Numerical analysis of dynamic T stress of moving interfacial crack

Abstract

A method to extract dynamic T stress term of moving interfacial crack is proposed. Anisotropic bimaterial which has subsonic crack propagation is considered, and interaction energy method is applied. Stress fields by the constant T stress and stress fields by the point force moving with the crack are obtained by using the series expansion method and Stroh formalism. J based interaction energy (P) between the constant T stress and the point force is calculated by Yeh formulation and the relation between interaction energy and T stress is obtained. Energy release rate and T stress of a moving interfacial crack are calculated numerically. Elastodynamic finite element code is developed to investigate fracture parameters for the propagating crack. Four nodes linear elastodynamic element is used and Newmark formulae are applied to integrate displacement and velocity. Node release method is adapted to simulate crack propagation along the interface. The energy release rate is calculated in the area moving with crack. T stress term is calculated from the interaction energy with a stress field formed by the moving point force. Five examples are solved to show the validity and time history of energy release rate and T stress. The energy release rate calculated from numerical analysis agrees well with an analytic solution and experimental results. The T stress of homogeneous specimen under the steady state condition shows a slightly different value compared with the stationary result. It is observed that the T stress of polymethyl methacrylate-steel specimen shows continuous change and the T stress of aluminum-polymethyl methacrylate specimen shows discontinuous jump when the initial crack initiates. From the result of the variation of T stress, the effect of T stress on the stability of crack propagation is observed.