From the critical plane analysis the corresponding critical plane angles are found to be h ¼ 33○ for Dang Van criterion and h ¼ 53○ for the Liu–Mahadevan criterion. (Fig. 7). Evaluation of the critical planes at different stress levels has also shown the independence of the critical planes from the applied nominal   stress.

Comprehensive analysis of the sub-surface region under the press-fit was made. Subsurface analysis reveals a slight  decrease in allowable defect size and, thus increased sensitivity to crack propagation (Fig. 8).The main difference between the two criteria is in terms of allowable defect size predicted near  the  T- transition. The Liu–Mahadevan criterion gives non-conservative results, with a critical defect greater than 700 lm, close to the T-

lot of smaller evident cracks located at a distance about 10 mm away from the contact edges at the both sides of the transition are observed (Fig. 2a).

According to the results presented in Fig. 7 location of initiation sites are successfully predicted by the applied criteria. A compre- hensive SEM analysis has been performed on the specimens sec- tioned from the critical regions in order to investigate depth, propagation path and origin of the cracks as well as the severity of the fretting damage on material surface (Fig. 9a). Propagating cracks originated from surface defects were observed in many cases (Fig. 9b and c). The typical size of the defect from which a propagating crack is nucleated is in the order of 350–400 lm in length which is consistent with the  value  predicted  by  both  of the criteria. In Fig. 9d a section of press-fit including non- propagating cracks with dimensions in the order of 200 lm in size is shown. The angles of propagation are measured to be 30° and 40° from the images presented in Fig. 9c and b, respectively which are comparable to the estimations made by the Dang–Van criterion.

Results of the experimental measurements and predictions of permissible defect sizes are tabulated in Table  3.

Allowable defect size [m] - Dang Van Criterion - F4 Axle

transition when compared to the estimations made by DangVan criterion.

In order to decide about applicability and prediction ability of the applied HCF criteria, investigation of surface defects present along contact surface close to the observed cracks was   done.

A visual inspection has been performed on the axle broken at 153 MPa (axle nr.1 in Table 2) for determination of crack shape, dimension and location. The analysis was focused on both sides of the T transition where the visible cracks were observed. The inspection revealed the presence of a major crack through the whole  thickness,  at  about  20 mm  from  the  border.  Moreover, a

Allowable defect size [m] - Liu Mahadevan Criterion - F4 Axle

Fig. 10. Surface critical defect size and critical plane for F4 axle – Minden type test rig.

Fig. 11. Sub-surface critical defect size for F4 axle under run-out condition – Minden type test rig: (a) Dang van criterion, (b) Liu–Mahadevan criterion.

42 S. Foletti et al. / International Journal of Fatigue 86 (2016)    34–43

3.3. F4 axle 600

In Fig. 10, results showing the non-propagating crack size for F4

When a nominal stress of 132 MPa (dashed line – failure condi- tion in Fig. 10) is applied, allowable crack size is predicted to be 450 lm in length for  the  Dang  Van  criterion,  while  a  size  of 430 lm is the prediction made by the Liu–Mahadevan criterion. This limitation increases to a level of 500 lm for an applied stress of 120 MPa, which is the loading condition for run-out    axles.