A discrete dislocation analysis of fatigue crack growth

Cyclic loading of a plane strain mode I crack under small scale yielding is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic solid. At each stage of loading, superposition is used to represent the solution i n terms of solutions for edge dislocations in a half-space and a non-singul ar complementary solution that enforces the boundary conditions, which is o btained from a linear elastic, finite element solution. The lattice resista nce to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formu lation through a set of constitutive rules. An irreversible relation betwee n the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, which permits crack growt h to emerge naturally. It is found that crack growth can occur under cyclic loading conditions even when the peak stress intensity factor is smaller t han the stress intensity required for crack growth under monotonic loading conditions; however below a certain threshold value of DeltaK(1) no crack g rowth was seen.