Finite element based stress concentration factors for pipes with local wall thinning

Based on detailed three-dimensional elastic FE analysis, the present work compiles the elastic stress concentration factor for a pipe with local wall thinning. To cover practically interesting cases, a wide range of pipe and defect geometries are considered, and both internal pressure and global bending are considered. Resulting values of stress concentration factors are tabulated for practical use, and the effects of relevant parameters such as pipe and defect geometries on stress concentration factors are discussed.     

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.     

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

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.     

Ductile failure analysis of API X65 pipes with notch-type defects using a local fracture criterion

A local failure criterion for API X65 steel is applied to predict ductile failure of full-scale API X65 pipes with simulated corrosion and gouge defects under internal pressure. The local failure criterion is the stress-modified fracture strain as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the effective stress). Based on detailed finite element (FE) analyses with the proposed local failure criterion, burst pressures of defective pipes are estimated and compared with experimental data. For pipes with simulated corrosion defects, FE analysis with the proposed local fracture criterion indicates that predicted failure takes place after the defective pipes attain maximum loads for all cases, possibly due to the fact that the material has sufficient ductility. For pipes with simulated gouge defects, on the other hand, it is found that predicted failure takes place before global instability, and the predicted burst pressures are in good agreement with experimental data, providing confidence in the present approach.     

Experimental study of low-cycle fatigue of pipe elbows with local wall thinning and life estimation using finite element analysis

Low-cycle fatigue tests were conducted using elbow specimens with local wall thinning. Local wall thinning was machined on the inside of the elbow in order to simulate metal loss from erosion corrosion. The local wall thinning was located in three different areas known as the extrados, crown and intrados. The elbow specimens were subjected to cyclic in-plane bending under displacement control without internal pressure. In addition, three-dimensional elastic-plastic analyses were also carried out using the finite element method. As a result, the crack penetration area and the crack growth direction were successfully predicted by the analyses. The fatigue lives estimated by the analyses were close to those obtained by the experiments.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part I: stress intensity factor and limit load solutions

The J-integral and the crack opening area are the main parameters required for a leak-before-break evaluation of a piping system. Stress intensity factor and limit load solutions have been widely used for evaluating these parameters in a simplified way. Solutions for the stress intensity factor and limit load for a pipe with a circumferential through-wall crack subjected to axial and bending loads are reviewed and compared in this study. Based on the comparisons, recommendations are then made on expressions for calculating these parameters.     

Fatigue strength for pipes with allowable flaws and design fatigue curve

To evaluate the structural integrity for nuclear power piping systems, low cycle fatigue tests were performed on 4 in. diameter carbon steel pipes with flaws. The flaws are local wall thinning, taking into account the minimum wall thickness required for design pressure and circumferentially part-through cracks based on the acceptance standards in the ASME Code Section XI. The applied load was four-point bending with or without an internal pressure under displacement-controlled conditions at ambient temperature. The results show that the flaws above do not influence the integrity of the piping system and pipes do not break within the seismic regime of stress and cycles.     

Correspondence between solar load ratio method for passive water wall systems and f-Chart performance estimates

A simple correspondence is demonstrated between passive solar system performance and active system f-Chart estimates. The equations describing a thermal network model of a passive water wall solar system are compared term by term with similar equations governing the heat balance in an active solar heating system, making possible an identification of appropriate passive system parameters with active system parameters comprising inputs to the f-Chart procedure. Comparisons of f-Chart predictions and results using the Solar Load Ratio method are made for sample cities in sixteen climatic zones. Results indicate a discrepancy of at most about 9 per cent solar fraction between the two methods in the cases studied.     

Failure pressure of straight pipe with wall thinning under internal pressure

The failure pressure of pipe with wall thinning was investigated by using three-dimensional elastic–plastic finite element analyses (FEA). With careful modeling of the pipe and flaw geometry in addition to a proper stress–strain relation of the material, FEA could estimate the precise burst pressure obtained by the tests. FEA was conducted by assuming three kinds of materials: line pipe steel, carbon steel, and stainless steel. The failure pressure obtained using line pipe steel was the lowest under the same flaw size condition, when the failure pressure was normalized by the value of unflawed pipe defined using the flow stress. On the other hand, when the failure pressure was normalized by the results of FEA obtained for unflawed pipe under various flaw and pipe configurations, the failure pressures of carbon steel and line pipe steel were almost the same and lower than that of stainless steel. This suggests that the existing assessment criteria developed for line pipe steel can be applied to make a conservative assessment of carbon steel and stainless steel.     

Determining local stress and limit load in a thick-walled tube with a hoop direction U-shaped notch under tension

This paper presents, in terms of the spherical section assumption, an effective method for determining the local stress and limit load of a thick-walled tube with an external hoop direction U-shaped notch under tension, and discusses the relationships of the stress concentration factor with notch depth t, radius of the notch root and the internal radius a₁ of the tube. Expressions for the elastoplastic local stress and limit load, which have not been considered by previous workers, are proposed. Comparison of the results of this paper with those of previous work for the case where a₁ = 0 shows that the method of this paper is simple and effective in engineering.     

Scattering and image contrast simulation for double wall radiography of pipes

Radiographic image quality, which is quantified by radiographic sensitivity measurements, is significantly influenced by parameters such as scattering, effective attenuation coefficient and image contrast. In the present work, the Monte Carlo method has been utilized to simulate Gamma ray scattering and image contrast for double wall radiography of pipes and some experiments have been designed to determine the radiographic sensitivity and measure the effective attenuation coefficient. Wire type image quality indicators were simulated as artificial defects and the threshold contrast and minimum optical density difference for viewing each wire were investigated. It was found that the maximum allowable source to film distance for double wall exposure and single wall viewing technique was 1.4 times the outside diameter of the pipe and the image contrast and radiographic sensitivity were higher for this technique in comparison with the double wall viewing technique. The double wall exposure and double wall viewing technique is proposed to be used when the minimum source to film distance is higher than 1.4 times the outside diameter.     

Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

An Improvement on the Method for Calculating the Capillary Limit of Axial—Grooved Heat Piper

A new model has been developed to predict the capillary limit of axial-grooved heat pipe.In the model the concepts of liquid saturation or liquid fraction of the cross-sectional area of groove,the modified relative permeability,absolute permeability of groove and Leverrt‘s function are used.The Leverrt‘s function is well represented by the functionf(s)=1(1/√5)(1/2-)^0.175.In the model the effects of gravitational force,capillary force and viscous force are considered.The calcuated results are in good agreement with existing experimental data reported in the literature.     

Wind resource estimates with an analog ensemble approach

The wind resource and energy assessment is key to a wind farm development project. It allows for establishing the feasibility and economic viability of the project over the typical 10- to 30-year lifetime of a wind farm. Recent studies show that the accuracy of assessments has substantial room for improvement. Estimating and reducing uncertainty is important to secure financing and ensure the confidence of investors. A new method is proposed and demonstrated for the long-term estimation of the wind speeds at a target site, a key step in assessments. The method is based on ensembles made of analogs between a short-term observational record from the target site and a long-term historical record from a nearby site or an atmospheric model. It provides a high-quality long-term wind resource estimate, characterized by an accurate wind speed time series and frequency distribution. It also provides a reliable estimate of the uncertainty based on the actual physical processes determining the current atmospheric flow rather than the climatological wind distribution.     

Erosion-corrosion failure of REAC pipes under multiphase flow

By using computational fluid dynamics (CFD) modeling and simulation, a predictive method was proposed to explore the erosion failure of reactor effluent air cooler (REAC) pipes with liner under multiphase flow. A theoretical model based on the erosion-corrosion effects of REAC on mixture turbulent flow was proposed for multiphase flow. Effects of various working conditions, liner shapes, and structures, as well as flow parameters on numerical simulations were investigated. Besides, the pipe’s erosion-corrosion rules under multiphase flow and the relationship between multiphase flow and erosion-corrosion under dangerous working conditions were studied. By CFD numerical simulations, the exact position where some typical pipes thinned and failed rapidly by erosion was found and the main factors causing erosion-corrosion failure were discussed. Finally, numerical results obtained by using the proposed method were compared with experimental results.     

A review of limit load solutions for cylinders with axial cracks and development of new solutions

Limit load solutions for axially cracked cylinders are reviewed and compared with available finite element (FE) results. New limit solutions for thick-walled cylinders with axial cracks under internal pressure are developed to overcome problems in the existing solutions. The newly developed limit load solutions are a global solution for through-wall cracks, global solutions for internal/external surface cracks and local solutions for internal/external surface cracks. The newly developed limit pressure solutions are compared with available FE data and the results show that the predictions agree well with the FE results and are generally conservative.