High-Precision Numerical Simulation Study of the Aging Precipitation Behavior in Al-Li Alloys Based on Improved Kampmann-Wagner Numerical (KWN) Model

The mechanical properties of alloys are closely related to the precipitation behavior of precipitated particles. Accurate calculation of the average radius and size distribution of the precipitated particles is essential for establishing the optimal heat treatment process and for monitoring the mechanical properties of the alloy. The traditional KWN model is solved using a first-order upwind scheme, which can lead to spurious diffusion during the calculation process, resulting in an overestimation of the calculated particle size distribution range. The improved KWN model addresses this issue by introducing a size distribution function, which transforms the basic variables of the control equations from extensive to intensive quantities. This modification converts the control equations into a hyperbolic equation with a source term, thereby enabling high-precision solutions for the KWN model. Based on these numerical models, the precipitation behavior of nearly spherical Al3Li precipitates in Al-7at.%Li alloy during aging at 190 degrees C is numerically simulated. It is found that the results obtained from the high-resolution model constructed with the Van Leer limiter are in excellent agreement with the experimental data. This model uses an upwind scheme at discontinuities to prevent numerical oscillations and employs the Lax-Wendroff scheme in smooth regions to enhance calculation accuracy, significantly improving the calculation accuracy of the average radius and size distribution (PSD) of the precipitates. The application of a high-resolution model to fit the experimental data results in an interfacial energy for the Al/Al3Li interface of 84 +/- 8mJ/m2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$84 \pm 8\;{\text{mJ}}/{\text{m}}<^>{2}$$\end{document}. Furthermore, this model has been employed to predict the PSD curves of the alloy under extended aging times, thereby providing critical scientific evidence and guidance for the formulation of the alloy's heat treatment process.