hydrogen, and dry argon, did not reveal any suchenvironmentally-sensitive propagation at ultralowgrowth rates. Furthermore, by extrapolation ofhigher (midrange) growth-rate data to near-threshold rates (a procedure, incidentally, whichshould be regarded with extreme caution), resultsof certain authors 46,47 suggest that near -thresholdcrack propagation may indeed be deceleratedin the presence of an 'aggressive' environment(e.g. salt water) compared to seemingly more inertenvironments such as air. Other data,21,22,31,39-41however, for various materials tested. in vacuosuggest the contrary behaviour of an environmentalcontribution to cracking at near-threshold rates.Conclusive information to resolve these issues isstill lacking.

In design, the concept of a fatigue-crack pro-pagation threshold is still infrequently utilized,except where there is an obvious source of veryhigh frequency loading,1-4 since it is often con-sidered to be overly conservative. However, therehas been a recent growing awareness in thenuclear industry that, for design and continuedsafe operation of reactor plants, such near-thres-hold data are required for both pressure-vesseland reactor-coolant piping steels (e.g. A533B,A50Blow-alloy steels, and 304 and 316 stainlesssteels, respectively) tested in simulated reactorenvironments. Such data, measured in air, pres-surized -water, and boiling-water reactorenvironments, are now appearing in the litera-ture.48,49 Similar data on candidate pressure-vessel steels for coal-gasifier and coal-lique-faction use, e.g. 2. 25Cr-1Mo steels, in simulatedenvironments, however, are not available, althoughnear-threshold fatigue-crack growth is a possi-bility in the pressure-vessel wall as a result ofhigh-cycle low-amplitude stresses generatedfrom small pressure and temperature fluctuationsof the system. Such 'operational transients' couldarise from real variations in coal feedrates,'clusters' of pulverized coal, combustion instabil-ities, and pressure fluctuations in feed and dis-charge lines for gases. Furthermore, typicalatmospheres in coal-conversion pressure vessels,namely, mixtures of water vapour, hydrogen,hydrogen sulphide, carbon monoxide, carbon di-oxide, ammonia, methane, and other hydrocarbonsat pressures exceeding 10 MPa with metal-walltemperatures around 350°C (Ref. 50), may wellaccelerate this slow subcritical growth.

Ritchie: FatiffUe-crack propagation in steels 207

It is the purpose in the present paper to pro-vide a critical review of existing information onnear-threshold fatigue-crack propagation in steels,and, in particular, to discuss these data in thelight of possible environmental interactions andcrack-closure concepts. Where possible, effectsare contrasted with crack-propagation behaviourat higher growth rates (exceeding 10-6 mm/cycle)and in other engineering materials.

EXPERIMENTAL MEASUREMENT OF NEAR-THRESHOLD GROWTH

It is pertinent at this stage to examine how suchlow growth rates are measured experimentallyand, in particular, how the value of the thresholdstress intensity 6.Ko can be defined. Whereasfatigue-crack propagation at conventional growthrates (Le. greater than around 10-5 mm/cycle)is typically measured under constant load (increas-ing stress intensity K) conditions, it is generallymore realistic to measure near-threshold growthrates, and the value of the threshold 6.Ko underdecreasing K conditions, in order to minimizetransient residual-stress effects.

In strict terms, the threshold stress intensity6.Ko should represent the alternating stress in-tensity where the growth rate is infinitesimal.However, for the purposes of practical measure-ment it is more useful to adopt an operationaldefinition for 6.Ko. This is best achieved in termsof a maximum growth rate, calculated from theaccuracy of the crack monitoring technique andthe number of cycles elapsed.21 In the system

used by the present author, 24 -27 crack length iscontinuously monitored using the dc electrical-pot~ntial technique, 51-5 3 and the threshold !:::J.Ko iscomputed from the highest stress intensity atwhich no growth can be detected within 107 cycles.In this particular case, the crack monitoringtechnique is at least accurate to 0.1 mm onabsolute crack length such that the threshold canbe defined in terms of a maximum growth rate of10-8 mm/cycle. Threshold levels are approached.using a load -shedding technique involving a pro-cedure of successive load reduction followed bycrack growth. Measurements of crack growthrate are taken at each load level, over incrementsof 1-1. 5 mm increase in crack length, after whichthe load is reduced by not more than 10/0, and thesame procedure followed. Larger reductions inload are liable to give premature crack arrestfrom retardation effects owing to residual plasticdeformation. The increments, over whichmeasurements of growth rate are taken, shouldrepresent distances at least four times 'largerthan the maximum plastic zone size generatedat the previous (higher) load level to minimizethese retardation effects caused by change inload. Furthermore, frequency must be maintainedconstant during this procedure since significantenvironmentally-induced transient crack-growthrate effects can result from variations in cyclicfrequency. 54 Following !:::J.Ko measurement, theload may be increased in increments and asimilar procedure adopted to measure growthrates. In this way, near -threshold data can bemonitored under both decreasing K and increas-ing K conditions in the same specimen. Providedcare is taken to minimize transient effects caused

80

ranga loading moda

• thrashold load raductiono low constant loado intarmadlata constant load• high constant load

thrasholdtasts

•+ flKO' thrashold ~ no growth in 107cyclas

tasting tachniqua tCT tastpiacas, 12·8 mm thick, 50-0 mm wida final failura, KIc

tastad at 5 and 50 Hz (sina wava) undar load controlcrack langth monitorad continuously using alactrical- potantial tachniqua •R= 0'05-0-70

highda/dN tasts

~ 10-4

0:I~~ 10-5o0:(!)

o 10-6«0:U

~ 10-7::>(!)

~~ 10-8

2 4 6 8 10 20ALTERNATING STRESS INTENSITY (6K= Kmax -Kmin) ,

1 Typical test procedures for obtaining fatigue- crack propagation data spanning entire range of growthrates from threshold levels to final failure



GENERAL NATURE OF FATIGUE-CRACKPROPAGATION IN STEELS

developing a standard for proposed test methodssimilar to the procedures described above. Suchguidelines for the establishment of fatigue -crackgrowth rates below 10-5 mm/cycle are likely tobe incorporated as modifications to the recentlyproposed ASTM Standard E647-78T for measure-ment of constant-load -amplitude growth ratesabove 10-5 mm/ cycle.

The application of linear -elastic fracturemechanics and related small-scale crack-tipplasticity has provided an empirical basis fordescribing the phenomenon of fatigue-crack pro-pagation.58 Most studies have confirmed that thecrack-growth increment per cycle (da/dN) isprincipally a function of the alternating stressintensity AK through a power-law expression ofthe form 59:

where A and m are experimentally-determinedscaling constants, and AK is given by the differencebetween the maximum and minimum stress inten-sities for each cycle, Le. AK == Kmax :- Kmin.This expression provides an adequate engineeringdescription of behaviour at the midrange of growthrates, typically 10-5-10-3 mm/cycle. At highergrowth rates, however, when Kmax approaches thefracture toughness (K Ie' Kc) or limit-load failure,equation (1) often underestimates the propagation

(1)da/dN == A(AK)m .

by changing the load, growth -rate data should beidentical when measured by these two procedures.

A typical test procedure for obtaining fatigue-crack propagation -rate data spanning the entirerange of growth rates from threshold levels tofinal failure is shown schematically in Fig. 1.

Other techniques have been used to measurethe threshold. These include determining an S/ Ncurve for cracked specimens with lifetime plottedagainst the initial value of AK, rather thanstress, 5,17,20 and a decreasing K techniqueachieved by cycling under constant deflectioncontro1.42, 55 Although relatively simple to instru-ment, for conventional compact and centre -crackedtension specimens, the latter technique suffersfrom the fact that the decrease in K is not rapidenough for efficient near-threshold crack-growthmeasurement. 55

The load-shedding (decreasing K) techniquecan be easily automated using a suitable crackmonitoring technique and computer-controlledclosed -loop testing mJl,chines. Such systems,utilizing a programmed constant decrease of thenormalized K-gradient, i.e. I AK-l. dAK/da I orI Krrlax. dKmaxi da I , have been developed usingseveral crack measurement techniques, namely,crack-opening displacement monitoring, 56 elec-tri cal-potential methods, 30 eddy -current crackfollowing,28 and elastic-compliance techniques.57

To provide some consistency in the measure-ment of near-threshold crack-growth rates andAKo values, the American Society for Testing andMaterials E. 24. 04 subcommittee is presently

ragima A

non- continuummachanisms

larga influanca of :

~ (j) microstructurllu (ij) maan strass~ (iii) anvironmant

E -4E10

"zu-toU

primary machanisms

ragima B

continuum machanism(striation growth)

Iittla influanca of :

(j) microstructura(ii) maan strass(iii) dlluta anvironmClnt(iv) thicknass

II KcI finalI failura

rClgima C

'static moda' machanisms(c1aavaga, intargranular,and fibrous)

larga influanca of :( i) microstructura(II) maan strass(iii) thicknassIittla influanca of:(iv) anvironmant

2 Schematic variation of fatigue-crack growth rate da/dN with alternating stress intensity AK in steels,showing regimes of primary crack-growth mechanisms


Ritchie: Fatigue-crack propagation in steels 209

a ductile striations in 9Ni-4Co steel at AK == 30 MN m-3/2; b additional cleavage fracture in mildsteel at AK == 40 MN m-3/2; c additional intergranular fracture in 4Ni-1~ 5Crsteel at AK == 40 MNm-3/2; d microvoid coalescence in 9Ni-4Co steel at AK == 70 MN m -3/2

3 Fractography of fatigue-crack propagation at intermediate (regime B) and high (regime C) growthrates in steels tested in moist air at R == O.1

rate, whereas at lower (near-threshold) growthrates it is generally conservative as AK approach-es the threshold stress intensity AKo (Fig. 2).

In steels, this sigmoidal variation of growthrates with AK has been characterized in terms ofdifferent primary mechanisms of fracture (Fig. 2).At the midrange of growth rates (regime B, whereequation (1) applies), fatigue failure generally isobserved to occur by a transgranular ductilestriation mechanism 60,61 as shown in Fig. 3a, andthere is often little experimentally observedvariation of growth rates with microstructure andmean stress. 62-64 At higher growth rates (regimeC), when Kmax approaches K Ie' static fracturemodes, such as cleavage, intergranular and fibrousfracture (Fig. 3b-d), occur in addition to striationgrowth, resulting in a marked sensitivity of pro-pagation rates to both microstructure and mean

stress. 62-65 At low (near-threshold) growth rates(regime A), there is similarly a strong influenceof microstructure and mean stress, although it isuncertain whether this can be directly related toa change in fracture mode. However, at such near-threshold stress intensities, the scale of plasticityapproaches the order of the microstructural sizescales, and measured propagation rates becomeless than an interatomic spacing per cycle, indi-cating that crack growth is not occurring uniformlyover the entire crack front.

An indication of this deviation from continuumcrack-growth mechanisms at near-thresholdlevels can be seen by comparing measured crack-propagation data with predictions based on crack-tip opening displacements as shown in Fig.4. Thelatter model, originally proposed by McClintock, 66considers striation growth to occur by alternating



80

1 latticaspacing 1 cycla

8

4

COD modal

300-M alloy staalaustClnitizCld at 8700e, oil qUClnchCld,tampClradanvironmant : air at 23°e, 45°/0 rCllativCl humidityR=O·05

6 8 10 20 40 60ALTERNATING STRESS INTENSITY (~K) ,MN m-3/2

4 Variation of fatigue-crack propagation in moist air at R == 0.05 with AK for ultrahigh-strength 30Q-Mmartensitic steel, quenched and tempered between 100° and 650°C to vary tensile strength from 2300to 1190 MN m-2, respectively; solid lines indicate predictions based on COD model for crack growth(equation (2))

shear 61 such that the crack -growth incrementper cycle should equal the cyclic crack -tip open-ing displacement t::..COD, i.e.

da == t::..COD ~ 0.49 M(2 (2)dN 2uy'E

where uy' is the cyclic flow stress and E theelastic modulus. It is clear frolp Fig. 4 thatwhereas such continuum models provide a reason-able description of crack-propagation behaviourat the midrange of growth rates, marked devia-tions are apparent at near -threshold levels.

There is no unifying picture of how the environ-ment may influence such fatigue- crack propaga-tion. At medium to high growth rates, severalmechanisms have been proposed which rely on anincreased chemical-reaction rate at the cracksurface. In one class of mechanisms, the accel-erating effect of the environment has been ascribedto increased mechanical failure caused by hydro-gen (produced by an enhanced cathodic -reactionrate or by adsorption from a hydrogen -containinggas such as H2 or H2S) entering the lattice. Thisis the basis of 'hydrogen embrittlement' theories,which suggest that the hydrogen atoms are trans-ported by diffusion or dislocation motion, 67 aheadof the crack tip, where they may induce hardeningor softening, 38 or accumulate at interfaces (grainboundaries, internal voids, and cracks) and lead todecohesion, 68, 69 or, in some circumstances,

internal gas pressures. 38 In certain materials,such as titanium and zirconium alloys, the pre-sence of hydrogen may lead further to the preci-pitation of brittle hydrides .38, 70,71 Other mechan-isms interpret environmentally-enhancedfatigue -crack growth in terms of an increasedanodic dissolution rate at the crack tip (active-path corrosion theories). Whereas it is nowgenerally 'accepted that environmental effects inhigh-strength steels are principally hydrogenembrittlement,72 in many materials, e.g. alumin-ium alloys, it is possible that both anodic andcathodic processes act in concert for moist oraqueous environments. Both processes result inincreased growth rates from the rupture of pro-tective oxide, and, in film -forming solutions, theenvironmental contribution to cracking can beconsidered as a function of the interaction betweenthe rate of oxide rupture from emerging disloca-tions at the crack tip, the rate of passivation, andthe rate of metal dissolution or hydrogen produc-tion at the bared surface. 46

Lower strength steels, i.e. with yield strengthsbelow 750 MN m-2, post a particularly interestingproblem in this regard since they are largelyinsensitive to environmentally-assisted crackingunder sustained loading in low -pressure hydrogen-containing and dilute aqueous environments.However, on cyclic loading such steels, whichrange from AISI 1020 mild steel to ASTM A533Band A542 nuclear and coal-gasifier pressure-


Ritchie: Fatigue-cr:ack propagation in steels 211

5 Influence of load ratio from R == o. 10 to o. 72on fatigue -crack growth in a normalizedO.55C-2. 23Mn pearlitic-martensitic steelof ay == 743 MN m-2 (after Ref. 78)

R=0·37R=0·50 \ R=0·27

10-8 vR=072 t t t vR=0·13 threshold ~K0

5 10 15 20 30ALTERNATING STRESS INTENSITY(llK),MNm-3/2

dboo

o

••••

NEAR-THRESHOLD FATIGUE-CRACKPROPAGATION

vessel steels, suffer significant environmental-assisted fatigue -crack propagation rates in hydro-gen 73-75 and hydrogen sulphide gas, 49, 73,74distilled and saltwater,47,76 simulated nuclear-reactor environments, 48,49 and low-pressure gasmixtures typical of gasifier atmospheres. 73,74Furthermore, measured crack-propagation ratesappear to be frequency dependent at the midrangeof growth rates (i.e. regime B in Fig.2),and fre-quency independent at somewhat lower propagationrates. 76 However, little information has beenobtained for the environmental contribution tocyclic cracking at near-threshold growth ratesbelow 10-6 mm/cycle in these steels, and, more-over, no mechanistic basis for this effect has beendeveloped, although it is widely considered to behydrogen related in origin.

Mechanical and environmental behaviourassociated with fatigue-crack propagation has beenwell documented, being the subject of many exten-sive reviews (see, for example, Refs. 65 and 77).However, in most cases, behaviour at very low,near-threshold rates has been overlooked. Torectify this, the effects of various mechanical,metallurgical, and environmental factors on near-threshold fatigue are examined in detail below.

markedly reduced yet not completely eliminated,although in all cases the value of the thresholdwas significantly higher than in air. Such resultsare a strong indication that marked effects of load

6. Variation of threshold I!Ko with load ratio Rfor martensitic 1. 4Ni-1Cr-Q. 3Mo high-strength steel (En 24), tempered at 200°C(~== 1570 :MN m-2) ~d at 500°C (ay ==lZ74 MN m-2); tests in laboratory all' (40%relative humidity) and vacuum (10-3 Pal(after Refs. 21 and 81)

1·0

oo \

vacuum

-------4--o

0·20 0040 0·60 0'80LOAD RATIO (R=Kmin /Kmax)

- - - tempered at 200°C--- tempered at 500°C

--.------- ----------- air

o

8·0!tIfz2...6.0

-2<J

g 4·0oIIf)W0:::I 2·0I-

Mechanical factors

Mean stress (or load ratio)

In fatigue studies, the effect of mean stress is oftenexpressed in terms of the stress or load ratioR(==Kmin/Kmax). Whereas little influence of Rcan be seen for the midrange of growth rates,near-threshold propagation is generally extremelysensitive to the load ratio. Studies in a wide rangeof steels and non-ferrous alloys, tested in ambient-temperature air,5-28, 31-44 indicate that the valueof 6.Ko is markedly decreased, and that propagationrates are increased, as the load ratio is raisedwithin a range of R from 0 to 0.9. Typical data,for a normalized medium -carbon steel, 78 areshown in Fig. 5. The load -ratio dependence onnear-threshold growth, however, is found to bereduced at negative R values, 79 with increasingtemperature, 6 with increasing strength in tem-pered martensitic steels, 26 and in inert atmo-spheres.21,37,39-41,80 For the last case, Beeversand co-workers21,37 observed that, for temperedmartensitic En 24 steel and Ti-6Al-4V testedin vacuo", near-threshold crack-propagation ratesand the value of 6.Ko were completely independentof load ratio (Fig. 6). This lack of an R-dependencefor tests under inert conditions has been confirmedfor low -alloy martensitic steels in vacuo by Irvingand Kurzfeld81 and for 316 stainless steel in vacuoand in helium by Priddle et al.31 Other studies ofmartensitic stainless steels80 and of Ti-6Al-4V(Refs. 39, 40), however, show that by testing invacuo, the dependence of 6.Ko on load ratio is



7 Influence of load ratio from R = 0.05 to 0.80on near-threshold fatigue-crack growth inair for normalized 2. 25Cr-1Mo pressure-vessel steel (SA387) of (]y= 290 MN m-2

(after Ref. 83)

ratio on near -threshold fatigue -crack propagationcan be attributed, at least partially, to some en-vironment interaction. The lack of a load -ratioeffect on higher (midrahge) growth rates is con-sistent with this argument, since at such fasterpropagation rates, the pertinent environmentalreactions may not be able to keep pace with thecrack velocity. Other explanations 6,7,19,35,42,79of the load -ratio effect have centred around thephenomenon of crack closure, first identified byElber82 in aluminium alloys at much higher stressintensities. The relative merits of the environ-mental and closure explanations are discussedbelow.

In low-strength ferritic steels, both Cookeand Beevers, 12 and Masounave and BaIlon 15found for a particular microstructure and .strength

(3)

level that the effect of load ratio was consistentwith the threshold occurring at a constant valueof Kmax or 6.Ko/1-R. Such behaviour is withoutexplanation, and has not been observed in higherstrength steels or other materials .

The influence of load ratio on the fatigue-crack propagation threshold 6.Ko in normalized2. 25Cr-1Mo steel (SA387 Class 2, Grade 22), apotential steel for coal-gasifier pressure-vesselconstruction, is shown in Fig. 7 for tests in am-bient-temperature moist air at. a strength levelof 290 MN m-2 (Ref. 83). It is apparent that thevalues of 6.Ko decreases with increasing loadratio up to R = O. 5, consistent with a constantvalue of Kmax at the threshold. Above R = 0.5,6.Ko remains constant, similar to behaviourreported for aluminium alloys. 42 As noted above,explanations for this effect are uncertain.

Testpiece geometry and crack sizeProvided conditions of linear elasticity are reason-ably valid, fatigue-crack growth can be generallyconsidered to be geometry independent, apartfrom variations in growth rate owing to changesin specimen thickness, e.g. departure from plane-strain conditions. In such instances, small differ-ences in the growth rate between specimens ofdifferent thickness can arise because of nominalyielding, changes in fatigue-fracture mechanismnear final failure, and perhaps closure effects.84

However, for near -threshold fatigue -crack growth,effects of thickness and specimen geometry shouldbe minimal because the low stress intensitiesinvolved invariably impose a condition of pre-dominately plane strain. This has been borne outby experiments in low-strength steels 55 andaluminium alloys 32 tested over a range of speci-men geometries and thicknesses.

The influence of crack size, on the other hand,has been shown to be particularly important.Classic experiments by Kitagawa and Takahashi 45

in low-strength steel have shown that, whereas thecondition for the non-propagation of a surfaceflaw could be related to a constant thresholdstress intensity 6.Ko for crack lengths in excessof around 1 mm, below this crack size.,.a transitionoccurred in which the fatigue-limit stress becamethe threshold condition for growth (Fig. 8). Topperand co-workers85,86 have attempted to rationalizethese data by defining the alternating stress inten-sity 6.K at elastic stresses" 6.a in terms of

where a is the crack length and ao a constantcharacteristic of a given material and materialcondition. Thus, by defining the threshold 6.Ko inthe usual way as the minimum value of 6.K forcrack growth, the threshold stress range 6.aTH isgiven by

'tJ•

1latticespacing Icycle ~

0-1 0-5 1 5CRACK LENGTH (2a), mm

1~2

d(2a) < 2x10-B mm /cyclQdN

2·25Cr-1Mo steQISA387 class 2 grade 22environment: air at 23°C, 30°10 relative humidityfrQquency: 50Hz, '/2T plate loca~on

R 6Ko, MNni 2• 0·05 g·Oo 0'30 6·96 0·50 5·1o 0'80 5'5

~~ fatigue limit R=Q

. ~

~::t!f 500

w(9z<{erN 200~IEw·z~2 100o..Jo 50mwerI.....

8 Effect of crack size on fatigue-thresholdconditions in Japanese HT80 steel (afterRef. 45)

(4)


Ritchie: Fatigue-crack propagation in· steels 213

such that as crack sizes become small, of theordex: of ao

dKodOTH == - == dOe (5)

~where dOe is the fatigue limit corrected for theappropriate R value. Equations (4) and (5) repro-duce exactly the data trend shown in Fig. 8, butat present there is no physical interpretation ofthe constant ao.

There is also limited evidence that near-threshold crack-growth rates are accelerated, andthe value of the threshold dKo decreased, atshorter crack lengths, i.e. for microcracks, 85 -8 7which, if substantiated, would provide a veryfeasible explanation to the existence of non-pro-pagating cracks. A more complete review of thedifferences and similarities between the near-threshold fatigue -crack propagation behaviour ofmicro - and macrocracks can be found in Ref. 88.

Frequency and wave shapeFor fatigue-crack propagation in the midrange of:growth rates, the general effect of decreasing thecyclic frequency is to increase the crack-growthincrement per cycle, due to enhanced environ-mental effects. 77 At near-threshold growth rates,however, very limited data exist, simply becauseof the limitations imposed by the high-frequencyresponse of conventional testing machines, andthe time factor involved in measuring low growthrates at very low frequencies. Results 55 on2219-T851 aluminium alloy indicated no effect onnear-threshold growth over a frequency range of25-150 Hz. Tests in 2024-T3 aluminium alloy atfrequencies between 342 and 832 Hz (Ref. 42),conversely, showed an increase in crack propaga-tion rate and a twofold decrease in dKo with in-creasing frequency, which was tentatively attri-buted to creep effects due to crack -tip heating. InD6ac steel, however, increasing the frequencyfrom 100 to 375 Hz resulted in lower near -thres-hold growth rates for. tests in dry argon, and noeffect in room air. 22

For low-strength ferritic steels, such asHSLA pipeline steels X-65 (Ref. 47) and A533-Band A508 nuclear pressure-vessel steels,49tested in water environments at frequencies be-tween 0.01 and 10 Hz, there is evidence showingmarked frequency-dependent crack propagationbehaviour for growth rates in excess of 10-5 mm/cycle, which becomes frequency independent atlower growth rates as the threshold is approached.Similar results have been seen in higher strenghHY 130 marine steels tested in salt solution. 76Companion tests in hydrogen sulphide gas 49 re-sulted in similar growth rates without any effectof frequency, even above 10-5 mm/cycle. Theenvironmentally-enhanced growth rates in waterand hydrogen sulphide, compared to those measuredin air, were accounted for in terms of hydrogenembrittlement, although the mechanism for the

embrittlement was not defined and no attempt wasmade to explain the transition from frequency-independent to frequency-dependent propagationrates in water above 10-5 mm/cycle.

The effect of wave form (Le. sinusoidal,square, and triangular) on near-threshold growthhas been examined in aluminium alloys and stain-less steels in room air. 32 For both materials nochange in dKo was observed for the various waveforms. In the same experiments, decreasing thefrequency from 130 to O.5 Hz for all wave shapesled to a decrease in dKo' perhaps reflecting theinfluence of the environment at low growth rates.

Microstructural factorsMaterial strength:;Fatigue-crack propagation in metals has beengenerally found to be largely unaffected by yieldstrength.89 In fact, for steels, raising the strengthby nearly an order of magnitude does not changecrack-propagation rates over the midrange ofgrowth rates by much more than a factor of twoor three. 65 However, at near -threshold levelsbelow 10-6 mm/cycle, a surprisingly largedependence of material strength has been ob-served on the value of the threshold dKo andon subsequent growth rates. In low-strengthferritic-pearlitic steels with yield strengths lessthan 500MN m-2, for example, values of thethreshold have been observed to decrease sig-nifi can tl y with increasing strength .11,1 6,18 Aneven larger effect has been reported for high - andultrahigh -strength martensitic steels (yieldstrengths between 1000 and 2000 MN m-2) with theexception that the controlling measure of strengthwas the cyclic, rather than the monotonic, yieldstress.2 6,27 Specifically, increasing the cyclicstrength led to marked increases in near-thresholdpropagation rates (Fig. 4), and a significant reduc-tion in dKo (Fig. 9). Cyclic softening can thus beregarded as extremely beneficial to improvingnear-threshold fatigue-crack growth resistance insteels.26,27 In low-alloy pressure-vessel steel,variations in monotonic yield strength between 300and 400 MN m-2 resulting from differences incooling rate experienced through the thickness ofa 184 mm thick plate, did not give rise to signifi-cant changes in near -threshold fatigue -crackgrowth resistance in a 2. 25Cr-1Mo steel, SA387(Ref. 83). However, in O. 5Cr-0. 5Mo-O. 25V steel,90coarse -grained precipitation -hardened ferriticmicrostructures showed significantly lower growthrates near dKo than higher strength bainiticormartensi tic structures.

The effect of strength on near-thresholdcrack-propagation behaviour is significantly lessat high R values,26,27,80,91 and not so evident inferritic-pearlitic steels. 91 The latter probablyresults from the fact that data on the lowerstrength steels cover a relatively narrow rangeof strengths and are subject to considerably morescatter. Furthermore, varying the strength insuch steels generally involves variations in the



•R=0·05

(7)

(6)

(9)

(8)

1ex: -au

AKo = AOTH ~1f(a + p')

= limit Aoe..fiTiTa-7p'

r-r _ 530vp --2

auwhere p I is in inches and au in ksi. Combiningequations (6)-( 8) gives

where ACJTHis the threshold stress and a the cracklength. Since the fatigue limit for steels (at R = -1)is generally found to be half the ultimate strength(O"u/2),correcting for R = 0 using the Goodmanrelationship yields

consistent with the experimentally observedincrease in fatigue limit with increasing strength.However, from the studies of Kuhn and Hardrath,93the Neuber constant p' appears inversely propor-tional to the ultimate tensile strength (raised tothe 4th power), and the following empirical rela-tionship is found for steels

growth rates in a single material, with varyingstrength, in vacuo is required to help resolve thisissue.

An intriguing aspect of the strength effect insteels is the fact that whereas the fatigue -crackpropagation threshold AKo is decreased with in-creasing strength, the well known fatigue limitAO"e,or endurance strength, is increased.26, 88,90Both parameters represent limits for fatiguedamage, 88 but the threshold AKo must be regardedas. the minimum stress intensity below which longmacrocracks do not grow, whereas the fatigue limitis generally the minimum stress below which shortmacrocracks do not initiate (i.e. by coalescence ofmicrocracks). Following the work of Topper andco-workers85,86 and McEvily,92 one can rational-ize this apparent inconsistency in the effect ofstrength by equating the characteristic length con-stant ao in equations (3)-( 5) to Neuber's effectivecrack-tip radius p', such that

consistent with the experimentally observeddecrease in threshold AKo with increasing strength.By comparison with Fig. 8, this indicates that atshort crack lengths (a ~ p'), the threshold stressAO"THwill be increased as the strength level israised, whereas at long crack lengths (a » p'),AOTHwill be decreased. These predictions areplotted in Fig . lOusing data from 300-M high-strength steel tempered between 100° and 650°C(Refs. 26,27,94) and equations (6)-(9). As dis-cussed by Fine and Ritchie, 88 this result is

~ quenchedand tempered• 0 isothermally transformed'fj. step cooled

1000 1500 2000CYCLIC YIELD STRESS (0';'), MN m-2

-2<14g ~,R=0·70o fj. ••.....-<:I 2 -0--------<9-0-----------0-(/)W0::~O

ferrite grain size which is also known to have amarked influence on near-threshold behav-iour .16,18,29

Results in non -ferrous alloys, however,reveal somewhat different behaviour. Small re-ductions in the threshold AKa have been observedin aluminium bronze44 and Al-Zn-Mg alloys43as the cyclic strength is decreased.· This is pre-cisely the opposite of behaviour observed insteels, but the magnitude of the effect is verymuch smaller, for example, increasing the cyclicflow stress by a factor of nearly two in the alu-minium alloy only results in an increase in AKofrom 2.5 to 3.7 MN m-3/2 (Ref. 43), whereas asimilar increase in strength in a tempered mar-tensitic 300-M steel leads. to a decrease in AKofrom 8.5 to 3.0 MN m-3/2 (Ref. 26).

Explanations for these effects are again un-certain. The small increase in AKo with iIicreasein flow stress for the non-ferrous materials havebeen attributed to a decrease in the alternatingplastic crack-tip opening displacement. 43,44However, reference to Fig. 4 clearly'shows thatsuch explanations are not applicable to steels. Inthis figure, growth -rate predictions based on theCOD model (equation (2)) are compared withexperimental data for an ultrahigh -strength mar-tensitic steel 300-M, tempered over a range oftemperatures from 100° to 650°C to vary thetensile strength from 2340 to 1190 MN m-2,respectively. It is apparent that not only does theCOD model predict a far too small dependence ofgrowth rates on strength but also predictions arein the wrong direction, i.e. higher strength re-suIts in a marked increase in near-thresholdgrowth rates whereas COD predictions show asmall decrease.

The dependence of near -threshold growth-rate behaviour on material strength in steels hasbeen rationalized, however, in terms of environ-mental arguments24,27 and notch-sensitivityeffects,92 as described below and in the 'Discus-sion' section of this paper. A comparison of

9 Variation of threshold Li.Ko with cyclic yieldstrength at R = 0.05 and 0.70 for O.4C-1. 76Ni-O.76Cr-1. 6Si ultrahigh-strength steel (30Q-M)tested in moist laboratory air



a, mm10-2

5000

fatiguez limits fj,Oez at R= 0

I-6~ 10

2

w(!)z«0::(J)(J)

W.0::tn 10

o--IoI(J)I.LJ0::I.-

curvez

abcd

tC2mpC2ring tC2mp., °C

100300470650

UTS, MN m-2

2238173716831186

b

dc

1000

N500 IE

z2

I

~100 <J

10

10-4 10-3

CRACK SIZE (a), in

10 Predicted variation of threshold stress ~aTH at R = 0 with crack size a from equations (6)-(9) basedon data for 300-M ultrahigh-strength steel tempered between 100° and 650°C to vary tensile strength

particularly significant for the alloy design ofsteels with improved resistance to very high cyclefatigue damage, since the optimum microstructuresdesired will depend upon whether structural designis to be based on initiation or propagation of a'fatal' flaw.

Grain size

Whereas refining grain size can be beneficial inraising the fatigue limit or endurance strength of(planar slip) materials, 95 the effect of grain sizeon fatigue -crack propagation has been observed to

8060

R=0·05

1 latticC2spacing 1cyclez --+

prior austC2nitez grain SiZC220JJ,m (870°C)-160JJ,m (1200°C)

R

0·050·700·050·70

300-M alloy stC2C21austC2nitlzC2d, oil qUC2nchC2d,tC2mpC2rezdat 300°CC2nvironmC2nt: air at 23°C, 45°/0 rezlativez humidityR = 0·05 and 0·70

austC2nitizingtC2mp., °C

870870

12001200

•o&/:).

"-zu-;u 10-3~w~ 0-40::1

I.-~ 10-5o0::(!)

~ 0-6u1«0::uW 10-7::::>(!)

~~ 10-8

2

i 'thrC2shold

4 6 8 10 20 40ALTERNATING STRESS INTENSITY (6K), MN m-3/2

Effect of prior austenite grain size (20-160 /llIl) on fatigue-crack growth in cyclic softening 300-Multrahigh-strength steel (cry= 1700 MN m-2) at R = 0.05 and 0.70 in moist laboratory air

11



1 latticespacing 1 cycle --.

prior austenitegrain sizC2, ~m

3090

150180

Fe-4 Cr-0·35C alloy steel, as quenchedaustC2nitizC2dfor 1h, oil qUC2nchC2d,untC2mpC2rC2denvironment; air at 27°C, 50°/0 relative humidityR=O'05

austenitizingtemp., °C

870100011001200

oVo

+ ~ + threshold 6KO

4 6 8 10 20 40 60 80ALTERNATING STRESS INTENSITY (6K), MN m-3/2

12 Effect of prior austenite grain size (30-180 #1ffi) on fatigue-crack growth in cyclic-hardening as-quenched Fe-Cr-C high-strength steel (cry= 1300 l\AN00-2) at R = 0.05 in moist laboratory air

13 Variation of threshold /1Ko with grain size forsteels at R = O. 05: for ferritic-pearlitic low-strength steels grain size refers to ferritiegrain size, whereas for martensitic high-strength steels, grain size refers to prioraustenite grain size

be negligible in most studies at inte~mediate growthrates.29,95-97 At low growth rates in room air,however, several workers16,18,24,27,33,36,98 haveobserved improved resistance to near-thresholdcrack propagation with coarser grain sizes.Robinson and Beevers 33 report an order of mag-nitude decrease in near -threshold growth rates ina -titanium after coarsening the grain size from20 to 200 11m. Similar effects have been seen inTi-6Al-4V (Refs. 36,98) and other basic a + {3

titanium -alloy systems. 98 Furthermore, a markedincrease in threshold 6.Ko values has been ob-served in a range of low-strength steels by increas-ing the ferrite grain size.16,18 In all of thesestudies, however, no attempt was made to controlstrength, and the effect of coarsening the grainsize may well have been masked by a concurrentdecrease in strength, which is known to increasemarkedly the threshold in steels. 27 Comparisonsat constant yield strength have been made in twohigh -strength steels, 300-M (Refs. 24-27) andFe-er-C (Ref. 29), where it was found that, in thecyclic softening 300-M, coarsening the prioraustenite grain size by almost an order of mag-nitude decreased near -threshold growth ratesyet left 6.Ko unchanged (Fig. 11),whereas, in cyclichardening Fe-er-C, similar coarsening of thestructure increased near-threshold rates and re-duced the threshold (Fig. 12). The variation ofthreshold with grain size for low- and high-strength steels is shown in Fig .13, and clearlyshows the contrasting behaviour between the twoclasses of steels.29

Several explanations have been proposed toexplain the grain -size effect, none of which isentirely satisfactory. It has been suggested, forexample, that since near-threshold growth is'microstructurally-sensitive', it may be confinedto specific crystallographic planes so that incoarser structures, greater deviations of the crackpath may occur from the plane of maximum ten-sile stress.16 Other authors24,99 have reasonedfor high-strength steels that, since plastic zonesare often confined within a single grain duringnear-threshold growth, the probability that hydro-

250

o high - strQngth stQQls• FQ-Cr-C (RQf.29)o 300-M (RQf.27)low-strQngth steQIs18• 1500-XOZX

low- strQngth stQQls(cJy < 500 MN m-2)~. .~.high-strQngth stQQls(cJy > 1300 MN m-2)

50 100 150GRAIN SIZE, J.1m

o

010~<I 8g 6o~ 4w~ 2I-

18

('\J 16M

IE 14z2 12



gen atoms, generated by chemical reactions withthe environment at the crack tip, can be swept intothe grain 'boundaries by dislocation motion, 67 ismuch smaller if the grain size is very large.Effectively, this hypothesis states, that by coarsen-ing the grain size, the environmel1tal contributionto near-threshold growth is reduced, and this isconsistent with an observed decrease in hydrogen-embrittlement susceptibility of high -strengthsteels as the grain size is increased.l0o However,the conflicting results observed in Fe-Cr-Csteel29 are not consistent with this explanation.A study of the influence of grain size (at constantstrength) in inert environments is required beforethis effect can be resolved.

StructureVery little information is available at present onthe relative resistance to near-threshold fatigue-crack propagation of particular microstructuresin metals (i.e. pearlite v. tempered martensite v.bainite, etc.), aside from data where particularstructures have been compared at differentstrength levels. For example, in aluminiumalloys,43 underaged structures appear to havefractionally better resistance than peak and over-aged structures whereas in tempered martensiticsteels, spheroidized structures offer far the bestresistance.27 Comparisons at constant strengthhave been made in 300-M ultrahigh-strengthsteel2 6,27 between isothermally-transformedstructures containing an interlath network ofretained austenite (volume fraction .....12~o)withina lower bainite-tempered-martensite matrix, andquenched and tempered fully martensitic struc-tures containing no austenite. Here, if the struc-tures are compared at equivalent monotonic yieldstrength, quenched and tempered microstructuresoffer greater resistance owing to their lowercyclic yield strength* (Fig. 14). However, whencompared at equivalent cyclic strength, iso-thermally-transformed structures offer margin-ally superior resistance, in the form of higherthresholds (Fig. 9), which is indicative 101 of theirsuperior resistance to environmentally-inducedcracking under monotonic loads. A similar smallbeneficial effect of interlath retained austenite onnear-threshold crack-propagation resistance intempered martensitic steels has been observedfor a 9Ni-4Co-0. 2C high-strength aerospacesteel HP 9-4-20 tested in moist air .102 It wasreasoned in this case that the role of the austeniteeffecti vely was to reduce the environmental con-tribution to cracking (i.e.from hydrogen embrittle-ment) by slowing down the rate of diffusion ofadsorbed· hydrogen atoms ahead of the crack tip.Alloy additions of silicon, similarly, may lead toa reduction in "diffusivity of hydrogen iniron.l03-105 Accordingly, silicon-modified 4340

*Isothermally-transformed structures do notcyclically soften due to deformation-inducedtransformation of retained austenite to marten-site.26

(300-M), with its lower susceptibility to sustained-load environmentally-assisted cracking, 101,106,107displays superior near-threshold· crack-propaga-tion resistance in moist air compared with un-modified 4340 at the same strength level, as shownin Fig. 15 (Ref. 108). In general, it appears thatmicrostructures with superior resistance tohydrogen -a~sisted or stress corrosion crackingunder monotonic loads will have a similar super-ior resistance to near-threshold fatigue-crackgrowth.10B

A particularly striking effect of micros true -ture has been observed in AIBI 1018 mild steel,where the production of duplex ferrite-martensitestructures can lead to increased near-thresholdcrack -propagation resistance and increasedstrength compared to conventionally heat-treatedsteel. 109 By suitable heat-treatment procedures,duplex microstructures where the martensiticphase a' is continuous and totally encapsulatesthe ferritic phase a were found to have increasedstrength (Oy == 452 MN m-2) and a significantlyhigher threshold (Li.Ko ~ 20 MN m-3/2), thansimilar structures where the ferritic phase sur-rounds the martensite (Oy == 293 ·MN m-2, Li.Ko ~10 MN m -3/2), as shown In Fig. 16. The result iscontrary to what one might expect for the relation-ship between strength and near -threshold be-haviour and is without explanation, yet it doesintroduce a very promising way of improving thefatigue-crack propagation resistance of low-carbonsteels without compromising other mechanicalproperties.

For non -ferrous metals, studies in Ti-6Al-4V at roughly constant strength (monotonic yieldstrengths between 835 and 1000 MN m -2) haverevealed a strong effect of structure near thethreshold.36 Ranked in order of greatest resis-tance to near-threshold growth, /3-annealed struc-tures were superior to transformed /3,followed byas-received. and martensitic structures. Thesemicrostructural differences were more pronouncedat low R values, as has been similarly observed inultrahigh-strength steels,26 and far less pro-nounced for tests in vacuo.'37 This latter fact onceagain reinforces the argument that microstruc-tural influences on near-threshold fatigue-crackpropagation are often primarily a consequence ofenvironmental effects, rather than inherentmechanical effects.

The effect of non-metallic inclusion content onnear-threshold fatigue behaviour has been exam-ined in a medium -strength pearlitic rail stee1.110Here it was found that, whereas decreasing the.volume fraction of inclusions (sulphide stringersand oxide -type) led to marked increases in thefatigue or endurance limit, no systematic effectwas observed on the value of the threshold Li.Ko'However, other studies 1:11on the influence ofsteelmaking practice on somewhat higher fatigue-crack propagation rates in nuclear pressure-vessel steel A533B have shown that the absenceof elongated Type 2 MnS inclusions and galaxiesof alumina inclusions by calcium treating or



0'050-700-050-70

c::i

~ 0-2u 1

300- Malloy st ClCl Iaustanitizad at 870°CClnvironmClnt : air at 23°C, 45°/0 rCllativCl humidity

hClat tClmpClr rJy, RtrClatmClnt (1h),OC MN m-2

• isothClrmal 250°C 300 1497• isothClrmal 250°C 300 1497o qUClnchCld 470 1497V qUClnchCld 470 1497

liKO,MN m-3/2

3-602-455'102-46

4

+ thrClshold ~KO

6 8 10 20ALTERNATING 'STRESS INTENSITY (~K), MN m-3/2

40 60 80

14 Comparison in martensitic 30o-M high-strength steel at constant monotonic strength of isothermally-transformed structure, containing 12% retained austenite, with quenched and tempered structure con-taining no austenite, at R = 0.05 and 0.70 in moist laboratory air; quenched and tempered structureundergoes cyclic softening (fly: = 1200 MN m -2) whereas isothermally-transformed structure remainscyclically stable (fly' = 1500 MN m-2).

electroslag remelting results in a significantimprovement in the isotropy of fatigue-crackgrowth behaviour and lower overall growth, rates.

Impurity -induced grain- boundary segregation

It is well known that the toughness of low-alloysteels can be severely impaired by heat-treatmentprocedures which result in the segregation ofresidual ~impurity elements, such as P, S, Sb, andso forth, to grain boundaries (temper embrittle-ment). Recently, it has become clear that impuritysegregation can also. degrade creep, stresscorrosion, and hydrogen -induced cracking resis-tance.25 There has been one study25 on the effectof prior impurity segregation on near-thresholdfatigue -crack propagation, conducted in an ultra-high-strength martensitic steel (300-M), testedin moist room air in the unembrittled and temperembrittled * conditions (at the same yield strengthand prior austenite graiIl: size). Here it was

*Auger studies indicated that the embrittlementresulted from a build-up of P, Si, Mn, and Ni inprior austenite grain boundaries. 25


found that, although no difference in crack propa-gation rates was observed between unembrittledand embrittled structures at the midrange ofgrowth rates, at near-threshold levels, impurity-induced embrittlement gave rise to vastlyaccelerated growth rates and a reduction in ~Koby almost 30/,0at both low and high load ratios(Fig. 17). This was accompanied by a significantincrease in the proportion of intergranular frac-ture in the embrittled steel close to the threshold.This large effect at very low growth rates, com-pared to little or no effect at higher intermediaterates, is again indicative of an enhanced environ-mental contribution to cracking in the impurity-embrittled structure, perhaps caused by aninteraction between residual-impurity- elementsand hydrogen atoms (generated by chemical re-actions with the moist air atmosphere at the cracktip) in prior austenite grain boundaries (see 'Dis-cus sion' section below).

Weld microstructure

Little information exists on the influence of weldsand weld microstructure on near -threshold fatigue-


60

1 latticaspacing 1 cycla ---.

R

0-050-700·050-70

rfy,MNm-2

1497149714971497

ilKO, 31MN m- 2 .•

3-80 .•.•.••2-44 .•.•.•: ••••5 10 _A06~:":::----. ..~~~

" ..;..~2-46 Q./" ~1;:"

~~.?~ ....:,...-~ .- .,••.............. ....•....~ .•.. .•..... .•.•.•

••••.•.•/ R=0'05••/.tE.. .•

•• - 1IJtr,•.••.... /.- ~• A. .•.- .•..

+

R=0·70

AISI 4340 and 300-M alloy stflfltsaustflnitizfld at 870°C, oil qUflnchfld, tflmpflradanvironmant : air at 23°C, 45°/0 ralativa humidityR = 0·05 and 070

staal tampar(1h),OC

• 4340 300o 4340 300A 300-M 4706 300-M 470

+ thrashold ~KO

4 6 8 10 20 40ALTERNATING STRESS INTENSITY (l1K), MN m-3/2

Comparison, at constant yield strength (0: = 1497 MN m-2), of fatigue-crack growth behaviour ofquenched and tempered 4340 and 300-M (4340 modified with 1.3%Si) ultrahigh-strength steels inmoist laboratory air at R = 0.05 and O.70 (after Ref. 108)

15

crack propagation, except for a few studies onaustenitic stainless steels. 30,112 In general,stainless steel weldments show little or no deteri-oration in fatigue-crack propagation resistancewhen compared to parent metal at intermediategrowth rates .113 At low growth rates, however,Type 304 and 316 weldments show faster crackpropagation rates than in parent metal, both atambient30 and higher112 temperatures in air. Noexplanations exist for this behaviour, apart fromsuggestions regarding the possible deleteriouseffect of the variable and coarser grained struc-ture within the weld.30 Limited results for weld-ments of mild steel indicate no change in thres-hold ~H ..o values between parent metal, heat-affected zone areas, and weld metal.! 7

Environmental factors

Temperature. Effects of temperature on near-threshold fatigue-

crack growth behaviour have been studied prim-arily in steels.6,17,31 Pook and Greenham17

observed no change in ~Ko between ambienttemperature and 300°C for tests on mild steel inair at low R values, whereas thresholds werehigher at 300°C for tests at high R values. Con- .versely, Paris et al.,6 inA533B and A508nuclearpressure-vessel steels,found the largest sensi-tivity of the threshold to. temperatures at low Rvalues (Le. R = O.1), and observed no change in~Ko over the temperature range, ambient to 350°C,at high R values (Le. R =0.7). Furthermore,although fatigue-crack growth (at R = O.1) was

4030

I/

II

//

/I

I~

If

JI~l::t

1:/

I~II,20

ilK, MN m-3/2

duplezx microstructurez a. a• a' contalnezd within a (dy= 293 MN m-2) •~ a containezd within (X,'(dy=452 MN m-~)

16 Variation of fatigue-crack growth rate withAI( for duplex microstructures in AISI 1018mild steel; duplex structures consist offerrite a and martensite 0;' (after Ref. 109)


220 Ritchie:· Fatigue-crack propagation in steels

60 80

1 lattic(2 •spacIng 1 cycl(2

6K0731MN m- 12

8'503-686'172·65

R

+ thr(2shold 6KO

4 6 8 10 20 40ALTERNATING STRESS INTENSITY (6K), MN m-3/2

300-M alloy st (2(2Iaust<lnitiz(2d at 8700e, oil qU(2nch<ld, t(2mp(2r<ld at 6500ecznvironmcznt : air at 23°C, 45°/0 rczlativcz humidityR= 0·05 and 0·70

t<lmp(2r cooling(1h) 7 °e rat<l

~ 650 oil qU<lnch 0·056 650 oil qU(2nch 0·70• 650 st<lP cool<ld 0·05o 650 stczp cool<ld 0'70

17 Effect of prior impurity-induced embrittlement on fatigue in 30o-M high-strength steel at R = 0.05and O.70 in moist laboratory air; step-cooled structure is temper embrittled, oil-quenched structureis unembrittled at same strength level «(Jy= 1070 :MN m-2)

most sensitive to temperature close to the thres-hold, there was no systematic increase in ~Kowith increasing temperature. Threshold valueswere found to be highest at ambient temperatureand at 350°C, and lowest at l80°C. No explanationshave been proposed for this behaviour. Thresholdvalues for 316 stainless steel, however, wereobserved to increase with temperature over therange 20°-700°C for tests in air, and to remainconstant over the same range of temperature fortests in vacuo and in helium.31 In the latter case,the evidence implies that the influence of temper-ature on near-threshold fatigue behaviour instainless steel at least is primarily a function ofenvironmental factors.

PressureFor high -strength martensitic steels tested inlow-pressure (10-100kPa) hydrogen gas, rates ofcrack growth under sustained loading have beenfound to be sensitive to the pressure of the sur-rounding gas to a degree dependent upon tempera-ture (see e.g.Refs. 58,114-117). At temperaturesbelow about O°C,steady-state growth rates appearto vary with the square root of the hydrogenpressure, between 0° and 40°C growth rates appearproportional to the first power of pressure, where-as between 40° and 80°C the dependence is to the1. 5-power of pressure.115 Limited studies undercyclic loading, where the environmental contri-bution to cracking can be considered to be hydro-gen embrittlement, tend to support these pressuredependences. However, there are no reportedstudies on the effect of pressure, in any environ-

ment, on near-threshold crack-propagation rates,either for low pressure (10-100 kPa) atmosphereswhere hydrogen embrittlement predominates, orfor high-temperature (350°C), high-pressure(10 MPa) atmospheres where hydrogen attackl18predominates. Since the latter environments areparticularly important with regard to pressure-vessel steels for coal gasification or liquifactionprocesses and pipeline steels for potential hydro-gen transport, this is an area where there is agreat need for future study.

Environmental speciesWhereas it is generally accepted that the nature ofthe environment plays a prominent role in influ-encing intermediate growth -rate fatigue -crackpropagation behaviour, opinion is still somewhatdivided with respect to the influence of theenvironment at near-threshold rates. On the onehand, there are the initial results of Paris andco-workers6,7,35 on low-strength steels andtitanium alloys which showed no variation inthreshold behaviour with change in environment,for tests at high frequency (160 Hz). Specifically,no change in near -threshold growth rates and thevalue of ~Ko at ambient temperature were ob-served for: (a) A533-B nuclear pressure-vesselsteel (Fig. 18) tested in air and distilled water6;(b) low-strength T-l steel tested in air, distilledwater, and hydrC'6en gas 7;and (c) Ti-6AI-4Vtested in air and dry argon of unspecified purity.35Somewhat similar results have been seen in high-strength D6ac steel and a 7050-T73651 aluminiumalloy,22 where threshold ~Ko values were un-



air .21, 31, 37-4 0, 80, 81 Cooke et al.21 found anincrease in 6.Ko from 5 to 7 MN m -3/2 at R:= 0.1and from 3 to 7 MN m-3/2 at R:= 0.7 for En 24steel, tempered at 500°C, tested.Jn vacuo (10-3 Pa)compared to air (Figs. 6 and 19). Similar studieson both high -purity and commercial-purity heatsof the same steel (UK equivalent of 4340) tem-pered at 200°C, confirmed the marked reductionsin near-threshold growth rates and the increasein 6.Ko for tests in vacuo compared to air81

(Fig. 6). In both cases, growth rates in vacuowere independent of load ratio over the rangeR := O. 1-0. 7 (Refs. 21,81). More recent data byLindley and Richards80 for 13%Cr martensiticstainless steels (En 56 and FV520B) also revealappreciable increases in 6.Ko in vacuo '(10-3 Palcompared with air at 70 Hz, although for thesesteels a slight R-ratio dependence on 6.Ko wasstill apparent in the inert environment. Similarbehaviour has been observed in non -ferrousalloys. In Ti-6AI--4V,for example, several in-dependent studies37,39,40 have shown increasesin 6.Ko' for tests in vacuo compared with air, ofthe order of 3-8 MN m-3/2 at R:= 0.35.Furthermore, Bathias et al.32 measured an in-crease in 6.Ko from 3.5 to 6. 1 MN m -3/2 atR := 0.01 in T651 aluminium alloy by testing in avacuum of 10-3 Pa compared with air. One is ledto believe here that the difference between thesetwo opposing sets of results lies principally in thenature of the 'inert' environment, i.e. high vacuum(better than 10-3 Pa) v. dry argon. First, how puremust the argon atmosphere be to produce noenvironmental action at the particular test fre-quency, and secondly, are rewelding effectsoccurring for cracking in vacuo? Typically im-purity contents of argon atmospheres are gener-ally quoted as being in the region of 20-50 ppmwater vapour, plus smaller quantities of oxygen,nitrogen, an,d hydrogen, which correspond to an


~ 4 R air vacuum~10- 0.2. 0~ 0.3. 0

E 06-07£ 6

E•..10-s

z"0ro 10-6~

19 Near-threshold fatigue-crack propagation inhigh -strength martensitic En 24 steel (tem-pered at 500OC),showing influence of loadratio from R := O. 17 to O. 73 in moist labora-tory air and in vacuum (10-3 Pal environ-ments (after Ref. 21)

distilled waterR=O'10spec no. 4Qf=160Hzo f=120 Hzdf =60 Hzspec no.5* f= 160 Hz6 f= 120 Hz

spec no.8o f= 160 Hz

room temp. airR=0·1

*~~

Q ~*Q~~

**~

~~Q

o

(no growth)10-9

5

•..Z"0

eu"0

18 Near-threshold fatigue-crack propagation inASTM A533B nuclear pressure-vessel steel(0. 2C-l. 5Mn-o. 7Ni-o. 5Mo),tested between60 and 160 Hz at R := 0.1, showing a com-parison of data for distilled water with 'best-fit· data line for room -temperature air (afterRef. 6)

changed in air and dry and wet argon atmospheresat 100-374 Hz, although near-threshold growthrates were marginally lower in dry argon com-pared to air in the steel and significantly lowerin the aluminium alloy. On the other hand, thereare results where significant decreases in near-threshold growth rates were observed by com-paring crack propagation in vacuo to laboratory


202

1//'f

l/1

/1./ I/ I- / //0• -to?

- I/ ItI_ '8l. I/ l

/- 0

/ - II II I

air---T l-stC2amI ~I I

_ air

o staam

•...-Z'0-tU'0

a and c near-threshold growth rates; b growthrates >10-6 mm/cycleBands of corrosion products on fatigue test-pieces of 9Ni-4Co high-strength steel(lIP 9-4-20)

20 Near-threshold fatigue-crack propagation inNi--Cr-Mo-V A471 rotor steel «1 = 880MN m -2) tested at R = 0.35, 100 lIz in air andsteam at 100OC,showing reduction in growthrates owing to environmental effects (afterRef. 120)

21

a b c

effective partial pressure of water vapour in theregion of 2 to 10-2 Pa, constituting a poorvacuum. 3 7 Comparison of fatigue behaviour inTi-6Al-4V'in rigorously purified argon and in a10-5 Pa vacuum revealed that propagation rates

'were almost identical at high growth rates, butdiffered by a factor of two in the region 10-5-

10-4 mm/cycle (Ref. 119). Differences at near-threshold growth rates would be expected to beeven more significant. Accordingly, it is felt thatthe absence of environmental effects in the formerset of results 6, 7,35 can be rationalized in termsof the fact that comparisons were not made witha truly inert reference environment. 37 Further,the extremely high frequencies utilized in thesetests would reduce significantly any environmen-tal influence. Precise resolution of this issue,however, must await near-threshold fatigue-crackpropagation data, for a single material, in vacuo,purified argon, and more aggressive environments,such as air, H20, H2, H2S, etc., over a range offTequencies. Additional evidence for an environ-mental effect on near-threshold behaviour can befound in the work of Pook and co-workers.17,20

They observed that, for zero-tension loading in

mild steel at ambient temperature, the value of!J.Ko was reduced from 7. 3 MN m -3/2 in SAE 30oil to 6. 0 MN m -3/2 in air, and significantlyreduced to 2. 0 MN m-3/2 in brine. '

There is also an added complication in aggres-sive or wet corrosive environments that near-threshold growth rates may be reduced comparedwith more inert atmospheres. This may arisefrom 'oxide-wedging' effects, where the presenceof thick corrosion products in the crack may pre-vent further access for environmental species(akin to passivation), or from certain environmentswhich promote crack branching or meandering.An example of these effects can be seen from thework of Tu and Seth120 on A470 and A471 Ni-Cr-Mo-V rotor steels where near-threshold growthrates were reduced and the threshold increasedwhen tests were conducted in steam as opposedto air at 100°C (Fig. 20).

Thus, although the extent of data is still some-what limited, there is good direct evidence in theliterature to support the hypothesis that near-threshold fatigue-crack propagation is environ-mentally sensitive. However, as with any corrosion-



a and b transgranular mode close to threshold at M = 5.5 MN m-3/2; c and d transgranular andintergranular modes at M = 6.5 MN m-3/2; e and jtotal absence of intergranular mode at highergrowth rates at t:J( = 11 MN m -3/2

22 Fractography of near-threshold fatigue-crack growth in HP 9-4-20 high-strength aerospace steel(cry = 1300 MN m-2), tested in moist laboratory air at R = 0.1

related process, there is unlikely to be a singleunifying mechanism for the extent of the environ-mentally-assisted contribution to cracking in allmaterials, and clearly much research is stillneeded to characterize these interactions.

FRACTOGRAPHY OF NEAR-THRESHOLD GROWTH

Although the precise mechanisms of fatigue-crackpropagation at low stress intensities are unknown,the morphology of near-threshold fracture surfaces



has been well characterized. Macroscopically, aband of corrosion product is generally seen onfracture surfaces at the exact location wheregrowth rates have been less than 10-6-10-7 mm/cycle (Refs. 13, 21, 23, 102). An example of this isshown in Fig. 21 for ambient-temperature air testson a high -strength 9Ni-4Co aerospace steel(HP 9-4':-20); no such corrosion product is apparentat higher growth rates.l02 This is clearly indica-tive of significant environmental action at near-threshold levels, even in air.

Microscopically, near-threshold growth hasbeen termed 'microstructurally-sensi-tive'13,21,33,34,36,37,41 owing to the presenceof isolated planar trans granular or intergranularfacets within a flat, ductile trans granular mode.Examples of such microstructurally-sensitivegrowth are shown in Fig. 22 for ambient -tempera-ture air tests on HP 9-4-20 steel, and should becompared with growth mechanisms at much highergrowth rates (Le. regimes B and C in Fig. 2) shownin Fig. 3d for the same steeL Note the presenceof intergranular facets within a planar transgranu-lar mode at stress intensities just above thethreshold (Fig. 22c). Very close to the threshold,the proportion of facets is generally small (""1%),increasing to a maximum of anywhere from 10 to80% as ~K is increased, and then gradually dimin-ishing at higher K values in the midgrowth rateregime. The maximum proportion of facetsappears to occur when the cyclic. plastic- zone sizeapproaches the grain size,13,21,33,34,36, 37, 41,81,99whereas the disappearance of facets seems tooccur when the -maximum plastic-zone size exceedsthe grain size. 99 Such facets are intergranular inferritic steels, 10,13,21,23-27,41,63, 78,80,81,99, 102and transgranular in austenitic stainlesssteels 30-32,41,121 and alloys of titan.-ium, 33-37,41, 70 aluminium,41 copper, 41,44 andnickel. 41 A survey of such fractures presented byBeevers,41 identifies the transgranular facets,termed 'cyclic cleavage', with {Ill} planes instainless steels, 121 nickel superalloys, andAl 2219-T6, {001}planes in AI-Zn-Mg, and {1017}in Ti-6A1-4V (Ref. 70), and so forth. It has beendemonstrated, by spiking the loading sequence,that such cyclic-cleavage facets in titaniumalloys 70 and 316 stainless steel, 121 form as aresult of continued load cycling, and thus are notcleavage cracking in the true sense.

In high-strength martensitic steels, the pre-sence of intergranular facets at near -thresholdgrowth rates appears to be additionally relatedto the possibility of impurity-induced grain-boundary segregation.25,27,81, 122, 123 This canbe appreciated by varying the tempering tempera-ture in 4340-type martensitic steels, where micro-structures subject t9 impurity segregation duringaustenitizing,122,123 tempered martensite em-brittlement, 122,123 or temper embrittlement25show significantly more evidence of intergranularseparation at near-threshold growth rates. Simi-1ar results have been observed by comparing high-purity heats with commercial (impure) heats of


En 24 steel,81 although, somewhat surprisingly,in many cases the presence or absence of inter-granular fracture did not appear to have muchdirect effect on near-threshold crack velocities.

A more important and clearly interrelatedaspect of such near-threshold facets is that theyappear to be primarily environmentally-induced.First, facets are not observed at intermediategrowth rates25-27 and are largely suppressed fortests in vacuo, dry air, and helium atmo-spheres.2 1,31, 37,80,81 Furtherm ore, intergranu-lar cracking in high-strength steels is commonlyassociated with hydrogen embrittlement, 68,69 andcleavage on {1017} in Ti-AI alloys coincides withthe habit plane of the hydrides. 71

Aside from the presence of the facets, fewmechanistic conclusions have been made fromfractographic studies of near-threshold fatiguesurfaces, principally because the fine-scaledetails (Le. striation spacings should they exist)are below the resolution obtained from scanningmicroscopy or replica work. Fractures appearmicroscopically very planar and transgranular,and, in general, resemble low-magnificationimages of fractures at intermediate growth rates.Certain authors 14 have claimed that near-thres-hold propagation occurs locally by a Mode IImechanism involving regions of intense shear,although such features have not been observed inmost fractographic studies on steels. For a morecomplete survey of near-threshold fracture-surface morphology the reader is referred toRefs. 41 and 81.

DISCUSSION

Environmental effects

It is apparent from the above that, unlike fatigue-crack propagation at intermediate growth rates,near-threshold behaviour is particularly sensitiveto microstructural factors such as cyclic strength,grain size, grain-boundary composition, structure,and so forth, in addition to being markedly depen-dent upon the mean load or R ratio. This micro-structural dependence is particularly encouragingfor the metallurgist since it implies that there isa potential for the alloy design of materials withimproved resistance to very high cycle, low-amplitude fatigue-crack propagation, a procedurewhich is extremely limited for the microstruc-turally-insensiti ve intermediate growth rates shortof increasing the elastic modulus. Furthermore, onthe basis of somewhat restricted and often conflic-ting results, it appears that such near-thresholdgrowth is dependent on the nature of the environ-ment. The question which arises is whether suchmicrostructural effects can be traced to thisenvironmental interaction or to some otherphenomena such as crack closure. 82 In view ofthe limited data available and the complexities ofvarying environmental mechanisms between dif-ferent materials, a conclusive answer to this ques-


By combining equations (11) and (12), and incorpor-

where 0y is the yield strength, R the load ratio, I

and Band B' are constants dependent upon tem-perature. At ambient temperatures in steelsB == 8 X 10-4 (MN m -2) -1 and B' == 5 X 10-2(MN m-3/2)-1.

Because of uncertainty in the magnitude ofvarious parameters in the model68, 69 for hydro-gen embrittlement (Le. Co and a), It is perhapspremature at this stage to utilize the above rela-tionships in a predictive capacity. However, suchequations do provide a useful basis for rational-izing the observed near-threshold fatigue-crackpropagation behaviour in high -strength steels.First, the occurrence of interg~anular fracture inhigh -strength steels during near -threshold crackgrowth in moist air (Fig. 22) or hydrogen-contain-ing gas atmospheres, and the absence of suchfracture for tests under inert conditions21, 31, 80, 81lends strong support to a hydrogen-embrittlementcontribution to crack growth. Secondly, on thebasis of equation (12), values of 1:J.Ko should belarger in inert environments, consistent with allreported experimental results (e.g. Figs. 6 and 19).Thirdly, the load-ratio and yield-strength effectson near-threshold growth (e.g. Figs. 5-7 and 19,and 4 and 9, respectively) are capable of interpre-tation since an increase in either parameter willresult in a larger hydrostatic stress state a, which,in turn, raises the local concentration of hydrogenahead of the crack tip (equation (11)) leading to areduction in t!:J.Ko (equations (12) and (13)). More-over, since the influence of load ratio arises fromsuch environmental interactions, it follows that ininert atmospheres, near -threshold growth ratesand threshold values should be less affected byload ratio, consistent with results21, 80,81 foraustenitic and martensitic low-alloy and stainlesssteels tested in air and vacuum (e.g. Figs. 6 and19). Thus, the observed effects of load ratio andstrength on fatigue-threshold behaviour in high-strength steels can be thought of in terms of anenhanced environmental contribution to crackgrowth arising from an increase in hydrostatictension. Additionally, increasing the load ratiowill raise Kmax, which, in turn, leads to a largerplastic stress gradient ahead of the crack tip, thusproviding a greater driving force for the transportof hydrogen into the region of maximum triaxiality.

Results,26,102 showing improved resistanceto near-threshold fatigue-crack propagation intempered martensitic structures containing almostcontinuous networks of interlath retained austenite(e.g. Fig. 14) are also consistent with this environ-mental model, since hydrogen diffusivity in the fcc

(13)

ating an expression for the maximum hydrostatictension, it can be shown 27 that

(10)

(11)

(12)

CH ( av )Co == exp RoT

tion is not possible at present. However, by exam-ining behaviour in high-strength steels, where theprimary mechanism of environmental attack duringfatigue -crac.k growth in moist air, water, and low-pressure hydrogen environments is hydrogenembrittlement,72 some consistent, yet necessarilysimplistic, explanation can be developed.27 .

In the absence of any environment, there aretwo physical models 124,125 for the existence of afatigue -crack propagation threshold wIilch give anexpression for Mo in the form

In the model of Weiss and Lal, 124 p* is taken asthe limiting microstructural dimension over whicha certain local critical fracture stress OF must beattained ahead of the crack tip for propagation tooccur, the constant C being numerically equal to.J372. The model of Sadananda and Shaninian, 125

on the other hand, equates the threshold with theminimum stress OF to nucleate a dislocation atthe crack tip~where p* is the minimum distancethat the dislocation can exist away from the tip(taken as the Burgers vector). In this form,equation (10) does not predict any variation of1:J.Ko with mechanical and microstructural factors(e.g. load ratio, strength, and so forth) under totallyinert conditions, consistent with the very limitedexperimental data available.21,32,37,81

However, in the presence of 'hydrogen -produc-ing, environments, cyclic stressing will lead tochemical reactive surface at the crack tip whereatomic hydrogen, evolved by cathodic reactions oradsorbed from the gas phase, can enter the latticeand diffuse under the driving force of the stressgradient into the region ahead of the crack tip. Inthe proposed hydrogen -embrittlement mechanismsfor high-strength steels, 38, 68,69 hydrogen is con-sidered to diffuse to the point of maximum hydro-static tension. (i.e. maximum dilatation), and lead toa reduction in cohesive strength. The enrichmentof hydrogen ahead of the crack tip is a function ofthe magnitude of the h·ydrostatic tension a, and isgiven thermodynamically by

where CHis the local hydrogen concentration atthe point of maximum dilatation, Co the equilibriumhydrogen concentration in the unstressed lattice,v the partial molar volume of hydrogen in iron,Ro the gas constant, and T the absolute tempera-ture. 68 Thus, if the reduction in cohesive strengthdue to hydrogen 1:J.o His assumed to be proportionalto CH' i.e. 1:J.0H== a CH' then in the presence of ahydrogen -producing environment, the Weiss andLal expression for the threshold becomes:



o

1000 1500 2000STRENGTH, MN m-2

Ritchie24-27

Paris et al.6Bucci et al?Pook5

Priddle and Jerram 10, 56

Beevers et al.78

Masounave and Bailon15,16,18Cooke et aI.12,13,31

p. =1500A

p. =800A

p. =300A

o

2

<? 140::

~ 12o~

<l 10o6 8IIf) 6w0::I 4I-

Crack-closure effects

To justify the existence of a fatigue -crack propa-gation threshold and to explain various character-istics of subsequent near-threshold crack growth,many authors have used arguments based on thephenomenon of crack closure.6,7,14,19,28,35,42,79,129,130 However, in the light of existing infor-mation, the role of closure on ultralow crack-propagation behaviour is somewhat open toquestion, as discussed below.

The concept of crack closure, first describedby Elber82 for crack growth at high stress inten-sities, relies on the fact that, as a result of plasticdeformation left in the wake of a growing fatiguecrack, it is possible that some closure of the cracksurfaces may occur at positive loads during theloading cycle. Since the crack is unable to propa-gate while it remains closed, the net effect ofclosure is to reduce the applied t::::.K value (com-puted from applied load and crack-length measure-ments) to some lower effective value /:i.Keff actu-

23 Variation of published data on threshold I:t..Koat R = 0 with strength for steels, showingpredictions of environmental model (equation(13»

propagation occurs at much slower near-thresholdgrowth rates .83 Mechanisms for this hydrogen-assisted growth, which certain authors 47,4 9 havetermed hydrogen embrittlement, are presently un-known, yet are unlikely to be similar to classichydrogen -embrittlement mechanisms (i.e. deco-hesion) operative in higher strength steels. Thus,until this hydrogen -induced contribution to crack-ing is understood, particularly close to t::::.Ko'rationalization of near-threshold fatigue~crackpropagation behaviour in low-strength steels isclearly not possible.

austenite is three to four orders of magnitudelower than in the bcc phase .10 1,126 Furthermore,the lower growth rates observed27 in coarsergrained structures (e .g. Fig. 11) can be rationalizedin terms of a lower probability of hydrogen atomsreaching a grain boundary, 9 9 as discussed above,although more recent data showing a decrease in/:i.Ko with increasing prior austenite grain size(Fig. 12) cast some doubt on this explanation.29However, heat treatments used to vary prioraustenite grain size in steels (e.g. by increasingaustenitizing temperatures) are liable to resultin other microstructural changes,29 such asvarying the distribution of grain -boundary em-brittling impurity elements.127 Finally, the effectof such impurity segregation in reducing thethreshold (Fig. 17) is readily explained in termsof this analysis, since the presence of residualimpurities in grain boundaries will also lead toreduced cohesion.2 5 There is also a possibil.ity ofsynergistic effects between hydrogen and impurityatoms 25 arising from the fact that such impuritiesmay act as recombination poisons for atomichydrogen.128

It is apparent, therefore, that by consideringthe environmental contribution of hydrogen tocrack growth, near-threshold fatigue behaviour inhigh -strength steels can be usefully rationalized interms of microstructure and load -ratio effects.As described in Ref. 27, the model can be utilizedsemiquantitatively by assigning reasonable valuesto equation (13), such that the experimentallyobserved trend of decreasing t::::.Ko with increasingstrength in steels can be correctly reproduced(Fig. 23). Further verification, however, mustawait more extensive data showing the influenceof mechanical and microstructural factors on near-threshold fatigue-crack propagation in high-strength steels under environmental and, particu-larly, inert conditions.

It is important to realize that the model des-cribed above is orily strictly valid for higherstrength steels where the environmental contribu-tion to cracking in the presence of hydrogen-producing environments can be modelled in terms.of a 'decohesion' mechanism of hydrogen embrittle-ment.38,68,69 Lower strength steels, such as mildsteel and certain pressure-vessel steels (e.g.A387) where yield strengths are below 500 MN m -2,similarly show marked effects of microstructureand mean stress at near-threshold growth rates inmoist air, and yet the possible enrichment of hydro-gen ahead of the crack tip, predicted from equa-tion (11), would be very small owing to the lowermagnitude of the hydrostatic tension. Thus, anyexplanation of the characteristics of near-thres-hold fatigue-crack growth behaviour for such low-strength steels in terms of a decohesion hydrogen-embrittlement model must be regarded as unlikely.However, as discussed above, such steels do showmarked environmentally-enhanced fatigue -crackpropagation above 10-6mm/cycle in H2, H2S, andwater environments, 47-49,73-75 and there areindications that similar hydrogen -assist~d crack


ally experienced at the crack tip. It follows fromthis argument that a threshold for crack growthwill be reached when the c"rack remains closedthroughout the entire loading cycle. CertainJapanese workers have claimed to verify this byreporting that at the threshold the range of effec-tive stress intensity LlKeff, based on surfacecompliance measurements, has no finitevalue. 129,130 Subsequent more extensive studieson a wider range of steels, however, failed to sub-stantiate this claim.19 Other authors 6,7,28,35,42have utilized the closure concept to explain theload -ratio effect on the assumption that as themean load is raised, the crack will remain openfor a larger portion of the cycle, thereby in-creasing LlKeff and hence the growth rate. Sucharguments have been applied to near-thresholdbehaviour in steels, 6,7,28 titanium, 35 andaluminium42 alloys, but with little or no experi-mental verification. There are, however, severalbasic problems with this explanation for near-threshold behaviour. First, it is difficult usingclosure arguments to account for the fact that theinfluence of load ratio becomes minimal at inter-mediate growth rates (regime B in Fig. 2) whereclosure is equally likely to occur. To counter this,it has been suggested14,131 that the closure effectmay be enhanced in the near-threshold region be-cause of the presence of a shear mode of fracturealthough, as discussed above, the notion that near-threshold failure mechanisms are essentiallyMode II in nature does not appear to be universaland, further, it is by no means certain why this initself should increase closure loads. Secondly,certain workers have observed that the level ofclosure in iriert environments is greaterthan132-134 (or at least equal to 135) the level inair. If the origin of the load -ratio effect weresimply crack closure, this would imply that near-threshold growth rates would be more sensitiveto load ratio in inert atmospheres, which iscontrary to all experimental observa-tions.21,31,37,39,40,80,81 Thirdly, there is nowa large body of evidence131,136,137 to suggestthat crack closure is essentially a surface (planestress) effect, having a minimal consequence oncrack growth under plane-strain conditions. Sincenear-threshold growth is invariably measuredunder plane-strain conditions, it seems unlikelythat crack closure could be primarily responsiblefor the marked dependence on load ratio. Theissue, however, must remain somewhat unresolvedsince there is still a certain degree of uncertaintyin the experimental measurement of closure; theelectrical-potential and compliance tec.hniquesused often yield inconsistent results .138,139

Undoubtedly, crack closure does occur duringfatigue-crack growth, but in the light of recentevidence by Wei et al., 140 which showed nosensible correlation between crack-propagationkinetics and LlKeff, models based on this conceptto explain crack-growth behaviour patterns atnear-threshold levels must be regarded asquestionable.


CONCLUDING REMARKS

In this paper, an attempt has been made criticallyto review existing information on the character-istics of near-threshold fatigue-crack propagationin steels with particular emphasis on the possiblerole of environmental contributions to crack growth.However, despite a rapidly increasing interest inthis field over the past five years, there is stillvirtually no mechanistic basis for near-thresholdbehaviour and still a comparative lack of reliableengineering data. Further, it is clearly apparentthat many fundamental questions remain un-answered, such as the precise role of the environ-ment especially in low- strength steels and therelevance of crack closure. Additionally, the use-fulness of threshold data to the problem of shortcracks, which are most often found in service, islargely unsolved, particularly in the light of therelationship between threshold data, representingthe fracture-mechanics approach to growth (orlack of growth) from long cracks, and the S-N andfatigue -limit data, representing principally initia-tion from short cracks. At first glance, it wouldseem that both parameters are closely relatedsince they both describe limits for fatigue damage,and yet, as described, by raising the strength of asteel the fatigue limit is generally increasedwhereas the threshold is decreased. Thus, foralloy-design purposes, procedures designed tooptimize high-cycle crack-propagation resistancewill not necessarily guarantee similar optimumresistance to crack initiation. Hence, before re-commendations can be made for the selection of asuitable material to withstand high-frequency low-amplitude cyclic loading, the relative importance ofcrack initiation and crack propagation must beclearly established.

The relevance of near-threshold crack-growthdata, however, cannot be underestimated. Defectsintroduced during fabrication or developed inservice become potential sources for catastrophicfailure from subcritical cracking at seeminglyimmeasurable growth rates where components aresubject to high -frequency low-amplitude cyclicloading. This is especially important where suchfluctuations are superimposed on a mean operat-ing stress which results. in extremely high loadratios. Examples of the use of threshold data fordesign and post-failure analysis are now becom-ing more .numerous, particularly in the electrical-supply industry for high -speed rotating equipmentand components subject to acoustic fatigue. How-ever, in other applications, such as large-scalenuclear and coal-conversion pressure vesselswhere small operational transient' stresses mayresult in significant near-threshold crack growthover long periods of time, relevant low growth-rate data for typical environments are still lack-ing. Although widely recognized in certaincountries (see e.g. Refs. 2-4, 80, and 141), rela-tively few studies are in progress in the USA and,despite the achievements of the last five years,there still remains an important need for both



fundamental and applied research on near-threshold fatigue behaviour.

ACKNOWLEDGMENT

The work was supported by the Fossil EnergyResearch Division of the US Department ofEnergy under contract No. EX-76-A-D1-2295.

REFERENCES

1. S. W. Hopkins, C. A. Rau, G. R. Leverant, andA. Yuen: 'Fatigue crack growth under spec-trum loads', STP 595, 125; 1976, Philadelphia,Pa, American Society for Testing andMaterials.

2. 1.Gray, M. D. Heaton, and G. O~tes: Proc. ofBritish Steel Corporation Conf. on 'Mechan-ics and mechanisms of crack growth' ,Cambridge University, April 1974, 264.

3. M. D. Heaton: 'The mechanics and physics offracture', 34; 1975, London, The MetalsSociety.

4. J.R.Griffiths and G.Oates: Met. Sci., 1977,11,285.

5. L. P. Pook: 'Stress analysis and growth ofcracks' , STP 513, 106; 1972, Philadelphia, Pa,American Society for Testing and Materials.

6. P. C. Paris, R. J. Bucci, E. T. Wessel, W. GClark, and T. R. Mager: ibid., 14l.

7. R. J. Bucci, W. G. Clark, and P. C. Paris:ibid., 177.

8. M. Klesnil and P. Lukas: Mater. Sci. Eng.,1972,9,231.

9. M. Klesnil and P. Lukas::Eng. Fract. Mech.,1972,4, 77.

10. E. K. Priddle: 'Constant awplitude fatiguecrack propagation in a mild steel at lowstress intensity: the effect of mean stress onpropagation rate', Technical Report RD/B/N2233, May 1972, Berkeley Nuclear Labora-tories, Central Electricity Generating Board.

11. H. Kitagawa, H.Nishitani, and- j. Matsumoto:'Proc.3rd into congr. on fracture', Vol. 5,Paper V-444/ A; 1973, DUsseldorf, VereinDeutscher EisenhUttenleute.

12. R.J.Cooke and C.J.Beevers: Eng. Fract.Mech., 1973, 5, 106l.

13. R. J. Cooke and C. J. Beevers: Mater. Sci.Eng.,-1974, 13, 20l.

14. A. Otsuka, K. Mori, and T. Miyata: Eng. Fract.Mech.,1975,7,429.

15. J.Masounave and J.-P. BaIlon: Scr. Metall ..,1975, 9, 723.

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35. R. J.Bucci,'P. C. Paris, R. VI. Hertzberg, R. A.Schmidt, and A. F. Anderson: 'Stress analysisand growth of cracks', STP 513,125; 1972,Philadelphia, Pa, American Society for Test-ing and lVJ:aterials. ,

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cal behavior of solids'; 1979, Tokyo, 118. P. G. Shewmon: ibid., 1976, 7A, 279.University of Tokyo Press. 119. R. P. Wei and D. L. Ritter: J. Mater., 1972,7,

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95. R.M.Pelloux: 'Ultrafine-grain metals', 231; 122. R. O. Ritchie: Eng. Fract. Mech., 1975,7,187.1970, Syracuse, NY, Syracuse University 123. R. O. Ritchie: PhD thesis, University ofPress. Cambridge, 1973.

96. A. W. Thompson and R. J. Bucci: Metall. 124. V.Weiss and D.N.Lal: Metall. Trans., 1974,Trans., 1973,4,1173. 5, 1946.

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J. Eng. Mater. Technol. (Trans. ASME, H), 126. J. H. Shively, R. F. Hehemann, and A. R.1979, 101, 86. Troiano: Corrosion, 1966,22,253.

99. J. D. Frandsen and H. L. Marcus: Scr. Metall., 127. G. Clark, R.O. Ritchie, and J. F. Knott:1975, 9, 1089. Nature Phys. Sci., 1972,239,104.

100. J. F. Lesser and W. W. Gerberich: Metall. 128. R. M. Latanision and H. Opperhauser: Me tall.Trans., 1976, 7A, 953. Trans., 1974,5,483.

10l. R. O. Ritchie, M. H. Castro Cedeno, V. F. 129. H. Nisitani and K. Takeo:,Eng. Fract. Mech.,Zackay, and E. R. Parker: ibid., 1978, 9A, 35. 1974,6,253.

102. R. O. Ritchie, V. A. Chang, and N. E. Paton: 130. A.Ohta and E. Sasaki: Int. J. Fract., 1975, 11,J. Fatigue Eng. Mater. Structures, 1979,1. 1049.

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104. E. E. Fletcher, W. E. Berry, and G. A. Elsen: 133. P. E. Irving, J. L. Robinson, and C. J. Beevers:ibid., 457. ibid., 619.

105. W. W. Gerberich: 'Hydrogen in metals', (eds. 134. P. E. Irving, J. L.Robinson, and C. J. Beevers:I. M. Bernstein and A. W. Thompson), 115; Int. J. Fract., 1973,9,105.1974, Metals Park, Ohio, American Society 135. V. Bachmann and D. Munz: ibid., 1975.11.713.for Metals. 136. T. C. Lindley and C. E. Richards: Mater. Sci.

106. C. B. Gilpin and N.A. Tiner: Corrosion, 1966, Eng., 1974,14,281.22,271. 137. F. J. Pitoniak,A. F. Grandt. L. T . Montulli, and

107. C. S. Carter: ibid., 1969,25,423. P. F.Packman:'Eng. Fract. Mech., 1974,6,663.108. R. O. Ritchie: 'Environment sensitive frac- 138. C.K.Clarke and G.e.Cassatt: iboid., 1977, 9,

ture of engineering materials " (ed. Z. A. 675.Foroulis), 538; 1979, New York, AIME. 139. V. Bachmann and D. Munz: ibid., 1979,11,61.

109. H. Suzuki and A. J. McEvily: Metall. Trans., 140. K. D. Unangst, T. T. Shih, and R. P. Wei: ibid.,1979, lOA, 475. 1977, 9, 725.

110. G. J. Fowler: Mater. Sci. Eng., 1979,39, 12l. 141. 'Crack arrest threshold ~Kth'; French Round111. A. D. Wilson: J. Pressure Vessel Technol. Robin Program on Threshold Testing, Groupe

(Trans. ASME, J), 1977,99,459. de la Commission de Fatigue, May 1978.112. P. Shaninian, H. H. Smith, and J. R. Hawthorne: (Translated by ASTM for E. 24. 04 Subcom-

Weld. J. Res. Suppl., ,1972,51, 527. mittee on Subcritical Crack Growth.)

© 1979 The Metals Society and the American Society for Metals


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