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.

Mode I steady-state crack growth is analysed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by a generalization of J2 flow theory which accounts for the influence of the gradients of plastic strains on hardening. The constitutive model involves one new parameter, a material length l, specifying the scale of nonuniform deformation at which hardening elevation owing to strain gradients becomes important. Gradients of plastic strain at a sharp crack tip result in a substantial increase in tractions ahead of the tip. This has important consequences for crack growth in materials that fail by decohesion or cleavage at the atomic scale. The new constitutive law is used in conjunction with a model which represents the fracture process by an embedded traction-separation relation applied on the plane ahead of the crack tip. The ratio of the macroscopic work of fracture to the work of the fracture process is calculated as a function of the parameters characterizing the fracture process and the solid, with particular emphasis on the role of l.