PSI - Issue 68

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Ela Marković et al. / Procedia Structural Integrity 68 (2025) 345 – 350 Ela Marković et al. / Structural Integrity Procedia 00 (2025) 000–000

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relationship is described by the widely used Basquin-Coffin-Manson (BCM) equation, which incorporates both elastic and plastic strain components: ) = ),% + ),7 = ( ( 2 / ) (2 ( ) - + ( ′ ∙ (2 ( ) 8 . (5) Here, ε a represents the total strain amplitude, which is decomposed into ε a,e and ε a,p , elastic and plastic strain amplitudes, respectively. E denotes Young’s modulus, while 2 N f represents the number of load reversals to failure. The fatigue parameters σ f ' and b are denoted as fatigue strength coefficient and exponent, respectively, whereas ε f ' and c are fatigue ductility coefficient and exponent, as stated by Li et al. (2015). For using the strain-life approach, it is essential to obtain values of fatigue parameters. When dealing with surface hardened components, this can be achieved through fatigue testing on at least two groups of specimens, ideally more, with one group representing the material at surface and the other representing the material at core of the surface hardened components. However, such testing is both time-consuming and expensive, which is why estimation methods are often preferred. The hardness method by Roessle and Fatemi (2000) relies only on Brinell hardness ( HB ) to predict fatigue properties and is utilized in this model. The relevant equations are as follows: ( 2 = 4,25 + 225; ( 2 = (0,32 5 − 487 + 191000)/ ; = −0,09; = −0,56. (6) Using these expressions, the values of fatigue parameters ( σ f ', ε f ', b, c ) for each node can be determined based on the corresponding hardness. As a result, each node is represented by its own strain-life curve, and the fatigue life (2 N f ) for every node is numerically calculated using the BCM expression (Eq. 5). The minimum fatigue life and its corresponding location within the component model are recorded. As an example, a specimen with a total length of 220 mm, width of 24 mm, and a notch radius of 5 mm, along with surface hardness of 550 HV and core hardness of 300 HV, is analyzed. Using the FE model, the nodal strain distribution is obtained which and used to calculate fatigue life at each node, as is shown in Fig 4. Loading applied is positive displacement (Δ y = 0.3 mm) which causes the total strain amplitude of approximately 4%. Fig. 4 shows the total strain distribution for the mentioned scenario from which fatigue life distribution is obtained for every node. As expected, the most critical part of this component is the notch root.

Fig. 4. Illustration of a strain amplitude distribution and fatigue life distribution for quarter geometry of a surface-hardened notched specimen-like component. 4. Conclusions The developed numerical model enables estimation of the fatigue life of surface-hardened, specimen-like components under uniaxial cyclic loading. Hardness distribution is calculated using an empirical equation and applied