Transformation plasticity has been intensively studied because of its significant impact on various industrial fabrication and forming processes. The widely used analytical macroscopic models are based on idealized microstructures and strong assumptions. Such models predict linear (or weakly non-linear) dependence between the transformation plastic strain rate and the applied load, whereas experimental evidence shows that this dependence becomes highly non-linear when the applied stress becomes non-negligible with respect to the macroscopic yield stress. Such a non-linear response is not fully understood especially for phase transformations arising at high temperatures for which the product phase is often softer than the parent phase, and involving visco-plastic behavior.

Therefore to overcome this difficulty, the first key contribution of this paper is to exhibit the detailed mechanisms leading to transformation plasticity in steels undergoing austenite to ferrite phase transformation at high temperature and to explain the non-linear dependence between the transformation plastic strain and the applied load. To do so, full-field simulations of visco-plastic polycrystalline aggregates undergoing phase transformations under applied load are performed. In addition, the second key contribution consists in upscaling the outcomes obtained at the scale of the polycrystal into a macroscopic statistical model, that can be used for large simulations of industrial processes. To do so, a database of computations with various initial microstructures, grain shape distributions, and applied loads have been performed, and used to derive the macroscopic statistical model. Of course, to create such a database, a relatively short computation time should be obtained for the full-field simulations, which is achieved by using a fast Fourier transform-based algorithm.