The solid-solid phase transformation is a widely studied phenomenon in Solid Mechanics. It is observed especially during welding or thermomechanical treatment of steels (austenite-martensite transition). It also helps to explain the unusual behavior of Shape Memory Materials, the formation of inclusions in heterogeneous materials, or damage the fragile part. The group Materials and Structures, we develop models of phase transformation in which phases can coexist within a material element, i.e., they are intimately mixed at the macroscopic scale. Each phase is represented by a volume ratio and a local deformation, the local deformation is related to the overall deformation by mixing law. Our models fit into the general framework of standard materials with internal connections; the constitutive laws are written using two potentials: the free energy potential for reversible aspects and dissipation potential for the dissipative aspects. The studied phase change can be reversible or irreversible. In the reversible case, we obtain a model of nonlinear elasticity, where the elastic energy is implicitly built by convexification of the energies of the individual phases. The irreversible case is obtained by introducing a proper pseudo-potential of dissipation. This model is implemented in two different contexts, namely the modeling of thermomechanical behavior of Shape Memory Materials as well as the simulation of welding processes. In the latter case, our model can describe both the microstructural changes and their effects on the thermomechanical behavior of steel. It integrates all the thermal, mechanical and metallurgical phenomena, and their interactions. This work not only allows accurate modeling the behaviors of multiphase steel but also analyzes the influence of different physical mechanisms (viscosity, transformation plasticity, etc.) on the behavior of steel. In addition, the approach takes into account the case where the phases have different behaviors: for example, the austenite phase (present at high temperature) has a viscoelastic behavior and martensite phase (present at low temperature) is elastoplastic. Algorithms of original calculations are developed and programmed in codes of finite elements.
Proportion of phases in a thermally affected zone during welding arc: comparison between the theoretical calculation and the experimental observation.