We suggest the phenomenological method of reconstructing the fields of residual stresses and plastic deformations in thin-walled cylindrical tubes made of Х18N10Т steel in the delivery state and after a simultaneous bilateral surface plastic hardening by the vibration-shot blasting of the surface with beads on a special vibrating stand. A cylindrical container filled with three-millimeter beads was attached to it. The tubes were 50 % filled with one-millimeter beads, and they were placed inside the container. The axis of the tube and the container coincided. The space between the tube and the container was 80 % filled with beads. The vibrational frequency of the stand was 18.5 KHz, the hardening time was 20 minutes. The tube in the container was rotated to ensure uniform hardening. We determined the experimental values of residual stresses σθ and σ z in the surface layers using the method of rings and strips with the procedure of the layer-by-layer electrochemical picking of the hardened layers. For this purpose, the experimentally measured values of the beam-strip deflection and the angular opening of the cut ring (changing the diameter) were used. The hardening anisotropy parameter which relates the axial and circumferential components of plastic deformation was introduced into the mathematical model. In solving the stated problems the hypotheses of plastic incompressibility of the material, the absence of secondary plastic deformations of the material in the compression region of the surface layer, as well as the hypothesis of flat sections and straight radii were used. We described the method aimed at solving this type of boundary value problems of reconstructing stress-strain states, which makes it possible to determine the missing component σ r and all the components of the tensor of residual plastic deformations (off-diagonal components of the tensors of stresses and deformations were not considered). The method of reconstructing the stress-strain state is universal, because it has shown its operability both in determining the technological fields of residual stresses, as well as the irreversible strains in the samples in the delivered state after mechanical operations, and after bilateral surface plastic deformation. The adequacy of the calculated data was verified, which was obtained using the phenomenological method of reconstructing the stress and strain fields of the experimental data for the samples in the delivery state and after hardening. The correspondence of the calculated and experimental data was matched. The numerical values are given for the anisotropy parameter connecting the circumferential and axial irreversible strains, for samples, in the delivery state, its numerical value is 0.1, and, for the hardened samples, it is 4.2. This indicates a significant anisotropy of the distribution of the axial and circumferential components of the residual strain tensor. It has been established that the compressive residual stresses are observed in the delivery state in the region adjacent to the inner surface, and the tensile stresses are observed in the layer on the outer surface. Only compressive stresses are observed in both regions after hardening, which significantly exceed in module similar stresses for the samples in the delivery state. The main results are illustrated by the tabular data and the corresponding diagrams of the distribution of residual stresses along the depth of the hardened layer.
The method of reconstruction of residual stresses and plastic deformations in thin-walled pipelines in the delivery state and after bilateral vibro-shock surface hardening with a shot
