Low cycle fatigue and ductile fracture for Japanese carbon steel piping under dynamic loadings

Dynamic fracture behavior of circumferentially cracked pipe is important to evaluate the structural integrity of nuclear piping from the viewpoint of the LBB concept under seismic conditions. Fracture tests have been conducted for Japanese carbon steel (STS410) circumferentially through-wall cracked pipes that are subjected to monotonic or cyclic bending loads at room temperature. In the monotonic-loading tests, the maximum load to failure increases slightly with increasing loading rate. The failure cycles can be expressed simply by ratio of the load amplitude to the plastic collapse load. Fracture analysis has been also conducted to model the pipe tests. A new equation for calculating ΔJ for a circumferentially through-wall cracked pipe subjected to bending has been proposed. The failure cycles under cyclic loads are satisfactorily evaluated using an elastic-plastic fracture mechanics parameter ΔJ.     

Development of a database of pipe fracture experiments

Over the last 35 years, researchers worldwide have conducted hundreds—if not thousands—of pipe fracture experiments. In the early years, researchers focused their attention on studying the failure pressure and crack propagation behavior of axially cracked pipe loaded by internal pressure. The earliest work was sponsored by the oil and gas industry and, as such, involved relatively thin-walled, low toughness carbon steel pipes. This work was eventually followed up by efforts in the USA and Germany on nuclear piping with axial cracks. In recent years, attention has turned to understanding the behavior of circumferentially cracked nuclear piping subjected to both pressure and bending loads. The loading histories for these experiments range from the relatively simple case of quasi-static, monotonic displacement control to the more complex cases of dynamic cyclic loading, and pipe system experiments. In this paper, two of the leaders in this research, i.e. Battelle in the USA and MPA Stuttgart in Germany, have collaborated to develop a database of pipe fracture experiments. The database includes data from other organizations as well as the data from Battelle and MPA. In addition, as part of this paper, an example of how the database was used to assess the failure pressure of axially cracked pipe is given.     

含环向贯穿裂纹弯管的J积分研究

弯管是核级管道的重要组成部分,同时也是比较容易出现裂纹的部位,所以有必要开展含裂纹弯管的断裂力学分析研究,以确保核级管道的结构完整性.本文采用ABAQUS软件,应用三维弹塑性断裂力学有限元方法对含环向贯穿裂纹的弯管进行了研究,得到了含环向贯穿裂纹弯管的J积分的数值分析结果.计算结果表明,弯曲半径对J积分的影响与裂纹的位置无关,与裂纹的大小关系密切.弯曲半径对含小裂纹弯管的J积分的影响并不明显,对含较大裂纹弯管的J积分而言,J积分随着弯曲半径比Rb/R增大而减小.在末端转角相同的情况下,壁厚比R/t与J积分近似成线性关系,即可以通过线性插值的方法进行计算.     

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson-Tvergaard-Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness (J_SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J_SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.     

Short circumferential through-wall cracked pipes subjected to stretch-bending load

The methods for assessment of elastic–plastic fracture behaviour of cracked components include the net section plastic collapse concept, the J-integral approach, and the two-parameter R-6 failure assessment diagram, Revision 3. These failure assessment methods are usually used to obtain fracture behaviour prediction with a reasonable degree of accuracy without carrying out complicated full-length numerical fracture analysis. In the current work, fracture experiments on stainless steel pipes with short circumferential through-wall cracks under stretch-bending load were conducted. Stretch-bending load refers to the loading situation where axial load is generated that is proportional or related to the applied bending load. The J-integral values derived from the experimental load-point load–displacement data under stretch-bending and pure bending conditions are compared to investigate the effect of axial load on the J–resistance curves. The results show clear dependence of crack resistance force on axial load for short circumferential cracks. Crack resistance force decreased noticeably for increased stretch-bending loading compared to pure bending loading.     

Leak-Before-Break analysis for Pickering ‘A’ Unit 1 and Unit 4 large diameter main steam line pipes

This paper presents a Leak-Before-Break (LBB) analysis of large diameter main steam line pipes (i.e. NPS 28″ and 30″) running from reactor building to main steam balance header in Pickering nuclear plant Unit 1 and Unit 4. Recent development in LBB technology summarized in U.S. Nuclear Regular Commission report NUREG/CR-6765 was adopted. Based on the tiered approach of LBB philosophy, this LBB analysis belongs to level 2 or level 3 LBB analysis. Detailed fracture tolerance analyses and leakage rate calculations were performed. EPFM (elastic plastic fracture mechanics) theory of J-integral, resistance curve versus ductile crack extension was adopted in carrying out all fracture tolerance analyses. Through-wall cracks in axial and circumferential directions on both straight pipes and elbows were postulated and analyzed. The loads applied on the postulated cracked pipes were obtained from detailed piping stress analysis under deadweight load, design pressure, thermal expansion, seismic design based earthquake (DBE) and thrust load due to the opening of relief valves. J-resistance data were derived from the lowest fracture toughness testing data obtained from Ontario Power Generation's PHT (primary heat transport) LBB material testing programs. A margin of 2 on crack size was chosen in establishing maximum allowable crack sizes. Leakage rates were calculated using SQUIRT Windows Version 1.1 program. The fluid inside the main steam line pipes was assumed single phase steam at 100% quality. One tenth of the calculated leakage rates was proposed as the requirement for minimum leakage detection capability. The paper concludes that the absence of through-wall crack larger than 91.16 mm in length should be maintained in order to ensure the structural integrity of large diameter main steam line pipes. In lieu of this crack size requirement, a reliable leakage detection capability which could quantify mass steam leakage rate of 0.01678 kg per second, or volume leakage rate of 1.01 l/min, should be in place. If both of the above two requirements are met, the Leak-Before-Break of these large diameter main steam line pipes is warranted.     

Fracture mechanics evaluation of small diameter piping considering the latest experimental results

The results obtained from investigations carried out on austenitic piping of small nominal diameter (DN80 and DN50) are introduced and discussed together with their assessment using fracture mechanics methods. Essential results are summarised as following. The pipes with flaws (fatigue crack) down to a depth to a_max/t=0.51 (DN80) as well as a_max/t=0.62 (DN50) and a circumferential extension of results 2α=120° reached bending angles up to 26°. The ASME collapse load (test collapse load) was exceeded considerably and the experimental maximum load could not be reached. Failure due to a leakage or rupture did not occur in any test. The maximum crack extension was 0.69 mm (DN80, a_max/t=0.51) resp. 0.3 mm (DN50, a_max/t=0.62). The experimental maximum load can approximately be assessed by the limit analysis. The fracture mechanics approximation methods GE/EPRI and LBB/NRC calculated a/t=0.4 and 2α=120° initiation loads above the experimental maximum load for pipes containing flaws. These results confirmed the procedures for the proof of integrity of small diameter piping by updating information on load, deformation and failure behaviour of austenitic piping damaged with circumferential flaws. Using these results may formulate a final safety concept for the proof of integrity of small diameter piping by completing the current concepts.     

Evaluation of ductile tearing in cracked pipes and elbows under bending

A major project was launched in France to develop leak-before-break methods applicable to the primary circuit of pressurized water reactors. An important aspect is to be able to calculate the resistance strength of piping components (tube or elbow) that contain a through-wall circumferential crack. This paper presents details of the development of an experimental method that can be used to define J-R curve, using experiments performed on cracked tubes and elbows at room temperature. Applications for components made from ferritic steel and austenitic steels are described. It is concluded that the procedure could be effective for characterizing the real behaviour of cracked pipes or elbows.     

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J_IC, dJ/da, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.     

Ductile crack growth simulation from near crack tip dissipated energy

A method to calculate ductile tearing in both small scale fracture mechanics specimens and cracked components is presented. This method is based on an estimation of the dissipated energy calculated near the crack tip. Firstly, the method is presented. It is shown that a characteristic parameter G_fr can be obtained, relevant to the dissipated energy in the fracture process. The application of the method to the calculation of side grooved crack tip (CT) specimens of different sizes is examined. The value of G_fr is identified by comparing the calculated and experimental load line displacement versus crack extension curve for the smallest CT specimen. With this identified value, it is possible to calculate the global behaviour of the largest specimen. The method is then applied to the calculation of a pipe containing a through-wall thickness crack subjected to a bending moment. This pipe is made of the same material as the CT specimens. It is shown that it is possible to simulate the global behaviour of the structure including the prediction of up to 90-mm crack extension. Local terms such as the equivalent stress or the crack tip opening angle are found to be constant during the crack extension process. This supports the view that G_fr controls the fields in the vicinity near the crack tip.     

Application of fracture mechanics methods in safety analysis of piping components in subcreep and creep behavior

A survey and review program for the application of fracture mechanics methods in elevated temperature design analysis and safety evaluation was initiated in December 1976. The first report [1] surveyed and assembled the material for a critical review of the theories of fracture and the application of fracture mechanics methods to life prediction and safety analysis of piping components. The second report [2] provided the basic concepts and a review of the problem areas associated with the development of analytical and experimental programs for a systematic evaluation and comparison of the currently available fracture mechanics theories. The basis for such an evaluation was described in terms of a series of benchmark problems which accurately specify conditions of geometry, loading and environment characteristic of large diameter piping systems in nuclear service.The objective of this third report is to establish a data base and detail the additional analytical techniques needed to confirm the validity of existing analytical methods and improve the state of the art in current problematic areas effecting the interpretation and extension of safety evaluation methods. The need for such a program in the elevated temperature field has been demonstrated by a number of independent surveys on various safety aspects of LMFBR related structural analysis methods and matetials problems. The results of this program, however, will be applicable not only to reactor plants operating at elevated temperatures, but will also lead to improvements of light water reactor evaluation methods for operating and accident conditions.The current state of elevated temperature reactor design technology is embodied in the standards and codes which provide guidance and minimum requirements for systematic design and evaluation procedures. These, however, do not necessarily provide specific absolute values which, if satisfied in the course of design, will guarantee thirty to forty years of uninterrupted life. There are numerous assumptions and approximations embodied in these standards concerning materials behavior, damage mechanisms, and failure modes at elevated temperature. There are also numerous areas of uncertainty and conflicting opinion in the interpretation of the existing test data and in the analysis and evaluation methods. Furthermore, the standards and codes leave some areas to the judgement of the designer, some of which require explicit justifications, but no standards or rules are provided.The overall safety therefore lies, at the present time, in the combination of rigorous enforcement of current standards, judicious application of experience with high temperature equipment even if not in nuclear service, and the surveillance of actual operating conditions. In the past, one criterion proposed for elevated temperature design has been that the time for crack initiation should exceed the design life. However, due to the complexities of the piping structures and the nature of the stress history during service, the evaluation of initiation times is difficult and often leads to uneconomical designs. In addition defects may exist in the component before it enters service. Hence, the knowledge of the growth rates of cracks and the residual strength of the components containing cracks is important in a realistic design evaluation. For more brittle materials and lower temperature applications where plasticity is restricted, linear elastic fracture mechanics methods have been developed. For more ductile materials where the plastic zones near the cracks are larger, linear fracture mechanics methods are not directly applicable, but in these nonelastic cases the opening displacement and J integral methods of assessment have been proposed. In the complex situation encountered in nuclear power plant design, the analysis must also account for cyclic thermal strains, time dependent creep, and the effect of harmful environments which are not explicitly treated in the above-mentioned methods. In this report an in-depth review is presented in sufficient detail to illustrate the degree of agreement between the theoretical and empirical methods available in the literature and indicate the scope of the additional analyses and experimental work needed for the development of reliable safety evaluation methodology.For pure cylindrical bending, cracks perpendicular to the load start to grow when reaches a critical value which is generally larger than the corresponding critical uniaxial tension value. There appears to be a thickness effect in the bending case which is probably due to interference from the compressive sides of the crack.For a circular plate with lateral pressure and small lateral displacements, results agree with the bending data when using the nominal bending stress . For larger displacements when bulging occurs, the results agree with the tensile data when the nominal tensile stress is used.For curves surfaces, such as a cylinder under internal pressure, the data agree with the expression developed by Folias both for axial cracks under hoop stress σ and for circumferential cracks under axial stress σ Generally, the expressions were accurate up to , showing a tendency to be lower than the experimental data at higher values of the parameter. The parameter is a promising one.To study the influence of cracks at different angles to the applied load, analysis and data are available including the stress component parallel to the crack in the stress field around a crack tip. This, together with the concept of a critical circumferential stress at a critical distance (α = 0.1) ahead of the crack provides improved correlation with fracture predictions for both the angle of fracture and the critical stress intensity factor for the angled cracks in flat plates.For a hollow cylinder under torsion with angled cracks, the best correlation was given by the same analysis although the results were not as conclusive as for the flat plate. From elastic theory useful curves for the variation of K₁, K₂, and K₃ around the border of an elliptically shaped crack are available.In a plane stress fracture the addition of a biaxial stress produces an increase in the apparent fracture toughness compared with the uniaxial case. However, there is as yet no evidence to show that there would be the same increase in a plane strain situation. Hence, in the absence of biaxial information the uniaxial fracture data may be the most conservative for flat plates. However, for shells there will also be a curvature effect.In an analogous manner, fatigue crack propagation rates appear to be less rapid under biaxial stresses than under uniaxial stress. However, this shift is not great and generallly will be masked by other effects such as environment and temperature service situations.The analysis of cracks in weldments with residual stress effects are also available. In the case of a crack in a weld the estimated residual stress distribution agreed reasonably well with some experimental data for elastic conditions. Results indicate that there can be a tensile stress intensity factor even when the original residual stress distribution has changed to compressive. A point to remember is that residual stresses near welds can be beyond yield.An analysis based on Lagrangean mechanics is useful for indicating the different effects of liquids and gases as pressurizing media in hollow pipes. The results show that whereas gases maintain their pressure as a crack begins to propagate, the pressure in the liquid can quickly decrease so that subsequent catastrophic failure is less likely even in large diameter piping.     

Pipe fracture safety analysis using limit load and J-integral techniques

J-integral fracture toughness tests were performed on full scale pipe specimens to assess the fracture safety performance of two reactor piping alloys. The two alloys investigated were ASTM A106 Grade B carbon steel and circumferentially welded Type 304 stainless steel.The full scale pipe fracture tests were performed on 1.2 m long, circumferentially cracked pipes loaded in four-point bending on a variably compliant test bed. Results of the experiments were analyzed using the limit load approach currently being considered for inclusion in Section XI of the ASME Code. The results were also evaluated using two tearing instability approaches. One approach assumed elastic-perfectly plastic material behavior and the other accounted for material hardening by requiring actual load and displacement data.The limit load analysis provided a good prediction of the maximum load carrying capacity of the pipe specimens in most cases. The results were especially good for the ASTM A106 steel pipes when the materials property data was used to calculate the flow stress. The J-integral tearing instability analysis was shown to accurately describe the ductile tearing instability behavior of the ASTM A106 steel pipe providing material hardening was taken into account.     

Fatigue studies on carbon steel piping materials and components: Indian PHWRs

This paper describes the results of fatigue studies on carbon steel piping materials and components of Indian Pressurized Heavy Water Reactors (PHWRs). The piping components include pipes and elbows, of outer diameter 219 mm, 324 mm and 406 mm, made of carbon steel (SA333 Gr.6 grade) material. Tests on actual pipes and elbows with part through notch were carried out to study the behaviour of crack growth under cyclic loading for different pipe sizes, notch aspect ratios, stress ratios, etc. During the tests, numbers of cycles for crack initiation from blunt notch were recorded with an accuracy of 0.1 mm. In conjunction with component tests, the experimental studies were also conducted on standard specimens to understand the effect of different variables such as size (thickness), type of specimen and components (elbow and pipe), welding, stress ratio, notch orientation on fatigue crack growth rate. The fatigue crack growth curve (da/dN versus ΔK) obtained from three-point bend specimen and pipe was compared with that given in ASME Section XI. The comparison shows that da/dN versus ΔK curves obtained from the specimen and pipe tests are nearly same. The analytical predictions for crack initiation and crack growth for the tested components were compared with experimental results. Such comparisons validate the modeling procedure for crack initiation and growth.     

An extension of the application of elastic-plastic assessment to cracked pipework systems

Some of the current methods for assessing cracked structures made of high toughness materials come under the scope of elastic-plastic fracture mechanics (EPFM). However, these methods only evaluate flawed sections and do not consider their inclusion into framed structures. Stress distributions in redundant structures vary with the stiffness of their elements. As the stiffness of cracked elements changes with crack length, the structure's stress distribution is modified by crack extension. This paper presents a method for assessing high toughness redundant cracked piping systems taking into account the interaction between stress distribution and crack extension. The methodology is illustrated by solving some examples using the proposed method and comparing the results with those that would have been obtained using conventional practices.     

Fracture mechanics analysis on the initiation and propagation of circumferential and longitudinal cracks in straight pipes and pipe bends

The safety potential against pipe fracture of a nuclear piping system is quantified using as an example the fuel circulating system of the THTR 300 MWe. A comparison of the size of cracks expected to occur during operation in the most unfavourable case with the critical crack sizes from the fracture mechanics aspect is used as a criterium for evaluation.A comprehensive test program was carried out to investigate the dependence of longitudinal and transversal crack sizes upon load (bending and internal pressure), pressure medium and temperature. The theoretical methods for predicting the critical crack sizes were checked by the test results.The conclusion is that pipe rupture does not need to be considered under the conditions investigated.     

损伤力学在核级管道LBB分析中的应用

基于Gurson损伤本构模型，开展了损伤力学在核级管道破前泄漏(1eak before break)分析中的应用研究对含环向贯穿裂纹直管在纯弯载荷作用下进行了三维弹塑性损伤．断裂力学有限元计算．并与弹塑性断裂力学有限元计算结果进行了比较分析。     

Fracture mechanics evaluation of the structural material for fast breeder reactors

Results of fracture mechanics investigations on austenitic steels used for LMFBRs (Liquid Metal Fast Breeder Reactors) are presented. A summary of reported tests on straight piping and elbows with through wall flaws is given which agree well with predictions made by using a plastic instability model. Crack growth experiments and calculations indicate that initial flaws will not extend significantly during service. Even if considerable crack growth is postulated cracks will penetrate the piping wall with a high safety margin to unstable crack configurations. Theoretical investigations of flawed structures under high strains show that the effect of crack size can be discussed similarly to the elastic range. The information demonstrate that with respect to the design requirements and operating conditions of LMFBRs a sudden rupture of the piping can be excluded. The integrity of the coolant boundary is given also in case of initial flaws.     

Probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws

A probabilistic model was developed for predicting elastic-plastic fracture response and reliability of circumferentially cracked pipes with finite-length, constant-depth, internal surface cracks subject to remote bending loads. It involves engineering estimation of energy release rate, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory. The underlying J-estimation model is based on the deformation theory of plasticity, a constitutive law characterized by power law model for stress-strain curve, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. New analytical equations were developed to predict J-integral and are shown to be fairly accurate when compared with generally more accurate elastic-plastic finite-element results. Using this J-estimation method, fast probability integrators and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the probability of crack initiation and net-section collapse as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology. The results show that probabilistic analysis based on net-section collapse (without any margin) may significantly overpredict the reliability of surface-cracked pipes.     

Stable crack growth of axial flaws in pressure vessels

The ductile crack growth of axial through and part-through cracks in a vessel under internal pressure has been studied experimentally to contribute to the fundamental problem whether or not and under which conditions resistance curves obtained from specimens can be transferred to large scale components. The experiments and numerical analyses are part of a research program on fracture mechanics failure concepts for the safety assessment of nuclear components.Whereas only an averaged crack extension is determined in specimen tests, the local propagation of cracks may be of main importance for surface cracks in vessels and pipes. In the present experiments, the surface cracks revealed the well known canoe shape, i.e. a larger crack extension has occurred in the axial direction than in the wall thickness direction. Two of these tests have been analysed by finite element calculations to obtain the variation of the J-integral along the crack front and the stress and strain state in the vicinity of the crack. The local crack resistance appeared to depend on the local stress state. To Predict ductile crack extension correctly, J_R-curves have to account for the varying triaxiality of the stress state along the crack front.