Fretting fatigue --- is there really an important effect of friction coefficient??

dear Colleagues

In writing a review of models on fretting fatigue, I am looking at the effect of friction coefficient.   Obviously, if friction is zero there is no fretting fatigue!   This goes without saying.

However, when I worked some time ago on a refinement of the very interesting simple model of Giannakopoulos and Suresh, see Ciavarella (2003), Ciavarella & Dini (2005), I found that unless friction is extremely small and tangential force is close to full sliding, there is no influence at all on friction coefficient!   This result is obtained both with my simplified crack analogue model, as well as the asymptotic models of Dini & Hills, see the comparison in Ciavarella & Dini (2005).    Besides, if friction coefficient is very high, we start to have serious problems of wear, and we have another problem.

Therefore, I would be very grateful if you could share with me any paper or published data showing the effect of friction coefficient, either confirming this conclusion or disproving it.  To me, the fretting fatigue stress concentration problem doesn't require complicated models of multiaxial state of stress, stress gradients corrections, as the problem is well understood as a crack analogue one.   Of course, many people like to verify old models in fatigue to publish more papers for academic purposes, to find they generally work all approximately ok!

Thanks in advance.   Feel free to ask me more details about the papers I indicate below ---- I attach PDF copies, or explanations.

Ciavarella, M. (2003). A ‘crack‐like’notch analogue for a safe‐life fretting fatigue design methodology. Fatigue & Fracture of Engineering Materials & Structures, 26(12), 1159-1170.

Ciavarella, M., & Dini, D. (2005). A refined CLNA model in fretting fatigue using asymptotic characterization of the contact stress fields. Fatigue & Fracture of Engineering Materials & Structures, 28(12), 1099-1112.

https://onlinelibrary.wiley.com/doi/full/10.1111/j.1460-2695.2005.00948…