PSI - Issue 66

Ramdane Boukellif et al. / Procedia Structural Integrity 66 (2024) 55–70 Ramdane Boukellif et al. / Structural Integrity Procedia 00 (2025) 000 – 000 = 1⁄ 2 ( 0 ⁄ 2 ){ 2 ( 0 ⁄2) − 3⁄2 ( 0 )+√[ 2 ( 0 ⁄2) − 3⁄2 ( 0 )] 2 +4 2 } (4) or for 2D-Mixed-Mode-Loading as follows: = ( 0 ⁄ 2 ){ 2 ( 0 ⁄2) − 3⁄2 ( 0 )} (5) In this case, the criterion is equivalent to the Maximum Tensile Stress MTS-criterion by Erdogan and Sih (1963). The crack deflection angle 0 has its maximum of 70.5° in case of pure Mode II (Schöllmann et al. (2002)). 2. Finite element model for prediction of crack paths on integrated raceways Despite being modelled as a three-dimensional component, the model corresponds to a planar model (see Fig. 2 (a)). Using the symmetrical boundary conditions on the side surfaces of the rolling element and ring, the model corresponds to an infinitely long cylindrical roller rolling over an infinitely wide ring with an infinitely wide crack. The initial crack with a defined friction coefficient between the crack surfaces is a through edge crack. The crack is perpendicular to the side surfaces of the ring. The crack grows evenly across the width of the ring, so that the stress intensity factors along the crack front are constant (see Fig. 2 (b)).

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Fig. 2: Model description for predicting the crack path under rolling contact fatigue, (a) model of the rolling element and the ring, (b) definition of the parameters used in crack growth simulations (Boukellif et al. (2024)).

During the rollover process, a constant contact force F and a constant drive torque M act at the center of the roller without slip, as shown in Fig. 2 (a). The drive torque M =500000 Nμm is used in all simulations. The rolling path is = 3000 μm long and is divided into 25 equal rolling increments (see Fig. 3). Assuming linear elastic fracture mechanics (LEFM), a fracture mechanics evaluation is carried out for each rolling increment, whereby the cyclic equivalent stress intensity factor ∆ and the crack kink angle are important quantities in the crack growth simulation. If ∆ is smaller than the threshold value, the crack cannot grow. In the case that ∆ ℎ <∆ <∆ , the crack is extended by ∆a taking into account the kink angle. If ∆ has a maximum value greater than ∆ ℎ , the crack grows without branching. The crack branches if ∆ has two maxima (see Fig. 3).