Mode-I stress intensity factors for cracked fin-shaped shell under bending

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O R I G I NA L PA P E R

W. J. Yuan

· Y. J. Xie

Mode-I stress intensity factors for cracked fin-shaped shell under bending

Received: 10 March 2020 / Revised: 6 October 2020 / Accepted: 15 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020

Abstract Determining the stress intensity factor (SIF) for cracked engineering structures under different loading conditions is one of the core issues of fracture analysis. A slender fin-shaped shell possesses both shell and beam characteristics, in the cross section of which some complex cracks, such as the circumferential and T-shaped cracks, may arise. There will be different singular stress fields next to crack tips for a cracked fin-shaped shell under bending. Based on the conservation law and elementary mechanics, a technique to determine SIFs is proposed in this article, which is simple and easy to understand. The SIFs calculated using the present method agree well with FEM results even if elementary mechanics is used.

1 Introduction Cracks in engineering structures are potential security risks. The SIFs are the key parameters to assess the safety of cracked engineering structures. Regarding infinite two-dimensional and three-dimensional elastomer crack problems, some of the closed solutions of SIFs can be conveniently given. However, for three-dimensional cracked solids with finite boundaries, such as a cracked slender fin-shaped shell, it is challenging to obtain analytical solutions for stress intensity factors other than by numerical methods. For cracked beam-like structures, much effort has been invested in a simple method to solve the SIFs. In 1986, Kienzler and Herrmann [1], who proposed a simple method for the approximation of stress intensity factors in cracked beams (see also Herrmann and Sosa [2]), assumed empirically that the strain energy release rate G for crack extension was equal to that for crack widening without specific justification. As such, Irwin’s G-K relationship was utilized to determine the SIFs. In 1990, Bazant [3] pointed out that this assumption was approximately valid within a correction factor, and that it could only be determined by optimum fitting of the exact solution. In contrast, Gao and Herrmann [4] demonstrated that this correction factor could be obtained by simple asymptotic matching with a standard limiting crack solution in 1992, and further made some corrections and clarifications for estimation of the stress intensity factor of an axially symmetric cracked beam. Under different loading conditions, Gao’s and Herrmann’s method was extended by Dunn et al. [5] in 1997 to assess the stress intensity factors of circumferentially cracked cylinders and rectangular beams. Similarly, by means of estimating the SIFs of cracked T-beams and bars, the extension of a simple and convenient method previously proposed by Kienzler and Herrmann was established by Ricci and Viola [6] in 2006. However, the problems pointed out by Bazant [3] still remained. In 1998, based on the two-/three-dimensional conservation law, Xie et