Mathematical modeling and numerical method for estimating the characteristics of non-isothermal creep based on the experimental data

The desire to reduce the mass of machines and structures while improving their quality, as well as to make the most complete use of the mechanical properties of materials, requires permanent improvement and development of known methods for calculating and analyzing the stress-strain state of materials under creep conditions.
The article proposes a numerical method for estimating the characteristics of the third stage of non-isothermal creep based on a set of creep diagrams constructed when processing test results for various values of nominal stress and temperature.
The method is based on the nonlinear regression model, the root-mean-square estimates of the parameters of which are found by linearization, including on the basis of difference equations describing the experimental results. The proposed numerical method can also be used to estimate the parameters of the third creep stage, when the experimental results are presented in the form of a set of test diagrams for only one temperature.
The results of testing the developed numerical method for processing the experimental results in the form of creep diagrams for the 09G2C alloy at different temperatures are presented. The reliability and efficiency of the calculation algorithms and methods of nonlinear estimation presented in the work are confirmed by the results of numerical and analytical studies and mathematical models of the third stage of non-isothermal creep constructed on the basis of experimental data.