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，其中很大一部分在凝固过程中演变。 由于涉及多个长度尺度，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化尺度的扩散过程，因此建模凝固是具有挑战性的。 技术中快速冷却过程（例如3D打印和激光焊接）的出现推动了人们对理解快速凝固期间微毫秒级时间尺度上的这种微结构演变过程的兴趣日益增长。在这里，强烈的非平衡效应导致亚稳相、热应变和塑性变形、密度不均匀性和相边界附近的空隙形成。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。这项研究的愿景是开发多尺度链的一致连接的理论，捕捉奇异的微观结构现象，在凝固过程中出现。该模型链的开发将分两个阶段进行。第一阶段将有作为其基础的经典密度泛函理论的现象学的一元和二元材料的基础上多点相关函数，适当简化，使PFC类模型的微观结构的演变是易于处理的模拟通过高性能计算。 这种场理论将包括过去相场晶体（PFC）型模型的成功元素的一致融合。这个新的PFC型模型的参数将被系统地量化对已知的实验材料的纯材料和合金的性能。这一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，以将微观PFC模型投影到传统类型的相场（PF）模型上，该模型基于表示顺序、取向、局部平均密度和浓度（对于合金材料）的平滑场。第二部分将扩大这种粗粒化方法的范围，进一步包括局部应变耦合到上述平滑场。这两种粗粒化方法将被应用于建立纯和合金材料的PFC模型，并最终在本提案中开发的上述新的二元PFC模型。如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，并且将通过粗粒化参数化地连接。这项研究的成果将为加拿大材料科学和材料工程研究人员提供一套工具，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学。

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.