PSI - Issue 42

Rita Dantas et al. / Procedia Structural Integrity 42 (2022) 1676–1683 Rita Dantas / Structural Integrity Procedia 00 (2019) 000–000

1682

7

condition of rotating bending, which should be around half of the ultimate stress ( σ u ). Therefore, the fatigue limit at 10 6 cycles should be around 410 MPa . However, for axial loading, the fatigue limit can be a bit lower, while frequency e ff ect, that sometimes is observed in high frequency testing, can increase this value. Therefore, the target stress range was defined between 300 MPa and 650 MPa . Therefore, after defining the stress range of interest and determining the main mechanical properties, the analytical formulation was applied to calculate geometry parameters and evaluate stress and strain in the critical cross-section. The radius of constant section ( R 2 ) was defined as 5 mm because of limitations related to the connection between the specimen and the ultrasonic machine. The other dimensions are defined to ensure the frequency of 20 kHz , while taking into account the stress range of interest defined in previous section. Thus, the geometrical dimensions for the smooth fatigue specimen are analytical determined and presented in Tab. 2.

Table 2. Geometrical dimensions considered in the analytical formulation [in mm] 2 R 1 2 R 2

L 2

L 1

4

10

23

13 . 93

Regarding the stress range, throughout the analytical formulation, it is determined that for geometrical dimensions selected, stresses amplitude between 198 MPa and 776 MPa can be tested, since the ultrasonic machine, in which the experimental campaign was performed, can only apply displacement amplitudes between 12 µ m and 50 µ m . The experimental campaign was conducted in a Shimadzu USF2000A machine, which is portrayed in Fig. 1. Thus, an experimental campaign of twenty specimens was performed and the results and respective mean curve obtained are plotted in Fig. 3. All specimens were polished before being tested and their surface roughness was also evaluated. As can be observed, the experimental data shows high scatter and the mean curve is almost an horizontal asymptote. The fatigue strength verified at 10 7 cycles is approximately around 510 MPa , which is higher than the value previous estimated for the conventional fatigue limit. This observation can be probably explained by a frequency e ff ect related to ultrasonic fatigue testing. Moreover, in almost every specimen, the crack initiated at the surface and only in a single specimen was observed an internal failure.

Fig. 3. S-N curve for S690 structural steel from experimental data obtained in an ultrasonic fatigue machine