How many critical planes? A perspective insight into structural integrity

The topic of material fatigue is a subject extensively investigated within both scientific and industrial worlds. Fatigue-induced damage remains a critical concern for a variety of components, encompassing both metallic and non-metallic materials, often leading to unexpected failures during their operational lifecycle. In cases necessitating the assessment of multiaxial fatigue, critical plane methodologies have emerged as a valuable approach. These methodologies offer the means to pinpoint the component's critical regions and anticipate early-stage crack propagation. Nevertheless, the conventional technique (i.e., plane scanning method) for computing critical plane factors is a time-intensive process, reliant on nested iterations, predominantly suited for research purposes. In numerous cases, where the critical area within a component is unknown in advance (i.e., primarily due to complex geometries and loading conditions) the method proves impractical. Furthermore, the plane scanning method does not provide a deep comprehension of the critical plane concept; indeed, it is just a numerical artifice for calculating stress and strain quantities on different planes. Recently, the authors introduced an efficient algorithm for evaluating critical plane factors. This algorithm is based on a closed form solution and is applicable to all instances where the maximization of a specific parameter, based on stress or strain components, is required. The methodology relies on tensor invariants and coordinates transformation principles thus enhancing the investigation of various critical plane methods. The paper addresses two formulations of the Fatemi-Socie critical plane factor and discusses how the number of critical planes depend on the loading conditions the component is subjected to. By the use of a closed form solution a deep insight of critical planes orientation can be achieved.