Contribution to the Evaluation of Stress Strain and Strain Life Curves

This paper presents an overview of different methods of performing a regression on the results of strain controlled tests to obtain the cyclic properties that are used to describe the strain life and stress-strain curves. For the strain-life curve, the approach of Coffin and Manson is used, whereas the cyclic stress strain curve is described using the approach of Ramberg and Osgood. Three different regression approaches are explained: a simple linear regression and a Deming regression, which are applied separately to the elastic part of the strain amplitude and the number of cycles and to the plastic part of the strain amplitude and the number of cycles, as well as a spatial regression applied to the stress amplitude, plastic strain amplitude, and number of cycles. Because the populations of the parameters that are to be approximated by the regression are usually unknown, Monte Carlo simulations are performed to simulate artificial strain-controlled tests as a basis for judging the accuracy of the approximation of the mean curves and the scatter around these curves. It is shown that all three regressions are almost equally accurate. By using the simulation results, factors for shifting the estimated properties to a confidence level of 10 % or 90 % are derived.