Numerical simulation of the formation of spherulites in polycrystalline binary mixtures

Abstract

Spherulites are growth patterns of average spherical form which may occur in the polycrystallization of binary mixtures due to misoriented angles at low grain boundaries. The dynamic growth of spherulites can be described by a phase field model where the underlying free energy depends on two phase field variables, namely the local degree of crystallinity and the orientation angle. For the solution of the phase field model we suggest a splitting scheme based on an implicit discretization in time which decouples the model and at each time step requires the successive solution of an evolutionary inclusion in the orientation angle and an evolutionary equation in the local degree of crystallinity. The discretization in space is done by piecewise linear Lagrangian finite elements. The fully discretized splitting scheme amounts to the solution of two systems of nonlinear algebraic equations. For the numerical solution we suggest a predictor-corrector continuation method with the discrete time as a parameter featuring constant continuation as a predictor and a semismooth Newton method for the first system and the classical Newton method for the second system as a corrector. This allows an adaptive choice of the time steps. Numerical results are given for the formation of a Category 1 spherulite.