The torsion problem of a cylindrical solid taking into account the material weakening

The weakening of the material begins reaching a critical level of stress state, is characterized by a decrease in the level of stress during growing deformations and can develop with an equilibrium accumulation of structural damage. The equilibrium accumulation of damage is possible if the given displacements of the boundary points are provided (that is, with “hard” loading) and if the rigidity of the loading system is sufficient. The design becomes unable to withstand the load only when zones with weakened connections are developed enough. Therefore, taking into account the full deformation diagram in the calculations allows to more accurately determine the load bearing capacity of the design. This paper gives an analytical solution for the problem of a homogeneous cylindrical solid torsion with a circular cross section with its hard loading taking into account the material weakening. Piecewise linear approximations of elastic and elastoplastic medium with a linear weakening at the supercritical deformation stage are considered. The diagrams are plotted regarding stress distribution over the cross section are given; the graphs of the maximum torque value and the extreme value of the relative angle of rotation on the parameters of the deformation diagram. The dependences of the torque on the relative angle of rotation of the sections for the stage of initial supercritical deformation, as well as the stage of supercritical deformation and fracture are determined. The graphs of the dependence of torque on the angle of rotation of the section are given. Reserves of the load bearing capacity of the design are identified. It is noted that taking into account the weakening of the material is expedient in strength calculations and in determination of the system’s safety factor.