A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations was developed. The model was intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite was simulated using a plane-strain discrete dislocation model. The phase transformation was modelled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto transformation problem was solved by using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions were specified. The constitutive rules used in discrete dislocation simulations were supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction were analyzed. The simulations indicated that plastic flow reduced the average stress at which transformation began, but it also reduced the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems could be activated even though transformation would not appear to be favorable, based upon the average stress. Conversely, the simulations indicated that the plastic hardening behavior was influenced by the reduction in the effective austenitic grain size due to the evolution of the transformation. During cyclic simulations, the coupled plasticity-transformation model predicted plastic deformations during unloading, with a significant increase in dislocation density. This was expected to be relevant to the development of meso- and macroscopic elasto-plasto-transformation models.

A Discrete Dislocation–Transformation Model for Austenitic Single Crystals. J.Shi, S.Turteltaub, E.Van der Giessen, J.J.C.Remmers: Modelling and Simulation in Materials Science and Engineering, 2008, 16[5], 055005 (26pp)