Combined Internal Pressure Research Articles

High-temperature creep rupture of low alloy ferritic steel butt-welded pipes subjected to combined internal pressure and end loadings

Constitutive equations are reviewed and presented for low alloy ferritic steels which undergo creep deformation and damage at high temperatures; and, a thermodynamic framework is provided for the deformation rate potentials used in the equations. Finite element continuum damage mechanics studies have been carried out using these constitutive equations on butt-welded low alloy ferritic steel pipes subjected to combined internal pressure and axial loads at 590 and 620 degrees C. Two dominant modes of failure have been identified: firstly, fusion boundary failure at high stresses; and, secondly, Type IV failure at low stresses. The stress level at which the switch in failure mechanism takes place has been found to be associated with the relative creep resistance and lifetimes, over a wide range of uniaxial stresses, for parent, heat affected zone, Type IV and weld materials. The equi-biaxial stress loading condition (mean diameter stress equal to the axial stress) has been confirmed to be the worst loading condition. For this condition, simple design formulae are proposed for both 590 and 620 degrees C.

Some recent developments on integrity assessment of pipes and elbows. Part I: Theoretical investigations

Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a system oriented methodology for integrity assessment of pipes and elbows, mainly for application to nuclear power plants. However, there is a scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of pipings. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part I of the paper, the theoretical investigations are discussed. Part II will cover the experimental investigations. The theoretical investigations considered the following issues: new plastic (collapse) moment equations of defect-free elbow under combined internal pressure and in-plane closing/opening moments; new plastic (collapse) moment equations of throughwall circumferentially cracked elbow, which are more accurate and closer to the test results; new ‘ η pl’ and ‘ γ’ functions of pipes and elbows with various crack configurations under different loading conditions to evaluate J– R curve from test data; and the effect of deformation on the unloading compliance of TPB specimen and throughwall circumferentially cracked pipe to measure crack growth during fracture experiment. These developments would also help to study the effect of stress triaxiality in the transfer of material J– R curve from specimen to component.

Predicting the First-ply Failure of Multilayered Composite Cylinders under Hygrothermal Loading

The present study deals with the effects of combined internal pressures, temperatures, and moistures on filament-wound multilayered composite cylinders for the plane-strain case. The analysis accounts for the failure pressure for various orientation angles under hygrothermal conditions. The Tsai-Wu criterion is used for checking the first-ply failure of layers. The chosen orientation angles are 15, 30, 45, 60, and 75.

Analytical and numerical analysis of bursting failure prediction in tube hydroforming

In this paper, bursting failure in tube hydroforming under combined internal pressure and independent axial feeding is predicted analytically and numerically. To predict the initiation of necking the Swift's criterion for diffuse plastic instability is adopted based on the Hill's general theory for the uniqueness to the boundary value problem. In addition, in order to predict fracture initiation the Cockcroft and Latham's ductile fracture criterion is introduced and evaluated from the histories of stress and strain calculated by means of finite element analysis. Finally, from the comparison with a series of tube bulge tests the prediction of the bursting failure based on the plastic instability and the ductile fracture criterion demonstrates to be reasonable so that these approaches can be extended to a wide range of practical tube hydroforming processes.

Analytical and numerical approach to prediction of forming limit in tube hydroforming

Analytical and numerical analyses of forming limit in tube hydroforming under combined internal pressure and independent axial feeding are discussed in this paper. To predict the initiation of necking, Swift's criterion for diffuse plastic instability is adopted based on Hill's general theory for the uniqueness to the boundary value problem. In addition, in order to predict fracture initiation, Oyane's ductile fracture criterion is introduced and evaluated from the histories of stress and strain calculated by means of finite element analysis. From the comparison with a series of tube bulge tests, the prediction of the bursting failure based on the plastic instability and the ductile fracture criterion demonstrates to be reasonable so that these approaches can be extended to a wide range of practical tube hydroforming processes.

Determination of Safe Operating Conditions for Non-gasketed Flange Joint under Combined Internal Pressure and Temperature

Performance of a flange joint is characterised mainly due to its ‘strength’ and ‘sealing capability’. A number of analytical and experimental studies have been conducted to study these characteristics only under internal pressure loading. However, with the advent of new technological trends for high temperature and pressure applications, an increased demand for analysis is recognised. The effect of steady state thermal loading is a well recognised problem and makes the problem more complex under combined application of internal pressure and temperature. The present design codes do not address the effects of temperature on the structural integrity and sealing ability. To investigate, joint strength and sealing capability under combined internal pressure and different steady state thermal loading, a 3D non-linear finite element analysis of non-gasketed flange joint is carried out and its behaviour is discussed. To determine the safe operating conditions or actual joint load capacity, the joint is further analyzed for different internal pressures and temperatures. In addition, effect of coefficient of thermal expansion of different flange joint component material is discussed and importance is highlighted.

Testing Systems for Ultrasonic Inspection of the Stressed State of Metal Structures and a Microcrack Locator Using Nonlinear Acoustic Effects

Results of field tests of ultrasonic checking systems for the stress-strained state of pipelines on a hydrostand are considered. Biaxial mechanical stresses induced by a combined load, i.e., internal pressure and bending, are determined. Results of testing a microcrack locator that uses nonlinear acoustic effects are presented.

Reference Stress Based Approach to Predict Failure Strength of Pipes With Local Wall Thinning Under Combined Loading

In the previous work carried out by the authors, a new method to estimate failure strength of a pipe with local wall thinning subject to either internal pressure or global bending has been proposed. The proposed method was based on the equivalent stress averaged over the minimum ligament in the locally wall thinned region, and the simple scheme to estimate the equivalent stress in the minimum ligament was proposed, based on the reference stress concept for creep stress analysis. This paper extends the new method to combined internal pressure and global bending. The proposed method is validated against FE results for various geometries of local wall thinning under combined loading. The effect of internal pressure is also investigated in the present study. Comparison of maximum moments, predicted according to the proposed method, with published full-scale pipe test data for locally wall thinned pipes under combined internal pressure and global bending, shows good agreement.

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.

Analytical approach to bursting in tube hydroforming using diffuse plastic instability

Analytical studies on onset of bursting failure in tube hydroforming under combined internal pressure and independent axial feeding are carried out. Bursting is irrecoverable phenomenon due to local instability under excessive tensile stress. In this paper, in order to predict the bursting failure diffuse plastic instability based on the Hill's quadratic plastic potential is introduced. The incremental theory of plasticity for anisotropic material is adopted and then the hydroforming limit and bursting failure diagram with respect to axial feeding and hydraulic pressure are presented. The influences of the plastic anisotropy on plastic instability, the limit stress and the bursting pressure are also investigated. Finally, the stress-based hydroforming limit diagram obtained from the above approach is verified with experimental results.

Limit load solutions for thin-walled cylinders with circumferential cracks under combined internal pressure, axial tension and bending

Limit load solutions for thin-walled cylinders with circumferential cracks under combined axial tension, bending and pressure are developed, considering the effect of pressure-induced hoop stress via the Mises yield criterion. The new solutions cover thin-walled cylinders with constant-depth or semi-elliptical surface cracks and through-wall cracks. The predictions of the new Mises-based limit load equation agree very well with elastic-perfectly plastic finite element results. However, net-section collapse equations, which ignore the hoop stress in the cylinder, tend to over-estimate the limit load when internal pressure is dominant. The solution for constant-depth cracks without crack closure is proposed for inclusion in fitness-for-purpose assessment procedures for constant-depth or semi-elliptical surface cracks and through-wall cracks.

Numerical prediction of bursting failure in tube hydroforming by the FEM considering plastic anisotropy

Bursting in tube hydroforming is an irrecoverable phenomenon due to local instability under excessive tensile stresses. In this paper, finite element analyses for the bursting failure prediction in tube hydroforming under combined internal pressure and independent axial feeding are carried out. The diffuse plastic instability of a tube is employed to numerically predict the hydroforming limit. For anisotropic tubes the incremental theory based on the Hill’s quadratic plastic potential is also adopted. Through the above theory, influences of the plastic anisotropy on the limit strain and the bursting pressure are investigated. Finally, it is concluded that the proposed approach would be able to predict the bursting failure numerically, therefore that can be extended to a wide range of practical tube hydroforming processes.

Finite element-based limit load of piping branch junctions under combined loadings

The limit load is an important input parameter in engineering defect-assessment procedures and strength design. In the present work, a total of 100 different piping branch junction models for the limit load calculation were performed under combined internal pressure and moments in use of non-linear finite element (FE) method. Three different existing accumulation rules for limit load, i.e., linear equation, parabolic equation and quadratic equation were discussed on the basis of FE results. A novel limit load solution was developed based on detailed three-dimensional FE limit analyses which accommodated the geometrical parameter influence, together with analytical solutions based on equilibrium stress fields. Finally, six experimental results were provided to justify the presented equation. According to the FE limit analysis, limit load interaction of the piping tees under combined pressure and moments has a relationship with the geometrical parameters, especially with the diameter ratio d/ D. The predicted limit loads from the presented formula are very close to the experimental data. The resulting limit load solution is given in a closed form, and thus can be easily used in practice.

Flexural behaviour of a polyvinyl chloride-lined glass-reinforced plastic composite multi-mitred pipe bend subjected to combined loads: A comparative finite element analysis and experimental case study

The flexural behaviour of a glass-reinforced plastic (GRP) multi-mitred pipe bend (MMPB) subjected to combined in-plane bending and internal pressure is presented in this paper. After construction of a polyvinyl chloride (PVC)-lined GRP MMPB, its behaviour subjected to in-plane bending, internal pressure and combined internal pressure and in-plane bending was studied. Small-and large-displacement laminated shell finite element analysis (FEA) results using ABAQUS FE were compared with experiments on an identical specimen. When modelling an MMPB subject to individually applied pressure and bending loads, comparisons exhibited good agreement between linear small-displacement FEA with experimental data. Only large-displacement FEA agreed with experiments when modelling MMPBs subject to combined pressure and bending loads. Large-displacement FEA showed geometrically non-linear behaviour closely matching the experimental trends.

Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram

Based on the mathematical formulations for predicting forming limits induced by buckling, wrinkling and bursting of free-expansion tube hydroforming, a theoretical “Process Window Diagram” (PWD) is proposed and established in this paper. The theory developed in the first part of the present work was formulated within the context of free-expansion tube hydroforming with both combined internal pressure and end feeding. The PWD is designed to provide a quick assessment of part producibility for tube hydroforming. The predicted PWD is validated against experimental results conducted for 6260-T4 60×2×320 ( mm) aluminum tubes. An optimal loading path is also proposed in the PWD with an attempt to define the ideal forming process for aluminum tube hydroforming. Parametric studies show that the PWD has a strong dependency on tube geometry, material property and process parameters. To the authors’ knowledge, this is the first attempt that a PWD is being formulated theoretically. Such a concept can be advantageous in deriving design solutions and determining optimal process parameters for tube hydroforming processes.

Behaviour of ±45° glass/epoxy filament wound composite tubes under quasi-static equal biaxial tension–compression loading: experimental results

Abstract The primary aim of this paper is to present results describing in detail the behaviour of ±45° E-glass/MY750 (GRP) tubes, of various wall thicknesses, subjected to equal biaxial tension–compression loading, generated under combined internal pressure and axial compression. The role played by the non-linear lamina shear has also been assessed by comparing various shear stress–strain curves for embedded laminae (extracted from tests on ±45° tubes subjected to circumferential: axial stress ratios SR=1:0, 1:−1 and 2.3:−1) with that of an ‘isolated’ lamina (measured from torsion of 90° tubes). Extracted shear failure strains, for embedded laminae, were more than four fold larger than those measured at ultimate failure for an ‘isolated’ lamina. Soft characteristics were observed in the embedded lamina and these were believed to be due to interaction between early matrix damage initiation (and propagation) and shear. Factors affecting the behaviour of the tubes, such as bulging, scissoring, thermal stresses and stress variation through the thickness are discussed.

Elastic–plastic fracture mechanics method for finite internal axial surface cracks in cylinders

This paper provides two types of engineering J estimation equations for cylinders with finite internal axial surface cracks under internal pressure. The first type is the so-called GE/EPRI type J estimation equation based on Ramberg–Osgood (R–O) materials. Based on detailed 3-D FE results using deformation plasticity, plastic influence functions for fully plastic J components are tabulated for practical ranges of the mean radius-to-thickness ratio, the crack depth-to-length ratio, the crack depth-to-thickness ratio, the strain hardening index for the R–O material, and the location along the semi-elliptical crack front. Based on tabulated plastic influence functions, the GE/EPRI-type J estimation equation along the crack front is proposed and validated for R–O materials. For more general application, for instance, to general stress–strain laws, the developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such a re-formulation provides a simpler equation for J, which is then further extended to combined internal pressure and bending. The proposed reference stress based J estimation equation is compared with elastic–plastic 3-D FE results using actual stress–strain data for a Type 304 stainless steel. Good agreement between the FE results and the proposed reference stress based J estimation provides confidence in the use of the proposed method for elastic–plastic fracture mechanics of pressurised piping.

축방향 관통균열 배관의 새로운 탄소성 J-적분 및 COD 계산식

This paper proposes engineering estimation equations of elastic-plastic J and COD for axial through-wall cracked pipes under internal pressure. Based on detailed 3-D FE results based on deformation plasticity. the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalized crack length, and the strain hardening. Based on these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against the 3-D FE results based on deformation plasticity. For more general application to general stress-strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic-plastic 3-D FE results using actual stress-strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimations.

내압이 작용하는 원주방향 관통균열 배관의 비선형 파괴역학 해석법

This paper provides engineering J-integral and crack opening displacement(COD) estimation equations for circumferential through-wall cracked pipes under internal pressure and under combined internal pressure and bending. Based on selected 3-D finite element calculations for the circumferential through-wall cracked pipes under internal pressure using the idealized power law materials, the elastic and plastic influence functions for fully plastic J-integral and COD solutions are found as a function of the normalized crack length and the mean radius-to-thickness ratio. These developed GE/EPRI-type solutions are then re-formulated based on the enhanced reference stress method. Such re-formulation not only provides simpler equations for J-integral and COD estimations, but also can be easily extended to combined internal pressure and bending. The proposed equations are compared with elastic-plastic finite element results using actual stress-strain data, which shows overall excellent agreement.

Elastic–plastic J and COD estimates for axial through-wall cracked pipes

This paper proposes engineering estimation equations of elastic–plastic J and crack opening displacement (COD) for axial through-wall cracked pipes under internal pressure. On the basis of detailed 3D finite element (FE) results using deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalised crack length, and the strain hardening. On the basis of these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against 3D FE results based on deformation plasticity. For more general application to general stress–strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress (RS) concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed RS based J and COD estimation equations are compared with elastic–plastic 3D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.