Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases

Transformation plasticity in steels (i.e., the anomalous plastic flow observed during the progress of a phase transformation) is usually attributed to two distinct physical mechanisms, which have been proposed by Greenwood and Johnson and Magee. This paper proposes a theoretical approach to the problem, in the case where the Magee mechanism is negligible and the phases are ideal-plastic. An explicit expression for the transformation plastic strain rate is obtained for a steel undergoing a transformation under a small applied stress; this expression is consistent with experiments conducted on various materials. A finite element simulation provides a confirmation of the theoretical formula and allows for a detailed examination of the validity of some physical hypotheses made in the treatment. It also allows for a study of transformation plasticity under high applied stresses. Based on these results, a general (i.e., applicable for all kinds of stresses applied) model is proposed in the case of ideal-plastic phases.