PSI - Issue 82

Kübra Polat et al. / Procedia Structural Integrity 82 (2026) 267–273 K. Polat, M. M. Topaç/ Structural Integrity Procedia 00 (2026) 000–000

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mean stress and stress amplitude to determine a material’s fatigue limit (Haigh, 1929; Sendeckyj, 2001). In this study, the fatigue failure potential of weight-reduction holes on the front axle beam due to notch effects was evaluated. Maximum stress values were evaluated using the Goodman–Haigh diagram to determine the fatigue safety of these hole geometries. The endurance limit (S e ) and the stress-life endurance limit (S e ꞌ) for steels with a tensile strength (S ut ) below 1400 MPa, are given in the literature as follows (Shigley et al., 1985):

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Here, the surface factor is represented as k a , the size factor as k b , the load factor as k c , the temperature factor as k d , and the fatigue strength reduction factor as k e . In this study, 42CrMo4 alloy steel was used for the front axle material, with a tensile strength (S ut ) of 1300 MPa and a yield strength of 877 MPa. The surface factor (k a ) was calculated as 0.335 using coefficients 57.7 (a) and −0.718 (b) for hot forging (Shigley et al., 1985; Topaç et al., 2016). The size factor (k b ) was determined as 0.75, considering a 95% stress area (A 0.95 ) for wide flange sections. The loading factor (k c ) and temperature factor (k d ) were taken as 1, corresponding to bending loads and ambient temperatures of 0-250°C (Shigley et al., 1985). FEA was used to determine the fatigue stress concentration factor (K f ). In fatigue calculations, vertical accelerations from road irregularities are typically considered by assuming the maximum dynamic load (P) on the axle is 2.25 times the static load (Heißing and Ersoy, 2010). To calculate the notch factor in critical regions, maximum equivalent stresses were obtained for both the initial and final designs at the same nodes. These values were used to calculate K f . The notch sensitivity factor (q) for steel structures was taken as 0.9 based on hole radii (Shigley et al., 1985). Using K f and q, the stress concentration factor (K t ) was determined (Eq. 2), and together with all applicable Marin factors, the strength limit (S e ) for all hole forms was calculated.

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Fatigue tests are typically conducted under cyclic bending with alternating tensile and compressive stresses (Hosford, 2009) and continue until crack initiation, with the prototype expected to endure the target number of cycles without failure (Topaç et al., 2009). In this study, the average stress (σ m ) and stress amplitude (σ a ) were calculated as follows:

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The minimum stress (σ min ) was assumed to be zero, as negative vertical contact forces are physically impossible; when contact between the tire and road surface is lost, σ min becomes zero. Literature shows that minimum stress in fatigue diagrams is typically near zero, making this assumption appropriate (Topaç et al., 2009; Topaç et al., 2024). Goodman–Haigh diagrams for Model 4, stress values of the axle beam models and the percentage reduction in axle mass compared to the reference geometry are shown in Fig. 7. The graph indicate that stress value at the critical region remain within the infinite life region, confirming safe design limits. 5. Conclusion In this study, the failure behavior of front axle beam designs with different hole configurations opened for weight reduction was investigated. The critical loading condition for the front axle beam was determined using various driving cases from the literature. Based on this critical loading case, topology optimization was performed to identify potential weight reduction regions. Using the optimization results, four different design models were developed, including a race-track hole, circular hole, elliptical hole, and four-arc hole, as reported in the literature. According to the results, the four-arc hole configuration (Model 4) was determined to be the most suitable form in terms of both weight reduction and stress. Under the critical loading case, it was found that the regions with maximum equivalent stress in these axle beam models were subjected to tensile stress. For this reason, the fatigue failure potential