Studies on Path Independent Integrals in Nonlinear Dynamic Fracture Mechanics

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Recently we have derived a path independent integral <T^*> which may give a unified theoretical background for linear (elastic) and nonlinear (elastoplastic) dynamic fracture mechanics. In this respect it is very important to find the relations between <T^*> integral and fracture process zone which exists in the vicinity of the crack-tip. In this research project, the invariance of <T^*> integral with respect to the shape of process zone was analytically and numerically verified.First, for an elastodynamically propagating crack, only the <T^*> integral (or equivalently J' integral which has the physical meaning of energy release rate) gives an invariant integral calue regardless of the shape of infinitesimal process zone. Other types of path independent integrals which are not equivalent to the energy release rate, depend on the shape of process zone. Furthermore, in the results of finite element simulation, it was found that the <T^*> integral closely relates with the energy flow into … More the process zone.For the finite element simulation of dynamic crack propagation, a comparison was made on stationary mesh procedure with various nodal release mechanisms and a simple moving mesh procedure. For elastic problems the stress intensity fractures were evaluated by the path independent J'integral. For simple moving mesh procedure is better suited for the simulation of elastodynamic crack propagation although difficulties were observed in the application of moving mesh procedure to elastoplastic dynamic crack propagation. Among the model release schemes, the linear relaxation scheme gives best results for elastodynamic as well as elastoplastic dynamic crack propagation.For cracks subject to various impact stress waves, the behavior of <T^*> integral was also investigated. In the case of a step-type stress wave loading, <T^*> integral varies linearly with time variation for any constitutive models including linear-elastic, elastic -viscoplastic and rate-independent elastoplastic cases. As the fluidity parameter of material increases, the time-slope of <T^*> integral becomes smaller and approaches to the rate-independent plastic behaviorIt was also found that the experimental measurement of <T^*> integral can be done by measuring the area under the load versus crack-opening displacement curve in an compact tension specimen. Less