Circumferential Through-wall Crack Research Articles

New unloading compliance correlation for throughwall circumferentially cracked pipe to measure crack growth during fracture tests

ABSTRACTCrack growth is generally measured during fracture experiment of specimen or component. The unloading compliance technique is commonly used for this purpose because of its simplicity. It infers the crack length from unloading compliance of cracked component. The pre‐requisite of this technique is the availability of an equation that correlates crack length with unloading compliance. While such correlations are available for compact tension and three‐point bend specimens, it is not available for big components such as pipe or pipe bend. Development of such a correlation for throughwall circumferentially cracked (TCC) straight pipe under bending, therefore, forms the objective of the present study. However, the challenge to develop such correlation for TCC pipe is that the equation should contain not only crack length as a function but also the current deformation or load level as a parameter. This is attributed to the fact that the circular cross section of the pipe ovalizes during deformation leading to change of bending stiffness of the cracked body. New compliance correlations have been proposed for TCC pipe under bending load considering these complexities. Elastic‐perfectly plastic material behaviour has been assumed to characterize the material stress–strain response. However, it has been shown that error due to this approximation with respect to the actual stress–strain behaviour is negligible if one chooses flow stress equal to average of yield and ultimate strength. The proposed correlations are expressed in terms of normalized parameters to make them independent of specific values of geometric dimensions such as radius, thickness and span length of four‐point bending loading system. Effectiveness of this normalization has also been verified by carrying out a sensitivity study.

Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments

Pressurized piping items in power plants may experience combined torsion and bending moments during operation. Currently, there is a lack of guidance in flaw evaluation procedures for combined loading modes of pressure, torsion and bending loads. Recently, collapse bending moments for pipes under torsion moments were analyzed by finite element modelling. Equivalent moments defined as the root of the sum of the squares of the torsion and bending moments are shown to be equal to pure bending moments for various diameter pipes containing circumferentially part through cracks. This paper focuses on behaviour of plastic collapse moments for pipes with circumferential through-wall cracks using finite element analysis, and describes the behaviour of the equivalent bending moments for flaw evaluation procedures, referring the results of part through cracked pipes.

원주방향 관통균열이 용접부 중앙에 존재하는 V-그루브 맞대기 용접배관의 한계하중 해석

본 논문에서는 용접부 중앙에 원주방향 관통균열이 있는 V-그루브 맞대기 용접 배관의 한계하중 해석을 수행하였다. V-그루브 맞대기 용접 배관이 그루브 각 45°, 90° 를 갖는 형상에 대한 한계하중 식을 제시하기 위해 용접 형상의 변화에 따른 용접부 너비를 정의하였고 강도불일치 비, 용접부 너비, 균열 길이 및 배관 반경 비에 대한 체계적인 변수 해석을 수행 하였다. 모재와 용접재는 탄성 완전소성재료로 가정하였으며 상불일치와 하불일치 조건에서의 인장 하중과 굽힘 하중에 대한 강도불일치 한계하중이 강도불일치 비(MF)와 형상변수(ψ)를 통해 정량화 됨을 유한요소 해석을 통해 확인하였다.

Generation of plastic influence functions for J-integral and crack opening displacement of thin-walled pipes with a short circumferential through-wall crack

Fracture mechanics parameters such as the J-integral and crack opening displacement (COD), are necessary for Leak-Before-Break (LBB) evaluation. The famous two estimation methods, the GE/EPRI and the Reference Stress Method (RSM), have their applicability limit with regard to the ratio of a pipe mean radius to thickness (Rm/t). In order to extend their applicability limit to a thin walled pipe, several finite element analyses are performed for the J-integral and COD, and then new plastic influence functions are developed for thin-walled pipes with a short circumferential through-wall crack. With the newly generated plastic influence functions, the GE/EPRI and the RSM give closer results with those obtained from detailed finite element analyses. In addition, C*-integral and COD rate are estimated by using the new plastic influence functions and they are well matched with elastic–creep finite element analysis results under the power-law creep condition. Since the LBB concept can be applied to a piping system in a Korean Sodium-cooled Fast Reactor (SFR) which is designed to have thin-walled pipes and to operate in high temperature enough to cause creep, this paper can be applied for the LBB assessment of thin-walled pipes with a short through-wall crack in the SFR.

Leak-Before-Break Under Beyond Design Basis Seismic Loading

The Atucha II nuclear power plant is a unique pressurized heavy water reactor (PHWR) being constructed in Argentina. The original plant design was by Kraftwerk Union (KWU) in the 1970's using the German methodology of break preclusion. The plant construction was halted for several decades, but a recent need for power was the driver for restarting the construction. The United States Nuclear Regulatory Commission (US NRC) developed leak-before-break (LBB) procedures in standard review plan (SRP) 3.6.3 Revision 1 for the purpose of eliminating the need to design for dynamic effects that allowed the elimination of pipe whip restraints and jet impingement shields. This SRP was originally written in 1987. The US NRC is currently developing a draft Regulatory Guide on what is called the transition break size (TBS). However, modeling crack pipe response in large complex primary piping systems under seismic loading is a difficult analysis challenge due to many factors. The initial published work (Wilkowski et al., “Robust LBB Analysis for Atucha II Nuclear Plant,” 2011 ASME PVP Conference, July 17–21, Baltimore, MD) on the seismic evaluations for the Atucha II plant showed that even with a seismic event with the amplitudes corresponding to the amplitudes for an event with a probability of 1 × 10−6 per year, that a double-ended guillotine break (DEGB) was pragmatically impossible due to the high leakage rates and total loss of make-up water inventory. The critical circumferential through-wall flaw size in that case was 94% of the circumference. This paper discusses further efforts to show how much higher the applied accelerations would have to be to cause a DEGB for an initial circumferential through-wall crack that was 33% around the circumference. This flaw length would also be easily detected by leakage and loss of make-up water inventory. These analyses showed that the applied seismic peak-ground accelerations had to exceed 25 g's for the case of this through-wall-crack to become a DEGB during a single seismic loading event. This is a factor of 80 times higher than the 1 × 10−6 seismic event accelerations, or 240 times higher than the safe shutdown earthquake (SSE) accelerations.

Experimental Investigation of Failure Estimation Method for Stainless Steel Pipes With a Circumferential Crack Subjected to Combined Tensile and Torsion Loads

When a crack is detected in a stainless steel pipe during in-service inspections, the failure estimation method given in codes such as the ASME Boiler and Pressure Vessel Code Section XI or JSME Rules on Fitness-for-Service for Nuclear Power Plants can be applied to evaluate the structural integrity of the cracked pipe. In the current codes, the failure estimation method includes the bending moment and tensile force due to pressure. The torsion moment is assumed to be relatively small and is not considered. Recently, analytical investigations considering multiaxial loads including torsion were conducted in several previous studies by examining the limit load for pipes with a circumferential crack. A failure estimation method for the combined bending moment, torsion moment, and internal pressure was proposed. In this study, the failure behavior of pipes with a circumferential crack subjected to multiaxial loads including the torsion is investigated to provide experimental support for the failure estimation method. Experiments were carried out on small size stainless steel cylinders containing a circumferential surface or through-wall crack, subjected to the combined tensile load and torsion moment. Based on the experimental results, the proposed failure estimation method was confirmed to be applicable to cracked pipes subjected to combined tensile and torsion loads.

비 이상화된 원주방향 관통균열이 존재하는 두꺼운 배관의 균열 성장 매개변수 계산

The present paper provides the elastic stress intensity factors(SIFs) of thick-walled cylinder with non-idealized circumferential through-wall cracks. For estimating these elastic SIFs, the systematic three-dimensional(3D) elastic finite element(FE) analyses were performed. In order to consider practical shape of thick-walled cylinder and non-idealized circumferential through-wall crack, the values of thickness of cylinder, reference crack length and crack length ratio were systematically varied. As for loading conditions, axial tension, global bending and internal pressure were considered. In particular, in order to calculate the SIFs of thick-walled cylinder with non-idealized circumferential through-wall crack from those of thick-walled cylinder with idealized circumferential through-wall crack, the correction factor representing the effect of non-idealized crack on the SIFs were proposed in this paper. The present results can be applied to accurately evaluate the rupture probabilities of nuclear piping considering actual crack growth behaviors.

Development of Leak-Before-Break Assessment Method for Japan Sodium Cooled Fast Reactor Pipe—Part 1 Crack Opening Displacement Assessment of Thin Wall Pipes Made of Modified 9Cr-1Mo Steel

This was carried out to establish crack opening displacement (COD) evaluation methods used in leak-before-break (LBB) assessment of sodium pipes of the Japan sodium cooled fast reactor (JSFR). For sodium pipes of JSFR, the continuous leak monitoring will be adopted as an alternative to a volumetric test of the weld joints under conditions that satisfy LBB. The sodium pipes are made of ASME Gr.91 (modified 9Cr-1Mo steel). Thickness of the pipes is small, because the internal pressure is very low. Modified 9Cr-1Mo steel has a relatively large yield stress and small work hardening coefficient comparing to the austenitic stainless steels which are currently used in the conventional plants. In order to assess the LBB behavior of the sodium pipes made of modified 9Cr-1Mo steel, the coolant leak rate from a through-wall crack must be estimated properly. Since the leak rate is strongly related to the COD, an appropriate COD assessment method must be established to perform LBB assessment. However, COD assessment method applicable for JSFR sodium pipes—thin wall and small work hardening material—has not been proposed yet. Thus, a COD assessment method applicable to thin walled large diameter pipe made of modified 9Cr-1Mo steel was proposed in this study. In this method, COD was calculated by classifying the components of COD; elastic, local plastic, and fully plastic. In addition, the verification of this method was performed by comparing with the results of a series of four-point bending tests at elevated temperature using thin wall modified 9Cr-1Mo steel pipe containing a circumferential through-wall crack. As a result, COD values calculated by the proposed method were in a good agreement with the experimental results for the uniform pipe without a weld. In the case that the crack was machined in the weld metal or heat affected zone (HAZ), the proposed method predicted relatively larger COD than the experimental results. The causes of such discrepancies were discussed by comparing with the results of finite element analyses. Based on these examinations, the rational leak rate evaluation method in LBB assessment was proposed.

Natural Crack Growth Analyses for Circumferential and Axial PWSCC Defects in Dissimilar Metal Welds

The natural crack growth analysis (sometimes referred to as advanced finite element analysis (AFEA)) methodology has been developed by the US NRC and the nuclear industry to evaluate the natural crack growth due to primary water stress corrosion cracking (PWSCC) in nickel-based alloy materials. The natural crack growth (or AFEA) methodology allows the progression of a planar crack subjected to typical stress corrosion cracking (SCC)-type growth laws by calculating stress intensity factors at every nodal point along the crack front and incrementally advancing the crack front in a more natural manner. This paper describes the step-by-step procedure enhancements that have been made to the existing AFEA methodology. A significant enhancement was the feature to evaluate axial crack growth, where the crack was contained within the susceptible material. This methodology was validated by performing an AFEA evaluation for the axial crack that was found in the V.C. Summer hot-leg dissimilar metal weld (DMW). Other enhancements to the AFEA methodology include: feature to handle nonidealized circumferential through-wall cracks, mapping of weld residual stress for crack growth, and determination of limiting crack size using elastic-plastic J-integral analysis that included secondary stress (weld residual stress and thermal transient stress) effects.

Numerical Analysis of JNES Seismic Tests on Degraded Combined Piping System

Nuclear power plant safety under seismic conditions is an important consideration. The piping systems may have some defects caused by fatigue, stress corrosion cracking, etc., in aged plants. These cracks may not only affect the seismic response but also grow and break through causing loss of coolant. Therefore, an evaluation method needs to be developed to predict crack growth behavior under seismic excitation. This paper describes efforts conducted to analyze and better understand a series of degraded pipe tests under seismic loading that was conducted by Japan Nuclear Energy Safety Organization (JNES). A special “cracked-pipe element” (CPE) concept, where the element represented the global moment-rotation response due to the crack, was developed. This approach was developed to significantly simplify the dynamic finite element analysis in fracture mechanics fields. In this paper, model validation was conducted by comparisons with a series of pipe tests with circumferential through-wall and surface cracks under different excitation conditions. These analyses showed that reasonably accurate predictions could be made using the abaqus connector element to model the complete transition of a circumferential surface crack to a through-wall crack under cyclic dynamic loading. The JNES primary loop recirculation piping test was analyzed in detail. This combined-component test had three crack locations and multiple applied simulated seismic block loadings. Comparisons were also made between the ABAQUS finite element (FE) analyses results to the measured displacements in the experiment. Good agreement was obtained, and it was confirmed that the simplified modeling is applicable to a seismic analysis for a cracked pipe on the basis of fracture mechanics. Pipe system leakage did occur in the JNES tests. The analytical predictions using the CPE approach did not predict leakage, suggesting that cyclic ductile tearing with large-scale plasticity was not the crack growth mode for the acceleration excitations considered here. Hence, the leakage was caused by low-cycle fatigue with small-scale yielding. The procedure used to make predictions of low-cycle fatigue crack growth with small-scale yielding was based on the Dowling ΔJ procedure, which is an extension of linear-elastic fatigue crack growth methodology into the nonlinear plasticity region. The predicted moments from the CPE approach were used using a cycle-by-cycle crack growth procedure. The predictions compare quite well with the experimental measurements.

Studies on the effect of compliance on fracture behaviour of carbon steel pipes with circumferential through-wall crack

The design of Nuclear Power Plant piping is based on Leak-Before-Break (LBB) design philosophy. The integrity of cracked nuclear piping system in LBB is often examined from conventional fracture mechanics. Conventionally the fracture analysis is performed by assuming infinite compliance of the piping system, which means that the stiffening effect of the connected uncracked piping system is fully neglected. However, in reality the ends of the pipe are connected to the rigid pressure vessels, primary coolant pipes, etc. In order to study the effect of compliance on the fracture behaviour of pipes, fracture studies were carried out on fourteen specimens of 219 mm outer diameter carbon steel pipes having circumferential through-wall crack. The fracture tests were conducted under four point bending. Out of the fourteen specimens, twelve specimens were tested in fixed end condition (finite compliance) and the remaining two specimens were tested in simply supported condition (infinite compliance). These pipes were made of SA 333 Gr. 6 carbon steel. Extensive instrumentation was carried out on these pipes to collect various data, e.g., load, load-line displacement (LLD), crack mouth opening displacement (CMOD), rotation at the ends (flanges), deflection at critical locations and surface crack growth. Surface crack growth was monitored using Image Processing Technique (IPT). The investigations have shown that the load carrying capacity of the pipes under finite compliance condition (fixed end condition) increases when compared to infinite compliance (simply supported condition). The load carrying capacity of the pipes under finite compliance weakly depends on the initial crack angle where as the load carrying capacity of the pipes under infinite compliance strongly depends on the initial crack angle. The safety margin is quite large particularly with a stiff piping system. This benefit in terms of increase in safety margin from LBB point of view is due to the moment redistribution. This paper discusses the effects of notch angle, span and the support conditions on the fracture behaviour of pipes with circumferential through-wall crack.

3차원 유한요소 한계해석을 이용한 원주방향 경사관통균열 배관의 소성한계하중

On the basis of detailed 3D finite-element (FE) limit analyses, the plastic limit load solutions for pipes with slanted circumferential through-wall cracks (TWCs) subjected to axial tension, global bending, and internal pressure are reported. The FE model and analysis procedure employed in the present numerical study were validated by comparing the present FE results with existing solutions for plastic limit loads of pipes with idealized TWCs. For the quantification of the effect of slanted crack on plastic limit load, slant correction factors for calculating the plastic limit loads of pipes with slanted TWCs from pipes with idealized TWCs are newly proposed from extensive 3D FE calculations. These slant-correction factors are presented in tabulated form for practical ranges of geometry and for each set of loading conditions.

Fracture investigations on piping system having large through-wall circumferential crack

In level-3 Leak-Before-Break (LBB) analysis, stability of a postulated through-wall circumferential crack is demonstrated by simplified fracture mechanics calculations. Detailed experimental studies, conducted by the authors, have revealed that the conventional assessment procedure used to demonstrate LBB is too conservative. There is a large factor of safety due to system indeterminacy. It was observed that the critical load of a cracked piping system (with even a large through-wall circumferential crack of about 120°) is of the order of 75–90% of the collapse load of the uncracked piping system. Reduction in load carrying capacity is even less for a piping system having an off-centre crack. This article discusses the above-mentioned aspects in detail. Detailed 3-D elastic-plastic finite element analyses of some of these tests were performed. The suitability of these numerical results to predict crack initiation load in light of the experimental data is discussed.

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.

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

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.

Finite element evaluation of the support-induced restraint effect on the limit loads of surface cracked tubes

Heat exchangers are widely used in electric power plants as well as petrochemical facilities. Typical heat exchangers consist of a number of thin-walled tubes, supports, a main body, and so on. Operating experience of the heat exchangers has shown that cracks of various morphologies frequently occur in the tubes. Therefore, an accurate integrity assessment of the cracked tube is very important from the viewpoint of safety and reliability. The heat exchanger tubes are supported at regular intervals by the supports and rotations of the tubes are restrained. In the authors' previous study, it was revealed that the limit loads for circumferential through-wall cracks are significantly affected by the supports and existing limit load solutions without considering the support-induced restraint effect differ from the actual failure load. However, the effect of the supports on the global limit load of surface cracked tubes has not been fully investigated. This paper provides detailed global limit load solutions for the tubes with circumferential surface cracks considering the restraint effect of the supports. Such solutions are developed based on three-dimensional finite element analyses. The resulting limit load solutions can be simply used in practical integrity assessment of the heat exchanger tubes.

A Probabilistic Assessment Technique Applied to a Cracked Heat Exchanger Tube Subjected to Flow-Induced Vibration

Flow-induced vibration is a common phenomenon in shell-and-tube heat exchangers. The resulting vibration can lead to component failure by fretting wear due to tube-to-tube support impact or by fatigue. Due to manufacturing considerations, many parameters such as support clearance, alignment, and friction at the supports are not exactly known and are represented by statistical distributions. This makes the use of deterministic equations inaccurate. This paper presents a methodology that can be used during component operation to monitor known flaws and ensure safe operation. The methodology incorporates Monte Carlo simulations to predict remaining service life of a vibrating heat exchanger tube with a small circumferential through-wall crack next to the tube sheet. Vibration excitation includes turbulence and low-level fluid-elastic forces. Leakage calculations are made on the through-wall crack as it grows to fracture. A Weibull distribution is given for the time-to-fracture and for the time for the leak rate to reach a threshold value. This statistical information can then be used to assess the remaining service life and whether LBB criteria will be met.

A practical application of an evaluation model for the restraint effect of pressure-induced bending on a plastic crack opening

This paper presents an evaluation model for the restraint effect of pressure-induced bending (PIB) on the opening of a circumferential through-wall crack (TWC) and a result of its application to the calculation of crack-opening displacement (COD) of postulated cracks for a practical leak-before-break (LBB) analysis. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and material tensile properties were used to investigate the influence of each parameter on the PIB restraint for the plastic COD. From these investigations, we proposed an evaluation model based on elastic–perfectly plastic behavior. Comparison with finite element analysis results demonstrated that the proposed model reliably estimated the PIB restraint effect on the plastic crack opening of a circumferential TWC and properly reflected the effect of each parameter within the range over which the analytical expression was derived. The model was then used to calculate restrained CODs of postulated cracks for a practical LBB analysis. When plastic crack behavior was considered, the PIB restraint effect was considerable for some LBB analysis cases of the primary piping systems in a typical nuclear power plant. This effect was estimated to be negligible by existing linear elastic-based models.

Stress intensity factors for slanted through‐wall cracks based on elastic finite element analyses

ABSTRACTBased on detailed 3‐dimensional (3‐D) elastic finite element (FE) analyses, the present paper provides stress intensity factors (SIFs) for plates with slanted through‐wall crack (TWC) and cylinders with slanted circumferential TWC. Regarding loading conditions, axial tension was considered for the plates, whereas axial tension, global bending and internal pressure were considered for the cylinders. To cover a practical range, the geometric variables affecting the SIF were systematically varied. Based on FE results, SIFs along the crack front, including the inner and outer surface points, were provided. The present results can be used to evaluate the fatigue crack growth or stress corrosion cracking behaviour of a slanted TWC and furthermore to perform detailed Leak‐Before‐Break analysis considering a more realistic crack shape.

The T-stress solutions for through-wall circumferential cracks in cylinders subjected to general loading conditions

The elastic T-stress is a parameter used to define the level of constraint at a crack tip. It is important to provide T-stress solutions for practical geometries to apply the constraint-based fracture mechanics methodology. In the present work, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. First, cylinders with a circumferential through-wall crack were analyzed using the finite element method. Three cylinder geometries were considered; defined by the mean radius of the cylinder ( R) to wall thickness ( t) ratios: R/ t = 5, 10, and 20. The T-stress was obtained at eight crack lengths ( θ/π = 0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, and 0.5000, θ is the crack half angle). Both crack face loading and remote loading conditions were considered including constant, linear, parabolic and cubic crack face pressures and remote tension and bending. The results for constant and linear crack face pressure were used to derive weight functions for T-stress for the corresponding cracked geometries. The weight functions were validated against several linear and non-linear stress distributions. The derived weight functions are suitable for T-stress calculations for circumferential cracks in cylinders under complex stress fields.