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. Plastic deformation is modelled 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. Calculations are carried out with different material parameters so that values of yield strength, cohesive strength and elastic moduli varying by factors of three to four are considered. The fatigue crack growth predictions are found to be insensitive to the yield strength of the material despite the number of dislocations and the plastic zone size varying by approximately an order of magnitude. The fatigue threshold scales with the fracture toughness of the purely elastic solid, with the experimentally observed linear scaling with Young?s modulus an outcome when the cohesive strength scales with Young?s modulus.

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([Delta]KI) 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.

Interface delamination during indentation of micron-scale ceramic coatings on metal substrates is modeled using discrete dislocation (DD) plasticity to elucidate the relationships between delamination, substrate plasticity, interface adhesion, elastic mismatch, and film thickness. In the DD method, plasticity in the metal substrate occurs directly via the motion of dislocations, which are governed by a set of physically based constitutive rules for nucleation, motion and annihilation. A cohesive law with peak stress characterizes the traction-separation response of the metal/ceramic interface. The indenter is a rigid flat punch and plane strain deformation is assumed. A continuum plasticity model of the same problem is studied for comparison. For low interface strengths (e.g. ), DD and continuum plasticity results are quantitatively similar, with delamination being nearly independent of interface strength, and easier for thinner, lower-modulus films. For higher interface strengths (), continuum plasticity predicts no delamination up to very high loads while the DD model shows a smooth increase in the critical indentation force for delamination with increasing interface strength. Tensile delamination in the DD model is driven by the accumulation of dislocations, and their associated high stresses, at the interface upon unloading. The DD model is thus capable of predicting the nucleation of cracks, and its dependence on material parameters, in realms of realistic constitutive behavior and/or small length scales where conventional continuum plasticity fails.

A recently developed finite element method for the modeling of dislocations is improved by adding enrichments in the neighborhood of the dislocation core. In this method, the dislocation is modeled by a line or surface of discontinuity in two or three dimensions. The method is applicable to nonlinear and anisotropic materials, large deformations, and complicated geometries. Two separate enrichments are considered: a discontinuous jump enrichment and a singular enrichment based on the closed-form, infinite-domain solutions for the dislocation core. Several examples are presented for dislocations constrained in layered materials in 2D and 3D to illustrate the applicability of the method to interface problems.

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 Kinit 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 [Delta]K-governed for sufficiently long cracks. Below a critical crack size the value of [Delta]KI at the fatigue threshold is found to decrease substantially with crack size and progressive cyclic crack growth occurs even when Kmax 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.

Small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a finite element solution. 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. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress fields are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly affected by the dislocation activity in the vicinity of the growing crack tip.

The influence of mode mixity on crack growth and failure at a metal/ceramic bimaterial interface is examined within the discrete dislocation (DD) plasticity framework. Plasticity occurs via the motion of dislocations embedded in a linearly elastic medium with physically based rules governing dislocation nucleation, motion and annihilation. The numerical procedure uses a new superposition technique, developed specifically to allow the efficient solution of DD problems containing elastic inhomogeneities. The existence of an interface crack in the unloaded configuration is assumed and the remote loading is given by the elastic bimaterial crack solution, in accordance with the small scale yielding assumption. A mode-independent cohesive zone law characterizes the interface ahead of the initial crack tip, with a small amount of viscous damping added to the interface constitutive description to avoid convergence problems. The model predicts crack growth with a resistance curve and an increasing fracture toughness with mode mixity, qualitatively similar to recent continuum plasticity calculations but much smaller in magnitude. The quantitative differences arise from the large opening stresses induced by dislocations which drives separation in cases where continuum plasticity can not. Crack tip blunting and shielding, the existence of preferential slip planes, localized regions of large deformation and competition between ductile and brittle fracture all emerge naturally from the boundary value problem solution and provide insight into the observed toughness trends.