Analytical Limit Loads for Tube Sections With Circumferential Degradation

2004 ◽  
Author(s):  
W. Reinhardt ◽  
X. Wang
Keyword(s):  
Analytical Solutions ◽  
Load Capacity ◽  
Bending Moment ◽  
Limit Load ◽  
Thin Wall ◽  
Plastic Limit ◽  
Tubes And Pipes ◽  
Limit Loads ◽  
Plastic Limit Load ◽  
Analytical Limit

The fracture mechanics evaluation of tubes and pipes with circumferential degradation typically requires that the plastic limit load capacity be evaluated under a combination of axial force and bending moment loading. Most available analytical solutions are thin-wall approximations and may not work well for heavy-wall applications. The present paper derives an analytical limit load for a cylindrical pipe or tube with a partial circumferential, partial through-wall flaw and its bounding cases (through wall partial circumferential and uniform circumferential part-throughwall flaw). The solution is not in closed form, but can be easily solved with available mathematical software like MathCAD. The obtained limit loads for a steam generator tube are compared to those from simplified analytical solutions. The effect of tube supports on the limit load of a tube with non-axisymmetric flaw is discussed with a simplified model.

Determination of Transition From Thin Shell to Thick Shell Theory for Torispherical Heads With Head Dish Radius to Thickness Ratios Under 20

2020 ◽  
Author(s):  
Barry Millet ◽  
Kaveh Ebrahimi
Keyword(s):  
Internal Pressure ◽  
Transition Point ◽  
Limit Load ◽  
Thick Wall ◽  
Ratio Test ◽  
Thin Wall ◽  
Plastic Limit ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Plastic Limit Load

Abstract This paper will clarify the point of transition where the behavior of the dish of a torispherical head goes from thin wall theory (collapse failure and membrane) to thick wall (burst failure) as the head dish radius to thickness ratios (L/t) gets smaller. There are several stated ratio limits for this transition. Three separate Welding Research Bulletins WRC 364 New Design Curves for Torispherical Heads[1], WRC 444 Buckling Criteria for Torispherical Heads Under Internal Pressure [3] and, WRC 501 Design of Torispherical and Ellipsoidal Heads Subjected to Internal Pressure[4] each provide a different definition of the transition point, that being 16.67, 15 and 20 respectively. This paper will review the actual test performed for L/t ratios from 20 down to 15 (which is the lowest ratio test run) and provide the results of a numerical desktop study in lieu of actual testing. Linear elastic, elastic perfectly plastic limit load and elastic plastic limit load finite element analysis will be parametrically run across many L/t ratios and the knuckle radius will be varied across the runs. The results will be reviewed to check through wall behavior to find the transition point of thin to thick wall behavior. These will also be compared against the existing ASME BVP Section VIII Division 2 [5] formulas.

Effect of Bend Angle on Plastic Limit Loads of Pipe Bends Under In-Plane Bending Moment

2016 ◽  
Author(s):  
Shunjie Li ◽  
Changyu Zhou ◽  
Jian Li ◽  
Xinting Miao
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Large Strain ◽  
Large Angle ◽  
Three Dimensional ◽  
Bending Moment ◽  
Limit Load ◽  
Bend Angle ◽  
Plastic Limit ◽  
Limit Loads

The effect of bend angle on plastic limit loads of pipe bends (elbows) under in-plane opening and closing bending moment is presented using three-dimensional large strain nonlinear finite element analyses. The results show that the presence of ovality significantly leads to the stress concentration in the middle cross section, which is the critical section of pipe bends. Meanwhile the state of stress concentration is also associated with the loading modes including the in-plane opening bending moment and the closing bending moment. Then plastic limit loads of pipe bends are further studied. It is found that plastic limit loads are decreasing with the increase of bend angles. Especially the variation of plastic limit loads of small angle pipe bends (bend angle from the 0 degree to 90 degree) is larger than that of large angle pipe bends (bend angle greater than 90 degree). Based on the finite element results, the present plastic limit load solutions are not fit for the large angle pipe bends (bend angle greater than 90 degree).

Plastic Limit Analysis of an Elbow with Various Wall-Thinning Geometries

2008 ◽  
Vol 385-387 ◽  
pp. 833-836
Author(s):  
Sang Min Lee ◽  
Young Hwan Choi ◽  
Hae Dong Chung ◽  
Yoon Suk Chang ◽  
Young Jin Kim
Keyword(s):  
Nuclear Power ◽  
Three Dimensional ◽  
Bending Moment ◽  
Limit Load ◽  
Nuclear Industry ◽  
Bend Angle ◽  
Piping System ◽  
Plastic Limit ◽  
Limit Loads ◽  
Wall Thinning

A piping system including straight pipes, elbows and tee branches in a nuclear power plant is mostly subjected to severe loading conditions with high temperature and pressure. In particular, the wall-thinning of an elbow due to flow accelerated corrosion is one of safety issues in the nuclear industry. In this respect, it is necessary to investigate the limit loads of an elbow with a wall-thinned part for evaluating integrity. In this paper, three dimensional plastic limit analyses are performed to obtain limit loads of an elbow with different bend angles as well as defect geometries under internal pressure and in-plane/out-of-plane bending moment. The limit loads are also compared with the results from limit load solutions of an uninjured elbow based on the von Mises yield criteria. Finally, the effects of significant factors, bend angle and defect shape, are quantified to estimate the exact load carrying capacity of an elbow during operation.

Plastic Limit Loads for Slanted Through-Wall Cracks in Cylinder and Plate Based on Finite Element Limit Analyses

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Doo-Ho Cho ◽  
Young-Hwan Choi ◽  
Nam-Su Huh ◽  
Do-Jun Shim ◽  
Jae-Boong Choi
Keyword(s):  
Finite Element ◽  
Crack Opening ◽  
Limit Load ◽  
Correction Factors ◽  
Plastic Limit ◽  
Opening Displacement ◽  
Limit Loads ◽  
Axial Tension ◽  
Reference Stress ◽  
Plastic Limit Load

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.)

Estimates of Plastic Limit Loads of Thick-Walled Cylinders With Non-Idealzied Through-Wall Cracks

2013 ◽  
Author(s):  
Tae-Song Han ◽  
Nam-Su Huh ◽  
Do-Jun Shim
Keyword(s):  
Fracture Mechanics ◽  
Structural Integrity ◽  
Limit Load ◽  
Ductile Material ◽  
J Integral ◽  
Plastic Limit ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Reference Stress ◽  
Plastic Limit Load

In order to assess a structural integrity of cracked components made of highly ductile material based on fully plastic fracture mechanics concept, an accurate plastic limit load of components of interest is crucial element. Such a plastic limit load can also be applied to estimate elastic-plastic J-integral based on the reference stress concept. In this context, during last several decades, many efforts have been made to suggest plastic limit load solutions of cracked cylinder. Recent works for evaluating rupture probabilities of nuclear piping indicate that the only use of idealized circumferential through-wall crack leads to very conservative results which in turn gives higher rupture probabilities of nuclear piping, thus the considerations of more realistic crack shape during crack growth due to primary water stress corrosion cracking (PWSCC) and fatigue and axial through-wall crack were recommended to come up with more realistic rupture probabilities of nuclear piping. Then, the needs of fracture mechanics parameters of non-idealized through-wall cracks both in axial and circumferential directions have been raised. In the present work, the plastic limit loads of thick-walled cylinder with non-idealized axial and circumferential through-wall cracks are proposed based on detailed 3-dimensional finite element analyses. The present results can be applied either to assess structural integrity of thick-walled nuclear piping with non-idealized through-wall cracks or to calculate elastic-plastic J-integral using the reference stress concept.

Simulation of Curved Fatigue Crack Growth with Calculation of the Plastic Limit Load

2009 ◽  
Vol 417-418 ◽  
pp. 45-48
Author(s):  
Holger Theilig ◽  
Dirk Holländer ◽  
Michael Wünsche
Keyword(s):  
Crack Growth ◽  
Crack Path ◽  
Limit Load ◽  
Simulation Algorithm ◽  
Plastic Limit ◽  
Limit Loads ◽  
Plastic Limit Load ◽  
Fully Automatic ◽  
Piecewise Parabolic ◽  
Automatic Simulation

In this paper a higher order crack path simulation algorithm for multiple interacting cracks is presented using piecewise parabolic curved increments including the consideration of the plastic limit loads. For this reason, the program PCCS-2D has been extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the FAD proce¬dure in combination with a numerical crack path simulation. Several numerical examples are pre¬sented to show the accuracy and the efficiency of the crack path simulation including the analysis of the plastic limit loads

Analysis and Experiments on the Plastic Limit Load of Elbows under Combined Pressure and In-Plane Closing Bending Moment

2013 ◽  
Vol 774-776 ◽  
pp. 1090-1097 ◽  
Author(s):  
Zhi Xiang Duan ◽  
Kun Shi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Safety Assessment ◽  
Bending Moment ◽  
Limit Load ◽  
Experimental Results ◽  
Plastic Limit ◽  
Element Analysis ◽  
Limit Pressure ◽  
Plastic Limit Load

This paper discusses the plastic limit load of elbows without defects and with local thinned area (LTA) in the extrados under combined pressure and in-plane closing bending moment. Finite element analysis (FEA) and experiments have been used. The results of FEA show that, for the elbows without defects, when the ratio of pressure to the limit pressure (P/PL) is smaller than 0.469, the limit moment of elbows increases with the increasing pressure; when the ratio (P/PL) is bigger than 0.469, the limit moment of elbow decreases with the increasing pressure. For the elbows with LTA, the FEA results show that with different LTA the variation of the limit load of elbows to the pressure is different. Perhaps, the limit moment of elbows always decreases with the increasing pressure. It is also likely that the limit moment of elbows increases with the increasing pressure and then decreases with the increasing pressure. The results of FEA are consistent with the experimental results. By fitting the results of FEA, the safety assessment figure for elbows under combined pressure and in-plane closing bending moment is drawn.

Plastic Limit Loads for Slanted Circumferential Through-Wall Cracked Pipes Based on Finite Element Limit Analysis

2011 ◽  
Author(s):  
Hyun-Min Jang ◽  
Doo-Ho Cho ◽  
Jae-Boong Choi ◽  
Young-Jin Kim ◽  
Nam-Su Huh ◽  
...  
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Limit Load ◽  
Correction Factors ◽  
Plastic Limit ◽  
Opening Displacement ◽  
Limit Loads ◽  
Plastic Limit Load

Based on detailed three-dimensional (3-D) finite element (FE) limit analyses, the plastic limit load solutions for pipes with slanted circumferential through-wall cracks (TWCs) subjected to axial tension, global bending and internal pressure are reported. The FE model and analysis procedure employed in the present numerical study were validated by comparing the present FE results with existing solutions for plastic limit loads of pipes with idealized TWCs. To quantify the effect of slanted crack on plastic limit load, the slant correction factors for calculating plastic limit loads of pipes with slanted TWCs from pipes with idealized TWCs were newly proposed via extensive 3-D FE calculations. These slant correction factors are presented in a tabulated form for practical ranges of geometry and each loading conditions. Moreover, the present FE plastic limit loads were also compared with the existing solutions of pipes with slanted TWCs. These FE plastic limit load solutions can be applied to estimate elastic-plastic fracture mechanics parameters and creep fracture mechanics parameters, such as elastic-plastic J–integral and crack opening displacement, creep C*-integral and creep crack opening displacement, based on the reference stress concept considering more realistic crack shape.

Shakedown and Limit Analysis of 45-Degree Piping Elbows Under Internal Pressure and Cyclic In-Plane Bending

2019 ◽  
Author(s):  
Heng Peng ◽  
Yinghua Liu
Keyword(s):  
Internal Pressure ◽  
Limit Analysis ◽  
Limit Load ◽  
Plastic Limit ◽  
Limit Loads ◽  
Integrity Assessment ◽  
Elastic Plastic ◽  
Plastic Limit Load ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract This paper carries out the shakedown and limit analysis of 45-degree piping elbows subjected to steady internal pressure and cyclic in-plane closing, opening and reverse bending moments by means of the recently proposed stress compensation method (SCM). Different geometries of the piping elbows and various combinations of these applied loads are investigated to create various shakedown limit and plastic limit load interaction curves. The plastic limit loads for single internal pressure and single bending moment calculated with the SCM are compared to those calculated with the twice-elastic-slope method. Full step-by-step elastic-plastic incremental finite element analyses are utilized to verify the structural cyclic responses on both sides of the curves obtained and further to confirm the correct shakedown limit loads and boundaries. It is shown that the SCM calculates the shakedown limit load accurately and possess more than 40 times the computational efficiency of the step-by-step elastic-plastic incremental method. The effects of the ratios of bending radius to mean radius and mean radius to wall thickness of the piping elbow as well as loading conditions on shakedown limit and plastic limit load interaction curves are presented. The results presented in this work provide a comprehensive understanding of long term response behaviors of the piping elbow under the combined cyclic loading and offer some essential points to be concerned for the design and integrity assessment of piping systems.

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