Applicability and prediction ability of the applied HCF criteria were checked by investigating the surface defects and the presence of non-propagating cracks. Micro and macro examinations of the contact along X direction were performed. Visual examination of the broken axles revealed presence of a major crack propagated

through whole thickness located at a position  5 mm  away from the transition edge (Fig. 2c). The run-out axle, tested at a nominal stress of 120 MPa, was sectioned in order to investigate presence of non-propagating cracks (Fig. 12). Measurements made on the run- out axle revealed the presence of material defects of 50–100 lms in depth with non propagating cracks in order of 100–150 lms in length. These results are in accordance with the limitation sets imposed by the application of the HCF   criteria.

The critical plane orientation h presented in Fig. 5b, indepen- dently from the applied nominal stress, is estimated to be equal to h ¼ 20○ for Dang Van criterion and h ¼ 40○ for the Liu–Mahade- van criterion. The estimation made by the Dang Van criterion is comparable with the angle measurements presented in Fig.   12.

In Fig. 11 subsurface analysis of the press-fit is presented for F4 axle. A slight sensitivity is observed as in the case of F1 axle.

The comparison between the two types of test rigs was made for failed F4 axles (Fig. 13). The predicted critical defect size was found to be approximately the same independent of the test rig used. However, considering the Vitry test rig, the predicted critical location for crack nucleation seems to be closer to the T-transition which is in contradiction with the experimental results, see Fig. 2b. A summary of the results for the acceptable defect size for F4 axles is presented in Table 3.

Finally, the comparison of the results with the inspection proce- dures presented in [7] was done. Hirakawa et. al. described an  cri-

Fig. 12. Non propagating crack at run-out condition observed by the fractographic analysis for F4  axle.

Fig. 13. Surface critical defect size for F4 axle at failure stress level – Minden vs

Vitry  type  test rig.

terion of 150 lm defect size for the wheelset dismantled after 300000 km of service. In the present study, a critical defect size with 540 lm in length with an 20° inclination to the press-fit sur- face was determined. When projected to the depth axis (d ¼ c sin h) a 185 lm deep crack is achieved which is comparable in size with the acceptance criteria given.

4. Conclusion

In the present study an analytical model in order to study fret- ting fatigue is presented. The procedure is based on application of two different multiaxial fatigue criteria on the stress path present under the press-fit seat obtained by FE analysis. For each criterion, the equivalent stress defined by the applied multiaxial fatigue cri- terion is compared with the fatigue strength expressed by the El- Haddad correction for the given crack  size. Allowable  crack sizes at the onset of crack propagation, predicted by the multiaxial fati- gue criteria, were defined as the limiting crack size for non- propagating cracks. Two different multiaxial fatigue criteria (Dang Van and Liu–Mahadevan) were applied on the FE results obtained by the analysis of stress path present along the press-fit contact and the results were compared with experimental results obtained in the Euraxles project. Considering the steep stress gradient encountered at the contact edge application of the presented method, which is based on the local stresses, has been limited to the point where the effect of stress singularity disappears. Starting from a point 2 mm away from the contact edge the selected mul- tiaxial fatigue criteria were applied to the local stress state acquired by FE analysis.The examined region was selected in order to cover all the possible failure regions recorded by the post-test analysis of press-fit surface.