Closed-Form Solutions for Stress Intensity Factor and Elastic Crack Opening Displacement for Circumferential Through-Wall Cracks in the Interface between an Elbow and a Straight Pipe under Internal Pressure

Leak-Before-Break (LBB) is one of important approaches applied to nuclear piping design. In the LBB assessment, it is important to evaluate crack instability and to predict leak rate based on a fracture mechanics concept, in which an idealized straight pipes with through-wall cracks (TWCs) are generally considered in the typical LBB analysis. On the other hand, in nuclear piping system, elbows are often connected with straight pipes by welding, in which cracks could occur as well known. Hence, accurate assessment needs to be performed for cracks in weldments joining an elbow and attached straight pipe. In the previous study, it has been revealed that crack instability of a TWC in the interface between an elbow and a straight pipe under bending moment could be different with that of a straight pipe with a TWC depending on a change of pipe thickness, radius of curvature and crack length. Especially, elbows attached to a pipe were more severe than straight pipes for relatively shorter crack length. Thus, a need of engineering solutions for cracks in the interface between an elbow and a pipe is raised for accurate LBB analysis on nuclear piping system. In this present study, stress intensity factor (SIF) and crack opening displacement (COD) are estimated via detailed 3-dimensional finite element (FE) elastic analyses for circumferential TWCs in the interface between an elbow and a straight pipe subjected to internal pressure. The geometric variables (pipe thickness, radius of curvature and crack length) affecting SIFs and CODs were systematically considered in order to cover actual ranges of geometric variables. Also, the effect of elbow on elastic fracture parameters was investigated by comparing the present results with the results from the previous straight pipe solution. Moreover, based on the present FE results, the shape factors (F, V) used for calculating SIFs and CODs are proposed for circumferential TWCs in the interface between an elbow and a pipe. The present results can be used to perform the accurate LBB assessment for nuclear piping system including elbows welded to a straight pipe.

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Derivation of applied stress-crack opening displacement relationships for the evaluation of effective stress intensity factor range

International Journal of Fracture ◽

10.1023/b:frac.0000022243.38144.ce ◽

2004 ◽

Vol 125 (3/4) ◽

pp. 371-386 ◽

Cited By ~ 2

Author(s):

D.L. Chen ◽

Z. Wang

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Crack Opening Displacement ◽

Applied Stress ◽

Effective Stress ◽

Crack Opening ◽

Stress Intensity Factor Range ◽

Opening Displacement ◽

Effective Stress Intensity Factor

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A Study of the Stress Intensity Factor and Crack Opening Displacement Relationship Between Uniform Thickness Pipe Bends and Non-Uniform Thickness Pipe Bends

Volume 6A: Materials and Fabrication ◽

10.1115/pvp2016-63421 ◽

2016 ◽

Author(s):

Kyung-Dong Bae ◽

Chul-Goo Kim ◽

Seung-Jae Kim ◽

Hyun-Jae Lee ◽

Yun-Jae Kim

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Crack Opening Displacement ◽

Elastic Stress ◽

Crack Opening ◽

Radius Of Curvature ◽

Uniform Thickness ◽

Opening Displacement ◽

Thickness Variations

This paper proposes the relationship of stress intensity factor and crack opening displacement between pipe bends with uniform thickness and those with non-uniform thickness. In actual case, pipe bends have thickness variations. Unlike typical pipe bends, heat induction bend pipes have significant thickness variations (non-uniform thickness) because of manufacturing process. When the ratio of radius of curvature and pipe radius is 3 for heat induction bend pipes, the thickness at intrados and extrados can be calculated by 1.75 times and 0.875 times of nominal thickness which is original thickness before manufacturing process, respectively. In this situation, it is difficult to apply existing elastic stress intensity factor and crack opening displacement results [1, 2] and it is essential to modify existing solution or to create new solution. In this paper, to find effect of pipe bends thickness variation, 90° through-wall cracked pipe bends with not only uniform thickness but also non-uniform thickness are considered. The ratios of radius and thickness are 5, 10 and ratios of pipe radius of curvature and radius are 3, 4 and 5. Loading condition is in-plane opening bending for intrados crack and closing bending for extrados crack. The through-wall crack sizes are 12.5%, 25% and 37.5% of circumferential cross section. Material of pipe bends is assumed to follow elastic behavior. The proposal is made by extensive finite elements analyses using ABAQUS [3], predicted elastic stress intensity factors for pipe bends with non-uniform thickness are compared with finite element results. The results show a good agreement. It may be useful to calculate elastic stress intensity factor for bends with non-uniform thickness without complex modeling and finite analyses.

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Stress Intensity Factor and Elastic Crack Opening Displacement Solutions of Complex Cracks in Pipe Using Elastic Finite-Element Analyses

Journal of Pressure Vessel Technology ◽

10.1115/1.4031128 ◽

2015 ◽

Vol 138 (1) ◽

Cited By ~ 7

Author(s):

Jae-Uk Jeong ◽

Jae-Boong Choi ◽

Nam-Su Huh ◽

Yun-Jae Kim

Keyword(s):

Finite Element ◽

Stress Intensity ◽

Internal Pressure ◽

Closed Form ◽

Crack Opening ◽

Crack Depth ◽

Loading Conditions ◽

Axial Tension ◽

Elastic Crack ◽

Geometric Variables

In the present paper, the closed-form expressions for the stress intensity factors (SIFs) and the elastic crack opening displacements (CODs) of complex-cracked pipes are derived based on the systematic three-dimensional (3D) elastic finite-element (FE) analyses. The loading conditions that are evaluated include global bending moment, axial tension, and internal pressure. In terms of geometries, the geometric variables affecting the SIFs and the elastic CODs of complex-cracked pipes, i.e., the crack angle of through-wall cracks (TWCs), the crack depth of fully circumferential, internal surface cracks in the inner surface of pipe, and the ratio of pipe mean radius to thickness, are systematically considered in the present FE analyses. The FE analysis procedure employed in the present study has been validated against the existing solutions for the circumferential TWC pipes. Using the present FE results, the shape factors of SIF and elastic COD for complex-cracked pipes are tabulated as a function of geometric variables. The results are applied for closed-form expressions of SIF and elastic COD when the pipe is subjected to simple loading conditions of bending, axial tension, or internal pressure. The proposed closed-form expressions can estimate SIF and elastic COD of complex-cracked pipes within maximum differences of 2.4% and 5.9% with FE results, respectively.

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EFG Virtual Crack Closure Technique for the Determination of Stress Intensity Factor

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.250-253.3752 ◽

2011 ◽

Vol 250-253 ◽

pp. 3752-3758 ◽

Cited By ~ 3

Author(s):

Xue Ping Chang ◽

Jun Liu ◽

Shi Rong Li

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Crack Closure ◽

Crack Opening ◽

Crack Tip ◽

Strain Energy Release ◽

Virtual Crack Closure Technique ◽

Opening Displacement ◽

Closure Technique

The aim of this paper is to introduce a virtual crack closure technique based on EFG method for thread-shape crack. The cracked component is discretized and the displacement field is determined using a coupled FE/EFG method, by which EFG nodes are arranged in the vicinity of crack tip and FE elements in the remain part in order to improve computational efficiency. Two typical parameters, nodal force and crack opening displacement attached to crack tip are calculated by means of setting up an auxiliary FE zone around crack tip. Strain energy release rate (SERR), further stress intensity factor (SIF) are determined by the two parameters. The method to calculate SIF is named as virtual crack closure technique based on EFG method. It is showed by several numerical examples that using the method presented in this paper, SIF on the crack tip can be obtained accurately.

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Closed Form Expressions for Fracture Mechanics Analysis of Cracked Pipes

Journal of Pressure Vessel Technology ◽

10.1115/1.3264435 ◽

1985 ◽

Vol 107 (2) ◽

pp. 203-205 ◽

Cited By ~ 63

Author(s):

A. Zahoor

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Fracture Mechanics ◽

Intensity Factor ◽

Internal Pressure ◽

Closed Form ◽

Bending Moment ◽

Axial Tension ◽

Mechanics Analysis ◽

Pipe Radius

Closed form stress intensity factor (K1) expressions are presented for cracks in pipes subjected to a variety of loading conditions. The loadings considered are: 1) axial tension, 2) remotely applied bending moment, and 3) internal pressure. Expressions are presented for circumferential and axial cracks, and include both part-through and through-wall crack geometries. The closed form K1 expressions are valid for pipe radius to wall thickness ratio between 5 and 20.

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