Evaluation of stress intensity factors for internally pressurised cylinders with surface flaws

The aim of this paper is to examine the different methods currently available for evaluating stress intensity factors in cylinders subjected to internal pressure and containing surface cracks. The techniques of analysis involve the use of both two- and three-dimensional models. For a given situation, the most pertinent choice of analysis is not yet clearly established because of the difficulty and uncertainty in interpreting the currently available experimental data. Consequently, it is of interest to review and compare the different analytical techniques now available, particularly with reference to their underlying assumptions.     

Use of the reflectionless stress intensity factor procedure to predict crack arrest during a hypothetical pressurized thermal shock event: The effect of initial crack size

A dynamic methodology based on the reflectionless stress intensity factor concept is used to examine the combined effects of pressure and thermal loads on crack arrest in a nuclear reactor pressure vessel that is subjected to a hypothetical pressurized thermal shock event. Earlier work, for the case of an initially infinitesimally shallow crack, has shown that the currently accepted ASME Code procedure is overly conservative in its arrest predictions when applied to the arrest of a crack deep in the vessel thickness. The present paper shows that this conclusion is also applicable to the case where the initial crack is not necessarily infinitesimally shallow.     

A finite-volume approach to the stress analysis of pressurized axisymmetric structures

A finite-volume procedure for determining the displacement fields and elastic stress distributions within structures that have axisymmetric geometries is presented. The production of a system of linear algebraic equations from the equilibrium equations of the cells that are used to represent the structure is described in detail. An iterative technique is employed to solve these equations and provide the displacement field from which the strain and stress fields can be found. The procedure is used to model two axisymmetric test problems and the stress distribution predicted by the formulation using cell meshes of increasing refinement is compared to analytical solutions and the variations predicted by various finite element procedures.     

A simplified method for calculating the stress intensity factor at crack arrest

This paper outlines a new, simplified method for approximating K_I at arrest during fast fracture events. The analysis method used in this report was developed as a simplified tool to approximate arrest conditions in a series of experiments performed by Combustion Engineering for EPRI. This simplified analysis method is applied to the CE/EPRI, HSST wide-plate, and ORNL pressurized-thermal-shock crack arrest experiments. The results presented in this paper are the first which use a single analysis technique, and thereby allow a comparison of these diverse experiments. This consistent evaluation places all the data from these experiments on an equal footing and provides a comparison with small specimen test data from the HSST program.     

A comparison of methods of calculating stress intensity factors for cracks in pipes and thin walled cylinders

This paper presents results of a study undertaken to compare stress intensity factor solutions for various crack geometries in pipes and thin walled cylinders against the equivalent flat plate K solutions. The exercise was restricted to cylinders and pipes with wall thickness to radius ratios (t/R) of 0·1.

The results of the exercise indicate that structural integrity assessments of pipes and thin walled cylinders which contain flaws should ideally incorporate representative stress intensity factor solutions. Nevertheless there are a number of crack geometries for which flat plate K solutions can provide reasonable estimates of the stress intensity factor.     

Experimental determination of the stress intensity factor for a part-through thickness crack

Based on the relationship between the stress intensity factor and the plastic zone size at the crack tip, an experimental method for the evaluation of the stress intensity factor for a part-through thickness crack is proposed. Approximating the geometrical shape of the crack to a semi-elliptical surface crack, an empirical K-expression for the surface crack in a plate under bend loading configuration is derived and verified experimentally where the new K-expression contains both crack depth and length as a crack tip singularity parameter. The experimental work makes use of newly developed etching techniques to reveal the plastic zone size in deformed A533B pressure vessel steel.     

A new plastic correction for the stress intensity factor of an under-clad defect in a PWR vessel subjected to a pressurised thermal shock

For the assessment of an under-clad defect in a vessel subjected to a cold pressurised thermal shock, plasticity is considered through the amplification β of the elastic stress intensity factor K_I in the ferritic part of the vessel. An important effort has been made recently by CEA to improve the analytical tools in the frame of R&D activities funded by IRSN. The current solution in the French RSE-M code has been developed from fitted F.E. calculation results. A more physical solution is proposed in this paper. This takes into account two phenomena: the amplification of the elastic K_I due to plasticity in the cladding and a plastic zone size correction in the ferritic part.     

A single procedure for helping PV designers to select silicon PV modules and evaluate the loss resistances

When a photovoltaic system is to be sized, different PV modules are considered. The optimisation of such systems is always the goal, but the choice of the PV module with best performance should also be considered. Nevertheless, selecting a module from catalogue data has certain inconveniences. First, because those data allow only comparisons with absolute magnitudes, the conclusions about which module is the most appropriate is not easy. Second, data provided in catalogues are not sufficient to know the module behaviour under conditions different from standard. This paper deals with the normalisation of the modules data by considering a base that allows for obtaining a “per unit” representation. For modelling and studying the modules under non-standard conditions it is necessary to know series and shunt resistances, but that is not easy. Then, by simulations, it is possible to show the influence of these resistances in the module behaviour.     

A simple method to evaluate the technical and economic feasibility of micro hydro power plants in existing irrigation systems

A simple method is proposed to site turbines and choose their power output, evaluate costs and incomes and provide useful indications for Micro Hydro Power (MHP) plant design in existing irrigation systems. This method, based on simple models available in literature and requiring a reduced number of input parameters easy to survey in preliminary design stages, has been applied and verified in an existing irrigation system located in Calabria (Italy).The results have highlighted that in the case study the smallest profitable turbine would produce 5 kW. A lower number of plants (with higher output) would produce no particular monetary savings compared to a greater number of smaller turbines. Furthermore, neither was the option of increasing pipeline diameter found to provide savings.In general, an appreciable potential from MHP operation has been shown in existing irrigation systems, providing a return on investment higher than that provided by the Italian financial market.Finally, MHP profitability noticeably increases with total annual operation time, being on average 55% higher in a wet year (eight months of electrical production/four month of irrigation) compared to a dry year (six months of electrical production/six months of irrigation).     

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.     

A simple approach to determine the solar cell diode ideality factor under illumination

A simple approach, which can estimate the diode ideality factor of a high efficiency pn junction solar cell under illumination by using its current-voltage data, is explained. We have proposed that an analytical method based on Lambert W-function is sufficient for the extraction of the diode ideality factor of a solar cell modeled by double junction behavior with considerable compliance. Various illumination intensities are also considered in order to specify the reliable limit of the method. The dependence of the ideality factor and the reverse saturation current with light intensity has also been investigated in order to provide insight into the alteration of electrical conduction at junction interface at room temperature.     

The effect of spatial incoherence in surface temperature fluctuations on the stress intensity factor in thermal striping

When incompletely mixed hot and cold fluid streams pass adjacent to the surface of a component of a structure, they can cause that component to suffer thermal fatigue damage. Spatial incoherence in the thermal fluctuations will affect the stress intensity factor (SIF), which is frequently calculated assuming perfect spatial coherence. A model is developed to assess this effect for a circumferential line crack in a thin cylinder. The dimensionless SIF can be increased or decreased by reduced spatial coherence, depending on a combination of factors such as Fourier number, Poisson ratio, scale of coherence and crack depth.     

An explicit integral expression for the stress intensity factor of a semi-elliptic surface crack subjected to thermal transient loading

An explicit integral expression for the stress intensity factor of a semi-elliptic surface crack in a plate subjected to thermal transient loading was developed. The stress intensity factor of a semi-elliptic surface crack in a plate, which is exposed to a step change of fluid temperature, was calculated on the basis of the weight function method. The change of the stress intensity factor for a semi-elliptic surface crack subjected to an arbitrary change of the boundary fluid temperature was obtained by Duhamel integration for the product of the step function result and the time varying fluid temperature. The result obtained by the present method has shown good agreement with those obtained by the influence function method. As a practical application, a parametric analysis was performed for the crack behavior during the emergency cool down of reactor coolant in the reactor pressure vessel. Also, the present expression can be effectively applied to the simulation of fatigue crack growth of a semi-elliptic surface crack subjected to various thermal transient loading.     

Stress intensity factors for internal and external cracks in pressurised thick-walled cylinders

Stress intensity factors for both internal and external semi-circular and semi-elliptical surface cracks in internally pressurised thick-walled cylinders of radius ratios between 2 and 3 are presented for a wide range of crack sizes. These solutions were obtained using the boundary integral equation (BIE) method for three-dimensional numerical stress analysis. Hoop strain distributions at the outer circumference of the cylinder are also presented for some external cracks, and shown to be useful for experimentally monitoring crack growth.     

Approximate expressions of maximum value of stress intensity factor of nozzle corner cracks

Based on the flat plate-nozzle model loaded by uniform uniaxial tension, through some suitable reduction and approximation, the maximum value of stress intensity factor (K_I)_max along a crack front can be expressed by the weight function method for the flat plate-nozzle that is loaded by the uniform uniaxial tension and cylinder-nozzle loaded by internal pressure separately. This approach can be valuable for the prediction of fatigue life and failure analysis of pressure vessels. The results so calculated are compared with those reported in the literature and from experiments here reported; and they show good agreement, the discrepancies being less than 15%. This shows that the approximate expressions are effective and can be used in practice.     

Neural network applied to prediction of the failure stress for a pressurized cylinder containing defects

An application of the neural network to predict the failure stress of a cylinder with penetrating flaws under internal pressure is studied in this article. The results from the new method are compared with the experimental results. In addition, the neural network method is used to analyze the sensitivity of parameters of a pressurized cylinder with defects. Satisfactory results are obtained. It is shown that the neural network could be a potential tool in engineering practice.     

A simple procedure for assessing thermal comfort in passive solar heated buildings

The Fanger thermal comfort equation is linearized and used to develop a procedure for assessing thermal comfort levels in passive solar heated buildings. In order to relate comfort levels in non-uniform environments to uniform conditions, a new thermal index called the “equivalent uniform temperature” is introduced.     

Creep fracture mechanics parameters for internal axial surface cracks in pressurized cylinders and creep crack growth analysis

In the present study, a low alloy Cr–Mo steel cylinder subjected to internal pressure at high temperature with a semi-elliptical crack located at the inner surface is considered. The creep crack driving force parameter C1-integrals calculated by finite element (FE) method, are compared with results from previous studies, which indicates that empirical equations may be inaccurate under some conditions. A total of 96 cases for wide practical ranges of geometry and material parameters are performed to obtain systematic FE results of C1-integral, which are tabulated and formulated in this paper. It is observed that the maximum C1-integral may occur neither at the deepest point nor at the surface point when the aspect ratio is large enough and the value of C1-integral is significantly sensitive to the crack depth ratio. Furthermore, based on the proposed equations for estimating C1-integrals and a step-by-step analysis procedure, crack profile development, crack depth, crack length and remaining life prediction are obtained for surface cracks with various initial aspect ratios. It is found that when the crack depth ratio is increased, there is no obvious convergence of crack aspect ratio observed. The magnitude of half crack length increment is always minor compared with the crack depth increment. In addition, the remaining life is much more dependent on the surface crack depth than on the surface crack length.     

Weight functions for the determination of stress intensity factor and T-stress for edge-cracked plates with built-in ends

This paper presents the weight functions for the determination of the stress intensity factor and T-stress solutions for edge-cracked plates with built-in ends under complex stress distributions. First, a compliance analysis approach is used to calculate stress intensity factor and T-stress for edge cracks in finite width plates with built-in ends with uniform or linear stress distributions acting on the crack face. The results serve as the reference solutions for the next step in which the approaches of deriving weight functions from reference stress intensity factor and T-stress solutions developed for stress boundary conditions are extended to obtain the corresponding weight functions for edge-cracked plates with built-in ends. Finite element analysis is conducted to validate the derived solutions. The weight functions derived are suitable for obtaining stress intensity factors and T-stress solutions under any complex stress field.