PSI - Issue 42

Teresa Morgado et al. / Procedia Structural Integrity 42 (2022) 1545–1551 Morgado et al./ Structural Integrity Procedia 00 (2019) 000 – 000 ∆ ℎ ≅ 3.3 × 10 −3 ( + 120)(√ ) 1/3 (1) Where ∆ ℎ is stress intensity factor range, is Vickers hardness and is the area of a defect projected onto the plane perpendicular to the maximum tensile stress obtained considering the extreme value. ≅ 1.43 ( + 120)/(√ ) 1/6 (2) Where is fatigue limit. ≅ 1.56 ( + 120)/(√ ) 1/6 (3) Where is the area of internal inclusion and is obtained considering the extreme value. In the same year, Murakami and Usuki (1989) studied the fatigue limit strength in steel based on statistics for extreme values of inclusion size. The principal objective was to predict fatigue strength ’s upper and lower limits. They considered that a specimen would have a lower fatigue limit when the inclusion is contained at the surface or when the inclusion is touching the surface. They already assumed that the sectional shape of inclusions was an ellipse. With this study, Murakami and Usuki (1989) conclude that the effect of inclusion on fatigue strength depends on its sizer, shape and location, which indicates that high-strength steels do not have a definite value of fatigue limit. In 1991, Murakami et al. (1991) studied the quantitative evaluation of the shape and size effects of artificially introduced alumina particles on the fatigue strength of steel and reanalysed the fatigue prediction equations. The prediction of the fatigue limit strength depends on the inclusion locations. For surface inclusions, subsurface inclusions, and internal inclusions, the limit fatigue strength is given by the equations (4), (5) and (6), respectively. ≅ 1.43 ( + 120)/(√ ) 1/6 (4) ≅ 1.41 ( + 120)/(√ ) 1/6 (5) ≅ 1.56 ( + 120)/(√ ) 1/6 (6) Where is the area of the defect estimated by extreme value statistics. A few years later, in 2014, Tajiri et al. (2014) realized rotating bending fatigue tests of cast aluminium alloy A356 using the specimens sampled at three locations of a large-scale component with different cooling rates. It used the formulation of Ueno et al. (2012) (equations 7 and 8) obtained by modifying Murakami’s equation to predict the fatigue limit of aluminium die-casting alloy. It was concluded that the predicted fatigue limit using the equations proposed by Ueno et al. (2012) was close to the experimental value. √ ≤ 1400 : ≅ 1.43 (75 + )/(√ ) 1/6 √ ≥ 1400 : ≅ 1.43 (450 + )/(√ ) 1/3 Where √ is the maximum defect size estimated by extreme value statistics. Schönbauer et al. (2016) studied the fatigue limit prediction of hardened stainless steel and calculated the fatigue limit with a generalised expression (9) by Murakami (2002). (7) (8) 1547 3