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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Fig. 1. (a) Parametrized specimen geometry; (b) boundary conditions that cause plane stress condition.

Since the goal is to determine the fatigue life of presented component-like specimens, the loading condition is set up to simulate a cyclic fatigue test, where the lower part of the specimen is clamped, and the upper part is subjected to either a force or displacement. Here, loading is simulated by applying a uniaxial positive displacement. Since the finite element analysis will include material nonlinearities, which significantly increase the computational time required for the solution, modelled specimen geometry will be further simplified by reducing it to a quarter of its original size using symmetry conditions. In Fig. 2, the boundary and symmetry conditions applied to the quarter specimen are illustrated, along with the parametrized variables that define the specimen geometry.

Fig. 2. (a) Boundary and symmetry conditions for modelled quarter specimen geometry; (b) parametrized variables including length, width and radius.

2.2. Hardness distribution in the specimen-like component After surface hardening, the material's surface exhibits increased strength and hardness, while the core remains softer, leading to a gradient in hardness and other material properties throughout the specimen's thickness. The component-like specimen is modelled to reflect this varying hardness distribution from the surface to the core. For this, the hardness profile is established using an empirical model for surface-hardened steel, as proposed by Lang (1989): ( ∗ )= "#$% + ( &'$()"% − "#$% ) ( ∗ ); (1) ( ∗ )=10 (+,-. ∗ ). ∗ ; ∗ = / 01 . Here, HV surface is the Vickers hardness value at the surface, HV core is the core hardness, and R ht is the depth at which the hardness reaches 80% of the surface hardness. The constants a and b , which depend on the heat treatment, are provided by the author and are specified as 0.1737 and 0.4218, respectively, for surface-hardened components. Since the model represents only one-quarter of the geometry, the left side (surface) displays the highest hardness value, while the right side (core) shows the lowest. Using the equation by Lang, hardness is applied to all nodes of the model as is shown in Fig. 3. This presents a scenario in which a specimen is surface hardened first, followed by the