Characterization of plastic collapse load determination in circumferentially through-wall cracked elbows

The solutions of cracked elbow are shown to be excessively conservative and on occasion, non-applicable to the cases for which they are intended. The objective of the work described in this paper is to use the 3D non-linear finite element method (FEM) backed up with experimental results to determine the collapse limit load. Non-linear finite element analyses were performed considering both material and geometrical non-linearity using the advanced fracture analysis code WARP3D. Various alternative methods are used to determine plastic collapse loads based on the FEM calculated load–displacement curves. The predicted collapse loads are compared to collapse loads determined by available solutions and finally these are compared to experimental results. The work can be considered as the source of the benchmark data that helped to shape the engineering treatment of piping elbows in design codes.     

Studies on the behavior of part-through circumferential crack at intrados in elbows under in-plane bending moment

This paper presents the behavior of part-through circumferential crack at intrados in elbows under in-plane bending moment. This is based on detailed non-linear (both material and geometric) finite element analysis performed on various sizes of elbows (generally used in piping industry), having different crack sizes. It is observed that some part of the crack always opens and some part gets closed irrespective of the mode of applied bending moment (opening/closing). The fraction of the crack that opens basically decides the weakening effect of the cracked elbow. It is observed that there is a threshold value of crack length and crack depth, before which no crack opening is observed under opening mode. Also as elbow becomes thinner, the threshold value of above two parameters increases. Quite interestingly, the part of crack which closes in opening mode opens under closing mode. The above mentioned study on the behavior of crack will be useful for fracture studies and limit load estimation especially when leak before break concept is to be employed.     

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.     

Elastic–plastic analysis of an elbow with a through-wall axial crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic–plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for R_m/t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, ‘n’ varied for 2, 3, 5, 7 and 10.     

Assessment of integrity of components in piping of 500 MWe PHWR: using R-6 method

The primary heat transport system of 500 MWe Indian PHWR comprises of straight pipes, elbows and headers. A study was conducted to qualify piping system for leak before break. R-6 method was used to assess integrity of system for leakage size crack (LSC), the margins on crack initiation load and unstable crack growth loads. Option 2 (material specific failure assessment diagram), Category 3 (ductile tearing) analysis was used for straight pipes, elbows and header. In order to enhance the confidence in the analytical results, detailed sensitivity analysis was also performed. For sensitivity analysis, variation in material properties, LSC was considered. The effect of variation in temperature on material properties was also considered. Tensile and fracture properties used for base and weld material data were generated from pipe material obtained from 220 MWe Nuclear Power Plant, under construction.     

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.     

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.     

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.     

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.     

Ductile fracture models and their potential in local approach of fracture

Since the pioneering studies conducted by McClintock, Rice and Tracey on the growth of cavities, many studies have covered modelling of ductile fracture; a non-exhaustive list is given of these studies. In the local approach of fracture, the models are used at the tip of cracks, and in the present state, only relatively simple models can be used to solve fracture problems in a complete manner, from material characterization to the analysis of cracked structures.The paper presents two types of models based on a critical ratio of cavity growth or on continuum damage mechanics. In the framework of the local approach of fracture, their possibilities are presented with constant references to experimental validation studies. This allows conclusions to be drawn regarding the effectiveness of the methods proposed and their undeniable contribution to fracture mechanics.     

Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.     

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.     

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.     

Modeling of reinforced concrete by the non-local microplane model

This paper reviews some recent results of non-local finite element fracture analysis of concrete structures using a non-local microplane material model. The microplane model and recently introduced non-local microcrack interaction approach are described briefly. It is demonstrated that the model used in smeared fracture finite element analysis does not exhibit mesh sensitivity. Results of a three-dimensional numerical study of fastening elements pulled out from cracked and uncracked reinforced concrete plates are shown. The capability of the model for correct prediction of the structural size effect is supported by one numerical example. In all examples numerical results are compared with experimental evidence and reasonably good agreement is observed.     

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.     

Probabilistic analysis of core shroud cracks

Traditional limit load analysis and fracture mechanics analysis have been applied to evaluate the integrity of the degraded nuclear power plant components. Although these methodologies are generally accepted by the regulatory authorities in the nuclear industry, conservatism introduced by the uncertainties of inspection, material property, crack geometry, applied loading, neutron environment, etc. is recognized to have great impact on the evaluation accuracy. A probabilistic analysis may overcome this shortcoming and reveal some additional insight to the problem. The purpose of the present study is to apply probabilistic methods to analyze the degraded core shroud, and to predict the quantitative risk of the cracked shroud. In the analysis, the loading condition, crack growth rate, material properties and existing defects are all considered random. A sample analytical result shows that, based on some previously observed data and under certain assumptions, the crack-through probability of the studied core shroud is in the order of 10⁻⁷ after 13 cycles of operation. The probability will increase considerably through operation cycles or operation years if no repair action is taken.     

The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint

An extensive investigation has been carried out on the sensitivity parameters determination describing the fracture behaviour of the body with a crack with respect to the character change of the true stress–strain curve with the dominant region of Lueders deformation. This paper presents the consideration on the change judgement of the J-integral and the constraint as the base parameters of two-parameter fracture mechanics. The Weibull stress model for cleavage fracture originally proposed by Beremin group requires calibration of two micromechanics parameters (m, σ_u). The Weibull stress σ_w seems to be a parameter for the prediction of cleavage failure of cracked bodies and the study is focused on the assessment of the effects of constraint loss on the cleavage fracture toughness (J_c). To quantify the effects of the constraint variation on the cleavage fracture toughness the form of the toughness scaling model based on the Weibull stress σ_w is investigated. Local material parameters have been calculated from Beremin approach and the calibration is performed on various approaches. Methods are based on the weakest link assumption and the incremental fracture probability, which depends not only on the maximum principal stress, but also on the equivalent plastic strain. The fracture resistance has been assessed using data from static tests of three point bend specimens.     

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.