Diffusion-assisted shrinkage of a spherical void

Vacancy diffusion plays an important role in the homogenization of microstructures and the “healing” of structural flaws in crystalline materials. In this work, we establish an analytical model taking into account the coupling between stress and diffusion for the void evolution in pure element materials if there is a difference between the partial molar volume of atoms and the corresponding one of vacancies. Provided that there is no difference between the partial molar volume of atoms and the corresponding one of vacancies, we use the model to analyze the shrinking of a spherical void in a spherical shell. Differential equations for the temporal evolution of the void are derived for two cases of constant surface loading and stress relaxation without surface loading. Numerical results illustrate that, under constant surface loading, the larger the spherical void with the same shell volume, the larger the “healing” time; the larger the shell volume with the same void size, the larger the “healing” time. Increasing the magnitude of hydrostatic pressure reduces the “healing” time of spherical voids. Without external loading, the smaller the spherical void, the faster the stress relaxation during the shrinking of the spherical void.