Non-Linear Effects in the Elastic Field of Single Dislocations

Abstract

We have seen in the preceding chapter that dislocations may be described as line singularities of the elastic field: linear elasticity theory predicts stresses and strains that vary as the inverse first power of the distance from the dislocation line and, therefore, are unbounded as this distance goes to zero. Thus, close to the singularities the strains become very large, and non-linear effects must be taken into account. On the other hand, in regions sufficiently far from dislocations, the stresses and strains are sufficiently small and may be adequately described by the linear theory. For this reason, and also on account of its simplicity, the linear theory of elasticity continues to be successfully applied for simulating crystal defects, e.g. in the study of the long-range stress field of dislocations, the interaction between distant imperfections, and in the calculation of defect energies¹.