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\begin{document}

\title{Closed form solution for Fatemi-Socie critical plane method in case of
linear elasticity and proportional loading}



\author[1]{Andrea Chiocca}%
\author[1]{Michele Sgamma}%
\author[1]{Francesco Frendo}%
\affil[1]{Universita degli Studi di Pisa Dipartimento di Ingegneria Civile e Industriale}%


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  \date{June 18, 2024}


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\begin{abstract}
The fatigue analysis of structural components is a relevant research
topic in both scientific and industrial communities. Despite major
advances in understanding, fatigue damage remains a significant issue
for both metallic and non-metallic components, sometimes leading to
unexpected failures of in-service parts. Among the different assessment
methodologies, critical plane methods have gained significance as they
enable identification of a component's critical location and direction
of early crack propagation. However, the standard plane scanning method
for calculating critical plane factors is computationally intensive and,
for that, it is only applied when the component critical regions are
already known. When critical areas are not easily identifiable due to
complex geometries, loads or constraints, a more efficient method for
evaluating critical plane factors would be required. This work presents
a closed form solution for efficiently evaluating the Fatemi-Socie
critical plane factor, in case of linear-elastic material behaviour and
proportional loading conditions, based on tensor invariants and
coordinates transformation laws. The proposed algorithm was tested on
different test cases (i.e. hourglass, notched and welded joint
geometries) under different loading conditions (i.e. tensile, bending
and torsion) and showed a significant reduction in computation time
compared to the standard plane scanning method.%
\end{abstract}%



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