Critical plane and critical distance approaches to assess damage under variable amplitude fretting fatigue loading

This paper summarises an attempt to formulate a design approach suitable for predicting the finite lifetime of mechanical assemblies subjected to constant/variable amplitude fretting fatigue loading. The proposed design methodology makes use of the Modified Wӧhler Curve Method (MWCM), applied in conjunction with the Theory of Critical Distance (TCD) and the Shear Stress-Maximum Variance Method (τ-MVM). In particular, the TCD (applied in the form of the Point Method) 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 point is then post-processed according to the MWCM which is a bi-parametrical criterion that estimates fatigue lifetime via the plane experiencing the maximum shear stress amplitude. Finally, the τ-MVM is used to calculate the stress quantities relative to the critical plane whose orientation is determined numerically by selecting the plane containing the direction experiencing the maximum variance of the resolved shear stress. Further, this direction is also used to perform the cycle counting by directly applying the classic Rain-Flow Method to post-process the resolved shear stress. The overall accuracy and reliability of the proposed approach is checked against a large number of new experimental results that were generated in the Sheffield Structures Laboratory under variable amplitude fretting fatigue loading.