Advanced phase field approach to dislocation evolution
Mahdi Javanbakht (Iowa State University), Valery Levitas (Iowa State University)
Discrete Dislocation Plasticity
Tue 2:40 - 4:00
RI Hall 108
Phase field approach (PFA) to dislocation evolution was developed just during the last decade and it is widely used for the understanding of plasticity at nanoscale. Despite significant success, there is still a number of points for essential improvement: (a) All of previous studies are based on small strain formulation. At the same time, plastic shear for n dislocations is of the order of 0.5 n, which is huge for multiple dislocations. (b) The equilibrium value of the order parameters for dislocations (and consequently, the Burgers vector) depend on stress tensor . (c) The dislocation height H is not defined by a theory but equal to the mesh size; i.e., the theory is in principle not objective and leads to mesh-dependent solutions. This is because the component of the gradient of normal to the dislocation plane, does not contribute to the energy, leading to zero width of the interface between the dislocation band and the rest of a crystal. In our work, a new PFA to dislocation evolution is developed. It is objective and based on fully large-strain formulation. Our local potential is designed to eliminate stress-dependence of the Burgers vector and to reproduce desired local stress-strain curve, as well as to obtain the mesh-independent H for any dislocation orientation. Our gradient energy contains an additional term, normal to the dislocation, which excludes localization of dislocation within height smaller than H but disappears at ; thus, it does not produce interface energy and does not lead to a dislocation widening. Problems for nucleation and evolution of multiple dislocations along the single and multiple slip systems, and the interaction of dislocations with an austenite - martensite interface are studied. A similar approach can be developed for partial dislocations and expended for dislocation reactions. Levitas V.I. and Javanbakht M. PRB, Rapid Communication, 2012, 86, 140101(R).