CYCLIC TORSION WITH INTERNAL PRESSURE OF PRE-STRETCHED THIN-WALLED CYLINDERS

Abstract

The article considers the following two tasks. 1) Strength calculations are carried out for a long thin-walled cylinder, the ends of which are not closed during reloading. At the first loading, the thin-walled cylinder is stretched by a longitudinal force leading to longitudinal plastic deformations. When reloaded, the cylinder twists and at the same time uniform pressure acts from the inside. It is noted that, in particular, the shaft of wind generators is subjected to such loading. It is proved that the equation of the yield curve in the plane of the normal and tangential stresses of the stress space is an ellipse, whose semi axes are a function of the mechanical characteristics of the material and the residual stresses after the first loading. 2) We consider cyclic twisting with internal pressure of pre-stretched thin-walled cylinders. The yield surface equation is obtained for a thin-walled cylinder under repeated loading τ + p. which stretched upon first loading. It is proved that the yield surface equations also yield the fatigue surface equations if the yield stress σ_(T.) is replaced by the fatigue stress σ_(0.) Expressions are found for the number of cycles required for fatigue failure under an asymmetric loading cycle under repeated loading. It is proved that in order to increase the number of cycles required for fatigue fracture, during the first loading, when the material is strengthened due to plastic deformation, and with repeated cyclic loading, the same stress components must take place. It is proved that if during repeated loading the end of the loading path is inside the endurance surface, then the number of cycles required for fatigue failure in an asymmetric loading cycle tends to infinity. Keywords: Initial loading, reloading, cyclic loading, strength, fatigue failure, plastic deformation, residual stress, yield surface.