Loading analysis of thick-walled shells in Ilyushin stress space during autofrettage

The study is devoted to the problem of applying the method of variable elasticity parameters, which uses the provisions of the deformation theory of plasticity, to solving problems of autofreting cylindrical shells loaded with internal pressure. The paper considers two cases of autofreting thick-walled cylindrical shells: with longitudinal stretching and without longitudinal stretching. When determining the stress-strain state, the shell material was considered incompressible and dependencies in the form of a power function and linear power functions were used to describe the deformation diagram of the material. The analysis of the loading process was carried out by studying the loading trajectories of various points of the shell wall in the Ilyushin stress space and the Nadai–Lode parameter for stresses. As studies have shown, in the case of autofreting with longitudinal tension, as well as when loading the shell with internal pressure up to destruction, loading is simple for all functions describing the deformation diagram, which proves the validity of solving such problems by the method of variable elasticity parameters. When autofreting the shell without longitudinal stretching, using a power approximation of the deformation diagram, the loading process up to destruction can be considered simple, which corresponds to Ilyushin’s theorem on simple loading. With the linear-power approximation of the deformation diagram, the process of loading the shell is not simple, but a comparative analysis of the stress state obtained with the power-law and linear-power approximation of the deformation diagram showed a slight difference at all stages of loading. Moreover, these differences decrease with increasing pressure, which allows us to conclude that the method of variable elasticity parameters can be applied to solving problems of autofreting cylindrical shells without longitudinal stretching, as well as loading such shells with internal pressure up to destruction.