PSI - Issue 57

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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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0.7

0.5

 =0

Figure 17: The critical position (depth) of subsurface crack influenced by the friction at the crack faces. The  K II maximum is obtained at certain subsurface depth, increasing with the crack faces friction. There exist certain analogy between the simpler RCF problem (presented in the current figure) and the problem of edge crack. The solution of the simpler problem elucidates more complex RCF scenarios. The parameter S1 , has certain effect on the crack criticality, however the proximity of crack to the raceway does not necessarily mean that  SIF is high. Although, one can intuitively expect that due to the intimacy of crack to the raceway and the contact pressure it experiences higher load, in reality it is not completely true. The dependence of  K II and  K III on the distance S1 is not monotonic, as follows from the results in Figs. 14 and 15, which is conditioned by the complex stress field (developed at the edge of rolling contact) and the crack faces friction. This can be demonstrated by using the simpler RCF problem, considering a subsurface crack, loaded by the moving Hertzian pressure. The semi-analytical solution of subsurface crack problem (see e.g. Chen et. al (1988), Kadin and Sherif (2017)) allows to indicate the crack location (depth) effect on  K II (see Figs. 17). To link this problem to the more complex one (the current problem) , let’s assume that the crack depth in Fig. 17, is analogous to the distance S1 . Thus, the similar non-monotonic trend is also indicated by Fig. 17: the subsurface crack experiences the maximum loading (in terms of  K II ) when it is embedded at certain depth. This is related to the orthogonal shear stress maximum, which is located at the depth of 0.5 b in the case of the plane-strain Hertzian contact (see e.g. Harris (1984)), defined in terms of the contact zone width, 2 b , and the maximum contact pressure, p 0 . The critical depth increases with the crack faces friction, which is also presented in Fig. 17. This occurs because compressive stresses (inducing crack faces friction) mitigate with the depth, thus for deeper cracks the friction between their faces gets lower resulting in higher values of shearing modes. The similarity between the current problem and the simpler one presented in Fig. 17, provides qualitive explanation of the numerical results in Figs. 13-15. 6. Conclusions The main goal of the presented work was to assess the criticality of a crack at the chamfer of a ceramic roller with respect to RCF. The work was performed based on the surface inspection of the roller and the numerical study. The inspection part aimed to identify the morphology of edge cracks, and based on the statistical data to define the most representative crack geometry. Based on the computational fracture mechanics, the criticality of the imperfection was assessed, by including several geometrical parameters into the parametric study. To simulate t he “worst case scenario” the critical loading conditions and relatively large crack size were assumed for the numerical analyses. Note, that the FE modeling is probably the most promising approach for the current problem. Indeed, an experimental study in this case is challenging, because it requires producing artificial features of accurate preassigned geometry at the roller edge, assuring roller orientation versus load and controlling accurate bearing misalignment. On the other hand, FE modeling allows to simulate numerically any contact conditions (accounting for the roller geometry and misalignment) and imperfections of various morphologies. Because of this we present only numerical simulations with wider