Quasi-brittle fracture of smooth shafts under torsion (stress-strain-based approach)

The nucleation of an edge annular concentric crack on the surface of a smooth cylinder made of an elastoplastic material with ultimate strain is considered. To obtain critical parameters of quasi-brittle fracture, a coupled (sufficient) fracture criterion of an elastoplastic material is used. Simple relations are obtained for the critical stresses, the length of the prefecture zone and the critical stress intensity factor (SIF) for the mode III fracture. In the framework of the proposed model, the critical SIF obtained by the sufficient criterion is a variable, it depends on the characteristic linear size of the material structure, the parameters of the stress-strain diagram, and the length of the crack. The rule of selecting the parameters of the proposed fracture model for two laboratory experiments is indicated: according to the stress-strain diagram of material under simple shear and critical SIF. The obtained critical parameters are conservative estimates of critical stresses. It is advisable to use these estimates in the calculation of steel structures operating at temperatures below the cold brittleness threshold.