A distributed dislocation stress analysis for crazes and plastic zones at crack tips

A distributed dislocation method is developed to obtain analytically the applied stress as well as the surface stress profile along narrow plastic zones at the tip of a crack in a homogeneous tensile stress field. Replacing the plastic zone by a continuous array of mathematical dislocations, the stress field solution of this mixed boundary value problem (the displacement profile of the plastic zone is fixed while the tensile stresses are zero across the crack) can be solved. A computer program based on this stress field solution has been constructed and tested using the analytical results of the Dugdale model. The method is then applied to determining the surface stress profiles of crazes and plane-stress plastic deformation zones grown from electron microprobe cracks in polystyrene and polycarbonate respectively. The necessary craze and zone surface displacement profiles are determined by quantitative analysis of transmission electron micrographs. The surface stress profiles, which show small stress concentrations at the craze or zone tip falling to an approximately constant value which is maintained to the crack tip, are compared with those previously computed using an approximate Fourier transform method involving estimation of the displacement profile in the crack. The agreement between the approximate method and the exact distributed dislocation method is satisfactory.