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The reliability of the fracture approach to environmentally 2. Engineering safe design J. Toribio*,

V. Kharin’

Department of Materials Science, ElviTna, 15192 La CoruRa, Spain Received

mechanics assisted cracking:

University

of La Corufia, ETSI Caminos,

Campus de

18 August 1997; accepted 9 October 1997

In Part 1 of this work, ample experimental evidence was presented of uncertainty in the fracture mechanics characteristics of environmentally assisted cracking. This paper addresses the soundness of the fracture mechanics approach to the phenomenon - the K-dominance over all the process constituents - and reveals the intrinsic variability of the crack growth kinetics curve v= v(K) and the threshold stress intensity factor Kr,,. Suggestions to consolidate the approach by a strictly local treatment are outlined and a procedure is proposed for engineering safe design against environmentally assisted cracking based on the idea of the worst crack tip situation as the intrinsic one for the material-environment system. 0 1997 Elsevier Science Ltd. All rights reserved.

Keywords: environmentally assisted cracking; fracture mechanics approach; safe design

Introduction In engineering design, the basic item of the fracture mechanics approach to environmentally assisted cracking @AC) is the crack growth kinetics curve or relationship between the crack growth rate u and the stress intensity factor K, u = v(K), and the partial concept that a special value of stress intensity factor does exist - the threshold one, K,, - below which no propagation occurs (or is negligible from the engineering point of view)‘v2. A previous paper3 gives a collection of manifestations of the non-uniqueness of the u(K)-curve which produce uncertainty in EAC evaluation. This raises doubts about the intrinsic character of the basic quantities and demonstrates a shortcoming of the current fracture mechanics treatment of EAC. In effect, this shows that the extent to which the &K&curve and threshold stress intensity factor K,, are the properties of only the material and the environment becomes an open issue and some problems on EAC evaluation using fracture mechanics still need to be solved. The aim of this paper is to provide materials and structural engineers with more stringent evaluation of the common fracture mechanics tools for design against EAC and make them aware of the inherent uncertainty

of the fracture mechanics approach regarding EAC. The meaning and significance of this approach to EAC are discussed, focusing on the items of the K-dominance of the key events of the entire process, and suggestions to improve it with a more rigorous treatment are proposed.

The nature of the Y( K)-dependence in EAC The data about ambiguous evaluation of EAC usin fracture mechanics discussed in the previous paper were obtained mostly from experiments with steels subjected to hydrogenous or corrosive environments, the latter in a wide spectrum of electrochemical conditions which promote EAC by different mechanisms from local anodic dissolution to cathodic hydrogenation assisted fracture. Nevertheless, these effects should be anticipated for diverse material-environment combinations since they proceed from interactions of common factors involved in a typical EAC processes. In otherwise identical couples (material-environment) the u(K)-relation seems to depend on a series of variables detailed in the previous study3 but not involved in the key material-environment function .!J= u*(KI@)

*Correspondence to J. Toribio. Tel.: +34 81 167000; fax: +34 81 167170. ‘On leave from Pidstryhach Institute for Applied Mechanics and Maths, 290601 Lviv, Ukraine.

(1)

where the asterisk stands to emphasise the predetermined nature of the ‘material’ relationship peculiar Materials & Design Volume 18 Number 2 1997

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to environmentally

assisted cracking: 2. Engineering

to the combination (material-environment) and Q, means a set of relevant global state variables of the environment, such as pressure (PI, temperature (27, electrochemical characteristics pH and applied potential, (I?,), chemical composition data, etc.: @ = (P, T, pH, E,,...}. Th is calls for a more rigorous evaluation and consolidation of the fracture mechanics approach to EAC which does not seem to be universally valid. The fracture mechanics treatment of EAC is based on the presumption that apart from the properties of the material and the environment, crack growth depends exclusively on: the stress intensity factor as the only ‘external’ variable, i.e. the process is K-dominated. Since EAC involves several physico-chemical events, the uniqueness of v(K)-curves becomes a question of exclusive K-dominance over all the responsible elements which are mainly the following: stress-strain state in the near tip fracture process zone; 0 supply of the harmful environmental agent(s) to prospective damage nuclei which comprises transport of the environmental substances within the crack canal to the vicinity of the tip, surface reactions (interactions) and in many cases the penetration of the agent through material to microstructural rupture sites; 0 near tip material degradation or damage facilitation by environmental substances. l

The constituents of EAC in diverse combinations (material-environment) have already been extensively discussed4-9, but the issues of their K-dominance have not received sufficient attention. The only apparently resolved item refers to the inelastic stress-strain state near the stationary crack tip under small scale yielding (SSY) where K-dominance is ensured with known standard validity limitations of linear elastic fracture mechanics (LEFM)*~“‘,’ ‘. The rigorously local fracture mechanics treatment of EAC

Turning to the other two of the above listed components of the process, it has become a common place in EAC science that parameters of the local near tip environment, such as pressure P, composition in terms of concentrations of related species, electrochemical characteristics pH and E, if relevant, and others which may be included in the set @, obviously differ from their bulk counterparts 4*12-18.This was justified for all kinds of harmful environments, i.e. for gases, corrosive liquids (aqueous electrolytes and others) and liquid (molten) metals. So, a proper characterisation of EAC requires the use of local parameters of the.environment in the crack tip region which may be collected in the correspondent set of variables denoted by + 8, where the initial crack v;idth wj correlates with the initial crack acuity represented by the crack tip radius or semi-width p, wi = 2p for a nearly parallel-sided crack, and 6 is the crack opening displacement over the whole crack area. Away from the close crack tip vicinity where the crack tip opening dis lacement 8, at SSY is known to be K-controlled4~“‘, P“, 6, a K*, the shape of the opened crack depends on the geometry and mode of loading of a particular solid, i.e. is not K-dominated. Besides this, in-crack reactions depend on the state of the crack surface, i.e. on the degree of its passivation, or the thickness and the integrity of the oxide layer, etc. Hence, the crack tip strain rate controlled at SSY by the stress intensity factor rate K’= dK/dt together with the crack growth rate U, both affect the near tip environment since they interfere with the kinetics of in-crack reactions, e.g. through bare surface creation rate. Summarising, relations between both sets of bulk and local (crack tip> environment characteristics may be expressed as follows acT = QCT(~,K,p,Q,8,K’,U,T)

(2)

where r is the total time of exposure to environment (reaction time). As a matter of fact, these relations are not plain functions but rather functionals over particular EAC histories. To emphasize this kind of relation, the hollow symbol outline is used throughout this paper. That is, instantaneous crack tip characteristics are defined not by the current values of the variables in the right-hand part of (2) but depend on the shapes of time-dependent functions standing there as the arguments along the interval 0

(3a)

K,,, = K,*wT

(3b)

have a better chance to be intrinsic characteristics of EAC. To follow this way of EAC evaluation and life assessment, the supposedly intrinsic characteristics (3) must be established either by testing with direct rhonitoring of the crack tip environment, or by mathematical simulation of the in-crack transport and reaction processes, combining either of them, if helpful, with simulations utilising workin ( hysical) models. All these ways have of this approach been explored 4,’ J’ ,14*16-18.Utilisation in engineering estimations of crack growth in structures involves prediction of the crack tip environment parameters aCT in service, i.e. again, it calls for mathematical or working models. This consolidated fracture mechanics approach, though substantially more sophisticated and costly, may be beneficial in applications requiring better accuracy. Though, it seems to be too complicated and expensive for common engineering designs. Monitoring crack tip environments in laboratory testing is a difficult but feasible job in contrast to monitoring components in service where it could hardly be performed with certitude. Thus, although more legitimate, this approach seems to be impractical for ordinary engineering practice, but beneficial in materials research to conduct purer experiments and derive more reliable comparative data. The intrinsic variability of v(K)-curues

However, focusing on the couple (material-local enviyet does not ensure the uniqueness of ‘local characteristics (3) of EAC. Apart from the local environment, care must be taken about K-dominance of the remaining EAC constituents: the subsequent stages of the transport of harmful species to rupture sites (i.e. surface reactions, entry and penetration towards damage nuclei), degradation reaction itself and even exclusive K-control over the stress-strain state near the tip of a growing crack at SSY. Under fixed environmental parameters of the set @a the kinetics of surface reactions with the relevant species and their permeation through material to microstructural damage sites may depend on the dynamics of crack tip surface strain, which is K.-governed at SSY, and on crack growth rate u since both of them affect the thickness and integrity of crack tip surface films, e.g. oxide as a barrier for hydrogen entry into metals in the case of hydrogen assisted cracking (HAc)21. Iri EAC processes which involve transportation of a damaging agent through a material (e.g. cracking of metals assisted by hydro en7,9,17.22or of concrete spoiled by aqueous substances2 8 > transport processes, such as diffusion and dislocational dragging are stress-strain dependent and their K-dominance even under SSY is not a trivial matter 24,25. Really, stress-strain assisted diffusion depends on the stress-strain field in an entire solid, including remote from the crack tip not K-con-

ronment)

safe design: J Toribio, V Kharin

trolled far-field. To this end, to ensure suitable accuracy of K-dominance of the diffusion within the fracture process zone calls for correspondent limitations on the relative sizes of the near tip regions as characteristic diffusion paths, i.e. of K-controlled elastic domain, plastic region and the fracture process zone2’, in the same way as regarding the mechanical stress-strain state to ensure the soundness of LEFM2*‘o~11. Again these transport modes depend on stress-strain dynamics26 represented by K’. Finally, accumulation of the poisoning agent in prospective locations of the fracture process zone at the moving crack tip starts simultaneously with the material’s exposure to environment and proceeds together with crack growth dependin on the particular process history at time 0 crack tip interactions which provide the strongest environmental impact on the crack tip zone. This calls for bounding procedures to establish the limits for the listed governing variables to evaluate the weakest EAC resistivity. Obviously, more extensive testing is required to find the worst among all possible behaviours. This could be reduced by appropriate modelling and development of simulation techniques. The meaning of threshold K,,

As a matter of fact, two different implementations of the idea of the EAC threshold K,, are used. The first of them, the conventional threshold’*36*37 considers Kth as the limit stress intensity factor below which a crack does not extend for ‘infinite’ time (or, in practice, for a reasonably long time base tB). According to the other, the threshold is thought to reflect the maximum environmental facilitation of cracking attainable in a material under certain conditions7. For evaluating the EAC resistivity the second is more general. Really, in certain cases the maximum degradation effect occurs on attaining the equilibrium between the crack tip environment and the amount of a harmful species in rupture sites or the corresponding degree of degradation (when it is markedly a kinetic process). This means that under stationary external conditions the equilibrium corresponds to the maxima of both in the steady state manner. The time At to attain this maximum harmful action and to prepare crack advance is ‘infinite’, At = ~3, and the effect on crack growth rate is still nil at a certain K level. To this end, the practical time base t, for valid K,, testing must be sufficient to approach reasonably this equilibrium of the responsible kinetic processes of transportation and degradation reaction, i.e. it must be as long as the characteristic relaxation time of the rate determining kinetic process. Materials & Design Volume 18 Number 2 1997

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Approach to environmentally


This Kth will then be the true physical threshold with regard to this kind of EAC. This corresponds to zero crack growth rate if the relaxation time for environment-related processes in EAC is much shorter than any time scale for other possible time-dependent creep-like effects irrelevant to EAC. Otherwise, the notion of the EAC threshold should be associated with environmental acceleration of cracking that somehow can proceed without environmental assistance. This meaning of the EAC threshold is quite relevant to HAC enabled by hydrogen transportation to rupture sites by diffusion up to the equilibrium steady state which rovides the maximal hydrogen concentration in metal3 r . The second of the cited meanings of the EAC threshold is more ample since it relates to the maximum environmental degradation achievable in the system either on the way to establishing a steady state equilibrium, or temporarily (instantaneously) as the transient extreme severity of environment attack. This is more relevant when different mechanisms of environmental effect on fracture operate simultaneously, such as hydrogen embrittlement, oxide film creationrupture and active-path dissolution in SCC6,8*21. Here certain process components may be dictated by dynamic factors, such as crack tip strain and fresh surface creation rates, where both K’ and the cm& wth Fs,18s2’. velocity may be involved as goveming,tiablts4, Then common long-term quasi static tests37 to define Kt,, as a safety margin turn out. to be inadequate for assessment of EAC tolerance because their background (though obviously not stated explicitly) idea of equilibrium as the worst situation is no longer relevant. This case deserves special attention in view of reported data on the effect of strain .dynamics on the severity of crack tip environment and about the decrease with faster straining of the lower-shelf K for EAC6,‘8,39-41. With this in mind, the concept of the true threshold for EAC may appear as follows: Kth is the maximum stress intensity factor at which environmental facilitation of cracking (i.e. either crack advance of growth acceleration due to environment) cannot yet occur in a given combination (material-environment), or for practical purposes, cannot be detected within reasonable time-crack-size resolution margins, under conceivable local conditions (steady-state or dynamic) which provide the extreme environmental harm at the crack tip. This definition implies consideration of the worst crack tip conditions in relation to the crack tip chemistry, synergism of degradation kinetics and straining dynamics, etc., which produce the most severe environmental attack on a material. These are in general variable during a typical EAC course, so this worst-state can be achieved temporarily at intermediate times. The corresponding threshold, K,,, as the lowest bound of detectable sensitivity of the cracking resistance to environment must be the intrinsic characteristic of the system.

Conclusions Examination

of the K-dominance

in EAC reveals the It

conceptual luck of the uniqueness of the v(K)-curve. 100,

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is rare that EAC can be comprehensively characterised by a single-value v(KMunction defined solely by the material and the environment. The v(K)-relation inevitably depends on an extensive set of variables, such as the stress intensity rate K’ and the stress intensity gradient dK/da, and this dependence must not be a plain function but rather a functional over a history of a particular course of EAC. A deal of uncertainty of EAC characterisation is eliminated in a rigorously local fracture mechanics approach where both mechanical and environmental factors are treated in terms of local variables related to the crack tip. However, this local interpretation of the crack growth kinetics curve still remains incomplete and does not meet the requirements for the intrinsic material curve. For certain key items of the cracking process the K-dominance can hardly be ensured. Even under small scale yielding when the inelastic near tip domain is well shielded from the surrounding body with a ring of K-controlled elastic stress-strain state, the very near tip stress-strain field turns out to be ill-defined employing solely K at rather low load levels, or for an extending crack, or under some kinds of environment attack in the crack tip which affect its shape. Fracture mechanics tools cannot work well in these cases. The way to lessen the uncertainty of EAC evaluations and to improve the conservatism of life assessments is outlined. It relies on finding out for a couple (material-environment) the worst possible crack tip situations which cause the fastest crack growth rate v, attainable at each K in a given system. The corresponding master curve v = v,JK) being the envelope for all possible v(K)-curves for a (materiul-environmerit) combination must be the intrinsic characteristic of a system which represents the weakest resistance against EAC. This implies associated definition of the threshold Z& which corresponds to the maximum degree of environmental degradation being the minimal K at which environmental facilitation of cracking can be ever noticed in a given system. This latter is not always actualised in the approach to equilibrium at long interaction times,. hut may occur temporarily while crack tip strain dynamiespromotes a worsening of the local enviromental attack; These concepts of the worst environmental impact achievable at the crack tip can be used in materials evaluation and design against EAC to provide reliable conservative estimates in the usual framework of engineering fracture mechanics.

Acknowledgements This work was.,funded by the Spanish DGICYT (Grant UE94-001) and Xunta de Galicia (Grants XUGA 118OlA93 and XUGA 118OlB95). 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.

Approach to environmental/y


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