Analysis of elliptical cracks perpendicular to the interface of two joined transversely isotropic solids

This paper presents a boundary element analysis of elliptical cracks in two joined transversely isotropic solids. The boundary element method is developed by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of stress intensity factors (SIFs) are obtained by using crack opening displacements. The results of the proposed method compare well with the existing exact solutions for an elliptical crack parallel to the isotropic plane of a transversely isotropic solid of infinite extent. Elliptical cracks perpendicular to the interface of transversely isotropic bi-material solids of either infinite extent or occupying a cubic region are further examined in detail. The crack surfaces are subject to the uniform normal tractions. The stress intensity factor values of the elliptical cracks of the two types are analyzed and compared. Numerical results have shown that the stress intensity factors are strongly affected by the anisotropy and the combination of the two joined solids.