Finite-deformation phase-field microelasticity with application to dislocation core and reaction modeling in fcc crystals

Abstract

The purpose of the current work is the formulation of finite-deformation phase-field microelasticity (FDPFM) and its application to the modeling of (i) the dislocation core and (ii) dislocation interaction/reaction on intersecting glide planes in fcc crystals. The corresponding model formulation is carried out in the context of continuum thermodynamics; for simplicity, isothermal, quasi-static conditions are assumed. The resulting model rests in particular on generalized Ginzburg–Landau relations for dislocation slip-line phase field evolution depending on the Peach-Koehler (PK) force. Restricting attention to (periodic) bulk single crystal behavior, the algorithmic formulation and numerical implementation of FDPFM employs Green function, spectral, and Fourier methods generalized to geometric non-linearity. More specifically, algorithms for control of either the mean deformation gradient, or the mean Cauchy stress (i.e., PK force control) are developed. As in ”standard” linear PFM, the free energy model in FDPFM is based on elastic, crystal and gradient contributions. In order to model dislocation interaction and reactions on multiple intersecting glide planes, the ”standard” 2D stacking-fault-energy-based PFM crystal energy is generalized here to 3D crystallographic form for dissociation, partial fcc dislocations and stacking fault formation. Comparison of FDPFM and atomistic (MS) simulation results for higher-order local continuous and discrete deformation measures (e.g., dislocation tensor) in the core of a dissociated edge dislocation in Au show generally good agreement. In addition, results from FDPFM and MS are compared for dislocation reactions in Al on two intersecting glide planes. In the case of collinear reaction, for example, good qualitative agreement with MS results is obtained only when the dislocation slip on multiple glide planes is energetically coupled in the crystal energy.