PSI - Issue 42

Lukáš Suchý et al. / Procedia Structural Integrity 42 (2022) 1128–1136 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1131

4

Table 2. Material properties Young´s modulus Yield strength Ultimate strength Tensile fatigue limit at = −1 Push-pull fatigue limit at = 0 torsional fatigue limit at = −1 torsional fatigue limit at = −1 (GPa) (MPa) (MPa) −1 (MPa) 0 (MPa) −1 (MPa) 0 (MPa)

C45+N

248.8 423.5

445.2

143.6 244.5

271.3 438.7

190 212

313 754

622 941

42CrMo4+QT

689

3. Numerical studies 3.1. Finite-element model

The FE model is the digital twin of the test specimen in the ABAQUS software. The geometry of the specimen is simplified in the distant area and smoothed in the failure area. The smallest element edge length was 8 µm in the vicinity of the contact edge. The element type is C3D8I. Due to the asymmetric loads, it is not possible to use symmetry planes. The input data for the load are taken from the mean values determined in the experiment at a survival probability of = 50%. These test loads are applied via kinematic coupling as a harmonic torsion signal superimposed by a spatially moving force vector of the rotating bending. Fig. 1 shows the meshing at the hub edge where crack initiation was observed in the experiment. The contact was defined as a penalty contact with a stiffness of 10 7 , and a constant friction coefficient of = 0.5 . 3.2. Calculation of equivalent stress The local stress state at the failure location (hub edge) can be classified as non-proportional due to the uncorrelated superposition of the time-dependent stress component. Such a critical stress state requires for its evaluation the use of special multiaxial strength hypotheses in the evaluation. Based on the critical-plane method, the authors in this study use a hypothesis of integral stresses. This type of hypothesis is known since Liu and Zenner [20] and was further developed by other authors, including Papuga [21] and Böhme [22]. The calculation of such an integral equivalent stress (Eq.3) is done in practice by summing the partial values of the section plane. In present study, the Böhme’s criterium [22] is used: , = √ 8 1 5 ∫ ∫ [(a 2 + b 2 )(1 + c ) 2 + d 2 ]sin =0 2 =0 ≤ −1 (3) In each section plane, the amplitude and the mean stress of the normal , and shear components , are calculated with the material parameters a , , , (see Appendix). While the determination of the normal stresses is unproblematic, the shear stresses are estimated by evaluating the plane shear components. The shear-stress path of a cutting plane is described with the aid of the smallest circumscribed circle. The shear amplitude of the respective plane then corresponds to the circle radius, and the mean stress is calculated using the position of the center of the circle. For the evaluation of the stress field in vicinity of the hub edge, the equivalent stress according to Böhme is determined for each node. For this purpose, the time-dependent stress tensor is transferred from the FE model to the programming routine. The equivalent stresses are then assigned to each node in the results file of the FE analysis and subsequently evaluated. 3.3. Critical-distance theory The aim of this paper is to perform a local strength assessment of the shrink-fit geometries presented. Since the stresses are numerically increased at the hub edge singularity and initial cracks are caused by tribological mechanisms,