PSI - Issue 57

Yuri Kadin et al. / Procedia Structural Integrity 57 (2024) 236–249 Kadin et. al / Structural Integrity Procedia 00 (2023) 000 – 000

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The imperfection is implemented in FE, as is schematically presented in Fig. 9. To facilitate FE meshing the solution domain is split into the two parts: the crack domain and the rest of the body (the roller domain). The domains are attached to each other by the standard ABAQUS constraint interact ion “Tie”, and the crack orientation angle (denoted here by  ), is varied by rotating the crack domain around the axis z ′, as is shown in Fig. 9. The semi -circular crack of the dimensions b and d is used in the current model which is consistent with the experimental observations, indicating that d is close to b /2 (see Fig. 6). The polar coordinate  , is used to designate the distribution of SIF along the crack front: K II (  ), K III (  ) and K I (  ). The crack location relatively to the raceway is defined with the distance S 1 (see Fig. 9). This distance was not systematically measured in the current experimental study, hence the S 1 variation and the effect of this parameter on SIF is explored in the current parametric study. Note that in the current work the roller chamfer is not rounded which is different from the previous model in Kadin et. al (2022). This is considered as flat in order to ease the modelling of the imperfection. The roller domain (see Fig. 10) corresponds to the fragment of roller which dimensions, D w × L , are present in Fig.1. The domain length in the y -direction is L /2 (meaning that only half of the roller is included in the model), and the height is D w /2. The domain length in x -direction, l , is taken as sufficient to mimic the infinity conditions. Recall, that the roller (and the inner ring) curvature (crowning) is taken into the account only for the contact pressure analysis, while it is assumed as flat for the imperfection modelling.

Fig. 10: FE model (meshed) of crack at the roller chamfer.

Chamfer (“Tie” constrain)

 xx

Roller domain

y

Penny crack

Crack domain

z

K I / K I analytical

Crack front coordinate,  °

Fig. 11: Mesh convergence analysis by the modeling a penny crack embedded in infinite space. The mesh density at the crack front provides reasonable accuracy level: the relative difference between the numerical and the analytical solution is around 3.5%.