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.

Estimates of Elastic Crack Opening Displacements of Slanted Through-Wall Cracks in Plate and Cylinder

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Nam-Su Huh ◽  
Do-Jun Shim ◽  
Yeon-Sik Yoo ◽  
Suhn Choi ◽  
Keun-Bae Park
Keyword(s):  
Finite Element ◽  
Crack Opening ◽  
Three Dimensional ◽  
Bending Moment ◽  
Element Model ◽  
Finite Element Analyses ◽  
Opening Displacement ◽  
Elastic Crack ◽  
Leak Before Break ◽  
The Finite Element Model

This paper provides tractable solutions for elastic crack opening displacement (COD) of slanted through-wall cracks in plates and cylinders. The solutions were developed via detailed three dimensional elastic finite element analyses. The COD values were calculated along the thickness at the center of the crack. As for the loading conditions, only remote tension was considered for the plates, whereas remote tension, global bending moment, and internal pressure were considered for the cylinders. The finite element model employed in the present analysis was verified by using existing solutions for a cylinder with an idealized circumferential through-wall crack. The present results can be used to evaluate leak rates of slanted through-wall cracks, which can be used as a part of a detailed leak-before-break analysis considering more realistic crack shape development.

Uncertainty Characterization of the CrCOD Circumferential Crack Opening Displacement Module for xLPR

2015 ◽  
Author(s):  
Richard Olson ◽  
Paul Scott
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Opening Displacement ◽  
Crack Face ◽  
Pipe Surface ◽  
Circumferential Crack ◽  
The Us ◽  
Experimental Values ◽  
Metal Weld

The US NRC/EPRI xLPR (eXtremely Low Probability of Rupture) probabilistic pipe fracture analysis program uses deterministic modules as the foundation for the calculation of the probability of pipe leak or rupture as a consequence of active degradation mechanisms, vibration or seismic loading. The circumferential crack opening displacement module, CrCOD, estimates crack opening displacement (COD) at the inside pipe surface, at the mid-wall thickness location, and at the outside pipe surface using a combined tension/crack face pressure/bending GE/EPRI-like solution. Each module has an uncertainty beyond the uncertainty of the xLPR data inputs. This paper documents the uncertainty for CrCOD. Using 36 pipe fracture experiments, including: base metal, similar metal weld, and dissimilar metal weld experiments; bend only and pressure and bend loading; static and dynamic load histories; cracks that range from short to long, the uncertainty of the CrCOD methodology is characterized. Module uncertainty is presented in terms mean fit and standard deviation between prediction and experimental values.

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.

J and COD Estimation for Throughwall Circumferentially Cracked Elbow Under Closing Moment: Analytical Scheme and Experimental Validation

2005 ◽  
Author(s):  
J. Chattopadhyay ◽  
A. K. S. Tomar ◽  
B. K. Dutta ◽  
H. S. Kushwaha
Keyword(s):  
Crack Opening ◽  
Numerical Test ◽  
Bending Moment ◽  
J Integral ◽  
Opening Displacement ◽  
Pipe Bend ◽  
Elastic Plastic ◽  
Analytical Scheme ◽  
Analytical Estimation ◽  
Fracture Assessment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J-integral and crack opening displacement (COD) for these piping components. Analytical estimation schemes to evaluate elastic-plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, no such schemes are available for throughwall circumferentially cracked elbow (or pipe bend), an important component for LBB analysis. In this paper, simple J and COD estimation schemes are proposed for throughwall circumferentially cracked elbow subjected to closing bending moment. The ovalisation of elbow cross section has a significant bearing on its fracture behavior. Therefore, unlike conventional deformation theory plasticity analysis, incremental flow theory is adopted considering both material and geometric non-linearities in the development of the proposed estimation schemes. Although it violates Ilyushin’s theorem, it has been shown that the resulting estimation schemes is still reasonably accurate for engineering purposes. Finally, experimental/numerical validation has been provided by comparing the J-integral and COD between numerical/test data and predictions of the proposed estimation schemes.

Unified Model for Fracture of Brittle Solids

2007 ◽  
Vol 280-283 ◽  
pp. 1739-1744
Author(s):  
Vladimir D. Krstić
Keyword(s):  
Residual Stresses ◽  
Crack Opening ◽  
Unified Model ◽  
Brittle Solid ◽  
Opening Displacement ◽  
Two Phase ◽  
Brittle Solids ◽  
Cylindrical Pores ◽  
Polycrystalline Solids ◽  
Phase Systems

A unified model for fracture of brittle solid based on crack opening displacement is presented. The model allows the prediction of elastic and fracture response of brittle materials containing spherical and cylindrical pores and polycrystalline solids containing anisotropic residual stresses. The analysis can also be used to predict spontaneous cracking and fracture of two phase systems possessing mismatch stresses.

A Two-Parameter Description of the Behaviour of a Process Zone at a Crack Tip: Part II — Determination of the Parameters

2004 ◽  
Author(s):  
E. Smith
Keyword(s):  
Process Zone ◽  
Crack Opening ◽  
Crack Tip ◽  
Relative Displacement ◽  
Zone Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Crack Face ◽  
Applied Loading ◽  
Crack Tip Opening

An earlier paper (Part I) has shown how key parameters associated with the uniform stress process zone model of a crack: crack tip opening displacement, process zone size, crack opening area and the effective opening area of the process zone, depend upon parameters that are associated with the relevant terms in the expansion of the expression, for the purely elastic situation, for the relative displacement of the crack faces or the stress ahead of an elastic crack. The earlier paper focussed upon the case where the non-linear (with regards to applied stress) contributions to the crack-process zone parameters were determined to the first two terms in increasing powers of the applied loading stress parameter. These terms depend upon the first two terms in the expressions for the crack face relative displacement on the stress ahead of the crack in the elastic situation. The first of these terms is related to the stress intensity factor. In this paper we show how the parameter g0, which defines the second term, can be determined for some idealised situations.

Effect of Weld Induced Residual Stresses on Pipe Crack Opening Areas and Implications on Leak-Before-Break Considerations

2002 ◽  
Author(s):  
Lee Fredette ◽  
F. W. Brust
Keyword(s):  
Residual Stresses ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Crack Size ◽  
Battelle Memorial Institute ◽  
Pipe Material ◽  
Correction Factors ◽  
Opening Displacement ◽  
Leak Before Break ◽  
Current Guidelines

The USNRC is anticipating updating their leak-before-break (LBB) procedures. One of the technical areas of concern in the existing procedures is the prediction of the crack-opening-displacements (COD) needed for estimating the postulated leakage crack size for a prescribed leakage detection capability. If cracks develop in the welded area of a pipe, as is often the case, residual stresses in the weld may cause the crack to be forced closed. Earlier studies have shown that pipe welding produces high residual stresses with a sharp stress gradient ranging from tension to compression through the thickness of the welded area of the pipe. The current guidelines are inadequate to predict crack size based on leak rates for cracks in welded areas of pipes. The current guidelines rely on the calculation of the crack-opening-displacement as related to pipe loading. Values from the current guidelines are used to predict a crack’s cross sectional area and, in turn, to determine the severity of an existing crack by monitoring in-service leakage rates. The equations currently in use are applicable to service loaded pipe material only. Residual stresses caused by cold work, welding, etc. are neglected. This study uses two and three dimensional finite element models and weld residual stress calculation software created at Battelle Memorial Institute to develop correction factors to be used with the traditional design equations. The correction factors will compensate for the effects of welding induced residual stresses on cracks in pipe welds. This study concentrates on type 316 stainless steel material properties, but the COD corrections should be equally applicable to all stainless steels, and also can be used for ferritic steels. A test matrix of pipe radius, thickness, and crack size was used to develop the equation correction factors. Pipe wall thicknesses (t) of 7.5 mm (0.295 in.), 15 mm (0.590 in.), 22.5 mm (0.886 in.), and 30 mm (1.181 in.) were studied in pipes with mean radius to thickness ratios of 5, 10, and 20. Cracks with half-lengths in radians of π/16, π/8, π/4, and π/2 were introduced in these virtual pipes. The matrix of results was used to produce correction factors for crack opening displacement equations applicable to a broad range of pipe sizes.

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

2019 ◽  
Vol 29 (4) ◽  
pp. 547-569 ◽  
Author(s):  
Mohamed Sahbi Loukil ◽  
Janis Varna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Crack Density ◽  
Opening Displacement ◽  
Crack Face ◽  
Out Of Plane ◽  
Crack Sliding Displacement ◽  
Element Method

The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated.

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

2020 ◽  
pp. 1045389X2096316
Author(s):  
MingHao Zhao ◽  
XinFei Li ◽  
Chunsheng Lu ◽  
QiaoYun Zhang
Keyword(s):  
Boundary Condition ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Crack Opening ◽  
Electric Displacement ◽  
Opening Displacement ◽  
Crack Face ◽  
Electric Boundary Condition ◽  
Electric Displacement Intensity Factor ◽  
Piezoelectric Semiconductors

In this paper, taking the exact electric boundary conditions into account, we propose a double iteration method to analyze a crack problem in a two-dimensional piezoelectric semiconductor. The method consists of a nested loop process with internal and outside circulations. In the former, the electric field and electron density in governing equations are constantly modified with the fixed boundary conditions on crack face and the crack opening displacement; while in the latter, the boundary conditions on crack face and the crack opening displacement are modified. Such a method is verified by numerically analyzing a crack with an impermeable electric boundary condition. It is shown that the electric boundary condition on crack face largely affects the electric displacement intensity factor near a crack tip in piezoelectric semiconductors. Under exact crack boundary conditions, the variation tendency of the electric displacement intensity factor versus crack size is quite different from that under an impermeable boundary condition. Thus, exact crack boundary conditions should be adopted in analysis of crack problems in a piezoelectric semiconductor.

The Relationship Between Stress Intensity Factor, Crack Opening Displacement and J-Integral in Zr-2.5 Percent Nb

1980 ◽  
Vol 102 (1) ◽  
pp. 97-100 ◽  
Author(s):  
L. A. Simpson
Keyword(s):  
Stress Intensity ◽  
Crack Opening Displacement ◽  
Crack Extension ◽  
Crack Opening ◽  
J Integral ◽  
Opening Displacement ◽  
Crack Face ◽  
Critical Crack ◽  
Wide Range ◽  
The Relationship

Crack opening displacement (COD) has been determined in Zr-2.5 percent Nb over a wide range of applied stress intensity, K. Prior to initiation of crack extension, COD was determined from measurements of stretch zones in specimens which had undergone hydrogen-induced, sub-critical crack growth. In post initiation measurements (during slow stable crack extension), COD was determined from crack face displacement. Both methods were self consistent and depended on the plastic-zone-corrected K in accordance with the Wells equation. The J-integral was also determined during stable crack extension using the method of Garwood, et al. The results are consistent with the COD measurements based on theoretical relationships between the two crack tip parameters.

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