# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 1997 Seminar Series**

*Discrete Dislocation Modeling of Plastic Flow Processes*

*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.