Simulating Microstructural Evolution using the Phase Field Method

Abstract

The key to predict material properties is the state of microstructure. Because microstructural evolution is a typical nonlinear, nonlocal, and multiparticle dynamic problem, computer simulations play an ever increasingly important role in predicting key microstructural features and their time evolution during various processes such as phase transformations, domain coarsening, and plastic deformation. A plethora of computational methods and algorithms have been developed in recent years to complement theoretical and experimental studies to explore the high dimensional material‐ and processing‐parameter space, which would not only lower the cost but also increase the efficiency of optimizing existing materials and developing new ones. In this article, a brief account of the basic features of each method, including the conventional front‐tracking methods and techniques without front‐tracking (such as Continuum/Microscopic/Coarse‐Grained Phase Field Method; Mesoscopic/Atomistic Monte Carlo; Cellular Automata; Discrete Lattice Model; Phase Field Crystal Model; Diffusive Molecular Dynamics; Microscopic Master Equations; Inhomogeneous Path Probability Method; and Molecular Dynamics) will be presented first, followed by detailed descriptions of the fundamentals of various phase‐field methods at different length scales and their model formulations. The applications of the phase field methods will be demonstrated by examples of coherent precipitation, grain growth, ferroelectric domain structure formation, dislocation core structures, and dislocation‐precipitate interactions. Existing challenges and future trends of the phase‐field methods are discussed at the end of the article.

Statistically equivalent representative volume elements (SERVE) for material behaviour analysis and multiscale modelling

“…Traditionally, simulation methods such as Monte Carlo [98], phase field [99][100][101], multi-phase field [102,103], and other methods were shown to create SEVM of high accuracy. The methods originate from alloy physics and thermodynamics established within phase transformation and kinetics theory, but these may carry a heavy computational cost that limits their use for MPSE design.…”

“…10,20,50,100, 200. The CDFs of the ensemble random vector channel width distributions are shown in Figure5(b), and the KS test statistics for N p = 10, 20, 50, 100 with respect to N p = 200 are respectively [0.0148, 0.0133, 0.0119, and 0.0102].…”

Phase field simulation of microstructures of Mg and Al alloys

“…This method was established on a diffused interface concept proposed by van der Waals [18,19], and subsequent development made by Cahn and Hilliard [20,21]. In the phase field method, microstructures of Mg and Al alloys are often described by two types of continuous fields, which are often called order parameters or field variables [22]. One type of the order parameters, i.e.…”

Microstructure and transformation texture evolution during α precipitation in polycrystalline α/β titanium alloys – A simulation study

“…In Section 2, we present an extension of a previously formulated 3D phase field model [12,29] to investigate both microstructure and texture evolution during a precipitation in polycrystalline titanium alloys. It is worth emphasizing that, based on gradient thermodynamics [30][31][32] and microelasticity theory [33][34][35][36][37], the phase field approach [38][39][40][41][42][43][44] (also called the diffuse-interface approach) offers an ideal framework to deal rigorously and robustly with the difficult challenges mentioned above. In particular, in combination with orientation distribution function (ODF) modeling [45] of simulated a + b microstructures, both micro-and macro-texture evolution accompanying the a + b microstructure evolution under different processing conditions can be documented.…”