Couplage entre champ de phases et plasticité cristalline continue – COUPHIN

Mechanical properties of metallic materials are strongly dependent on their microstructure, i.e. on the shape and spatial arrangement of the different phases in the materials. It is thus important, from both fundamental and industrial viewpoints, to understand and control the microstructure evolution. The phase field method as emerged as the most powerful method for tackling microstructure evolutions during phase transformations, especially when elastic coherency stresses are generated in solids. However, in many materials, the microstructure evolutions are coupled with a plastic activity, and there is presently no satisfactory extension of the phase field method taking this coupling into account. The general aim of the project is to fill this gap by coupling a phase field model with a model of continuum plasticity. It must be stressed that applying continuum plasticity at the scale of the microstructure will lead to meaningful results only if crystal anisotropy as well as size effects are included in the plasticity model. Therefore, a state-of-the-art continuum plasticity model is needed, where internal lengths associated to dislocations in crystalline materials are incorporated (e.g. Cosserat or strain gradient formulations). This goal will be achieved by associating three partners having strong expertise in both phase field models and generalized continuum mechanics. The model will be built step by step by increasing the complexity of the plasticity models to be incorporated within the phase field approach, following a consistent thermodynamic framework. Two different numerical methods will be used for implementing the model, and their efficiencies will be compared on benchmark cases carefully defined. As well, an asymptotic analysis of the model will be performed to relate the parameters of the diffuse interface model to physical parameters entering sharp interface models. Finally, the model will be applied on two metallic alloys undergoing phase changes associated with plasticity: nickel base superalloys and steels. (i) Nickel base superalloys used in the disks and turbine blades of the turboreactors reach amazing mechanical properties at high temperature due their microstructure which consists in a the regular arrangement of cuboidal precipitates inside a matrix. In service, aging of the microstructure leads to a rafting of the precipitates and ultimately to a topological inversion. During this project, this complex microstructural evolution, which leads to a drastic decrease of the mechanical properties, will be characterized using a dedicated phase field model. (ii) Controlling the appearance of Widmanstätten ferrite is often of crucial importance for improving toughness in low-alloy steels. But the growth mechanisms of this morphology is still harshly discussed although it has been studied for a long time. No firm conclusion has been drawn, partly because the relaxation of coherency stresses involve a complex coupling between morphological evolutions and plasticity. This coupling will be thoroughly investigated thanks to the model developed during the project. This project, at the edge of the phase field approach at the mesoscale, will open large possibilities in the field of materials science and engineering in the near future, for dealing with phase transformations at solid-state in crystalline materials.