Britta Nestler

A phase field concept for multiphase systems

Abstract The phase field theory describing the evolution of a dual phase boundary is extended to multiphase problems: Each phase is identified with an individual phase field and the transformation between all pairs of phases is treated with its own characteristics. The governing differential equations for the evolution of the multiphase system are derived by minimizing the free energy functional. This free energy functional is expanded in a series over the pair energies between the different phases, where the local fluctuations of one phase are treated with respect to its counter-phase. The proposed generalized multiphase concept reproduces the dual phase system as a limiting case. The relevance of the model for metallic systems is discussed with respect to eutectic and peritectic solidification and grain growth.

The multiphase-field model with an integrated concept for modelling solute diffusion

Abstract A recent formulation of a multiphase-field model is presented. The approach is employed to numerically simulate phase transitions in multiphase systems and to describe the evolution of the microstructure during solidification processes in alloy systems. A new method for modelling solute diffusion in a binary alloy within N different phases with varying solubilities and different diffusion coefficients is integrated in the multiphase-field model. The phase-field/diffusion model derived is compared with the previous Wheeler, Boettinger and McFadden (WBM) model in a limiting case. The set of coupled evolution equations, the phase-field model equations and the concentration field equation is solved using control volume techniques on a uniform mesh. With the input of the specific phase diagram, thermophysical and materials data of the chosen real FeC alloy system, the multiphase-field method is successfully applied to compute the peritectic solidification process of steel. The numerical calculations of the peritectic reaction and transformation are presented.

A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures

In this paper, we extend the multi-phase-field concept, recently developed to model pure systems involving grains, to multi-phase alloy systems. We derive a phase-field model in a general form which has the flexibility to model a variety of binary alloys. In particular, our new model provides a framework for describing and numerically simulating the solidification of both eutectic and peritectic systems. We report computations that exhibit a wide range of realistic phenomena, including eutectic lamellae spacing selection by the annihilation of lamellae through competitive over-growth by their neighbours as well as tip splitting of individual lamellae. Our results are consistent with the scaling predictions of the classical Jackson and Hunt theory of eutectic lamellae. With regards to peritectic growth, we report simulations that exhibit many characteristic features of the peritectic phase transition: below the peritectic temperature the peritectic phase grows preferentially along the properitectic phase by solute diffusion in the liquid until the parent phase is engulfed. The subsequent peritectic transformation continues by solid diffusion on a longer timescale.

A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions

We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen--Cahn system to a multiphase interface problem with curvature-dependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen--Cahn system, the normal to an interface between phases i and j is modeled by the irreducible representations

On anisotropic order parameter models for multi-phase system and their sharp interface limits

(u_i\nabla u_j - u_j\nabla u_i)/{|u_i\nabla u_j - u_j\nabla u_i|}

A Diffuse Interface Model for Alloys with Multiple Components and Phases

, where ui and uj are the ith and jth components of the vectorial order parameter

Phase-field model for solidification of a monotectic alloy with convection

\bu\in \rz^N

Phase field modeling of fracture and stress-induced phase transitions

.In the vectorial case, the dependence of the limiting surface tensions and mobilities on the bulk potentials of the Allen--Cahn system is not given explicitly but in terms of all the N components of the planar stationary wave solutions. One of the issues of this paper is to find bulk potentials which allow a rather easy access to the resulting surface tensions and mobilities. We compare numerical computations for planar and circular phase bound...

Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys

Abstract For a general class of diffuse anisotropic multi-phase order parameter (or phase-field) models we use formally matched asymptotic expansions to determine the asymptotic limit when a small parameter related to the thickness of the interface tends to zero. In the case of anisotropic Allen-Cahn systems we obtain in the limit that the interface moves by anisotropic mean curvature flow. At triple junctions a force balance holds which in the anisotropic case includes shear forces (Herring torque terms) acting normal to the interface. We further identify the singular limit of anisotropic Cahn-Hilliard systems.

Phase-field modelling of solute trapping during rapid solidification of a Si–As alloy

A nonisothermal phase field model for alloys with multiple phases and components is derived. The model allows for arbitrary phase diagrams. We relate the model to classical sharp interface models by formally matched asymptotic expansions. In addition we discuss several examples and relate our model to the ones already existing.