A critical distance/plane method to estimate finite life of notched components under variable amplitude uniaxial/multiaxial fatigue loading

The present paper summarises the main features of a design technique we have devised to specifically perform, by post-processing the linear-stress fields in the vicinity of the assumed crack initiation sites, the fatigue assessment of notched components subjected to in-service variable amplitude (VA) uniaxial/multiaxial fatigue loading. In more detail, fatigue damage is estimated through the Modified Wöhler Curve Method (MWCM) applied along with the Theory of Critical Distances (TCDs), the latter being used in the form of the Point Method (PM). According to the philosophy on which the linear-elastic TCD is based, the adopted critical distance is treated as a material property whose length increases as the number of cycles to failure decreases. To correctly apply the MWCM, the orientation of the critical plane is suggested here as being calculated through that direction experiencing the maximum variance of the resolved shear stress. Further, the above direction is used also to perform the cycle counting: since, by definition, the resolved shear stress is a monodimensional stress quantity, fatigue cycles are counted by taking full advantage of the classical three-point Rain Flow method. From a philosophical point of view, the real novelty contained in the present paper is that eventually all the different pieces of theoretical work we have done over the last 15 years by investigating different aspects of the uniaxial/multiaxial fatigue issue are consistently brought together by formalising a design methodology of general validity. The accuracy and reliability of the proposed fatigue assessment technique was checked by using 124 experimental results generated by testing notched cylindrical samples of carbon steel C40. The above tests were run under three different load spectra, by exploring uniaxial as well as in- and out-of-phase biaxial situations, in the latter case the axial and torsional load signals being not only characterised by non-zero mean values, but also by different frequencies. To conclude it can be said that such a systematic validation exercise allowed us to prove that the proposed approach is highly accurate, resulting in estimates falling within the constant amplitude (CA) fully-reversed uniaxial and torsional scatter bands used to calibrate the method itself (this holding true independently of both complexity of the applied VA loading path and sharpness of the tested notch).

► Local multiaxial stress cycles can accurately by counted using the Maximum Variance Method.
► The MWCM applied along with the PM is successful in estimating VA multiaxial fatigue lifetime of notched components.
► The MWCM applied along with the PM can be applied by directly post-processing linear-elastic FE results.