Physics of Dislocation Patterning and Size Effects in Plasticity

Catholic University Of America, Washington DC

Investigators

Abstract

This grant supports theoretical research on the elastic-plastic response of crystalline solids. The objectives of the project include: (1) characterizing and understanding the thermodynamics driving coalescence of dislocations into ordered structures in two dimensions, and (2) investigating the origins of size effects in plasticity. Dislocation patterning has been extensively modeled as a non-equilibrium process governed by competing kinetics, but the thermodynamics driving the coalescence of dislocations into ordered structures is not well understood. This project considers the simple case of screw dislocations under shear in two dimensions, and models their coalescence into slip bands using both simulation and theory. Simulation studies are carried out using an idealized model of a crystal under anti-plane shear with constant strain rate, a system that is a close analog of the two-dimensional XY rotor model under driving boundary conditions. It is conjectured that slip-band formation in 2D represents a non-equilibrium quench into two-phase coexistence between defect-rich and defect-poor phases. Characterization of the underlying equilibrium phase diagram, scaling behavior, and flow properties of the defect-rich phase will be used to derive constitutive laws for plasticity in two dimensions. Dislocation patterning in three-dimensional crystalline solids is far more complex, involving dislocation entanglement and a host of inherently 3D mechanisms. While no 2D model can accurately describe a real 3D material, this work will provide at least qualitative insight into the competition between energy and entropy in evolution of dislocation microstructures. The project's second goal is to gain insight into the origin of size effects in plasticity. Recent experiments show that some mechanical properties of crystalline solids vary with sample size in the range below ~ 100 microns. Size effects are observed in torsion and bending but not in simple tension, suggesting that strain gradients play an important role. Efforts to build strain gradient effects in continuum plasticity theory point to the importance of a characteristic length scale whose origin is not fully understood. To find out what mechanisms are involved, simulation studies of dislocation patterning will be carried out using both the idelaized two-dimensional model and more realistic molecular dynamics in two and three dimensions. Geometries will include (1) a ductile slit crack loaded in shear, (2) torsion/bending of a beam, and (3) pullout of a thin fiber from a soft metal matrix. In each case multiple simulations will be preformed for samples of different sizes and the results will be compared to the predictions of continuum strain gradient theories. %%% This grant supports theoretical research on the elastic-plastic response of crystalline solids. The objectives of the project include: (1) characterizing and understanding the thermodynamics driving coalescence of dislocations into ordered structures in two dimensions, and (2) investigating the origins of size effects in plasticity. Successful completion of this project will increase our knowledge of the mechanical propoerties of materials, including their failure. ***