Stress intensification due to the crack outside/inside a finite fiber in 3-D elastic matrix

Abstract

The influence of an elastic inclusion in the shape of cylindrical fiber with rounded edges on an elliptic (penny-shaped) crack under the remote load of surrounding infinite elastic matrix is investigated. A crack lying both in a matrix and in a fiber is involved into analysis. The corresponding 3-D problem is numerically simulated by the improved boundary integral equation method. To this end, the strongly singular boundary integral equations on the matrix–fiber interface and the hypersingular boundary integral equations on the crack-surface are transformed into new form, where the solution behavior near the crack front is accounted implicitly. This modification allows the direct determination of the stress intensity factors in the crack vicinity after solution of equations by the collocation technique. Numerical examples concern symmetric problem for the crack which is perpendicular to the axis of fiber, the uniform tensile loading at infinity along the fiber axis is applied to the matrix. The shielding or amplification effects of the fiber on the crack is analyzed by the mode-I stress intensity factor depending on the crack location and distance relative to the interface, the elliptic crack aspect ratio, the fiber length and the material combination of the matrix and the fiber. The situations with a spherical inclusion and penny-shaped crack are considered as the particular cases and compared with the known results.