Min-Max Approach to Shakedown and Limit Load Analysis for Elastic Perfectly Plastic and Kinematic Hardening Materials

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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A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247jsa521 ◽

2009 ◽

Vol 44 (6) ◽

pp. 407-416 ◽

Cited By ~ 3

Author(s):

P J Budden ◽

Y Lei

Keyword(s):

Finite Element ◽

Plastic Material ◽

Yield Criterion ◽

Limit Load ◽

Cylinder Wall ◽

Perfectly Plastic ◽

Elastic Perfectly Plastic ◽

Von Mises ◽

Inside Radius ◽

Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

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Plastic Limit Loads for Piping Branch Junctions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.345-346.1377 ◽

2007 ◽

Vol 345-346 ◽

pp. 1377-1380 ◽

Cited By ~ 1

Author(s):

Yun Jae Kim ◽

Kuk Hee Lee ◽

Chi Yong Park

Keyword(s):

Three Dimensional ◽

Limit Load ◽

Plastic Limit ◽

Perfectly Plastic ◽

Plastic Materials ◽

Wide Range ◽

Pipe Radius ◽

Plastic Limit Load ◽

The Mean ◽

Elastic Perfectly Plastic

The present work presents plastic limit load solutions for branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) FE limit analyses using elastic-perfectly plastic materials. The proposed solutions are valid for a wide range of branch junction geometries; ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0.

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Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

Volume 3: Design and Analysis ◽

10.1115/pvp2006-icpvt-11-93297 ◽

2006 ◽

Author(s):

Hany F. Abdalla ◽

Mohammad M. Megahed ◽

Maher Y. A. Younan

Keyword(s):

Plastic Material ◽

Limit Load ◽

Material Model ◽

Large Displacement ◽

Small Displacement ◽

Pipe Bend ◽

Perfectly Plastic ◽

Loading Patterns ◽

Elastic Perfectly Plastic ◽

Shakedown Limit

In this paper the shakedown limit load is determined for a long radius 90-degree pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic-perfectly-plastic material model. The second technique is an iterative based technique which uses the same elastic-perfectly-plastic material model, but incorporates large displacement effects accounting for geometric non-linearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic-plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equals or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. 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. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

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Application of a Sixth Order Generalized Stress Function for Determining Limit Loads for Plates with Triangular Penetration Patterns

Computational Mechanics: Developments and Applications ◽

10.1115/pvp2002-1298 ◽

2002 ◽

Cited By ~ 1

Author(s):

J. L. Gordon ◽

D. P. Jones

Keyword(s):

Finite Element ◽

Fourth Order ◽

Limit Load ◽

Sixth Order ◽

Numerical Representation ◽

Order Function ◽

Practical Applications ◽

Perfectly Plastic ◽

Unit Cells ◽

Elastic Perfectly Plastic

The capability to obtain limit load solutions of plates with triangular penetration patterns using fourth order functions to represent the collapse surface has been presented in previous papers. These papers describe how equivalent solid plate elastic-perfectly plastic finite element capabilities are generated and demonstrate how such capabilities can be used to great advantage in the analysis of tubesheets in large heat exchanger applications. However, these papers have pointed out that although the fourth order functions can produce sufficient accuracy for many practical applications, there are situations where improvements in the accuracy of in-plane and transverse shear are desirable. This paper investigates the use of a sixth order function to represent the collapse surface for improved accuracy of the in-plane response. Explicit elastic-perfectly plastic finite element solutions are obtained for unit cells representing an infinite array of circular penetrations arranged in an equilateral triangular array. These cells are used to create a numerical representation of the complete collapse surfaces for a number of ligament efficiencies (h/P where h is the minimum ligament width and P is the distance between hole centers). Each collapse surface is then fit to a sixth order function that satisfies the periodicity of the hole pattern. Sixth-order collapse functions were developed for h/P values between .05 and .50. Accuracy of the sixth order and the fourth order functions are compared. It was found that the sixth order function is indeed more accurate, reducing the error from 12.2% for the fourth order function to less than 3% for the sixth order function.

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Plastic collapse load analysis for circumferential cracked cylinder under pure torsion

MATEC Web of Conferences ◽

10.1051/matecconf/201819202023 ◽

2018 ◽

Vol 192 ◽

pp. 02023

Author(s):

Sutham Arun ◽

Thongchai Fongsamootr

Keyword(s):

Limit Load ◽

Fe Model ◽

Plastic Collapse ◽

Collapse Load ◽

Pure Torsion ◽

Perfectly Plastic ◽

Torsion Moment ◽

Elastic Perfectly Plastic ◽

Distribution Of Stress ◽

Cracked Cylinder

This paper aims to analyze the plastic collapse moment of circumferential cracked cylinder under pure torsion using the NSC approach and 3D FE model. The material considered in this work is assumed to be elastic-perfectly plastic. The influences of geometric parameters of crack and cylinder, such as Rm/t, a/t and θ/π on solution of plastic collapse load are also investigated. The analysis shows that for the case of a/t < 0.75, the values of limit torsion moment can be estimated by NSC analysis which provides conservative results. However, for the case of deeper crack, a/t ≥ 0.75, the limit load solution predicted by NSC approach may not be safe, because the distribution of stress at yielding state does not correspond to the NSC assumption. Therefore, the approximated solution of collapse torsion moment for the case of deeper crack with a/t ≥ 0.75 is proposed based on FE analysis.

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Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

Journal of Pressure Vessel Technology ◽

10.1115/1.4006559 ◽

2012 ◽

Vol 134 (6) ◽

Cited By ~ 5

Author(s):

Phuong H. Hoang ◽

Kunio Hasegawa ◽

Bostjan Bezensek ◽

Yinsheng Li

Keyword(s):

Finite Element ◽

Pressure Vessel ◽

Large Strain ◽

Bending Moment ◽

Limit Load ◽

Elastic Plastic ◽

Perfectly Plastic ◽

Plastic Materials ◽

Weighted Factor ◽

Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

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Plastic Limit Loads for Through-Wall Cracked Pipes Using Finite Element Limit Analysis

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.321-323.724 ◽

2006 ◽

Vol 321-323 ◽

pp. 724-728

Author(s):

Nam Su Huh ◽

Yoon Suk Chang ◽

Young Jin Kim

Keyword(s):

Finite Element ◽

Limit Analysis ◽

Structural Integrity ◽

Three Dimensional ◽

Limit Load ◽

Plastic Behavior ◽

Plastic Limit ◽

Integrity Assessment ◽

Perfectly Plastic ◽

Elastic Perfectly Plastic

The present paper provides plastic limit load solutions for axial and circumferential through-wall cracked pipes based on detailed three-dimensional (3-D) finite element (FE) limit analysis using elastic-perfectly plastic behavior. As a loading condition, both single and combined loadings are considered. Being based on detailed 3-D FE limit analysis, the present solutions are believed to be valuable information for structural integrity assessment of cracked pipes.

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Incorporation of Strain Hardening Effect Into Simplified Limit Analysis

Journal of Pressure Vessel Technology ◽

10.1115/1.4002059 ◽

2010 ◽

Vol 132 (6) ◽

Cited By ~ 1

Author(s):

P. S. Reddy Gudimetla ◽

R. Adibi-Asl ◽

R. Seshadri

Keyword(s):

Lower Bound ◽

Strain Hardening ◽

Limit Load ◽

Element Analysis ◽

Active Volume ◽

Limit Loads ◽

Reference Volume ◽

Perfectly Plastic ◽

Tangent Method ◽

Elastic Perfectly Plastic

In this paper, a method for determining limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including a certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be elastic perfectly plastic. Typical strain hardening curves such as bilinear hardening and Ramberg–Osgood material models are investigated. This paper also focuses on the plastic reference volume correction concept to determine the active volume participating in plastic collapse. The reference volume concept in combination with mα-tangent method is used to estimate lower-bound limit loads of different components. Lower-bound limit loads obtained compare well with the nonlinear finite element analysis results for several typical configurations with/without crack.

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Inf–sup conditions on convex cones and applications to limit load analysis

Mathematics and Mechanics of Solids ◽

10.1177/1081286519843969 ◽

2019 ◽

Vol 24 (10) ◽

pp. 3331-3353 ◽

Cited By ~ 1

Author(s):

Jaroslav Haslinger ◽

Stanislav Sysala ◽

Sergey Repin

Keyword(s):

Yield Criterion ◽

Failure Mechanisms ◽

Limit Load ◽

Convex Cones ◽

Mesh Adaptivity ◽

Limit Loads ◽

Perfectly Plastic ◽

Dual Cones ◽

Geotechnical Stability ◽

Load Analysis

The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems. The majorants of the limit load are computed and expected failure mechanisms of structures are visualized using local mesh adaptivity.

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