A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—I. Derivation of general relations

Empirical models have been proposed for the anomalous plastic behaviour of steels during phase transformations; they distinguish between classical plasticity (response of the material to variations of the stresses or the temperature) and transformation plasticity (response of the material to variations of the proportion of the phases). This paper uses the Hill-Mandel homogenization method to provide theoretical foundations for such models. Without postulating arbitrarily the existence of an extra plastic strain of a new unknown type on a microscopic scale, it is shown that the distinction between (macroscopic) classical and transformation plasticity is a consequence of the homogenization process; furthermore the transformation plastic strain rate decomposes naturally into two terms which can be interpreted as corresponding to the well-known Greenwood-Johnson and Magee mechanisms. An interesting property of dilatometric diagrams is also proved in the course of the treatment.