Frank A. McClintock

Creep relaxation of stress around a crack tip

Abstract Plane-strain numerical solutions have been obtained for the power-law creep relaxation of crack tip stresses subsequent to an initial elastic response. Explicit time integration is coupled with an initial-strain, finite element calculation. For cost effective, automatic time step control, the Irons-Treharne-Cormeau stable time step estimate is used to restabilize the calculation between steps 5–50 times larger. This finite element scheme is readily adaptable to realistic (and complicated) creep flow relations. Numerical results are presented for the plane-strain shallow Mode I tensile edge crack under constant applied load and creep exponents of 3 and 10. The calculated short-time amplitude of the singular HRR crack tip field under small-scale creeping conditions determines stresses that are within 1.5% of those predicted, using the elastic stress intensity factor K I with the Riedel-Rice approximation. This precedes a longer time transition to a steady-state value that is given in terms of the path-independent integral C ∗ . Time-dependent crack opening displacements and velocities and the growth of regions where creep strains exceed the elastic strains are also presented.

Elastic-plastic mechanics of steady crack growth under anti-plane shear

Abstract F or a crack with steady growth under anti-plane shear, analysis shows a primary plastic zone included in an angle of ±19.7° ahead of the crack tip, and two very thin secondary (reverse) plastic zones along the crack flanks, each included in an angle of 0.37°. Numerical solutions give the shape of the plastic zones which determine the active and residual plastic strains, and give the crack tip displacement, which is approximately 0.07 of that for monotonic loading without growth. The length of the primary plastic zone is almost the same as that without growth, but the thickness is about 3/5 as great. Coupled with ductile fracture criteria, the present results predict initially stable crack growth, whereas analyses based on the simplification of yielding on just one plane predict unstable fracture immediately following initiation.

A DISLOCATION MECHANICS-BASED CRYSTALLOGRAPHIC MODEL OF A B2-TYPE INTERMETALLIC ALLOY

A crystallographic slip based model for cubic oriented NiAl single crystals is derived from an idealization of the dislocation network observed in the active slip systems, viz. {110} 〈110〉. The crystallographic model successfully accounts for the cyclic steady-state behaviour of crystals subjected to strain histories within the range ϵ〈100〉 = ϵm ± 0.5%, for ϵm = 0 and 35%, at 750 and 850°C. It accurately predicts the flow stress dependence on temperature, strain rate and dislocation density arising from the lattice resistance to dislocation motion and from discrete obstacle resistance due to dislocation interactions. The kinematic and isotropic hardening modes associated with defect trails left behind by gliding dislocations and dislocation storage, respectively, are properly represented. The average distance that dislocations have to glide for their density to increase beyond the level needed to balance dynamic recovery processes was predicted to be approximately 260 times the random forest dislocation spacing. Measured dislocation densities at different mean strains were found to be consistent with the predictions of the theoretical model.

Travelling cracks in elastic materials under longitudinal shear

The solution for the stress field around the tip of a crack subjected to longitudinal shear (antiplane strain) and travelling with a constant velocity in an elastic medium, as given by Bilby and Bullough (1954), has been extended to a configuration analogous to the tensile case studied by Craggs (1960). As in the case of tensile cracks, the applied stress required for constant velocity is lower for higher crack velocity and there is a critical velocity approximately 0.6 times that of the shear wave velocity above which the crack will branch. Similar stress levels are found using two different fracture criteria : the Griffith energy criterion and the criterion of critical shear strain averaged over a critical area.

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

Abstract A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m 2 ), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration . Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher . Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.

Statistics of Brittle Fracture

From a simple statistical model of occasional cracked grain boundaries, a statistical distribution of strength is derived which does not fall into any of the three asymptotic forms of extreme value distributions. The size effects for this new extreme-value distribution are similar to those of the third asymptote with an exponent of about m = 4, but it is necessary to drop 5 or 6 standard deviations below the median in order to reduce the failure probability to 1 in 106, which corresponds more to the first asymptote, m = ∞. Stress gradient effects, leading to notch insensitivity, are reviewed for the third asymptotic distribution, and a method for correlating scatter in strength with position of failure in three-point bend specimens is derived and illustrated.

Ductile fracture in sheets under transverse strain gradients

The fully plastic fracture of a metal sheet subjected to a small transverse gradient of tensile strain near a reinforcement is modeled as mode I fracture under transverse plane strain (TPS). Necking and fracture were analyzed by assuming that they were set by prior uniform strains and then necking displacements. Equations for the spreading of TPS necking and fracture were thus derived for a sheet with strain gradient. Experiments on tapered specimens confirmed the expected fracture displacements within 12 percent, but Moiré studies suggest the agreement may be fortuitous. In any event, in-plane transverse displacements and normal strains in the crack growth direction, as well as shear strains, were negligible. This should simplify any future numerical analysis.

Fracture of Graphite Composites Under Shock Loading.

A previously obtained set of experimental data on the failure of three‐dimensional graphite composites under shock loading was examined. The critical event was determined to be fracture in the fiber bundles parallel to the shock direction. Physical considerations, as well as a simple approximate equation and a computer model of the fiber bundle fracture, show rather definitely that for pulse widths less than 0.5 μsec the variability in the strength of the individual fibers is the primary cause of the observed stress–pulse‐width relationship. The assumptions of the computer model include a static stress concentration around the broken fibers and a fiber strength described by an extreme value distribution.

A criterion for plane strain, fully plastic, quasi-steady crack growth

Plane strain fracture by hole growth in ordinary-sized parts of low-to-medium strength steels is essentially rigid-plastic, and may be approximated as non-hardening. Quasi-steady crack growth for such materials is predicted for crack-tip fields approximated by a pair of slip lines, such as unequally grooved specimens in tension and deep singly-face-cracked specimens under combined bending and tension. The crack growth increment Δa is given in terms of material parameters, far-field geometry, and loadings and their increments.For the rigid-plastic, non-hardening approximation, stress and strain increment fields for growing cracks are identical to those for stationary cracks. For fields with a pair of symmetric slip-lines, the flanks of the decohering zone turn out to be rigid, and the decohering zone does not affect the crack-tip opening angle (CTOA), which then depends only on the micromechanisms of hole nucleation, growth and linkage by flow localization or fine cracking. These mechanisms are in turn approximately controlled by the near-field plasticity parameters: the angle of the slip plane θs, and the normal stress and displacement increment across the slip plane σs and Δus. Note the three-parameter characterization of the near-tip fields, in contrast to the one- or two-parameter characterization in elastic or nonlinear elastic fracture mechanics.A sliding off and shear-cracking model for a growing crack, based on a hole growth equation, gives an approximate CTOA in terms of σs, θs, and material parameters. When hole nucleation strain is negligible, the estimated CTOA exhibits an inverse exponential dependence on σs and a higher order parabolic dependence on θs. For a given material, a series of fully plastic crack growth experiments is suggested to determine the approximate material parameters needed to characterize the dependence of CTOA on σs and θs, or from kinematics, of the shear strain behind the slip plane, γf, on σs.

Thermal fatigue degradation of an overlay coating

Abstract The degradation of a 92 μm-thick NiCoCrAlY overlay coating applied with electron beam physical vapor deposition to single crystals of a nickel base superalloy (CMSX-3) was studied by subjecting thin disk-shaped specimens to 6000 thermal cycles with different rates of heating (from 520 °C to 1090 °C on 4.5 s, 6 s and 20 s) and cooling (to 520 °C in 7 s and 15 s). Diffusion during coating deposition and the subsequent heat treatments to allow for further substrate precipitate growth and coating-substrate interdiffusion gave a 10 μm β-α-γ transition zone between the coating and substrate, which grew to 80 μm and transformed into a single γ phase after cycling for the most severe history (Δecoatel + Δecoatcreep = 0.83%). A A 100 h isothermal test at 1090 °C revealed little thinning of the coating, no interface voids, and no cracking. Cyclic degradation consisted of severe cracking, which in some cases propagated well into the substrate, and critically depended on the calculated coating strain ranges and oxides cooling stresses. Two different crack initiation process were observed in the absence of initial surface defects (pits). At normal cooling rates (15 s), cracks appeared to originate from interface (Kirkendall) voids that grew from the original coating-substrate interface towards the coating surface. These voids were associated with calculated coating strain ranges of 0.57% and above. At high cooling rates (7 s), giving maximum calculated oxide stresses of 218 MPa rather than 116 MPa, there was early cracking of the protective oxide scale with cracks initiating at the coating surface.