A simplified model for cavity growth along a grain-boundary by coupled surface and grain-boundary diffusion

Following a model for the sintering of a row of grains by Sun et al. (1996) , a simplified model is developed for cavity growth along a grain-boundary by surface and grain-boundary diffusion. The cavity surface is approximated by two arcs of equal radius truncated by the grain-boundary. The arcs evol ve by changing the radius and the intersection angle they make with the gra in-boundary. A variational principle for the coupled diffusion problem is u sed to obtain the rate equations for the two degrees of freedom which are n umerically integrated to follow the cavity growth. The simplified model can be reduced to the well established equilibrium cavity growth model for the limiting case of fast surface diffusion. A validity map for the model is c onstructed by comparing the approximate solutions with full numerical solut ions over a wide range of values of relative diffusivity, initial dihedral angles and applied stresses. It is found that the simplified solution can b e used under most of the practical conditions. The model described here is two dimensional although the approach can be easily extended to axisymmetri c cases. (C) 2000 Editions scientifiques et medicales Elsevier SAS.