A discrete dislocation analysis of near-threshold fatigue crack growth

Abstract

Analyses of cyclic loading of a plane strain mode I crack under small-scale yielding are carried out using discrete dislocation dynamics. The formulation is the same as used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. The dislocations are all of edge character and are modeled as line singularities in an elastic solid. 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. Either reversible or irreversible relations are 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 as could occur in a vacuum or in an oxidizing environment, respectively. In accord with experimental data we find that the fatigue threshold Δ K th is weakly dependent on the load ratio R when the reversible cohesive surface is employed. This intrinsic dependence of the threshold on R is an outcome of source limited plasticity at low R values and plastic shakedown at higher R values. On the other hand, Δ K th is seen to decrease approximately linearly with increasing R followed by a plateau when the irreversible cohesive law is used. Our simulations show that in this case the fatigue threshold is dominated by crack closure at low values of R. Calculations illustrating the effects of obstacle density, tensile overloads and slip geometry on cyclic crack growth behavior are also presented.