Problem of two coplanar Griffith cracks running steadily under three-dimensional loading

Abstract

In this paper, the three-dimensional problem of two coplanar Griffith cracks propagating uniformly in an elastic medium has been considered. Equal and opposite tractions which are triaxial in nature are applied to the crack surfaces. The two-dimensional Fourier transforms have been used to reduce the mixed boundary value problem to the solution of triple integral equations. In order to solve the problem, the transformed surface displacement has been expanded in a series of Chebyshev polynomials which is automatically zero outside the cracks and also satisfies the edge conditions. Finally Schmidt method has been used to determine the unknown constants occurring in the series. Numerical calculations are carried out to obtain the crack opening displacement and also the stress intensity factors for different values of the parameters.