Crystal plasticity and hardening: A dislocation dynamics study

Following the publication of several seminal studies, discrete dislocation dynamics has become well-established as a means of analysing the response of ductile crystals and polycrystals to mechanical loading. Developments undertaken by different authors have followed two principal directions: (i) the use of simple 2D formulations that do not seek to capture correctly the details of slip geometry, but allow some insight to be developed into the trends and relationships, and (ii) large scale 3D simulations seeking to represent correctly the geometry of dislocation segments, and their spatial distribution and interaction. The former is computationally inexpensive and fast, but fails to capture the effects of grain orientation. The latter is associated with large overheads in terms of the computational effort. The purpose of the present study is to propose and develop an intermediate level approach, whereby the geometry of the crystal slip is captured to a greater degree, while computational difficulty is kept to a minimum. The results are analysed in terms of the dependence of yield stress and cyclic hardening on the crystal orientation and dislocation interaction with each other and with the grain boundaries.