Elastic-Plastic Torsion of a Multilayered Rod

The article is devoted to elastic-plastic torsion of a multilayered rod under torque. It is assumed that the rod consists of several layers. Each layer has its own elastic properties, but the plastic properties of both layers are the same. For simplicity, a three-layer rod is considered. The contact boundaries of the layers are located along the x-axis. The lateral boundary of the rod is free of stresses, the displacements and stresses are continuous at the interlayer boundaries. The stress tensor components at a point are calculated, using the contour integrals obtained from the conservation laws calculated on the edge of the cross section. Then, the second invariant of the stress tensor is compared with the yield strength. At the points where the yield strength is reached, the plastic state occurs, and the remaining parts are elastic. This lets us construct a boundary between the plastic and elastic regions. This method provides a way to calculate the elastic-plastic boundaries for the standard rolled profiles of rods. This issue will be considered in future studies. It should be noted that previously, using the conservation laws, the main boundary value problems were solved for the plastic two-dimensional medium, elastic-plastic torsion of isotropic rods and elastic media for finite-sized bodies.