A refined CLNA model in fretting fatigue using asymptotic characterization of the contact stress fields

Using the Atzori–Lazzarin criterion, the first author has recently proposed a unified model for fretting fatigue (FF), called the crack‐like notch analogue (CLNA) model. Two possible types of behaviour were suggested: either ‘crack‐like’ or ‘large blunt notch,’ and these are immediately studied in the typical condition of constant normal load and in phase oscillating tangential and bulk loads. The former condition (‘crack‐like’) was treated by approximating the geometry to the perfectly flat one of the crack analogue (CA), improved in some details, reducing all possible geometries to a single contact problem. The latter (‘large blunt notch’), with a simple peak stress condition i.e. a simple notch analogue model. In the present paper, the calculation of the ‘crack‐like’ behaviour is improved using the recent asymptotic characterisation developed by Dini, Hills and Sackfield, which extracts the asymptotic singular stress field of the fretting contact. A significant difference is found in the ‘equivalent’ geometric factor obtained for the Hertzian geometry, particularly near full sliding, where the new criterion is more conservative, but still not large enough to permit to find, for example in Nowell's FF experimental data, if the refinement is an improvement of predictive capabilities. In flatter geometries, the difference is expected to be even smaller than in the case of the Hertzian geometry, and in this case, the original CLNA model, for its simplicity, remains a very convenient simple closed form criterion.