The Stress Field near the Dislocation Pile‐Up Type Defects in Anisotropic Elasticity

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Abstract
A general expression is obtained for the stress field at any point of infinite anisotropic crystals containing defects of the dislocation pile‐up type (e.g. pile‐ups, deformational twins, cracks, thin crystals of martensite). The stresses are expressed in form of an analytic continuation of the density of dislocations from the line of the pile‐up into the complex plane. The formulas obtained are valid for any geometrical arrangement of the defects, taking into account their non‐zero Burgers vectors and giving stresses due to the defects only. The interaction of a line source (i.e. a line force and a dislocation simultaneously) with the mentioned defects is investigated. The results may be used for an unified description of the adhesion forces, non‐linearity of the media, and plastic zone near the defects in terms of some integral coefficients. The concrete calculations are mainly reduced to the evaluation of the complex constants determining the stress field near a single dislocation. The constants are expressed and the stresses written in terms of elastic moduli for the defects lying in the direction of the orthotropic symmetry of the crystal. As a limiting case the general formulas for stresses near dislocation pile‐ups in isotropic media are found.

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