Analysis of a phase-field finite element implementation for precipitation

Precipitation hardening is an essential mechanism in materials design of age-hardenable aluminium alloys. The occurrence and distribution of nano-sized particles in such alloys can lead to superior material properties. During thermo-mechanical processing, these particles evolve dynamically as function of temperature and applied load. Therefore, sophisticated modelling frameworks are required to study the underlying phenomena of this microstructural evolution in depth. Phase-field method based on the diffuse interface approach has been successfully employed in literature to study particle nucleation and growth, as well as equilibrium particle shapes. Although phase-field models provide reliable results due to the flexible adaption of the free energy, the method is computationally expensive, requiring efficient solution schemes. The finite-element discretization in deal.II can overcome scalability disadvantages and can outperform standard finite-difference codes. In this work, we used adaptive mesh refinement and adaptive time-stepping and investigate how AMR and the use of the same stiffness matrix for a certain amount of time steps affect the performance of the phase-field model. Particle growth simulations are performed to outline the major benefits of the finite element phase-field model. The numerical strategy is shown to be effective regardless of the initial particle shape by considering different particle morphologies. The results illustrate a significant increase in simulation performance with the applied numerical techniques.