A discrete dislocation analysis of mode I crack growth

Small scale yielding around a plane strain mode I crack is analyzed using d iscrete dislocation dynamics. The dislocations are all of edge character, a nd are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of sol utions for edge dislocations in a half-space and a complementary solution t hat enforces the boundary conditions. The latter is non-singular and obtain ed from a finite element solution. The lattice resistance to dislocation mo tion, dislocation nucleation, dislocation interaction with obstacles and di slocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the disp lacement jump across a cohesive surface ahead of the initial crack tip is a lso specified, so that crack growth emerges naturally from the boundary val ue problem solution. Material parameters representative of aluminum are emp loyed. For a low density of dislocation sources, crack growth takes place i n a brittle manner, for a low density of obstacles, the crack blunts contin uously and does not grow. In the intermediate regime, the average near-tip stress fields are in qualitative accord with those predicted by classical c ontinuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the c ohesive strength. The crack growth history is strongly affected by the disl ocation activity in the vicinity of the growing crack tip. (C) 2000 Elsevie r Science Ltd. All rights reserved.