NUMERICAL SIMULATION OF DISCRETE DISLOCATION DYNAMICS: EFFECTS OF TIME STEP INTEGRATION

F. LANGHI; P.J SÁNCHEZ; A.E. HUESPE

Barrcelona

Congreso; Computational Plasticity XI Fundamentals and Applications, Barcelona, Spain, September 2011; 2011

Following the works of Van der Giessen, Needleman and co-workers, we have developeda numerical 2-D model for simulating the dislocation dynamics occurring in a crystal, during a plasticdeformation 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]), theinteraction 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 rather large numberof dislocations is chaotic, we shown in this contribution that by adopting an alternative time integrationscheme, it is possible to get more accurate results with larger integration time steps. The principalcontribution of this paper is the new integration scheme.As a first analysis, we compare the numerical response of the dislocation system, i.e. the instabilitybehavior reported in [2], using both integration procedures: i) the explicit one proposed in [3] and ii) thenew 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 resolutionof the dislocation pileup has a very important effect in capturing the yield stress of the dislocationsystem. Again, this test is performed with both integration schemes. We compare the computationalcosts required in each case.Finally, a third study corresponds to the numerical simulation of a single crystal specimen (2D), witha random distribution of sources and obstacles, subjected to uniaxial tension and bending. These resultsfollow closely that reported in Cleveringa et al. ([2]).