Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. With increasing demand for specialized lightweight, high strength structures, failure of inhomogeneous solids has been receiving increased attention. Such inhomogeneous solids include structural composites such as bonded and sandwich structures, layered and composite materials as well as functionally graded solids. Many of such solids are composed of brittle constituents possessing substantial mismatch in wave speeds, and are bonded together with weak interfaces, which may serve as sites for catastrophic failure (Rosakis and Ravichandran (2000)). In the present study numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes is presented. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) rate sensitivity. To describe suitably the time and temperature dependent effects observed experimentally during dynamic loading processes the kinetics of microdamage has been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic–plastic response can be obtained. The identification procedure is developed basing on the experimental observations. The finite difference method for regularized elasto-viscoplastic model is used. The edge-cracked bimaterial specimen is considered. In the initial configuration, the height of the specimen is equal to 30 cm, width is 12.5 cm and the length of the initial crack is equal to 2.5 cm. The length of the boundary over which impact is applied is equal to 5 cm, the rise time is fixed at 0.1 ls and the impact velocity is varied. The impact area is localized symmetrically or asymmetrically to the shorter axis of the specimen (symmetry axis of the cohesive band). Basing on the available data of recent experimental observation Rosakis et al. (1999) that have been carried out for relatively thin specimens both the plane stress and plane strain conditions are considered. The material of the specimen is AISI 4340 steel, while PMMA is the cohesive band, both modelled by thermo-elasto-viscoplastic constitutive equations with effects of isotropic hardening and softeninggenerated by microdamage mechanisms and thermomechanical coupling. Fracture criterion based on the evolution of microdamage is assumed. Both, isothermal and adiabatic processes are considered. Particular attention is focused on the investigation of the interactions and reflections of stress waves and the influence of these waves on the propagation of macrocrack within the interface band. The propagation of the macroscopic crack within the material of the interface band for both symmetrical and asymmetrical impact cases has been investigated. It has been found that macrocrack-tip speeds vary from the shear wave speed to the dilatational wave speed of the material and is higher than the Rayleigh surface wave speed. This result is in accord with the experimental observations performed by Rosakis et al. (1999