fracture mechanics characteristics of the phenomenon - the crack growth kinetics vWcurve and ... assisted cracking; fracture mechanics approach; safe design.
Materials
& Design, Vol. 18. No. 2, pp. 87-94, 1997 0 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0261-3069/97 $17.00 + 0.00
ELSEVIER
PII: SO261-3069(97)00092-7
The reliability of the fracture mechanics approach to environmentally assisted cracking: 1. Uniqueness of the v(K)-curve J. Toribio*,
V. Kharin’
Department of Materials Science, Elvfia, 15192 La Coruiia, Spain Received
University
of La Coruiia,
ETSI Caminos,
Campus de
18 August 1997; accepted 3 October 1997
This paper analyzes the reliability of the fracture mechanics approach to environmentally assisted cracking in engineering design. A wide collection of experimental evidences of uncertainty in the fracture mechanics characteristics of the phenomenon - the crack growth kinetics vWcurve and the threshold stress intensity factor K,, - is presented. Although these basic fracture mechanics items are supposed to depend so/e/y on the material and the environment, they are notably sensitive to the influence of a wide family of test/service variables, producing loss of confidence in materials 0 1997 Elsevier Science Ltd. All rights reserved. evaluation and structural integrity assessment.
Keywords: environmentally
assisted cracking; fracture mechanics approach; safe design
Introduction Engineering design frequently includes problems of environmentally assisted cracking (EAC) in materials and structures, a phenomenon which appears in diverse forms, such as stress corrosion cracking @CC), hydrogen assisted cracking (HAC), liquid metal embrittlement (LME), etc.‘. In this framework, the fracture mechanics approach has proved effective for materials evaluation and structural integrity assessment *TV. Confining the consideration to the domain of linear elastic fracture mechanics (LEFM), the keystone of the approach is the crack growth kinetics curve: a plot of crack growth rate u vs. stress intensity factor K. It is defined between the limit crack growth resistance of a material (the fracture toughness K,, i.e. the K value for which crack growth needs no environmental assistance) and the threshold K,, obviously defined as the maximum K level at which EAC cannot be detected for a reasonably long time or, equivalently, the crack growth rate u is still zero, u(K,,) = 0, with appropriate accuracy (Figure I). The idea of the uniqueness of v(K)-curves and thresholds Kth as intrinsic characteristics of material-environment systems forms the backbone of the approach and ensures the soundness of applica-
*Correspondence to J. Toribio. Tel.: 167170. ‘On leave from Pidstryhach Institute Maths, 290601 Lviv, Ukraine.
+34 for
81 167000; Applied
fax:
Mechanics
+34
81 and
tions in engineering design. This uniqueness ensures true matching of the similitude of the crack tip events and, consequently, of crack behaviour in laboratory test specimens and in structural components in service. Therefore it opens the way to reasonable predictions of crack propagation under different circumstances. When for a given material-environment combination the U(K )-curve including Kth is indeed unique, any discrepancy between predicted and observed behaviours should be attributed to roughness in analysis or experimental scatter but not to the concept4. Otherwise conceptual weakness makes the predictions less reliable and calls for more constraints on testing to obtain reliable characteristics of the crack growth resistance parameters in an aggressive environment. A significant body of experimental data supports the presumption of the uniqueness of the fracture mechanics characteristics of EAC3,5-8. However, this widely used approach is not always valid and not only from the limited efficacy of LEFM which fails when an extended plastic zone appears near a crack tip. It is not restricted either to the known phenomenon of a member thickness influence on the crack growth resistance. Another concern related especially to EAC arises since ample experimental evidence exists (although dispersed in a wide literature) regarding ambiguity of EAC characterisation in situations where K-controlled small scale yielding (SSY) at the crack tip was apparently maintained, i.e. LEFM as a mechanical tool should presumably be sound. This part of the revision of the fracture mechanics Materials
& Design
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Environmentally
assisted cracking:
1. Uniqueness
of the Q(@-curve: J. Toribio, V. Kharin global state variables of the environment, such as pressure (P), temperature CT), electrochemical characteristics pH and applied potential, (E,) and chemical composition data, etc.: Q, = {P, T, pH, E “,... }. The righthand part in Equation (1) is considered to be a plain function, i.e. current magnitudes of its arguments render a certain value of v. Correspondingly, the threshold is considered to be the physical constant of a given (material-environment) system, Kth = Kg(@). EAC testing to determine the v(K)-curve and Krh consists in controlled loading/deformation of a precracked specimen under specified environmental conditions and registration of a variation of crack size a with time t: a = a(t)9’10. Data processing yields the crack growth rate v = da/dt and the stress intensity factor
K
KC
K = Ff,(a)
Figure 1 Schematic crack growth kinetics curve with three distinct stages: strong K-dependence within regions I and III and plateau domain II
approach to environmentally assisted fracture outlines the common treatment of EAC and intends to provide a comprehensive list of missed testing/service parameters capable of influencing crack behaviour to make one aware of the factors for the risk of environmentally assisted fracture.
Current fracture mechanics treatment of EAC This section describes the common fracture mechanics approach to EAC for engineering materials evaluation and structural integrity assessment3*5,9-11. The keystone of analyses of cracks in solids is the idea of the mechanical autonomy of the crack tip zone4,12*13,i.e. that all processes related to local rupture and crack advance rely only on the material itself and on some single variable representing the loading intensity in the near tip fracture process zone irrespective of geometry and mode of loading of a particular cracked solid. The stress intensity factor K is believed to serve well for this purpose if SSY conditions4 of the applicability of LEFM are obeyed and some fixed ‘out-of-plane’ (i.e. through-the-thickness or transverse to crack front) deformation constraint of crack tip plasticity is maintained, such as plane stress, zero (common plane strain) or non-zero (generalised plane strain) transverse strainingr4. In EAC the crack growth rate, U, is the key variable which takes into account both mechanical and environmental effects. It is commonly assumed that for a given system (material-environment) equal K produce equal u values3*‘T8 so that the corresponding v(K)-curve becomes the function of only the material and the external environment v = v*(KI@,)
( >
The asterisk is used throughout this paper to emphasise the predetermined nature of the ‘material’ function as the relationship determined solely by the combination (material-environment) and the underlined boldface vector notation Q, indicates a set of relevant 88
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(2)
where F is the generalised load (applied force or displacement) and fp is a geometry-dependent term of a corresponding K-solution for a solid (specimen) with a crack4*‘*,“. Finally, the v(K)-curve can be drawn as a parametric plot v(t)--K(t). The threshold Kt,, may be obtained by means of crack initiation and crack arrest techniques. In crack initiation tests an increasing stress intensity factor is applied from an initial value K, substantially lower than the expected threshold (in step-wise ‘rising-holding’ or monotonous manner) up to initiation of crack growth. When crack arrest techniques are used, a gradually decreasing K(a) is applied during EAC from excessively high values Kj > K,, u to crack self-arrest when approaching the threshold”*’ If . In practice, as the threshold Kth is accepted the maximal K value bearable for a reasonably long time t, with no detectable EAC. The appropriate time base t, is determined from service requirements or experience9~“. For valid testing, precautions must be taken regarding the specimen pre-cracking by fatigue. By analogy with standards for evaluation of fracture toughness* K,, such as ASTM Standard E-39916, the terminal stage of the pre-cracking should be accomplished at a maximum cyclic stress intensity factor K,,, as low as possible’“, preferably below the expected Kth for EAC. No other constraints are usually imposed on EAC testing to obtain the supposedly intrinsic curve v = v(K) and constant K,,, of a material-environment system. The threshold K,,l and v(K)-curve are powerful tools for EAC evaluation and control since they are believed to contain comprehensive data for a particular system (material-environment). Krh determines the condition of crack non-propagation max K(F,a,b)
SK,,(@)
(3)
where maximum is taken over the entire front of a crack whose geometry, as an example, is’represented by two characteristic sizes a and b like the axes of a semi-elliptical surface crack. The v(K)-curve in Equation (1) defines the equa*This paper does not discriminate between plane-strain and plane-stress states focusing on specific environment-related aspects of the topic.
Environmentally
assisted cracking:
7. Uniqueness
of the 8(&wve:
J. Toribio, V. Kharin
tions to predict crack growth2,3*5, as in the following system of differential equations for a semi-elliptical crack
where K, and K, are the stress intensity factor values at corresponding ellipse axes. Solving Equation (4), crack extension with time may be calculated depending on the applied load F and actual or anticipated initial crack dimensions a, and b,. For a single-size through-the-thickness crack of length a, the equation like (4) is easily integrated to yield the time to failure fr using the corresponding stress intensity factor solutron K = K(F,a) for certain solid geometry and loading3 a&Q tf
=
da / a, u* (K(F,a)kD) 1
(5)
where the limit crack size a, corresponds to the achievement of the fracture toughness K,, i.e. K(F,aJ
Uncertainty of the fracture characterisation of EAC
mechanics
= KC
The predictive capability of this fracture mechanics approach to EAC relies on the uniqueness of the u(K)-curve as the characteristic of a specific couple (material-environment). This is considered to be ensured in an obvious manner of LEFM, i.e. by maintaining SSY during crack propagation according to standard requirements about LEFM validity in terms of the sizes of the crack, the ligament and the near tip plastic zone3’4”6. However, the next section displays a complicated dependence of experimental u(Khrves and K,,, on a wider set of testing/service variables. Their influence, but not the accuracy of data acquisition and processing, causes unacceptable variability of EAC resistance characteristics. This uncertainty damages the reliability of material qualification and life prediction.
Knu Figure
Figure 3 Influence on measured Klh and u(K)-curve of the maximum stress intensity factor during fatigue pre-cracking of specimens (curves 1 and 2 correspond to low and high K,,,, respectively)
2
thresholdsI^
Effect of fatigue pre-cracking regime on measured EAC
The following paragraphs describe several factors causing a lack of uniqueness of the fracture mechanics characteristics of EAC. These effects are not attributes of singular material-environment couples, although their exact origins in particular cases may be specific. To this end, the discussion does not go into speculation about the involved physico-chemical-mechanical interactions, but emphasises the testing characteristics which can alter the result. This also implies that peculiarities of an operation routine of a component may affect EAC in service.
Fatigue pre-cracking
The procedure of fatigue pre-cracking of specimens for subsequent EAC tests, namely, its terminal portion, is responsible for initial crack acuity and residual plastic strains and stresses in the vicinity of the crack tip. These factors are commonly recognised as important for any initiation of crack growth, EAC not being an exception. Most of the related studies17-19 concern the role of the maximum cyclic stress intensity factor K,,, at pre-cracking with fixed stress ratio K,,JK,,, = 0, where Kmin is the minimal cyclic stress intensity factor. The general trend shows that measured thresholds increase with higher K,,, so that invalid excessive values of K,, may be obtained, as seen in the rising right-hand branch of the plot in Figure 2. However, the opposite trend may be obtained in the domain of low (K,,,)20 so that a minimum on the K,,(K,,,)-graph apparently exists (Figzue 2). Moreover, under constant K maxp pre-cracking with gradually increasing Kmin at the final stage produces an even lower value of K,,, marked by point A in Figure 2”. Fatigue pre-cracking can also alter the whole v(K)Materials & Design Volume 18 Number 2 1997
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Overload K
V. Kharin
0
4-J’
Crack bluntness dp
Figure 5 Common relationship and initial crack bluntness p
between measured threshold K,,
Initial crack bluntness
ti
K
Figure 4 The effects of pre-EAC loading history: (a) trends of measured K,,, dependence on overload stress intensity factor; (b) variation of u(K)-curve with duration of pre-loading in air at about the same Kj (an arrow indicates the trend of variation with the increase of holding time I~)
curve so that a total deceleration effect of the increasing Km,, on EAC (Figure 3) may be frequently encountered’s,‘9. It seems that the role of pre-cracking is not confined to the initiation of EAC, but affects the EAC proceeding even beyond the residual plastic zone. Prior overload and load hold
Measured K,, and v(K)-curves are found to vary depending on the magnitude of single overloads and time of load hold in an inert environment (e.g. argon or air) before EAC. Overload, i.e. application of some stress intensity factor greater than the initial one Ki in the subsequent EAC test, causes an increase of measured Kl,, with overload above a certain leve121-23 as shown in Figure 4(a). Overloads also influence the evaluation of threshold affectin the incubation period for delayed cracking initiation2 6:y2’ so that it may cause a wrong choice of a time base t, in experiments. Overloading also slows down the crack growth kineticsZ. Besides this, the effect of the pre-EAC loading depends on the time of load holding t, despite the apparent absence in tested materials of time-dependent relaxation and creep-like processes2’j. Experiments display a shift of v(K)-curves in the direction of lower crack growth rate at the same stress intensity factor for longer fh (Figure 4b). This behaviour is consistent with that described in the previous section if considered related to the maximum K attained in the pre-EAC history which governs crack sharpness and also to residual plasticity fields in the near tip zone. 90
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Initial crack tip radius or semi-width p as a measure of crack sharpness has a stron direct influence on the measured Kth (Figure 5) 27*2f A limit bluntness value p* apparently exists below which the effect disappears, enabling one to determine a conservative lower shelf value of KG. This looks similar to the case in ordinary fracture toughness testing3,29. Crack size (length or depth)
Data from interlaboratory research programmes3’ implied that the threshold is somehow affected by the crack length since abnormal scatter the Kth was observed. Furthermore, for short cracks the thresholds were found lower and crack growth rates faster 3’ along the v(K)-curves, especially in its plateau-like portion (Figure 6). With sh o rt cracks, a sort of pseudo-plateau appeared where the v( K&curve declined. This behaviour was observed in tests with specimens having edge cracks of several millimetres in depth whereas the estimated plastic zone sizes were lo-30 pm and thus the influence of specimen side proximity on the near tip elastoplastic stress-strain field might be negligible. This argues for the concept of the chemically short crack to qualify this effect, in contrast to the mechanically short crack associated with the crack tip plasticity scale; both these notions are basically the same as those raised for fatigue cracking32. This is supported by the detected differences of in-crack chemistries between short and long cracks31. K(a)-variation during EAC test: stressintensity gradient dK/da
Test specimens used in EAC studies have various K(a)-calibrations10p’5 depending on the geometry and loading device (gripping system), e.g. maintaining fixed load or constant displacement. Two kinds of K variations are distinguished: (i> increasing K(a), stress intensity gradient dK/da > 0, obviously achieved at sustained load; and (ii) decreasing K(a), stress intensity gradient dK/da < 0, associated with constant displacement tests. Concerning the evaluation of Kth, these two tech-
Environmentally
assisted cracking:
1. Uniqueness
of the v(@-curve: J. Toribio, V. Kharin
Figure 6 Influence of crack length on measured K,, and u(K)-cuwe (curves 1 and 2 correspond to short and long cracks, respectively)
niques9~‘0 - crack initiation with K increase from below the threshold and crack arrest when K decreases from Ki > Krh - may give different results: thresholds determined at crack arrest (dK/da < 0) were reported to be either higher33 or lower34 than those obtained in an alternative way. Different variations of K with crack length a during EAC caused significant discrepancies between crack growth rates in the plateau portion of v(K)-curves35: a lower stress intensity gradient dK/da slowed down the crack growth rate (Figure 7). Initial stressintensity factor
The influence of initial conditions, i.e. initial applied stress intensity factor K,, on K,, and u(K)-curves may be anticipated from tests performed with a crack selfarrest technique (dK/da < 01, although it does not look clear36. There, v(K)-data display deep drops of crack growth rate with apparent threshold values fitting into some scatter band for different values of Ki. This band, and the scatter of crack growth rate, are unacceptably wide, which seems to denote some kind of combined mechanical-environmental action on the
dKiifa
c,
Figure 7 Relative decrease of plateau u as a function of stress intensity gradient in terms of the ratio of u(d K/da) to crack growth rate obtained under conditions of sustained stress intensity factor K(a) = const, i.e. at d K/da = 0
K Figure 8 The effect of initial loading condition - initial applied stress intensity factor K, - on the u(K)-curve: (a) according to data26B34v37from tests with rising K(a); (b) from constant stress intensity factor tests38,3gshowing transition periods
threshold value dependent on test duration, i.e. on an environmental attack time. Spectacular effects of Ki > K,, in EAC tests under rising K(a), i.e. dK/da > 0, have been observed34*37-39 poisoning the idea of the u(K)-curve uniqueness for a (material-enuironment) system. Starting EAC tests with greater initial stress intensity factor values K;, < Ki, < Ki3 shifted the u(K)-curves to faster crack velocities (Figure 8a) 26.34,37.In other studies38,39 u(K)-curves for different Ki reveal transient behaviour towards some reference curve (Figure db). Test interruption
More evidence of the lack of the u(K)-curve uniqueness is given by interrupted EAC tests with recess without loadz”*37. Here, crack growth, initiated at some Ki, continued along the primary u(K)-curve (curve 1 in Figure 9) up to a certain point A where K, > Ki, then a test was interrupted holding a specimen with no load; after some time EAC was re-started at approximately the same stress intensity factor Ki (point A’ in Figure 9). This caused a significant decrease of crack growth rate in a wide range of K (curve 2 in Figure 91, when the crack grew apparently beyond the region affected by residual plastic strains produced at the test interruption point. Test dynamics: loading (displacement)rate
The dynamics of the near tip stress-strain state is the key variable for EAC since near tip material degradation and crack growth depends on how rapidly each of the responsible factors advances, i.e. near tip stressingstraining and kinetic reactions of environment-induced Materials
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A 1 b
/
2 dWdt
A” /
Iii
b K
Figure 9 The effect of test interruption and re-start on the U(K)curve: curve 1 corresponds to an initial run of EAC interrupted at point A; curve 2 relates to reinitiated cracking at A’; arrows indicate the direction of EAC proceeding
degradation. The effects of test dynamics - dependence of the environment sensitive material behaviours on applied rates of loading or displacement (elongation, straining, etc.) - have been reported since the very first studies. It should be noted that any global test dynamics parameter - externally applied displacement, strain, or load rate - can serve only as a control variable, not suitable for quantitative comparison of data. In accordance with the LEFM concept of the K-controlled autonomy of the crack tip region, the relevant reference variable is the local measure of crack tip straining dynamics4’, i.e. the stress intensity rate K’= dK/dt. Although in published data test dynamics were expressed in different terms, such as rates of loading, elongation, crack opening, etc., the discussion continues here in terms of the stress intensity rate as a common representative variable. The role of test dynamics on EAC was noticed in monotonously rising load tests where apparent Kth was measured as the K value at which environmental facilitation of cracking was first detected. The most typical data36,41-44 show that the measured threshold decreases with slower loading/straining rate up to some apparently constant lower shelf value considered to be the ‘true’ K,, (branch 1 of the curve in Figure IOa and a shift of Krh in Figure I&). Nevertheless, other data45-49 reveal the opposite trend, i.e. a decrease of the threshold at faster K’ to an apparent minimum of the measured Kth with loading rate (branch 2 in Figure IOa and a shift of Kth in Fipre I&). With regard to the influence of the test dynamics on crack growth rate, performed studies showed both trends in relation to cracking facilitation/retardation, too. In some cases, faster loading produced an elevation of the u,(K)-curve as a whole (Fi re I&), or at least clearly lifted the plateau velocity4 .P*46,50*51, whereas other data 36 display non- m o n o tonous u-alteration at increasing displacement rate (Figure IOb): retardation of EAC at rather slow strain rates whereas for faster loading the trend changes to the first one. At any rate, despite the controversies over the sign of the effect, its quantitative significance has been well demonstrated. Transient behuvioum
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F
-Km
K
Figure 10 Influence of loading dynamics on EAC: (a) dependence of K,, on loading rate; (b) and cc) experienced trends of variation of the u(K)-curve and K,, on test dynamics (arrows indicate the direction of variation of measured characteristics with rising stress intensity rate)
v(K)-curve as a single-valued function (Equation (1)) of the material and the environment is drawn from observations of transient behaviours where EAC proceeds with varying crack growth rate in spite of maintaining a constant stress intensity factor and environmental parameters. In specimens with constant K(a) = Ki > K,,, transient periods were in evidence38*39 where v gradually increased to a certain steady-state crack growth rate V,,(K) (Figure II). Besides this, after an abrupt step-wise change of the stress intensity factor or environment characteristics during EAC, the crack growth rate remained variable during a considerably long time at newly established constant test parameters before reaching some stationary value52,53. Therefore, an equal stress intensity factor does not always produce the same crack growth rate.
Conclusions Although ample testing and service experience do confirm a reasonable efficacy of fracture mechanics as the keystone of damage control procedures in many cases, the results quoted show that the same stress intensity factor does not always yield equal crack velocities in otherwise identical couples (material-environment). Observed deviations cannot be related to imperfect experimentation and are systematic in distinct to obvious statistical scatter of test data. This uncertainty as regards the basic fracture mechanics characteristics of
Environmentally
assisted cracking: 7. Uniqueness Testing--Pt.
11 12 13 14
Figure 11 Schematic variability of crack growth rate during EAC tests under constant K conditions with different K values Ki, < Kj2 (curves 1 and 2 correspondingly)
EAC, i.e. of the v(K)-curve and the threshold Kth, can cause invalid - excessively optimistic - material evaluation and non-conservative life assessment. The uncertainty of the u( K)-curve and Ktlr means that the process in general is not exclusively Kdominated. The background interactions involved in EAC have been addressed in depth in numerous studies, but no attempt has been made to elucidate the matter of K-dominance over the whole family of contributing events as the check-point for the soundness of the fracture mechanics treatment of EAC. These issues have not been investigated with sufficient thoroughness. Revising the matter of K-control over the EAC constituents is expected to yield more restrictions on procedures of materials testing and structural performance evaluation to ensure safe (conservative) assessments of EAC.
Acknowledgements This work was funded by the Spanish DGICYT (Grant UE94-001) and Xunta de Galicia (Grants XUGA 11801A93 and XUGA 11801B95). One of the authors (VKh) is also indebted to the Spanish Office of NATO (Scientific Affairs Division) and DGICYT (Grant SAB95-0122) for supporting his stay as a visiting scientist at the University of La Coruiia.
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