Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

Reese E Jones,Giacomo Po,Jonathan A Zimmerman

doi:10.5539/jmsr.v5n4p44

Abstract

<p class="1Body">The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused on the system-level material response that use DD-generated information to enhance the fidelity of plasticity models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity flow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density tensor fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations, we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Our results show that, for the case of torsion, the two material models can produce comparable spatial dislocation density distributions.</p>

Highlights

The importance of accurate simulation of the plastic deformation of ductile metals in the design of structures and components to performance and failure criteria is well known
Lengths are normalized to the material’s Burgers vector b= |b| = 2.556 Å, stress-like quantities are normalized by G, the drag coefficient is set at B=10-4 Pa-s, and time is normalized by τ = B/G = 2.08 fs
Given that initially the dislocation network consists entirely of loops, the total dislocation density tensor starts at zero which gives some support to assuming that Fp = I in the initial state of the material modelled with Crystal plasticity (CP)

Summary

Introduction

The importance of accurate simulation of the plastic deformation of ductile metals in the design of structures and components to performance and failure criteria is well known. Plasticity models describe the influence of elastic and inelastic deformation on stress within a body that undergoes a specific displacement/loading path. These models are conventionally constructed with parameters, such as elastic constants, yield stress and work hardening, fitted to experimentally measured data. More recent models cast this response in a finite deformation framework, and decompose the plastic portion of the velocity gradient into separate contributions from various families of dislocations, each associated with a specific slip system (Kuchnicki et al, 2006; Lee et al, 2010; Zhao et al, 2016)

Methods

Results

Discussion

Conclusion