R-curve behavior of BaTiO3- and PZT ceramics under the influence of an electric field applied parallel to the crack front

The fracture resistance curves (R-curves) of BaTiO₃ and commercial PZT–PIC 151 were measured with compact tension specimens under the influence of an electric field applied parallel to the crack front. A strong influence of the electric field on the starting and plateau value was found as well as on the length of the R-curve. Generally a toughness increase was detected with increasing electric field. The toughening effect is estimated from the change in crack tip stress intensity induced by ferroelastic domain switching near the crack tip using the weight function formalism developed for stress-induced transformation toughening of zirconia ceramics. In order to obtain a quantitative prediction of toughening, ferroelastic and ferroelectric properties were measured.     

Effect of switching stresses on domain evolution during quasi-static crack growth in a ferroelastic single crystal

The present paper demonstrates the effect of switching stresses on domain evolution and fracture toughening during quasi-static crack growth in elastically isotropic ferroelastic single crystals with transversally isotropic ferroelastic strains. With a simple switching algorithm and crack propagation procedure, domain evolution is simulated in an exemplary material with semi-infinite crack under mode I loading, starting from a mono-domain configuration. Domain reorientation is found to be strongly affected by switching stresses, which therefore have to be considered in the context of domain evolution modelling and fracture toughening. Before the onset of crack growth a needle-like domain is formed at the tip of the stationary crack, but this does not effect the crack tip stress intensity factor. Elongation of this domain during the onset of crack growth causes a large increase of the fracture toughness. Domain separation in a later stage results in toughness reduction. The subsequent domain evolution indicates a periodic formation of needle-like domains as observed in soft ferroelastic materials.     

Micromechanisms of fatigue crack growth in a single crystal Inconel 718 nickel-based superalloy

The fatigue crack growth behavior of an experimental, single crystal alloy, of equivalent nominal chemical composition to Inconel 718 is presented. Fracture modes under cyclic loading were determined by scanning electron microscopy. The results of the fractographic analyses are presented on a fracture mechanism map that shows the dependence of the fatigue fracture mechanisms on the maximum stress intensity factor, K_max, and the stress intensity factor range, ΔK. Crack-tip deformation mechanisms associated with fatigue crack growth were studied using transmission electron microscopy. The relative effects of ΔK and K_max on the fatigue crack growth behavior of this material are discussed within the context of a two-parameter crack growth law. The influence of grain boundaries on the fatigue crack growth resistance of materials such as Inconel 718 is also discussed in light of the results of this investigation.     

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.     

Temperature-dependent R-curve behavior of Pb(Zr1−xTix)O3

The crack growth resistance behavior of polycrystalline Pb(Zr_1?xTi_x)O₃ has been characterized in a novel experimental arrangement between 24 and 140 °C. Experimental measurements were carried out on compact tension specimens submerged in a temperature-controlled silicone oil bath. The results show a decrease in the observed shielding toughness, leading to an overall reduction in the maximum toughness. The temperature-dependent stress–strain behavior and elastic properties were characterized, providing an insight into the effect of the changing ferroelastic properties on the temperature-dependent fracture behavior.     

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.     

Discrete dislocation plasticity modeling of short cracks in single crystals

The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The fracture properties are specified through an irreversible cohesive relation. Under monotonic loading conditions, with the applied stress below the yield strength of the uncracked specimen, the initiation of crack growth is found to be governed by the mode-I stress intensity factor, calculated from the applied stress, with the value of K_init decreasing slightly with crack size due to the reduction in shielding associated with dislocations near a free surface. Under cyclic loading, the fatigue threshold is ΔK-governed for sufficiently long cracks. Below a critical crack size the value of ΔK_I at the fatigue threshold is found to decrease substantially with crack size and progressive cyclic crack growth occurs even when K_max is less than that required for the initiation of crack crack growth in an elastic solid. The reduction in the fatigue threshold with crack size is associated with a progressive increase in internal stress under cyclic loading. However, for sufficiently small cracks, the dislocation structure generated is sparse and the internal stresses and plastic dissipation associated with this structure alone are not sufficient to drive fatigue crack growth.     

Discrete dislocation modeling of fatigue crack propagation

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small-scale yielding are carried out using discrete dislocation dynamics. Cracks along a metal–rigid substrate interface and in a single crystal are studied. The formulation is the same as that used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. The cyclic crack growth rate log(da/dN) versus applied stress intensity factor range log(ΔK_I) curve that emerges naturally from the solution of the boundary value problem shows distinct threshold and Paris law regimes. Paris law exponents in the range 4 to 8 are obtained for the parameters employed here. Furthermore, rather uniformly spaced slip bands corresponding to surface striations develop in the wakes of the propagating cracks.     

A discrete dislocation analysis of near-threshold fatigue crack growth

Analyses of cyclic loading of a plane strain mode I crack under small-scale yielding are carried out using discrete dislocation dynamics. The formulation is the same as used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. The dislocations are all of edge character and are modeled as line singularities in an elastic solid. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Either reversible or irreversible relations are specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading as could occur in a vacuum or in an oxidizing environment, respectively. In accord with experimental data we find that the fatigue threshold ΔK_th is weakly dependent on the load ratio R when the reversible cohesive surface is employed. This intrinsic dependence of the threshold on R is an outcome of source limited plasticity at low R values and plastic shakedown at higher R values. On the other hand, ΔK_th is seen to decrease approximately linearly with increasing R followed by a plateau when the irreversible cohesive law is used. Our simulations show that in this case the fatigue threshold is dominated by crack closure at low values of R. Calculations illustrating the effects of obstacle density, tensile overloads and slip geometry on cyclic crack growth behavior are also presented.     

Electrochemical aspects of stress corrosion crack growth in austenitic stainless steel

The stress corrosion crack velocity and stress corrosion threshold stress intensity, K_Isce, at potentials at or slightly different to the open circuit potential have been measured under potentiostatic control for 18Cr10Ni0.5Ti stainless steel in aqueous 46% LiCl at 105°C. In all cases, both stage 1 and stage 2 growth rate dependence on K is demonstrated. For potential vs. corrosion potential values 360 to ?50mV, a linear dependence of stress corrosion threshold stress intensity on the square root of the polarization applied was found.     

Intergranular crack tip oxidation in a Ni-base superalloy

High-temperature intergranular crack tip oxidation under a single 600 s long sustained tensile load at 700 °C was studied for the Ni-base superalloy Allvac 718Plus. High-resolution analytical techniques showed oxidation to take place at and immediately ahead of the tip of an open crack, forming a closed but layered oxide structure about the prior (now oxidized) grain boundary. Near the prior grain boundary the oxide is Ni-rich, with a Co-enriched layer furthest away from the metal and a Fe-enriched region below this. A Cr-rich oxide is present below the outer Ni-rich oxides throughout the crack, also in the direction of crack growth. This is believed to have a hindering effect on oxidation ahead of the crack. Ni₃(Nb,Al) γ′ precipitates close to the grain boundaries were found to oxidize and form regions of near-stoichiometric NiO within the oxide layers. Remaining constituents of γ′ (e.g. Al and Nb) were found to be enriched in the surrounding oxidized matrix and also to produce thin oxide layers near the interface between the unoxidized metal and the Cr-rich oxide. The formation of the crack tip oxides is discussed with regard to thermodynamics, kinetics and the influence of applied mechanical load.     

Mechanism study on subcritical crack growth of flabby and intricate ore rock

1 Introduction Because of the effects of diagenetic process and tectonic movement, lots of jointed plane of weakness with different contacted characteristics exist in the practicable rock mass. The deformation and fracture mechanisms of the rock mass are…     

Effect of hydrogen peroxide on crack growth rate in X70 pipeline steel in weak acid solution

An investigation of the effect of hydrogen peroxide (H₂O₂) on corrosion crack growth can be considered as a necessary stage in a study of the SCC of pipeline steels in the presence of dissolved oxygen and other oxidants. It was found that the presence of hydrogen peroxide at a low concentration (5?mM) results in a deceleration of the crack growth. With an increase in the concentration of H₂O₂, the crack growth rate increases. The change in the steel corrosion rate at various H₂O₂ concentrations agrees with the dependence of the crack growth rate on the oxidant concentration. The conclusion has been made that the crack growth in a weakly acidic electrolyte (pH 5.5) is determined by the metal dissolution process. Hydrogen charging of the metal indirectly affects the crack growth by increasing the surface coverage with hydrogen, which decreases the steel dissolution rate.     

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.     

Cyclic compression behavior of a Cu–Zr–Al–Ag bulk metallic glass

The cyclic compression behavior of a Cu₄₅Zr₄₅Al₅Ag₅BMG was investigated in order to elucidate the damage initiation and growth mechanisms. The present Cu₄₅Zr₄₅Al₅Ag₅ BMG was found to have a fatigue-endurance limit of 1418 MPa and fatigue ratio of 0.77. Fracture under cyclic compression occurred in a pure shear mode. The fracture surface forms an angle of 41° with respect to the loading axis. This angle was similar to the monotonic compressive fracture angle for the present BMG. The cyclic compression fracture surface displays a morphology nearly identical to the monotonic compression fracture surface. In addition to many shear bands and cracks, areas of “chipping” were commonly found on the outside surfaces of the fatigue specimens. An attempt was made to measure crack growth rates, and two types of crack growth behavior were found. With the first type, the growth rate decreased with cycles due to the decrease in the driving force for crack propagation. With the second type, the crack growth rate increased with cycles after chipped areas developed. The fatigue deformation process for BMGs under cyclic compression was carefully studied and rationalized.     

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.     

Predictions of the initial non- steady- state crack growth behavior in the creepjfatigue of the nickel- base superalloy AP1

Using the fracture mechanics parametersK and C* to analyze cyclic crack growth test results carried out on the nickel-base superalloy API, the effects of test frequency on the initial incubation time followed by transient cracking rates and the steady-state secondary crack growth rates were considered. The crack-ing behavior at 700 °C for this material exhibits a frequency dependence over a range of 0.001 to 10 Hz. It has been shown that, at high temperatures under steady-state cracking conditions, fatigue processes are most dominant at high frequencies, and conversely, time-dependent creep dominates at low frequen-cies. The creep cracking rate is described by a model linked to the exhaustion of available ductility in a creep process zone at the crack tip, and the fatigue rate is linked to the Paris Law equation. For the sec-ondary regime of crack growth, the effects of frequency are described in a cumulative damage model de-veloped for creepJfatigue interaction. For the crack incubation and the transient process under initial loading, the model is extended to predict the cracking behavior in the creep regime at low cyclic frequen-cies. For the higher frequencies, fatigue dominates and creep transient effects are not observed experi-mentally.     

Effect of applied potential on fatigue crack propagation behavior of API X80 steel in seawater

In the present study, the fatigue crack propagation (FCP) tests were conducted on X80 steel in air and artificial seawater (ASW) under various applied potentials to establish optimum and safe working limits of cathodic protection (CP). The slow strain rate test (SSRT) was also conducted on the X80 BM specimens in ASW under CP potential to identify the susceptibility of hydrogen affecting the FCP behavior. The CP potential of ?850 and ?1,050 mV_SCE suppressed the environmental effect of seawater on the FCP behavior of X80 BM and WM specimens, showing almost identical da/dN-ΔK curves for both air and ASW environments. The SSRT in ASW under CP potential of ?1,050 mV_SCE suggested that the X80 BM specimen steel is susceptible to hydrogen embrittlement, but the effect of hydrogen was believed to be marginal in affecting the FCP behavior of the X80 specimens at a loading frequency of 10 Hz. The FCP behavior of high strength X80 steel is discussed based on the fractographic observation to understand the FCP mechanism in seawater under various CP potentials.     

Hold-time effect on the elevated-temperature crack growth behavior of solid-solution-strengthened superalloys

The fatigue crack growth behavior of two solid-solution-strengthened superalloys, Ni-based HAYNES^® 230 and HASTELLOY^® X, was studied at 816 and 927 °C in laboratory air. The fatigue crack growth tests were conducted following a baseline triangular waveform of 0.33 Hz. Various hold times were introduced at the maximum load to study the hold-time effect. Fracture mechanics parameters, K, C¹, C_t, and (C_t)_avg, were applied to correlate the crack growth rates at different temperatures for both HAYNES 230 and HASTELLOY X alloys. For both alloys, the fatigue cracking path was mainly transgranular at 816 and 927 °C. The cracking path became dominantly intergranular if the hold time increased to 2 min, indicating that the time-dependent creep damage mechanisms were in control. When the time-dependent damage dominated (temperature ⩾816 °C and hold time ⩾2 min), the crack growth rates can be correlated with C_t or (C_t)_avg parameters. The C_t and (C_t)_avg parameters were capable of consolidating data from different temperatures and different alloys.     

Fatigue crack growth in 2024 aluminum alloy with inhomogeneous solidification microstructure

This study reports the investigation of the fatigue crack growth behavior in 2024 aluminum alloy billets manufactured using the direct chill casting (DCC) and electromagnetic casting (EMC). It was expected that the billets produced from these different casting procedures would vary in terms of their microstructure. Therefore, they should exhibit different fatigue crack growth behavior. The results showed that, the structure of the middle center portion of both billets is not homogeneous and relatively coarse, while the structure of the center and edge portions is homogeneous compared with the structure of the middle center portion. As fatigue crack growth extended through many grains having different morphologies, it became unstable through the overall crack path, and the Paris zone almost disappeared. The effects of 5% rolling and commercially rolled DCC billets on the fatigue crack growth rate were also investigated. Striations were enhanced around Al₂Cu particles refined by commercial rolling, and fatigue crack growth was stable until large crack length.