Large strain elasto-plasticity for diffuse interface models

Abstract

Most solid-state phase transformations are accompanied by large deformations, stemming either from external load, transformation strains or plasticity. The consideration of such large deformations will affect the numerical treatment of such transformations. In this paper, we present a new scheme to embed large deformations in an explicit phase-field scheme and its implementation in the open-source framework OpenPhase. The suggested scheme combines the advantages of a spectral solver to calculate the mechanical boundary value problem in a small strain limit and an advection procedure to transport field variables over the calculation grid. Since the developed approach should be used for various sets of problems, e.g. simulations of thermodynamically driven phase transformations, the mechanic formulation is kept general. However, to ensure compatibility with phase-field methods using the concept of diffuse interface, the latter is treated with special care in the present work.

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

“…Multiplying the above expression with J and taking note of Eqs. (13) and (14) together with (4), the Clausius-Duhem inequality can equivalently be written as…”

Large deformation framework for phase-field simulations at the mesoscale

“…The previous state of the framework presented in [14] has been expanded by a consistent coupling of material anisotropies and deformation-induced rotations, as presented in the two examples. First, a rolling-like deformation of a polycrystal volume element has been performed successfully.…”

“…However, the numerical implementation proposed in this paper is based on a spectral solver relying on linearity of the underlying mechanical problem. Thus, the (pseudo) linear relationship (14) is very convenient. It should be emphasized that special care is required in order to conserve the objectivity of Eq.…”

“…In our previous publication [14] we benchmarked the developed method against solutions obtained by a commercial finite-element software Simulia Abaqus [15], which uses the classical Lagrangian approach of continuum mechanics. The results showed a good agreement for investigated strains of up to 30% along with some deviations in the interface region that could be traced back to the elasto-plastic homogenization scheme.…”

Modelling of flow behaviour and dynamic recrystallization during hot deformation of MS-W 1200 using the phase field framework

“…The crystal plasticity kinetics is based on a model from Hutchinson [11][12][13] and were incorporated into the phase field framework by Borukhovich and Engels [14]. Starting with the approach by Borukhovich and Engels in this study we implemented the physically based recovery model by Verdier et al [15] in order to differentiate between single effects.…”