Dislocation Dynamics and Strain Hardening in Metals
Nicolas Bertin, Hamed Akhondzadeh
A long-term goal of our group is to use dislocation dynamics (DD) simulations to predict the stress-strain curves of metals and alloys. In particular, we are interested in the strain-hardening behavior, in which the stress required to deform the material (beyond yield point) continues to rise with increasing strain. For this purpose, we use and continue to develop the ParaDiS simulation program.
In a DD simulation, a dislocation network is discretized into a large number of segments. At every time step, the forces on the segments are computed based on elasticity theory. The velocities of the segments are computed based on the forces and the network evolves by the motion of the dislocation segments, as well as reactions (e.g. annihilation, junction formation).
The bottleneck of current DD simulations lies in its very high computational cost. So the stress-strain curves can be predicted up to a very small amount of strain (e.g. ~1%) under typical conditions. Our long term goal is to develop more efficient parallel algorithms and take advantage of advanced computing architectures (e.g. coprocessors, GPUs) to enable the prediction of the σ(ε) curves to much higher strains (e.g. 10%). We are also interested in developing continuum theories of plasticity based on information gained from DD simulations (e.g. by analyzing the structure of dislocations network).
The following figure shows a snapshot of a DD simulations and the predicted stress-strain curve for single crystal Cu deformed along the  direction.