University of Minnesota
Aerospace Engineering and Mechanics
Winter 1999 Seminar Series



Scale-Dependent Crystal Plasticity


Prof. David M. Parks

Department of Mechanical Engineering Massachusetts Institute of Technology


Abstract


Recently, several models of scale-dependent crystal plasticity have been proposed in order to account for experimentally-observed scale effects such as indentor-size dependence of hardness and grain-size effects on polycrystalline strain hardening. A conceptual basis underlying many of the models is Ashby's interpretation of "geometrically-necessary" dislocation density as related to plastic slip gradient, with attendant hardening associated with the on-going interactions of glissile dislocations with both the "statistically-stored" and the "geometrically-necessary" dislocation densities. Although the fundamental concept of geometrically-necessary dislocation density is intimately related to the spatial organization of the lattice, several isotropic (lattice-less) versions of the models have been developed by introducing invariant measure(s) of the plastic strain gradient tensor and conjugate material length scales of order lattice spacing divided by the square of yield strain. In contrast, we retain the lattice and the material curl of plastic deformation gradient (equivalently, the spatial curl of inverse elastic deformation gradient), quantifying Nye's tensor as fundamental. For the FCC lattice, algorithms associate geometrically-necessary densities of pure screw (six systems) and edge (twelve systems) dislocations with Nye's tensor. These densities, in conjunction with statistically-stored dislocation density, define the deformation resistances of each crystallographic slip system. The model is realized via finite elements within which Nye's tensor and dislocation density are evaluated. A typical application demonstrates the grain-size dependence of polycrystalline strain hardening. Results from both idealized planar double-slip models and full three-dimensional simulations are presented and discussed.

Friday, February 12, 1999
209 Akerman Hall
2:30-3:30 p.m.


Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.