A dislocation model for the plastic relaxation of the transformation strain energy of a misfitting spherical particle

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Department of Materials Science and Engineering


A dislocation approach is developed to explain the dependency of the plastic zone size on precipitate size and misfit for a spherical misfitting particle. The dislocation model is predicated upon the punching and mutual interaction of dislocation prismatic loops and is used to explain the presence of both prismatic loops and dense tangles of dislocations surrounding the precipitate. The plastic zone is modeled as a series of concentric dislocation loop shells which can climb and glide in such a way as to minimize the energy of the system; the extent of climb and glide being limited by the critical resolved shear stress of the matrix phase. It is found that plastic zone size is a strong function of particle size. As particle size increases, the ratio of plastic zone radius to particle radius increases. For large particles, plastic zone radii approach the predictions of earlier work in which the three dimensional elasto-plastic problem for a misfitting sphere was solved exactly using the Prandtl-Reuss equations and von Mises yield criterion.

Publication Title

Acta Metallurgica