The role of grain boundaries (GBs) and especially the migration of GBs is of utmost importance in regard of the overall mechanical behavior of polycrystals. By implementing a crystal plasticity (CP) theory in a multiphase-field method, where GBs are considered as diffuse interfaces of finite thickness, numerically costly tracking of migrating GBs, present during phase transformation processes, can be avoided. In this work, the implementation of the constitutive material behavior within the diffuse interface region, considers phase-specific plastic fields and the jump condition approach accounting for CP. Moreover, a coupling is considered in which the phase-field evolution and the balance of linear momentum are solved in each time step. The application of the model is extended to evolving phases and moving interfaces and approaches to strain inheritance are proposed. The impact of driving forces on the phase-field evolution arising from plastic deformation is discussed. To this end, the shape evolution of an inclusion is investigated. The resulting equilibrium shapes depend on the anisotropic plastic deformation and are illustrated and examined. Subsequently, evolving phases are studied in the context of static recrystallization (SRX). The GB migration involved in the growth of nuclei, which are placed in a previously deformed grain structure, is investigated. For this purpose, three approaches to strain inheritance are compared and, subsequently, different grain structures and distributions of nuclei are considered. It is shown, how the revisited method contributes to a simulation of SRX.

The phase-field method is well established for simulating microstructure evolution in computational materials science, providing a numerically efficient tracking of interfaces and surfaces by means of an order parameter. The derivation of its evolution equation is usually based on a variational approach or a corresponding principle of virtual power. Both approaches consider the order parameter as an additional degree of freedom and assume a diffuse interface region from the outset. This work examines the interpretation of the order parameter as an internal state variable, instead of an additional degree of freedom, since it represents an observable rather than a controllable quantity. Furthermore, the phase-field method is considered as an approximation of the sharp interface theory of a continuum containing a singular surface. A Cauchy continuum with a material singular surface is considered as starting point. The evolution equation of the order parameter is derived consistently in the context of continuum thermodynamics by exploitation of the Clausius–Duhem inequality. In this context, the equation of heat conduction and the thermomechanical coupling is discussed regarding the diffuse interface region and the role of the latent heat due to phase evolution. Based on restrictions of the free energy, special cases of the evolution equation are presented. For a special case, the coincidence of the evolution equation obtained by the presented approach and the classical variational approach is demonstrated. Based on the presented approach, the classical Allen–Cahn/Ginzburg–Landau equation is obtained by assuming a spatially homogeneous temperature distribution.

An implementation of the crystal plasticity theory in the context of the multiphase-field method provides a numerically efficient tracking of evolving grain boundaries, modeled as diffuse interfaces. In literature, several approaches exist for the implementation of the plastic material behavior within the diffuse interface, based on interpolation, homogenization, or the mechanical jump conditions. Among these, only the jump condition approach exhibits an intrinsic relationship to the sharp interface (SI) theory. Therefore, in the work at hand, the implementation of the crystal plasticity theory within the jump condition approach, referred to as phase-specific plastic fields approach (PSPFA), is discussed in detail. The PSPFA is compared to the interpolation approach, referred to as common plastic fields approach (CPFA), using three-dimensional benchmark simulations of a bicrystal set-up. The comparison reveals that the PSPFA and SI coincide convincingly regarding the accumulated plastic slip and the Mises stress. In contrast, a significant deviation of CPFA and SI is observed both quantitatively and qualitatively, not only within the diffuse interface region, but throughout the complete simulation domain. A variation of the interface width illustrates that this observation can be transferred to the normal components of the total strain, even for smaller interface widths. Consequently, a quantitative estimate of the plastic material behavior, which is crucial for the prediction of the dynamic behavior of grain boundaries, is only provided by the PSPFA. The application of the crystal plasticity in the context of PSPFA to more complex microstructures is illustrated with respect to a periodic honeycomb-structure and an octotuple.