DDLab Manual 01

Introduction

Professor Wei Cai in the Department of Mechanical Engineering at Stanford University with the team at the Lawrence Livermore National Laboratory has developed the new dislocation simulation code, ParaDiS (Parallel Dislocation Simulator) and DDLAB (Dislocation Dynamics Lab.). Dislocation simulation enables us to control of the simulation conditions and to access the positions of all dislocation lines at each given time. Since the time and length scales in dislocation simulation codes are on the order of seconds and microns, respectively, which are similar with experiments, they can show realistic insights that help answer fundamental questions in small-scale plasticity, such as motion and interaction of dislocations in small volumes. With the use of massively parallel computers, ParaDiS can deal with the large number of dislocations in an effcient way. However, the structure of cods of ParaDiS written by C is quite complicated, code modifications are not easy so DDLAB, a simpler matlab version of ParaDiS was designed. Since MATLAB has built-in commands for computation, DDLab has a much simpler structure than that of ParaDiS.

Although DDLAB does not support the parallel computation, it is enough to deal with simple dislocation problems, for instance, consisting of two or three dislocations. It was created to test new codes before implementation into ParaDiS.

The purpose of this document is to give a brief description of the DDLAB software for end users who are interested in writing input files and running simulations using the software. This document does not provide an exhaustive description of the algorithms in the code, but rather gives a description of necessary elements of the input deck for the code and the execution procedures. If advanced users are interested in the algorithms of the code, they may simply look at the source code. We have tried to write and organize the subroutines in a compact yet readable manner.

Input parameters of DDLab

There are various input parameters in DDLab. In this section, we don't give a detailed expla- nation of each parameter but we explain some. The relation between parameters will be explained in more detail in the following sections.

We can divide all input parameters into the following categories. 1. Dislocation structure : rn, links 2. Mobility : mobility 3. Integrator : integrator 4. Topological changes : lmax, lmin, areamin, areamax, rmax, rann, rntol, doremesh, docollision, desepraration 5. Time controls : totalstpes, dt0 6. Display controls : plotfreq, plim, viewangle, printfreq, printnode 7. Materials constant : MU, NU, Ec, a 8. Miscellaneous : appliedstress, maxconnections

Nodal representation of dislocation structure

Before seeing rn and links, we need to know how to represent dislocation structure in DDLAB. Figure 1: Nodal representation of dislocation structure Fig 1 shows a simple approach that can represent an arbitrary dislocation network. The dislocations are specified by a set of nodes that are connected with each other by straight segments. Each segment has a nonzero Burgers vector. Because the Burgers vector is defined only after a sense of direction is chosen for the dislocation line, we can define bij

Self consistency in DDLab units

The unit system of DDLab input file should be self-consistent. We recommend to input all variables in S.I. units.

For instance, stresses in Pascal, distances in meter, times in seconds and velocities in m/s.

The mobility law is such that $v=M(\sigma \cdot b)$

with b in meter, $\sigma$ in Pascal, and v in m/s. That makes the mobility parameter M in $Pa^{-1}s^{-1}$.

We often use the drag coefficient $B=M^{-1}$ in the mobility law. The unit of $B$ is $Pas$

As another option, we can change the unit for distance (including both nodal positions and Burgers vectors) to nm, whereas the unit for stress is still Pa, the unit of time is still second, and the unit for mobility is still $Pa^{-1}s^{-1}$.