Mathematical model and numerical analysis method for dynamic fracture in a residual stress field

Residual stress field is a self-equilibrium state of stress in the bulk solid material with the inhomogeneous field of the inelastic deformations. The high level of tensile residual stress often leads to dynamic fracture resulting in the instantaneous and catastrophic destruction of the materials because the cracks are fed with the strain energy initially stored in the bulk materials due to the residual stress. The dissipation of the strain energy with crack growth results in the release and the redistribution of the residual stress. In this paper, we propose an effective mathematical model and a numerical analysis method for dynamic fracture in residual stress field. We formulate the dynamic behavior of solid continuum with residual stress field in the context of particle discretization scheme finite element method. This formulation enables the appropriate evaluation of (i) release and redistribution of residual stress due to dynamic propagation of the cracks and (ii) the effect of the elastic wave on crack propagation, which are the most substantial problems on dynamic fracture in residual stress field. We perform the experiments and the simulations of dynamic fracture process in chemically tempered glass sheets with residual stress field to validate the proposed numerical analysis method. The simulation results show remarkable agreement with the experiments of the catastrophic failure of the glass sheets with residual stress field in all aspects of crack behavior. These results indicate that the proposed model and method can rigorously evaluate the release and the autonomous redistribution of the residual stress in the dynamic fracture process.