与离散位错动力学渐进相容的新型位错连续统动力学模型研究

Developing theory of crystal plasticity at dislocation level has its great value in many engineering applications. For instance, deciphering the mechanisms underlying various dislocation patterns formed in crystals will boost the design of fatigue-resisting materials. A solid understanding of the role played by the less-frequently-happening climb motion of edge dislocation is useful for formulating the creep behaviour of crystalline materials. A qualified dislocation dynamical model for capturing the above-mentioned phenomena should well trade-off between resolution and computational efficiency, and one such candidate is the model of dislocation continuum, where the density distribution of dislocation is of interest. However, conventional continuum models of dislocations fail to achieve the aforementioned goals, because many small-scale mechanisms that play a role in the determination of material macroscopic properties are still missing. This project aims at systematically developing the continuum plasticity theory of dislocation density, which properly summarises the collective behaviour of the underlying discrete dislocations. At the level of theory completion, we will focus on studies in the following two aspects: 1) effective description of the formation, migration and dissociation of various self-locked dislocation substructures induced by singular short-range dislocation interactions; 2) incorporation of the mechanisms of dislocation cross-slip and climb into the continuum framework. With the derived model, the role played by dislocation dynamics in dislocation pattern formation and plastic deformation of materials that involve non-planar motion of dislocation will be studied.

发展以位错密度为基本变量的位错连续统动力学模型将有助于深入了解晶体材料长时塑性形变内部细观结构的运行机理，从而为材料的优化设计提供帮助。经典位错连续统动力学模型因无法解析细观尺度上具有奇异性的位错间短程相互作用以及各种位错非平面运动机理而无法被应用于晶体长时塑性形变模拟问题研究中。本项目将致力于系统发展与细观离散位错动力学渐进相容的位错连续统动力学模型。在理论构建层面，本项目期待在以下两方面取得突破：1) 在连续统模型中有效地刻画各种位错局部自锁结构的形成，输运以及拆分机制；2) 将螺位错交滑移以及刃位错攀移机制嵌入到位错连续统描述框架中。在模型应用层面，本项目将尝试揭示对金属材料疲劳具有预兆性的各种位错组态的形成机理，并开展对蕴含位错非平面运动机制的长时塑性变形过程的数值模拟仿真。

发展高效且保真的跨尺度分析与预测方法具有重要的科学与工程价值。美国自然科学基金委2020年《计算力学愿景与挑战性问题》报告中明确指出，“仍需大力发展用于解决涵盖跨尺度、跨时空多物理场实际问题之方法”(efforts are still required to attack realistic problems that combine multi-physics information across scales and (space and time) domains). 跨尺度建模中一个亟需解决的挑战性问题是，如何将细观尺度信息整合，为宏观预测所用。在资助期内，积极探索不同跨尺度系统数学结构层面上的共性特征，深入开展渐进分析-机器学习有机耦合方法的系统研究，并将该系统方法应用于分析位错动力学、辐照条件下晶体材料细观气泡演化以及可3D打印之含渐变微结构型材等不同跨尺度系统的宏观行为，希冀为跨尺度材料研究与设计提供坚实的理论支撑。..项目基本按照既定计划方向发展。在该项目资助下，共发表第一/通讯作者论文8篇。其中1篇发表于物理学顶级期刊PRL，2篇发表于固体力学旗舰期刊JMPS，1篇发表于计算力学顶级期刊CMAME，1篇发表于固体力学重要期刊IJSS等。同时关于点缺陷长时模拟研究还应用于二氧化铀燃料力学性能分析研究。

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