Modeling rapidly growing cracks in planar materials with a view to micro structural effects

Abstract

Dynamic fracture behavior in both fairly continuous materials and discontinuous cellular materials is analyzed using a hybrid particle model. It is illustrated that the model remarkably well captures the fracture behavior observed in experiments on fast growing cracks reported elsewhere. The material's microstructure is described through the configuration and connectivity of the particles and the model's sensitivity to a perturbation of the particle configuration is judged. In models describing a fairly homogeneous continuous material, the microstructure is represented by particles ordered in rectangular grids, while for models describing a discontinuous cellular material, the microstructure is represented by particles ordered in honeycomb grids having open cells. It is demonstrated that small random perturbations of the grid representing the microstructure results in scatter in the crack growth velocity. In materials with a continuous microstructure, the scatter in the global crack growth velocity is observable, but limited, and may explain the small scattering phenomenon observed in experiments on highspeed cracks in e.g. metals. A random perturbation of the initially ordered rectangular grid does however not change the average macroscopic crack growth velocity

Offsetting Losses: Bargaining Power and Rebel Attacks on Peacekeepers

“…One of the most debated is the choice of the strain energy split (Eqs. (4) and (5)). In the split we have used, damage evolution is driven by tensile strain-related energy.…”

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