It was recalled that deformation in the vicinity of a crack tip was governed by the presence of plastic strains and plastic-strain gradients. Statistically stored and geometrically necessary dislocations, related to these measures of deformation, played a vital role in fatigue crack growth in metals. Both kinds of dislocation were responsible for crack advance as well as for crack-tip shielding. A novel cohesive zone model, for the description of fatigue crack growth in metals, was introduced. The model incorporated the stress fields due to dislocations into the constitutive model of the cohesive zone. The plastic deformation characteristics were calculated by using a finite element model, while the stress at the crack tip - due to many dislocations - were expressed by using analytical expressions which were derived from the stress field of an individual dislocation. The cohesive strength was overcome by a combination of stresses arising from material separation; enhanced by the stresses due to dislocations. Crack growth was estimated for constant-amplitude loading, and the overload case. The estimated dislocation densities were similar to those obtained by means of discrete dislocation simulations. Significant crack closure was observed. A fatigue crack growth threshold and Paris-law dependence of the fatigue crack growth rate upon ΔK were predictions of the model. Overloading was considering with regard to the dislocation density distribution and the resultant fatigue-crack growth-retardation. The results compared well with experimental data on face-centered cubic metals.

A Cohesive Zone Model Based on the Micromechanics of Dislocations. S.Brinckmann, T.Siegmund: Modelling and Simulation in Materials Science and Engineering, 2008, 16[6], 065003