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

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Heng Peng ◽  
Jun Shen ◽  
Yinghua Liu ◽  
Haofeng Chen
Keyword(s):  
Internal Pressure ◽  
Limit Load ◽  
Plastic Limit ◽  
Element Analysis ◽  
Shakedown Analysis ◽  
Integrity Assessment ◽  
Elastic Plastic ◽  
Computation Efficiency ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract This paper carries out the limit and shakedown analysis of 45 deg piping elbows made up of elastic–perfectly plastic materials by means of the recently proposed stress compensation method (SCM). The elbows are subjected to steady internal pressure and cyclic in-plane closing, opening, and reversed bending moments. Different geometries of the piping elbows and various combinations of these applied loads are investigated to generate various plastic limit and shakedown limit load interaction curves. The plastic limit bending moment and plastic limit internal pressure calculated with the SCM are compared to those determined by the twice-elastic-slope approach. Full step-by-step (SBS) elastic–plastic incremental finite element analysis (FEA) is 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 possesses about 40 times the computation efficiency of the SBS elastic–plastic incremental method. The effects of the ratios of mean radius to wall thickness and bending radius to mean radius of the piping elbow as well as the loading conditions on the plastic limit and shakedown limit load interaction curves are presented. The results presented in this work give a comprehensive understanding of long-term response behaviors of the piping elbow subjected to cyclic loadings and provide some guidance for the design and integrity assessment of piping systems.

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.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Internal Pressure and Bending Moments

2021 ◽  
Author(s):  
Heng Peng ◽  
Yinghua Liu
Keyword(s):  
Yield Strength ◽  
Internal Pressure ◽  
Limit Analysis ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Bending Moments ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract In this paper, the Stress Compensation Method (SCM) adopting an elastic-perfectly-plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analysed. The present method is incorporated in the commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of practical piping elbows.

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.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Inner Pressure and Bending Moments

2020 ◽  
Author(s):  
Heng Peng ◽  
Yinghua Liu
Keyword(s):  
Yield Strength ◽  
Limit Analysis ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Bending Moments ◽  
Plastic Limit ◽  
Inner Pressure ◽  
Plastic Limit Load ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract The stress compensation method (SCM) for shakedown and limit analysis was previously proposed and applied to elastic-perfectly plastic (EPP) piping elbows. In this paper, the SCM is extended to account for limited kinematic hardening (KH) material model based on the extended Melan’s static shakedown theorem using a two-surface model defined by two hardening parameters: initial yield strength and ultimate yield strength. To validate the extended SCM, a numerical test on a cylinder pipe is performed. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to inner pressure and cyclic bending moments. Various loading combinations are investigated to create the shakedown limit and plastic limit load interaction curves. The effects of the material hardening, angle of the elbow and loading conditions on the shakedown limit and plastic limit load interaction curves are presented and analysed. The present method is incorporated in the commercial software of Abaqus and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of practical piping elbows.

Limit Load Finite Element Analysis of Thick-Walled Cylinders with Surface Cracks under Combined Internal Pressure and Axial Tension

2011 ◽  
Vol 341-342 ◽  
pp. 416-420 ◽  
Author(s):  
Mahdi Maarefdoust ◽  
Pooria Akbarzade
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Surface Defects ◽  
Axial Loading ◽  
Limit Load ◽  
Pressure Vessels ◽  
Element Analysis ◽  
Integrity Assessment ◽  
Applied Loading ◽  
Approximate Analytical Solutions

Limit load analysis of defect free thick walled pipes and cylinders subjected to internal pressure and combined internal pressure and axial loading is commonly performed as part of integrity assessment procedures for transmission pipelines and pressure vessels across the industry. Moreover the potential impact of environmental assisted or accidental damage that result in creation of surface defects and consequently affects the ability of vessel to withstand the applied loading conditions. This paper attempts to demonstrate the effect of surface defects on the limit load of cylinders by use of finite element method. ABAQUS software has been used for FE analysis and modeling. Approximate analytical solutions for benchmark model have been used for validation/verification of numerical results.

scholarly journals Plastic limit load of ellipsoidal pressure vessel head with nozzle under internal pressure loading

2013 ◽  
Vol 18 (4) ◽  
pp. 1263-1274 ◽  
Author(s):  
V.N. Skopinsky ◽  
N.A. Berkov ◽  
A.B. Smetankin
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Limit Load ◽  
Rate Of Change ◽  
Pressure Loading ◽  
Plastic Limit ◽  
Elastic Plastic ◽  
Limit Pressure ◽  
Plastic Limit Load ◽  
Plastic Limit Pressure

Abstract A new method and numerical procedure for determining the plastic limit load in an ellipsoid-cylinder intersection using the elastic-plastic finite element analysis are presented. The proposed method is based on the maximum criterion of the rate of change of the relative plastic work. For the elastic-plastic analysis of the nozzle connections the 2D finite element method and plasticity theory with strain hardening are used. The results of the comparison of the plastic limit pressure obtained on the basis of different known criteria and the proposed criterion are presented. A parametric study of ellipsoidal heads with a nozzle under internal pressure loading was performed. The effects of nondimensional geometric parameters of shell intersection on the plastic limit pressure are discussed.

Limit Load Solutions for Pipes With Through-Wall Crack Under Single and Combined Loading Based on Finite Element Analyses

2006 ◽  
Vol 129 (3) ◽  
pp. 468-473 ◽  
Author(s):  
Nam-Su Huh ◽  
Yun-Jae Kim ◽  
Young-Jin Kim
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Limit Analysis ◽  
Limit Load ◽  
Combined Loading ◽  
Thickness Effect ◽  
Plastic Behavior ◽  
Plastic Limit ◽  
Integrity Assessment ◽  
Plastic Limit Load

The present paper provides plastic limit load solutions for axial and circumferential through-wall cracked pipes based on detailed three-dimensional (3D) finite element (FE) limit analysis using elastic-perfectly plastic behavior. As a loading condition, axial tension, global bending moment, internal pressure, combined tension and bending, and combined internal pressure and bending are considered for circumferential through-wall cracked pipes, while only internal pressure is considered for axial through-wall cracked pipes. In particular, more emphasis is given for through-wall cracked pipes subject to combined loading. Comparisons with existing solutions show a large discrepancy in short through-wall crack (both axial and circumferential) for internal pressure. In the case of combined loading, the FE limit analyses results show the thickness effect on limit load solutions. Furthermore, the plastic limit load solution for circumferential through-wall cracked pipes under bending is applied to derive plastic η and γ factor of testing circumferential through-wall cracked pipes to estimate fracture toughness. Being based on detailed 3D FE limit analysis, the present solutions are believed to be meaningful for structural integrity assessment of through-wall cracked pipes.

Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique

2006 ◽  
Vol 128 (4) ◽  
pp. 618-624 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Internal Pressure ◽  
Bending Moment ◽  
Limit Load ◽  
Heat Fluxes ◽  
Bench Mark ◽  
Pipe Bend ◽  
Elastic Plastic ◽  
Shakedown Limit

In this paper a simplified technique is presented to determine the shakedown limit load of a 90-degree pipe bend subjected to constant internal pressure and cyclic in-plane closing bending moment using the finite element method. The simplified technique determines the shakedown limit load without performing time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two finite element analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed in the pipe bend. In order to gain confidence in the simplified technique, the output shakedown limit moments are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of the pipe bend. The shakedown limit moments output by the simplified technique are used to generate the shakedown diagram of the pipe bend for a range of constant internal pressure magnitudes. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. In order to get acquainted with the simplified technique, it is applied beforehand to a bench mark shakedown problem namely, the Bree cylinder (Bree, J., 1967, J. Strain Anal., 3, pp. 226–238) problem. The Bree cylinder is subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the simplified technique showed very good correlation with the analytically determined Bree diagram of the cylinder.

Limit Load Analysis of Cracked Components Using the Reference Volume Method

2006 ◽  
Vol 129 (3) ◽  
pp. 391-399 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Elastic Modulus ◽  
Three Dimensional ◽  
Local Limit ◽  
Limit Load ◽  
Multiple Cracks ◽  
Element Analysis ◽  
Limit Loads ◽  
Integrity Assessment ◽  
Reference Volume ◽  
Volume Method

Cracks and flaws occur in mechanical components and structures, and can lead to catastrophic failures. Therefore, integrity assessment of components with defects is carried out. This paper describes the Elastic Modulus Adjustment Procedures (EMAP) employed herein to determine the limit load of components with cracks or crack-like flaw. On the basis of linear elastic Finite Element Analysis (FEA), by specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible distributions can be generated, to obtain lower and upper bounds limit loads. Due to the expected local plastic collapse, the reference volume concept is applied to identify the kinematically active and dead zones in the component. The Reference Volume Method is shown to yield a more accurate prediction of local limit loads. The limit load values are then compared with results obtained from inelastic FEA. The procedures are applied to a practical component with crack in order to verify their effectiveness in analyzing crack geometries. The analysis is then directed to geometries containing multiple cracks and three-dimensional defect in pressurized components.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

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