A level set approach to simulate grain growth with an evolving population of second phase particles

In numerous polycrystalline materials, grain size is controlled by second phase particles (SPPs) that hinder the grain boundaries (GBs) by pinning mechanisms. The Smith–Zener pinning (SZP) model describes the physical interaction between SPPs and GBs. Both of them can evolve when applying a heat treatment to the material. As industrial forging processes involve hot deformation steps near the solvus temperature, it is thus of prime importance to characterize the evolution of the SPPs due to their impact on the final microstructure, notably on the grain size. The level set (LS) method is classically used to describe the influence of SPPs on grain growth (GG) by considering the simulated particles as inert and represented by static holes in the used finite element (FE) mesh. A new formalism to model GG mechanism under the influence of the SZP phenomenon, able to take into account evolving particles is proposed. It involves the representation of SPPs by a LS function and a particular numerical treatment around the grain interfaces encountering SPP, making possible the modelling of SPPs evolution without altering the undergoing pinning pressure. Validation and comparison of the new method regarding previous FE-LS formulation in 2D and 3D simulations and an application on GG under the influence of dissolving particles are described.