Elasto-Plastic Micro-Macro Modelling of Solid-Solid Phase Transformation ; Application to Transformation Induced Plasticity

Abstract
Classical plasticity (dislocation motion) coupled to deformation due to lattice changes (phase transformation) occurs in several materials where interfaces are moving under external forces (TRIP (TRansformation Induced Plasticity) steels, even shape memory alloys). In the case of steels (transformation induced plasticity) the internal stress associated with the phase change induces a large additional plastic flow inside austenite and martensite. We propose a rnicromechanical modelling of such a phenomenon based on a decomposition of stswrain rate into an elastoplastic part and a given lattice inelastic strain rate field. Using usual Green functions method, a concentration tensor for the total strain rate field is obtained. The self consistent approximation allows to determine the behavior of the equivalent material and the equivalent transformation strain rate. Applications in the case of cooling under constant applied stresses and isothermal loading give results in good agreement with Finite Element calculations and theoretical results.