Andrea Chiocca

The integrity assessment of structural components under complex loading conditions relies on the evaluation of the fatigue damage typically arising from stress concentrations, such as geometric irregularities, notches, weld beads, grooves etc. Various methodologies, including the Notch Stress Approach (NSA), the Theory of Critical Distances (TCD), the Strain Energy Density (SED), and the Critical Plane (CP) concept, have been pivotal in assessing fatigue strength for notched and welded components. Recent works combine some of the above mentioned methodologies, while other works propose to vary the embedded parameters accounting for the loading type or the fatigue lives, trying to improve the accuracy of the fatigue assessment process. This paper introduces a novel approach, the Effective Critical Plane (ECP), which is founded on the critical plane concept. The CP factor is, however, calculated starting from an averaged, over a small volume, stress–strain field. The size of the averaging volume is assumed to be a material parameter and is determined by a best fitting procedure over different experimental data sets. The novel approach is illustrated by means of the Fatemi-Socie and the Smith-Watson-Topper CP damage factors. Its potential application to other CP formulations is straightforward, as well. Literature experimental data for low carbon steel specimens possessing different notches and loading conditions are used to validate the method’s capability in accurately determining the fatigue life and to set the radius of the averaging volume for the given material and CP parameter. A spherical volume or circular area are used in case of fully 3D or 2D numerical models, respectively. Results are compared to those of some of already existing methods, namely SED, TCD and the Modified Wöhler Curve Method.

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 remains a major issue for both metallic and non-metallic components, sometimes resulting in unforeseen failures for in-service parts. Among all the assessment methodologies, critical plane methods have gained relevance as they allow the identification of the component’s critical location and the direction of early crack propagation. However, the standard method for calculating critical plane factors is time-consuming, typically involving nested loops, and is mainly used in a research context or when the critical areas of the component are known. Often, though, critical regions cannot be identified due to complex geometries, loads, constraints, or the need for rapid industry-based fatigue assessments. In this work, an efficient algorithm for calculating critical plane factors, aimed at expediting 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 their combinations. The methodology maximizes the parameter using tensor invariants and coordinate transformation laws. To validate the proposed methodology, without losing generality, the "Fatemi-Socie" critical plane factor was considered. The new algorithm was tested on different geometries (e.g., hourglass, notched, and welded joint geometries) under various loading conditions (e.g., proportional/non-proportional, uniaxial, and multiaxial loading) and demonstrated a significant reduction in computation time compared to the standard plane scanning method, without compromising solution accuracy.

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.