PSI - Issue 42

Denny Knabner et al. / Procedia Structural Integrity 42 (2022) 561–569 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

566

6

in the parameter matrix could not be tested. This is due to the power limits of the piezoelectric actuators. Due to the described behaviour, however, it is possible to extend the results by the fictitious extrapolation points shown in gray. 4. Tribological adaption of a failure hypothesis As explained in Section 1, the strength evaluation of fretting fatigue requires a criterion that takes into account the local variation in fretting-fatigue strength as a function of the parameters slip amplitude and contact pressure. Depending on the magnitude of slip amplitude and contact pressure, the fretting-fatigue strength may vary or, if at least one of the two parameters is zero, the failure may even be purely stress based. For this purely stress-based failure there are already many approaches resulting from plain fatigue problems in the high-cycle-fatigue domain. It therefore makes sense to use one of these approaches and to extend it to the case of fretting fatigue. The authors decided to use Böhme ’ s hypothesis [34] as the initial hypothesis, which can be justified as follows:  According to Papuga ’ s Benchmark [35] the prediction quality is quite close to the best criteria PCN and PIN for plain fatigue.  It is a multiaxial stress criterion, and multiaxial stresses are a major factor in contact problems.  Compressive stresses are correctly accounted for, which is not the case with many other criteria. Equation (1) is used to calculate the equivalent stress according to the Böhme hypothesis. , = √ 1 8 5 ∫ ∫ [( ∙ 2 + ∙ 2 ) ∙ (1 + ∙ ) 2 + ∙ ∙ ] ∙ sin =0 2 =0 (1) The original formulation of the failure criterion is the comparison of the equivalent stress with the fixed value of the fatigue limit in fully reversed axial loading, −1 . The adaptation is now done by substituting this value by the fretting-fatigue strength as shown in Figure 5a. is a two-dimensional parameter derived from the variables of slip amplitude and contact pressure (Equation (2). The determination was made by curve fitting from the experimental data as shown in Figure 5b. For = 0 MPa , this approach is identical to the original formulation of the Böhme criterion, since then gives the plain fatigue strength. = 449 − 10.78 ∙ − 15.23 ∙ + 0.3921 ∙ 2 − 1.005 ∙ ∙ + 0.7733 ∙ 2 − 0.00309 ∙ 3 − 0.001732 ∙ 2 ∙ + 0.05782 ∙ ∙ 2 (2) a) b)

Fretting fatigue strength σ FF (MPa) 20 0 100 200 300 400

, −1

Original failure criterion:

15

Substitution

10

5

Adaption:

40

60

= ( , )

Figure 5: a) – Adaptation of Böhme ’ s failure hypothesis by substitution of the threshold value; b) – Determination of the fretting-fatigue strength as a function of slip amplitude and contact pressure by means of curve fitting