Coupled 3D Dislocation Modeling at Nano- and Micro-Scales

The performance of crystalline materials varies depending on the considered scale. To understand the size dependence of materials properties, the interaction and evolution of defects are essential. As such, the role played by dislocations is crucial for modeling metallic materials. In essence, a dislocation is a default in the crystalline periodicity that creates long-range stress fields, which makes the modeling of dislocation dynamics a challenging problem. This thesis concentrates on the development of a novel multiscale method, which couples concurrently dislocation dynamics at nano- and micro-scales. A version of this method, the \textit{Coupled Atomistic and Discrete Dislocations} (CADD), exists for two-dimensional problems. Its three-dimensional extension (CADD3d) is developed theoretically, and then implemented including the necessary parallel computing aspects. The proposed model requires two main building blocks, which are linked to general dislocation properties. The first component is the correction field of the linear elasticity solution for dislocation cores. The core structures are pre-computed by modeling straight dislocations with arbitrary mixed angles using atomistic simulations. The obtained results are validated by extending the variational Peierls-Nabarro method. Finally, the templates including the core correction field are generated from the calculated core structures. The second building block is the mobility law of dislocations. The dislocation mobilities for several orientations and temperatures are studied with atomistic simulations, and validated by comparisons to theoretical models. The mobility law is characterized by two damping mechanisms, the phonon viscosity and the phonon radiation effects. CADD3d is then examined by studying several benchmark problems, which prove that the CADD3d method is a valid approach to couple atomistic and discrete dislocation dynamics including when multiple curved dislocations dynamics have to be considered. Furthermore, to highlight the applicability of CADD3d for material plasticity problems, a Frank-Read source in an aluminum alloy is studied. The application result provides interesting insights on the mechanisms of solid-solution strengthening and grain-hardening effects at the nano and micro scales.

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