PSI - Issue 53

João Alves et al. / Procedia Structural Integrity 53 (2024) 236–245 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2. State of the art Murakami et al. (1989) conducted a study investigating the relationship between fatigue limit stress, stress intensity factor at the threshold, and the size and localization of inclusions in steel. Their findings led them to the conclusion that this phenomenon can be effectively described by the primary tests employed in the industry, including hardness testing and non-destructive defect inspection tests. Consequently, they developed equations 1 and 2, which predict the variation in stress intensity at the crack propagation threshold ( ∆ ) and the stress fatigue limit ( ), using as input hardness (Hv) and geometric defect area (area). ∆ =3.3×10 −3 ( +120)( � ) 1 3 (1) =1.43( +120)/( √ ) 1 6 (2) In the same study, equation 3 was also developed, which counts the influence of internal inclusions. =1.56( +120)/( √ ) 1 6 (3) However, Murakami and Usuki (1989) observed that in high-strength steels, their fatigue strength is significantly influenced by inclusions within the metallic matrix. Establishing a precise numerical value proved challenging, leading to the proposal of two thresholds: an upper and a lower threshold. The lower threshold is defined by equation 4, where inclusions have the most adverse impact on fatigue behavior. In contrast, the upper threshold, as outlined in equation 5, assumes the absence of inclusions since defects do not typically cause fatigue fractures in high-strength steels. =1.41( +120)/( √ ) 1 6 (4) =1.6 (5) Other researchers have applied the equations introduced by Murakami to forecast fatigue limit stress. For instance, Matsunaga et al. (2003) examined the fatigue behavior of a Ti-6Al-4V alloy featuring various microstructures in the presence of artificial defects. They utilized two sets of specimens: the first group comprised artificial holes that had undergone post-processing to eliminate irregularities around the edges, such as burrs or pre-cracks. In contrast, the second group consisted of untreated artificial holes. Following the fatigue tests, Matsunaga et al. (2003) drew several conclusions, with one of the most significant findings being the greater severity of pre-crack existence in the second group. Despite having the same defect area, this group exhibited fatigue limit stress values 20~60 MPa lower than those in the first group. This result highlights the improved applicability of equation 2 in predicting the fatigue limit stress for the second group. Tajiri et al. (2014) studied the effects of defects distributed over three specimens of an A356 aluminum alloy produced by casting. To this end, the author used the model proposed by Ueno (2012), represented by equations 6 and 7, which suggested modifying the Murakami equations in their study of the presence of artificial defects in an aluminum alloy produced by casting. =1.43( +75)/( √ ) 1 6 (6) =1.43( +450)/( √ ) 1 3 (7) However, during the mechanical tests, the authors (Tajiri et al., 2014) obtained different fatigue limit stress results from those obtained by the models, leading them to slightly adapt by modifying how the defect area was counted. Fig.