The plastic limit load solutions for cylinder and plate with slanted through-wall cracks (TWCs) are developed based on the systematic three-dimensional (3D) finite element (FE) limit analyses. As for loading conditions, axial tension, global bending, and internal pressure are considered for a cylinder with slanted circumferential TWC, whereas, axial tension and internal pressure are considered for a plate and a cylinder with slanted axial TWC. Then, the verification of FE model and analysis procedure employed in the present numerical work was confirmed by employing the existing solutions for both cylinder and plate with idealized TWC. Also, the geometric variables of slanted TWC which can affect plastic limit loads were considered. Based on the systematic FE limit analysis results, the slant correction factors which represent the effect of slanted TWC on plastic limit load were provided as tabulated solutions. By adopting these slant correction factors, the plastic limit loads of slanted TWC can be directly estimated from existing solutions for idealized TWC. Furthermore, the modified engineering estimations of plastic limit loads for slanted TWC are proposed based on equilibrium equation and von Mises yield criterion. The present results can be applied either to diverse structural integrity assessments or for accurate estimation of fracture mechanics parameters such as J-integral, plastic crack opening displacement (COD) and C*-integral for slanted TWC based on the reference stress concept (Kim, et al., 2002, “Plastic Limit Pressure for Cracked Pipes Using Finite Element Limit Analyse,” Int. J. Pressure Vessels Piping, 79, pp. 321–330; Kim, et al., 2001, “Enhanced Reference Stress-Based J and Crack Opening Displacement Estimation Method for Leak-Before-Break Analysis and Comparison With GE/EPRI Method,” Fatigue Fract. Eng. Mater. Struct., 24, pp. 243–254; Kim, et al., 2002, “Non-Linear Fracture Mechanics Analyses of Part Circumferential Surface Cracked Pipes,” Int. J. Fract., 116, pp. 347–375.)
The present paper provides the enhanced estimation of plastic J-integral and crack opening displacement (COD) for circumferential transition crack from surface to through-wall crack in cylinder based on detailed finite element analysis. The effects of circumferential transition crack on plastic J-integral and crack opening displacement have been systematically investigated for practical ranges of cylinder geometries and materials of interest. Then, the plastic influence functions (h1, h2) employed in the GE/EPRI method have been proposed to quantify those effects on plastic J-integral and COD. Furthermore, the J-integral and COD estimations based on the reference stress method using optimized reference load have also been introduced for circumferential non-idealized TWC in cylinder. Then, in order to gain the confidence in the proposed methods, the results from those proposed estimates were compared with elastic-plastic FE results by using actual stress-strain data and Ramberg-Osgood fit constants for TP 316 stainless steel. The present results can be expected to apply on various structure integrity assessments and to accurate plastic J-integral and COD estimation for circumferential non-idealized TWC in cylinder.
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The present paper proposed the modified limit load solution related to code case N-513-4 which is currently actively researched. To apply to assessment method for an elbow in code case N-513-4, the crack should be postulated as the idealized circumferential through-wall crack (TWC). For this reason, it could be led to overestimate the results due to the assumption of real crack shape. Then, the many research which is related to an accurate solution for a straight pipe by considering realistic crack has been investigated. However, the accurate solution for the elbow with non-idealized TWC is still lacked. Therefore, based on three-dimensional finite element model, the effect of non-idealized circumferential TWC on plastic limit load was investigated under internal pressure. To do this, the finite element (FE) model and analysis procedure employed in the present numerical study were validated by comparing the present finite element analyses result with existing solutions for idealized TWC in the elbow. Then, the correction factor for calculating plastic limit load was newly proposed as a tabulated form by considering practical ranges of geometry.
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