Analysis of various equivalent stress options for describing the creep rupture process under a complex stress state

Abstract

Three basic and two equivalent stresses complicated by a parameter are considered. The basic equivalent stresses are the maximum normal stress, the von Mises equivalent stress, and the double maximum shear stress. To determine the effect of each basic equivalent stress on the time at the time of failure, their two linear combinations with one material parameter are considered. One of them is a combination of the maximum normal stress and the von Mises equivalent stress (proposed by A. Lebedev, 1965). The other is a combination of the maximum normal stress and the doubled maximum shear stress (proposed by V. V. Nazarov, 2019). The results of lengthy tests of tubular specimens under the action of the axial force and torque are analyzed to determine which variant of the equivalent stress better describes the process of long-term strength, as well as to establish the effect of each basic equivalent stress on the time at the moment of failure in a complex stress state. The unknown parameters are calculated by finding extrema through the solution search menu (Microsoft Office Excel), where the minimum error is taken as the target condition. From the analysis of the errors of the total discrepancy between the experimental data and the approximation in the form of the power dependence between the time at the time of failure and the nominal equivalent stress, it has been found that a linear combination of the maximum normal stress and the doubled maximum shear stress in all the cases considered offers the best approximation of the long-term strength process. From the analysis of the values of material parameters in complicated equivalent stresses, it is not possible to extend the effect of each maximum stress on all the considered series of lengthy tests.