A new level set - finite element formulation for anisotropic grain growth

International audienceGrain growth in metallic materials is often detrimental to the desired properties of finished components. As such, predicting the evolution of amicrostructure undergoing grain growth under specic conditions of temperature and stress is crucial to controlling the microstructure, andtherefore the properties, of formed metal parts.Even so, a grain boundary is a complex 5 dimensional object [1] that evolves in order to minimize thermodynamic potentials [2] and whosemovement is thermally activated. The intrinsic properties of these boundaries vary based on crystallographic variables, the misorientation M, aswell as topological ones, the normal to the grain boundary n, which vary in space. This means that quantities commonly associated to grainboundaries such as grain boundary energy, , or mobility, m, are not constants for a given material at a given temperature, but functions of thegrain boundary character B = (M, n). Models for driving forces do exist for normal dependent grain boundary energies (n) [2]. However, thedependence of the grain boundary energy to crystallographic variables (M), and more notably the gradients of this component of the energy,is not clearly formulated in the classical models for grain growth.This work aims to formulate, develop and implement a grain growth simulation framework that can take into account aspects of the gradient ofanisotropy of grain boundary energy using a level-set (LS) description of the microstructure and a finite element (FE) resolution of the physicalproblem. This framework is tested for high ratios of anisotropies, with the max-min ratio of energy values of the order of ten (the order of a twinboundary with respect to a general grain boundary). The behavior of anisotropic systems in this new formulation is different and closer toanalytical values as compared with anisotropic systems in the classical formulation of the problem. The new formulation is able to predict theequilibrium angles of triple junctions associated with the energies of the boundaries that meet at the triple point. In polycrystal simulations, theresults in terms of microstructural evolutions and their kinetics follow new tendencies as compared with results from classical formulations