Computational modeling of dynamic fracture and breakdown in disordered media

Mechanism of fracture in amorphous materials is one of the important issues that remain unsolved in materials science and engineering. In a wide range of glassy materials, mechanical deformation usually involves localized shear bands, adiabatic heating and complex fractured surface morphology. These phenomena are connected to the kinetics of fracture or breakdown process. This dissertation reports the recent progress on some disordered models and phenomenological models employed for understanding the mechanism of deformation and fracture in glassy materials.; Several disordered models are used to investigate the effects of disorder and inhomogeneities on dynamics of fracture and breakdown. Using Monte Carlo simulation, we found two-stage kinetics of breakdown process in the disordered Ising models. In short-time regime, the evolution can be described by a universal power-law scaling. At the late stage, the evolution is well explained by the nucleation theory for first-order phase transition. These results are consistent with the finite-size scaling analysis of these models and the observation from experiments. Solvable models such as the mean-field and Gaussian random-field models are analyzed exactly to prove the dynamics of breakdown process.; A phenomenological theory is proposed in particular for deformation of metallic glasses. Based on the concept of free-volume defect, a Ginzburg-Landau free energy functional of deformed amorphous solid is constructed. Fractured surface morphology is modeled by two coupled kinetic equations: one for cracks and another for the defects. Deformation heterogeneity is observed and fracture surface is found to show complex patterns. Langevin equation for free-volume defect, elastic equation with re-constructible boundary and thermal diffusive equation are treated simultaneously to simulate the crack propagation and branching in plane-stress system with a single-edge notch. The shear bands are found to be consistent with experimentally observed shear localization in front of the crack tip. The branching of crack is also observed and the crack tip velocity shows instability when branching occurs.; These works using the computational modeling and simulation contribute a significant part to the understanding of fracture and breakdown process and also extending the knowledge of nonequilibrium dynamical phase transition to the kinetic process during fracture and breakdown process in amorphous materials.