The processes of complex loading structural steel for a five-link piecewise broken strain path

The paper proposes a mathematical model of the theory of elastoplastic processes for the variety of strain paths such as multi-link straight-line polygonal paths. The constitutive equations of the proposed mathematical model, as well as the methodology of experimental studies, are based on the vector representation of the strain and stress proposed by Ilyushin. In the mathematical model, the approximations of the functional are used, which depend on all parameters of the inner geometry of the strain path. The governing equations of the mathematical model are reduced to the Cauchy problem. A numerical solution to the latter and the calculated results are obtained using the fourth-order Runge-Kutta method.
The experimental data on the complex loading (combined tension-compression and torsion) of a thin-walled tubular sample made of steel 45 according to a deformation program consisting of five straight sections with different break angles of the strain path are presented. The vector and scalar properties of the material are studied.
A mathematical model of the theory of elastoplastic processes is verified by comparing the calculated results with the data of a physical experiment. It is shown that the applied mathematical model gives a qualitatively and quantitatively satisfactory description of the main effects of a complex plastic straining for the variety of strain paths such as multi-link polygonal strain paths.