From Discrete Dislocation Dynamics to Crystal Plasticity - A Spatio-Temporal Coarse-Graining Approach

从离散位错动力学到晶体塑性 - 时空粗粒方法

• 批准号: 1435624
• 负责人: Amit Acharya
• 金额: $ 36.63万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-15 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1435624&HistoricalAwards=false
• 关键词: Discrete; Dislocation; Dynamics; Crystal; Plasticity

The objective of this work is to develop and demonstrate the fundamentals of a predictive, next-generation, computational tool for microstructure-sensitive design of metallic components of modern machines that are subjected to mechanical stress and deformation. The generally irreversible deformation of metallic materials at the macroscopic scale called plastic deformation arises due to the motion of vast numbers of defects in their underlying regular crystalline structure under applied loading. Such defect motions lead to special spatial patterns of organization of multiple defects called microstructure, and it is known that this defect microstructure has significant effect on the material's macroscopic properties like strength and ductility. The individual defect motions occur at much smaller length scales and much faster time scales than those of macroscopically observed plastic deformation, thus requiring a mathematical process of averaging to define the macroscopic model of collective behavior of defects from the microscopic dynamics. This award supports the development and validation of such a macroscopic model from microscopic fundamentals through multiscale mathematical and computational modeling. The project addresses a key scientific question with significant impact on society. A great deal of modern manufacturing, design of light-weight, high-strength structural materials and materials for gas turbines for energy and aerospace applications all depend upon understanding of microstructure evolution and its effect on material properties. Widely used industrial design codes do not at present make use of microstructure sensitive material models. This research will develop a truly material microstructure-sensitive model for plastic strength and dislocation microstructure evolution that has the potential to revolutionize the way metallic materials are designed in many industries, bringing about significant cost and energy savings for the US economy. The research tightly integrates the fields of Applied Mathematics, Mechanics of Materials, and Materials Science, and this will lead to fruitful interdisciplinary interplay of ideas between these fields, all directed to very practical outcomes, including the training of students which will enhance the US workforce in science and technology. Efforts will be made to archive developed computer codes at the NSF supported Pittsburgh Supercomputing Center to enable systematic, free, widespread access to interested practitioners.The challenge of this work is to develop a novel computational tool for accurate multi-scale simulations of plasticity and dislocation microstructure evolution in crystalline materials. The tasks addressed will be the computation of plastic strength and associated microstructure of a material at the meso and macroscale directly from the underlying motion of crystal defects. This application is a paradigmatic complex system, with immense practical relevance. Specifically, an exact, but non-closed, partial differential equation based theory representing the evolution of space-time averaged dislocation dynamics will be utilized, that contains well-defined place-holders for microscopic dislocation dynamics based input. These inputs, typically prescribed as phenomenological constitutive assumptions, will be replaced in this work by a carefully designed coupling, on the "slow" time-scale of meso-macro response, with time-averaged response of "fast", local (on the macroscopic scale) Discrete Dislocation Dynamics simulations. The overall strategy is based on novel and sound continuum mechanical principles like a conservation statement for topological charge carried by crystal defects coupled to macroscopic elasticity as well as modern mathematical tools like Young Measure theory for averaging multi-time scale response of nonlinear Ordinary Differential Equations. Interestingly, this approach for solving a patently practical problem involves finite dimensional dynamical system input into an overarching infinite dimensional dynamical system.

这项工作的目标是开发和演示下一代预测计算工具的基础知识，用于对承受机械应力和变形的现代机器金属部件进行微观结构敏感设计。金属材料在宏观尺度上通常不可逆的变形（称为塑性变形）是由于其底层规则晶体结构中的大量缺陷在施加载荷下的运动而产生的。这种缺陷运动导致被称为微观结构的多个缺陷组织的特殊空间模式，并且众所周知，这种缺陷微观结构对材料的宏观性能（例如强度和延展性）具有显着影响。与宏观观察到的塑性变形相比，单个缺陷运动发生的长度尺度要小得多，时间尺度要快得多，因此需要平均数学过程来从微观动力学定义缺陷集体行为的宏观模型。该奖项支持从微观基础到多尺度数学和计算建模，开发和验证这种宏观模型。该项目解决了一个对社会产生重大影响的关键科学问题。许多现代制造、轻质、高强度结构材料以及能源和航空航天应用燃气轮机材料的设计都依赖于对微观结构演变及其对材料性能影响的理解。目前广泛使用的工业设计规范并未使用微观结构敏感材料模型。这项研究将开发一个真正对材料微观结构敏感的塑性强度和位错微观结构演化模型，该模型有可能彻底改变许多行业金属材料的设计方式，为美国经济带来显着的成本和能源节约。该研究紧密结合了应用数学、材料力学和材料科学领域，这将导致这些领域之间思想的富有成效的跨学科相互作用，所有这些都旨在产生非常实际的成果，包括对学生的培训，这将增强美国的劳动力在科学技术方面。将努力将开发的计算机代码存档在 NSF 支持的匹兹堡超级计算中心，以便感兴趣的从业者能够系统、免费、广泛地访问。这项工作的挑战是开发一种新颖的计算工具，用于精确的多尺度塑性和位错模拟晶体材料的微观结构演变。所解决的任务将是直接根据晶体缺陷的潜在运动计算材料在细观和宏观尺度上的塑性强度和相关微观结构。该应用程序是一个典型的复杂系统，具有巨大的实际意义。具体来说，将利用代表时空平均位错动力学演化的精确但非封闭的基于偏微分方程的理论，该理论包含用于基于微观位错动力学的输入的明确定义的占位符。这些输入通常被规定为现象学本构假设，在这项工作中将被精心设计的耦合所取代，在中观-宏观响应的“慢”时间尺度上，具有“快”的时间平均响应，局部（在宏观尺度）离散位错动力学模拟。总体策略基于新颖且可靠的连续介质力学原理，例如与宏观弹性耦合的晶体缺陷所携带的拓扑电荷的守恒声明，以及现代数学工具，例如用于平均非线性常微分方程的多时间尺度响应的杨氏测度理论。有趣的是，这种解决明显实际问题的方法涉及将有限维动力系统输入到总体无限维动力系统中。