Sensitivity analysis of a phase field model for static recrystallization of deformed microstructures

Abstract

Static recrystallization is a process whereby dislocation-free grains are nucleated in a deformed microstructure, and then newly recrystallized grains grow and consume the previously existing grains. This paper describes a phase field model for static recrystallization, along with details of the implementation and simulation results. Recrystallized grains are seeded utilizing a probabilitybased method, including a hold time to allow the order parameters to adjust to seeded grains. The nominal simulation time is corrected to account for the nuclei hold and for the time required for a nucleus to grow from its critical size to the seeded size. Microstructural evolution was simulated for two-and three-dimensional systems, and the fraction recrystallized was quantified via Avrami kinetics. The resulting Avrami time exponents were in agreement with the expected values for sitesaturated nucleation. The variability in the Avrami parameters was quantified by simulating the recrystallization of the same underlying polycrystalline microstructure but using different seed locations. Additional simulations were performed to determine the influence of the deformed microstructure on recrystallization, specifically investigating the effects of the spatial distribution of the initial dislocation density within the microstructure as well as the morphologies of the polycrystalline microstructure. For the significantly deformed polycrystalline microstructures examined in this work, it is shown that microstructural evolution is primarily driven by stored energy in dislocations rather than grain boundary energy.

Microstructure evolution in 439 stainless steels under tensile: phase field simulation and experiment

“…Based on Hillert predictions in a 3D model [43], in this system, α = 1, ρ = 9/8. It is revealed by equation (21), that small grains are expected to shrink at a higher rate. Nevertheless, with increasing grain size, the grain growth rate increases as the grain size exceeds the critical size.…”

“…The successful application of phase field models in simulating microstructure evolution has been thoroughly demonstrated [20][21][22][23]. Ideal grain growth can be captured by phase field models [24][25][26], also some computational studies on the effect of an external load on grain growth and texture evolution have been conducted [14,27].…”

Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density

“…This formula is identical to those used in [16,25,37,46], except that in these previous works, ρ i was a constant associated with the i th grain, and therefore these models could not treat intra-granular inhomogeneity nor a decay in the dislocation density as the grain boundaries migrate.…”

“…To work in concert with the experimental characterization tools to provide an in-depth understanding of how the combined effects of grain boundary energy and the stored energy impact the microstructure evolution within a sample undergoing CHT, a computational model that considers both driving forces is necessary. Phase-field (PF) models are commonly utilized to simulate microstructure evolution [18][19][20], such as solidification [21][22][23][24], recrystallization [25,26], and chemical reaction [27][28][29]. In a PF model, the thermodynamics for the material system being modeled is incorporated into the free energy functional that is used to compute the driving force for evolution, and the microstructure is described by field variables (often referred to as order parameters) that can be conserved or non-conserved over the domain.…”

“…A few PF models have been developed to study the influence of anisotropy in grain boundary energy [33], anisotropy in grain boundary mobility [34,35], and second-phase particles [36] on the dynamics of AGG. Higgins et al presented a PF model [16] that extended recrystallization models developed by Moelans et al [37] and Gentry and Thornton [25] to account for the contribution of stored energy as the driving force for grain boundary migration. Their simulations showed that the additional driving force allows for the grains with a low dislocation density to consume the grains with a high dislocation density.…”