Application of the average field method to the prediction of stable shapes of coherent precipitates under uniaxial stresses

Stable shapes of misfitted precipitates are discussed with mechanical free energy minimization criterion. The Mori–Tanaka concept of the ‘average field’ is applied to evaluate stress and strain in the materials containing the precipitates with various volume fractions. With the phenomenon of rafting in superalloys in mind, the stable shapes are calculated for coherent precipitates with purely dilatational (or constrictive) misfit strains in materials under uniaxial external stresses. Maps to show the stable shapes are obtained for various volume fractions of the precipitates as a function of magnitudes of external stresses, misfit strains and elastic moduli. Effects of the volume fraction on the stable shapes of precipitates are discussed.