moving singularities (crack analogues) in fretting fatigue

    The stress concentration induced by fretting fatigue was studied with a simple "Crack Analogue" model (CA) by the MIT group of Suresh in the late 1990's, which was then "improved" by the present author to take into account simply both contact loads and bulk stresses loads, and even the case of finite stress concentration in the so-called "Crack Like Notch Analogue" (CLNA) model.

    Now, this is for the case where a punch is oscillating but for most of the contact area is "stuck" to the counterbody. In other words, the contact stresses are exactly analogue to those of a crack, and during fatigue, they oscillate like those induced in a crack.

    The MIT group never considered two cases

1) if the contact changes size during loading, then the "singular" field (assuming infinite friction) would also move in space.  Hence, any particular point on the surface of one of the bodies experiences an oscillating stress with moving singularity.

2) even if the contact area is fixed, but the punch has gross motion (like in fretting wear), the singularlty also moves.

These two problems result in a case which has no equivalent in standard fatigue, since it corresponds to a "crack" that is oscillating in size at each cycle. How would you treat the fatigue problem in this case?

In any case, are you aware of any published experimental work involving fretting fatigue or fretting wear, with a changing contact area, which uses crack analogue concepts and moving singularities?

References

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., & Macina, G. (2003). A note on the crack analogue model for fretting fatigue. International journal of solids and structures, 40(4), 807-825.

    Ciavarella, M. (2006). Some observations on the CLNA model in fretting fatigue. Tribology international, 39(10), 1142-1148.

    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.

    Ciavarella, M. (1998). The generalized Cattaneo partial slip plane contact problem. I---Theory. International Journal of solids and structures, 35(18), 2349-2362.

    Davies, M., Barber, J. R., & Hills, D. A. (2012). Energy dissipation in a frictional incomplete contact with varying normal load. International Journal of Mechanical Sciences, 55(1), 13-21.

    Fleury, R. M. N., Hills, D. A., Ramesh, R., & Barber, J. R. (2016). Incomplete contacts in partial slip subject to varying normal and shear loading, and their representation by asymptotes. in press, Journal of the Mechanics and Physics of Solids. http://dx.doi.org/10.1016/j.jmps.2016.11.016

    Giannakopoulos, A. E., Lindley, T. C., & Suresh, S. (1998). Aspects of equivalence between contact mechanics and fracture mechanics: theoretical connections and a life-prediction methodology for fretting-fatigue. Acta materialia, 46(9), 2955-2968.

    Hills, D. A., Thaitirarot, A., Barber, J. R., & Dini, D. (2012). Correlation of fretting fatigue experimental results using an asymptotic approach. International Journal of Fatigue, 43, 62-75.

Johnson, K. L., (1987). Contact mechanics. Cambridge University Press, Cambridge (UK).

    Nowell, D., Dini, D., & Hills, D. A. (2006). Recent developments in the understanding of fretting fatigue. Engineering Fracture Mechanics, 73(2), 207-222.

    Putignano, C., Ciavarella, M., & Barber, J. R. (2011). Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads. Journal of the Mechanics and Physics of Solids, 59(12), 2442-2454.

    Rajasekaran, R., & Nowell, D. (2006). Fretting fatigue in dovetail blade roots: experiment and analysis. Tribology International, 39(10), 1277-1285.