Energy variations in diffusive cavity growth

The assignment of boundary values for the chemical potential and the calculation of energy release rates for the growth of creep cavities along grain boundaries by self-diffusion are discussed. It is assumed that the boundaries are flat and that surface and gran-boundary diffusion are the dominant transport mechanisms. As matter diffuses from the void surface into and along the grain boundary, misfit residual stresses are induced to alleviate the high stress concentration ahead of the cavity apex. As a result, it is shown that the contribution of strain energy terms to the chemical potential can be neglected in typical cases. Also, contrary to the Griffith crack extension model, the energy dissipation incurred by diffusive removal of material from the cavity surface and deposition in the grain boundary is a major term in the energy transfers associated with cavity growth. The primary energy sink in diffusive cavity growth arises from the work done by the grain-boundary normal stress when matter is inserted in the near-tip region by diffusion, and not from the loss of strain energy of matter that is removed from the cavity at its tip or from a work of bond separation. Thermodynamic restrictions on the angle formed by the void surfaces at their apex, where they join the grain boundary is described. The derivation of boundary values for the chemical potential is carried out in a manner appropriate for arbitrarily large but elastic distortions of material near the cavity tip and, by contrast to most previous work in the area. Rigorously the effects of surface tension, as distinct from surface energy, is included.