Correction of erroneous normal stress calculation for critical plane based fatigue criteria

Abstract

Fatigue criteria for nonproportional loading often rely on the premise that damage initiates on the plane with the highest shear stress range. Due to the reciprocity of shear stress, at least two equivalent planes in 3D space can be found. Among these, the most critical plane is determined by its normal stress, as tensile stress on the crack surface facilitates damage formation. Many loading scenarios give rise to multiple or even an infinite number of planes with identical shear stress ranges, making it challenging to identify the most critical one. Current critical plane search methods do not address this problem, even though incorrect assessments of normal stress can lead to substantial overestimation of the fatigue life — by up to several orders of magnitude. In this work, we present a new procedure that reliably identifies the most critical plane by explicitly considering normal stress when multiple planes exhibit equivalent shear stress ranges. Our findings show that state-of-the-art methods introduce substantial errors in more than 10% of sinusoidal loading scenarios by failing to account for this additional criterion.