Computational Modeling of Self-organization of Dislocations and Mesoscale Deformation of Metals

Anter El-Azab
Seminar

Dislocations are important line defects in crystals. They are responsible for the ductility of metals, which is metals' most critical property. A key feature of the dynamics of dislocation systems is that they self-organize in various patterns under mechanical loading and these patterns control the plastic deformation and fracture behavior of metals. For over 70 years, metallurgists, physicists, mathematicians, and mechanical engineering have been trying to build predictive models of metal deformation starting with dislocation properties. Direct numerical simulations of dislocation ensembles proved to be a challenging task. The concepts of statistical mechanics were exploited to develop continuum dislocation dynamics models. In this context, building the dislocation kinetic equations from the bottom up, i.e., by connecting the discrete and continuum representations of dislocations, results in a closure problem requiring to evaluate the spatial and temporal dislocation correlations in dislocation systems. We demonstrate that this approach is able to predict all experimental observables: the stress-strain behavior including hardening, self-organization of dislocations and dislocation density evolution, slip distribution and distorted crystal shape, and the local elastic strain and lattice rotation at the mesoscale. Our preliminary results show that cross slip is the most crucial mechanism for triggering cell structure formation in fcc metals from initial random dislocation configurations; that cells are 3D crystal sub-regions surrounded by dislocations walls in all directions; that cells form, disappear, and reappear as a result of the motion of cell walls; and that the average cell size refines according to the similitude principle observed in related experiments. We conclude by discussing the connection between the current work and data-intensive X-ray measurements on deformed crystals performed at the Advanced Photon Source (APS).