Discrete Dislocations Interacting with a Mode I Crack

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 linear elastic, 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 jumps across a cohesive surface ahead of the initial crack tip is also specified, so that crack initiation and crack growth emerge naturally. Material parameters representative of aluminum are employed. Two cases are considered that differ in the strength and density of dislocation obstacles. Results are presented for the evolution of the dislocation structure and the near-tip stress field during the early stages of crack growth.