PSI - Issue 77

J.A. Alves et al. / Procedia Structural Integrity 77 (2026) 440–446

444

Table 4. Partially reversible fatigue tests and equivalent stresses. σ m (MPa) σ a (MPa) N f (Cycles)

σ Goodman (MPa)

σ Gerber (MPa)

σ Soderberg (MPa)

σ ASME (MPa)

120 120 120 150 105 133 133 133 216 216 216 240 240 240 360 360 360 315 315 315 315

360 360 360 450 315 400 400 400 360 360 360 400 400 400 360 360 360 315 315 315 315

1.46E6 1.31E8 2.44E8 3.65E5 2.89E8 1.20E9 3.57E8 4.06E8 2.28E5 5.97E7 1.43E8 9.78E4 7.33E6 2.51E5 2.43E6 6.01E6 4.04E6 1.43E6 7.00E6 3.40E7 2.65E8

415 415 415 540 356 469 469 469 473 473 473 545 545 545 600 600 600 484 484 484 484

366 366 366 462 319 408 408 408 382 382 382 430 430 430 428 428 428 358 358 358 358

427 427 427 560 365 484 484 484 502 502 502 584 584 584 683 683 683 537 537 537 537

364 364 364 459 318 406 406 406 375 375 375 421 421 421 408 408 408 346 346 346 346

Under partially reversible loads tests, only one specimen reached the run-out condition, while the others failed between 9 . 78 E 4 and 2 . 89 E 8 cycles. Accordingly, each fatigue life obtained under partially reversible loading was associated with its corresponding equivalent stress. Subsequently, S–N curves were plotted for each model, correlating the equivalent stress with the number of cycles to failure (see Fig. 3).

Fig. 3. S-N curves

To quantify the inaccuracy of the models, the stress variation (z) and the standard deviation of stress ( S t ) were calculated. The value of z represents the di ff erence between the experimental stress (ES) at R = –1 and the stress predicted by the modified Basquin equation (CS) for each model at the same fatigue life. This di ff erence is then normalized by the calculated stress (Equation 6). The parameter S t corresponds to the standard deviation of the z, computed according to Equation 7(Yadav and Ajit (2022)).

ES − CS | CS

z = |

(6)