Two axle geometries, F1 Geometry tested by Politecnico di Milano on a Vitry type test rig and F4 Geometry tested both on a Minden (by DB – Deutsche Bahn) and Vitry (by SNCF – National society of French railways) type test rig, will be considered in  pre-

sent paper. Here D and d are the maximum and minimum    diame-

ters at the transition of press-fit, see Fig. 1a. The dimensional details of the tested axles are reported in Table 1. The F1 geometry was designed to obtain the axle body fatigue limit of free surfaces without press fits as described by the European Standard EN- 13261 [6].

On the contrary, the F4 geometry has been designed to evaluate the   fatigue   limit   at   press-fit.   The   selected   diameter ratio D=d ¼ 1:12 is the minimum accepted value in the design of axles that may be reached in service due to some consecutive seat re- profiling made in maintenance  [6].

The F4 axles tested both on Minden or Vitry test rig are identical in terms of diameter of the seat (D), diameter of the body (d), the corresponding diameter ratio (D/d) and the shape of the transition (radius and length). There are differences in the dummy hub press fitted on the axle to recreate the normal wheelset condition. More details about test rigs and axles geometry can be found in Ref. [19]. Considering the unexpected fretting failures at press fit the ver-

ification  of  the  proposed  method  was  processed  with  the   data

Allowable defect size [m] - Liu Mahadevan Criterion - F1 Axle

acquired from F1 and F4 axles. Results obtained from fatigue   test-

ing and corresponding macro examination are presented in Table 2

for different values of applied nominal bending stresses computed at the maximum axle diameter. Location and distribution of cracks, detected by magnetic particle inspections, made on broken axles of types F1 and F4, are shown in Fig.  2.

The proposed method has been applied to the results obtained by the FEA analysis of the press fit. Both of the multiaxial fatigue criteria were applied on the acquired stress state separately. The ratio s between the torsional and the axial fatigue limit, which is

typically  s ¼ sw=rw  ¼ 0:85  for  materials  containing  defects,  was

kept constant independent of the defect size for the Liu–Mahade- van criterion [25]. The fatigue properties of EA4T steel have been taken from Refs. [26,27], where a series of fatigue tests in presence

of microdefects were carried for  determining  rw0   and pffiaffiffirffiffieffiffiaffiffiffi0ffiffi (see

Eq. (2)).

3.1. Finite element model

Several FE analyses have been carried out to simulate experi-

Fig. 8. Sub-surface critical defect size for F1 axle under run-out condition: (a) Dang van criterion, (b) Liu–Mahadevan   criterion.

mental tests to obtain the stress  path  in  the  critical  regions  of the shaft [28]. 3D FE model has been obtained by the revolution

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

of a 2D solid mesh in order to obtain regular distribution of solid elements. The starting 2D solid mesh was built by adapting Abaqus rectangular elements CAX4R. An element size of 0.25 × 0.25 mm was selected in the area of interest which is the volume including the press fit seat and sub-surface associated with it (Fig. 3). Linear type of elements, convergence of which has been found to be sim- ilar to that of parabolic elements for the given size as presented by an earlier report published by the project, were selected [29]. The obtained 3D model is composed of Abaqus C3D8R elements (8- node linear brick) with reduced integration and hourglass control. The interaction between shaft and wheel is modeled with a standard surface to surface contact. Tangential behavior is described with a linear friction coefficient equal to 0.6 as it was experimentally evaluated in the Euraxles project  starting  from the press fitting diagram and from the strain measurements along the transition. The interference fit was introduced in the first step with the use of maximum value supplied by technical drawings (0.313 mm for F1 axle and 0.277 mm for F4 axle). The bending load was applied to a reference node, linked to the interested section by a coupling-joint. In Fig. 4a the boundary conditions used in the Vitry type test for F1 axle are presented. X axis displacements were