The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack : Part I: Bending deformation is load-controlled

A net-section stress failure criterion is currently used to determine the critical size of circumferential crack for austenitic stainless steel as used in nuclear reactor piping systems. The acceptable crack size for prescribed applied loadings is determined by assuming that failure occurs when the stress across the net-section (that is the pipe cross-section area reduced by the crack area) attains a critical value, the stress at the cracked section being calculated on the basis of the undeformed pipe configuration. However, an axial compressive load can give an increased bending moment if the stress calculation is based on the deformed pipe configuration. This paper therefore examines the effect of an axial compressive load, superimposed upon a bending load, on the failure of piping due to the presence of a through-wall circumferential crack. The results show that the failure assessment should be based on the deformed configuration even when the axial load is only a small fraction of the pipe's Euler critical load, or otherwise the net-section stress approach can give non-conservative failure predictions.     

Crack growth resistance methodologies for austenitic stainless steels

The paper reviews the methodologies that are being used to quantify the effect of cracks in austenitic stainless steel structures. As a framework for discussion, these methodologies, i.e. net-section stress and tearing modulus, used to describe respectively the onset of crack extension and crack stability, are considered with regard to the behaviour of a circumferential through-wall crack in a piping system.     

Application of the net-section stress approach to pipe failure

Theoretical results for centre-cracked panels, deforming under plane stress tensile loading conditions, are used to assess the applicability of the net-section stress approach fo? predicting the onset of crack extension at a through-wall crack in a pipe, fabricated from a very ductile material and subjected to an applied bending moment. For a given pipe diameter, the appropriate net-section stress should be essentially constant over a wide range of crack sizes; however, this stress does vary appreciably with pipe diameter. The net-section stress approach therefore has a range of useful applicability but great care must be exercised when using the approach outside this range.     

The difference between the fracture initiation and maximum load net-section stresses for a cracked structure

Experimental results for 304 stainless steel centre-cracked panels containing through-thickness cracks have been interpreted as indicating critical net-section stresses both for the initiation of fracture and for maximum load attained after a limited amount of stable crack growth, the fractional difference between these stresses being $\text{～ 10\%}$. By applying results from recent developments in general yield fracture mechanics, this paper shows that this small difference depends on the ligament width. This dependency has important implications when the net-section stress approach is applied to the development of leak-before-break criteria for structures containing part-through cracks.     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

Crack resistance of austenitic pipes with circumferential through-wall cracks

For a monotonously increasing load the correct evaluation of the crack resistance properties of a structure is essential for safety analyses. Considerable attention has been given to the through-wall case, this is generally believed to be the controlling case with regard to complete pipe failure. The maximum load conditions for circumferential crack growth in pipes under displacement-controlled loading has been determined. The need for crack resistance curves, measured on circumferentially through-wall cracked straight pipes of austenitic stainless steel 316 L under bending, is emphasized by the limitation in the data range from small specimens and by the differences in the fracture mechanics procedures. To address these issues and to improve calculational methods a joint fracture mechanics programme is being performed by Electricité de France, Novatome and Siemens-Interatom. The working programme contains experimental and theoretical investigations on the applicability of small-specimen data to real structures.     

The instability of radial growth of a part-through and part-circumference circumferential crack in a stainless steel pipe subject to bending deformation. Part II—The effect of a superimposed axial compressive load

In the context of the integrity of nuclear reactor piping systems, this paper examines the effect of an axial compressive load, superimposed upon bending loads, on the unstable development of a part-through and part-circumference circumferential crack into a through-wall crack in a stainless steel pipe. Results are obtained for axial compressive stresses up to 20% of the material's yield stress, this being reckoned to be a reasonably large compressive stress level. The results show that if the bending deformation is load-controlled, the failure assessment should be based on the deformed pipe configuration, otherwise the failure predictions will be non-conservative. On the other hand, with displacement-controlled bending deformation an axial compressive stress does not have an adverse effect on crack stability.     

Leak-before-break: An integrated approach for high energy piping

An integrated approach that involves system design, thermal hydraulics, materials, and fracture mechanics analyses to assure that pipe failure is highly unlikely is described. This approach is based on a leak-before-break (LBB) premise and includes through-wall flaw detectable leakage, through-wall flaw stability, and part-through-wall flaw fatigue crack propagation calculations. A successful application of LBB can reduce the amount of excessive pipe rupture restraint hardware. Assuring LBB not only reduces initial construction, future maintenance, and radiation exposure costs, but the overall safety and integrity of the plant are improved. This last benefit comes about from gaining additional insight into the piping systems and their capabilities. Details of the LBB methodology are presented here with specific examples for two pressurized water reactor lines (one inside containment fabricated of stainless steel, and the other outside containment made from ferritic steel). The application of this approach at Beaver Valley Power Station—Unit 2 indicates that pipe rupture hardware is not necessary for stainless steel lines inside containment as small as 6-in (152 mm) nominal pipe size that have passed screening criteria designed to eliminate potential problem systems (such as the feedwater system). Similarly, some ferritic steel lines as small as 3-in (76 mm) diameter (outside containment) can qualify for pipe rupture hardware elimination.     

The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack: Part II: Bending deformation is displacement-controlled

In the context of the integrity of nuclear reactor piping systems, this paper examines the effect of an axial compressive load on the instability of growth of a through-wall circumferential crack in a stainless steel pipe that is subjected to displacement-controlled bending deformation. The analytical procedure is based on the deformed pipe configuration, and with the aid of the tearing modulus methodology, the instability criterion is expressed in terms of the magnitude of the compressive load, pipe geometry parameters, and the material's fracture and flow characteristics. The results show that a compressive load can have an adverse effect on crack stability when the axial load is only a small fraction of the pipe's Euler critical load. This conclusion is in general accord with the conclusion for the case where a pipe is subject to load-controlled bending deformation.     

Plastic limit pressures for cracked pipes using finite element limit analyses

Based on detailed finite element (FE) limit analyses, the present paper provides approximations for plastic limit pressure solutions for plane strain pipes with extended inner axial cracks; axi-symmetric (inner) circumferential cracks; axial through-wall cracks; axial (inner) surface cracks; circumferential through-wall cracks; and circumferential (inner) surface cracks. In particular, for surface crack problems, the effect of the crack shape, semi-elliptical or rectangular, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy for short circumferential through-wall cracks and for surface cracks (both axial and circumferential). Being based on detailed 3D FE limit analysis, the present solutions are believed to be accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.     

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.     

The effect of an axial compressive load on the stability of a circumferential crack in a stainless steel pipe that is built-in at both ends

Against the background of the integrity of boiling water reactor piping systems, this paper investigates the effect of an axial compressive load on the stability of a circumferential crack in a stainless steel pipe that is built-in at both ends. One end is fixed, while the other, though allowed to move in an axial direction, is subject to a transverse displacement, and crack instability is examined when this displacement is fixed. The circumferential instability of a through-wall crack and the radial instability of a part-through and part-circumference crack are both examined. For both types of instability, it is shown that a compressive load has an adverse influence on crack stability only when the compressive load is a large fraction (>0·5) of the Euler critical load.     

Creep test of type 304 stainless steel tube containing a notch subjected to internal pressure

This paper summarises the results of experimental creep tests of type 304 stainless steel tube subjected to internal pressure at 650°C. The equipment used was especially developed for these tests.

The tubes without notches were tested at pressures of 9·32 and 7·36 MPa. Test results indicate that the rupture time of the tubes without notches is in good agreement with that of uniaxial specimens when the maximum stress is taken as the rupture criterion. The tubes containing axial and circumferential surface notches were tested at a pressure of 7·36 MPa. Test results indicate that the ductile fracture theory is applicable to the life prediction in the case of axial notches.

An electric potential method was very useful for monitoring the creep crack growth from the notch root. The relationship between the creep crack growth rate and the fracture mechanics parameter, σ_net or K₁, was investigated.     

Analysis of the failure performance of internally pressurised piping with surface flaws

Because of frequent failures of the Atucha PWR moderator circuit branch piping, which is made of stainless steel type AISI 347 (DIN 1.4550), studies have been made, involving the application of several fracture mechanics criteria, in order to determine the conditions of leak-before-break (LBB) and the critical crack length of the piping.These studies lead to the conclusion that, for straight pipe of outside diameter 219 mm and 16 mm wall thickness, with a circumferential flaw and with the principal stress being in bending, the LBB criteria are satisfied, the critical crack length being of the order of 400 mm.A better mechanical finishing and heat treatment was suggested in order to improve the resistance to crack initiation.     

Measurement of leak-rate through fatigue-cracks in pipes under four-point bending and BWR conditions

Leak-rate tests were performed using 114 mm and 165 mm (4 and 6 in) diameter, schedule 80 pipes made of austenitic stainless steel SUS304 and carbon steel STS42. Each pipe contained a through-wall fatigue crack and was mounted on a four-point bending machine of 400 kN maximum loading. Tests were done under a pressure of 7 MPa, with a subcooling temperature. The leak rate was measured by a Venturi flow meter and a differential pressure transducer attached to the pressure vessel. Comparisons of the effect of pipe material, diameter and crack angle were made. This paper shows that from a Leak-Before-Break viewpoint, the stainless-steel pipe is superior to the carbon-steel one, and that the pipe with the larger diameter is better than the one with the smaller diameter. No unstable fracture was observed in the tests.     

Fracture investigations on piping system having large through-wall circumferential crack

In level-3 Leak-Before-Break (LBB) analysis, stability of a postulated through-wall circumferential crack is demonstrated by simplified fracture mechanics calculations. Detailed experimental studies, conducted by the authors, have revealed that the conventional assessment procedure used to demonstrate LBB is too conservative. There is a large factor of safety due to system indeterminacy. It was observed that the critical load of a cracked piping system (with even a large through-wall circumferential crack of about 120°) is of the order of 75–90% of the collapse load of the uncracked piping system. Reduction in load carrying capacity is even less for a piping system having an off-centre crack. This article discusses the above-mentioned aspects in detail. Detailed 3-D elastic-plastic finite element analyses of some of these tests were performed. The suitability of these numerical results to predict crack initiation load in light of the experimental data is discussed.     

The net-section stress at the onset of crack extension: Part 2—The effects of geometric configurational parameters

A detailed examination of the effects of configurational parameters underlines the limited range of applicability of the approximate approach by which the onset of crack extension at a crack tip is related to the attainment of a critical net-section stress. The examination shows that the net-section stress is very sensitive to configurational geometry.     

Experimental calibration of stress intensity factor for piping with circumferential through-wall crack

A survey of the literature shows that the existing stress intensity factor solutions for circumferential through-walled cracks in piping may be classified into three categories. One category is based on Sanders' analytical results for long pipe cracks, with various corrections in the short crack range and different curve-fitting formulae to give convenient closed form expressions. The second category consists of various independent finite element solutions. Each of these solutions is for a discrete pipe geometry and crack length and so is not practical to be used in fracture mechanics analysis. Lastly there is Kanninen & Zahoor's solution, derived independently of Sanders' results. Comparison showed that the results from the first two categories roughly agreed but were vastly different from Kanninen & Zahoor's results. Experimental calibration using the strain gauge method and the fatigue crack growth rate back-tracking method has been carried out. The experimental results agreed with the family of solutions derived from Sanders' work. Details about this experimental calibration are presented.     

Residual stresses in girth butt welded pipes and treatments to modify these

A number of Type 304 stainless steel pipes are used in the primary cooling systems of nuclear plants. Intergranular stress corrosion cracks (IGSCC) were found at some welded joints in these piping systems due to very high tensile residual stress, sensitization of the material due to welding, and corrosive environment, all occurring simultaneously. Investigations have shown that at least one of the above factors must be eliminated to prevent IGSCC.

This report describes experimental results on the temperature variations during pipe welding by conventional techniques and by the heat sink welding (HSW) technique. The mechanism of residual stress generation due to welding is also discussed. The pipe used in these experiments was 4B Sch80 Type 304 stainless steel. It was found that the temperature distribution through the thickness of the pipes was almost uniform for the conventional welding technique, but had a very sharp gradient for HSW. In the pipe axial direction, the temperatures varied sharply for both welding techniques. This implies that the sensitization of metal due to HSW is lighter than that of conventional welding and that the residual stress on the inside surface of the heat sink welded pipe is compressive.

The induction heating stress improvement (IHSI) method has been investigated analytically and experimentally. In the IHSI method, a pipe is heated with an induction coil while cold water is pumped through it. This causes a temperature gradient throughout the pipe wall which generates high thermal stresses. This, in turn, generates compressive stresses on the inner surface of the pipe. This method is designed to eliminate tensile residual stresses near the weld heat affected zone on the inner surface.

Temperature analysis and subsequent thermoelastic-plastic analysis show that tensile weld residual stresses at a joint were changed into compressive stresses on the inner surface of a pipe. It was confirmed experimentally that these stresses suppressed fatigue crack propagation in the heat affected zone (HAZ) of a welded pipe. Therefore, the IHSI method is effective not only in preventing crack initiation but also in suppressing crack propagation.

As for the relaxation of residual stresses, no significant relaxation was measured when external loads were applied at as much as 80% of the yield strength in the experiments.     

Remaining life assessment and optimal design of statically indeterminate pipe system with circumferential crack

This paper examines the J–R curve theory in elastic-plastic fracture mechanics and crack extension resistance in order to analyze the large-scale yielding of statically indeterminate pipe structure with a circumferential crack. The dJ/da characteristic can be utilized to measure that the crack is stable ductile fracture or unstable ductile fracture and to analyze the crack growth rate. The total propagation time of the crack until collapse can be computationally estimated by numerical analysis that is presented in this paper. The further analysis of dJ/da and optimization is to maximize the crack propagation time during the crack growth before reaching plastic collapse. Both of the center-point crack and end-point crack are investigating cases for analyzing the mechanics and engineering design. These analysis and design strategies developed in this paper are useful for the safety performance of a structural pipe under crack deformation.