PSI - Issue 77

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

441

loading with equivalent non-reversed loading, including classical models such as Goodman, Gerber, and Soderberg, which are widely applied in both academia and industry (Dieter et al. (1988)). Nevertheless, equivalence models, like others, have a long history of application in the low- and high-cycle fatigue regimes, highlighting the need to assess their validity in the VHCF domain (Liu et al. (2010); Furuya et al. (2019)). The verification of classical models under VHCF conditions has been the focus of recent research; for example, Shiozawa (2012) proposed a modification of Basquin’s equation for VHCF applications.The present work focuses on adjusting non-reversed fatigue tests conducted using ultrasonic equipment by applying the Goodman, Gerber, Soderberg, and ASME Elliptic equivalence models, and comparing the results with fully reversed tests performed on a structural steel (DIN 34CrNiMo6), in order to evaluate their applicability within the VHCF regime.

Nomenclature

E Young’s modulus σ uts Ultimate tensile strength σ y Yield strength R Stress ratio a,b Basquin parameters N f Number of cycles to failure

2. Material and Methods

The mechanical properties of the steel were obtained according to ASTM E8 / E8M-24 and ASTM E111-17 stan dards (E28 Committee (b,a)). Table 1 presents the average values from three tests.

Table 1. Mechanical properties of DIN 34CrNiMo6 steel. E (GPa)

σ y (MPa)

σ uts (MPa)

210

760

900

2.1. Fatigue test

Fatigue tests were conducted using a Shimadzu USF-2000A ultrasonic testing machine operating at 20 kHz. Hourglass-shaped specimens were manufactured with one thread for fully reversed tests and two threads for par tially reversible tests (see Fig. 1). All tests were performed with a pulse-pause of 200 ms at ambient temperature of 23 °C. To assess the fatigue life, 24 tests were performed under fully reversed loading conditions ( R = − 1) at stress amplitudes between 35% and 60% of the σ uts (Table 2). In the second experimental phase (Table 3), 21 tests were conducted with stress amplitudes ( σ a ) ranging from 35% to 50% of σ uts to ensure extended fatigue life. The selected stress ratios included tensile / compression conditions ( R = − 0 . 25 and R = − 0 . 50) and fully tensile loading ( R = 0). The tests were conducted until the specimen failure or run out in 1 . 20 E 9 cycles. σ m = σ a − 1 − R R − 1 (1)