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.     

J integral estimation fracture analysis for circumferentially cracked carbon steel piping

The three-segment fitting method is presented to describe the material stress-strain curves with yield plateaus. A J integral estimation approach for carbon steel piping with circumferential through-wall cracks was developed. Failure assessment curves obtained using three options in the CEGB R6 approach were proposed for GB20 carbon steel piping under bending. The initiation and maximum moments predicted by the J estimation approach presented in this paper are quite close to the experimental values.     

A statistical based circumferentially cracked pipe fracture mechanics analysis for design or code implementation

This paper discusses a simple engineering approach to evaluate surface flaws in carbon steel or stainless steel piping and their weldments. It is based on statistical data from a large number of pipe fracture experiments. To ensure a reasonably conservative approach, a 95-percent confidence level was established. Toughness and pipe size effects are accounted for in one correction factor, while ovalization and flow stress effects are accounted for in two other factors. The limitations and possible improvements to such an approach are also discussed.     

Fatigue behavior of pipes containing multiple flaws in inner surface

In this work was studied the growth behavior of multiple cracks in the inner surface of pipes. The fatigue tests were performed using two kinds of test pipes, i.e., the straight pipes and bend pipes of AISI Type 304L stainless steel, having 320 mm in outer diameter and 35 mm in thickness approximately.The crack growth curves obtained by the fatigue tests were compared with the analytical curves of two kinds of crack growth prediction methods. One method is based on the ASME Boiler and Pressure Vessel Code, Sec. XI. Another method is based on the procedure in which the crack growth formula is applied to both the surface and thickness directions. The analytical crack growth curves predicted by the ASME Code are conservative for the test results of the straight and bend pipes. However the results of bend pipe test suggest that the procedure of the ASME Code may give an unconservative fatigue life under the certain condition.On the other hand, the test results of the straight pipes can be evaluated reasonably and those of the bend pipes can be evaluated conservatively by the latter method.     

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.     

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.     

Application of statically indeterminate fracture mechanics, SIFM, to a circumferentially cracked cylinder problem

The method of statically indeterminate fracture mechanics called SIFM is an application of elastic–plastic fracture mechanics to statically indeterminate problems. Application of SIFM has been developed for axially cracked cylinder problems. Its application was modified to a circumferentially cracked cylinder. The component might be loaded by combined transient thermal and mechanical loading. This was applied to simulate pressurized thermal shock, PTS, experiment, NKS-3, carried out by MPA. The predicted result from SIFM shows good agreement with the NKS-3 experimental one.     

Crack shape evolution of surface flaws under fatigue loading of austenitic pipes

From the results of fatigue crack growth and fracture tests of a Ni–Fe base superalloy (Incoloy 908), an improved fatigue life analysis model has been derived from the framework of Newman and Raju. For a plate geometry with an initial semi-elliptical surface crack in its thickness direction, the new model can predict the evolution of crack aspect ratio for a wide range of initial crack geometry for Incoloy 908 that has been considered as the primary candidate for the ITER central solenoid conduit. The improved model is applied to the ITER central solenoid magnet life prediction. The model predicted the conduit fatigue lives that are about two times the values obtained by assuming the constant aspect ratio during the crack growth, for both free-standing and bucked against central solenoid designs. Therefore, we recommend the improved model for the best estimate design analysis of future magnet conduit.     

Fatigue and fracture behavior of straight pipe with flaws in inner surface

Fatigue and fracture tests of piping models with flaws in the inner surface were carried out to investigate the fatigue crack growth, coalescence of multiple cracks and fracture behavior.Two straight test pipes with and without weldment in the test section of AISI type 304L stainless steel were tested under almost the same test conditions by imposing moment loads. Three artificial defects were machined in the inner surface of the test section of the test pipes and the fatigue test was performed until the cracks coalesced and grew through the thickness. Subsequently, a static load was imposed on the test pipe which contained a large crack in the test section.The fatigue test results are compared with an analytical crack growth behavior predicted by the method described in the Section XI of ASME Code, and show slower crack growth than that of the prediction. From the fracture test results, it is found that the test pipes can endure considerably high load.     

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.     

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%.     

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.     

Ductile fracture of cracked steel plates

A simple relationship between loading for crack initiation, or onset of ductile tear, and crack length is presented for center-cracked plates of mild steel. Formulation of the nonlinear boundary-value problem is based on incremental theory of plasticity for Prandtl-Reuss materials. Quasi-static solutions corresponding to a series of incremental loading conditions are obtained by the mothod of finite elements. Tests conducted on plates of two types of mild steel agree with numerical results.     

Fracture mechanics analysis of a pressure vessel with a semi-elliptical surface crack using elastic-plastic FEM-calculations

Results of an elastic-plastic three dimensional finite element analysis for a semi-elliptical surface crack inside a pressure vessel is presented. The calculations were performed by the finite element program ADINA, incorporating von Mises yield condition and isotropic hardening. The calculations were performed up to that pressure level where general yield of the ligament takes place. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic as well as of elastic-plastic fracture mechanics.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

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.     

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.     

Shakedown analysis of elastic-plastic structures

Behavior of elastic-plastic structures under repetitive and fluctuating loads is considered in this paper. Plastic deformation either stabilizes after a finite number of cycles or continues during the cycling. In the first case the structure is said to have shaken down to the boundary at the loading program. If plastic deformation does not stabilize an elastic-plastic structure becomes unserviceable due to either alternating plasticity when yielding occurs repeatedly in the opposite senses or accumulation of plastic strains and progressive increase of permanent displacements. This paper attempts to survey the shakedown theory, including the accommodation of a structure to the prescribed loading range as well as inadaptation and unserviceability.The notion of shakedown, incremental collapse, ratchetting and alternating plastic deformation are first illustrated with examples. The fundamental theorems on shakedown and inadaptation are presented next, attention being directed to generalizations of the classical Melan and Koiter theorems. Applications of the theorems are given. Available methods for determining the shakedown range on generating self-equilibrated stress fields are discussed. Special techniques applicable to problems involving both dead and fluctuating loads are invoked. Recent studies accounting for inertia forces, geometrical changes, material hardening, variation of material properties with temperature, displacement assessment, etc. are referred to.     

Probabilistic fracture failure analysis of nuclear piping containing defects using R6 method

Failure analysis of in-service nuclear piping containing defects is an important subject in the nuclear power plants. Considering the uncertainties in various internal operating loadings and external forces, including earthquake and wind, flaw sizes, material fracture toughness and flow stress, this paper presents a probabilistic assessment methodology for in-service nuclear piping containing defects, which is especially designed for programming. A general sampling computation method of the stress intensity factor (SIF), in the form of the relationship between the SIF and the axial force, bending moment and torsion, is adopted in the probabilistic assessment methodology. This relationship has been successfully used in developing the software, Safety Assessment System of In-service Pressure Piping Containing Flaws (SAPP-2003), based on a well-known engineering safety assessment procedure R6. A numerical example is given to show the application of the SAPP-2003 software. The failure probabilities of each defect and the whole piping can be obtained by this software.