Meijie Tang

Enabling strain hardening simulations with dislocation dynamics

Numerical algorithms for discrete dislocation dynamics simulations are investigated for the purpose of enabling strain hardening simulations of single crystals on massively parallel computers. The algorithms investigated include the /(N) calculation of forces, the equations of motion, time integration, adaptive mesh refinement, the treatment of dislocation core reactions, and the dynamic distribution of work on parallel computers. A simulation integrating all of these algorithmic elements using the Parallel Dislocation Simulator (ParaDiS) code is performed to understand their behavior in concert, and evaluate the overall numerical performance of dislocation dynamics simulations and their ability to accumulate percents of plastic strain.

Dislocation multi-junctions and strain hardening

At the microscopic scale, the strength of a crystal derives from the motion, multiplication and interaction of distinctive line defects called dislocations. First proposed theoretically in 1934 (refs 1–3) to explain low magnitudes of crystal strength observed experimentally, the existence of dislocations was confirmed two decades later. Much of the research in dislocation physics has since focused on dislocation interactions and their role in strain hardening, a common phenomenon in which continued deformation increases a crystals strength. The existing theory relates strain hardening to pair-wise dislocation reactions in which two intersecting dislocations form junctions that tie the dislocations together. Here we report that interactions among three dislocations result in the formation of unusual elements of dislocation network topology, termed ‘multi-junctions’. We first predict the existence of multi-junctions using dislocation dynamics and atomistic simulations and then confirm their existence by transmission electron microscopy experiments in single-crystal molybdenum. In large-scale dislocation dynamics simulations, multi-junctions present very strong, nearly indestructible, obstacles to dislocation motion and furnish new sources for dislocation multiplication, thereby playing an essential role in the evolution of dislocation microstructure and strength of deforming crystals. Simulation analyses conclude that multi-junctions are responsible for the strong orientation dependence of strain hardening in body-centred cubic crystals.

Scalable Line Dynamics in ParaDiS

We describe an innovative highly parallel application program, ParaDiS, which computes the plastic strength of materials by tracing the evolution of dislocation lines over time. We discuss the issues of scaling the code to tens of thousands of processors, and present early scaling results of the code run on a prototype of the BlueGene/L supercomputer being developed by IBM in partnership with the US DOE’s ASC program.

A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics

Dislocations intersecting free surfaces present a challenge for numerical implementation of traction-free boundary conditions in dislocation dynamics simulations. The difficulty arises when singular analytic expressions of dislocation stress fields need to be used in combination with numerical methods to calculate image stress fields due to the free surfaces. A new hybrid method is developed here in which the singular and non-singular parts of the image stress are dealt with separately. The analytic solution for a semi-infinite straight dislocation intersecting the surface of elastic half-space is used to account for the singular part of the image stress, while the remaining non-singular part is treated using the standard finite element method. The numerical advantages of this decomposition are demonstrated with examples.

Simulation and modelling of forest hardening in body centre cubic crystals at low temperature

In body centred cubic (bcc) crystals at low temperatures, the thermally activated motion of screw dislocations by the kink-pair mechanism governs the yield properties and also affects the strain hardening properties. In this work, the average strength of dislocation junctions is derived and numerically estimated in the case of Nb and Ta crystals. This allows us to extend an existing simulation of dislocation dynamics in bcc crystals to the case of the motion of a screw dislocation line through a random distribution of forest obstacles. Numerical results are presented in the case of Ta crystals and at two temperatures, 160 K and 215 K. They are complemented by a simple model that applies quite generally to bcc metals at low temperatures. It is shown that forest hardening is made up of two contributions, a free-length effect that depends on the length of the mobile screw segments and whose dependence on forest obstacle density is logarithmic and a line tension effect linearly proportional to the obstacle density. As a result of the thermally activated character of screw dislocation mobility, the relative weight of the two contributions to forest hardening depends on the temperature and strain rate.

Massively-Parallel Dislocation Dynamics Simulations

Prediction of the plastic strength of single crystals based on the collective dynamics of dislocations has been a challenge for computational materials science for a number of years. The difficulty lies in the inability of the existing dislocation dynamics (DD) codes to handle a sufficiently large number of dislocation lines, in order to be statistically representative and to reproduce experimentally observed microstructures. A new massively-parallel DD code is developed that is capable of modeling million-dislocation systems by employing thousands of processors. We discuss the general aspects of this code that make such large scale simulations possible, as well as a few initial simulation results.

Simulations on the growth of dislocation density during Stage 0 deformation in BCC metals

This study focuses on modelling the behaviour of single crystal tantalum in Stage 0 characterized by the large activity of edge dislocations and relative inactivity of screw dislocations. The multiplication of dislocation density is investigated using dislocation dynamics (DD) simulations and a dislocation density based continuum model of single crystal plasticity. The DD simulations are used to guide the constitutive development of the continuum model and to determine its material specific parameters. While not all of the material constants needed by the continuum model can be determined, due to the limited strain histories considered in the simulations, interpreting the DD simulations through a dislocation mechanics based continuum plasticity model allows for the efficient extraction of scaling laws controlling the growth of dislocation density.

Dislocation Image Stresses at Free Surfaces by the Finite Element Method

The finite element method has been routinely used to calculate the image stresses of dislocation segments. When these segments intersect with surfaces, the image stresses at the surfaces diverge singularly. At the presence of these singularities, both convergence and accuracy of using the finite element method need to be examined critically. This article addresses these issues with the aim toward the application of dislocation dynamics simulations in thin films.

Tight-binding molecular dynamics simulations on point defects diffusion and interactions in crystalline silicon

Tight-binding molecular dynamics (TBMD) simulations are performed (i) to evaluate the formation and binding energies of point defects and defect clusters, (ii) to compute the diffusivity of self-interstitial and vacancy in crystalline silicon, and (iii) to characterize the diffusion path and mechanism at the atomistic level. In addition, the interaction between individual defects and their clustering is investigated.

Boundary Conditions for Dislocation Dynamics Simulations and Stage 0 of BCC Metals at Low Temperature

In 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.