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.     

Approximate evaluation method for ductile fracture analysis of a circumferentially through-wall-cracked pipe subjected to combined bending and tension

To estimate the structural integrity of the Light Water Reactor piping, combined loading consists of a tensile load due to internal pressure and a bending load under seismic conditions should be considered as a basic loading mode. However, theoretical investigation on the methodology to evaluate ductile fracture behavior is not adequate to date. In this study, an approximate evaluation method, ‘LBB.ENGC’, for ductile fracture analysis of a circumferentially through-wall-cracked pipe subjected to combined bending and tension was newly developed. This method can explicitly incorporate the contribution of both tension and bending. The effect of growing crack is also considered in the method. The LBB.ENGC was then applied to the full-scale pipe fracture tests. Based on the comparison with experimental results as well as finite element calculations, it could be ascertained that the LBB.ENGC could well predict ductile fracture behavior under combined loading. The effect of combined loading on ductile fracture was sensitivity-studied using the LBB.ENGC. As a result, it was quantitatively found that the superposition of longitudinal stress reduced the maximum bending load of cracked pipe.     

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.     

Fracture behavior of straight pipe and elbow with local wall thinning

Fracture behavior of pipes with local wall thinning is very important for the integrity of nuclear power plant. Then we studied the fracture behavior of straight pipe and elbow with local wall thinning. For the straight pipe, failure mode, limit load and allowable wall thinning limit based on plastic deformation ability have been studied systematically. Twenty two straight pipe specimens were tested. The failure mode was divided into four types; cracking, local buckling, ovalization and plastic collapse (ovalization+buckling). Maximum load was successfully evaluated using plastic section modulus and modified flow stress, in dependent to failure mode. For the elbow, plastic collapse and low cycle fatigue fracture by reversed loading have been tested using ten specimens. Observed failure modes were ovalization and local buckling under monotonic loading, and were local buckling and cracking under cyclic loading, especially local buckling promoted crack initiation. Test results were compared with ASME design curve and allowable limit of local wall thinning will be discussed.     

Proposal of failure criterion applicable to finite element analysis results for wall-thinned pipes under bending load

In this work, a failure criterion applicable to large strain Finite Element Analysis (FEA) results was proposed in order to predict both the fracture mode (collapse or cracking) and the limit bending load of wall-thinned straight pipes. This work was motivated from the recent experimental results of Tsuji and Meshii (2011); that is, fracture mode is not always collapse, and the fracture mode affects the limit bending load. The key finding in comparing their test results and a detailed large strain FEA results was that the Mises stress distribution at the limit bending load of a flawed cylinder was similar to that of a flawless cylinder; specifically, in case of collapse, the Mises stress exceeded the true yield stress of a material for the whole “volume” of a cylinder with a nominal wall thickness. Based on this finding, a failure criterion applicable to large strain FEA results of wall-thinned straight pipes under a bending load that can predict both fracture mode and limit bending load was proposed and was named the Domain Collapse Criterion (DCC). DCC predicts the limit bending load as the lower value of either the M_c^FEA, which is the load at which the Mises stress exceeds the true yield strength of a straight pipe for the whole “volume” with a nominal wall thickness (fracture mode: collapse), or the M_c^FEAb, which is the load at which the Mises stress in a section of the flaw ligament exceeds the true tensile stress (fracture mode: cracking). The results showed that the DCC could predict the fracture mode appropriately and the experimental limit bending load fundamentally on the conservative side within a maximum 20% difference regardless of the fracture mode. Another advantage of the DCC is that it uses the true yield and true tensile strength as the critical strength of the material and not the ambiguous flow strength.     

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.     

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.     

动态载荷下奥氏体不锈钢管道LBB环向贯穿裂纹稳定性实验及理论分析方法研究

管道环向贯穿裂纹是否稳定是评判管道是否满足破前漏（LBB）设计准则的标准之一,为确保LBB技术安全可靠,对管道环向贯穿裂纹在动态载荷下的稳定性进行实验研究。采用水平冲击机对含环向贯穿裂纹的管道依次进行加载速度为1.22、2、3、4 m/s的高温不带运行压力的冲击实验,以获得各应变率下的实验极限载荷值,并与工程理论分析计算结果进行比较。分析表明:奥氏体不锈钢管道环向贯穿裂纹在动态载荷下的失效模式为塑性失稳;经实验验证,在工程中对承受动态载荷的奥氏体不锈钢管道进行LBB分析时,采用美国核管会标准审查大纲3.6.3破前漏评估程序（SRP 3.6.3）中的极限载荷理论分析方法具有较高的工程安全性,若同时选用准静态下的材料力学性能,则工程安全性更高。      

Tests on large scale LMFR piping Part I: crack resistance properties of through-cracked straight 700 mm nominal diameter pipes tested under bending at ambient temperature and 550°C

Knowing the crack resistance properties of a structure is essential for fracture mechanics safety analyses. Considerable attention has to be given in many cases to the through-wall case, since this is generally believed to be the controlling case with regard to complete pipe failure. Within a cooperative fracture mechanics programme of Electricite de France (EdF), Novatome and Siemens/KWU, bending tests with monotonously increasing load on circumferentially cracked straight pipes of typical liquid metal fast reactor (LMFR) main piping dimensions were performed. In this paper a summary report is given on crack resistance curves based on the crack tip parameters S, J and JM. The data are compared with those of C(T) specimens. The experiments have demonstrated an enormous potential for stable crack extension under global bending which is a typical loading for LMFR piping structures. The results of checking the transferability of laboratory specimen crack growth characteristics to the cracked pipes on the austenitic stainless steel 316 L demonstrate that the fracture mechanics concept for a reliable transfer of crack resistance data from small specimen geometries to large structures needs further qualification for high toughness materials.     

Plastic limit load of welded piping branch junctions under internal pressure

In this work, a simplified estimation formula for plastic limit load of defect-free welded piping branch junctions subjected to the internal pressure is established. The relationship takes into account the effect of the internal forces between the run and branch pipe around the intersecting line. The formula is built on the following process: First, an equation between the limit load and internal force of branch pipe surrounding the intersection is derived on the basis of the force equilibrium condition. Secondly, regarding this internal force as an external force acting on the intersection of run pipe, the approximate solutions of internal force around the intersection on run pipe, under the plastic limit load, are given. Finally, referring to the von-Mises yield criterion, the plastic limit load of two intersecting cylindrical shells is then obtained. The formula’s suitability and feasibility applied in engineering practice is also validated with finite element analysis and experimental results in the paper.     

An approximative solution for limit load of piping branch junctions with circumferential crack and finite element validation

This paper is concerned with the prediction of limit load of the piping branch junctions with circumferential crack under internal pressure. Recently, we have developed a new approach for predicting the limit load of two-cylinder intersection structures with diameter ratio larger than 0.5, which has been successfully applied to defect free cases under various loading conditions. In the present work, we consider the extension of the approach to cover cracked piping branch junctions. On the basis of stress analysis in the vicinity of intersection line, a closed form of limit load solution for piping branch junctions with circumferential crack was developed. Then, 36 finite element (FE) models of piping branch junction with various dimensions of structure and crack were analyzed by using nonlinear finite element software. The limit loads from FE analysis and the proposed solution are compared with each other. Overall good agreement between the estimated solutions and the FE results provides confidence in the use of the proposed formulae for defect assessment of piping branch junctions in practice.     

Determination of the dynamic fracture toughness using a new stress pulse loading method

This paper presents a method for the determination of the dynamic fracture toughness K_Id of metallic materials at loading rates K_I of about . The method is derived from the known split Hopkinson pressure bar technique and uses a well-defined stress pulse for the loading of a fatigue precracked specimen. The interpretation of the experimental data is strictly based on a numerical analysis of the specimen under the given dynamic loading conditions. It is shown, that a conventional quasi-static approach would yield incorrect fracture toughness values. The results for some steels confirm, that the fracture toughness decreases with increasing loading rate. Therefore, in some sense the fracture toughness versus temperature curve determined with the presented stress pulse method can be regarded as lower bound curve.     

Numerical modeling of crack propagation and shielding effects in a striping network

Thermal fatigue cracking is observed in some components of nuclear power plants. The residual lifetime prediction of cracked components is necessary to determine maintenance programs. An automatic procedure is developed for 2D modeling of multiple crack propagation within the finite element software Code_Aster^® to evaluate the crack growth rate and shielding effects in a multicracked structure in thermomechanical fatigue. It consists in a global remeshing method to model crack growth and includes a propagation strategy based on the crack length increment. A set of parametric studies is analyzed for a cracked pipe to evaluate the influence of geometrical and loading parameters on the residual lifetime of the crack network.     

含环向贯穿裂纹管道断裂力学工程方法影响函数的计算研究

为拓宽美国电力研究所(EPRI)工程方法的应用范围,本文通过一系列三维弹性、弹塑性断裂力学有限元分析,计算了含裂纹管道的裂纹张开位移(COD);基于有限元COD结果研究了EPRI方法中的关键影响甬数h2,并详细阐述了拉-弯组合载荷情况下h2的计算方法.为了验证该方法,将计算的h2值与EPRI已有的h2值进行比较;将基于计算的h2值所求得的COD结果与管道裂纹评定程序(PICEP)中工程实例的COD结果进行比较.结果表明,计算的h2值、COD结果均与参考值吻合良好,证明了本文h2值计算方法的正确性.     

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.     

Fracture assessment of shallow-flaw cruciform beams tested under uniaxial and biaxial loading conditions

A technology to determine shallow-flaw fracture toughness of reactor pressure vessel (RPV) steels is being developed for application to the safety assessment of RPVs containing postulated shallow surface flaws. Matrices of cruciform beam tests were developed to investigate and quantify the effects of temperature, biaxial loading, and specimen size on fracture initiation toughness of two-dimensional (constant depth), shallow, surface flaws. The cruciform beam specimens were developed at Oak Ridge National Laboratory (ORNL) to introduce a far-field, out-of-plane biaxial stress component in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock or pressure–temperature loading of an RPV. Tests were conducted under biaxial load ratios ranging from uniaxial to equibiaxial. These tests demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for an RPV material. The cruciform fracture toughness data were used to evaluate fracture methodologies for predicting the observed effects of biaxial loading on shallow-flaw fracture toughness. Initial emphasis was placed on assessment of stress-based methodologies, namely, the J–Q formulation, the Dodds–Anderson toughness scaling model, and the Weibull approach. Applications of these methodologies based on the hydrostatic stress fracture criterion indicated an effect of loading-biaxiality on fracture toughness; the conventional maximum principal stress criterion indicated no effect. A three-parameter Weibull model based on the hydrostatic stress criterion is shown to correlate with the experimentally observed biaxial effect on cleavage fracture toughness by providing a scaling mechanism between uniaxial and biaxial loading states.     

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.     

Stability of circumferential through-cracks in ductile pipes

An analysis of tearing instability is presented for a pipe with a circumferential through-crack. Loading conditions consisting of a large external axial force and a bending moment, together with an internal pressure, have been considered. The mechanical behavior of the material is assumed to be elastic perfectly-plastic. Instability has been studied under fixed grip conditions, following the application of loads which correspond to the plastic limit load of the cracked cross-section. The values of the applied tearing modulus have been expressed in terms of geometrical factors such as pipe length, pipe radius, and the length of the crack. Numerical examples have been calculated to obtain an estimate of the critical value of the length-to-radius ratio, for the case that the tearing modulus of the material is known.     

Reference stress based fracture mechanics analysis for circumferential through-wall cracked pipes: experimental validation

This paper presents experimental validation of the reference stress based J estimates for circumferential through-wall cracked (TWC) pipes, recently proposed by the authors. Using the pipe test data for circumferential TWC pipes given in the Pipe Fracture Encyclopedia [Pipe Fracture Test Data, vol. 3, Battelle, 1997], the predicted fracture initiation and instability loads according to the proposed reference stress method are compared with experimental ones as well as predictions according to the reference stress method embedded in R6. The results show that both the R6 method and the proposed method give conservative estimates of initiation and maximum moments for circumferential TWC pipes, compared to experimental data. For longer cracks, the proposed method reduces the conservatism embedded in the estimated J according to the R6 method, and the resulting predictions are less conservative, compared to those from the R6 method. For shorter cracks, on the other hand, the proposed method reduces possible non-conservatism embedded in estimated J according to the R6 method, and the resulting predictions are slightly more conservative.