Effective mobility of BCC dislocations in two-dimensional discrete dislocation plasticity
Two-dimensional discrete dislocation plasticity (2D-DDP) has shown to be a powerful tool for studying micro-plasticity problems such as size effects in single crystals, fracture of bimaterial interfaces, delamination of thin films, fatigue crack growth etc. The power of 2D-DDP lies in the application of edge dislocation dipoles as the vehicle for plastic slip. The loss of accuracy in the description of dislocation structures compared to full 3D simulations is counter-balanced by its computational simplicity and the possibility to reach larger plastic strains. The constitutive rules for dislocation evolution in 2D-DDP used so far are tuned to FCC crystals. Extending the 2D-DDP framework to study BCC micro-plasticity problems requires modification of the existing constitutive rules. One of the key challenges in extending the method to BCC materials is that, contrary to FCC, the mobilities of edge and screw dislocations in BCC crystals differ vastly from each other, so that the screw mobility will be rate limiting the plastic slip. Thus, a method is required to map the edge and screw mobilities of dislocation loops into an effective mobility to be used in 2D. To do so, we here propose a 3D-to-2D procedure that is based on the notion of conservation of plastic strain rate. The consequence of this approach is that the effective 2D mobility for FCC crystals is not simply equal to the uniform mobility of a dislocation loop, as has been assumed by all 2D models to date, but also on the size of edge dipoles. In order to assess the consequences of this departure from the current literature, we considered a few key problems involving plasticity size effects and crack growth, and compared the predictions assuming constant mobility versus the proposed effective mobility. After observing that, overall, the predictions do not deviate substantially, we proceed with application of the 3D-to-2D procedure to compute the effective 2D mobility for BCC materials based on their edge and screw mobilities. The validation of the approach is done by comparison of the predicted rate sensitivity of polycrystalline iron with the experimental rate sensitivity at room temperature, which are found to be in fairly good agreement.