The Theory of Critical Distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading

Abstract The present paper summarises an attempt of reformulating the so-called Theory of Critical Distances (TCD) to make it suitable for estimating finite life of notched components subjected to variable amplitude (VA) uniaxial fatigue loading. In more detail, similar to the design strategy we have suggested as being followed under constant amplitude (CA) loading, the VA linear-elastic formalisation of the TCD proposed here takes as a starting point the assumption that the critical distance value is a material property whose length decreases with increasing of the number of cycles to failure. Through a systematic validation exercise done using ad hoc generated experimental results, it was shown that the TCD, applied in the form of both the Point (PM), Line (LM), and Area Method (AM), is successful in estimating VA lifetime of notched metallic materials by simply calculating an equivalent critical distance having length which depends not only on the features of the assessed load spectrum, but also on the profile of the post-processed stress field. The accuracy and reliability of this alternative formalisation of the TCD was checked by using numerous experimental results generated by testing, under fully-reversed VA axial loading, notched cylindrical samples of a commercial medium-carbon steel containing three different stress raisers. Further, in order to more accurately verify the sensitivity of the proposed definition for the VA critical length to the features of the assessed load history, two spectra were investigated: the first one was characterised by a conventional Rayleigh distribution, whereas the second was used to study the effect of those cycles of low stress amplitude. Such a validation exercise allowed us to prove that the TCD is highly accurate also in estimating fatigue damage in notched components subjected to VA loading: this result is definitely encouraging, fully supporting the idea that the TCD can safely be used to design real notched components damaged by in-service VA load histories.