Development of a unified chain of phase field theories for multi--scale modelling of solidification microstructure evolution

大多数材料的性能是由它们的微观结构决定的，其中很大一部分是在凝固过程中形成的。由于涉及多个长度尺度，从界面动力学和原子尺度上的固态缺陷到在中尺度上设置微观结构模式尺度的扩散过程，因此建模凝固是具有挑战性的。随着快速冷却技术（如3D打印和激光焊接）的出现，人们越来越有兴趣了解快速凝固过程中微毫秒级的微观结构演变过程。在这里，强烈的非平衡效应导致了亚稳定相、热应变和塑性变形、密度非均匀性和相边界附近空洞的形成。目前还没有一致的建模平台来研究这些固有的多尺度现象。本研究的愿景是发展多尺度链一致连接的理论，以捕获在凝固过程中出现的奇异微观结构现象。这个建模链的开发将分两个阶段进行。第一阶段将以基于多点相关函数的一元和二元材料的经典密度泛函理论现象学为基础，适当简化以呈现类似pfc的微观结构演变模型，该模型可用于通过高性能计算进行模拟。该场理论将包括过去相场晶体（PFC）类型模型中成功元素的一致融合。这种新型PFC模型的参数将根据已知的纯材料和合金的实验材料特性进行系统的量化。这个建模链的第二阶段将包括两个部分。第一部分将开发一种粗粒化方法，将微观PFC模型投影到基于表示有序、取向、局部平均密度和浓度（对于合金材料）的光滑场的传统相场（PF）模型上。第二部分将扩大这种粗粒化方法的范围，以进一步包括局部应变耦合到上述光滑场。这两种粗晶化方法都将应用于纯材料和合金材料的PFC模型，并最终应用于上述在本提案中开发的新的二元PFC模型。由此获得的相场模型将保留生成PFC理论的几个关键微观特性的物理特性，并将通过粗粒化进行参数化连接。这项研究的结果将为加拿大材料科学和材料工程的研究人员提供一个工具集，用于模拟不同尺度下快速凝固现象中非传统微观结构演变过程的物理过程。

The properties of most materials are determined by their microstructure, a large part of which evolves during solidification. Modelling solidification is challenging because of the multiple length scales involved, from interface kinetics and solid-state defects at the atomic scale to diffusional processes that set the scale of microstructure patterning on the mesoscale. The emergence of rapid cooling processes in technology (e.g. 3D printing and laser welding) has driven a growing interest to understand such microstructure evolution processes on time scales of micro-milliseconds during rapid solidification. Here, strong non-equilibrium effects lead to meta-stable phases, thermal strain and plastic deformation, density heterogeneity and void formation near phase boundaries. There is presently no consistent modelling platform to study these inherently multi-scale phenomena. The vision of this research is to develop multi-scale chain of consistently connected theories that captures exotic microstructure phenomena that arise during solidification processes. The development of this modelling chain will be done in two stages. The first stage will have as its foundation the phenomenology of classical density functional theory for unary and binary materials based on multi-point correlation functions, duly simplified to render a PFC-like model for microstructure evolution that is tractable for use in simulations via high performance computing. This field theory will comprise a consistent fusion of successful elements of past phase field crystal (PFC) type models. The parameters of this new PFC type model will be systematically quantified against known experimental materials properties of pure material and alloys. The second stage of this modelling chain will comprise two parts. The first part will develop a coarse graining methodology to project a microscopic PFC model onto a traditional type of phase field (PF) model based on smooth fields representing order, orientation, local average density and concentration (for the case of alloy materials). The second part will expand the scope of this coarse graining methodology to further include local strain coupling to the aforementioned smooth fields. Both coarse graining methodologies will be applied to established PFC models for pure and alloy materials, and ultimately to the aforementioned new binary PFC model developed in this proposal. Phase field models so-obtained will retain the physics of several key microscopic properties of the generating PFC theory, and will be parametrically connected through coarse graining. The outcomes of this research will provide Canadian researchers in materials science and materials engineering a toolset for modelling the physics of non-traditional microstructure evolution processes in rapid solidification phenomena at different scales.