R6 Method Research Articles

528 熱時効ステンレス鋳鋼管の弾塑性破壊評価について

Fracture toughness of stainless steel casting (duplex stainless steel) is reduced under the condition about 300℃ by the thermal aging. For the flaw evaluation on thermal aged duplex stainless steel pipes, Fracture Assessment Curve (FAC) of R6 Option2 method is calculated using the stress-strain curve and J-resistance curve of thermal aged duplex stainless steel. To evaluate the fracture load on thermal aged duplex stainless steel in simple method, corrective factor is prepared in order to convert limit load based on net section criteria to fracture load based on R6 method.

Probabilistic fracture analysis of a straight pipe with through-wall circumferential crack using R6 method

Deterministic fracture analysis of cracked structures has been successful in demonstrating the behavior of structures under observed or postulated flaws. The key ingredients in a deterministic fracture mechanics analysis are the initial crack size, crack-driving force, applied stress and material properties. However, crack size, postulated accidental loading, mechanical and fracture parameters are often subjected to considerable scatter or uncertainty. Hence, the result of fracture mechanics analysis must be viewed with some skepticism. Quite often, conservative bounds on inputs are employed on these by providing a conservative estimate to fracture. However, it may lead to predict the overly conservative and unrealistic results. These uncertainties encourage us to adopt a statistical or probabilistic approach to the structural integrity. R6 is a well-known engineering assessment procedure for the evaluation of the structural integrity of the flawed structure. This paper presents the determination of failure probabilities of a straight pipe with a through-wall crack in the circumferential direction, using the R6 method. The pipe is subjected to an in-plane bending moment. The scatter in the crack size, mechanical and fracture properties are considered. The probability of failure is studied for variation in applied loads. Monte Carlo simulation is used to find the failure probability. The study is performed by constructing failure assessment diagram (FAD) using all the three options of R6. The results are compared with the approximate analytical formulations and with those available in the literature.

Development of a PFM code for evaluating reliability of pressure components subject to transient loading

In order to improve the PFM methodology and to evaluate the reliability and integrity of an aged RPV, the PFM code PASCAL is being developed. This code evaluates the conditional probability of crack initiation and fracture of pressure components subject to a transient loading based on Monte Carlo simulation. In addition to the common functions established in existing codes, the code has some original functions and features in the elasto-plastic fracture criterion based R6 method, the simulation models for the semi-elliptical crack extension and the effect of thermal annealing, improvement in Monte Carlo simulation and so on. This paper describes the main features of the code, the results of verification analysis and case studies on influence parameters by using above functions. The verification analysis and case studies are carried based on NRC/EPRI PTS benchmark problem. The basic performance of the code was verified by comparing the results with those by existing codes. From the result of case studies, the effectiveness and performance of main functions are examined and the influence of some parameters, such as fracture criterion, WPS, semi-elliptical crack extension models, existence of overlay clad, initial aspect ratio on the failure probability are also discussed.

K-0805 延性き裂進展解析法を導入したPFMコード開発 : 第1報:R6法に基づく延性き裂進展解析機能の導入(S11-2 構造健全性評価(2))(S11 構造健全性評価)

K-0805 延性き裂進展解析法を導入したPFMコード開発 : 第1報:R6法に基づく延性き裂進展解析機能の導入(S11-2 構造健全性評価(2))(S11 構造健全性評価)

Simplified J-estimations based on the Engineering Treatment Model for homogeneous and mismatched structures

This paper presents simplified J-estimation equations for defective homogeneous and strength mismatched structures, based on the Engineering Treatment Model (ETM). For homogeneous structures, two modifications are made to the existing ETM J-estimation equations; firstly a modification of the contained yielding solutions, and secondly modification of J-estimation equations for materials exhibiting Lüders strain. Based on the proposed J-estimation equations for homogeneous structures, J-estimation equations for welded structures with strength mismatch are proposed. The proposed J-estimation equations for both homogeneous and mismatched structures are then compared with selected elastic–plastic finite element results. The comparisons show excellent agreement and so provide confidence in the use of the proposed J-estimation equations for defect assessment. Finally, comparison with another simplified method, the R6 method, is discussed.

The engineering treatment model and comparison to R6 revision 3

The formalism presented in the engineering treatment model (ETM) as well as the background of the method are assessed. Special attention is focused on different assumptions and properties of the ETM. The validity and use in an engineering fracture analysis is considered, and the ETM is compared to R6 revision 3 failure assessment diagrams (FADs) options 1 and 2. A discussion concerning the usability of ETM and its possible deficiencies is presented. The comparison presents the similitude between the crack driving force estimates of the ETM and FAD treatments based on the R6 method.

Low alloy steel piping test for fracture criteria of leak before break

A total of seven pipe fracture tests were performed to provide the data for establishing fracture criteria of leak before break for the low alloy steel pipe, which is expected to be applied to reactor coolant piping and feedwater piping in advanced PWRs in Japan. Test pipes were 6-inch and 8-inch diameter pipes made of SFVQ1A or STPA24 low alloy steel. A circumferential through-wall crack was introduced at the center of a pipe, and four-point bending load was applied without internal pressure. Stable crack extensions were observed in all of the experiments. The net-section criteria (NSC), R6 method option 2 and option 3 were used to estimate the maximum applied load. The predicted values by three kinds of evaluation methods were compared with the experimental loads. Most of the predicted maximum loads agreed well with the experimental maximum loads within 20% difference. The NSC gave the most accurate prediction but also gave unconservative results in some test cases. The predicted maximum loads by R6 option 2 were conservative in all of the test cases. From the viewpoint of conservativeness R6 method can be used for evaluation of the low alloy steel pipe fracture. Therefore, the leak before break (LBB) concept could be applied to the protective design standard against pipe break for the material.

Structural integrity assessment for a flawed titanium pipe

This paper reports an assessment performed on a flawed titanium pipe, containing longitudinally oriented internal- and external-surface cracks, using both deterministic and probabilistic R6 methods. The assessment results were evaluated with respect to the methods used in assessment. According to the assessment results, the titanium pipe still had the required capacity to fulfill its commission although with the stated defects. In order to further improve the integrity status of the titanium pipe, some procedures have been proposed.

確率論的破壊力学に基づく軽水炉配管のＬＢＢ成立性評価

This paper describes Probabilistic Fracture Mechanics (PFM) analyses for quantitative evaluation of the likelihood of Leak-Before-Break (LBB) of Light Water Reactor's (LWR's) piping. The PFM analyses in general assume probabilistic distributions of initial crack size, applied stress cycles, crack growth laws, fracture criteria, leakage detection capability, defect inspection capability and so on. Referring to the deterministic procedure for LBB evaluation, most appropriate PFM models and data for LBB evaluation are discussed. Here the LBB index is newly proposed in order to quantitatively evaluate the likelihood of LBB. Through intensive sensitivity analyses, it is clarified that the LBB is more likely to occur for larger diameter pipe; the performance of leakage detection significantly affects the LBB likelihood; the LBB likelihood increases with plant's aging even conservatively assuming leak detection capability; the R6 method (Category 1, Option 1) for fracture criterion gives very conservative results; and In-Service Inspection (ISI) reduces the increase rate of failure probability than the failure probability itself.

Simplified stable crack growth analyses of welded CT specimens—comparison study of [formula omitted], reference stress and R6 methods

This paper describes some simplified stable crack growth analyses of two kinds of inhomogeneous CT specimens. The one is machined from a submerged are welded plate of a nuclear pressure vessel A533B Class 1 steel, while the other is machined from an electron-beam welded plate of the A533B Class 1 steel and a high strength HT80 steel. In both specimens, initial cracks are placed to be normal to the fusion line. The ratio of yield stresses of the weld metal and the base metal of the A533B Class 1 steel is about 1·15, while that of the HT80 and the A533B Class 1 steels is about 1·4. The generation phase crack growth analyses using the GE EPRI and the reference stress methods are performed, calculating an applied load ( P) and the J-value, while the application phase analyses of analyses using the R6 method are performed to calculate the maximum value of the applied load ( P max ). Finally, some modification procedures of the three simplified estimation schemes are discussed in order to apply them to inhomogeneous material regimes.

Experimental check of existing methods of fracture strength analysis

Tests were carried out with ST-2-type specimens and large-sized specimens of 15Kh2NMFA steel (1930 x 300 x 65 mm in size) with a central through crack and a semielliptic surface crack. It was established that the J{sub R}-curves plotted for the large-sized specimens with a central through crack are located higher than the corresponding curves for the ST-2-type specimens. The fracture strength of the specimens with a central through crack was calculated according to the GE EPRI procedure. It was shown that the results of numerical calculations depend strongly on the technique of approximation of the stress-strain diagram by the Ramberg-Osgood relation and on the accuracy of the evaluation of the term (P/P{sub 0}){sup n+1}. By using the R6 method (version I), one can avoid all these difficulties and obtain a conservative estimate of the values of fracture loads. For the large-sized specimens with a semielliptic surface crack, we used the interpolation criterion and demonstrated the applicability of the method under consideration to the evaluation of fracture loads.

J-integral Analysis Based on Failure Assessment Diagram and Its Application to Evaluation of Crack Growth Due to Cyclic Overload in Carbon Steel Pipes.

R 6 method proposed by U. K. CEGB (Central Electricity Generating Board, present Nuclear Electric plc) was applied to fracture evaluation using a failure assessment diagram (FAD). Since FAD has been developed based on J-integral criterion, J-integral can be inversely estimated using FAD. Because the fatigue crack growth rate is determined by J-integral value, it is suggested that R 6 method can be applied not only to fracture assessment but also to low-cycle fatigue crack growth assessment. Carbon steel pipes with a defect were monotonically and cyclically fractured to confirm the applicability of the crack growth assessment method using FAD. In the monotonic bending tests, J-resistant curve obtained by R6 method agreed with that obtained by η-Factor approach. In the cyclic bending tests, fatigue lives could be successfully estimated by the analysis using R 6 method.

Investigations in fracture mechanics failure concepts with thermomechanically rolled steels

Abstract Thermomechanically rolled steels of quality StE-480 TM and a conventional mild steel (St 52-3) were investigated in instrumented Charpy impact tests, fracture mechanics tests, tension tests with fatigue precracked specimens and wide plate tests with notched specimens (CNT or DENT) up to a maximum load of 4 MN. Several specimens were welded. The results were used for determining various transition temperatures and for checking several actual safety concepts of linear elastic and elastic-plastic fracture mechanics, namely the K I -concept, two methods basing on CTOD (CTOD design curve and PD 6493), and two methods using J -integral (EPRI and R6). Of these methods the new version of the R6 methods seems most promising. J -integral values of wide plates calculated with various finite element programs agreed rather well with one another and with experimental results.

Analysis of two simplified methods (R6 & GE-EPRI) for circumferential crack stability in leak-before-break applications

The Ainsworth method (R6 Option 2) and the GE-EPRI method are compared and analysed. These J-estimation schemes allow us to assess at low cost, crack stability in piping systems, which is an important step in Leak-Before-Break applications. The reliability, flexibility and self-consistency of the two methods are examined by focusing on the effect of geometry, nature of loading and superposition of tension and bending. The GE-EPRI method, based on Finite Element results, is used to check the validity of the hypothesis on which the simplifications in the R6 method for through-wall circumferentially cracked pipes rely. The R6 method appears to be easier to use for the treatment of secondary loads. It is shown that, the Ainsworth Failure Assessment Line, derived in the single load case, is still valid for combined proportional tension and bending loads, provided the appropriate limit load formula is chosen.

Elastic-plastic fracture analysis of carbon steel piping.

The elastic-plastic fracture of carbon steel piping having various pipe diameters and crack angles was analyzed using the latest CEGB R6 approach (R6 method) and ASME Screening Criteria (SC method). Results obtained are as follows: (1) It is necessary to apply the elastic-plastic fracture criterion instead of the plastic collapse criterion by increasing the pipe diameter and the crack angle, (2) For the standard pipes (from 6B to 26B), the plastic collapse criterion can stand within the crack angle of 24°. (3) The SC method gives a more conservative estimation than the R6 method. (4) A simplified elastic-plastic fracture analysis procedure based on the R6 method is proposed, where the unstable fracture moment can be calculated on the basis of the plastic collapse moment and the tabulated reduction factor.

Fracture Mechanics Made Easy

The R6 method of evaluating the integrity of cracked structures was devised to provide a standardised procedure with the following objectives: to provide a method of analysis for failure avoidance; to be user insensitive; to be relatively simple in application; to be well validated. This required the standardisation of treatment material properties, both tensile and toughness data, as well as developing a standard format of analysis. Some of the background to the procedure is described, paying particular attention to these issues, and how the procedure is applied in practice.

Comparative Evaluation of Fracture Mechanics Methodologies as Applied to Offshore Structural Design and Integrity Analyses

A comparative study was performed to evaluate the three most widely used elastic-plastic fracture mechanics methodologies. The three methods are the crack opening displacement (COD) design curve, which is widely used in the offshore industry, the British Central Electricity Generating Board (CEGB) R6 method, and the J-resistance curve method. Analyses of various flawed geometries based on these three methods were performed using consistent material fracture properties. The results of both the COD and R6 methods were compared with those of the J-resistance curve, which is the most rigorous of the three methods. The results of the COD concept, following BSI PD 6493 procedures, appear to be conservative at applied stress levels below 60 percent of the material yield strength and unconservative above this value. However, the results of the R6 method appear to be consistently conservative. The behavior of COD design curve solutions can be improved when the structural geometry and the actual stress-strain relationship are properly considered in the analyses.

Fracture assessment of a PWR pressure vessel

The Second Report of the Marshall Study Group [1] reviewed the design of a pressure vessel to identify those regions which were most sensitive to the expected loading conditions. The design and loading conditions, including the pressure test, were also reviewed. A stress analysis data base of sufficient detail was established to permit a full fracture analysis to be carried out. After reviewing currently available methods for fracture assessment the CEGB R6 method was adopted. Selected normal and upset, emergency and fault transients were considered. Initiation defect sizes for normal and upset transients were generally large. In the beltline and nozzle shell course, for example, the minimum initiating height for an extended line defect was approximately 70 mm. For emergency and fault conditions, providing upper shelf material properties apply, the height to initiate semi-elliptical defects exceeds 25 mm and cracks substantially larger than this will extend by only small amounts in a ductile manner and remain stable. If during the large LOCA upper shelf material properties cannot be maintained semi-elliptic defects 6 to 10 mm high may propagate transversely parallel to the inside surface of the vessel. This may be limited by warm prestressing.