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

摘要

Following a model for the sintering of a row of grains by Sun etal. (l996), a simplified model is developed for cavity growth along agrain- boundary by surface and grain--boundary diffusion. The cavitysurface is approximated by two arcs of equal radius truncated by thegrain-boundary. The arcs evolve by changing the radius and theintersection angle they make with the grain--boundary. A variationalprinciple for the coupled diffusion problem is used to obtain therate equations for the two degrees of freedom which are numericallyintegrated to follow the cavity growth. The simplified model can bereduced to the well established equilibrium cavity growth model forthe limiting case of fast surface diffusion. A validity map for themodel is constructed by comparing the approximate solutions with fullnumerical solutions over a wide range of values of relativediffusivity, initial dihedral angles and applied stresses. It isfound that the simplified solution can be used under most of thepractical conditions. The model described here is two dimensionalalthough the approach can be easily extended to axisymmetric cases.