Microbranching in mode-I fracture using large scale simulations of amorphous and perturbed lattice models

Shay I. Heizler, David A. Kessler
Department of Physics, Bar-Ilan University, Ramat-Gan, IL52900 Israel
arXiv:1503.08616 [cond-mat.stat-mech], (30 Mar 2015)


   title={Microbranching in mode-I fracture using large scale simulations of amorphous and perturbed lattice models},

   author={Heizler, Shay I. and Kessler, David A.},






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We study the high-velocity regime mode-I fracture instability using large scale simulations. At large driving displacements, the pattern of a single, steady-state crack that propagates in the midline of the sample breaks down, and small microbranches start to appear near the main crack. Some of the features of those microbranches have been reproduced qualitatively in smaller scale studies on both a model of an amorphous materials (via the continuous random network model) and using perturbed lattice models. These previous studies (using ${cal O}(10^4)$ atoms) pointed to the need for performing larger scale simulations (${cal O}(10^6)$ atoms), in order to achieve more physically realistic results. In this study, larger scale simulations were performed using multi-threading computing on a GPU device. First, we find that the microbranching pattern appears to be converging with the lattice width, i.e. the relative width of the microbranch region $delta y/W$ decreases with increasing lattice width ($W$). This is a crucial test if the lattice simulations are to be used as an appropriate model for the experiments. Second, the microbranches using larger scale lattices yield sufficiently large microbranches as to enable a check of the statistics of the microbranches. The simulations reproduce the growth of the size of a microbranch as a function of the crack velocity, as well as the increase of the amplitude of the electrical resistance RMS as a function of the crack velocity. In addition, the simulations yield the correct branching angle of the microbranches, and the power law governing the shape of the microbranches seems to be lower than one, so that the side cracks turn over in the direction of propagation of the main crack as seen in experiment.
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