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.

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.

Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

2014 ◽  
Vol 1651 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Evolution Equations ◽  
Continuum Theory ◽  
Orientation Distribution ◽  
Line Length ◽  
Second Order ◽  
Dislocation Dynamics ◽  
Alignment Tensor ◽  
Length Changes ◽  
Edge Dislocations

ABSTRACTIn the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

scholarly journals Leaving the Slip System ‐ Cross Slip in Continuum Dislocation Dynamics

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Benedikt Weger ◽  
Thomas Hochrainer
Keyword(s):  
Slip System ◽  
Cross Slip ◽  
Dislocation Dynamics ◽  
Continuum Dislocation Dynamics

Influence of Initial Defects on the Mechanical Properties of Single Crystal Copper: Discrete Dislocation Dynamics Study

2018 ◽  
Vol 913 ◽  
pp. 627-635
Author(s):  
Ming Yi Zhang ◽  
Min Zhong ◽  
Shuai Yuan ◽  
Jing Song Bai ◽  
Ping Li
Keyword(s):  
Dislocation Density ◽  
Single Crystal ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Single Crystal Copper ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
Stress Curve ◽  
Initial Dislocation Density

In this paper, three dimensional discrete dislocation dynamics method was used to quantitatively investigate the influence of initial defects on mechanical response of single crystal copper. Both the irradiation defects (interstitial loops) and random dislocation lines with different densities are considered. The simulation results demonstrate that the yield strength of single crystal copper is higher with higher initial dislocation density and higher interstitial loop density. Dislocation density increases quickly by nucleation and multiplication and microbands are formed during plastic deformation when only the random dislocation lines are initially considered. Characteristics of microbands show excellent agreement with experiment results. Dislocation multiplication is suppressed in the presence of interstitial loops, and junctions and locks between dislocations and interstitial loops are formed. Dislocation density evolution shows fluctuation accompanied with strain-stress curve fluctuation.

Two- and Three-Dimensional EBSD Measurement of Dislocation Density in Deformed Structures

2010 ◽  
Vol 160 ◽  
pp. 17-22 ◽  
Author(s):  
David P. Field ◽  
Colin C. Merriman ◽  
Ioannis N. Mastorakos
Keyword(s):  
Free Surface ◽  
Dislocation Density ◽  
Bulk Material ◽  
Ion Beam ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Dislocation Dynamics ◽  
Three Dimensions ◽  
Lattice Curvature ◽  
Orientation Data

Electron backscatter diffraction (EBSD) techniques have been used to measure the dislocation density tensor for various materials. Orientation data are typically obtained over a planar array of measurement positions and the minimum dislocation content required to produce the observed lattice curvature is calculated as the geometrically necessary (or excess) dislocation density. The present work shows a comparison of measurements in two-dimensions and three-dimensions using a dual beam instrument (focused ion beam, electron beam) to obtain the data. The two-dimensional estimate is obviously lower than that obtained from three-dimensional data since the 2D analysis necessarily assumes that the third dimension has no curvature in the lattice. Effects of the free-surface on EBSD measurements are discussed in conjunction with comparisons against X-ray microdiffraction experiments and a discrete dislocation dynamics model. It is observed that the EBSD measurements are sensitive to free-surface effects that may yield dislocation density observations that are not consistent with that of the bulk material.

scholarly journals Boundary conditions for dislocation dynamics simulations and stage 0 of BCC metals at low temperature

2001 ◽  
Vol 677 ◽  
Author(s):  
Meijie Tang ◽  
Ladislas P. Kubin
Keyword(s):  
Low Temperature ◽  
Dislocation Density ◽  
Boundary Conditions ◽  
Dislocation Dynamics ◽  
Body Centered Cubic ◽  
Density Evolution ◽  
Bcc Metals ◽  
Effective Boundary ◽  
Effective Boundary Condition ◽  
Dynamics Simulations

ABSTRACTIn order to study the dislocation density evolution of body centered cubic (bcc) crystals at low temperature by dislocation dynamics (DD) simulations, we investigated carefully three different boundary conditions (BC) for DD, i.e., the quasi-free surface BC, the flux-balanced BC, and the periodic BC. The latter two BCs can account for the dislocation loss from the boundary of the finite simulation box. PBC can also eliminate the influence of surfaces and improve the line connectivity. We have found that the PBC provides a convenient and effective boundary condition for DD simulations and have applied it to the study of dislocation density evolution of bcc metals during stage 0 deformation at low temperature.

scholarly journals Influence of Size on the Fractal Dimension of Dislocation Microstructure

Metals ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 478
Author(s):  
Yinan Cui ◽  
Nasr Ghoniem
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Two Dimensional ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
Transmission Electron ◽  
Dynamics Simulations ◽  
2D And 3D ◽  
Microscopy Images

Three-dimensional (3D) discrete dislocation dynamics simulations are used to analyze the size effect on the fractal dimension of two-dimensional (2D) and 3D dislocation microstructure. 2D dislocation structures are analyzed first, and the calculated fractal dimension ( n 2 ) is found to be consistent with experimental results gleaned from transmission electron microscopy images. The value of n 2 is found to be close to unity for sizes smaller than 300 nm, and increases to a saturation value of ≈1.8 for sizes above approximately 10 microns. It is discovered that reducing the sample size leads to a decrease in the fractal dimension because of the decrease in the likelihood of forming strong tangles at small scales. Dislocation ensembles are found to exist in a more isolated way at the nano- and micro-scales. Fractal analysis is carried out on 3D dislocation structures and the 3D fractal dimension ( n 3 ) is determined. The analysis here shows that ( n 3 ) is significantly smaller than ( n 2 + 1 ) of 2D projected dislocations in all considered sizes.

Creep Analysis of Cr-Mo Steels Using a Dislocation Based Constitutive Modelling

2004 ◽  
Vol 449-452 ◽  
pp. 117-120 ◽  
Author(s):  
Hyoung Seop Kim ◽  
Min Hong Seo ◽  
Sun Ig Hong ◽  
Sung Ho Kim ◽  
Woo Seog Ryu
Keyword(s):  
Kinetic Equation ◽  
Dislocation Density ◽  
Metal Forming ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Creep Behaviour ◽  
Constitutive Modelling ◽  
Internal Variables ◽  
Dislocation Glide ◽  
Creep Analysis

In order to analyze the creep behaviour of Cr-Mo steels, an elasto-viscoplastic constitutive model based on dislocation density considerations is described. A combination of a kinetic equation, which describes the mechanical response of a material at a given microstructure in terms of dislocation glide, and evolution equations for internal variables characterising the microstructure provide the constitutive equations of the model. Microstructural features of the material are implemented in the constitutive equation. The internal variables are associated with the total dislocation density. The model has a modular structure and can be adjusted to describe a particular type of materials behaviour and metal forming processes. In this paper, the predicted creep behaviour of Cr-Mo steels is compared with the experimental results.

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