Longitudinal Shearing of a Weakly Bonded Fiber Composite

The longitudinal shearing of a unidirectional fiber composite which sustains slippage at the fiber-matrix interface is studied theoretically. An expression for the effective shear modulus of the composite, assuming a dilute concentration of fibers, is derived. The necessary quantities are found from the solution to the problem of a single slipping fiber in an infinite matrix. A singular integral equation governing this problem is derived and solved numerically. Results for the progression of slip and for the effective shear modulus are presented.