PSI - Issue 57

Lucas Carneiro Araujo et al. / Procedia Structural Integrity 57 (2024) 144–151 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

146

3

SWT mod ≤

(2) Where the equivalent stress, SWT mod , is obtained from Eq. 1 and is the uniaxial fatigue strength, which can be easily obtained from the parameter √ , as we will see hereafter. 2.1. Fatigue Strength Estimation The model of the parameter √ proposed by Murakami presents a significant advantage in that it enables the estimation of the fatigue strength ( ) for materials with micro defects, eliminating the need for actual fatigue tests. When dealing with superficial defects of known size and shape, the model requires the input of the square root of the defect's projected area ( √ ) and the material hardness (Hv) measured in Vickers, as represented by Eq. 3. = 1.43( (√ +) 120) 1/6 (3) In the Eq. 3, represents the fatigue limit in MPa for materials with micro defects, Hv denotes the Vickers hardness measured in kgf/mm ² , and √ is expressed in µm. It should be noted that the plane on which the defect's area is projected is the one perpendicular to the direction of the greatest principal stress under uniaxial loading conditions. However, when it comes to determining the area of internal defects like non-metallic inclusions or pores, which can exist in varying quantities, sizes, and shapes, a statistical analysis must be conducted to determine the likely largest defect present based on the volume of material. This largest estimated defect is referred to as √ (Murakami, 1994, 2019; Murakami et al., 1994). Murakami considered the most detrimental type of internal defect to be the one in direct contact with the free surface. When a crack originates around this type of defect, it typically propagates and occupies the entire weakened area between the defect and the free surface. This "extra" area must be taken into account when calculating the √ . Consequently, the lower bound of the uniaxial fatigue limit is defined as follows: = 1.41( (√ + 120) ) 1/6 (4) 2.2. Principal stresses amplitude A mechanical component under a loading history, such as the following described by Eqs. 5 and 6, that includes normal stress amplitude ( ) and shear stress amplitude ( ), along with angular frequency (ω), time (t), and phase angle (δ) . = ( ) (5) = ( + ) (6) For each instant of time the maximum and minimum principal stresses and their corresponding directions can be obtained using eigenvalues and eigenvectors of the stress tensor generated (Dowling, 2013). With a cyclic loading history, each principal stress vector, , and , , traces a closed path, for example, see Fig. 1, where the path described by the principal stresses for a combined and out-of-phase loading are depicted. By applying the Maximum