Simulation of martensitic phase transition progress with continuous and discontinuous displacements at the interface

The problem formulation for martensitic phase transition (PT) progress in elastoplastic materials at small strains, based on a recently proposed thermomechanical approach [V.I. Levitas, Mech. Res. Commun. 22 (1995) 87; V.I. Levitas, J. Phys. IV, Colloque C2, 5 (1995) 41.], is presented. Stress history dependence during the transformation process is a characteristic feature of the PT criterion. To define the PT progress a corresponding extremum principle for PT is used (without any kinetic equations). A relatively simple mechanical model for incoherence at interfaces is proposed. The problem of progress of PT in a cylindrical sample with a moving coherent and incoherent interface is analyzed by the finite element method (FEM) using a layer-by-layer progression technique. It is shown that the incoherent interface has low mobility or cannot move at all, which agrees with known experiments. Possible reasons of formation of discrete microstructure (discontinuously transformed subdomains) such as incoherence, perfect plasticity or plasticity with hardening are modeled and discussed. The elastic problem of progress of PT for the same cylindrical sample with coherent interface has also been solved using an element-by-element progression technique. It is shown that the shape variation of the transformed region during PT progress is insensitive to mesh refining.