The aim of this work is to model the strong coupling between mechanical loading, thermal loading paths and microstructure under anisothermal conditions for multiphase multi-component alloys accounting for elasto-viscoplastic behaviour. It has been observed that the phase transformation in this type of material under thermo-mechanical loading is not only due to the diffusion process [1]. Phase field analysis is used here to model the mechanical coupling of diffusion and phase transformation. An illustration of a simulation of the dissolution of a precipitate in a matrix under plastic shear is given in figure 1 [2]. Through this example, it is shown that the phase field method is promising to account for both the morphology and the kinetics of phase transformation.

An example of the coupling of diffusion, phase transformation and mechanics that has been observed experimentally is the rafting observed in the single-crystal nickel  (γ/γ') superalloy. At high temperature and under mechanical loading, the precipitates coalesce in an anisotropic manner to form a lamellar structure of rafts in {100} type cubic planes. To model this case, a binary Ni-Al system within a two phases γ (Ni) and γ' (Ni 3 Al) is considered. Different types of loading were simulated such as relaxation, creep, fatigue and fatigue-creep in order to study the effect of coupling between diffusion, phase transformation and viscoplasticity on the morphology of the phases, on their volume fraction and on the transformation kinetics. An illustration of a simulation of the rafting of γ' (Ni 3 Al) precipitates in the γ (Ni) matrix is given in figures 2. The creep test was simulated at temperature T=950°C with an applied stress σ = 240 MPa along axis 1. The initial microstructure is composed of γ' (Ni 3 Al) cubic precipitates in the γ (Ni) matrix [3]. Periodic boundary conditions are applied to the edges.

The phase field method was used to model the rafting process, taking into account strong couping between mechanical loading, phase transformation and diffusion of chemical species. Using this modelling, an attempt of simulating fatigue and fatigue-creep tests will be presented. In addition, the change of phase morphology due to different types of applied loading was simulated. Those changes affects the mechanical properties of the material.

References
[1] An, T. F., et al. "Effect of the θ–α-Al2O3 transformation in scales on the oxidation behavior of a nickel-base superalloy with an aluminide diffusion coating." Oxidation of Metals 54.3-4 (2000): 301-316.
[2] Kais Ammar; Benoît Appolaire; Samuel Forest. Splitting of dissolving precipitates during plastic shear: A phase field study. Comptes Rendus. Physique, (2021), pp. 1-18.
[3] Cottura, M., Le Bouar, Y., Finel, A., Appolaire, B., Ammar, K., & Forest, S. (2012). A phase field model incorporating strain gradient viscoplasticity: application to rafting in Ni-base superalloys. Journal of the Mechanics and Physics of Solids, 60(7), 1243-1256.