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

大多数材料的性能由其微观结构决定，其中很大一部分是在凝固过程中演化的。模拟凝固是具有挑战性的，因为涉及多个长度尺度，从原子尺度的界面动力学和固态缺陷到在介观尺度上设定微结构图案尺度的扩散过程。快速冷却技术(如3D打印和激光焊接)的出现促使人们越来越有兴趣了解快速凝固过程中在毫秒级时间尺度上的组织演变过程。在这里，强烈的非平衡效应导致亚稳定相、热应变和塑性变形、密度不均匀和相界附近空洞的形成。目前还没有一个统一的建模平台来研究这些固有的多尺度现象。这项研究的愿景是开发多尺度的一致连接的理论链，以捕捉在凝固过程中出现的奇异微结构现象。这个模型链的开发将分两个阶段进行。第一阶段将以基于多点关联函数的一元和二元材料的经典密度泛函理论的现象学为基础，适当地简化以提供一个类似PFC的微观结构演化模型，该模型易于通过高性能计算在模拟中使用。这一场论将包括过去相场晶体(PFC)类型模型的成功元素的一致融合。这种新的PFC类型模型的参数将根据已知的实验材料、纯材料和合金的性质进行系统的量化。这个模型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模型投影到传统类型的相场(PF)模型上，该模型基于表示有序、取向、局部平均密度和浓度的平滑场(对于合金材料)。第二部分将扩展这种粗粒化方法的范围，以进一步包括对上述光滑场的局部应变耦合。这两种粗粒化方法都将应用于已建立的纯材料和合金材料的PFC模型，并最终应用于本提案中开发的上述新的二元PFC模型。这样得到的相场模型将保留生成PFC理论的几个关键微观性质的物理性质，并将通过粗粒化参数连接起来。这项研究的结果将为加拿大材料科学和材料工程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结构演变过程的物理模型。

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.