Dislocation Patterns – Fractals or Cells? February 20, 2008

1. 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

2. 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

3. 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

4. Computational Grand Challenge of Simulating Dislocations • 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

5. Development of ParaDiS 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Building a scientific community in dislocation dynamics • 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

16. Future Work • 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