A discrete model was developed for analyzing the interaction between plastic flow and martensitic phase transformation. The model was intended to simulate microstructure evolution in a single crystal of austenite that transformed non-homogeneously into martensite. Plastic flow in the untransformed austenite was simulated by using a plane-strain discrete dislocation model. The phase transformation was modelled by the nucleation and growth of discrete martensitic regions, embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plastic transformation problem was solved by using the superposition of analytical solutions for 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 by additional evolution rules which accounted for the phase transformation. In order to illustrate the basic features of the model, simulations were made of specimens under plane-strain uniaxial extension and contraction. The simulations indicated that plastic flow reduced the average stress at which transformation began, but it also reduced the transformation rate when compared with control simulations without plasticity. Due to local stress fluctuations caused by dislocations, martensitic systems could be activated even though transformation did not appear to be favorable: based upon the average stress. On the other hand, the simulations indicated that the plastic hardening behaviour was influenced by a reduction in the effective austenitic grain size due to 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 information was relevant for the development of meso- and macroscopic elasto-plastic 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