Phase-field simulations of nucleation, growth, and coarsening of $\beta_1$ precipitates in Mg-Nd alloys

TL;DR

This study develops a phase-field simulation workflow, using experimental data to accurately model the nucleation, growth, and coarsening of $eta_1$ precipitates in Mg-Nd alloys during aging, aiding in optimizing material properties.

Contribution

The paper introduces a method to parameterize phase-field models with experimental data for simulating precipitate evolution in magnesium alloys.

Findings

Successfully integrated experimental data into phase-field simulations.

Enabled quantitative predictions of precipitate nucleation and growth.

Provided a pathway to optimize aging processes for desired precipitate densities.

Abstract

The spatial distribution and morphology of precipitates formed during aging are key factors that determine the precipitation hardening response of various magnesium-rare earth alloys. In recent years, the use of high-performance computing clusters and massively parallel frameworks has enabled quantitative simulations of the evolution of individual and multiple precipitates at relevant length and time scales. However, predictive modeling of precipitate evolution remains challenging, in part because many key thermodynamic and kinetic parameters governing the underlying physics are either unknown or have a high degree of uncertainty. In this work, we developed a workflow in which experimental data were used to parameterize a phase-field model to perform two-dimensional (2D) simulations of concurrent nucleation and evolution of $\beta_1$ precipitates in magnesium-neodymium alloy during aging. Matrix composition and precipitate number density at different aging times were obtained from atom probe tomography and transmission electron microscopy measurements, respectively. We applied a stereological method to estimate the three-dimensional (3D) number densities from experimental cross-sectional transmission electron micrographs. The estimated 3D number density data were then converted to effective 2D number densities. The effective 2D number density and composition data were used to determine the required model parameters by minimizing the discrepancy between simulation and experimental results. The parameterized model allows for quantitative phase-field simulations of nucleation and growth of $\beta_1$ precipitates, which can be employed to optimize aging time to achieve a target number density of precipitates. This work highlights an approach to overcome the challenges associated with parameterizing a coupled phase-field and nucleation model.