The isotropic limit in anisotropic dislocation theory Green's functions in a crystal containing a dislocation pile‐up

A simple method is developed which provides the transition from two‐dimensional anisotropic ekpressions of dislocation theory to isotropic ones. Anisotropic expressions are given for the stress and displacement fields near a dislocation pile‐up (martensite crystal, crack, twin, slip band) in the presence of a single dislocation or a line force lying parallel to the pile‐up. By use of the method presented here, the corresponding isotropic formulae are obtained. These expressions are the Green's functions of dislocation theory for crystals containing a pile‐up type of defect.