Fracture mechanics safety analysis of components based on fracture mechanics characteristics combined with multiaxiality of the stress state

Currently several parameters for quantifying the crack tip constraint in fracture mechanics specimens as well as in cracked components are under discussion. The parameters are briefly described and compared on the basis of analyses of fracture mechanics specimens. The parameters are able to show loss of constraint, but for high constraint situations the predictions are inconsistent. It is shown that one parameter is able to explain different fracture modes at the same load level for a small scale fracture mechanics specimen and a large scale component like specimen.     

Comparison of elastic-plastic fracture mechanics criteria

To assess the integrity of a cracked structure, using materials data obtained from simple laboratory tests, it is essential to define materials properties which are independent of the shape and the size of the specimen and of the loading system applied to it. In those situations where either the specimen or the structure fails after significant yielding has taken place, there is considerable speculation about the materials parameters which are relevant.By extending the Griffith equation for the stability of a perfectly elastic cracked body, the authors derive a fracture criterion which is applicable in the post-yield regime. Comparisons are made with procedures based on the $\text{J-}\text{contour}$ integral, equivalent energy and crack opening displacements and with the post-yield fracture mechanics of Heald, Spink and Worthington,⁸ and Dowling and Townley.⁹     

Some applications of fracture mechanics in power engineering

This paper is complementary to the paper by Corten in reviewing the current status of fracture mechanics techniques, paying particular attention to application aspects. After summarising the reasons for applying fracture mechanics, the various approaches are summarised; the choice of appropriate method for components that show some yield before failure is described. Information needed to complete a full fracture mechanics treatment is tabulated, and examples of various applications given. Mention is made of current proposals for standard specifications based on fracture mechanics. Attention is drawn to where uncertainties may arise.     

Fracture mechanics assessment of industrial pressure vessel failures

Fracture mechanics assessment procedures, such as BSI PD6493; 1991, R6 and ASME XI, have become well established in industry. These published procedures provide methods for assessing the acceptability of flaws in fusion welded structures. For such procedures to be used with confidence, it is essential that their application be validated by comparison with large scale fracture mechanics tests, and actual structural failures. This paper describes eight industrial pressure vessel failures, for which PD6493 fracture assessments have been performed. It has been demonstrated that the assessment procedures are safe to use, provided that input data are reliable.     

A calculational round robin in elastic-plastic fracture mechanics

Eighteen organisations participated in this EPFM numerical analysis round robin which treated the same three-point bend problem as a similar round robin conducted by ASTM four years earlier. The work involved the calculation of overall deformation, J, CTOD and crack profile using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime.

It was found that all of the elastic solutions were accurate to within a few per cent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. Apparently no significant progress has taken place in the state of the art of numerical EPFM analysis over the four-year interval. The paper discusses the reasons for this scatter and draws tentative conclusions on the most suitable numerical analysis methods in EPFM.     

The application of fracture mechanics in thermally stressed structures

There is considerable interest in calculating stress intensity factors at crack tips in thermally stressed structures, particularly in the power generation industry where the safe operation of both conventional and nuclear plant is founded on rigorous safety cases. Analytical methods to study such problems are of limited scope, although they can be extended by introducing numerical techniques. Purpose built numerical methods, however, offer a much greater and more accurate solution capability and in particular the finite element method is well advanced. Such methods are described, including how stress intensity factors can be obtained from the finite element results. They are then applied to a range of thermally stressed problems including plates with central cracks and cylinders with axial and circumferential cracks. Both steady state and transient temperature distributions arising from typical thermal shocks are considered.     

The use of probability theory in fracture mechanics—A case study

A probabilistic approach to fracture mechanics in the form of a typical case study is described wherein the integrity of a high-pressure water pipeline is assessed. An analysis methodology is discussed incorporating the probability density functions of defect sizes, the statistics of defect occurrences and the statistical distribution of material properties. This method enables the analyst to supply a very simple assessment of safety, based on the probability of failure (a single number) which may be compared to accepted industrial standards (e.g. 10⁻⁶ for nuclear applications). It is argued that this method often offers the only way to scientifically and economically assess the integrity of fracture prone structures.     

Use of probability with linear elastic fracture mechanics in studying brittle fracture in pressure vessels

This paper deals with one phase in the development of statistical methodology for a fracture mechanics analysis of the failure of nuclear steam supply system components, in particular that of brittle fracture in the beltline region of the pressure vessel resulting from various transients. It introduces a probability structure into the deterministic linear elastic fracture mechanics calculations. The resulting estimates of probability of brittle fracture reflect not only variation due to heterogeneity of vessel material but also uncertainties in the effect of embrittlement of the vessel steel due to neutron irradiation. Using importance sampling in conjunction with Monte Carlo simulation we estimate that, for the operational transients considered, the probability of brittle fracture conditional on the presence of an Appendix G flaw is less than $\text{2 × 10}{}^{\mathrm{?10}}$.     

Technical application of fracture mechanics to thin-walled structures

This paper reviews recent developments in the application of fracture mechanics to such structures as welded steel tanks, ships, and thin-wall pressure vessels, with particular attention to Japanese work. It describes methods for estimating critical crack size and safe working conditions, taking into account such fabrication variables as angular distortion, welding residual stress, prestrain, plate curvature and stress concentration. Whilst most of the paper is devoted to a consideration of the conditions for crack instability, it also discusses crack arrest and gives experimental results for the effect of thickness on both initiation and arrest.     

Elastic-plastic fracture mechanics analysis of an SENB specimen

This paper describes the elastic-plastic analysis of a Single Edge Notched Bend (SENB) specimen, a specimen commonly used for the determination of the fracture toughness of a material. First, a two-dimensional convergence study is described to investigate the influence of mesh size on the global response of the specimen and the fracture mechanics parameters J and COD. Then a three-dimensional analysis is compared with experimental results. The three-dimensional computational results show a good agreement with the experiments, except for the load region where the global deformations were dominated by the Lueders zone in the material stress-strain curve.     

Elastic-plastic FE calculations for a fracture mechanics analysis of a weld in the ligament of a CT specimen

Results of elastic-plastic FE calculations on four plane strain models of a CT-100 specimen, (a) with a weld in the ligament, (b) of base material only, (c) of welding simulated material only and (d) of weld material only, are compared and discussed in the light of fracture mechanics aspects. Regarding the cleavage fracture regime, considerably higher crack opening stresses are obtained in the welded specimen than in the base material specimen, as soon as small-scale yielding occurs. Conservative evaluation of the crack opening stresses of the welded joint can be achieved by using the welding simulated material properties. The J-integrals determined by the energy release rate using the method of virtual crack extension are equal for the four material models up to about 200 N mm⁻¹. Above this level, the behaviour of the welded specimen and that of the base material model are still similar, while a higher force is necessary for the welding simulated material model and the weld material model to reach the same J-value as for the two others. The crack opening profile of the welded specimen is asymmetric to the fusion line which lies in the ligament. The half profile of the heat-affected zone side is comparable to that of the welding simulated material model and the half profile of the weld material side to that of the base material model. A higher maximum of the equivalent strain on the heat-affected zone side than on the weld material side may explain why cracks tend to run into the base material region of the weld under conditions of stable crack growth. General yield of the welded specimen occurs on the base material side, whereas on the weld material side only a small plastic zone is visible, comparable to that in welding simulated material at the same load.     

Fracture mechanics approach for failure of adhesive joints in wind turbine blades

Composite components of wind turbine blade are assembled with adhesive. In order to assess structural integrity of blades it is needed to investigate fracture of joints. In this study, finite element analysis based on fracture mechanics was conducted to characterize failure of adhesive joint for wind turbine blade. The cohesive zone model as proposed fracture mechanics approach was verified through the comparison of numerical results with experimental data. Finite element models of wind turbine were developed to predict damage initiation and propagation. Numerical results based on fracture mechanics showed that failure was initiated in the edge of the adhesive bond line due to high level of shear stress prior to reaching the extreme design loading and propagated progressively.     

Probabilistic fracture mechanics analysis of a nuclear pressure vessel for allocation of in-service inspection

To find whether there are significant differences in fracture probability between various regions in a reactor pressure vessel a limited probabilistic fracture mechanics (PFM) study was carried out. The loading was assumed to be deterministic, whereas some of the other quantities involved were assumed to be of random character. A simple, mainly analytical probabilistic model was developed. The critical event was taken as unstable crack growth without any ensuing crack arrest. All random information on the J_R vs Δa behaviour was assumed to be contained in a single scalar parameter. Various distributions such as the Weibull and the log-normal distributions were assumed for this parameter to judge the sensitivity of results to various assumptions. The initial size of pre-service defects was assumed to follow the OCTAVIA distribution. Possible time-dependent crack growth such as fatigue or stress corrosion cracking was treated in a simplified manner assuming deterministic material properties.

Various regions (and crack geometries) were considered and the fracture and leakage probabilities were calculated for a number of load cases. The fracture probabilities were strongly dependent on the assumption made for the fracture toughness distribution, but the order of the fracture probabilities of the regions seemed to be relatively unaffected by this. The leakage probabilities are in most cases much lower than the fracture probabilities, indicating that consequence considerations are not very important for non-destructive test (NDT) allocation purposes. It is also concluded that probabilistic methods of the present kind may be a useful tool for judging which locations should be the primary targets for NDT.     

Importance of fracture criterion and crack tip material characterization in probabilistic fracture mechanics analysis of an RPV under a pressurized thermal shock

Using a probabilistic fracture mechanics code, the importance of the choice of fracture criterion and the material fracture resistance characterization at the crack tip is elucidated in the failure probability analysis of an reactor pressure vessel. The paper describes the procedure to evaluate the crack extension based on R6, where an increase in fracture resistance by ductile crack extension is considered. Two standard J–resistance curves are prepared for applying the elasto-plastic fracture criterion by R6 tearing.Case studies concerning the effect of the tearing fracture criterion were carried out using a severe pressurized thermal Shock transient. Results are discussed with respect to the fracture criterion, the material J–resistance curve, the algorithm for evaluating the crack tip fracture toughness and the initial crack geometry.The introduction of the elasto-plastic fracture criterion significantly contributes to removal of over-conservatism in applying a linear elastic fracture criterion. It was also confirmed that the algorithm of the re-evaluation method for crack tip fracture toughness has to be correctly applied.     

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

Abstract

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.     

A generic approach for a linear elastic fracture mechanics analysis of components containing residual stress

A review of through thickness transverse residual stress distribution measurements in a number of components, manufactured from a range of steels, has been carried out. Residual stresses introduced by welding and mechanical deformation have been considered. The geometries consisted of welded T-plate joints, pipe butt joints, tube-on-plate joints, tubular Y-joints and tubular T-joints as well as cold bent tubes and repair welds. In addition, the collected data cover a range of engineering steels including ferritic, austenitic, C–Mn and Cr–Mo steels. The methods used to measure the residual stresses also varied. These included neutron diffraction, X-ray diffraction and deep hole drilling techniques. Measured residual stress data, normalised by their respective yield stress have shown an inverse linear correlation versus the normalised depth of the region containing the residual stress (up to 0.5 of the component thickness). A simplified generic residual stress profile based on a linear fit to the data is proposed for the case of a transverse residual tensile stress field. Whereas the profiles in assessment procedures are case specific the proposed linear profile can be varied to produce a combination of membrane and bending stress distributions to give lower or higher levels of conservatism on stress intensity factors, depending on the amount of case specific data available or the degree of safety required.     

Validation of analyses used in the fracture mechanics assessments of welds containing defects

The British Standard PD 6493 and the Central Electricity Generating Board (UK) R-6 approaches were used to estimate the failure conditions for a set of defective weldments that were tested to destruction under four point bending. Prior to the destructive testing, the defects had been ultrasonically sized by a number of independent operators, and it was seen that there was some considerable variation between operators, and between predicted and actual defect parameters.

Both the actual and the predicted defect parameters were used as input data, with the relevant material properties in the failure assessment procedures. However, some assumptions were made in calculating the failure stress levels using the PD 6493 approach, and in calculating the plastic collapse load required in the R-6 method.

This paper describes the approximations used, and in addition gives the results of a sensitivity analysis performed on the ‘defect tolerance’ of the four weld types.