Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 100017

100017 - Vector Density Continuum Dislocation Dynamics: Progress in Deformation Kinematics and Dislocation Kinetics 

Theoretical models of dislocation mediated plasticity generally falls into one of two categories: phenomenological theories that describe macroscopic plasticity (e.g. crystal plasticity models) or the simulation of discrete dislocations (discrete dislocation dynamics). The former fits empirical relations using nuanced intuitions from the motion of dislocations and thus lacks the rigor of a first-principles theory of plasticity. The latter retains too much detail, and a lack of computational scalability as well as an inability to properly describe the kinematics of finite deformation. In this poster presentation we outline the major features of vector density continuum dislocation dynamics, which we suggest strikes a middle road between these two extremes. Vector density dislocation dynamics represents dislocations by means of a continuous vector density field in the crystal which describes both the density of dislocation lines at a given point and their average line tangent. In this presentation we consider dislocations in FCC crystals, which involves the treatment of 12 dislocation densities, one per unique slip system. This first-principles treatment of dislocation based plasticity allows implementation of many important aspects of dislocation physics. In our presentation we showcase three important areas of progress in the development of this theoretical framework. First, we show recent progress in the kinematics of dislocation dynamics at finite deformation, especially in stress controlled simulations. These effects allow continuum dislocation dynamics to model the geometrical nonlinearities and lattice rotations which occur at large strains. Secondly, we present recent implementations of dislocation reactions and junctions. Because of the separate densities treated on various slip systems, these reactions result in coupling terms between the dislocation transport equations on each slip system. Additionally, the knowledge of the line tangent information peculiar to vector density continuum dislocation dynamics allows reactions to be incorporated in a straightforward manner. A correctly implementation of reactions is important as reactions and junctions are known to be a significant mechanism of strain hardening. Lastly, we present recent insights into the short-range interactions of dislocations by means of the dislocation correlation functions. Correctly capturing the short range stress field is essential for understanding the emergence of dislocation patterns in metals, and thus for correctly describing their plastic response. The importance of all three of these lines of progress will be synthesized into a picture of the state of the art in vector density continuum dislocation dynamics. All of these areas of dislocation dynamics will be discussed with an eye towards important open problems in micron-scale plasticity.

Presenting Author: Joseph Pierre Anderson Purdue University

Presenting Author Biography: Joseph Pierre Anderson is a PhD. student at Purdue University's School of Materials Engineering. He studies the statistical aspects of dislocation motion, especially the role of dislocation correlations in short-range dislocation interactions.

Authors:

Joseph Pierre Anderson Purdue University
Khaled Abdelaziz Purdue University
Vignesh Vivekanandan Purdue University
Anter El-Azab Purdue University