Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method.

2014 ◽  
Vol 1651 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Mehran Monavari ◽  
Thomas Hochrainer
Keyword(s):  
Discontinuous Galerkin ◽  
Crystal Plasticity ◽  
Evolution Equations ◽  
Total Curvature ◽  
Time Integration ◽  
Three Dimensional ◽  
Conserved Quantity ◽  
Dislocation Dynamics ◽  
Slip Systems ◽  
Continuum Dislocation Dynamics

ABSTRACTIn the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

MRS Advances ◽  
2016 ◽  
Vol 1 (24) ◽  
pp. 1791-1796 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Slip System ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Structure Evolution ◽  
Internal Variables ◽  
Plastic Shear ◽  
Continuum Dislocation Dynamics ◽  
Dynamics Simulations

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Multiscale Crystal Plasticity Simulation with Pseudo-Three-Dimensional Model on Ultrafine-Graining Based on Evolution of Dislocation Structures

2008 ◽  
Vol 584-586 ◽  
pp. 1057-1062 ◽  
Author(s):  
Yoshiteru Aoyagi ◽  
Naohiro Horibe ◽  
Kazuyuki Shizawa
Keyword(s):  
Slip System ◽  
Dislocation Structure ◽  
Crystal Plasticity ◽  
Three Dimensional ◽  
Slip Rate ◽  
Dislocation Cell ◽  
Reaction Diffusion Equations ◽  
Slip Systems ◽  
Dimensional Model ◽  
Three Dimensional Model

In this study, we develop a multiscale crystal plasticity model that represents evolution of dislocation structure on formation process of ultrafine-grained metal based both on dislocation patterning and geometrically necessary dislocation accumulation. A computation on the processes of ultrafine-graining, i.e., generation of dislocation cell and subgrain patterns, evolution of dense dislocation walls, its transition to micro-bands and lamellar dislocation structure and formation of subdivision surrounded by high angle boundaries, is performed by use of the present model. Dislocation patterning depending on activity of slip systems is reproduced introducing slip rate of each slip system into reaction-diffusion equations governing self-organization of dislocation structure and increasing immobilizing rate of dislocation with activation of the secondary slip system. In addition, we investigate the effect of active slip systems to the processes of fine-graining by using the pseudo-three-dimensional model with twelve slip systems of FCC metal.

Higher order alignment tensors for continuum dislocation dynamics

2013 ◽  
Vol 1535 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Total Curvature ◽  
Higher Order ◽  
Distribution Functions ◽  
Dislocation Dynamics ◽  
Symmetric Tensors ◽  
Materials Modeling ◽  
Continuum Dislocation Dynamics ◽  
Alignment Tensors ◽  
Higher Order Tensors

ABSTRACTDislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

On the Selection of Active Slip Systems in Rate Independent Crystal Plasticity

2013 ◽  
Vol 554-557 ◽  
pp. 1147-1156
Author(s):  
Markus Orthaber ◽  
Thomas Antretter ◽  
Hans Peter Gänser
Keyword(s):  
Crystal Plasticity ◽  
Dislocation Dynamics ◽  
Slip Systems ◽  
Rate Dependency ◽  
Low Viscosity ◽  
Rate Dependent ◽  
Cross Hardening ◽  
The Individual ◽  
Active Slip ◽  
Regularized Model

Non-uniqueness of the set of active slip systems is a crucial issue in crystal plasticity. To avoid this problem one may perform viscoplastic regularization. This introduces a certain rate dependency, while many crystals are known to behave rate independently. One would require very low viscosity parameters in the regularized model to resemble the experimental behavior of rate independent crystals, which in turn entails numerical difficulties. Furthermore, no direct approach is known to model deformation banding using viscoplastically regularized models. Hence, to adequately treat rate independent crystal plasticity an alternative method is needed. The proposed method, Maximum Dissipation Crystal Plasticity (MDCP), achieves uniqueness by selecting the set of active slip systems according to its dissipation. In a finite element calculation, a system of coupled quadratic equations is solved at every integration point to define the material behaviour. This approach is formally equal to the method of incremental energy minimization recently proposed by Petryk et al. It can be shown that a viscoplastically regularized model is a limiting case of MDCP, giving similar results when cross hardening becomes negligible. Nevertheless, recent 3D dislocation dynamics calculations by Devrince et al. show that cross hardening in fcc crystals is far more important than self hardening. In such cases MDCP gives results distinctly different from its rate dependent counterpart. Fewer slip systems are selected by MDCP, resulting in more slip on the individual active systems. The proposed method is numerically implemented as an Abaqus user material subroutine within the large deformation framework, such that the simulation of arbitrary load cases is possible.

Continuum dislocation dynamics: Towards a physical theory of crystal plasticity

2014 ◽  
Vol 63 ◽  
pp. 167-178 ◽  
Author(s):  
Thomas Hochrainer ◽  
Stefan Sandfeld ◽  
Michael Zaiser ◽  
Peter Gumbsch
Keyword(s):  
Crystal Plasticity ◽  
Physical Theory ◽  
Dislocation Dynamics ◽  
Continuum Dislocation Dynamics
Sign in / Sign up

Export Citation Format

Share Document