Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: linear and power-law strain hardening

TLDR: In this article, complete solutions to the displacement, stress and strain fields, plastic zone size and misfit energy are calculated for an isotropic misfitting spherical precipitate under the assumptions of von Mises' yield criterion and incremental plasticity.

Abstract: Complete solutions to the displacement, stress and strain fields, plastic zone size and misfit energy are calculated for an isotropic misfitting spherical precipitate under the assumptions of von Mises’ yield criterion and incremental plasticity. Analytical solutions are obtained for the case of linear strain hardening while a numerical technique is necessary for the case of power-law hardening. Large changes in the stress field in the regions surrounding the precipitate are observed when contrasted with the elastic state. The energy of the relaxed state is found to be a strong function of the strain-hardening parameter as is the plastic work done during the relaxation process. The plastic zone size, however, is not strongly dependent upon the strain-hardening parameter and for a homogeneous precipitate is independent of it.