Sobolev Sergey L, Tokmachev Mikhail G, Kolobov Yuri R
Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry, Russian Academy of Sciences, 142432 Chernogolovka, Russia.
Department of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, National Research University "Higher School of Economics", 123458 Moscow, Russia.
Materials (Basel). 2023 Feb 15;16(4):1622. doi: 10.3390/ma16041622.
Motivated by the fast development of various additive manufacturing technologies, we consider a mathematical model of re-solidification of multicomponent metal alloys, which takes place after ultrashort (femtosecond) pulse laser melting of a metal surface. The re-solidification occurs under highly nonequilibrium conditions when solutes diffusion in the bulk liquid cannot be described by the classical diffusion equation of parabolic type (Fick law) but is governed by diffusion equation of hyperbolic type. In addition, the model takes into account diffusive interaction between different solutes (nonzero off-diagonal terms of the diffusion matrix). Numerical simulations demonstrate that there are three main re-solidification regimes, namely, purely diffusion-controlled with solute partition at the interface, partly diffusion-controlled with weak partition, and purely diffusionless and partitionless. The type of the regime governs the final composition of the re-solidified material, and, hence, may serve as one of the main tools to design materials with desirable properties. This implies that the model is expected to be useful in evaluating the most effective re-solidification regime to guide the optimization of additive manufacturing processing parameters and alloys design.
受各种增材制造技术快速发展的推动，我们考虑一种多组分金属合金再凝固的数学模型，这种再凝固发生在金属表面的超短（飞秒）脉冲激光熔化之后。再凝固发生在高度非平衡条件下，此时溶质在本体液体中的扩散不能用经典的抛物型扩散方程（菲克定律）来描述，而是由双曲型扩散方程控制。此外，该模型考虑了不同溶质之间的扩散相互作用（扩散矩阵的非零非对角项）。数值模拟表明，存在三种主要的再凝固模式，即界面处有溶质分配的纯扩散控制模式、溶质分配较弱的部分扩散控制模式以及完全无扩散和无分配模式。模式的类型决定了再凝固材料的最终成分，因此，可作为设计具有理想性能材料的主要工具之一。这意味着该模型有望用于评估最有效的再凝固模式，以指导增材制造工艺参数的优化和合金设计。
