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.

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.

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 Limit Loads for 90-Degree Scheduled Pipe Bends Subjected to Constant Internal Pressure and Cyclic Bending Moments

2008 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Small Displacement ◽  
Bending Moments ◽  
Pipe Bend ◽  
Hardening Material ◽  
Cyclic Bending ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load for a long radius 90-degree pipe bend was previously developed [1, 2]. The simplified technique utilizes the finite element method and employs the small displacement formulation to determine the shakedown limit load (moment) without performing lengthy time consuming full cyclic loading finite element simulations or utilizing conventional iterative elastic techniques. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure. In the current paper, a parametric study is conducted through applying the simplified technique on three scheduled pipe bends namely: NPS (Nominal Pipe Size) 10" Sch. No. 20, NPS 10" Sch. No. 40 STD, and NPS 10" Sch. No. 80. Two material models are assigned namely; an elastic-perfectly-plastic (EPP) material and an idealized elastic-linear strain hardening material obeying Ziegler’s linear kinematic hardening (KH) rule. This type of material model is termed in the current study as the KH-material. The pipe bends are subjected to a spectrum of constant internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns namely: in-plane closing (IPC), in-plane opening (IPO), and out-of-plane (OP) bending moment loadings of the pipe bends. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the scheduled pipe bends for the spectrum of constant internal pressure magnitudes. A comparison between the generated shakedown diagrams for the pipe bends employing the EPP- and the KH-materials is presented. Relatively higher shakedown limit moments were recorded for the pipe bends employing the KH-material at the medium to high internal pressure magnitudes.

Plastic Limit Analysis Using the Simplified Theory of Plastic Zones

2021 ◽  
Vol 143 (2) ◽  
Author(s):  
Hartwig Hübel
Keyword(s):  
Limit Analysis ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Maximum Load ◽  
Load Level ◽  
Material Behavior ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Plastic Zones

Abstract The simplified theory of plastic zones (STPZ) was mainly developed to determine strain ranges and accumulated strains in the state of shakedown at cyclic loading between prescribed levels of loading. Kinematic hardening is an indispensable feature of the STPZ. The plastic limit load, however, is defined for monotonic loading and elastic–plastic material behavior without hardening. Simply assigning a zero value or a numerically very low value of the tangent modulus when applying the STPZ is generally not possible due to arising numerical instabilities. It is, therefore, not immediately obvious how the STPZ can be used to determine the maximum load level that can be applied to a structure without developing a kinematic mechanism. This paper describes the theory and the analysis steps required and provides some illustrative examples. Typically, between one and three linear elastic analyses and some local calculations are required to provide either the exact value or at least a reasonable estimate of a range of the plastic limit load, as well as of the associated stress and strain fields and displacements that are not provided by classical limit analysis.

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.

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 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.

Research on Safety Assessment Method for Pressure Pipe With Incomplete Welding Defects Under Complicated Loadings

2010 ◽  
Author(s):  
Zhijiang Jin ◽  
Xianping Wan ◽  
Chenghang Jiang
Keyword(s):  
Internal Pressure ◽  
Safety Assessment ◽  
Limit Load ◽  
Assessment Method ◽  
Curved Surface ◽  
Assessment Procedure ◽  
Plastic Limit ◽  
Pressure Pipe ◽  
Welding Defects ◽  
Plastic Limit Load

Since most pressure pipe materials have good toughness, the failure mode of pipe is usually the plastic failure controlled by limit load. The incomplete welding defect is very common in the pipe, and its existence will reduce the load-carrying capacity of pipes. The pipe with incomplete welding defects can be continued using only after passing the appropriate safety assessment, so the research on safety assessment procedure for pressure pipe with incomplete welding defects under combined bending, torsion and internal pressure loadings has a great theoretical and practical engineering value. By using theoretical analyzing method of plastic limit load, the plastic limit load of pressure pipe with different defect size or pipe diameter ratio are calculated in this paper, then safety assessment curved surface and its express equation are obtained by fitting calculation data. Finally a safety assessment procedure is developed for pressure pipes under combined bending, torsion and internal pressure loadings according to the curved surface.

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.

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