PSI - Issue 19

T. Kato et al. / Procedia Structural Integrity 19 (2019) 238–248

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Author name / Structural Integrity Procedia 00 (2019) 000 – 000

 and the normal stress  n (normal to the shear stress plane) in the Findley model. The critical planes are determined from the shear stress plane with the highest calculated fatigue damage. The Findley model can be expressed as follows. ∆ , = (∆ + ∙ , ) (1) Here,   eq,max is the pure shear stress range with the equivalent fatigue damage in the multiaxial stress state,  n,max is the value of  n at the maximum fatigue damage, and k is a material constant (=0.3538). k is obtained by applying the shear fatigue limit as   eq,max , axial fatigue limit is converted to shear stress as   , and maximum stress normal to the   plane is  n,max . The fatigue damages at the subsurface increase for larger values of   eq,max . The loading conditions at which the subsurface cracks are more likely to be initiated can be identified by comparing the values of   eq,max obtained from the finite element analyses. The values of   eq,max for each wheel size are shown in Figure 12.   eq,max is calculated from the average stresses at the subsurface for a depth of 3 – 6 mm and the average stresses of three different contact positions respectively. B38 wheel and H36 wheel have approximately equivalent   eq,max , however J33 wheel has a lower   eq,max than the B38 and the H36 wheels. This suggests that RCF cracks are less likely to initiate in the J33 wheel compared to the B38 and the H36 wheels. This result corresponds to the relationship between the maximum contact pressures calculated from the Hertzian theory and the wheel size in Table 1. The values of   eq,max while applying the tread braking are shown in Figure 13.   eq,max is also calculated from the average stresses at the subsurface for a depth of 3 – 6 mm, however, in this case, the stresses of the contact positions in the tread center are only used. Both   eq,max during braking and after cooling are lower than that before braking, and particularly,   eq,max during braking is the lowest. This indicates that the RCF cracks are less likely to initiate during braking or after cooling in this braking condition.

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 eq,max (MPa)

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Wheel size (inch)

Fig. 12. Equivalent maximum shear stress range   eq,max with different wheel sizes.