A cohesive zone model based on the micromechanics of dislocations

Abstract

The deformation in the vicinity of a crack tip is governed by the presence of plastic strains and plastic strain gradients. Statistically stored and geometrically necessary dislocations related to these measures of deformation play a vital role in fatigue crack growth of metals. Both kinds of dislocation are responsible for crack advance as well as for crack tip shielding. We introduce a novel cohesive zone model for the description of fatigue crack growth in metals. The model incorporates the stress fields due to dislocations into the constitutive model of the cohesive zone. While the plastic deformation characteristics are calculated using a finite element model, the stress at the crack tip due to multitudes of dislocations are expressed by analytical expressions which are derived from the stress field of an individual dislocation. The cohesive strength is overcome due to a combination of stresses arising from material separation enhanced by the stresses due to the dislocations. Crack growth for constant amplitude loading and the overload case is computed. The computed dislocation densities are similar to those obtained by discrete dislocation simulations. Significant crack closure is observed. A fatigue crack growth threshold and Paris law dependence of the fatigue crack growth rate on ΔK are outcomes of the model. Overload is discussed with respect to the dislocation density distribution and the resulting fatigue crack growth retardation. These results compare well with experimental findings of fcc metals.