Numerical Simulation of Discrete Dislocation Dynamics: efects of time steo integration

F. LANGHI; P.J. SÁNCHEZ; A.E. HUESPE

Barcelona

Conferencia; XI International Conference on Computational Plasticity Fundamentals and Applications (COMPLAS XI 2011); 2011

ECCOMAS, IACM

Following the works of Van der Giessen, Needleman and co-workers, we have developed a numerical 2-D model for simulating the dislocation dynamics occurring in a crystal, during a plastic deformation process, which is subjected to rather general boundary conditions (see [1-2]). In the original contribution presenting this model (see [1], as also, the paper of Amodeo et al [3]), the interaction between dislocations, obstacles, etc. is simulated using an explicit time integration scheme. Even when in [4] (V. S. Deshpande et al.) it is shown that the interaction between a  ather large number of dislocations is chaotic, we shown in this contribution that by adopting an alternative time integration scheme, it is possible to get more accurate results with larger integration time steps. The principal contribution of this paper is the new integration scheme. As a first analysis, we compare the numerical response of the dislocation system, i.e. the instability behavior reported in [2], using both integration procedures: i) the explicit one proposed in [3] and ii) the new scheme here described; when similar integration time steps are adopted. We also analyze the test proposed in Chakravarthy et al. ([5]), where it is shown that a successful resolution of the dislocation pileup has a very important effect in capturing the yield stress of the dislocation system. Again, this test is performed with both integration schemes. We compare the computational costs required in each case. Finally, a third study corresponds to the numerical simulation of a single crystal specimen (2D), with a random distribution of sources and obstacles, subjected to uniaxial tension and bending. These results follow closely that reported in Cleveringa et al. ([2]).