Exact Analysis of Mode-III Cohesive Fracture of a Cylindrical Bar in Torsion

Abstract

Abstract The mechanics of mode-III defect initiation and quasi-static growth is examined by analyzing a torqued cylindrical bar separated at its midsection by a nonuniform, nonlinear cohesive interface. The exact analysis is based on the elasticity solution to the problem of a cylinder subjected to nonuniform shear traction at one end and an equilibrating torque at the other. The formulation leads to a pair of interfacial integral equations governing the relative rigid body rotation and the interfacial separation field. The cohesive interface is assumed to be modeled by three Needleman-type traction–separation relations characterized by a shear strength, a characteristic force length and, depending on the specific law, other parameters. Axisymmetric penny, edge, and annular interface defects are modeled by a strength function which varies with radial interface coordinate. Infinitesimal strain equilibrium solutions are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. Results show that for increasing remote torque, at small values of force length, brittle behavior occurs that corresponds to sharp crack growth. At larger values of force length, ductile response occurs similar to a linear “spring” interface. Both behaviors ultimately give rise to the failure of the interface. Results for the stiff, strong interface under a small applied torque show excellent agreement with the static fracture mechanics solution of Benthem and Koiter (1973, “Asymptotic Approximations to Crack Problems,” Mechanics of Fracture, Vol. 1, G.C. Sih, ed., Noordhoff, Leyden, pp. 131–178) for the edge cracked, torsionally loaded cylindrical bar. Extensions of the theory are carried out for (i) the bi-cylinder problem and (ii) the decohesive, frictional interface problem.