The numerical resolution efficiency of phase-field models is limited by grid friction, grid anisotropy and pinning. The 1D sharp phase-field model eliminates grid friction and pinning by a global restoration of Translational Invariance (TI) in the discretized phase-field equation (Phys. Rev. Lett. 121, 025501, 2018). In 3D global TI restricts the beneficial modeling properties to a finite number of fixed interface orientations. We propose an accurate scheme to restore TI locally in the local interface normal direction. At one-grid-point interface resolutions, the new model captures the formation of isotropic seaweed structures without spurious dendritic selection by grid anisotropy.
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively parallel computer architectures such as Graphic Processing Units. However, one known drawback of this method is that the discretization of differential terms involving spatial derivatives introduces a spurious lattice anisotropy that can influence the solid-liquid interface dynamics. We find that this influence is significant for the case of polycrystalline …
The near-rapid solidification conditions during additive manufacturing can lead to selection of non-equilibrium phases. Sharp interface models via interface response functions have been used earlier to explain the microstructure selection under such solidification conditions. However, most of the sharp interface models assume linear superposition of contributions of alloying elements without considering the non-linearity associated with the phase diagram. In this report, both planar and dendritic Calphad coupled sharp interface models have been implemented and used to explain the growth-contro…
Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp interface behavior of a binary alloy phase field model onto the CGM kinetics of Aziz et al. [1], with a controllable partition coefficient k(V ). We demonstrate the parameterizations that allow the phase field model to map onto the corresponding CGM or classical sharp interface models. We also demonstrate that the mapping is convergent for different interface …
We use three-dimensional phase-field simulations to investigate the dynamics of the two-phase composite patterns formed upon during solidification of eutectic alloys. Besides the spatially periodic lamellar and rod patterns that have been widely studied, we find that there is a large number of additional steady-state patterns which exhibit stable defects. The defect density can be so high that the pattern is completely disordered, and that the distinction between lamellar and rod patterns is blurred. As a consequence, the transition from lamellae to rods is not sharp, but extends over a finite…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which…
Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption, and includes non-equilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability which, interfering with the Mullins-Sekerka instability, is similar to that, found by Cahn in grain-boundary motion.
我们扩展了相场方法来模拟多面材料的凝固。我们的方法包括使用一个近似的伽玛图与圆形的尖点，可以任意接近真正的伽玛图与尖锐的尖点，对应于多面的方向。相场方程在薄界面极限下求解，并在固液界面处达到局部平衡[A。卡玛和W J. Rappel，Phys.Rev.E53，R3017（1996）]。我们的方法的收敛性首先证明了平衡形状。然后研究了过冷熔体中多面针状晶体的生长，作为过冷度和尖点振幅δ的函数，γ图的形式为1+ δ（|sin（θ）|+|cos（θ）|).相场结果与实验观察到的标度定律“λ与V的平方根成反比”一致，其中λ是小面长度，V是生长速率。此外，V和λ与三角洲的变化被发现是合理的预测由近似尖锐的界面分析理论，包括毛细管效应，并假设圆形和抛物线的形式，针晶体的前部和尾部粗糙的部分，分别。
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface moves relative to the grid. For this problem, a new simulation method is developed that manifestly conserves mass, and that simulates the motion of the interface to second order in the grid size. When applied to an isothermal simulation of solidification from solution in 1D at 50% supersaturation for only 5 grid points, the motion of the interface is accura…
Operando study of the evolution of peritectic structures in metal solidification by quasi-simultaneous synchrotron X-ray diffraction and tomography
University of Hull（赫尔大学）；Westlake University（西湖大学）；Diamond Light Source Ltd.（钻石光源有限公司）；Research Complex at Harwell（哈韦尔研究综合体）；Kunming University of Science and Technology（昆明理工大学）
Instability of a binary eutectic solidification front to morphological perturbations due to rejection of a ternary impurity leads to the formation of eutectic colonies. Whereas, the instability dynamics and the resultant mi- crostructural features are reasonably well understood for isotropic systems, several experimental observations point to the existence of colonies in systems with anisotropic interfaces. In this study, we extend the un- derstanding of eutectic colonies to anisotropic systems, where only certain orientations of the solid-liquid or solid-solid interfaces are thermodynamically…
