Crack Opening Displacement Estimation Research Articles

Numerical Method for Predicting Permeability of Laminated Composites at Cryogenic Temperature

The numerical method for predicting the permeability of a laminated composite based on matrix cracks is improved to meet the application at a cryogenic temperature. The number of the parameters that depends on experiments is reduced in this numerical method to save costs. The semianalytical damaged constitutive model of cracked plies, the crack density estimation method, the crack opening displacement estimation, and the effective leakage conductance calculation are improved by involving the temperature or thermal strain. Stiffness degradation of a carbon fiber reinforced plastic lamina with different thicknesses and temperatures is obtained by the proposed constitutive model to validate the effect of temperature; and the degradation of the transverse modulus is found to subside with the increasing temperature when the crack densities are the same. The effective leakage conductance of cross-ply laminates, under biaxial loading, is estimated at cryogenic and room temperatures by using three different average methods. The estimation results agree well with the available experiments in the specimens with a uniform thickness of cracked plies. The simulation results indicate that the easier occurrence of leakage at the cryogenic temperature is owing to the significant degradation of the stiffness at cryogenic temperature instead of the thermal strains.

On elastic-plastic and creep fracture mechanics parameters estimates of non-idealized axial through-wall crack in pressurized pipe

The present paper provides engineering estimates for plastic J-integral and crack opening displacement (COD) of a non-idealized axial through-wall crack (TWC) in pipes based on detailed 3-dimensional finite element (FE) analyses. The behaviors of plastic J-integral and COD of a non-idealized axial TWC in typical pressurized pipes in nuclear power plants were systematically investigated. The FE model and analysis procedure employed in this study were verified by comparing the present FE results with the limited existing solutions for pipes with an idealized axial TWC. Based on the FE results, the new plastic influence functions, h1 and h2, which include the effect of a non-idealized TWC on plastic J-integral and COD, are provided as tabular solutions. By employing the plastic influence functions, plastic J-integral and COD of a non-idealized axial TWC along crack front can be directly predicted based on GE/EPRI method. In the present paper, plastic J-integral and COD estimates based on the reference stress concept have also been suggested. Finally, the estimated results were compared with elastic-plastic FE results by using actual stress-strain data and Ramberg-Osgood constants for TP 316 stainless steel. In addition, the engineering estimates proposed in this study were extended to estimating the creep fracture mechanics parameters at elevated temperature. Based on Norton and RCC-MRx creep models, C*-integral and creep COD rate values predicted from the present engineering solutions were validated by comparing with creep FE results. The results provided in this paper demonstrate that the present estimates can be applied to calculating plastic J-integral and COD, C*-integral, and creep COD rate of a non-idealized axial TWC.

EngineeringC*‐integral and COD estimates for nonidealized circumferential through‐wall cracked pipes at elevated temperature

AbstractIn this study, creep fracture mechanics parameters,C*‐integral and crack opening displacement (COD) rate, are estimated for a nonidealized circumferential through‐wall crack (TWC) in pipes. The GE/EPRI and enhanced reference stress (ERS) methods are employed. As for creep condition, the Norton and RCC‐MRx creep models are considered for secondary and primary‐secondary creep strain, respectively. The bending moment, axial tension, and internal pressure are applied to a pipe with a nonidealized circumferential TWC, as individual loads. Three‐dimensional elastic‐creep finite element (FE) analyses are performed, and the predictions from the GE/EPRI and ERS methods are compared with FE results. For the Norton creep model, both methods show good agreement with the FE results. For the RCC‐MRx creep model, only the ERS method can be used, and it provides accurate predictions comparing with FE results. Based on the comparison results, the use of the present engineeringC*‐integral and COD estimation methods for nonidealized circumferential TWC is validated.

Engineering Approach Based on Reference Stress Concept for Calculating J and Crack Opening Displacement of Complex-Cracked Pipes

In this study, an engineering approach for estimations of fracture mechanics parameters, i.e., J-integral and crack opening displacement (COD), for complex-cracked pipes was suggested based on reference stress concept, where stress-strain data of the material was used to assess structural integrity of complex-cracked pipes. In the present study, new reference loads that can reduce the dependency on strain hardening of the material have been suggested for complex-cracked pipes under each loading mode. By using the proposed optimized reference load for complex-cracked pipes, J-integral and COD estimation procedures have been proposed based on the reference stress concept together with the elastic solutions for complex-cracked pipes. The predicted J-integrals and CODs based on the proposed method have been validated against published experimental data and FE results using actual stress–strain data. Moreover, the predictions using the proposed methods are also compared with those using the existing solutions for simple through-wall cracks (TWCs) based on reduced thickness analogy concept.

Fully plastic crack opening analyses of complex-cracked pipes for Ramberg-Osgood materials

The plastic influence functions for calculating fully plastic Crack opening displacement (COD) of complex-cracked pipes were newly proposed based on systematic 3-dimentional (3-D) elastic-plastic Finite element (FE) analyses using Ramberg-Osgood (R-O) relation, where global bending moment, axial tension and internal pressure are considered separately as a loading condition. Then, crack opening analyses were performed based on GE/EPRI concept by using the new plastic influence functions for complex-cracked pipes made of SA376 TP304 stainless steel, and the predicted CODs were compared with FE results based on deformation plasticity theory of tensile material behavior. From the comparison, the confidence of the proposed fully plastic crack opening solutions for complex-cracked pipes was gained. Therefore, the proposed engineering scheme for COD estimation using the new plastic influence functions can be utilized to estimate leak rate of a complex-cracked pipe for R-O material.

Reference stress based J and COD estimation of circumferential through-wall cracked elbows under in-plane bending

This paper proposes J-integral and crack opening displacement (COD) estimation equations based on the reference stress method for circumferential through-wall cracked elbows under in-plane bending. For best estimates of J and COD, an optimized reference load, used to define the reference stress, is given. The proposed equations are compared with detailed finite element results. They are further validated against eight published full-scale pipe test data. Comparison of crack initiation and maximum loads shows good agreement.

Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

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)1 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, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.

Elastic–plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic–plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic–perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.

Elastic‐plastic fracture mechanics assessment for steam generator tubes with through‐wall cracks

ABSTRACTSThe present work provides an elastic‐plastic fracture mechanics (EPFM) assessment scheme for a steam generator tube with a through‐wall crack under internal pressure. Noting that the geometry and material are rather uniform for steam generator tubes, and furthermore the only loading to be considered is internal pressure, an engineering EPFM analysis method is proposed to assess through‐wall cracks in steam generator tubes. Important outcomes of the present work are closed‐form approximations for J and crack opening displacement (COD). Sufficient confidence in the proposed J and COD estimates is gained from good agreements with the finite element results over a wide range of the crack length and pressure magnitude. Another important element of the EPFM assessment is to determine relevant J‐resistance curve for steam generator tubes. To improve the accuracy of predicting tube failure, the present paper also proposes a new method to determine fracture toughness using an actual tubular specimen instead of using a standard specimen, from which J‐resistance curves of steam generator tubes are obtained. Using the proposed J and toughness estimates, maximum pressures of steam generator tubes with through‐wall crack are estimated based on EPFM analysis, which is compared with experimental results and predicted ones based on limit load approach.

Improved J and COD estimation by GE/EPRI method in elastic to fully plastic transition zone

It is well known that conventional GE/EPRI method over-estimates the J-integral and crack opening displacement (COD) 1 COD varies along the crack length. It is zero at the crack tips and maximum at the middle. Throughout this paper, COD denotes the maximum crack opening displacement at the middle of crack length. 1 in the elastic to fully plastic transition zone. The present paper investigates this issue and attempts to rectify this error. An improved GE/EPRI method is proposed with the modifications of α (Ramberg–Osgood coefficient) term in the equation of plastic J and COD. The proposed method has been experimentally and numerically validated.

Elastic–plastic J and COD estimation schemes for throughwall circumferentially cracked elbow under in-plane closing moment

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) 1 COD varies along the crack length. It is zero at the crack tips and maximum at the middle. Throughout this paper, COD denotes the maximum crack opening displacement at the middle of crack length. 1 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.

원자력 배관의 공학적 파단전누설 해석을 위한 균열열림변위 계산

This study presents methods to estimate elastic-plastic crack opening displacement (COD) for circumferential through-wall cracked pipes for the Leak-Before-Break (LBB) analysis of pressurized piping. Proposed methods are based not only on the GE/EPRI approach but also on the reference stress approach. For each approach, two different estimation schemes are given, one for the case when full stress-strain data are available, and the other for the case when only yield and ultimate tensile strengths are available. For the GE/EPRl approach, a robust way of determining the Ramberg-Osgood (R-O) parameters is proposed, not only for the case when detailed information on full stress-strain data is available but also for the case when only yield and ultimate tensile strengths are available. The COD estimates according to the GE/EPRI approach, using the R-O parameters determined from the proposed R-O fitting procedures, generally compare well with the published pipe test data. For the reference stress approach, the COD estimates according to the method based on both full stress-strain data and limited tensile properties are in good agreement with pipe test data. In conclusion, experimental validation given in the present study provides sufficient confidence in the use of the proposed method to practical LBB analyses even though when information on material's tensile properties is limited.

Elastic–plastic J and COD estimates for axial through-wall cracked pipes

This paper proposes engineering estimation equations of elastic–plastic J and crack opening displacement (COD) for axial through-wall cracked pipes under internal pressure. On the basis of detailed 3D finite element (FE) results using deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalised crack length, and the strain hardening. On the basis of these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against 3D FE results based on deformation plasticity. For more general application to general stress–strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress (RS) concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed RS based J and COD estimation equations are compared with elastic–plastic 3D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.

Quantification of pressure-induced hoop stress effect on fracture analysis of circumferential through-wall cracked pipes

This paper provides engineering J and crack opening displacement (COD) estimation equations for through-wall cracked (TWC) pipes under internal pressure and under combined internal pressure and bending. Based on selected 3-D FE calculations for the TWC pipe under internal pressure using power law materials, elastic and plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the normalised crack length and the mean radius-to-thickness ratio. These developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such re-formulation not only provides simpler equations for J and COD estimation, but also can be easily extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic–plastic 3-D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.