Thick-walled Cylindrical Vessels Research Articles

Creep of autofrettaged thick-walled FGM cylindrical vessel

In this research work, the creep of thick-walled cylindrical vessels made of FGM with autofrettaged-treated was investigated using the analytical method. At different plastic depths and a variety of internal pressures for elastic modulus and yield stress constants ( n1 and n4), changes in residual creep strain rate (radial and circumferential) and final creep strain rate are investigated. The obtained results show that the circumferential stresses in the autofrettage have different values depending on the depth of the plastic. In the equivalent stress diagram, the resulting stress at the plastic points of the vessel reaches the yield stress of the FGM, and the stress decreases along the radius. If [Formula: see text] is increased from 1 to 1.8, the maximum creep strain rate decreases (for several n4, the dimensionless plastic depth is equal to 1.8). The results show that up to a dimensionless plastic depth of 1.5, the change in residual strain rate is negligible. The slope of the graphs for the dimensionless depths above 1.6 increases sharply. A comparison of the maximum circumferential stress as a function of plastic depth for the present work and the study by Darijani shows very good agreement between the two studies.

Burst Pressure Solutions of Thin and Thick-Walled Cylindrical Vessels

Abstract Pressure vessels (PVs) are widely used in the energy industry. Accurate burst pressure is critical to structural design and safe operation for both thin and thick-walled PVs. The traditional strength theories utilized a single-parameter material property, such as the yield stress or the ultimate tensile stress (UTS) to develop failure models for determining the yield or ultimate pressure carrying capacity in the PV design. The UTS-based Barlow formula is a typical burst pressure model developed from the Tresca strength theory that provides the basis for developing regulation rules and failure models for different industry design codes, such as ASME BPVC, ASME B31.3, and ASME B31G, among others. In order to reduce the conservatism of the Tresca strength model, ASME BPVC recently adapted failure models developed from the von Mises strength theory for the PV design and analysis. It has been commonly accepted that the burst pressure of pipelines depends on the UTS and strain hardening exponent, n, of the pipeline steel. An average shear stress yield theory was thus developed, and the Zhu-Leis solution of burst pressure was obtained as a function of UTS and n for thin-walled line pipes. Experiments showed that the Zhu-Leis solution provides an accurate, reliable prediction of burst pressure for defect-free thin-walled pipes. In order to extend the Zhu–Leis solution to thick-walled cylindrical PVs, this paper defined three new flow stresses, modified the traditional strength theories, and obtained three new burst pressure solutions that are valid for both thin and thick-walled cylindrical vessels. The proposed flow stresses are able to describe the tensile strength and the plastic flow response of PVs for a strain hardening steel. The associated strength theories were then developed in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. From these new strength theories, three burst pressure solutions were obtained for thick-walled cylinders, where the von Mises solution is an upper bound prediction, the Tresca solution is a lower bound prediction, and the Zhu-Leis solution is an intermediate prediction of burst pressure for thick-walled cylinders. Finally, the proposed burst pressure solutions were evaluated and validated by two large datasets of full-scale burst tests for thick-walled tubes and for thin-walled pipes.

Weight function procedure for reduced order fracture analysis of arbitrary flaws in cylindrical pressure vessels

Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. This approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.

Investigating the Effect of Internal Pressure and Thickness of Thick-Walled Cylindrical Vessels on the Ratcheting Strains under Compressive Cycling Loading Using the Quasi-Creep Method

Thick-walled vessels have many applications in military, chemical, and aerospace industries and also in nuclear facilities. Increasing the internal pressure inside these vessels can take some of the layers of the vessel into the plastic zone. If this happens several times, we will see the accumulation of plastic strains called ratcheting. This paper assumes that the thick-walled vessel is subjected to a cyclic internal pressure between zero and a maximum value. In order to analyze this phenomenon, first, we present the quasi-creep method, and then we validate this method using the finite element Abaqus Software based on the combined hardening model. Then we employ this method to evaluate the effect of internal pressure and thickness of the vessel on the amount of ratcheting strains in different cycles. In the end, the results of this research and the accuracy and speed of the quasi-creep method are stated.

Investigation of displacement and stress fields in pressurized thick-walled FGM cylinder under uniform magnetic field

In this paper, an analytical solution is presented for computing mechanical displacements and stresses in a thick-walled cylindrical pressurized vessel made of functionally graded materials (FGM). The pressure vessel is subject to axisymmetric mechanical loading within a uniform magnetic field. The analytical model of the pressurized vessel was constructed, where the radial continuous varying of elastic modulus and permeability along the thickness was assumed. It has been assumed that the elastic modulus and permeability are varying through thickness of the FG material according to a nonlinear general distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, was derived from the mechanical equilibrium equation with the consideration of the Lorentz force resulting from the magnetic field. The distributions of the displacement and stresses were determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the magnetic field, non-homogeneity parameter and internal pressure on the magneto-elastic response of the functionally graded cylindrical vessel. Thus, these parameters have remarkable effects on the distributions of radial displacement and radial and circumferential stresses.

Análisis dimensional del comportamiento hiperelástico del tubo arterial bajo un estado multiaxial de tensiones

A study of the behavior of the arterial blood vessel was performed by resorting to the mechanics of hyperelastic solids, for this is a currently well-established means to understanding a number of phenomena of concern among physicians and biomedical engineers. As regards this organ, it was modelled as a thick walled cylindrical vessel where the material energy function comprised the characterization of microstructural features of the tissue, such as anisotropy and fiber orientation dispersion. The static equilibrium problem for implementing this model represented the adventitia and media layers of the arterial wall, while its solution was simple thanks to assuming an axisymmetric deformation pattern. It is found that the fiber orientation factor along with the other dimensionless quantities of the same order of magnitude had the most influence on the arterial blood vessel radial stiffness. These results were processed using dimensional groups, thereby facilitating interpretation in the light of the many parameters that the whole model considers.

A comparative study of thermal and hydraulic autofrettage

Thermal autofrettage is a potential process to generate beneficial compressive residual stresses at and around the inner wall of a thickwalled cylinder for increasing its pressure carrying capacity. Due to its simplicity and inexpensive arrangement, it can compete with the conventional hydraulic autofrettage process. In this work, a comparative study of the thermal autofrettage and the hydraulic autofrettage is carried out. As the thermal autofrettage does not require hydraulic power pack, the process is more economical than the hydraulic autofrettage. The thermal autofrettage process is also studied for the thick-walled cylindrical vessels subjected to high thermal gradient with or without pressure and is compared with the hydraulic autofrettage. Comparison shows that for cylinders subjected to high thermal gradient without pressure, the thermal autofrettage is superior to the hydraulic autofrettage.

Prediction of Yielding Onset and Spread Pattern in Functionally Graded Thick-Walled Cylindrical Vessel Subjected to Thermo-Mechanical Loading

This research is concerned with the prediction of yield behavior of functionally graded (FG) thick-walled cylindrical pressure vessel under the combination of internal pressure and temperature gradient. In order to obtain the yield onset location and plastic growth zone, we applied Von-Mises yield criteria besides Prantle-Reuss flow rule in plane strain condition. This approach results in defining new formulation in order to determine the elastic limit pressure. In such cases as internal pressure with /without thermal gradient, the start and the spread of plastic zone are predicted. Moreover, the distributions of stress components are obtained along with the radial direction in elastic and plastic regions. The analysis results show that both FG power index and temperature gradient influence the commencement of plastic deformation. Using the appropriate choice of the FG parameters and the specified thermal gradient, the plastic zone can commence simultaneously from inside, outside or intermediate radius.

The Bauschinger Effect's Influence on the Stress Intensity Factors of a Semi-Elliptical Crack Emanating From an Erosion at the Bore of a Fully Autofrettaged Pressurized Cylinder

The benefits of autofrettage for thick-walled cylindrical vessels as a means of improving the vessel's durability and sustainability have been addressed in the published literature. However, the presence of the Bauschinger effect (BE) complicates the overall effect of autofrettage, especially when complex three-dimensional crack geometries emanating from erosions at the cylinder bore are considered. In this paper, the BE's impact on the stress intensity factors (SIFs) on such cracks is investigated. The effect of various erosion geometrical configurations on the mode I SIF distribution along the front of a semi-elliptical crack, emanating from the deepest line of the erosion surface (DLES) at the bore of an autofrettaged, pressurized thick-walled cylinder of outer-to-inner radius ratio, Ro/Ri = 2, is investigated. Both autofrettage with BE (BEDA) and Hill's ideal autofrettage residual stress field (BEIA) are considered and simulated by an equivalent thermal load. The SIFs are determined for the semi-elliptical cracks of various crack depths to wall thickness ratio, a/t = 0.05–0.25, and ellipticities, a/c, ranging from 0.5 to 1.5, emanating from the DLES via Ansys software and the nodal displacement method. Three groups of erosion geometries are considered: (a) arc erosions of constant relative depth, d/t, equal to 5% and with relative radii of curvature, r′/t, between 5% and 30%; (b) semi-elliptic erosions of constant relative depth, d/t, of 5% with erosion ellipticity, d/h, varying from 0.3 to 2.0; and (c) semicircular erosions of relative depth, d/t, between 1% and 10% of the wall thickness. KIP, the SIF due to pressurization, is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. It is found that the absolute value of KIA, the SIF due to autofrettage, is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, the combined SIFs of deep cracks are found to be significantly enhanced by the presence of autofrettage and might result in a shortening of the vessel's fatigue life by up to an order of magnitude. Counteracting this, the combined SIFs are found to be significantly higher for BEDA cases than for BEIA cases. Therefore, the vessel's fatigue life can be profoundly influenced by the presence of the BE.

Steady-State Creep Deformations and Stresses in FGM Rotating Thick Cylindrical Pressure Vessels

AbstractIn the present study, a closed-form analytical solution for the steady-state creep stresses of rotating thick cylindrical pressure vessels made of functionally graded materials (FGMs) is carried out. Norton's law governs the creep response of the material. Exact solutions for stresses and strain rate are obtained under the plane strain condition. How different material parameters involved in Norton's law affect radial and circumferential stresses together with the equivalent strain rate in rotating thick-walled cylindrical vessels under internal pressure is investigated. The result obtained shows that the property of FGMs has a significant influence on the equivalent creep strain rate and stresses distributions along the radial direction.

A Study of the Combined Effects of Erosions, Cracks and Partial Autofrettage on the Stress Intensity Factors of a Thick Walled Pressurized Cylinder

For the investigation of cracked problems in thick-walled pressurized cylindrical vessels, the displacement-based finite element method has become one of the main computational tools to extract stress intensity results for their fatigue life predictions. The process of autofrettage, practically from the partial autofrettage level of 30% to full autofrettage level of 100%, is known to introduce favorable compressive residual hoop stresses at the cylinder bore in order to increase its service life. In order to extract the fatigue life, stress intensity factors (SIFs) need to be obtained a priori. The necessity for determining SIFs and their practical importance are well understood. However, it is usually not a trivial task to obtain the SIFs required since the SIFs largely depend on not only the external loading scenarios, but also the geometrical configurations of the cylinder. Our recent work has shown that the Bauschinger effect (BE) may come into play and affect the effective SIFs significantly for an eroded fully autofrettaged thick-walled cylinder. In this study, we further investigate the SIFs for the Bauschinger effect dependent autofrettage (BEDA) and the Bauschinger effect independent autofrettage (BEIA) at various autofrettage levels. The crack is considered to emanate from the erosion's deepest point in a multiply eroded cylinder. The commercial finite element package, ANSYS v12, was employed to perform the necessary analysis. A two-dimensional model, analogous to the authors' previous studies, has been adopted for this investigation. The residual stress field of autofrettage process, based on von Mises yield criterion, is simulated by thermal loading. The combined SIFs are evaluated for a variety of relative crack lengths with cracks emanating from the tip of erosions with various geometrical configurations and span angles. The effective SIFs for relatively short cracks are found to be increased by the presence of the erosion and further increased due to the BE at the same autofrettage level, which may result in a significant decrease in the vessel's fatigue life. Deep cracks are found to be almost unaffected by the erosion, but may be considerably affected by BE as well as by the level of partial autofrettage.

Finite Deformation Thermoelasticity of Thick-Walled Cylindrical Vessels Based on the Multiplicative Decomposition of Deformation Gradient

In this article, a brief review of the multiplicative decomposition of the deformation gradient into mechanical and thermal parts is given up. To model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the logarithmic strain measure is considered for implementation in the governing equations of finite deformation thermoelasticity. Using this constitutive law and assuming the so-called mechanically incompressible material, the thermoelastic stress distribution in the thick-walled cylindrical vessels under steady-state thermal loading and internal/external pressures is determined analytically in the cases of small and finite deformations.

Shakedown of Thick Cylinders With Radial Openings Under Thermomechanical Loadings

Shakedown and ratcheting behaviors of thick-walled cylindrical vessels with radial openings subjected to cyclic thermomechanical loadings are investigated by the inelastic finite element analysis. Different shakedown and ratcheting responses are described in the modified Bree diagram considering the influences of various opening radius ratios ri/Ri, thickness ratios Ro/Ri as well as different axial stress states. Then, two simplified shakedown assessment methods of perforated cylinders are discussed. The results indicate that elastic/plasticity shakedown boundary reduces significantly owing to the presence of a radial opening while varies slightly with the opening radius, which can be defined as 1.2 approximately in the modified Bree diagram for conservative elastic/plasticity shakedown evaluation. Moreover, shakedown/ratcheting boundary decreases significantly with increasing the opening radius or decreasing the axial stress. Finally, comparing with the calculated results, the two simplified methods are verified to be accurate and intuitive to estimate the shakedown behaviors of perforated cylinders under various thickness and opening radius conditions.

Design of thick-walled cylindrical vessels under internal pressure based on elasto-plastic approach

By considering the Bauschinger effect and the yield criterion of Tresca, an exact elasto-plastic analytical solution for a thick-walled cylindrical vessel made of elastic linear-hardening material is derived. Having the working pressure and geometric dimensions of the vessel, the distribution of the hoop and equivalent stresses are optimized in the way that the distribution of stresses becomes smooth in the vessel wall. Based on two optimizing methods of the hoop and equivalent stresses, the best autofrettage pressure is determined. It is shown that this pressure is more than the working pressure and depends on the three following variables: Bauschinger effect, working pressure and geometric dimensions. In the next stage, the main task is to determine the wall thickness having the working pressure. To do this, two different design criteria namely; (i) optimizing the hoop stress distribution and (ii) assuming a suitable percent of yielding in the wall thickness are used. In the last step, for different types of structural materials under different working pressures, a number of different plots are given for the ratio of outer to inner radii and the best autofrettage pressure. It is shown that the design of vessels based on the elasto-plastic methods is much more economic than elastic methods. Also, it is seen that for a non-hardening material, the design of vessel is only done for the working pressure less than unit value.

Stress Analysis of Functionally Graded Thick-Walled Cylindrical Vessels

In this paper, a simple and accurate method is presented to determine deformations and stresses in thick-walled cylindrical vessels made of functionally graded materials under internal pressure and uniform temperature. The governing equation with the consideration of varying Young’s modulus and thermal expansion coefficient along the radial direction is derived from the basic equations of axisymmetric plane strain problems in elasticity. The comparison with the corresponding numerical solution indicates that the proposed solution has excellent convergence and accuracy. The effects of the coefficients, which affect Young’s modulus and the thermal expansion coefficient, on the deformation and stresses in thick-walled cylindrical vessels are investigated.

Unified Solutions to the Limit Load of Thick-Walled Vessels

Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter b, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion (b=0) give the lower bound of the plastic limit load, while those according to the twin shear strength criterion (b=1) are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter (b≈0.5). Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.

Creep deformations and stresses in thick-walled cylindrical vessels of functionally graded materials subjected to internal pressure

Steady-state creep of thick-walled cylindrical vessels made of functionally graded materials subjected to internal pressure is investigated in this paper. Taking material parameters involved in Norton’s law to be the functions of the radial coordinate, a simple and accurate method is developed from the strain rate–stress relations, Norton’s law, deformation compatibility condition and equilibrium equation of axisymmetric, plane strain problems. The proposed approach is employed to calculate stresses and creep strain rates in the thick-walled cylindrical vessels. How variations of material parameters along the radial direction affect the stresses in the vessels is examined.

The Effect of Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Vessel

The distribution of the mode I stress intensity factor (SIF), resulting from autofrettage, along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of an overstrained thick-walled cylinder is studied. The three-dimensional analysis is based on the “two-crack depth level model” previously proposed and is performed via the finite element method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of KIA, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing n=n1+n2=8-128 cracks, a wide range of crack depth-to-wall thickness ratios, a1∕t=0.01-0.4, and various crack ellipticities, a1∕c1=0.3-1.5, are evaluated for a cylinder of radii ratio Ro∕Ri=2. The results clearly indicate that unevenness, as reflected in KIA distribution, depends on all three parameters (i.e., the number of cracks in the array, cracks’ depth, and cracks’ ellipticity). The “interaction range” for the different combinations of crack arrays and crack depths is then evaluated. The range of influence between adjacent cracks on the maximal SIF, KAmax, is found to be dependent on the density of the array, as reflected in the intercrack aspect ratio, as well as on the cracks’ ellipticity.

Experimental strain analysis of the high pressure strain gauge pressuretransducer and verification by using a finite element method

The finite element method (FEM) was used in this study for theanalysis of the strain distribution of a strain gauge pressure transducer forhydrostatic pressure measurements up to 150 MPa. The pressure transducer, whichwe investigated, on the basis of `thick-walled cylindrical vessel' theory hasa free steel active element. Pressure is applied to the inside and both openends of this active element. The symmetrical shape of the transducer and allthe design parameters of the active element were selected in such a way as toensure that a symmetrical stress and strain distribution was obtained even atthe maximum working pressure of the transducer. The FEM analysis was conductedby investigating one half of the element in three dimensions. This paperpresents the FEM output strain values for the area where the strain gaugeswere bonded. The validity of those values was established by comparing themwith the results obtained from the strain gauge measurements. The relativedifference between the two sets of values determined to be lower than 13% ofthe full scale. The two kinds of measuring elements were made of two differentmaterials; AISI 4340 steel and Invar steel, which work in the hydraulic gaugepressure ranges of up to 150 and 100 MPa respectively. The transducers werecalibrated using piston pressure balance. The metrological specifications of atotal of eight specimens were evaluated. Although the scope of the study isonly an application of the FEM, this evaluation also suggests that this typeof transducer can be used with an estimated uncertainty of up to 0.1% of thefull scale. However, this uncertainty can be improved by a small modificationin design, to reduce the reproducibility and hysteresis errors of the device,which are the main parameters in the evaluation of the uncertainty. Theresults presented in this paper will be helpful for practical static pressuremeasurements as well as for the appropriate design of this kind of pressuretransducer using the FEM.

Fiber Orientation in Composite Structures for Optimal Resistance to Creep Failure

The objective of this research is to provide an approximate but reliable method of assessing various fiber configurations in a metallic composite structure with the intent of achieving optimal resistance to creep failure. The approximate method, envisioned as an early design tool, is based on an upper bound on the creep rupture time and an associated representative failure stress. The latter is evaluated and compared for different fiber configurations, thereby identifying the configuration with optimal creep rupture resistance. A substantial saving in computational time is realized by avoiding a detailed analysis of the actual failure process. Application is made to reinforced thinand thick-walled cylindrical vessels under interior pressure.