On the Influence of Weak Spatial Disorder on the Stress Fields of Finite Dislocation Walls

Abstract

AbstractNumerical simulations of the three‐dimensional elastic stress fields associated with finite ordered and weakly disordered dislocation walls are carried out. The walls consist of discrete dislocations which are regarded as piecewise linear defects embedded within an otherwise isotropic elastic medium. The dislocation line vectors and Burgers vectors involved constitute a simple cubic lattice. The dislocations are subdivided into small segments. Two basic types of dislocation walls are studied, namely, a finite small angle tilt boundary and a finite dislocation cell wall consisting of 45° edge dislocation dipoles. The tilt boundary consists of 100 straight parallel dislocations. The dipole wall contains 100 alternately antiparallel edge dislocations. For both wall types the influence of weak spatial disorder on their stress fields is investigated. For this purpose non‐straight dislocations with a fractal dimension of 1.05 are used instead of straight dislocations. The study substantiates that weak spatial disorder considerably affects the stress field in the vicinity of the dislocation walls. However, the course of the long‐range stress is not predominantly determined by spatial disorder of the dislocation lines but by the finite geometry of the walls. The maximum shearing stress which is associated with the finite tilt boundary reveals a strong (but not exponential) decay in the direct vicinity of the wall. A local minimum occurs within a distance which exceeds the dislocation spacing in the wall by less than one order of magnitude. A local stress maximum is generated within a distance which exceeds the dislocation spacing by about two orders of magnitude. Finally, a long‐range stress field is predicted which corresponds to the solution obtained for a corresponding super‐dislocation with bsuper = 100bsingle (bsuper the Burgers vector of the super‐dislocation, bsingle the Burgers vector of the dislocations in the wall). The stress field of the dipole wall is not negligible but reveals short‐ and intermediate‐range stress components which decay with 1/distance.