Abstract
In this thesis, a new set of finite element formulations are developed for computer simulation of microstructural evolution which is controlled by solid-state diffusion and grain-boundary migration. The finite element formulations are based on the classical cubic spline interpolation and form a natural extension of the linear finite element scheme which was first developed by Pan, Cocks and Kucherenko (1997). The cubic spline elements are however much more efficient numerically than the previous linear elements and make it possible to undertake large scale computer simulations of microstructural evolution using ordinary personal computers. The newly developed finite element scheme is then used to study the sintering process of powder compacts. Two important issues are addressed in this thesis. First, the sintering kinetics of large pores is investigated in details. An established theory due to Kingery (1967) predicts that a pore will shrink only if its coordination number (number of grains surrounding the pore) is less than a critical value which depends on the dihedral angle of the powder material. However, there are increasing experimental evidences contradicting this theory. Very large pores were observed to shrink continuously in the sintering process. The numerical study presented in this thesis demonstrated that the critical coordination number theory is in fact not a general rule. The computer simulations show that a very large pore does shrink unless it is surrounded by identical grains, which is obviously not true in any real powder compact. Secondly, the finite element scheme is used to study the anisotropic shrinkage during the sintering process. The numerical study reveals the key factors which control anisotropic shrinkage and shows that models based on continuum mechanics are unable to capture the critical influence of these key factors.