Steady-state diffusional growth of an axisymmetric cavity on a grain boundary

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Abstract
The steady-state diffusional growth of an axisymmetric cavity on a grain boundary is analysed by using a power-dissipation method and by assuming a steady state in which the rate of decrement of the free energy of the system (or power dissipated by the diffusional process) with the growth process should have a stationary value. An isotropic material under hydrostatic tension is considered and it is assumed that bulk diffusion and changes in the elastic energy of the material with the diffusional process can be neglected. The equations governing the steady-state growth of the cavity are found and approximate methods of finding the velocity of growth at the tip of the cavity and the steady-state shape of the cavity are given.