Stress analysis in a sheet with multiple cracks

Abstract

• Three- dimensional formulation of elasticity is used to derive dislocation solution in an elastic sheet. • Integral equations are constructed for multiple interacting cracks. • Numerical solution for the integral equations are carried out for a single and two Interacting cracks. • Contrary to two-dimensional problems modes II and III fracture occur simultaneously. • The stress intensity factors vanishes at a crack corners. The stress field due to the presence of a Volterra dislocation in an isotropic elastic sheet is obtained. The stress components exhibit the familiar Cauchy type singularity at dislocation location. The solution is utilized to construct integral equations for elastic sheets weakened by multiple embedded or edge cracks. The cracks are perpendicular to the sheet boundary and applied traction is such that crack closing may not occur. The integral equations are solved numerically and stress intensity factors (SIFs) are determined on a crack edges.