The determination of cost-effective NDE inspection schedules for structures containing defects based on probabilistic fracture mechanics

Modern fracture mechanics analysis techniques can confidently estimate critical defect sizes, but due to certain parameters, such as defect size and occurrences, material properties, as well as loading, being statistically distributed, a probabilistic approach must often be adopted. A robust analytical method has been developed, which incorporates two-dimensional defect size distributions, detection probabilities, elastic-plastic critical defect size estimations, as well as fatigue crack growth analysis, to estimate the probability of fracture failure of structures containing defects. It is argued that the probability of failure as an output of an integrity assessment is directly relatable to cost factors and based on this relationship, a powerful procedure is presented to establish cost-effective fracture control meaures such as inspection schedules. The procedure is based on the premise that the probability of failure multiplied by the cost of failure yields a cost, termed the probable cost of failure, which gives an indication of how much money should be spent on fracture control. A cost-effective fracture control measure is then defined as a measure which would cost less to implement than the amount of money saved in probable failure expenses due to the introduction of the measure. The application of this principle is illustrated with a case study.     

Post-yield fracture mechanics theory and its application to pressure vessels

A post-yield fracture mechanics theory is presented based on Bilby, Cottrell and Swinden-Dugdale model solutions for cracks in bodies of finite width and subject to stress gradients. The model solutions are in good agreement with computed elastic-plastic values of the path independent integral J up to loads of 0·8 of the collapse load in the case of a cracked plate subject to bending. As an example, the model is applied to a thermal transient in a pressure vessel. The possibility of cracking and failure of a nozzle was considered. It is shown that a semi-circular crack will grow into an extended defect. Therefore, in the main analyses, axial symmetry and infinitely long longitudinal and fully circumferential cracks were considered. The post-yield fracture mechanics solutions are presented in the form of elastic-plastic stress intensity factors. Within the geometric approximations it is shown that longitudinal cracks are more dangerous than circumferential ones and can result in general yielding across, and full penetration of, the pressure vessel wall. In addition, linear elastic fracture mechanics under-estimates the danger of deep cracks and in some circumstances can considerably overestimate the critical size of small cracks. It is shown that the addition of a residual pressure stress considerably reduces the predicted critical defect sizes.     

Evaluation of the effect of metallurgical variables on materials behaviour and reference curves

An integral part of the safety assessment of nuclear pressure vessels and piping is the quantitative estimation of defect growth in both a stable and an unstable manner during service. This estimation is essential for determining whether any defect detected during inspection should be repaired or whether the size of the defect even after its expected growth is small enough to leave the integrity of the vessel unaffected.

The most important stable defect growth mechanism is that of environmentally assisted cyclic crack growth. Recent results indicate that it is markedly affected by sulphur content and/or manganese sulphide morphology and distribution. This implies that an essential improvement in component safety has been gained by currently applied steelmaking practices, which result in extra low sulphur content, generally below 0·010 wt.%, and in the round shape and small size of inclusions through, e.g. calcium treatment, hence considerably reducing the effect of the environment on crack growth rate. This further implies that the ASME Section XI reference curves for environmentally accelerated cyclic crack growth are conservative for steels produced by current steelmaking practices.

The ASME Section XI applies predominantly linear elastic fracture mechanics to assess the effects of cracks on the integrity of nuclear power plant components. Unstable linear elastic fracture often propagates by a cleavage mechanism. The cleavage fracture process has recently been shown to be of a statistical nature in both ferritic and bainitic steels. The carbide size distribution plays a dominant role in controlling the fracture toughness of these steels. A cleavage fracture model has been developed, by which both the expectance value and the probability limits of the fracture toughness, K_IC, can be predicted. The probability limits given by the model are shown to be consistent with the experimental observations. The application of the model to the data on which the ASME Section XI reference fracture toughness curve is based indicates that the reference curve is slightly unconservative.     

Fracture of a steampipe—Analysis in terms of fracture mechanics

An investigation into metallurgical aspects of a large steampipe failure is described. It is explained how measurement of the local thinning of the fractured material allowed the toughness of the failed lap weld to be estimated. This information is then linked with the initial defect sizes by means of fracture mechanics relationships to predict stresses to cause local breaching and crack propagation along the pipe. A stress at least five times the nominal service stress must have been present to cause the failure. This was verified in controlled burst tests of identical pipes containing artificial defects similar to the one present at the site of the failure.A by-product of the investigation is a verification of some fracture mechanics relationships and the development of means for finding toughness at a location of fracture after the event.     

Theoretical determination of reference stress for partially penetrating flaws in plates

The reference stress concept is a very powerful tool for use in the stress analysis of non-linear materials. It can be applied to estimate the deformation and fracture behaviour of flawed and unflawed components. When applied to flawed components it is employed in conjunction with fracture mechanics concepts to predict failure. The aim of this paper is to develop a reference stress solution for partially penetrating defects in plates which are subjected to combined axial and bending loading. A solution relevant to ‘global’ collapse of the entire cross-section containing the defect is obtained. The treatment represents the defect by a circumscribing rectangle. A range of shapes and sizes of defect (i.e. rectangle) is considered. As expected, it is found that smaller reference stress values are obtained for the ‘global analysis’, particularly for large defects, than from those that are produced from estimates based on ‘local’ collapse of the uncracked ligament ahead of the defect.     

Fatigue crack growth in multi-pass butt-welded joints of mild steel

Fatigue crack growth rate properties obtained by testing multi-pass butt-welded joints in the through-the-thickness direction are presented along with a characterization of the mild steel base material. Edge-notched four-point-bending specimens are used to investigate R-ratio, specimen geometry and post-weld heat-treatment effects on fatigue crack growth rates. The pervasive influence of residual stresses on welded joint fatigue testing using the fracture mechanics approach is also discussed. For these multi-pass joints, conservative fatigue crack growth rates are obtained with post-weld heat-treated specimens.     

Use of the overpressure test to indicate fitness for purpose of a ferritic pressure vessel

A study is presented of the efficacy of customary proof testing practices. The fracture mechanics methods used in the study are first shown to estimate approximately the immunity observed after proof testing experimental vessels. The overstress required to assure a useful number of operating cycles is calculated for some typical cases, by considering growth in service of the maximum cracklike defect which could survive the pressure test, allowing for tearing. A wide range of possible fracture toughness, effects of geometry and operating temperature are included. The significance of fatigue crack growth enhancement during approach to fracture is estimated. The calculations and a discussion of more general issues confirm that the overpressure test is a valuable demonstration of pressure vessel integrity.     

Fatigue crack growth calculations for a vessel internal corner crack under repeated thermal transients

A problem of current fundamental and industrial interest is the structural integrity of pressure vessels containing defects when subjected to repeated thermal shock at constant internal pressure. The component considered is a nozzle to a hemispherical pressure vessel intersection containing a defect at the internal corner. A range of 12 cases of thermal shock loads characterised in severity by two dimensionless parameters, the Biot (B) and Fourier (F) numbers, were applied. Estimation of remaining life for each case was carried out based on the PD6493 procedure. Numerical modelling of the crack growth from the quadrant shaped crack showed that more severe shocks accelerate crack growth while less severe shock leads to slow growth or eventual crack arrest. The effect of the Biot and Fourier parameters on the remaining life of the component was quantified. A methodology that comprises of heat transfer, thermal stress and fracture mechanics of defect assessment is applied to a problem of industrial interest.     

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.     

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.     

Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an “independent” relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint (Q-parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.     

The use of acoustic emission methods as aids to the structural integrity assessment of nuclear power plants

Since it is an integral method permitting continuous monitoring and remote defect location, acoustic emission offers promising benefits for the nuclear industry. Particular potential applications relating to the integrity of the primary pressure boundary of nuclear reactors that are considered in this report are the detection of flaws during pre-service and requalification hydrotests, and continuous monitoring for crack growth and leakage.The correlations between fracture mechanics and acoustic emission are discussed on the basis of certain fundamentals of material emission behaviour. The influence of instrumentation and of aspects related to wave propagation on the detectability and evaluation of acoustic emission signals is considered.The conclusion reached is that at the present time acoustic emission can be used predominantly during hydrotests as a search method for cracks. Although some degree of characterization and sizing of defects may be obtained on the basis of empirical data, a quantitative evaluation of defect severity based on fracture mechanics cannot yet be made satisfactorily. It is expected that a considerable improvement in this respect may be achieved by applying a transfer correction that takes into account the depth position and directivity pattern of the source.The technique of leak detection by acoustic emission shows promising results permitting the location and quantification of leaks. Practical experience and future research work are expected to enhance the accuracy and detection sensitivity.     

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.     

Different fracture performance of all-steel and all-aluminium cylinders with axial cracks

The linear elastic and the nonlinear elasto-plastic fracture mechanics analysis on all-metal (all-steel and all-aluminum) cylinder with different axially oriented cracks were carried out using the three-dimensional finite element method and the experimental method. The crack mouth opening displacement CMOD and the crack driving forces (K_I for elastic deformation state and J_I for elasto-plastic deformation state) of the all-steel cylinder and the all-aluminum cylinder containing axial deep cracks, were obtained. Through analysis of the calculated CMOD and crack driving forces for the all-steel cylinder and the all-aluminum cylinder with cracks, whose sizes are often met, respectively, in the engineering applications, the fracture behaviors of the two kinds of all-metal cylinders are compared. The CMOD for the two kinds of all-metal cylinders with external axial cracks were measured by an experimental method and good agreements between the calculated CMOD and tested CMOD were reached. Some CMOD and crack driving force expressions about the crack sizes, internal pressure and location along the crack front are obtained.     

Stress intensity factors for a pipe-plate welded joint

A major component of any linear elastic fracture mechanics model for fatigue crack growth is the calculation of the crack tip stress intensity factor. This is particularly difficult for welded joints due to the complex geometry. While some data are available for cracks in welded T-plate joints, there is relatively little data available for larger cracks in more complex tubular joints. Such cracks are of significant interest since the most practical application of fracture mechanics models is the prediction of remaining life for cracks discovered in service.

A pipe-plate joint has been developed as a simplified model of tubular joint geometries for fatigue studies. Two such specimens have been tested in air, with detailed monitoring of crack growth behaviour using potential drop techniques. These data were used to obtain crack growth rate data from which estimates of stress intensity factors were made. Separately, finite element analyses for various discrete crack configurations were performed. The results of these analyses are presented and discussed, with particular emphasis on the accuracy of the results and the implications for fracture mechanics modelling.     

An analysis of crack extension by corrosion fatigue in a crude oil pipeline

Corrosion fatigue subcritical crack extension was found to be the most likely cause of four service failures in an 864-mm (34 in) diameter and 7·14-mm (0·281 in) wall thickness crude-oil pipeline. The results of examination of the failures are summarised and a fracture mechanics analysis of corrosion fatigue crack extension in the pipeline, from initial defect to critical size, is presented. The analysis is based on fatigue crack growth rate data measured in crude oil, saturated with H₂S, and an operational pressure fluctuation spectrum in the pipeline, acquired from the pressure records at pump station discharges. The additional effects of frequency of shutdowns and hydrostatic pressure tests are considered. The fatigue crack growth lives are calculated for various depths of initial defects.     

Allowable defect sizes in a sour crude oil pipeline for corrosion fatigue conditions

A fracture mechanics treatment of corrosion fatigue crack growth rates is used to estimate corrosion fatigue life and allowable defect depths for specified lives of sour crude oil pipelines.The present study is based on a case history of a major Canadian crude oil pipeline that experienced five fatigue failures during its first 10 years of operation. Characteristic pressure fluctuation spectra have been derived from pump stations' pressure records. Fatigue crack growth rates for various crack configurations and orientations, and the effects of environment (crude oil with hydrogen sulphide content from zero to saturation) on these have been measured in the laboratory.Calculated fatigue lives have been verified by full-scale pipe tests pressurized with crude oil containing 100 ppm of hydrogen sulphide, using the characteristic pressure spectrum simulating operating conditions.     

Crack propagation life prediction of a perforated plate under thermal fatigue

Superheater outlet headers of boilers are well known to be subjected to the cycling of high pressure and high thermal stress during plant operations. Thermal stresses during cyclic operation are generally severest on the inside surface of the ligaments between the stub-tube holes, where many examples of ligament cracking due to thermal fatigue have been found recently. A method to predict the crack propagation life of the ligaments of boiler headers under thermal fatigue has been required. Firstly in this paper, to model the crack propagation behavior of the ligament regions of boiler headers, a perforated plate of normalized and tempered 2 1/4Cr–1Mo steel was examined under out-of-phase thermal fatigue at a maximum temperature of 600°C in the air. Inelastic analysis of the perforated plate under thermal fatigue was carried out, and the nonlinear fracture mechanics parameters such as the J and C^* integral were obtained by the line integral for observed cracks. A simplified method was proposed for predicting these parameters under displacement-controlled conditions such as thermal fatigue. In this method, the change of the macroscopic stress–strain relation of the perforated plate with propagating cracks was combined with the reference stress concept under displacement-controlled conditions. The predicted fracture mechanics parameters from this method coincided well with those from the inelastic analysis. The prediction of the crack propagation life on the basis of the proposed method provided a good correspondence with the test results of the perforated plate under thermal fatigue.     

Analysing the influences of weld size on fatigue life prediction of FCAW cruciform joints by strain energy concept

The effect of weld size on fatigue life of flux cored arc welded (FCAW) cruciform joints containing lack of penetration (LOP) defect has been analysed by using the strain energy density factor (SEDF) concept. Moreover, new fracture mechanics equations have been developed to predict the fatigue life of the cruciform joints. Load carrying cruciform joints were fabricated from ASTM 517 ‘F’ grade steel. Fatigue crack growth experiments were carried out in a vertical pulsar (SCHENCK 200 kN capacity) with a frequency of 30 Hz under a constant amplitude loading (R=0). It was found that the crack growth rates were relatively lower in the larger welds fabricated by the multipass welding technique than the smaller welds fabricated by the single pass welding technique.