Elastodynamic Response of a Cracked Fiber-Reinforced Body to a Non-Uniform Transient Plane-Strain Loading

1. Summary

A near-tip, transient, elastodynamic solution is presented for the plane-strain problem of a crack in a fiber-reinforced composite body subjected to a non-uniform loading, which is suddenly and symmetrically applied to the crack faces. Interest is focused on the stress field in the immediate vicinity of the crack edge during a small time-interval right after the application of loading and, therefore, the cracked body is considered of infinite extent and the crack itself of semi-infinite length. The loading consists of a pair of equal, but opposite, line concentrated normal forces which have a step-function time dependence. In this way, the present solution provides the Green’s function for more general cases of spatially/temporally non-uniform loading. The fiber-reinforced composite is modeled as elastic orthotropicwith four different material constants. The mathematical diffraction problem is solved in an exact manner through integral transforms, an analytic-function decoupling technique, asymptotics and convolutions. Our results provide the time variation of the crack-tip stress intensity factor. These results may serve to quantify the fracture resistance of fiber-reinforced composite materials.