A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part II: Two-dimensional characterization and boundary kinetics

Abstract

A companion paper presented the formulation of a phase-field model – i.e., a model with regularized interfaces that do not require explicit numerical tracking – that allows for easy and transparent prescription of complex interface kinetics and nucleation. The key ingredients were a re-parametrization of the energy density to clearly separate nucleation from kinetics; and an evolution law that comes from a conservation statement for interfaces. This enables clear prescription of nucleation through the source term of the conservation law and of kinetics through an interfacial velocity field. This model overcomes an important shortcoming of existing phase-field models, namely that the specification of kinetics and nucleation is both restrictive and extremely opaque.In this paper, we present a number of numerical calculations – in one and two dimensions – that characterize our formulation. These calculations illustrate (i) highly-sensitive rate-dependent nucleation; (ii) independent prescription of the forward and backward nucleation stresses without changing the energy landscape; (iii) stick–slip interface kinetics; (iii) the competition between nucleation and kinetics in determining the final microstructural state; (iv) the effect of anisotropic kinetics; and (v) the effect of non-monotone kinetics. These calculations demonstrate the ability of this formulation to precisely prescribe complex nucleation and kinetics in a simple and transparent manner.We also extend our conservation statement to describe the kinetics of the junction lines between microstructural interfaces and boundaries. This enables us to prescribe an additional kinetic relation for the boundary, and we examine the interplay between the bulk kinetics and the junction kinetics.