J-estimation Scheme Research Articles

New engineering J-estimation schemes for complex cracked pipes based on energy equivalence concept

A complex crack has 360° internal surface crack in the circumferential section of the pipe and through-wall crack in the same section. Previous studies have shown that the fracture behavior of complex crack is different from those of through-wall crack or surface crack. Therefore, it is necessary to develop the new engineering scheme to accurately predict the fracture characteristics of a complex cracked pipe. This study proposes the new approximate J-estimation scheme for complex cracked pipe subject to bending moment. The method is based on the concept of an energy equivalence between cracked pipe and reduced thickness pipe without a crack. Elastic-plastic J-integral solution is provided in closed-form. To derive the solution, both the energy release in the radial direction of the surface crack and the circumferential direction of the through-wall crack were considered. To verify the proposed solution, J-integral was calculated for various geometric variables and material properties, and compared with the calculation results using the GE/EPRI based J-estimation scheme of the complex crack. Also, the effect of consideration of crack propagation direction on J-integral was systematically analyzed.

Instability moment predictions for complex through-wall cracked pipes of low alloy steel

The complex through-wall cracks (TWC) that have been discovered in the dissimilar metal weld of nuclear power plants have different fracture behavior compared with the simple TWC that is typically assumed in a flaw evaluation. In this regards, a number of prior research has aimed at developing an appropriate J-estimation scheme and constructing of the J-R curve that can be utilized for complex crack analysis. In the present paper, instability moments of complex TWC pipes of low alloy steel were calculated through the crack driving force diagram approach, employing J-estimation formula for complex crack recently developed. As a fracture property, the test data of complex crack tension (CCT) specimen was used. Comparing with the prediction results of FE analysis using a damage model, it was observed that this procedure could provide an accurate prediction of the instability moment with the reasonable conservatism.

Strain-based J-estimation scheme for fracture assessment of misaligned clad pipelines with an interface crack

A reference strain J-estimation formulation is developed to perform the fracture assessment of misaligned clad pipelines containing a circumferential part-through crack located at the interface of weld metal and outer pipe. An extensive parametric study including a total of 896 finite element (FE) models is carried out to investigate the effects of various parameters (pipe diameter, crack depth, crack length, centreline offset, strength mismatch level, and strain hardening exponent) on the J-integral. Then, the estimation formulation characterizing the linear relationship between the J-integral and the applied displacement loading is proposed using the standard least square fitting, and a goodness of fit for the J-integral values obtained from the formulation and the FE analysis is endorsed. Finally, the application range of the estimation formulation is mostly extended by conducting further comparative study.

Plastic influence functions for calculating J-integral of complex-cracks in pipe

In this study, the plastic influence functions, h1, for estimates of J-integral of a pipe with a complex crack were newly proposed based on the systematic 3-dimensional (3-D) elastic-plastic finite element (FE) analyses by using Ramberg-Osgood (R-O) relation, in which global bending moment, axial tension and internal pressure were considered as loading conditions. Based on the present plastic influence functions, the GE/EPRI-type J-estimation scheme for complex-cracked pipes was suggested, and the results from the proposed J-estimation were compared with the FE results using both R-O fit parameters and actual tensile data of SA376 TP304 stainless steel. The comparison results demonstrate that although the proposed scheme provided sensitive J estimations according to fitting ranges of R-O parameters, it showed overall good agreements with the FE results using R-O relation. Thus, the proposed engineering J prediction method can be utilized to assess instability of a complex crack in pipes for R-O material.

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.

Effect of Combined Loading Due to Bending and Internal Pressure on Pipe Flaw Evaluation Criteria

Considering a rational maintenance rule of Light Water Reactor piping, reliable flaw evaluation criteria are essential to determine how a detected flaw is detrimental to continuous plant operation. Ductile fracture is one of the dominanant failure modes to be considered for carbon steel piping, and can be analyzed by the elastic-plastic fracture mechanics. Some analytical efforts have been provided as flaw evaluation criteria using load correction factors such like the Z-factors in the JSME codes on fitness-for-service for nuclear power plants or the ASME boiler and pressure vessel code section XI. The present correction factors were conventionally determined taken conservatism and simplicity into account, however, the effect of internal pressure which would be an important factor under an actual plant condition was not adequately considered. Recently, a J-estimation scheme, “LBB. ENGC” for ductile fracture analysis of circumferentially through-wall-cracked pipes subject-ed to combined loading was newly developed to have a better prediction with more realistic manner. This method is explicitly incorporated the contribution of both bending and tension due to internal pressure by means of the scheme compatible with an arbitrary combined loading history. In this paper, the effect of internal pressure on the flaw evaluation criteria was investigated using the new J-estimation scheme. A correction factor based on the new J-estimation scheme was compared with the present correction factors, and the predictability of the current flaw evaluation criteria was quantitatively evaluated in consideration of internal pressure.

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.

Effect of Combined Loading Due to Bending and Internal Pressure on Pipe Flaw Evaluation Criteria

Considering a rational maintenance rule of Light Water Reactor piping, reliable flaw evaluation criteria are essential to determine how a detected flaw is detrimental to continuous plant operation. Ductile fracture is one of the dominanant failure modes to be considered for carbon steel piping, and can be analyzed by the elastic-plastic fracture mechanics. Some analytical efforts have been provided as flaw evaluation criteria using load correction factors such like the Z-factors in the JSME codes on fitness-for-service for nuclear power plants or the ASME boiler and pressure vessel code section XI. The present correction factors were conventionally determined taken conservatism and simplicity into account, however, the effect of internal pressure which would be an important factor under an actual plant condition was not adequately considered. Recently, a J-estimation scheme, “LBB. ENGC” for ductile fracture analysis of circumferentially through-wall-cracked pipes subject-ed to combined loading was newly developed to have a better prediction with more realistic manner. This method is explicitly incorporated the contribution of both bending and tension due to internal pressure by means of the scheme compatible with an arbitrary combined loading history. In this paper, the effect of internal pressure on the flaw evaluation criteria was investigated using the new J-estimation scheme. A correction factor based on the new J-estimation scheme was compared with the present correction factors, and the predictability of the current flaw evaluation criteria was quantitatively evaluated in consideration of internal pressure.

J-Integral Evaluation of Single-Edge Notched Specimens under Mixed-Mode I/II Loading

Abstract Standard test methods of mixed-mode fracture toughness still do not exist, even though a decrease of fracture toughness with increasing Mode II (shear components) has been observed for a number of steels. A J-estimation scheme for mixed-mode loaded single-edge notched specimens is therefore developed in this paper. In accordance with the ASTM Standard E 1820-99, the evaluation of the plastic part of J is based on the measurement of the dissipated plastic energy weighted by a ηpl-factor. Two different approaches for the ηpl-factor are derived. Factors from both showed good correlation with finite element calculations for the specific case of a compact-tension-shear specimen (C(TS)), Finally, a simple clip gage setup for the measurement of the crack-opening displacements needed for the evaluation of the dissipated plastic energy is presented. The problem of the qualification of the mixed-mode crack initiation data is not specifically addressed, but some general comments on this topic are given at the end of the paper.

Estimates of Crack-Driving Force in Surface-Cracked Elbows

The objective of this effort was to assess whether a simple relationship could be developed between the behavior of surface cracks in straight pipe and in elbows. If such a geometric relationship could be developed, then a simple multiplier could be applied to the current straight-pipe solutions that are already used in codes and standards such as the ASME or other codes. In order to accomplish this objective, solutions from elbow and straight-pipe elastic-plastic fracture mechanics (EPFM) analyses were used along with experimental data. The elbow EPFM solution came from a J-estimation scheme developed during the IPIRG-2 program. These solutions were for an elbow with a pressure at the design stress limits of Section III of the ASME Code for typical nuclear piping steels. Significant efforts were undertaken in that program to develop J-estimation schemes for axial (along the side of the elbow) and circumferential surface cracks (centered on the extrados) in elbows under constant pressure and in-plane bending. These analyses were developed using the GE/EPRI methodology of determining an elastic and plastic contribution to J, and developing the appropriate functions through a matrix of EPFM finite element analyses. Even with this large matrix of FEM analyses, only one circumferential crack length and one axial crack length were investigated. Hence, it was desirable to develop a method to extend the analysis capabilities to other crack geometry, as well as developing a simplified procedure. A comparison of the elbow to straight-pipe moment versus crack-driving force curves showed that there is a simple multiplier linearly related to the ASME B2 stress index for elbows of different R/t ratios. Hence, a simplified procedure was determined where the straight-pipe solution could be multiplied by a function of the elbow stress indices to give the maximum load prediction of the surface-cracked elbow. Comparisons were made to circumferential surface-cracked elbow data from the IPIRG-2 program, and an axial surface-cracked elbow test conducted by EDF. The comparisons showed the simplified methods to be quite promising.

J-R Curves From Circumferentially Through-Wall-Cracked Pipe Tests Subjected to Combined Bending and Tension—Part II: Experimental and Analytical Validation

In Part I (Miura and Wilkowski, 1998) of this paper, the theory of the two η-factor solutions for circumferentially through-wall-cracked pipes subjected to combined bending and tension due to internal pressure was presented. These solutions seemed to give reasonable predictions by comparing with the existing simplified J-estimation scheme. It was also ascertained that the J would be underestimated if the effect of the internal pressure was not properly considered. Consequently, this paper presents the application of these solutions to full-scale pipe tests. The tests were performed at 288°C (550°F) under combined bending and internal pressure. The materials used for the tests were both carbon steel and stainless steel. The effect of combined loading on the J-R curves was determined and compared to C(T) specimen J-R curves. The solutions were then verified by using three-dimensional finite element analysis.

破壊力学 参照応力法によるＪ積分簡易評価法の開発

Non-linear fracture mechanics is one of the most effective approaches for the integrity assessment of high temperature components. J-integral is a feasible parameter to represent fracture behavior in the non-linear regime. However, there are many difficulties in calculating an accurate value of J-integral in actual components. Some simplified methods have been proposed to estimate the J-integral, and applicability of those methods has been recognized. Although J-estimation scheme based on the reference stress method has an advantage to be applicable to many problems, the method has not been established yet. This paper presents a detailed procedure and applications for ductile fracture, creep-fatigue inhomogeneous and three-dimensional problems.

Analysis of Part-Throughwall Crack in a Pipe Under Combined Tension and Bending

J-resistance curve solution is developed for a circumferential part-throughwall crack in a pipe under combined tension and bending. The J solution can be applied with load-displacement-crack extension data from one pipe test. Material resistance curves are developed for part-throughwall cracks in Type-304 stainless steel base material and SAW weld, and SA333 Gr6 and A106 GrB carbon steel base materials. Posttest tearing instability analyses are performed to predict the load carrying capacity of pipes containing part-throughwall cracks and to assess the accuracy of a Jestimation scheme solution.

An Analysis of a Crack in Weld by Using Near-Field as Well as Far-Field Crack Parameters

A study of ductile crack growth characteristics in stainless steel welds is reported in this paper. A hybrid-type analysis of combined experimental, analytical, and predictive procedures on the subject is addressed. The study focuses on the effects of a stress/strain interaction phenomenon occurring between the crack tip and the weld-base material interface. Clear dependence of the crack initiation fracture characteristics on the weld size relative to the specimen size was found. Also, fracture toughness of a tungsten inert gas weld is shown to be comparable to that for the base stainless steel metal, whereas that of a submerged arc weld is shown to be significantly lower than the base metal. Because of the stress/strain nonproportionality associated with a local unloading due to crack growth in a ductile material, the use of a crack-tip parameter such as ΔTP* or Jˆ-integral was emphasized. On the other hand, prediction of a crack instability was attempted using a less rigorous J-estimation scheme procedure.