scholarly journals A link between microstructure evolution and macroscopic response in elasto-plasticity: Formulation and numerical approximation of the higher-dimensional continuum dislocation dynamics theory

2015 ◽  
Vol 72 ◽  
pp. 1-20 ◽  
Author(s):  
Stefan Sandfeld ◽  
Ekkachai Thawinan ◽  
Christian Wieners
Keyword(s):  
Microstructure Evolution ◽  
Numerical Approximation ◽  
Dislocation Dynamics ◽  
Higher Dimensional ◽  
Elasto Plasticity ◽  
Continuum Dislocation Dynamics ◽  
Macroscopic Response

Continuum dislocation dynamics-based grain fragmentation modeling

2019 ◽  
Vol 114 ◽  
pp. 252-271 ◽  
Author(s):  
A.H. Kobaissy ◽  
G. Ayoub ◽  
L.S. Toth ◽  
S. Mustapha ◽  
M. Shehadeh
Keyword(s):  
Dislocation Dynamics ◽  
Grain Fragmentation ◽  
Continuum Dislocation Dynamics

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.

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