Asymptotic analysis of a crack in a power-law material under combined in-plane and out-of-plane shear loading conditions

A crack-tip fields for power-law hardening materials under combined in-plane and out-of-plane shear loading conditions are investigated. The governing equations of the asymptotic crack-tip fields are formulated from two stress functions, one for the in-plane stresses and the other for the out-of-plane shear stresses. These stress functions are of separable functional forms of r and /gq, which represent the polar coordinates centered at the crack tip. Perturbations of the governing equations were carried out. The singular behavior and the angular functions of the crack-tip in-plane and the out-of-plane shear stresses obtained from the perturbation analysis agree well with the results of the finite element computations of P and S (J. Mech. Phys. Solids 38, 161, 1990; J. appl. Mech., in press, 1989). In particular, the results from the perturbation analysis indicate that the singularity of the mode I in-plane stresses is slightly stronger than that of the mode III out-of-plane shear stresses under combined mode I and III conditions, whereas the singularity of the mode III out-of-plane shear stresses is slightly stronger than that of the mode II in-plane stresses under combined mode II and III conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28816/1/0000650.pd