An efficient algorithm for critical plane factors evaluation

Fatigue of structural components is a widely discussed subject on which extensive research is still being carried out, both in the scientific and industrial communities. Fatigue damage still represents a major issue for both metallic and non-metallic components, sometimes leading to unforeseen failures for in-service parts. Among all the assessment methodologies, critical plane methods gained a lot of relevance, as they allow the identification of the component’s critical location and the direction of early crack propagation. However, the standard method employed for calculating critical plane factors is very time-consuming as it makes use of nested for/end loops and, for that reason, it is usually applied in a research context, or when the critical areas of the component are known. Very often, however, the critical regions cannot be identified, due to complex geometries, loads or constraints, or the fatigue assessment has to be carried out with tight time scheduling, which is typical of the industry. In this work, an efficient algorithm for calculating critical plane factors, useful to speed up the fatigue assessment process, is presented. The algorithm applies to all critical plane factors that require the maximization of a specific parameter based on stress and strain components or a combination of them. The methodology maximizes the parameter utilizing tensor invariants and coordinates transformation law. In order to validate the proposed methodology, without loosing generality, the Fatemi-Socie critical plane factor was considered. The new algorithm was tested on different geometries (i.e. hourglass, notched and welded joint geometries) under different loading conditions (i.e. proportional/non-proportional, uniaxial and multiaxial loading) and showed a significant reduction in computation time respect the standard plane scanning method, without any loss of solution accuracy.