Dislocation patterns fractals or cells february 20 2008
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Tom Arsenlis. Dislocation Patterns – Fractals or Cells? February 20, 2008. Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551.

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Dislocation patterns fractals or cells february 20 2008 l.jpg

Tom Arsenlis

Dislocation Patterns –

Fractals or Cells?

February 20, 2008

Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344

UCRL-PRES-236631


Dislocation dynamics simulation team l.jpg

LLNL

Vasily Bulatov

Gregg Hommes

Tomas Oppelstrup

Tim Pierce

Moono Rhee

Meijie Tang

Jaime Marian

Close Collaborators

Stanford U. – Wei Cai, Chris Weinberger

Florida State U. – Anter El Azab, Jie Deng

Visualization Support

Richard Cook

Rebecca Springmeyer

Financial Support

NNSA ASC Program

DOE OBES

DOE GNEP

LLNL Lawrence Fellow Program

LLNL M&IC Computing

Dislocation Dynamics Simulation Team


Simulations are used to uncover the nature of dislocation interactions and patterning l.jpg
Simulations are used to uncover the nature of dislocation interactions and patterning

  • Motivation

    • Abundance of TEM evidence that dislocations may form patterns

    • Experimental evidence is post mortem – process of formation is unknown

    • Correlation between patterning and strength is unclear

  • Method

    • Perform large scale dislocation dynamics simulations using ParaDiS

    • Use statistical analysis tools and continuum plasticity concepts to understand dislocation interactions


Slide4 l.jpg

Computational Grand Challenge of Simulating Dislocations interactions and patterning

  • Volumes and time scales over which dislocations form structures are still too large to be simulated with molecular dynamics

  • Dislocations interact through long (~1/r) elastic fields

  • Dislocations tend to cluster and form patterns

  • Dislocations multiply by several orders of magnitude during plastic processes

  • Strong near field interactions lead to discontinuous topological events

Edge Dislocation J.P. Hirth

Frank Read Source W.C. Dash


Development of paradis l.jpg
Development of ParaDiS interactions and patterning

The Parallel Dislocation Simulator is a line dynamics code developed at LLNL to directly simulate materials strength and strain hardening

  • Physics Features

    • A non-singular theory of dislocations has been developed

    • New treatment of dislocation core reactions

  • Parallel-Computation Features

    • Order-N methods for force calculations using a fast multipole method

    • Adaptive mesh refinement algorithm that optimizes geometric discretization

    • Time varying spatial domain decomposition for dynamic load balancing

The ParaDiS project combines a unique code on our unique massively parallel platforms


Dislocation dynamics distills the atomic degrees of freedom into dislocation degrees of freedom l.jpg
Dislocation Dynamics distills the atomic degrees of freedom into dislocation degrees of freedom

Fully nodal representation of dislocation network

Algorithm

discretization node

1

physical node

b10

Node force

elastic and core

0

b01

2

b02

b03

Node velocity

material specific

3

Move nodes

topology changes

  • Burgers vector sum rule

  • For each node

  • b01+ b02 + b03= 0

  • For each segment

  • b01+ b10 = 0


Visualization of simulations shows that dislocation patterning may be emerging l.jpg
Visualization of simulations shows that dislocation patterning may be emerging

Multiple dislocation collisions create structures that appear to act as static anchors of the microstructure


Dislocation density evolution analyzed to reveal effect of deformation history and rate l.jpg
Dislocation density evolution analyzed to reveal effect of deformation history and rate

  • Dislocation configurations in a pair of simulations are investigated to reveal the tendency to pattern as a function of deformation rate

  • Dislocations multiply faster at higher deformation rates


Dislocation correlation functions are calculated to quantify structure formation l.jpg
Dislocation correlation functions are calculated to quantify structure formation

  • Patterning is observed with a characteristic wavelength of 2 mm

  • Patterns become weaker with increasing deformation

    • Higher deformation rates lead to weaker patterns


Correlation functions reflect the crystallographic nature of plastic deformation l.jpg
Correlation functions reflect the crystallographic nature of plastic deformation

  • Patterns follow the glide directions of dislocations

  • At lower strain rates patterns persist longer in deformation history


Velocity distributions highlight the difficulty in reaching low strain rates l.jpg
Velocity distributions highlight the difficulty in reaching low strain rates

  • Dislocations do not belong to two distinct populations

    • Velocity distribution is smooth and continuous

  • Distributions have long tails and sharpen as deformation rate is decreased

    • Presents a challenge for time integration at low deformation rates


Coarse graining paradis simulations for common strength and strain hardening models l.jpg
Coarse graining ParaDiS simulations for common strength and strain hardening models

  • Stress strain, dislocation density, and dislocation flux histories are taken as output from which to construct coarse model

    Shown: [111] orientation

    Strainrate = 1e5

    Temperature = 600K

    Pressure = 30GPa


Dislocation density evolution and strength interaction is fit well with three parameters l.jpg
Dislocation density evolution and strength interaction is fit well with three parameters

Dislocation strength interaction fit with one constant to departure of mobility function from ideal behavior

Dislocation evolution fit is found by minimizing an L2 norm error of integrated rate equation


Dislocation strength interactions change with dislocation structure and loading conditions l.jpg
Dislocation strength interactions change with dislocation structure and loading conditions

  • Interaction coefficients change as a function of the character of the dislocation density

    • function of the mobility ratio of edges and screws

  • Interaction coefficient is always larger for the more mobile species

    • Negative interaction coefficients indicate cooperative motion


Building a scientific community in dislocation dynamics l.jpg
Building a scientific community in dislocation dynamics structure and loading conditions

  • Distributed an updated version of ParaDiS to our collaborators – 30+ research groups

    • Improved dynamic load balancing scheme, improved documentation, fixed bugs

  • Launched community web site: paradis.stanford.edu

  • Organizing International Meetings

    • Dislocations 2008 – Hong Kong

    • Multiscale Materials Modeling 2008 Conference -Tallahassee, FL


Future work l.jpg
Future Work structure and loading conditions

  • Performing relaxation simulations to see if patterns are amplified with the removal of load

  • Implementing a fully-implicit time integrator to build a dislocation quasi-statics tool capable of simulating low strain rate behavior

  • Augment formalism to treat partial dislocations

  • Adding capability to simulate dispersion strengthened alloys