Continuum Dislocation Dynamics Modeling of Mesoscale Crystal Plasticity at Finite Deformation

晶体金属的机械变形是由在外力或应力作用下称为位错的缺陷的运动和相互作用引起的。当单个晶体变形时，位错相互作用导致自组织位错微结构或图案的形成。这些图案被认为控制着金属的机械强度和失效。它们在金属制造中也很重要，因为它们提供了通过组合机械变形和加热来优化材料行为的方法。虽然很久以前就观察到了位错图案，但目前还没有理论或计算框架来预测在任意变形下金属中位错图案的形成。本研究旨在通过实现基于连续体位错动力学方法的计算建模框架来弥合这一关键差距，该框架基于连续体位错动力学方法在介观尺度上显式地表示位错及其相互作用。这样的概括将使晶体材料中的材料行为能够准确预测，并最终将导致结构合金制造过程的现实模型。在这项研究中获得的科学知识将被纳入研究生课程，所开发的工具将向更广泛的研究界传播。重点是通过研究生研究助教培养女性和代表性不足的学生。通过计算模型研究在变形时导致金属单晶中各种位错微结构的集体位错机制。将最近发展起来的基于连续位错动力学的计算框架推广到有限晶体变形，作为研究的方法。该模型从理论上反映了单晶的细观变形响应，包括位错形态、塑性滑移分布和晶体变形、内部弹性场以及整体应力应变响应和平均位错密度演化。研究内容包括：建立有限变形条件下的连续体位错动力学方程，并将这些方程与晶体的应力平衡和变形运动学相耦合，用有限元方法求解位错动力学和晶体力学耦合方程组，在此基础上建立晶体细观变形通用程序，模拟感兴趣的位错微结构，并利用电子显微镜和X射线技术获得的开放文献微观结构数据对预测结果进行验证。

Mechanical deformation of crystalline metals is caused by motion and interactions of defects called dislocations under applied forces or stresses. As the individual crystals deform, dislocation interactions lead to the formation of self-organized dislocation microstructures or patterns. These patterns are believed to control the mechanical strength and failure of metals. They are also important in metal manufacturing as they provide the way to refine the material behavior through combined mechanical deformation and heating. Although dislocation patterns were observed long ago, there is currently no theoretical or computational framework for predicting their formation in metals under arbitrary deformation. This research aims to bridge this critical gap by implementing a computational modeling framework that explicitly represents dislocations and their interactions at the mesoscale based on the continuum dislocation dynamics method. Such a generalization will enable accurate prediction of material behavior in crystalline materials, and it will eventually lead to realistic models of the manufacturing processes of structural alloys. Scientific knowledge obtained in this research will be incorporated into graduate curriculum and the developed tools will be disseminated to the wider research community. A particular focus will be given to the training of female and underrepresented students through graduate research assistantships.The collective dislocation mechanisms that induce various dislocation microstructures in metal single crystals under deformation will be investigated by computational modeling. A recently developed computational framework based on continuum dislocation dynamics will be used as the method of investigation after generalization to finite crystal deformation. This modeling framework is theoretically founded to capture the full mesoscale deformation response of single crystals from dislocation properties, which includes the dislocation patterns, plastic slip distribution and crystal distortion, internal elastic fields, as well as the overall stress-strain response and average dislocation density evolution. The investigation includes the following research tasks: formulating the governing continuum dislocation dynamics equations at finite deformation and coupling these equations with the stress equilibrium and deformation kinematics of crystals, solving the coupled system of dislocation dynamics and crystal mechanics equations using the finite element approach, building a community available code for mesoscale deformation of crystals based on the above, and simulating the dislocation microstructures of interest and validating the predictions using open literature microstructure data obtained by Transmission Electron Microscopy and X-ray techniques.