Modelling crack growth for creep and fatigue loading

Estimates of creep crack growth in engineering components under steady load conditions are usually based on the application of fracture mechanics concepts. In particular the creep parameter C* has become widely used together with creep crack growth data obtained from laboratory tests. There are now a number of practical methods to utilise experimental data. For high temperature components, which are subjected to cyclic (fatigue) as well as creep loading, the estimation of the fracture mechanics parameters becomes much more difficult, and consequently the extent to which the growth of pre-existing cracks grow by creep and fatigue is difficult to quantify. In this paper the response of Type 316L stainless steel is examined. This material progressively strain hardens under reversed cyclic loading, and the creep behaviour also changes. Using uniaxial fatigue and creep results, fracture parameter maps are developed to establish the appropriate regimes for creep-fatigue crack growth. Using the maps a model is developed which can predict the combined effect of fatigue and creep on crack growth. The implications of the model are discussed in relation to the limitations of obtaining results from laboratory tests at short times, and the assessment of practical engineering components.     

Effect of intermittent unloading or reversed loading on high temperature crack growth behaviour of Grade 91 steel under constant tensile load

Abstract

As a part of the efforts for developing a reliable assessment procedure for crack growth in high temperature components, crack growth tests at various loading conditions were performed on Grade 91 steel. 1T compact tension specimens of 20 mm thickness were kept under constant tensile load at 600°C, but periodically unloaded or reversely loaded to compressive side to observe these effects on deformation behaviour as well as crack growth behaviour. It was found that periodical reversed loading accelerates crack growth due to re-acceleration of inelastic deformation during load holding, but its extent was not as large as predicted by creep J-integral in a conventional way. The predictions were improved by introducing an additional parameter to take account of creep damage recovery which was caused by the excursion to compressive load.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part III: estimation of crack opening area

Evaluation of the crack opening area (COA) plays a central role in the evaluation of the critical crack length for a detectable leak for piping systems. Simplified evaluation methods for the COA for a circumferential through-wall crack in a pipe subjected to axial and bending loading or their combination is reviewed in this paper. Elastic solutions are compared and recommendations are given. Plastic solutions by the reference stress method are compared with nonlinear finite element solutions. The reference stress method tends to overestimate the COA for medium or large crack angles. Considerable improvement is achieved by making empirical modifications to the limit load expressions used in the calculation of the reference stress.     

Emerging technology for component life assessment

Operating plant component damage and failure experience is reviewed. Loading conditions such as thermal stratification and striping, turbulent flow and flow-induced vibrations are often found to limit useful life, even though such loadings were typically not considered when the components were designed. High cycle thermal and mechanical fatigue are identified as important damage mechanisms. A new method of correlating fatigue data and extrapolating to the very high cycle regime is described.

The results of environmental degradation testing during the past fifteen years have shown that such effects are much more deleterious than previously assumed. Therefore environmental and aging effects must be taken into account in evaluating the reliability and dependability of components for extended periods of operation. Since most of the available data on environmental effects focus on measured crack growth rates, methods of developing improved fatigue life evaluation methods which include environmental effects on crack growth rates are now being developed.

Fatigue tests on polished specimens are characterized by nominal stress amplitudes over yield, where linear elastic fracture mechanics (da/dn vs. ΔK) methods, such as those used in the ASME Code, are not valid. The small plastic zone corrections used in the Code do not account for the plastic crack-driving energies encountered in low-cycle fatigue testing. J-integral solutions are used herein to evaluate the growth of cracks in these specimens. This approach can be shown to correlate the growth of cracks over the entire range of loading from elastic to grossly plastic conditions in widely different geometries and sizes, including the growth of very short cracks for materials of major interest in pressure vessels and piping. It can be used to correct S-N fatigue life evaluation, curves for known differences in crack growth rates whether they are due to corrosion-assisted fatigue or other variables.

Environmental effects on the crack initiation phase of fatigue failure can be directly incorporated into S-N life evaluation curves. Once the crack propagation effects are included, the resulting improved S-N curves provide a means for plant operators to evaluate the current condition of these components and systems, taking into account the cumulative damage from operating transients and cycles which the plant has experienced. The safe residual life can then be evaluated using the S-N curves to include cumulative damage for the anticipated future period of operation. This plant life evaluation approach is applicable even where in-service inspections are not feasible. It provides a sound quantitative basis for making repair/replacement decisions.     

Principles of the German approach to the analysis of flawed structures

The analysis of flawed structures in the linear elastic regime (LEFM) has been treated very extensively, especially in the framework of the 4th German nuclear programme. Investigations with large specimens have demonstrated the applicability of the LEFM for a variety of materials ranging from low to high toughness levels. In the elastic-plastic (EPFM) regime, however, especially the J-integral method has been used for quantifying the safety margin, because with a required value of upper shelf Charpy energy alone this quantification is not possible.

A correlation between the crack initiation value J_i and Charpy upper shelf energy was evaluated experimentally, justifying the generally upgraded upper shelf energy level adopted in the Code. Furthermore, this correlation can be employed when fracture toughness values are not available as is mostly the case for irradiated material from surveillance programmes.

To cope with the problems resulting from repeated transients in a complex component, incipient crack intitiation and propagation under cyclic thermal load have been investigated experimentally and theoretically on a RPV nozzle corner in the HDR plant and on a thick-walled (200 mm) hollow cylinder subjected to pressurized thermal shock (PTS). Since the OCA code covers only the linear elastic range, for this loading case elastic-plastic fracture mechanics calculations have been carried out by means of the Finite Element Method. The first test performed with high toughness material has shown good agreement with the J-integral approach. Additional validation tests are under way to demonstrate the lowest tolerable toughness level to withstand PTS without catastrophic failure.

With respect to critical flaw sizes in degraded piping and vessels, the ‘leak before break’ limit curve for different loading conditions has been established and experimentally validated using piping and model vessels of different sizes, crack configurations and toughness levels.

The still existing uncertainties in the detection, sizing and interpretation of signals from nondestructive examination are the background of NDE validation programmes for both medium size and full size reactor pressure vessels. Acoustic emission trials as well as extensive ultrasonic (US) examinations will be pursued in cooperation programmes, last but not least in the framework of PISC III.     

Flaw analysis in steam generator tubes

This paper presents the flaw assessment programme undertaken in France for PWR steam generator tubes affected by stress corrosion cracking. Failure criteria were deduced from burst tests on various crack configurations. Stresses and critical crack sizes were estimated for all operating conditions. The corresponding leak rates during normal operation were computed after validation of the model. Then it was shown that a significant primary-to-secondary leak should precede tube failure.     

Fracture response of pipelines subject to large plastic deformation under bending

Demand for long-distance offshore pipelines is steadily increasing. High internal pressure combined with bending/tension, accompanied by large plastic strains, along with the potential flaws in girth welds make the structural integrity of pipelines a formidable challenge. The existing procedures for the fracture assessment of pipelines are based on simplified analytical methods, and these are derived for a load-based approach. Hence, application to surface cracked pipes under large deformation is doubtful. The aim of this paper is to understand and identify various parameters that influence the fracture response of cracks in pipelines under more realistic loading conditions. The evolution of CTOD of a pipeline segment with an external circumferential surface crack is investigated under pure bend loading as well as bending with internal pressure. Detailed 3D elastic–plastic finite element simulations are performed. The effects of crack depth, crack length, radius-to-thickness ratio and material hardening on fracture response are examined. The results show that at moderate levels of CTOD, the allowable moment capacity of the pipe decreases significantly with increase in internal pressure. Further, the variation of CTOD with strain can be well approximated by a simple linear relationship.     

Probabilistic fracture mechanics analysis of nuclear piping considering variation of seismic loading

In conventional probabilistic fracture mechanics (PFM) analyses, seismic loading is considered as a large deterministic value, although there exists the variation of the seismic load as well as response of building and components. On the other hand, such stochastic behaviours have already been taken into account in the field of seismic probabilistic safety assessment. This paper proposes a new PFM model for nuclear piping that takes into account the variation of seismic loading. The distribution in ground acceleration is modelled with the seismic hazard curve. The distribution in piping response during a seismic event is modelled with a log–normal distribution. Since the seismic load has large variation, when not adopting an upper limit to the distribution in seismic stress, the break probability calculated from the present PFM analysis becomes equal to the probability that the seismic stress exceeds the collapse stress of a sound pipe. This implies that the existence of a crack has no effect in these PFM analyses, and this result does not satisfy the purpose of PFM analysis to evaluate the failure probability per crack. Therefore, the seismic stress was limited to the collapse stress of a sound pipe in the present PFM analysis to evaluate the conditional break probability per crack.     

Fitness for service of welded components under creep and creep–fatigue loading

The welded materials are prone to damage particularly in heat-affected zones in base metal as well as in fusion line and weld metal. Therefore the treatment of welded components operating in the creep and creep–fatigue regime is of immediate industrial interest. It needs to be addressed by a methodology that will be developed and incorporated into design codes such as ASME, as well as in Fitness-for-Service assessment procedures. Assessment of welded components for Fitness-for-Service is addressed in fragments in various procedures. This is due to the complex microstructures of weldments that include base metal, heat-affected zone and weld metal. The R5 high temperature assessment procedure, produced by BE in the UK, formalized the methods for base metals loaded in static and creep–fatigue with sections describing the treatment of welds. Subsequently, procedures for assessing defects at high temperature, similar to those in R5, have been included in British Standards, the French A16 procedure and in API 579. Section 8 of the recent European thematic network FITNET Fitness-for Service procedure which is incorporated into R5, specifies methods for assessing defects in structures operating at high temperatures and subject to creep and creep–fatigue loading conditions. The reliability of the structural assessments following the codes depends strongly on availability of reliable data required as input data. Most of the data obtained to date on high temperature materials has been reported on creep crack growth (CCG), ignoring the creep crack initiation (CCI) where as creep–fatigue data is scarce. Recent European and international collaborative effort included EC projects CRETE and ECCC, and ESIS TC11, WG on High Temperature Testing of Welds concentrated on CCI as well as CCG testing and analysis of industrial specimens and assessment. This has led to development of a Code of Practice for High Temperature Testing of Weldments via Int. Institute of Welding (IIW) to be presented to ISO for standardization.     

Engineering guide to assessment of creep crack initiation on components by Two-Criteria-Diagram

To assess creep crack initiation on components, it is necessary to consider the stresses at the crack tip as well as in the remaining ligament or farfield region. For that aim the Two-Criteria-Diagram was established. The method was proven by a large number of creep crack initiation results from small and large scale specimens as well as components. In this paper some practical aspects for using the Two-Criteria-Diagram are described. A code of practice for the use of Two-Criteria-Diagram for creep and creep fatigue loading is given. The extension to the latter and the limits of applicability are discussed. The determination of crack initiation in a cast steel containing defects is described as an example showing the advantages of the method for engineering applications.     

Numerical analysis of IPIRG cracked pipe experiments subjected to dynamic and cyclic loading

This report contains results of a finite element study aiming to identify the influence of loading history and geometry for cracked pipes subjected to complex loading. The experiments have been performed within the International Piping Integrity Research Group (IPIRG) Program. The majority of the numerically analyzed experiments were conducted on straight pipes with an outside diameter of 168 mm and containing a large circumferential through-wall crack. The considered pipes were loaded in four-point bending under displacement control and at a temperature of 288°C. The types of loading were combinations of either quasi-static or dynamic and also monotonic or cyclic loading with different loading ratios R. Some analyses were also performed on surface-cracked pipes subjected to slow, monotonic loading.

In the finite element study, 20-node solid elements were used for the through-wall cracked pipes and a combination of shell and non-linear line spring elements for the surface-cracked pipes. Stable crack growth was simulated by gradual node relaxation and crack closure is accounted for by using simple contact elements. The J-integral for a remote contour is calculated and used as a characterizing fracture parameter although the cyclic loading violates the theoretical basis for this procedure. The near-tip J can not be used for growing cracks because of the weak energy singularity. The results of the numerical study confirm the trends from the experiments in that a high loading rate has a negative influence on the fracture properties of the studied carbon steel and that large cyclic loading, especially at R = −1, lowers the apparent J_R-curve for both carbon and stainless steels. To some extent geometry effects appear to be present when comparing the results from pipes containing surface cracks and through-wall cracks with results from CT specimens. These effects are more pronounced for large amounts of stable crack growth than at initiation.     

A study on fatigue crack growth in the high cycle domain assuming sinusoidal thermal loading

The assessment of fatigue crack growth due to turbulent mixing of hot and cold coolants presents significant challenges, in particular to determine the thermal loading spectrum and the associated crack growth. The sinusoidal method is a simplified approach for addressing this problem, in which the entire spectrum is replaced by a sine-wave variation of the temperature at the inner pipe surface. The loading frequency is taken as that which gives the shortest crack initiation and growth life. Such estimates are intended to be conservative but not un-realistic. Several practical issues which arise with this approach have been studied using newly-developed analytical solutions for the temperature and stress fields in hollow cylinders, in particular the assumptions made concerning the crack orientation, dimensions and aspect ratio. The application of the proposed method is illustrated for the pipe geometry and loadings conditions reported for the Civaux 1 case where through wall thermal fatigue cracks developed in a short time, but the problem is relevant also for fast reactor components.     

Linear elastic stress intensity factors for cracks in nuclear pressure vessel nozzles under pressure and temperature loading

Stress intensity factors for two different nozzle geometries and different crack sizes are evaluated for pressure and thermal loading utilising three-dimensional elastic finite element models.The results are compared to available experimental data and a procedure is proposed to estimate the maximum of the stress intensity factor for arbitrary crack size and loading conditions.     

Computational simulation of fatigue crack growth and demonstration of leak before break criterion

A thick plate with a semi-elliptical surface crack subjected to remote tension and tension fatigue loading is considered for the analysis. In the present study the material is assumed to have variable fracture toughness in the surface and thickness directions. Material with isotropic fracture toughness is also considered. The developed three dimensional finite element code which has the capability to handle singularity and evaluate fracture parameter based on force method is used to characterise the fatigue crack growth. Parametric study involving various initial crack sizes is carried out and Foreman’s equation is used to predict the crack growth. Various regions viz. break, leak before break are obtained.     

Influence of mechanical and environmental variables on crack growth in PWR pressure vessel steels

Knowledge of the propagation rates of sub-critical cracks exposed to primary circuit coolant is essential for the use of defect assessment procedures for validation of PWR pressure vessel integrity. The results of research programmes conducted by the UKAEA to assess the conditions under which the PWR environment influences crack propagation of low alloy steels under cyclic and steady loading are described. The measured corrosion fatigue crack propagation rates for low and medium sulphur steels in good quality flowing water were well below those predicted by the ASME Section XI, Appendix A assessment curves, but higher rates were attainable for high sulphur steel or under adverse environmental conditions. No influence of material microstructure due to welding was observed in high flow water.No susceptibility to stress corrosion has been observed in bolt-loaded specimen tests on a range of parent steels and weldments. Cracking in slow strain rate tests was observed only at high potentials, such as were produced by the presence of dissolved oxygen, unless the specimen orientation was such as to maximise access of PWR coolant to sulphide inclusions in the steel.The implications of the data for operating plant and progress with the development of improved methods for assessing crack growth in operating plant are discussed.     

Analysis of crack arrest event in NESC-1 spinning cylinder experiment

In the NESC-1 spinning cylinder test, a large surface-breaking flaw in a thick steel cylinder component was subjected to high primary and secondary stresses produced by combined rotation and thermal shock loading. The crack was arrested after relatively small amounts of ductile tearing and cleavage crack extension. Finite element analyses have been carried out to obtain static elastic stress intensity factors for the initial and arrested crack under constant load and constant displacement boundary conditions. Applied static elastic stress intensity factors for the arrested crack have been compared with the plane strain crack arrest toughness values measured using small-scale compact crack arrest (CCA) specimens. The present analyses of the crack arrest event in the NESC-1 spinning cylinder test have concluded: (1) Applied static elastic stress intensity factors are reduced significantly for the lobe-shaped arrested crack which developed from the initial semi-elliptical surface crack as a result of the localised cleavage crack propagation. This reduction in crack driving force is likely to be the main reason for crack arrest. (2) The analysis carried out and comparison with the full-scale experiment confirm the prevailing approach to the assessment of crack arrest that brittle propagation will stop if the applied crack driving force falls below the crack arrest toughness. (3) The results justify the use of the static elastic stress intensity factor as the crack propagation driving force parameter and the static plane strain crack arrest toughness as the resistance parameter for crack arrest evaluation for small relative crack jump dimensions. (4) The small-scale CCA tests can be employed to evaluate crack arrest in a large cylinder of the same material.     

The potential drop method for monitoring crack growth in real components subjected to combined fatigue and creep conditions: application of FE techniques for deriving calibration curves

The potential drop technique is a robust method to provide continuous in situ crack growth monitoring of real power-plant components. For a correct assessment of the crack depth, accurate calibration curves for the geometry at hand are required. The problem entails determining the electrical potential field in a body usually characterised by a complicated geometry as a function of the growing crack. Finite element analysis procedures are first applied to optimise the technique (i.e. to determine the best location for the PD leads) and secondly to provide theoretical calibration curves. The validity of this procedure has been assessed in laboratory component tests under both thermal fatigue and multiaxial creep loading. Post-test measurements of the crack depth underline the accuracy of the FE calibration technique.     

Experimental creep life assessment of tubular structures with geometrical imperfections in welds with reference to fast reactor plant life

Creep damage is a major life limiting factor for components operating at high temperature. For the fast breeder reactor (FBR), the hot sodium pool components and the steam generator are critical in determining the operating temperatures from structural mechanics considerations. Therefore, creep fatigue damage at various critical locations is estimated based on viscoplastic analyses, in compliance with the high temperature design rules of RCC-MR. In addition, welded joints of steam generator tubes with spigots made of modified 9Cr–1Mo and the welds of fuel pins made of 20% cold worked stainless steel to annealed end plugs, which have certain geometrical imperfections in the welds are also critical and the applicability of existing design rules to these components needs to be investigated carefully. Towards assessing the life of such tubular components realistically, accelerated tests were conducted simulating the creep damage to rupture. The generated test data were investigated by applying the existing creep damage assessment procedure recommended in the design code RCC-MR and the results demonstrated that with the recommended multiaxial creep damage assessment rule, the creep crack initiation lives have been predicted accurately. Further, the extrapolated life predicted by applying an appropriate Larson–Miller parameter indicates that the circumferential welds in the steam generator tubes and fuel pins are not life limiting factors in the design.     

The exhaustion of creep ductility in 1CrMoV steel

The calculation of creep damage due to secondary (self equilibrating) stresses for the lifetime assessment of critical locations in components subject to creep-fatigue loading at high temperatures may be determined in terms of ductility exhaustion. A new Spindler type stress-modified creep ductility exhaustion model has been developed for 1CrMoV steel in which the rupture ductility is dependent not only on creep strain rate, stress and temperature, but also on a material pedigree function.     

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

Different from previous two-dimensional thermal weight function (TWF) method, a three-dimensional (3D) TWF method is proposed for solving elliptical interface crack problems in bimaterial structures under a transient thermal loading. The present 3D TWF method based on the Betti's reciprocal theorem is a powerful tool for dealing with the transient thermal loading due to the stress intensity factors (SIFs) of whole transient process obtained through the static finite element computation. Several representative examples demonstrate that the 3D TWF method can be used to predict the SIFs of elliptical interface crack subjected to transient thermal loading with high accuracy. Moreover, numerical results indicate that the computing efficiency can be enhanced when dealing with transient problems, especially for large amount of time instants.