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.     

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.     

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.     

Correlation of in-plane bending test and FEA results for thin-walled elbows

The objective of this study is to validate a finite element analysis (FEA) simulation methodology to predict the global behavior of thin-walled elbows subjected to in-plane bending. Two in-plane closing mode bending tests and one in-plane opening mode bending test were conducted on 2″ schedule 10 elbows, and a nonlinear FEA procedure was used to simulate the tests. A detailed FEA study was carried out to determine the relative importance of weld size and location, measured wall thicknesses, and original cross-section dimensions on the reconciliation results. When the weld bead was included in the analysis, the reconciliation results for load–displacement behavior and some of the strain measurements were excellent. For those cases in which the strain measurements reconciliations were not so good, a possible explanation is provided.     

Bending failure by flattening of circumferentially cracked pipes

The bending failure by cross-section flattening of circumferentially cracked pipes has been studied. Flattening may be described by four plastic hinges and is caused by the vertical component of the axially directed bending stresses. An analytical expression for the failure moment of a material subject to strain hardening is given.     

Ductile fracture behavior of circumferentially cracked type 304 stainless steel piping under bending load

A ductile pipe fracture test program has been conducted in Japan Atomic Energy Research Institute (JAERI) to investigate the ductile fracture behavior of circumferentially cracked pipes and to demonstrate the validity of the leak before break concept in LWR pipings.In the paper are described the scope of the pipe test program and current test results for 6-inch diameter type 304 stainless steel pipes. Test pipes with a through-wall or a part-through crack in the circumferential direction were bent under low or high compliance condition, and stable or unstable pipe fracture behavior was investigated. J based tearing instability criterion and the net section collapse criterion are compared with the pipe test results, and the validity of these fracture criteria is discussed. Furthermore, geometries of acceptable flaws in pipes are evaluated considering the leak before break condition.     

Safety assessment of pipes with multiple local wall thinning defects under pressure and bending moment

The safety assessment of pipes with local wall thinning defects is highly important in engineering. Most attention has been paid on the safety assessment of pipe with single local wall thinning defect, while the studies about multiple local wall thinning defects are not nearly enough. However, the interaction of multiple local wall thinning defects in some conditions is great, and may have a great impact on the safety assessment. In the present standard API 579/ASME FFS, the safety assessment of pipes with multiple local wall thinning defects is given, while as well as the influence of load condition, the influences of arrangement and relative depth of defects are ignored, which may influence the safety assessment considerably. In this paper, the influence of the interaction between multiple local wall thinning defects on the remaining strength of pipes at different arrangements and depths of defects under different load conditions (pressure, tension-bending moment and compression-bending moment) are studied. A quantified index is defined to describe the interaction between defects quantitatively. For different arrangements and relative depths of defects, based on a limit value 0.05 of the quantified index of the interaction between defects, a relatively systematic safety assessment of pipes with multiple local wall thinning defects under different load conditions has been proposed.     

Post-collapse cross-sectional flattening of thick pipes in plastic bending

Post-collapse cross-sectional flattening of a thick pipe at the centre of a plastic hinge formed during excessive bending due to unrestrained pipe whip is analysed with an aim to ascertain the extent of flow choking and consequent reduction of blowdown force. Based on the experimentally observed similarity between the plastic collapse mode of the critical pipe section during bending and plastic deformation of a ring under lateral compression, the effect of excessive bending on pipe section flattening is simulated using some well known analytical models for section collapse. A theoretical relationship between post-collapse bend curvature and section flattening is proposed for relatively thick pipes made of strain hardening material. The calculations made using the above relationship are found to compare well with those observed experimentally.     

Evaluation of throughwall crack pipes under displacement controlled loading

Tearing modulus solutions are developed for flawed throughwall pipes subjected to displacement controlled loading. Two cases of loading were considered: (1) a displacement controlled bending loading, and (2) a displacement controlled axial tension loading. A revised version of the EPRI J-integral estimation scheme is used in the development of the solutions. These solutions can be used for the entire range of elastic-plastic loading, from linear elastic, contained yielding, to large scale yielding of the crack section. Experimental data from pipes in bending were used to assess the accuracy of the compliant loading solutions. The evaluations were performed using elastic plastic J-integral (J) and tearing modulus (T) analysis methods. These solutions are shown to have good accuracy when used to predict the experimental results. The methodology and procedure can also be applied to part-throughwall cracks. These solutions have application to the leak before break fracture mechanics analyses.     

Effects of local wall thinning on net-section limit loads for pipes under combined pressure and bending

This paper provides plastic limit loads of pipes with local wall thinning under combined pressure and bending, by quantifying effects of the axial extent and the shape of local wall thinning. The effect of the axial extent on plastic limit loads is not so significant for bending but could be more significant for internal pressure. It is also found that the effect of the shape of local wall thinning on limit loads could be significant. Thus idealization of local wall thinning as a rectangular shape rather than a circular one could lead to significantly conservative estimates of maximum loads, which is also supported by comparison with published full-scale pipe test data.     

Proposal of limit moment equation applicable to planar/non-planar flaw in wall thinned pipes under bending

In this paper, a limit bending moment equation applicable to all types of planar and non-planar flaws in wall-thinned straight pipes under bending was proposed. A system to rationally classify the planar/non-planar flaws in wall-thinned pipes was suggested based on experimental observations focused on the fracture mode. The results demonstrate the importance of distinguishing between axial and circumferential long flaws in wall-thinned pipes.     

Finite-element analyses of post-collapse plastic bending of thick pipes

A comparative study of the application of four different types of finite-elements namely elbow (ring), shell, solid, and generalised plane strain to model the post collapse bending behaviour and flow area reduction in an initially straight thick cylindrical pipe made of a highly non-linear material is presented to evaluate their effectiveness. Large strain-large bending FE analyses were performed in each case and the results of moment-curvature relations and pipe-section deformation predictions are compared. The study shows that although solid elements do provide a reasonably accurate and effective solution these are computationally more expensive, while the generalised plane strain finite-elements yield an equally effective and reasonably accurate solution to the problem but are less expensive.     

Crack growth and fracture behaviour of pipes with circumferential defects under internal pressure and superimposed alternating bending load

Pipes made of 20 MnMoNi 5 5 steel and an MnMoNiV special melt, with an external diameter of 800 mm, wall thickness of 47 mm and length of up to 5500 mm, were provided with circumferential defects of defined length and depth. The pipes were loaded by internal pressure and a superimposed alternating bending moment. During the tests, deformation and crack growth were determined in the wall thickness and circumferential direction, and these were compared with calculated values. Pipes with an outer diameter of 226 mm and a wall thickness of 20 mm were used to investigate the leak-before-break behaviour in the dynamic sphere. These pipes also were made of 20 MnMoNi 5 5 steel and an MnMoNiV special melt, and were loaded with internal pressure and an alternating bending moment. The excitation took place at the resonance frequency of the pipes. The pipes also contained circumferential defects of defined length and depth.     

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.     

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.     

A simple approach for failure bending moments of straight pipes

Based on more than 100 experimental results a simple approach for calculating the failure bending moment of a straight pipe is given. Similar to limit load theory a constant stress distribution is assumed over the cross section, whereas stress intensity is expressed by a function of pipe geometry and work-hardening capability of the material.     

Crack opening displacement of circumferential through-wall cracked cylinders subjected to tensile and through-wall bending loads

This study is concerned with crack opening displacements (CODs) of cylinders with a circumferential through-wall crack which is subjected to tensile and through-wall bending loads. A series of FEM analyses were performed in various scaled cylinders, and then the present results on the CODs were compared with the previous studies. Especially, the crack opening behaviors of the large scaled cylinders under a membrane stress and a through-wall bending stress were characterized evidently in this study. The present results are expected to be valid for the leakage evaluation of structures which is subjected to internal pressure and thermal distribution.     

Crack initiation, crack growth and fracture behaviour of large diameter pipes with circumferential defects under internal pressure and superimposed alternating bending load

Pipes made of steel 20 MnMoNi 5 5 and MnMoNiV-special melt having an external diameter of 800 mm, wall thickness of 47 mm, and length of up to 5500 mm were provided with circumferential defects of defined length and depth. They were loaded by internal pressure and a superimposed alternating bending moment. During the tests deformation and crack growth were determined in the wall thickness and circumferential direction. Pipes with an outer diameter of 226 mm and a wall thickness of 20 mm were used to investigate the leak-before-break behaviour in the dynamic sphere. These pipes were also made of steel 20 MnMoNi 5 5 and a MnMoNiV-special melt and were loaded with internal pressure and an alternating bending moment. The excitation took place at the resonance frequency of the pipes. The pipes also contained circumferential defects of defined length and depth.     

Characterization of PWR vessel steel tearing under severe accident condition temperatures

In the event of a severe core meltdown accident in a pressurised water reactor (PWR), core material can relocate into the lower head of the vessel resulting in significant thermal and pressure loads being imposed on the vessel. In the event of reactor pressure vessel (RPV) failure there is the possibility of core material being released towards the containment.On the basis of the loading conditions and the temperature distribution, the determination of the mode, timing, and size of lower head failure is of prime importance in the assessment of core melt accidents. This is because they define the initial conditions for ex-vessel events such as core/basemat interactions, fuel/coolant interactions, and direct containment heating. When lower head failure occurs (i) the understanding of the mechanism of lower head creep deformation; (ii) breach stability and its kinetic of propagation leading to the failure; (iii) and developing predictive modelling capabilities to better assess the consequences of ex-vessel processes, are of equal importance.The objective of this paper is to present an original characterization programme of vessel steel tearing properties by carrying out high temperature tearing tests on Compact Tension (CT) specimens.The influence of metallurgical composition on the kinetics of tearing is investigated as previous work on different RPV steels has shown a possible loss of ductility at high temperatures depending on the initial chemical composition of the vessel material. Small changes in the composition can lead to different types of rupture behaviour at high temperatures.The experimental programme has been conducted on various French RPV 16MND5 steels for temperatures ranging from 900 °C to 1100 °C. Comparisons between the tests performed on these various 16MND5 steels show that this approach is appropriate to characterize the difference in ductility observed at high temperatures.The aim of this experimental study is also to contribute to the definition of a tearing criterion by identifying, on the basis of CT results, the related material parameters at temperatures representative of the real severe accident conditions.This experimental campaign has been carried out in partnership with IRSN in the framework of a research programme whose purpose is to complete the mechanical properties database of 16MND5 steel and to model tearing failure in French RPV lower head vessels under severe conditions (Koundy et al., 2008).     

Evaluation of toughness requirements in cracked components based on fracture-mechanics methods

Different fracture-mechanics based defect assessment procedures have been checked using results of wide-plate tests. The CTOD-Design-Curve-Approach, the CEGB-R6-routine, the EPRI-approach and methods using Finite-Element-Computations to evaluate the crack driving force lead to safe predictions of the failure behaviour of components as long as the limits of application are considered carefully. Reversing the conventional procedure of defect assessment, the CTOD-Design-Curve approach and the FEM based method can be used to derive toughness requirements. The requirements depend on the component and defect geometry, the strength of the material and the safety criterion. For practical application simple diagrams have been evaluated showing the required toughness e.g. as a function of crack length or material strength.