A closed-form solution for evaluating the Findley critical plane factor

The fatigue assessment of structural components is a significant topic investigated both in the academia and industry. Despite the significant progress in comprehension over the past few decades, fatigue damage remains a significant challenge, often leading to unexpected component failures. One commonly used approach for fatigue assessment is the critical plane analysis, which aids in identifying the critical location and early crack propagation direction in a component. However, the conventional method for calculating critical plane factors is computationally demanding and is typically utilized only when the critical regions of the component are already known. In situations where the critical areas are difficult to be identified due to complex geometry, loads, or constraints, a more efficient method is required for evaluating critical plane factors. This research paper introduces an analytical algorithm to efficiently evaluates the widely used Findley critical plane factor. The algorithm operates within the framework of linear-elastic material behavior and proportional loading conditions, relying on tensor invariants and coordinate transformation laws. The algorithm has been tested on different component geometries, including a box-welded joint and a tubular specimen, subjected to proportional loading conditions such as tension, torsion, and a combination of them. The analytical method allowed a significant reduction in computation time while providing the exact solution of critical plane factor and critical plane orientations.