Numerical modelling of transformation-induced damage and plasticity in metals

In multiphase carbon steels, irreversible martensitic transformations from a parent austenitic phase are often accompanied by plastic deformations in the surrounding phases and damage growth in the martensitic product phase. In the present communication the interactions between these complex processes are studied through three-dimensional numerical analyses, where the response of the austenitic phase is simulated using a phase-changing damage model and the response of the surrounding matrix is mimicked with a plasticity model. A numerical update algorithm is provided for the phase-changing damage model, which is based on a fully implicit backward Euler scheme formulated within the framework of finite deformations. The consistent tangent operator for the model is computed using a numerical differentiation technique. Special attention is given to the robust and accurate treatment of the various constraints related to the volume fractions and damaged volume fractions of the transformation parent and product phases. The numerical analyses of a multiphase carbon steel microstructure illustrate the effect of the transformation, plasticity and damage processes on the overall stress-strain response and on the transformation and damage evolutions of the sample for various austenite crystal orientations. The computed responses are in qualitative agreement with experimental results reported in the literature. In terms of the numerical model, a variation study of the mesh density shows that the numerical results tend to converge upon mesh refinement.