Advances in COD Equations — Circumferential Through-Wall Cracks

2012 ◽  
Author(s):  
Bruce A. Young ◽  
Rick J. Olson ◽  
Matthew Kerr
Keyword(s):  
Finite Element ◽  
Crack Opening ◽  
Full Range ◽  
Independent Solution ◽  
Loading Conditions ◽  
Finite Element Analyses ◽  
Crack Face ◽  
Elastic Plastic ◽  
Piping Systems ◽  
Bending Loads

Non-linear fracture mechanics equations for through-wall cracks in a pipe are used to analyze piping systems for either critical flaw size or critical loading conditions as part of probabilistic Leak-Before-Break (LBB) failure analyses under the eXtremely Low Probability of Rupture (xLPR) program co-sponsored by the U.S. Nuclear Regulatory Commission (US NRC) and the Electric Power Research Institute (EPRI). The xLPR analysis techniques use a large number of independent analysis solutions to determine an overall assessment of system failure probability. As part of the assessment, each independent solution requires the solution of the crack opening displacement (COD) for a through-wall crack (TWC) in a pipe under the prescribed loading conditions. The COD evaluations are then used to determine a leak rate for the given load conditions and crack sizes. The purpose of this paper is to present results which advance the start-of-the-art for determining the elastic-plastic functions for crack opening displacements (COD) for a TWC in a pipe system under combined tension and bending loads. The current method used to determine COD in xLPR, a blending of tension and bending solution from the GE-EPRI Handbook, determined the continuum equations using structural finite element analyses with shell type elements. Since that body of work was undertaken, there have been significant advancements in computing capability such that structural finite element analyses with three-dimension continuum elements are currently feasible. The use of continuum elements provides several advantages over shell elements; such as, the ability to elicit details of variation in the COD through the thickness of the pipe wall and to apply pressure to the crack face due to the internal pipe pressure. Furthermore, the original GE-EPRI solutions were limited for the case of combined tension and bending loads. The existing GE-EPRI solutions for combined loading conditions are limited to pipe radius-to-wall thickness (R/t) ratios of 10 or greater, typical of those piping systems found in the boiling water reactor (BWR) fleet. For the PWR piping systems of concern today, which are subject to primary water stress corrosion cracking (PWSCC), the R/t ratios are typically 5 or less. As a result of the limitations with the existing GE-EPRI method for predicting COD, Battelle and US NRC staff set out to develop a comprehensive COD prediction tool for combined loadings which would be applicable to both PWR as well as BWR piping. This effort involved a matrix of over 1,200 finite element analyses for a full range of pipe sizes, R/t ratios, through-wall crack (TWC) lengths, and internal pipe pressures. It is anticipated that there will be several parts to this effort. Part I, discussed in this paper, focuses on the development of the model and the initial investigation into the elastic- and elastic-plastic fitting functions for the prediction of COD (i.e., the V and h functions). Future parts of this effort will focus on such issues as the effect of restraint of pressure induced bending on COD, the effect of weld residual stresses on COD, J-Integral estimation schemes, and development of variable crack-face pressure.

Elastic-Plastic Analysis of an Elbow With Axial Part-Through Internal Crack at Crown Under In-Plane Bending

2008 ◽  
Author(s):  
K. M. Prabhakaran ◽  
S. R. Bhate ◽  
V. Bhasin ◽  
A. K. Ghosh
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Bending Moment ◽  
Internal Crack ◽  
J Integral ◽  
Finite Element Analyses ◽  
Integrity Assessment ◽  
Elastic Plastic ◽  
Axial Part ◽  
Plane Bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires evaluation of J-integral. The J-integral values for elbows with axial part-through internal crack at crown under in-plane bending moment are limited in open literature. This paper presents the J-integral results of a thick and thin, 90-degree, long radius elbow subjected to in-plane opening bending moment based on number of finite element analyses covering different crack configurations. The non-linear elastic-plastic finite element analyses were performed using WARP3D software. Both geometrical and material nonlinearity were considered in the study. The geometry considered were for Rm/t = 5, and 12 with ratio of crack depth to wall thickness, a/t = 0.15, 0.25, 0.5 and 0.75 and ratio of crack length to crack depth, 2c/a = 6, 8, 10 and 12.

A Simple Approach for Including Weld Residual Stresses in the Calculation of Pipe Circumferential Through-Wall Crack Opening Displacements

2016 ◽  
Author(s):  
Richard Olson
Keyword(s):  
Residual Stresses ◽  
Axial Force ◽  
Analytic Solution ◽  
Crack Opening ◽  
Bending Moment ◽  
Generalized Solution ◽  
Finite Element Analyses ◽  
Opening Displacement ◽  
Crack Face ◽  
Basic Equations

Current methodologies for predicting the crack opening displacement (COD) of circumferentially through-wall cracked pipe do not include the effect of weld residual stresses (WRS). Even the most advanced COD prediction methodology only includes the effect of applied axial force, bending moment, and crack face pressure. For some years, it has been known that weld residual stresses do alter the COD, but there has been no convenient way to include them in a COD prediction without doing case-specific finite element analyses. This paper documents a generalized solution for including WRS effects on COD. The model uses a closed-form analytic solution to approximate the crack face rotations that the WRS would induce which, subsequently, can be added to the typical axial force-bending-crack face pressure COD solution. The methodology is described and the basic equations for the solution are presented. Following this, application to cases to evaluate the efficacy of the approach are presented which show a mixture of results ranging from amazingly good to “of questionable value” with respect to the FEA results.

The Evaluation of Crack Opening Areas for Through-Wall Cracks in the Vicinity of Pipe Branch Connections

2011 ◽  
Author(s):  
Colin Madew ◽  
John Sharples ◽  
Richard Charles ◽  
Peter Gill ◽  
Peter Budden
Keyword(s):  
Complex Geometry ◽  
Crack Opening ◽  
Element Analysis ◽  
Crack Face ◽  
Analysis Techniques ◽  
Simple Geometry ◽  
Bending Loads ◽  
Complicated Geometry ◽  
Crack Face Contact ◽  
Plate Geometry

A number of papers have been presented at previous ASME PVP conferences, which have evaluated the crack opening areas (COA) and stress intensity factors (K), using elastic finite element analysis techniques, for through-wall cracks in a region where an attachment is welded to a plate. This was a simplified geometry aimed at representing a more complicated geometry of a pipe-branch connection. A number of analyses were considered and conclusions made on the estimation of COA and K using simple handbook solutions. More recently the analyses included the application of nonlinear geometry and the addition of crack face contact when applying bending loads. This paper is a continuation of these previous studies, assessing through-wall cracks in a more realistic pipe-branch connection geometry. The calculated COA and K values for the more complex geometry are compared to values from pipe models with no branch connections, in a similar manner to that applied in the previous work on the simplified plate geometry. Judgments are made on the conservatism, or otherwise, of the estimated COA and K for the more complex geometry solutions compared to the simple geometry solutions.

Some finite-element stress analyses of simulated diffusion-bonded lap joints

1977 ◽  
Vol 12 (4) ◽  
pp. 331-338 ◽  
Author(s):  
T R Gurney
Keyword(s):  
Finite Element ◽  
Plate Thickness ◽  
Lap Joints ◽  
Loading Conditions ◽  
Finite Element Analyses ◽  
Stress Concentrations ◽  
Young’S Moduli ◽  
Similar Materials ◽  
Finite Element Stress ◽  
Stress Analyses

A series of finite-element analyses have been carried out on lap joints between similar materials and between two materials with Young's moduli in the ratio 3:1. The main objectives of the work were to determine the influence of the ratio between the overlap distance and the plate thickness on the stress concentrations at the ends of the plates, and to examine the influence of tapering the ends of the plates. In the course of the work, comparisons were made between various loading conditions.

Computer-Aided Reliability Finite Element Methods

1991 ◽  
Vol 34 (5) ◽  
pp. 46-52
Author(s):  
David Followell ◽  
Salvatore Liguore ◽  
Rigo Perez ◽  
W. Yates ◽  
William Bocchi
Keyword(s):  
Finite Element ◽  
Stress Relaxation ◽  
Finite Element Methods ◽  
Mesh Generation ◽  
Electronic Equipment ◽  
Finite Element Analyses ◽  
Elastic Plastic ◽  
Computer Aided

Finite element analyses (FEA) have emerged as a process for assessing stresses and strains in electronic equipment in order to compute the expected structural life. However, potential pitfalls may compromise accuracy. Guidelines have been established to improve the accuracy of these results. A method has been outlined that allows simplified linear FEAs to be used instead of the more complex elastic-plastic nonlinear FEA. Guidelines for mesh generation have been established to eliminate arithmetic errors caused when materials with large stiffness differences are adjacent to each other. The accuracy of FEAs when dealing with very small dimensions has been verified. Procedures for combining various loadings in order to predict life have been established for materials that exhibit stress relaxation and for those that do not. With these guidelines, FEAs can be an effective tool to predict the structural life of electronic equipment.

Estimation of Stress Intensity Factors due To Welding Residual Stresses for Circumferentially Cracked Pipes

2012 ◽  
Author(s):  
Chang-Young Oh ◽  
Ji-Soo Kim ◽  
Yun-Jae Kim ◽  
Young-Jin Oh ◽  
Kyoungsoo Lee ◽  
...  
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Residual Stresses ◽  
Stress Intensity Factors ◽  
Finite Element Analyses ◽  
Intensity Factors ◽  
Crack Face ◽  
Simple Method ◽  
Weld Geometry ◽  
Nonlinear Stress

This paper proposes a simple method to estimate stress intensity factors due to welding residual stresses. In this study, finite element analyses for circumferentially cracked pipe are performed to calculate stress intensity factors. Four cracked geometries and two types of weld geometry are considered. KI-solutions for the nonlinear stress distribution on the crack face were determined in accordance with codes and standards. The results are compared with KI-solutions from finite element results. It is found that proposed simple method agrees well with FE results.

A Simplified Analysis Method for Complex Piping Systems in Elastic-Plastic-Creep Range

1985 ◽  
Vol 107 (2) ◽  
pp. 148-156
Author(s):  
O. Watanabe ◽  
H. Ohtsubo
Keyword(s):  
Finite Element ◽  
Present Method ◽  
Constitutive Relations ◽  
Plastic Behavior ◽  
Piping System ◽  
Curved Beams ◽  
Elastic Plastic ◽  
Piping Systems ◽  
Creep Deformations ◽  
Plastic Creep

The present paper describes a simplified finite element method for analysis of behavior of complex piping systems under elevated temperature. Elastic-plastic-creep deformations of a piping system under a combined moment loading can be analyzed by the present method. The system is idealized by straight and curved beams, and derivation of the finite element equation is based on the force method. The unified constitutive relations are used for creep and plastic behavior, where plastic deformation is treated as a limiting case of creep. The numerical results are compared with previous experimental ones, which verifies the validity of the proposed method. Elastic follow-up problem of a piping system of actually complex configuration is also solved by the present method.

Flexibility Factors and Stress Indices for Piping Components With D/T ≧ 100 Subjected to In-Plane or Out-of-Plane Moment

1988 ◽  
Vol 110 (4) ◽  
pp. 374-386 ◽  
Author(s):  
T. Fujimoto ◽  
T. Soh
Keyword(s):  
Finite Element ◽  
Wall Thickness ◽  
Large Diameter ◽  
Thin Wall ◽  
Finite Element Analyses ◽  
Empirical Formulas ◽  
Stress Evaluation ◽  
Stress Indices ◽  
Piping Systems ◽  
Out Of Plane

The finite element analyses are carried out for the several piping components (D/T ≧ 100) subjected to in-plane or out-of-plane moment. For the stress evaluation of the chemical plant piping systems, ANSI B31.3 is usually applied. But the stress intensification factors and flexibility factors in this code are mainly for a heavy-wall-thickness pipe, so it is necessary to reconsider these factors for a thin-wall-thickness pipe with a large diameter. In our study, several finite element analyses using MSC/NASTRAN program were performed on the pipe bends (elbow or miter bend, 0.01 ≦ h ≦ 0.2) and the unreinforced fabricated tees (50 ≦ D/Tr ≦ 300, 0.5 ≦ d/D ≦ 0.95, 0.25 ≦ Tb/Tr ≦ 0.95), and the empirical formulas for the flexibility factors and the stress indices, due to out-of-plane or in-plane moment, were proposed. Experimental stress analyses for the piping components with D/Tr = 127 were also carried out, and it was confirmed that the results agreed well with the numerical ones.

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