Understanding the kinetics of static recrystallization in Mg-Zn-Ca alloys using an integrated PRISMS simulation framework

Recrystallization is a phenomenon in which a plastically deformed polycrystalline microstructure with a high dislocation density transforms into another that has low dislocation density. This evolution is driven by the stored energy in dislocations, rather than grain growth driven by grain boundary energy alone. One difficulty in quantitative modeling of recrystallization is the uncertainty in material parameters, which can be addressed by integration of experimental data into simulations. In this work, we compare simulated static recrystallization dynamics of a Mg-3Zn-0.1Ca wt.% alloy to experiments involving thermomechanical processing followed by measurements of the recrystallization fraction over time. The simulations are performed by combining PRISMS software for crystal plasticity and phase-field models (PRISMS-Plasticity and PRISMS-PF, respectively) in an integrated computational materials engineering framework. At 20% strain and annealing at 350 °C, the model accurately describes recrystallization dynamics up to a mobility-dependent time scale factor. While the average grain boundary mobility and the fraction of plastic work converted into stored energy are not precisely known, by fitting simulations to experimental data, we show that the average grain boundary mobility can be determined if the fraction of plastic work converted to stored energy is known, or vice versa. For low annealing temperatures, we observe a discrepancy between the model and experiments in the late stages of recrystallization, where a slowdown in recrystallization kinetics occurs in the experiments. We discuss possible sources of this slowdown and propose additional physical mechanisms that need to be accounted for in the model to improve its predictions.

💡 Research Summary

This paper presents an integrated computational framework that couples crystal plasticity finite element (CPFE) simulations with phase‑field (PF) modeling to predict the static recrystallization kinetics of a Mg‑3Zn‑0.1Ca (wt %) alloy, referred to as ZX30. The authors first experimentally characterize the microstructure evolution of ZX30 after various thermomechanical treatments: plane‑strain compression to true strains of 5 %, 10 % and 20 % at 200 °C, followed by isothermal annealing at 250 °C, 300 °C and 350 °C for different hold times. Recrystallized fractions are quantified using electron backscatter diffraction (EBSD) grain‑orientation‑spread (GOS) maps, where grains with GOS < 1° are considered recrystallized.

The computational side uses the open‑source PRISMS‑Plasticity code to simulate the deformation step. The deformation gradient is multiplicatively decomposed into elastic and plastic parts, and a set of basal slip, prismatic slip and tensile twin systems is modeled as pseudo‑slip mechanisms. A power‑law shear rate relation with a stress exponent and a hardening matrix governs slip resistance evolution. Plastic work (Wₚ) is computed from the stress‑power integral, and a fraction β (typically 1–15 %) of this work is assumed to be stored as dislocation energy (Eₛ = β Wₚ). The spatial distribution of Eₛ obtained from CPFE serves as the driving‑force field for the subsequent PF simulation.

The PF model, implemented in PRISMS‑PF, represents each grain by an order parameter ηᵢ. The free‑energy functional includes interfacial energy and a bulk term proportional to the local stored‑energy difference ΔEₛ between parent and recrystallized grains. Grain‑boundary migration is driven solely by ΔEₛ (curvature contributions are neglected because stored‑energy driving forces dominate at the high strains studied). The migration velocity is expressed as v = M ΔEₛ, where M is the average grain‑boundary mobility. Recrystallization nuclei are introduced at a density measured experimentally, and the evolution of the recrystallized volume fraction X(t) is extracted from the PF fields.

A key result is that, for the high‑temperature case (350 °C, 20 % strain), the simulated X(t) curves match the experimental data when a time‑scale factor τ = t · (M_ref/M) · (β/β_ref) is applied. This demonstrates that, under conditions where stored‑energy driving forces far exceed capillarity, the recrystallization kinetics are controlled by the product of average boundary mobility and the stored‑energy conversion fraction. Consequently, if β can be measured independently (e.g., by calorimetry or in‑situ diffraction), the average mobility M can be extracted from the scaling factor, and vice‑versa.

At lower annealing temperatures (≤300 °C), the experiments show a pronounced slowdown of recrystallization in the later stages, which the current model fails to capture. The authors attribute this discrepancy to several physical mechanisms that are not included in the present PF formulation: (1) solute drag caused by Zn and Ca segregation to grain boundaries, which reduces mobility; (2) shear‑coupled grain‑boundary migration, where boundary motion is coupled to tangential lattice shear and becomes strongly temperature‑dependent; (3) anisotropy of both grain‑boundary energy and mobility with respect to misorientation and boundary plane, leading to a distribution of local migration rates that cannot be represented by a single average M; and (4) temperature‑dependent nucleation rates, where fewer new recrystallized grains form at lower temperatures, limiting overall growth.

The paper further discusses how the inverse problem—determining β from a known M or M from a known β—can be solved analytically using the derived relationships between the JMAK‑type time constant, stored‑energy driving force, and boundary mobility. This provides a practical route to calibrate the most uncertain parameter in recrystallization modeling.

Finally, the authors outline future work: incorporating atomistic calculations (e.g., molecular dynamics or density‑functional theory) to obtain orientation‑dependent mobility and energy data; adding a solute‑drag term to the PF free energy; implementing a shear‑coupled migration law; and validating the extended model with real‑time X‑ray tomography of grain‑boundary motion. Such enhancements would improve predictions for low‑temperature annealing and broaden the applicability of the framework to other low‑cost Mg alloys.

In conclusion, the study demonstrates that an integrated PRISMS‑based CPFE‑PF workflow can quantitatively reproduce static recrystallization kinetics of Mg‑Zn‑Ca alloys at high temperatures, while also highlighting the need for additional physics to capture low‑temperature behavior. The methodology offers a pathway to extract otherwise inaccessible material parameters (boundary mobility, stored‑energy conversion efficiency) from combined simulation‑experiment datasets, thereby advancing the predictive capability of recrystallization modeling for lightweight structural alloys.