Strain and stress field calculations for precipitates and dislocation loops using affine transformations

Abstract

Starting from the covariant formulation of the linear theory of elasticity the elastic strain and stress fields inside and outside precipitates are calculated using appropriate affine coordinates. Explicit integral formulae well suited for numerical evaluation are derived for ellipsoidal, cylindrical, polyhedral, and plate-like particles as well as rhomboidal and elliptical dislocation loops, allowing for an arbitrary homogeneous stress-free strain and elastic anisotropy. The application of the results in precipitate structure analysis by diffraction contrast image matching will be considered in a subsequent paper.