Effects of octahedral to spherical precipitate-shape transition on elastic strain energy due to misfit precipitates in materials with cubic structures

Abstract

When elastic moduli are anisotropic, the elastic strain energy of materials containing precipitates with purely dilatational misfit strains depends on the precipitate shape. This dependence is discussed for the octahedral to spherical shape transition. Precipitates modelled as superspherical shapes described by ( x 1 2/ a 2) p/2 +( x 2 2/ a 2) p/2 +( x 3 2/ a 2) p/2 ⩽1 with various values of p (1⩽ p⩽2) and embedded in matrices with cubic structure are treated. The micromechanics inclusion problem is solved with the assumption of the same elastic moduli for the precipitates and matrices to calculate the elastic strain energy. When the anisotropy ratio of the elastic moduli is larger than unity, octahedral precipitates cause larger elastic strain energy than spherical precipitates. However, the precipitate-shape dependence of the elastic strain energy is not monotonic and the elastic strain energy peaks for an intermediate shape between octahedral and spherical. The stability of misfit precipitates of octahedral shape is discussed.