PSI - Issue 68

Saeid Hadidimoud et al. / Procedia Structural Integrity 68 (2025) 788–794 Saeid Hadidimoud et al. / Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction In the analysis and design of thick-walled cylinders, consideration of practical conditions that affect their load carrying capacity is necessary (Zerbst et al. 2000). The presence of cracks of various orientations, loci, shapes, and sizes would significantly impact the integrity of cylinder and potentially, is likely to cause premature failure under load levels far below the estimations that are based on implementation of structural integrity assessment codes. Additionally, the very likely and unavoidable presence of residual stresses in practice due to various sources such as fabrication (e.g. welding), proof testing (e.g. autofrettage), handling, maintenance, and loading histories could also have a significant impact on the load-carrying capacity of the vessel. Limit load estimation for open-end and closed-end cylinders requires careful evaluation of various service conditions and consideration of possible defects (especially around the weld seams) to ensure accurate results and a reliable design of the structure. The limit load of crack-free cylinders under different loading scenarios is widely studied through analytical and numerical approaches. Gangling (1988) derived the plastic limit pressure of open-end thick-walled cylinders using the twelve-angled polygonal yield criterion. Gao (1992) also proposed analytical solutions based on the von Mises criterion for open-end cylinders made of strain-hardening materials. Dixon and Perez (2008) provided simple explicit equations for limit load of open-end cylinders subjected to internal and external pressures using finite element analyses. For closed-end cylinders made of elastic linear-hardening materials, Gao (2007) proposed an analytical solution using strain gradient plasticity theory. In cases of combined loading, when the structure is subjected to axial tension in addition to internal pressure, Hales and Budden (1992) provided analytical equations for closed-end thick-walled cylinders based on maximum shear stress (Tresca) failure criterion. Ainsworth (2000) derived a solution for the limit load of closed-end cylinders under internal pressure and axial load for elastic-perfectly plastic materials using von Mises criterion. A limit load solution for circumferentially cracked thin-walled cylinders under combined loading was developed by Lei and Budden (2005). Gao et al. (2008) provided approximate analytical solutions for closed-end cylinders under combined loading, both for crack-free and fully circumferentially cracked cylinders, which were verified through comparison with finite element solutions. The effect of residual stresses, particularly through the application of autofrettage to cylinders, has been comprehensively investigated. Studies also aimed to explore the role of Bauschinger effect factor. General solutions for the elastic-plastic analysis of thick-walled cylinders after autofrettage were provided by Parker (2001), Perry and Aboudi (2003) and Perl (2006). Solutions and studies on autofrettage were mainly focused on the beneficial effect of residual stresses where the stresses arising from service loading oppose the residual stresses. In the following sections, geometry and material properties and other details of the finite element model are described and the steps taken in conducting the numerical simulations in ABAQUS finite element analysis tool are outlined. Then, the results of simulations are compared with the available analytical solutions. For cases where no analytical solutions have been proposed, the results of FE simulations are presented. Findings from the study provide an overview of the influence of material response, crack configuration, and residual stresses on the limit load of defective thick-walled cylinders under combined loading.

Nomenclature

Yield strength of material Poisson's ratio Young's Modulus

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Linear strain-hardening modulus Inner radius Outer radius Mean radius Thickness of the cylinder wall Radios Ratio Half-length of the cylinder Radius of the plastic region Pressure

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