Comparison of Two Bulk Energy Approaches for the Phasefield Modeling of Two-variant Martensitic Laminate Microstructure

Abstract

The unusual thermomechanical properties of shape memory alloys are closely connected to the formation and evolution of their microstructure. At lower temperatures, shape memory alloys typically consists of martensitic laminates with coherent twin boundaries. We propose a large strain phasefield model for the formation and dissipative evolution of such two-variant martensitic twinned laminate microstructures. Our model accounts for the coherence-dependence of the interface energy density and contains a Ginzburg-Landau type evolution equation. We introduce two conceptually different modeling approaches for the regularized bulk energy, i.e. external and internal mixing. We construct a suitable gradient-extended incremental variational framework for the proposed formulation and discretize it by use of finte elements. Finally, we demonstrate the modeling capabilities of our formulation by means of two-dimensional finite element simulations of laminate formation in two-phasic martensitic CuAlNi and compare the energetic modeling properties of the two proposed bulk energy approaches.