Formulating stress corrosion cracking growth rates by combination of crack tip mechanics and crack tip oxidation kinetics

A theoretical equation for stress corrosion crack growth rate of austenitic alloys in high temperature water is reformulated based on crack tip asymptotic fields and crack tip transient oxidation kinetics. A general oxidation kinetic law is introduced, emphasizing the role of mass transport through solid oxide film at the crack tip. The effects of several parameters on crack growth rate are evaluated. The results are compared with available experimental data and other equations. A good prediction of the effect of K on stress corrosion cracking growth rate of typical austenitic alloys in simulated light water reactor environments has been achieved.     

Explanation of an apparent abnormality in fatigue crack growth rate curves in titanium alloys

A surprising phenomenon is investigated where titanium alloys exhibit no threshold fatigue crack growth value if K_max in the K_max-constant testing procedure exceeds a certain value. The crack growth rate increases with decreasing ΔK up to final fracture. The phenomenon was found repeatedly for Ti–6Al–2Sn–4Zr–6Mo above K_max=21 MPa√m (equal to 72% of K_IC), and its causes were investigated. The same crack growth rates as in the K_max-constant test were reproduced by two independent experimental procedures, the so-called “jump” test and sustained K cracking experiments along with a calculation. It is demonstrated that the observed phenomenon is not a special crack growth feature or a new phenomenon, but simply caused by time-dependent crack growth, which is known to exist in titanium alloys or steels. Fractographic work revealed that intergranular crack growth along α and transformed β grain boundaries increases with decreasing ΔK and increasing K_max value, accompanied by creep deformation in the transformed β grains. The conditions for time-dependent cracking are believed to be a sufficiently high stress and strain field in the crack tip region, along with hydrogen-assisted cracking.     

Influence of local stress on initiation behavior of stress corrosion cracking for sensitized 304 stainless steel

To investigate the influence of local stress on initiation behavior of stress corrosion cracking (SCC) for sensitized Type 304 stainless steel, cracking process during constant load SCC test was monitored and recorded with an in situ crack observation system. The changes in number of cracks, sum of crack length and cracked area on the specimen surface with test time were identified from the cracking images analyzed by image processing. In the SCC tests, many cracks were initiated and coalesced on the surface, and the coalescence of cracks played an important role to primary crack growth. The influence of applied stress on crack initiation was different from that on crack growth. In addition, there was a difference between influences of stress on incubation period to crack initiation and crack initiation rate. Due to these differences, a stress of 0.8S_y was thought to cause relatively many cracks compared with 0.5S_y and 1.3S_y (S_y = 200 MPa). Through quantitative estimation of distribution in local stress around a crack by finite element analysis method, it was deduced that the crack initiation is influenced not only by bulk stress applied at the end of the body, but also by local stress formed around pre-existing cracks. According to pre-existing cracks, stress enhancement accelerates the crack growth, while the stress relaxation causes the suppression of new crack initiation. Based on the experiment and analysis results, three types of growth process were suggested, which are caused by propagation itself, by new crack initiation at vicinity of the crack tip, and by coalescence of approaching cracks. Then, it was concluded that, in order to predict/simulate the cracking behavior of this SCC system, the influence of local stress on the crack initiation should be taken into account.     

Critique of the Ford-Andresen film rupture model for aqueous stress corrosion cracking

The Ford-Andresen film rupture model for aqueous stress corrosion cracking has obtained a prominent position in the nuclear reactor industry. The model is said to have superior predictive capabilities because it is derived from a fundamental understanding of the film rupture-repassivation mechanism of crack advance. However, a critical review shows that there are conceptual and mathematical problems with the Ford-Andresen model development; there are inconsistencies among the stated and implied assumptions, the crack tip current density expression lacks the necessary dependence on crack tip strain rate and the fundamental proportionality that exists between crack tip strain rate and crack growth rate is overlooked and omitted from the model development. Consequently, the Ford-Andresen model must be considered neither phenomenologically nor fundamentally supported.     

Effects of local damage on asymptotic stress field of a growing creep crack

A parametric study on the effects of local damage field on the crack-tip stress field of a growing Mode I creep crack is performed in the framework of Continuum Damage Mechanics (CDM). According to the results of creep crack growth analysis based on CDM and Finite Element Method, the damage distribution1-(D/D _cr)=h(θ)r^m represented by a power law function of the radiusr from the crack tip is postulated for the damage variableD. The damage effects are incorporated into the Norton creep law by means of the hypothesis of strain equivalence of CDM. The resulting two-point boundary value problems of differential equations for the growing creep cracks in the states of plane strain and plane stress are solved by means of a shooting method. For a given creep exponentn of the Norton law, the exponentp of the asymptotic stress field σ _ij ∞r ^p is found to be governed by the exponentm of the power law damage distributionr ^m.     

The effect of iodine content and specimen orientation on stress corrosion crack growth rate in Zircaloy-4

The influence of specimen orientation, stress intensity factor (K_I), and iodine concentration on the iodine-induced stress corrosion cracking growth rates in Zircaloy-4 was investigated in iodized methanol solutions at ambient temperature. When K_I is lower than 20 MPa.m^1/2, the intergranular and mixed intergranular/transgranular crack propagation rates increase linearly with (K_I − K_I,th), K_I,th being the onset of propagation stress intensity factor. The increase in iodine content induces an increase of the crack growth rate for a given K_I, and a decrease of the K_I,th. The specimen orientation is a second order parameter. A crack propagation law, depending on iodine content, is proposed.     

Predicting the mechanisms and crack growth rates of pipelines undergoing stress corrosion cracking at high pH

A fundamentally based mathematical model was developed with the goal to predict, as a first step, the crack growth rate (CGR) of high pH stress corrosion cracking (SCC) of buried steel pipelines. Two methods were used to predict CGRs and for both methods the model has included the film rupture and repassivation mechanism. The two methods are distinguished by the expression used to determine the active anodic current density at the crack tip. In the first method, this current density is expressed by the anodic polarization curve with a large peak current density and the prediction tends to yield a larger CGR and a lower pH at the crack tip. By contrast, when the Butler–Volmer equation is used to express the crack tip anodic current density, with a predicted low CGR the chemistry at the tip does not appear to have any significant change due to the high buffer of the solution.The predicted mechanism responsible for the steady-state crack growth is shown to be the balance between the increasing stress intensity factor as the crack grows, which tends to increase the crack tip strain rate and thus the CGR, and the change of the crack tip condition, which, for large CGRs, is the significant shift in the more negative direction of the crack tip potential, and for low CGRs, the increase of ferrous ion concentration, and either tends to decrease CGR.Limitations currently existing in the model and proposal for further development of the model are discussed.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials

In this paper, a plasticity-corrected stress intensity factor range ΔK_pc is developed on the basis of plastic zone toughening theory. Using this new mechanical driving force parameter for fatigue crack growth (FCG), a theoretical correlation of Paris’s law with the crack tip plastic zone is established. Thus, some of the important phenomena associated with the plastic zone around the fatigue crack tip, such as the effects of load ratio R, overload and T stress on the FCG behavior, can be incorporated into the classical Paris’s law. Comparisons with the experimental data demonstrate that ΔK_pc as a single and effective mechanical parameter is capable of describing the effects of the load ratio, T stress and overload on the FCG rate. The FCG rate described as a function of ΔK_pc tested under a simple loading condition can also be used for other complex loading conditions of the same material.     

The characteristics of hydrogen diffusion and concentration around a crack tip concerned with hydrogen embrittlement

Previously, we proposed a physical model for hydrogen diffusion and accumulation around the crack tip and performed accurate numerical analysis which takes account of the effects of both hydrogen diffusion and accumulation due to the stress gradient. Based on this analysis, the characteristics of hydrogen accumulation around the crack tip were clarified.Since the characteristics of stress corrosion cracking and corrosion fatigue are dominated by chemical anodic reaction, hydrogen embrittlement and dislocation mechanism, to perform the analysis on the competitive phenomenon by these mechanism and to relate the sensitivity of hydrogen embrittlement to the characteristics of corrosion fatigue, it is necessary to construct a exact physical law on the characteristics of hydrogen diffusion and concentration and to formulate the characteristics as a simple function such as diffusion constant, D, yield stress σ_ys, and stress intensity factor, K. The effect of stress field such as plane strain and plane stress on the hydrogen embrittlement is necessary to be clarified as the effect of specimen thickness on the hydrogen embrittlement.In this paper, based on this view point, the effect of D, σ_ys, and K on hydrogen embrittlement were investigated and formulated. A quantitative parameter which characterize hydrogen embrittlement was proposed for both cases of plane strain and plane stress conditions as the effect of specimen thickness on the hydrogen embrittlement.     

Transient and steady state crack growth kinetics for stress corrosion cracking of a cold worked 316L stainless steel in oxygenated pure water at different temperatures

The stress corrosion cracking (SCC) growth kinetics for a cold worked 316L stainless steel was continuously monitored in high purity water at different temperatures and dissolved oxygen (DO) levels under a K (or K_max) of 30 MPa m^0.5. The total SCC test time was more than 8000 h to make sure the steady state crack growth rate under each test condition could be reached. Crack growth rate (CGR) increases with increasing temperature in the range 110-288 °C. A typical intergranular-cracking mode is identified. Depending on the previous test condition, especially the temperature, three kinds of crack growth kinetics, i.e., increasing with testing time then becoming steady, being constant during the whole period, or decreasing with test time then becoming steady, are identified and discussed. Time-dependent and testing history-dependent crack growth modes were confirmed in two series of tests in 2 ppm DO and 7.5 ppm DO pure water. The apparent activation energies are calculated and compared with other data in different environments under different applied loading levels for understanding the cracking mechanism.     

Elucidating the variables affecting accelerated fatigue crack growth of steels in hydrogen gas with low oxygen concentrations

The objective of this study was to quantify the effects of mechanical and environmental variables on oxygen-modified accelerated fatigue crack growth of steels in hydrogen gas. Experimental results show that in hydrogen gas containing up to 1000 v.p.p.m. oxygen fatigue crack growth rates for X52 line pipe steel are initially coincident with those measured in air or inert gas, but these rates abruptly accelerate above a critical ΔK level that depends on the oxygen concentration. In addition to the bulk gas oxygen concentration, the onset of hydrogen-accelerated crack growth is affected by the load cycle frequency and load ratio R. Hydrogen-accelerated fatigue crack growth is actuated when threshold levels of both the inert environment crack growth rate and K_max are exceeded. The inert environment crack growth rate dictates the creation of new crack tip surface area, which in turn determines the extent of crack tip oxygen coverage and associated hydrogen uptake, while K_max governs the activation of hydrogen-assisted fracture modes through its relationship to the crack tip stress field. The relationship between the inert environment crack growth rate and crack tip hydrogen uptake is established through the development of an analytical model, which is formulated based on the assumption that oxygen coverage can be quantified from the balance between the rates of new crack tip surface creation and diffusion-limited oxygen transport through the crack channel to this surface. Provided K_max exceeds the threshold value for stress-driven hydrogen embrittlement activation, this model shows that stimulation of hydrogen-accelerated crack growth depends on the interplay between the inert environment crack growth increment per cycle, load cycle frequency, R ratio and bulk gas oxygen concentration.     

Measurements of fibre bridging during fatigue crack growth in Ti/SiC fibre metal matrix composites

High spatial resolution synchrotron X-ray strain mapping has been used to map the elastic matrix and fibre strains in the vicinity of a fatigue crack in a Ti–6Al–4V/SCS6 SiC fibre composite. A 0.61 mm fatigue crack was initiated and grown in three-point-bending. By using an in-situ loading stage it was possible to map the crack opening (longitudinal) strain distribution at K_appl=K_max and K_appl=0. In the far field region, significant thermally induced stresses were evident, being compressive in the fibres and tensile in the matrix. Around the notch and in the wake of the crack tip essentially no residual strain and only small interfacial shear stresses were found in the unloaded case, indicative of a debonded/damaged interface. At K_max the maximum tensile stress in the matrix is in the vicinity of the crack tip, whereas for the SiC fibres the maximum stress is in the bridging zone in the wake of the crack. The perturbed zone extends about ±1.5 mm either side of the crack. It was at the boundary of this zone that the maximum interfacial shear stresses (∼80 MPa) were measured in the loaded stage. A small area of tensile strain in front of the crack tip in the unloaded condition suggests frictional resistance from the bridging fibres acts to keep the crack slightly open. A simple three-dimensional finite element model has been developed to help interpret the results. The crack is introduced statically by node release and the Coulomb friction law governs the interface strength. The results of the model are compared to the synchrotron strain measurements. This comparison confirms the degradation of the interface strength in the wake of the crack.     

Corrosion fatigue behavior of dissimilar metal weldments under nominal constant ΔK loading mode in a simulated BWR coolant environment

Corrosion fatigue behavior of the dissimilar metal weldment, Alloy 52-A508, under a simulated BWR coolant condition was studied. Corrosion fatigue crack growth rates of the dissimilar metal weldments were observed to increase with crack extension under the nominal constant ΔK loading mode. It could be accounted for by a decrease in the Cr and Ni contents and the crack closure effect with the weld depth. Finite element analysis on the welding residual stress was performed. The trend of analytical results agreed well with that of the residual stress measurements obtained by a hole-drilling strain gauge method.     

An alternative to the Shoji crack tip strain rate equation

Fundamentally derived crack tip strain rate (CTSR) equations are being sought for use in modelling stress corrosion crack growth. The CTSR equation derived by Shoji and coworkers is gaining prominence in modelling the effects of cold work on stress corrosion cracking of nuclear reactor materials due to an ability to model the effects of yield stress and strain hardening on CTSR. However, the Shoji equation is compromised by assumptions that are inconsistent with the Gao-Hwang (GH) crack tip strain equation that was used in derivation of Shoji’s equation. Moreover, the GH equation appears to have been incorrectly derived. As a result, the Shoji equation cannot be considered fundamentally supported. An alternative to the Shoji equation is developed here by extending the Rice, Drugan and Sham CTSR equation to include strain hardening.     

A comparison of SCC velocity measurements under conditions of constant load and constant displacement

The SCC velocity for 2024-T351 aluminium alloy in aqueous 3% NaCl solution was measured employing DCB specimens oriented for crack propagation in the SL and ST orientations. For lower values of the nominal or applied stress intensity factor, K_app, the results obtained under constant load (increasing K_app) and constant load-point displacement (decreasing K_app) agree well. For higher values of K_app, significantly lower crack velocities can be obtained in constant displacement tests, as a result of greater crack branching. Procedures that can minimize the difference between K_app and the effective stress intensity factor at the crack tip are discussed.     

Simulation of crack growth during hydrostatic testing of pipeline steel in near-neutral pH environment

The objective of this investigation was to understand the role of crack dimension, hydrogen, room-temperature creep and loading procedure on crack growth during hydrostatic testing of pipeline steels in near-neutral pH aqueous soil environments. Crack growth was found during hydrotesting, but was not linearly related to the stress intensity factor at the crack tip. Crack growth is mainly driven through the internal-hydrogen-assisted-cracking mechanism, instead of the hydrogen-environmental-assisted-cracking mechanism. Excessive plastic deformation induced by room-temperature creep prior to hydrotesting reduces crack advance during hydrotesting. Lower loading rate generally induces larger crack growth by hydrostatic loading. More crack growth occurs during loading in high stress regime.     

Quantification of creep cavitation damage around a crack in a stainless steel pressure vessel

In this paper, metallographic sectioning and non-destructive small angle neutron scattering (SANS) are used to map the level of creep cavitation around a surface breaking crack in a stainless steel pressure vessel. The cracking developed during 65,000 h service at an operating temperature of around 525 °C and was promoted by the accumulation of creep strain resulting from relaxation of tensile residual stresses associated with a nozzle attachment weld. The distribution and evolution of the cavities is discussed in terms of existing models of creep cavitation failure based on a ductility exhaustion model in which the corresponding multi-axial creep ductility, expressed as the von Mises strain at failure, is a function of the strain rate and stress state. An empirical approach has been adopted for describing the effects of stress state on ductility, which takes into account cavity nucleation as well as cavity growth by creep deformation, and is similar to local approach models for ductile crack growth. Crack initiation is conceded when the creep damage parameter D_c⩾1. The measured creep cavitation results are found to be in reasonable accordance with such a model.     

Crack tip chemistry and electrochemistry of environmental cracks in AA 7050

The role of the crack environment in establishing environment-assisted crack (EAC) propagation in AA 7050 alloys is elucidated. A suite of mini-electrodes provided real-time in situ measurements of the crack potential, pH, and chloride concentration during stage II cracking in a chromate-chloride electrolyte under electrochemical control. For material aged to an EAC-susceptible condition, crack growth during an incubation period is characterized by tip polarization to near the applied electrode potential (E_App) and bulk-like chemistry near the crack tip. In contrast, establishment of high-rate crack growth coincided with the development of an acidic, high chloride concentration tip environment and tip depolarization. During steady state high rate crack growth, the tip potential was ∼−0.85V_SCE; near-tip potential gradients were ∼1 V/cm. Large ohmic potential drop within fast-growing cracks is indicative of net anodic current in the near tip region and increased mass transport resistance within the crack due to solid corrosion products and/or hydrogen bubble formation. Microinjection of a corrosion-inhibiting or corrosion-promoting solution at the tip suppresses or prompts, respectively, the transition from incubation to high-rate cracking, highlighting the intimate dependence of the crack growth kinetics on the local chemistry. The exceptional EAC resistance of over-aged AA 7050 is intrinsic; injection of an acidic aluminum chloride solution at the tip of a crack of this material while polarized to a high E_App failed to induce brittle crack advance.     

On Modeling Hydrogen-Induced Crack Propagation Under Sustained Load

The failure of hydrogen containment components is generally associated with subcritical cracking. Understanding subcritical crack growth behavior and its dependence on material and environmental variables can lead to methods for designing structural components in a hydrogen environment and will be beneficial in developing materials resistant to hydrogen embrittlement. In order to identify the issues underlying crack propagation and arrest, we present a model for hydrogen-induced stress-controlled crack propagation under sustained loading. The model is based on the assumptions that (I) hydrogen reduces the material fracture strength and (II) crack propagation takes place when the opening stress over the characteristic distance ahead of a crack tip is greater than the local fracture strength. The model is used in a finite-element simulation of crack propagation coupled with simultaneous hydrogen diffusion in a model material through nodal release. The numerical simulations show that the same physics, i.e., diffusion-controlled crack propagation, can explain the existence of both stages I and II in the velocity versus stress intensity factor (V–K) curve.     

Effect of metallurgical variables on the stress corrosion crack growth behaviour of AISI type 316LN stainless steel

Mill-annealed AISI type 316LN stainless steels, received from two different sources (one indigenous (SS-2) and the other foreign (SS-1)), were tested for stress corrosion cracking (SCC) resistance in a boiling acidified environment of NaCl. SCC results indicated a remarkably lower value of plateau crack growth rate (PCGR) and higher values of K_ISCC and J_ISCC for SS-2, which was attributed to the lower effective grain boundary energy resulting from a higher amount of copper in it. Cold working reduced K_ISCC and PCGR; while thermal aging and welding decreased K_ISCC and increased PCGR vis-à-vis the annealed material.