The present work virtually simulates the experimental tests due to De Los Rios et al. 3 with the loading configurations shown in Table 1. The tests were carried out in air. Those tests used un-notched solid round specimens made of a ferrite-pearlite 0.4% carbon steel. The material had an ultimate tensile stress equal to 580 MPa and an average monotonic yield stress\(\ \sigma_{y}\) = 400 MPa. The minimum diameter of the specimens was 7.3 mm. The mean grain size was 36 µm with a standard deviation equal to 13 µm.
Table 1(a) lists two sets of experimental parameters corresponding to two-step cumulative fatigue damage. Those tests are simulated as follows. From the predicted \(S/N\) curve, the average number of cycles to fracture at the two stress ranges \({\sigma}_{o1}\) and\({\sigma}_{o2}\) are \(N_{f_{1}}\)and \(N_{f_{2}}\) respectively. A specimen is randomly configured and virtually tested at\({\sigma}_{o1}\)for\(\ N_{1}\ \),\(<N_{f_{1}}\), cycles. The stress range \({\sigma}_{o2}\ \)is, then, applied for \(N_{2}\) cycles when fracture takes place. The two stress levels are utilized to execute virtual tests with L-H and H-L sequences. Further, the test is repeated with specimens having the same configuration but with different values of\(\ \frac{N_{1}}{N_{f_{1}}}\) .
The experimental parameters of six repeated two-step block loading tests, T1-T6, are listed in Table 1(b). The parameters of a test are (1) the stress amplitude \(\sigma_{o1}\)of the first loading block which is applied for \(N_{1\ }\)cycles and (2) the stress amplitude\(\sigma_{o2\ }\)of the second loading block which has\(N_{2}\ \)cycles. A randomly configured specimen is virtually tested for \(N_{1}\)cycles at \(\sigma_{o1}\)and, then, for \(N_{2}\) cycles at\(\text{\ σ}_{o2}\). That loading configuration is repeated till the fracture of the specimen. Further, the test is repeated with 7 specimens having different surface configurations.