Methods of construction of the generalized hardening curve

Abstract

The development of new structural materials and increasing requirements for the efficiency and safety of operation of structures and at the same time, reducing their material consumption, tighten the requirements for the accuracy of the experimental and calculated parts of the study. The experimental implementation of the entire spectrum of stress-strain states of samples of structural elements requires the destruction of a large number of samples, the creation and maintenance of cost equipment. Therefore, the search for effective methods for calculating the predicted critical loads for structural elements and determining a realistic safety factor is an urgent task. Stresses and strains throughout the process of loading the material are monitored by deformation curves. In this study attention is paid to the area of hardening of the deformation curve, which reflects the plastic deformation of the material after reaching the yield strength. The stress strain curves in principal stresses and principal strains are primary for further processing and analysis. The aim of the work is to propose an universal method for obtaining a model of the hardening section of a generalized deformation curve for plastic metal materials, which would be better consistent with the experimental data for each specific material. To this end, equivalent stresses and strains are introduced, which are a generalization of the two “classical” approaches of von Mises and Tresca. The model contains a single parameter p, which is determined by the results of several simple experiments. To find the optimal value of p, statistical estimation of quality and errors is used. Application of the method for plastic materials will allow satisfactory accuracy to describe the generalized deformation curve and to predict the stress-strain state of the material at various ratios of principal stresses. In combination with the methods of taking into account the geometry of structures, the obtained generalized curve can be used to predict the values of real stresses arising by structural elements under load.