On separation of a rigid linear inclusion (Q2754726)

Homogeneous isotropic matrix containing a finite rigid inclusion is loaded at infinity by uniform tensile loads parallel to inclusion. In the vicinities of inclusion tips, zones of plastic flow are developed. Strips of plastic flow are modelled by sliding cracks under prescribed tangential stresses on their surfaces. First, the corresponding mixed boundary value problem of elasticity is solved by the Kolosoff-Muskhelishvili technique. Under the assumption that energy of separation per unit length is constant, a first-order differential equation for determination of the critical load is obtained. A formula for the working length of inclusion depending on the number of cycles load is derived.