A discontinuous Galerkin model for precipitate nucleation and growth in aluminium alloy quench processes

This paper presents a finite element model for precipitate nucleation and growth during the quench phase of aluminium alloy manufacturing processes. A discontinuous Galerkin model for steady advection-diffusion problems predicts the thermal response in a continuous quench process. The thermal history drives a precipitate evolution model, based on a discrete representation of the particle size distribution in each local material neighborhood. This approach can require as many as 10⁵ degrees of freedom per spatial location. A second discontinuous Galerkin finite element procedure is presented to solve this seemingly massive problem. The new method scales linearly in both the number of elements and in the number of precipitate degrees of freedom per location. Thus, it is feasible to directly embed the discrete precipitate evolution model in a macroscopic process simulation. Numerical examples demonstrate the effectiveness of the quench model and the feasibility of obtaining materials with graded microstructures through precision control of conventional quench processes.