A STAR-SHAPED CRACK IN A COMPOSITE MATERIAL

Abstract

The stress and displacement fields are determined in the neighbourhood of a star-shaped crack in a composite material. It is assumed that a thin infinite place has been formed by wedges of same vertical angle 2aplha and are even in number. For the sake of simplicity it is assumed that the alternative wedges are elastic and rigid respectively. It is also assumed that there are cracks of unit length originating from the centre of the plate, and that all cracks are opened by the same pressure. By symmetry the problem has been reduced to a mixed boundary value problem for an elastic wedge. Mellin transorm method has been used to reduce the mixed boundary value problem to a simultaneous set of dual integral equations involving inverse Mellin transform. The set of dual equations have been solved in the dase when alpha = pie/2 by solving a pair of coupled Abel integral equations and the quantities of physical importance have been determined. Finally, it is shown that the dual equations of the present paper, for alpha=pie/2, through the Mellin transform reduce to those obtained by Chakrabarthi and Lowengrub through Fourier transform by using the Convolution theorem for Mellin transform. The paper demonstrates further use of integral transforms to crack problems in composite materials.