University of Minnesota
Aerospace Engineering and Mechanics
Fall 1997 Seminar Series



Discrete Dislocation Modeling of Plastic Flow Processes


Professor Alan Needleman
Division of Engineering
Brown University


Abstract


Plastic deformation in crystalline metals is a consequence of the motion of large numbers of dislocations, and much is known about dislocation mechanics from both the atomistic and continuum perspectives. However, only relatively recently have general analyses of the collective behavior of large numbers of discrete dislocations been undertaken. A framework for analyzing boundary value problems, where plastic flow arises from the collective motion of large numbers of discrete dislocations, is described. The dislocations are modeled as line defects in an isotropic linear elastic solid. The stresses and strains are written as superpositions of fields due to the discrete dislocations and complimentary (or image) fields that enforce the boundary conditions and account for interaction with second-phase particles. This leads to a linear elastic boundary value problem for the image fields which is solved by the finite element method. Hence, the long range interactions between dislocations are accounted for through the continuum elasticity fields. Drag during dislocation motion, interactions with obstacles, and dislocation nucleation and annihilation are incorporated into the formulation through a set of constitutive rules. Results are presented for a two-dimensional model composite consisting of elastic reinforcements in a crystalline matrix having a single slip system and subject to simple shear. Both the behavior under monotonic loading and the residual stresses on unloading are considered. The plastic stress-strain response and the evolution of the dislocation structure are outcomes of the boundary value problem solution. The predictions are contrasted with those of a conventional continuum slip crystal plasticity analysis


Friday, October 17, 1997
209 Akerman Hall
2:30-3:30 p.m.


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