A discrete dislocation analysis of near-threshold fatigue crack growth

Analyses of cyclic loading of a plane strain mode I crack under small-scale yielding are carried out using discrete dislocation dynamics. The formulat ion is the same as used to analyze crack growth under monotonic loading con ditions, differing only in the remote stress intensity factor being a cycli c function of time. The dislocations are all of edge character and are mode led as line singularities in an elastic solid. The lattice resistance to di slocation motion, dislocation nucleation, dislocation interaction with obst acles and dislocation annihilation are incorporated into the formulation th rough a set of constitutive rules. Either reversible or irreversible relati ons are specified between the opening traction and the displacement jump ac ross a cohesive surface ahead of the initial crack Lip 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 thr eshold DeltaK(th) is weakly dependent on the load ratio R when the reversib le cohesive surface is employed. This intrinsic dependence of the threshold on R is an outcome of source limited plasticity at low R values and plasti c shakedown at higher R values. On the other hand, DeltaK(th) is seen to de crease approximately linearly with increasing R followed by a plateau when the irreversible cohesive law is used. Our simulations show that in this ca se the fatigue threshold is dominated by crack closure at low values of R. Calculations illustrating the effects of obstacle density, tensile overload s and slip geometry on cyclic crack growth behavior are also presented. (C) 2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.