PSI - Issue 4

Hans-Jakob Schindler / Procedia Structural Integrity 4 (2017) 48–55 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

6

53

(b)

(a)

Fig. 4: (a) Stress profile (normalized by the nominal stress) on the x-axis due to the service load. (b) Stress profile on the x-axis due to the press-fit with d = 0.3 mm. The SIF due to the service load and the pre-stresses (as given in Fig.3(b) and Fig. 4, respectively) are calculated by the weight function for edge cracks in 2D, corrected for the curved crack-front of a thumbnail crack. The resulting SIF are shown in Fig. 5 as a function of the crack depth. Note that the sharp compressive stress-peak in the vicinity of the surface (i.e. at x = 0 in Fig. 3 (b)) is disregarded in the calculation of K Irs (a). Based on the guideline IIW-1965  K th (R=0) was assumed to be 6 MPa · m 0.5 (Hobbacher 2004). As mentioned above, the stresses due to the press-fit as given in Fig. 4(b) can be considered as additional residual stresses, so the superposition of the two curves shown in Fig. 5(b) has to be inserted as K Irs (a) in eq. (5). The results of the numerical integration of eq. (5) for repeated application of the load spectrum given in Table 1 are shown in Fig. 6(a). For comparison, three different cases of residual stresses are considered: i) measured residual stresses as shown in Fig. 3(b) (but disregarding the sharp peak at the surface), ii) zero residual stress (i.e. a safe life prediction without taking residual stresses into account) and iii) the hypothetical case with residual stresses being only 50% of the measured ones. The comparison in Fig. 6(a) indicates that effect of the residual stresses on residual safe life is huge. The stresses due to the press-fit depend linearly on the difference d between the diameters of the conical bore in the wheel and the corresponding cross-section of the axle. For the considered compound axle/wheels its nominal value is d = 0.3 mm, but due to tolerances it can vary in a certain bandwidth. In order to demonstrate the effect of d on the calculated safe life, 6/b) shows the crack growth curves for three values of d. Obviously, the effect of d on the calculated safe life is significant.

Table 1. Nominal stresses and number of load-cycles on a travelled distance of 40 km

Nominal stress [MPa]

75.2

66.4

62.2

47.0

44.2

40.2

32.7

29.7

Number of cycles in 40 km

1

107

72

214

786

1287

5860

5788