Energetic upscaling strategy for grain growth. i: Fast mesoscopic model based on dissipation

Abstract Tailoring microstructures by optimizing fabrication or forming processes is a challenge for metal industries. However, predicting microstructure evolution implies to develop models at the scale of the polycrystal, which is incompatible with large scale simulations of processes. In this context, we propose an energetic upscaling strategy to model anisotropic grain growth at large scale without loosing detailed grains statistics. Thus, a fast mesoscopic model is necessary to establish a large database of computations in order to develop a macroscopic model whose state variables contain statistical descriptors of the microstructure. This paper focuses on a fast mesoscopic model based on Voronoi-Laguerre tessellations, which are updated at each time step to capture grain growth. Several energetic contributions are considered at different scales. The grain boundary energy is obtained as a function of misorientation from molecular dynamics, and the dissipated power is obtained from crystal plasticity theory. The evolution law at the mesoscopic scale is obtained by considering all energetic contributions in the representative volume element, and from thermodynamic laws and approximate mass conservation. This upscaling approach reaches short computation time, which is essential to establish the database underlying the macroscopic model. Basic grain statistics are validated by comparison to classical models. Moreover, a good agreement is observed with an experiment conducted on pure iron. The model is then used to analyze the evolution of detailed statistics. To capture grain growth at macroscopic scale, it is necessary to consider couplings between means and standard deviations of various distributions (e.g., size, shape, misorientation etc.)