Stability of postcritical deformation during torsion of thick-walled cylindrical solid

Ensuring the strength, reliability and safety of structures requires studying the issues of inelastic deformation zones occurrence and development which result from equilibrium accumulation of damages. Material postcritical deformation characterized by a decrease in the stress level during growing deformations is one of the damages accumulation effects. Application of postcritical deformation theory basic provisions to carry out structures refined strength analysis with additional deformation and strength reserves identification is expedient. Calculation of softening processes stability related to loading systems rigidity is necessary. Consideration of analytical solutions where occurrence and development of softening zones are taken into account is expedient to illustrate main theoretical positions of postcritical deformation mechanics. The analytical solution to the hollow cylindrical solid torsion problem where material softening stage and loading system rigidity are considered is obtained. Two-link and three-link approximations of the complete material deformation diagram are considered. Diagrams of shear stresses distribution over the cross-section are shown; various postcritical deformation zones development scenarios existence is noted. Loading diagrams are built; torque maximum value dependence on material parameters and rod geometry is defined. The strength and deformation reserves of the structure are revealed. Conditions for complete loading diagram implementation are determined, the loading system rigidity influence is noted. Therefore, rationality and necessity of taking into account material softening stage and loading system rigidity in structural design are concluded.