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A Dynamic Phase-field Model for Structural Transformations and Twinning: Regularized Interfaces with Transparent Prescription of Complex Kinetics and Nucleation. Part I & Part II

Vaibhav Agrawal, Kaushik Dayal, Carnegie Mellon University

Part I: Formulation and one-dimensional characterization

 doi: http://dx.doi.org/10.1016/j.jmps.2015.04.010

The motion of microstructural interfaces is important in modeling twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces need to be explicitly tracked, but have the advantage that the kinetics of existing interfaces and the nucleation of new interfaces can be transparently and precisely prescribed. In contrast, phase-field models do not require explicit tracking of interfaces, thereby enabling relatively simple numerical calculations, but the specification of kinetics and nucleation is both restrictive and extremely opaque. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. Consequently, phase-field models cannot be confidently used in dynamic settings.

This shortcoming of existing phase-field models motivates our work. We present 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 are 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 kinetics – through a distinct interfacial velocity field. A formal limit of the kinetic driving force recovers the classical continuum sharp-interface driving force, providing confidence in both the re-parametrized energy and the evolution statement. We present some 1D calculations characterizing the formulation; in a companion paper, we present more extensive 2D calculations.

 

 

Part II: Two-dimensional characterization and boundary kinetics

doi: http://dx.doi.org/10.1016/j.jmps.2015.05.001

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 there 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 junction kinetics.

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