PSI - Issue 81

Ivan Shatskyi et al. / Procedia Structural Integrity 81 (2026) 240–243

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structures and have been published in review papers. A review of the reliability assessment criteria for pipelines with corrosion defects operating under internal pressure was conducted in the article by Amaya- Gómez et al. (2019). This study also includes estimations of the internal pressure that an intact pipe can withstand, given its geometry and material strength. A review on composite patch repairs of shell structures and the most important parameters affecting their efficiency and durability is provided by Mohammadi et al (2020). Of particular theoretical and practical interest is the construction of simple and effective models for assessing the strength of damaged structures with coatings. In the works of Shatskii (1989, 2001), a crack model with hinged edges was introduced to simulate the influence of a flexible coating. The analysis of the influence of flexible coatings on the stress state and limit equilibrium of cylindrical shells with cracks was carried out by both numerical and asymptotic methods in the works of Shatskyi et al. (2018, 2019). The finite element analysis of the patched pipe was performed in Lam et al. (2011), Zarrinzadeh et al. (2017a), with experimental and numerical fatigue crack growth analysis in Zarrinzadeh et al. (2017b), as well as a comparison of the conditions with and without patch repair in Meriem-Benziane et al. (2015). Limit load solutions for axially cracked hollow cylinders are reviewed and compared with the finite element method results available at that time in the work of Lei (2008). Despite numerous general theoretical results, specific problems persist in practice, necessitating the development of simple engineering methods for calculating the strength of repaired pipe-like structures without resource-intensive numerical computer analysis. Based on previous theoretical results, this study aims to develop a calculation technique for evaluating the strength of a cracked pipe repaired by a composite sleeve. This calculation technique includes comparing the results obtained with the strength of both the unrepaired pipe and the pipe without defects for a certain set of given geometric and mechanical parameters. 2. Materials and methods Let us consider a fragment of the pipe of radius R and thickness h with a longitudinal crack of length l 2 under internal pressure p and repaired by an inner bandage of thickness cov h as it is shown in Fig.1. We assume that the bandage is long enough compared to the crack so that the length of the bandage does not affect the stress distribution in the vicinity of the defect. The task is to evaluate and compare the strength of the damaged and restored pipe with the unrestored and with the undamaged one.

Fig. 1. Scheme of the pipe with the longitudinal crack repaired by the inner bandage.

Depending on the presence or absence of defects in the pipe and stages of its renovation, we used different calculation models for the strength estimation of the pressured pipeline. For the limit pressure estimation of the pipe without defects, we use Barlow's formula (see Adams et al. (2018), Amaya Gómez et al. (2019 ), Singh (2021)):

R h

[ ] 1    .

(1)

p

For the strength estimation of the pipe with a longitudinal crack without restoration, we use the asymptotic formula obtained by Folias (1984):

K

64 5

 R h l c



  

  

2 

1

1

.

(2)

p

  2

