When 10:30 AM - 11:30 AM Jan 30, 2015
Where 1670 Beyster Building
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Statistical dislocation dynamics modelling of metal deformation at the mesoscale

Anter El-Azab
Purdue University, School of Nuclear Engineering and School of Materials Engineering

A wide range of mesoscale dislocation patters have been observed in deformed metals. These patterns are believed to influence the hardening behaviour and the plastic fracture of metals. In this presentation, a brief historical perspective on the dislocation patterns and related early models will be given. The current dislocation dynamics models will also be assessed from the viewpoint of predicting dislocation patterning and strain hardening of crystals. The bulk of this talk will be dedicated to introducing a statistical mechanical approach to dislocation dynamics; this is a transport type approach in which the space-time evolution of the dislocation density is described by a set of kinetic equations, one per slip system, which are solved concurrently with an eigenstrain formulation of the stress boundary value problem. Application of the statistical mechanics concepts to build 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 correlation effects. We demonstrate that this approach is able to predict all experimental observables: the stress-strain behaviour including hardening, dislocation pattern formation and dislocation density evolution, plastic strain/slip distribution and distorted crystal shapes, and the local elastic strain and lattice rotation at the mesoscale. The 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 with an outlook as to how to turn dislocation dynamics into a formal theory of metal deformation. This work was supported by the U.S. DOE Office of Basic Energy Sciences, Division of Materials Science & Engineering via contract # DE-FG02-08ER46494 at Florida State University and by funding from the School of Nuclear Engineering at Purdue University.

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