Estimating the orientation of Stage I crack paths through the direction of maximum variance of the resolved shear stress

•The MVM is suitable for determining the orientation of the plane of maximum shear stress amplitude.•The MVM is capable of estimating the orientation of Stage I crack paths.•The MVM is a tool suitable for using the critical plane concept in situations of practical interest. Our formalisation of the Shear Stress-Maximum Variance Method takes as a starting point the hypothesis that, in ductile materials subjected to fatigue loading, the crack initiation planes, i.e. the so-called Stage I planes, are those containing the direction experiencing the maximum variance of the resolved shear stress. From a computational point of view, the most remarkable implication of the above assumption is that, as soon as the variance and covariance terms characterising the considered load history are known, the effective time needed to estimate the orientation of the critical plane does not depend on the length of the load history itself. Further, such a computational efficiency is seen to be associated with an high-level of accuracy in estimating fatigue lifetime of both plain and notched engineering components, this holding true under constant as well as under variable amplitude uniaxial/multiaxial fatigue loading. In this scenario, by assuming that the orientation of Stage I planes can directly be determined through the orientation of Stage II crack paths, the present paper investigates whether, independently from the degree of multiaxiality and non-proportionality of the applied loading history, the direction of maximum variance of the resolved shear stress is also capable of accurately estimating the orientation of Stage I crack paths.