F4-Vitry 1 120 Failed  (N ¼ 7:70x106   cycles) Wheel  seat  at  about  10 mm from  the T-transition

F4-Vitry 2 108 Run-out (N ¼ 107 cycles)

F4-Vitry 3 120 Run-out (N ¼ 107 cycles)

F4-Vitry 4 132 Failed (N ¼ 4:98 × 106 cycles) Wheel  seat  at  about  10 mm from  the T-transition

F4-Vitry 5 120 Failed (N ¼ 2:10 × 106 cycles) Wheel  seat  at  about  10 mm from  the T-transition

F4-Minden 1 132 Failed (N ¼ 107 cycles) Wheel seat at about 4 mm from the T-transition

F4-Minden 2 126 Failed (N ¼ 107 cycles) Wheel seat at about 15 mm from the T-transition

F4-Minden 3 120 Run-Out (N ¼ 107  cycles)

F4-Minden 4 132 Failed (N ¼ 107 cycles) Wheel seat at about 7 mm from the T-transition

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

2. The proposed method

The procedure is based on a finite element (FE) analysis so as to obtain the stress path under the press fit seat. The stress tensor is used as input in a multiaxial high cycle fatigue (HCF) criterion to determine an equivalent  stress:

req ¼ f .HCF criterion; .rij .; X; Y . ð1Þ

as a function f of the selected multiaxial HCF criterion and the stress tensor .rij . at a specific location in the press fit seat identified by

the coordinates X and  Y.

The so obtained equivalent stress is checked against the fatigue limit of the material expressed as a function of defect size through the El-Haddad correction, [18]:

sffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where c is the crack depth of the inclined crack length along the critical plane predicted by the multiaxial fatigue criteria (Fig.  5b).

2.1. Multiaxial high cycle fatigue criteria

Two different multiaxial high cycle fatigue criteria (the Dang Van criterion and the Liu–Mahadevan criterion) have been used in the proposed procedure. In literature, applicability of the selected criteria have been discussed several times for the analyt- ical solution of rolling contact and fretting type of fatigue failures [9,21,22].