Continuum Dislocation Dynamics Modeling of Mesoscale Crystal Plasticity at Finite Deformation

结晶金属的机械变形是由运动和被称为位错的缺陷在施加的力或应力下的相互作用引起的。当单个晶体变形时，位错相互作用导致自组织位错微观结构或图案的形成。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结合机械变形和加热来改进材料行为的方法。虽然位错模式在很久以前就被观察到，但目前还没有理论或计算框架来预测任意变形下金属中它们的形成。本研究旨在通过实现一个基于连续位错动力学方法的计算建模框架来弥合这一关键差距，该框架明确表示位错及其在中尺度上的相互作用。这种概括将使晶体材料的材料行为的准确预测成为可能，它将最终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纳入研究生课程，开发的工具将向更广泛的研究界传播。将特别注重通过研究生研究助理奖学金培训女性和人数不足的学生。本文将通过计算模型研究变形下金属单晶中引起各种位错微观结构的集体位错机制。最近发展的基于连续位错动力学的计算框架在推广到有限晶体变形后将被用作研究方法。该模型框架旨在从位错的形态、塑性滑移分布和晶体畸变、内部弹性场以及整体应力-应变响应和平均位错密度演化等方面全面捕捉单晶的中尺度变形响应。调查包括以下研究任务：建立了有限变形时的控制连续位错动力学方程，并将其与晶体的应力平衡和变形运动学耦合，利用有限元方法求解了位错动力学与晶体力学方程的耦合系统，在此基础上建立了晶体中尺度变形的社区可用代码。并模拟感兴趣的位错微观结构，并使用通过透射电子显微镜和x射线技术获得的公开文献微观结构数据验证预测。

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.