Continuum Dislocation Dynamics Modeling of Mesoscale Crystal Plasticity at Finite Deformation

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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.