3.1. General Methodology

As proposed earlier, estimations will be performed separately for steels grouped according to alloying element content since it was shown in [9,21] that the cyclic stress–strain behavior of these groups statistically significantly differed.

In the framework of this study, for estimation of cyclic stress–strain behavior, i.e., curves, monotonic properties are used, which were proved to be statistically significant for the estimation of cyclic yield stress R_e′ for each steel group (Table 1) as published in an earlier study [27]. Since it was proved there that R_e′, as a point on the cyclic stress–strain curve, can be successfully estimated using monotonic properties, it is assumed that by adding plastic strain amplitudes Δε_p/2 to monotonic properties already proven as statistically significant for estimation of R_e′, the whole cyclic stress–strain curve can be successfully estimated. The motivation for determination and using only significant, i.e., relevant monotonic properties for estimation of cyclic stress–strain parameters and curves is obtaining a favorable ratio between the number of input variables and the number of available datasets for ANN training, as explained in more detail in Section 3.3.

Overview of monotonic properties that proved to be relevant for estimation of cyclic yield stress R_e′ of unalloyed, low-alloy, and high-alloy steels.

Details on the forward stepwise regression procedure used for the identification of relevant monotonic properties for estimation of cyclic yield stress R_e′ are provided in [21,27].

The procedure of estimation of cyclic stress–strain behavior is given in the flow chart in Figure 1. Even though most steps are easily understandable, the term “chosen values of Δε_p/2” must be addressed. The investigation and results presented here are the first steps towards the development of the method for estimation of materials’ cyclic stress–strain behavior using experimental data points instead of (cyclic) stress–strain curve points calculated using a certain model and the corresponding material parameters. As a result, the parameters of any appropriate material model could then be determined. This investigation, however, is based on the calculation of those data points (Δσ/2–Δε_p/2) determined using the cyclic Ramberg–Osgood material behavior model. Since the plastic part of the cyclic stress–strain curve (Δσ/2–Δε_p/2) calculated using the R–O model is a straight line in the double logarithmic diagram, theoretically only two points—any two points on the curve—are needed for the determination of the line. However, since the aim of this research is to set foundations for comprehensive estimation of cyclic stress–strain curves using experimental data points, i.e., actual plastic strain amplitudes and monotonic properties as independent variables (inputs), in this investigation, two variations in the number of data points for each material were used:

Flow chart of the cyclic stress–strain curves estimation using ANNs.

The second option with multiple (5) values of plastic strain amplitudes serves to evaluate the performance of ANNs for a larger number of data points.