PSI - Issue 42

Lucas Carneiro Araujo et al. / Procedia Structural Integrity 42 (2022) 163–171 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

167

5

= ( ) = ( + )

(15)

(16) Where and are the amplitudes of the normal and shear stresses respectively, is the angular frequency, is time and is the phase angle between the loads. During the tests, the ambient temperature was controlled and kept between 20 to 26 °C, the applied frequencies were between 5 and 15 Hz, depending on the load level. All tests were carried out with a loading ratio of -1, that is, mean stress equals zero. Were applied different ratios between shear stress amplitudes and normal stress amplitudes corresponding to 0, 0.5, 1, 2 and ∞ , where the values of 0 and ∞ correspond to push-pull and pure torsion loading, respectively. For the combined loads in-phase and 90º out-of-phase tests were performed. The objective in carrying out the tests was to obtain at least one failure and one run-out for each one of the different loading conditions. The run-out criterion was set equal to 2 10 6 cycles and the complete rupture of the specimen was From the analysis of inclusions and the extreme statistics method, conducted by Machado et al (2020)[11], the computed value of √ was 145 and 121 μ m for two different sample cutting planes, 90º and 45° respectively, used in the calculation of the fatigue limits considering the natural defects of the material, according to Eqs. (13) and (14). To calculate the fatigue limit considering the presence of the micro hole, according to Eqs. (11) and (12), it was only necessary to calculate its projected area in a plane perpendicular to the direction of the maximum principal stress in push-pull and torsion, according to the definition of the √ parameter, due to the geometry of the manufactured hole, the computed √ of its projections were 550 and 618 μ m. The obtained fatigue limits from the √ parameter model where = 271 and = 235 considering the material inclusions and = 220 and = 182 considering the presence of the micro-hole. The material constants required to calibrate the critical plane criteria considered in this work were obtained by using the fatigue limits estimated with the √ parameter ( and ), given in Error! Reference source not found. . The results obtained with this calibration and their comparison with experimental data are presented in the next sections. used as a failure criterion. 5. Results and discussion 5.1. Fatigue limits from √ parameter

5.2. Uniaxial and multiaxial fatigue results

First will be presented the comparisons between the predictions of the multiaxial fatigue models and the experimental data regarding the tests carried out with smooth specimens under the effect only of the non-metallic inclusions inherent to the material.