A second order numerical scheme for the annealing of metal–intermetallic laminate composite: A ternary reaction system

Abstract

Metal–Intermetallic Laminate (MIL) composites are laminate structures that are fabricated by optimizing unique benefits of constituent components to have attractive physical and mechanical features, such as high strength, stiffness, and toughness. The synthesis of MIL composites involves annealing reaction of multiple metallic elements at high temperatures. In this work, we propose, analyze, and implement a second-order semi-implicit scheme for the annealing of a ternary metallic reaction system. The robustness of such a numerical scheme is demonstrated by various numerical experiments, as well as the expected accuracy tests. At the theoretical level, we provide a detailed convergence analysis, which confirms the second-order accuracy in both the temporal and spatial discretization. Moreover, this numerical scheme is used to study the annealing process of the Al–Fe–Ni ternary system. The computation reproduces the formation of the Al-rich and Ni-rich layers in the annealing process. We present the computational results as diffusion paths in a ternary phase diagram, with a nice agreement with that of experimental data. We also study the growth kinetics of the two layers by calculating the rate constant and kinetic exponent of the reaction. The morphology of interfaces between different layers is thoroughly investigated as well. The computational results indicate that the numerical scheme is an effective, useful tool for predicting the microstructure evolution in the annealing process of a ternary reaction system.