THE ANNULAR CRACK IN A NONHOMOGENEOUS MATRIX SURROUNDING A FIBER UNDER TORSIONAL LOADING .1. INNER CRACK-TIP AWAY FROM OR TERMINATING AT THE INTERFACE

The axisymmetric problem of an elastic fiber perfectly bonded to a non homogeneous elastic matrix which contains an annular crack surrounding the fiber under axially symmetric shear stress is considered. The pro blem is formulated in terms of a singular integral equation with a Cau chy type kernel. When the inner crack tip terminates at the interface with discontinuous modulus, the stress singularity is not -1/2. Stress intensity factors are given when the inner crack tip is away from and at the interface.