C. Westwood et al., A simplified model for cavity growth along a grain-boundary by coupled surface and grain-boundary diffusion, EUR J MEC A, 19(1), 2000, pp. 17-30
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.