Modeling of growth and impingement of spherical grains
Materials Transactions JIM, 37 (10):
1595-1601 (1996)Abstract
A model was developed to simulate the growth and impingement of spherical
grains, which are frequently encountered in the solidification, recrystallization
and other processes in association with phase transformations. The
initial grain was assumed as spherically approximated 128 faces polyhedron.
Various cases were investigated under different conditions of final
number of grains, nucleation and spatial distribution. The validity
of the Kolmogorov, Johnson-Mehl and Avrami (KJMA) equation was examined
for various cases. The results proved that KJMA equations are valid
for the real volume and the effective surface area (effective for
later growth) calculations under the conditions of site saturation/constant
growth rate and the conditions of constant nucleation rate/constant
growth rate. When the grain shape is not maintained same throughout
the process, the results show that the effective surface area deviate
largely from the KJMA equation even though the KJMA equation is approximately
valid to calculate the real volume. Finally, when the spatial distribution
of grains is non-random, clustered or ordered, the KJMA equation
is not valid and the deviation from it is large especially at the
end of transformation both for the real volume and for the effective
surface. Even when the KJMA equation is not valid for the effective
surface area, Rath's empirical equation is effectively applicable
for it, though the physical meaning of the parameters used in it
is not clear.