Thick-walled Spherical Pressure Vessels Research Articles

Elasto-plastic solution for thick-walled spherical vessels with an inner FGM layer

Purely elastic, partially and fully plastic stress states in a thick-walled spherical pressure vessel with an inner functionally graded material (FG) coating subjected to internal and external pressures are developed analytically in this paper. The modulus of elasticity and the uniaxial yield limit of the FG coating layer are considered to vary nonlinearly through the thickness. Using Tresca’s yield criterion and ideal plastic material behavior, the plastic model is established. Under pressure loading, the scenario in which the plastic deformation starts from inner surface of FG coating layer is taken into account. Having increased the pressure loading, it is assumed that the FG coating layer becomes fully plastic and the yielding commences subsequently at the inner surface of homogenous part. Essentially, the variation of FG parameters in the radial direction is properly adjusted in order to achieve the stated yielding scenario. Furthermore, axisymmetric finite element model is performed to validate the accuracy of the analytical results. It is concluded that the elastic and plastic response of the spherical pressure vessel are influenced by grading parameters and coating behavior.

Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials

This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, the effect of increasing the heat flux and pressure on the propagation of the plastic zone are investigated. Furthermore, the effect of change in Poisson’s ratio on the value of the critical material parameter is demonstrated. The present study is also validated by comparing the numerical results for thick elasto-plastic spherical shells available in the literature. To the best of the authors’ knowledge, in previous studies, exact thermo-elasto-plastic behavior of FGM thick-walled sphrical pressure vessels has not investigated.

Time-dependent thermo-elastic creep analysis of thick-walled spherical pressure vessels made of functionally graded materials

Assuming that the thermo-elastic creep response of the material is governed by Norton's law and material properties, except Poisson's ratio, are considered as a function of the radius of the spherical vessel, an analytical solution is presented for calculation of stresses and displacements of axisymmetric thick-walled spherical pressure vessels made of functionally graded materials. This analytical solution could be used to study the time and temperature dependence of stresses in spherical vessels made of functionally graded materials. Creep stresses and displacements are plotted against dimensionless radius and time for different values of the powers of the material properties.

A comparison between multi‐layered and functionally graded spherical pressure vessels

AbstractTwo analytical models are developed for elastic multi‐layered and functionally graded thick walled spherical pressure vessels subjected to uniform internal pressure. Simple and comprehensive recursive algorithms are proposed for the multi‐layered vessel. In the model for functionally graded one, the modulus of elasticity is assumed to vary in radial direction according to a power law. Stress distributions of those vessels are compared and the results are presented in graphical form. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastic analysis of heterogeneous thick-walled spherical pressure vessels with parabolic varying properties

On the basis of plane elasticity theory (PET), the displacement and stress components in a thick-walled spherical pressure vessels made of heterogeneous materials subjected to internal and external pressure is developed. The mechanical properties except the Poisson’s ratio are assumed to obey the parabolic variations throughout the thickness. Effect of material inhomogeneity on the elastic deformations and stresses is investigated. The analytical solutions and the solutions carried out through the FEM have a good agreement. The values used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements, and stresses distributions.

Residual stress analysis of autofrettaged thick-walled spherical pressure vessel

In this study, residual stress distributions in autofrettaged homogenous spherical pressure vessels subjected to different autofrettage pressures are evaluated. Results are obtained by developing an extension of variable material properties (VMP) method. The modification makes VMP method applicable for analyses of spherical vessels based on actual material behavior both in loading and unloading and considering variable Bauschinger effect. The residual stresses determined by employing finite element method are compared with VMP results and it is demonstrated that the using of simplified material models can cause significant error in estimation of hoop residual stress, especially near the inner surface of the vessel. By performing a parametric study, the optimum autofrettage pressure and corresponding autofrettage percent for creating desirable residual stress state are introduced and determined.

The Beneficial Contribution of Realistic Autofrettage to the Load-Carrying Capacity of Thick-Walled Spherical Pressure Vessels

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only a few of such studies exist for spherical ones. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a one-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elastoplastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations yield a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl–Reuss flow rule and the differential equation is solved by the explicit finite difference method. The existing 2D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The presently obtained residual stress field is then validated against three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field. The new code is applied to a series of spherical pressure vessels yielding two major conclusions. First, the process of autofrettage increases considerably the maximum safe pressure that can be applied to the vessel. This beneficial effect can also be used to reduce the vessel’s weight rather than to increase the allowable internal pressure. Second, the specific maximum safe pressure increases as the vessel becomes thinner. The present results clearly indicate that autofrettaging of spherical pressure vessels can be very advantageous in various applications.

Thermal Simulation of an Arbitrary Residual Stress Field in a Fully or Partially Autofrettaged Thick-Walled Spherical Pressure Vessel

The equivalent thermal load was previously shown to be the only feasible method by which the residual stresses due to autofrettage and its redistribution, as a result of cracking, can be implemented in a finite element (FE) analysis of a fully or partially autofrettaged thick-walled cylindrical pressure vessel. The present analysis involves developing a similar methodology for treating an autofrettaged thick-walled spherical pressure vessel. A general procedure for evaluating the equivalent temperature loading for simulating an arbitrary, analytical or numerical spherosymmetric autofrettage residual stress field in a spherical pressure vessel is developed. Once presented, the algorithm is applied to two distinct cases. In the first case, an analytical expression for the equivalent thermal loading is obtained for the ideal autofrettage stress field in a spherical shell. In the second case, the algorithm is applied to the discrete numerical values of a realistic autofrettage residual stress field incorporating the Bauschinger effect. As a result, a discrete equivalent temperature field is obtained. Furthermore, a FE analysis is performed for each of the above cases, applying the respective temperature field to the spherical vessel. The induced stress fields are evaluated for each case and then compared to the original stress. The FE results prove that the proposed procedure yields equivalent temperature fields that in turn simulate very accurately the residual stress fields for both the ideal and the realistic autofrettage cases.

Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials

In this paper, we present an accurate method to carry out elastic analysis of thick-walled spherical pressure vessels subjected to internal pressure. Two kinds of pressure vessel are considered: one consists of two homogeneous layers near the inner and outer surfaces of the vessel and one functionally graded layer in the middle; the other consists of the functionally graded material only. The effects of Young's modulus of the outer layer, and Young's modulus and geometric size of the middle layer on the deformations and stresses in the vessels consisting of the three different layers are examined. A method to obtain an almost constant circumferential stress in the vessels consisting of the functionally graded material only is investigated.

Integral Hydro-Bulge Forming of Single and Multi-Layered Spherical Pressure Vessels

The recently developed integral hydro-bulge forming (IHBF) process was utilized in the manufacturing of single and multi-layered spherical pressure and storage vessels. Single-layered spherical vessels of 1.6-mm thickness and diameters of 316.5, 634.1, and 953.2 mm were manufactured. As an alternative means of manufacturing thick-walled spherical pressure vessels, the IHBF procedure was modified and used informing double-layered composite pressure vessels with an effective thickness of 15 mm. The results showed that the modified IHBF process may successfully be applied in the manufacturing of multi-layered spherical vessels of various thicknesses and diameters. In this paper, the conventional and modified IHBF procedure will be outlined and the experimental results and analysis will be presented. Finally, areas where further work is needed are identified.

Creep of metallic thick-walled spherical vessels subject to pressure and radial thermal gradient at elevated temperatures

A theoretical analysis has been made of the distribution of stress and strain in metallic thick-walled spherical pressure vessels subject to internal and external pressures at elevated temperatures, and also to a radial thermal gradient across the wall thickness of the sphere. The analysis deals with the general case where creep strains and elastic strains occurring as a result of the applied pressure and existing thermal gradient are both of significant order. The analysis is illustrated by a specific example.