Thick-walled Cylindrical Pressure Vessels Research Articles

Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

Exact solutions of burst pressure for defect-free, thick-walled cylindrical pressure vessels with capped ends are developed using the flow theory of plasticity in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. The material is assumed to obey a power-law strain hardening rule, and the finite strain theory is adopted to describe large plastic deformation. On this basis, internal pressure is obtained as a complex polynomial function of effective strains on the inside and outside surfaces of the pressure vessel with the use of the Bernoulli numbers. At burst failure, the effective strains and stresses on the inside and outside surfaces are first determined, and then three flow solutions of burst pressure are obtained as a power series function of the diameter ratio (Do/Di), strain hardening exponent (n), and ultimate tensile stress (UTS). The power series solution is confirmed to agree well with the exact flow solution of burst pressure in a closed-form for each yield criterion, and the results show that the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction of burst pressure. Two sets of full-scale burst test data are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin-walled pipes and thick-walled cylindrical pressure vessels.

Thermo-elastic analysis of functionally graded porous thick-walled cylindrical pressure vessels with variable thickness subjected to mechanical and thermal loading by higher-order shear deformation theory

The aim of this research is to analyze the displacements, strains, and stresses is made in the thick-walled cylindrical pressure vessels with a variable thickness subjected to mechanical and thermal loading created of functionally graded porous materials with clamped-clamped boundary conditions. Linear profile is considered for variable thickness. Initially, the governing equations of thick-walled cylindrical shells are extracted using the energy method for a non-homogeneous functionally graded porous material (FGPM) with the power law function of mechanical and thermal properties under mechanical and uniform thermal loading. In this research, by utilizing the application of higher-order shear deformation theory (HSDT) and multi-layers method (MLM), a semi-analytical solution is provided to analyze symmetrical deformations and stresses. Due to the lack of analytical solution for differential equations of the variable thickness cylindrical shell, using the multi-layers method, the variable thickness cylindrical shell is divided into fixed thick disks. Finally, the solutions of each disk are analytically obtained and sum of them are employed for the whole cylindrical shell. The material used in the cylindrical vessel is a porous ceramic-metal, with alumina (Alumina, alpha Al2O3,99.5%) for ceramic and aluminum for metal that is a novel idea for thick-walled cylindrical pressure vessels with a variable thickness. Apart from the Poisson ratio, the characteristics of the materials are believed to change following a power law function in the radial direction of the cylindrical shell. The governing equations, which make up a system of differential equations with variable coefficients, have been resolved using MLM. The research explored how high-level approximations affect different parameters, such as radial and axial displacements, stresses, and strains. To demonstrate the efficiency and precision of the MLM and accurateness of the results, a result comparison is carried out between MLM method and MAM and FEM method. To study the mechanical behavior of the cylindrical pressure shell, some numerical findings were presented, examining the impact of different amounts of non-homogeneity (gradient index), porosity, and mechanical and thermal loads on it.

Effect of length in rotational autofrettage of long cylinders with free ends

Thick-walled cylindrical and spherical pressure vessels are often subjected to autofrettage, a process in which the vessel is loaded at the inner wall to cause a partial or complete plastic deformation emanating from the inner wall, followed by unloading. This introduces the beneficial compressive residual stresses in the vicinity of the inner wall. Depending on the type of the loading, there are five different types of autofrettage processes— hydraulic, swage, explosive, thermal and rotational. This article analyzes the rotational autofrettage, in which the cylinder to be autofrettaged is loaded by rotating it about its longitudinal axis. The centrifugal forces cause the required plastic deformation in the cylinder. Hence, when the cylinder is unloaded by bringing it to rest, compressive hoop residual stresses are introduced in the vicinity of its inner wall. When long cylinders are rotated about their axes, the distribution of axial stress changes with length of the cylinder and affects the generation of the residual stresses in the autofrettaged cylinder. This effect is investigated here by a finite element method (FEM) analysis of rotational autofrettage of cylinder made up of A723 gun steel. The FEM analysis using ABAQUS® package reveals the presence of tensile axial residual stresses in the vicinity of the inner wall of the cylinder, which increase with length. The tensile residual stresses can be mitigated by constraining the ends of the cylinder during the rotational autofrettage.

Three-Dimensional Stress Analysis for Semi-Elliptical Cracks in the Connection of Cylinder-Hemispherical Head for Thick-Walled Cylindrical Pressure Vessels

These pressure vessels are made by different type of heads. One of them is hemi-spherical head. The area of geometrical discontinuity, like the connection of the cylinder to its hemi-spherical head, are the most susceptible areas for crack initiation along their welds. So it is worthwhile to consider cracks located at this connection. The purpose of this article is to investigate the effect of variation of stress field and geometry of problem on distribution of Stress Intensity Factor (SIF) for a semi-elliptical surface crack which is located at the connection of cylinder to its hemispherical head. The three dimensional finite element analysis is performed by employing singular elements along the crack front. The ratio of crack depth to crack length (a/c) ranged from 0.3 to 1.2; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the cylinder geometry parameter of vessel ranged from 1.2 to 2. For better comparison the results are normalized and reported in non-dimensional formats. The results show that the crack configuration, vessel thickness and radius have significant influence on the stress intensity factor distribution along the crack front. Also For a fixed and the maximum value of SIF occur in the cylindrical part and approximately near the deepest point of crack; not on the deepest point of crack depth and this may be due to changing stress field in this connection. The stress intensity factors are presented in suitable curves for various geometrical configurations providing useful tool for the fracture mechanics design of cracked pressure vessels.

Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels

An analytical solution is presented to analyze the thermoelastoplastic response of a rotating thick-walled cylindrical pressure vessel made of functionally graded material (FGM). The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. The uncoupled theory of thermoelasticity is used, and the plane strain condition is assumed. The material properties except for Poisson's ratio, are assumed to vary nonlinearly in the radial direction. Elastic, partially plastic, fully plastic, and residual stress states are investigated. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the vessel. It is assumed that‏ the inner surface is exposed to an airstream and that the outer surface is exposed to a uniform heat flux. Tresca's yield criterion and its associated flow rule are used to formulate six different plastic regions for a linearly hardening‏ condition. All these stages are studied in detail. It is shown that the thermoelastoplastic stress response of a rotating FGM pressure vessel is affected significantly by the nonhomogeneity of the material and temperature gradient. The results are validated with those of other researchers for appropriate values of the system parameters and excellent agreement is observed.

Fatigue and fracture behavior of A516 steel used in thick-walled pressure vessels

In this paper, the growth of semi elliptical crack in the walls of thick walled cylindrical pressure vessels has been investigated. Considering the importance of the crack growth problem in cylindrical pressure vessels provides a numerical and experimental 3D model for the growth of fatigue crack and estimating the fatigue life of pressure vessels. Because of available geometric geometric and physical parameters, it can be predicted the problem of the fatigue life of these pressure vessels more precisely in comparison with existing standard tests which are experimental and numerical. A most common specimen of thick walled tanks, steel, is analyzed for conducting experimental tests. The mechanical properties and fatigue behavior of A516 steel have been determined experimentally. For estimating the crack growth and calculation of fatigue life, boundary element method and linear fracture mechanics equations have been used. Finally, the experimental results for fatigue crack growth were compared with numerical method, which yielded acceptable results. The overall results show a good agreement between the experimental data and the numerical results.

A Review of Theoretical and Experimental Research on Various Autofrettage Processes

Autofrettage is a metal forming technique widely incorporated for strengthening the thick-walled cylindrical and spherical pressure vessels. The technique is based on the principle of initially subjecting the cylindrical or spherical vessel to partial plastic deformation and then unloading it; as a result of which compressive residual stresses are set up. On the basis of the type of the forming load, autofrettage can be classified into hydraulic, swage, explosive, thermal, and rotational. Considerable research studies have been carried out on autofrettage with a variety of theoretical models and experimental methods. This paper presents an extensive review of various types of autofrettage processes. A wide range of theoretical models and experimental studies are described. Optimization of an autofrettage process is also discussed. Based on the review, some challenging issues and key areas for future research are identified.

Maximizing working pressure of autofrettaged three layer compound cylinders with considering Bauschinger effect and reverse yielding

One of the most effective methods for increasing capacity of thick-walled cylindrical pressure vessels is creating compressive residual stress in their walls. This can be applied by using multilayer shrink fitted or autofrettaged cylinders or combination of these methods. In this study, for a three layer compound cylinder, effects of interference fit values and their locations and autofrettage pressure were studied on the working pressure. Analytical and numerical results show that proper values and locations of the applied interferences can increase the capacity up to two times versus simple cylinder. Applying low-pressure autofrettage (less than one quarter of full autofrettage) on the compound cylinder can more increase the working pressure.

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Functionally graded materials (FGM) are advanced composite materials whose mechanical properties vary continuously from one surface to another at macro level. Thick walled annular structures are widely used in industry as nuclear reactors, long pipes used for carrying gases/oil, pressure vessels etc. Elastic analysis of FG thick-walled cylindrical and spherical pressure vessels subjected to internal pressure alone are studied. The material properties, Young' s modulus-Poisson' s ratio, are assumed to obey a graduation with the power-law function through the wall thickness. Under these assumptions, the governing equations of the vessels become a two-point boundary value problem. The analytical solution of such an equation cannot be obtained except for simple grading functions. Complementary Functions Method is performed to solve governing equation in order to obtain displacement and stress distributions depending on inhomogeneity parameters.

Instability and axisymmetric bifurcation of elastic-plastic thick-walled cylindrical pressure vessels

This article presents a theoretical and numerical investigation of the instability and bifurcation of metallic thick-walled cylindrical pressure vessels loaded by combinations of large pressure and axial force. A general bifurcation theory is developed considering elastic-plastic material behavior with non-linear isotropic hardening. The constitutive law is based on applying the von Mises yield criterion in association with the normality rule. Instability limit loads and deformations are obtained and compared with those associated with axisymmetric bifurcation. The developed theory is validated by comparing the theoretically obtained results with those obtained numerically using nonlinear finite element simulations. It is shown that axisymmetric bifurcation occurs at descending loads after the instability limit has been reached. The unstable regular deformation, which continues under descending loads prior to bifurcation, is more evident in shorter cylinders where the delay of bifurcation after instability depends on the loading combination. While in some cases, bifurcation immediately follows instability, leading to catastrophic failure, in some other cases axisymmetric bifurcation is delayed so much that it does not occur at all, even after extremely large unstable regular deformations have developed under descending loads, which provides the opportunity for further energy absorption through unstable, albeit regular plastic deformations. This investigation addresses and provides a solution for a long-standing unresolved problem. The findings provide valuable information in the safety design of extremely loaded pressure vessels.

Эффект Баушингера в толстостенных цилиндрических сосудах давления с открытым торцем

Эффект Баушингера в толстостенных цилиндрических сосудах давления с открытым торцем

Time-Dependent Thermomechanical Creep Behavior of FGM Thick Hollow Cylindrical Shells Under Non-Uniform Internal Pressure

In this paper, a theoretical solution for time-dependent thermo-elastic creep analysis of a functionally graded (FG) thick-walled cylinder based on the first-order shear deformation theory is presented. The cylinder is subjected to the non-uniform internal pressure and distributed temperature field due to steady-state heat conduction from inner to outer surface of the cylinder. Mechanical and thermal properties except Poisson’s ratio are assumed to vary along the thickness direction based on a power function. The creep constitutive model is on the basis of the Norton’s law. The effects of the temperature gradient and FG grading index on the creep stresses of the cylinder are investigated. A numerical solution using finite element method is also presented and good agreement was found. Although previous publications presented analytical solutions for creep analysis of thick-walled cylindrical pressure vessels under uniform pressure, to the best of the authors’ knowledge, so far, no analytical solution has been provided for time-dependent creep analysis of FG cylinder under non-uniform internal pressure. The results of this study are applicable for designing optimum FG thick-walled cylinder.

Thermomechanical analysis of hyperelastic thick-walled cylindrical pressure vessels, analytical solutions and FEM

In this investigation, employing the multiplicative decomposition of the deformation gradient, both analytically and numerically thermomechanical analysis of a hyperelastic thick-walled cylindrical pressure vessel are presented. The exp−exp energy density function due to its excellent agreement with experiments and including exponential terms for compressible and particularly incompressible materials is used to predict the hyperelastic response of elastomers. It is found that the radial and axial stresses are more sensitive to variation of the angular velocity than the hoop stress. Also, the variation of the axial stretch has the most significant effect on the axial and hoop stresses. Moreover, the behavior of the axial stress, for a constant axial stretch λ, depends on the value of λ whether it is larger than 1 or not, while in the inner radius of the vessel, the hoop stress has the same behavior for various values of the axial stretch. It is concluded that the positive temperature gradient leads to tensile radial stress and compressive hoop and axial stresses in the rotating cylinder, and the increase in the temperature gradient leads to increase in all stress components. The radial and hoop stresses through the wall-thickness are more sensitive to the temperature change than the thermal axial stress. Moreover, increasing the angular velocity makes the cylinder more unstable, while the stability increases with λ > 1. It is deduced that the more axial stretch in the inner radius of the pressure vessel, the more stable it is. It was shown that the comparison of the results of Finite Element and analytical method shows a good fit as a verification of the analytical solution. This analytical solution can be used either for parametric study (material or geometrical parameters) of the pressure vessels or for design and optimization that involve a large number of simulations where computational cost is a crucial parameter.

A Finite Element Method Study of Combined Hydraulic and Thermal Autofrettage Process

Autofrettage is a metal working process of inducing compressive residual stresses in the vicinity of the inner surface of a thick-walled cylindrical or spherical pressure vessel for increasing its pressure capacity, fatigue life, and stress-corrosion resistance. The hydraulic autofrettage is a class of autofrettage processes, in which the vessel is pressurized using high hydraulic pressure to cause the partial plastic deformation followed by unloading. Despite its popularity, the requirement of high pressure makes this process costly. On the other hand, the thermal autofrettage is a simple method, in which the residual stresses are set up by first maintaining a temperature difference across the thickness of the vessel and then cooling it to uniform temperature. However, the increase in the pressure carrying capacity in thermal autofrettage process is lesser than that in the hydraulic autofrettage. In the present work, a combined hydraulic and thermal autofrettage process of a thick-walled cylinder is studied using finite element method package ABAQUS® for aluminum and SS304 steel. The strain-hardening and Bauschinger effects are considered and found to play significant roles. The results show that the combined autofrettage can achieve desired increase in the pressure capacity of thick-walled cylinders with relatively small autofrettage pressure. For example, in a SS304 cylinder of wall-thickness ratio of 3, an autofrettage pressure of 150 MPa enhances the pressure capacity by 41%, but the same pressure with a 36 °C higher inner surface temperature than outer surface temperature can enhance the pressure capacity by 60%.

Time-Dependent Creep Analysis for Life Assessment of Cylindrical Vessels Using First Order Shear Deformation Theory

AbstractIn the present study, assuming that the thermo-elastic creep response of the material is governed by Norton's law, an analytical solution has been developed for the purpose of time-dependent creep response for isotropic thick-walled cylindrical pressure vessels. To study the creep response, the first-order shear deformation theory (FSDT) is applied. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT for time-dependent creep response of cylindrical pressure vessels. The novelty of the present work is that it seeks to investigate creep life of the vessels made of 304L austenitic stainless steel (304L SS) using Larson-Miller Parameter (LMP) based on FSDT. Using this analytical solution, stress rates are calculated followed by an iterative method using initial thermo-elastic stresses at zero time. When the stress rates are known, the stresses at any time are obtained and then using LMP, creep life of the vessels are investigated. The Problem is also solved, using the finite element method (FEM), the result of which are compared with those of the analytical solution and good agreement was found. It is found that the temperature gradient distribution has significant influence on the creep life of the cylinder, so that the maximum creep life is located at the outer surface of the cylinder where the minimum value of temperature is located.

Exact and Numerical Elastic Analysis for the FGM Thick-Walled Cylindrical Pressure Vessels with Exponentially-Varying Properties

Abstract Assuming exponential-varying properties in the radial direction and based on the elasticity theory, an exact closed-form analytical solution is obtained to elastic analysis of FGM thick-walled cylindrical pressure vessels in the plane strain condition. Following this, radial distribution of radial displacement, radial stress, and circumferential stress are plotted for different values of material inhomogeneity constant. The displacements and stresses distributions are compared with the solutions of the finite element method (FEM).

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.

Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials

The objective of this study is to obtain the exact elasto-plastic deformations and stresses of rotating thick-walled cylindrical pressure vessels made of functionally graded materials (FGMs) under plane strain condition. The plastic stresses and deformations are obtained, using Tresca’s yield condition, and its flow rule under the assumption of perfectly plastic material behavior. The material properties are assumed to vary according to power law functions, and the Poisson’s ratio is assumed constant. To the best of the authors’ knowledge, in previous studies in which exact elasto-plastic behavior of rotating FGM thick-walled cylindrical pressure vessels was investigated, variation of material density was ignored, while density is not constant in this type of structures. In the present work, rotation, internal and external pressure and variation of material properties are considered simultaneously.

Yield Onset of Thermo-Mechanical Loading of FGM Thick Walled Cylindrical Pressure Vessels

Yield Onset of Thermo-Mechanical Loading of FGM Thick Walled Cylindrical Pressure Vessels

Yield Onset of Thermo-Mechanical Loading of FGM Thick Walled Cylindrical Pressure Vessels

Yield Onset of Thermo-Mechanical Loading of FGM Thick Walled Cylindrical Pressure Vessels