Mode III Cohesive Fracture of a Cylindrical Bar in Torsion

摘要

This paper examines the mechanics of mode III defect initiation and quasi-staticgrowth by analyzing a torqued cylindrical bar separated at its midsection by anonuniform, nonlinear cohesive interface. The analysis, which is exact, is based on theelasticity solution to the problem of a cylinder subjected to a nonuniform sheartraction at one end cap and an equilibrating torque at the other. The formulation leadsto a pair of interfacial integral equations governing the rigid body rotation and theinterfacial slip field, i.e., the jump discontinuity in circumferential displacement acrossthe interface at midsection. The cohesive interface is assumed to be modelled by aNeedleman-type force-slip relation characterized by a shear interface strength and acharacteristic force length. Radially symmetric interface defects are modeled by ashear interface strength which varies with radial interface coordinate. Infinitesimalstrain equilibrium solutions, which allow for rigid body rotation, are sought byeigenfunction approximation of the solution of the governing interfacial integralequations.Solutions indicate that quasi-static defect initiation and propagation occur underincreasing remote torque. For small values of characteristic force length, brittlebehavior occurs that is readily identifiable with the growth of a sharp crack. At largervalues of force length ductile response occurs which is more characteristic of a linear“spring” interface. Both behaviors ultimately give rise to abrupt failure of theinterface. Results for the stiff, strong interface under a small applied torque showconsistency with the static fracture mechanics solution of Benthem and Koiter [1] forthe torsionally loaded cylindrical rod containing an annular crack The final section ofthe paper discusses preliminary results for the maximum principal stresses andassociated principal planes which are used to help clarify the issue of the initiation ofan array of oblique tensile cracks at the crack tip.