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### Mode III Cohesive Fracture of a Cylindrical Bar in Torsion

#### Abstract

This paper examines the mechanics of mode III defect initiation and quasi-static growth by analyzing a torqued cylindrical bar separated at its midsection by a nonuniform, nonlinear cohesive interface. The analysis, which is exact, is based on the elasticity solution to the problem of a cylinder subjected to a nonuniform shear traction at one end cap and an equilibrating torque at the other. The formulation leads to a pair of interfacial integral equations governing the rigid body rotation and the interfacial slip field, i.e., the jump discontinuity in circumferential displacement across the interface at midsection. The cohesive interface is assumed to be modelled by a Needleman-type force-slip relation characterized by a shear interface strength and a characteristic force length. Radially symmetric interface defects are modeled by a shear interface strength which varies with radial interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body rotation, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. Solutions indicate that quasi-static defect initiation and propagation occur under increasing remote torque. For small values of characteristic force length, brittle behavior occurs that is readily identifiable with the growth of a sharp crack. At larger values of force length ductile response occurs which is more characteristic of a linear â€œspringâ€ interface. Both behaviors ultimately give rise to abrupt failure of the interface. Results for the stiff, strong interface under a small applied torque show consistency with the static fracture mechanics solution of Benthem and Koiter [1] for the torsionally loaded cylindrical rod containing an annular crack The final section of the paper discusses preliminary results for the maximum principal stresses and associated principal planes which are used to help clarify the issue of the initiation of an array of oblique tensile cracks at the crack tip.