A lamellar inhomogeneity near a multiphase reinforcement

Abstract

In composites, the stress intensity factors (SIFs) of a lamellar inhomogeneity near a multiphase reinforcement are of interest. Based on extension of Eshelby’s equivalent inclusion method, a unified approach is presented to study the effect of a multiphase inhomogeneity on the SIF at the tip points of two- and three-dimensional lamellar inhomogeneities under nonuniform far-field loadings. Alteration of the SIF due to the presence of a coating layer around the inhomogeneity is addressed. Furthermore, the effect of geometry and stiffness of each phase of a multiphase reinforcement on the mixed mode SIFs of a lamellar inhomogeneity is investigated. In contrast to cracks whose SIFs are the same for uniaxial and multiaxial far-field loadings, all axial far-field applied stresses, which are parallel or perpendicular to the anticrack plane, result in the square root stress singularity at the anticrack tip points. However, only those components of the far-field shear stress whose couple vector is perpendicular to the anticrack plane would generate nonvanishing mixed mode SIFs, whereas for the shear components with couple vectors parallel to the anticrack plane, the SIF vanishes.