PSI - Issue 42

Lucas Carneiro Araujo et al. / Procedia Structural Integrity 42 (2022) 163–171 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 3 The material constantes and can be obtained from the uniaxial fatigue limit in fully reverse push-pull or bending, −1 , and from the fatigue limit in fully reverse torsion, −1 , according to Eqs. (3) and (4), where = −1 / −1 . = 1 √ − − 0.5 1 (3) = −1 2√ − 1 (4) The Susmel and Lazzarin model, also known as the Modified Wöhler Curves Model (MWCM), assumes as critical plane the one with the maximum shear stress amplitude, τ , , and among the planes of τ , the one that experiences maximum normal stress, , [17,18]. ( , ∅ ) : ,∅ { ( , ∅)} = τ , (5) Thus, the failure criterion of the MWCM model can be exposed by Eq. (6), where and are material constants that can be obtained from fully reversed push-pull and torsional fatigue limits, −1 and −1 . They are calculated according to Eqs. (7) and (8) respectively. τ , + ≤ (6) = −1 − −1 2 (7) = −1 (8) The variable , Eq. (9), quantifies the influence of the normal stress on the fatigue damage. Due to the shape of Eq. (6), it requires a limit value, , to be numerically consistent with the phenomenological effect of the normal stress on fatigue endurance as can be seen in Eq. (10). = , , (9) = −1 2 −1 − −1 (10) These two critical plane models use as variables and , , the maximum normal stress is trivial to compute, the shear stress amplitude is not. There are several ways to calculate it, but in this work, the Maximum Rectangular Hull (MRH) algorithm is used [19,20]. Besides being very simple to implement, it can consider the effect of non proportional stress histories. 3. Fatigue limit estimation from √ parameter To obtain the material constants of the critical plane criteria, the fatigue limits obtained from the √ parameter will be used, as already mentioned. The big advantage of √ parameter proposed by Murakami and Endo (1983) [13 – 15] is that one can obtain the the nominal fatigue limit for fully reversed axial loading, in MPa, for materials with small defects without the need to carry out fatigue tests. Regarding superficial defects of known size and shape only are required the square root of the defect’s projected area ( √ in μ m) and the material hardness in Vickers ( in kgf/mm 2 ), the expression to obtain is represented by Eq. (11). = 1.43( + 120) (√ ) 1/6 (11) 165