On the estimation of finite lifetime under fretting fatigue loading

The aim of this paper is to formulate and validate an alternative design approach suitable for predicting finite lifetime of mechanical assemblies subjected to constant amplitude (CA) fretting fatigue loading. The design methodology being proposed is based on the use of the Modified Wӧhler Curve Method (MWCM) applied in conjunction with both the Theory of Critical Distance (TCD) and the Shear Stress-Maximum Variance Method (τ-MVM). In more detail, the TCD, applied in the form of the Point Method (PM), is used to take into account the damaging effect of the multiaxial stress gradients acting on the material in the vicinity of the contact region. The time-variable linear-elastic stress state at the critical locations is then post-processed according to the MWCM which is a bi-parametrical criterion that estimates fatigue lifetime via the stress components relative to those planes experiencing the maximum shear stress amplitude. Thanks to its specific features, the MWCM is capable of modelling not only the presence of non-zero mean stresses, but also the degree of multiaxiality and non-proportionality of the local load history being investigated. In this setting, the τ-MVM is used to calculate the stress quantities relative to the critical plane whose orientation is determined numerically by locating that plane containing the direction experiencing the maximum variance of the resolved shear stress. The accuracy and reliability of the proposed design methodology was checked against a number of experimental data taken from the literature and generated by testing four different metallic materials. The agreement between experiments and estimates being obtained strongly supports the idea that the proposed approach can be used to perform a rapid assessment of mechanical assemblies damaged by in-service fretting fatigue loading.