Phase Transformation Kinetics Model for Metals

TL;DR

The paper develops a phase-field-based kinetics model for solid-solid metal transformations by extending the Levitas-Preston framework to arbitrary pressure, enabling calculation of interface speeds, critical nuclei energies, and nucleation rates for homogeneous, grain-site, and dislocation-mediated pathways. It combines a quartic Gibbs free energy in an order parameter with TDGL dynamics and KJMA theory to predict the time evolution of phase volume fractions under ramp loading, demonstrated on the $\alpha$-Fe$\rightarrow$ $\epsilon$-Fe transition. Key contributions include explicit expressions for A–M interface speeds, 1D and 3D nuclei energies and widths, site-specific nucleation rates, and a quantitative assessment of microstructure sensitivity (grain size, dislocation density) on transformation kinetics. The results underscore the substantial influence of microstructure on phase transformation timing and overshoot pressures, and highlight the need for detailed microstructural characterization to improve predictive capability in metallic systems under high-rate loading.

Abstract

We develop a new model for phase transformation kinetics in metals by generalizing the Levitas-Preston (LP) phase field model of martensite phase transformations (see Levitas and Preston (2002a,b); Levitas, Preston and Lee (2003)) to arbitrary pressure. Furthermore, we account for and track: the interface speed of the pressure driven phase transformation, properties of critical nuclei, as well as nucleation at grain sites and on dislocations and homogeneous nucleation. The volume fraction evolution of each phase is described by employing KJMA (Kolmogorov, 1937; Johnson and Mehl, 1939; Avrami, 1939, 1940, 1941) kinetic theory. We then test our new model for iron under ramp loading conditions and compare our predictions for the $α\toε$ iron phase transition to experimental data of Smith et al. (2013). More than one combination of material and model parameters (such as dislocation density and interface speed) led to good agreement of our simulations to the experimental data, thus highlighting the importance of having accurate characterization data for the microstructure of the sample under consideration.

Figures (7)

• Figure 1: Coexistence curve and spinodals. Parameters $\Delta T$ and $\xi$ can be estimated using Eq. \ref{['eq:G12']} and $x$ is defined in Eq. \ref{['eq:G18']}.
• Figure 2: We show the widths of martensitic (left) and austenitic (right) critical nuclei as functions of $x$ for different values of parameter $\xi$. Values $x=-1$ (left) and $x=1$ (right) correspond to the A$\to$M and M$\to$A spinodals, respectively.
• Figure 3: We show the martensitic (left) and austenitic (right) critical nuclei energies as functions of $x$ for different values of parameter $\xi$.
• Figure 4: We present $r_\text{max}/r_0$ and $\varepsilon_c^\text{dis}/\varepsilon_c^\text{hom}$ versus $\alpha$, as well as values of our fit $f^\text{dis}(\alpha)$ and the corresponding errors.
• Figure 5: We show the $\epsilon$ Fe volume fraction versus ramp pressure for constant loading rates of 1, 10, 100, and 1000 GPa/$\mu$s at 300K. The left pane includes only homogeneous nucleation whereas the right pane includes the additional effects of nucleation on dislocations (with dislocation density 10$^{12}$m$^{-2}$) and nucleation on grain boundaries with average grain diameters of $D=100\mu$m and grain boundary thicknesses $\delta$ of 0.1nm. Clearly, the epsilon volume fraction rapidly increases to unity at pressures $\sim$13--16 GPa for the chosen loading rates.