Thick-walled Spherical Vessels Research Articles

Stress analysis of rotating thick-walled nonhomogeneous sphere under thermomechanical loadings

In this work, a rotating thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure under thermal loading was analyzed within the context of three-dimensional elasticity theory. An analytical formulation was established for computing the displacement and stress fields. It has been assumed that the mechanical and thermal properties are varying through thickness of the functionally graded material (FGM) according to a power-law nonlinear expression, while Poisson's ratio is considered as constant. Based on equilibrium equation, Hooke's law, stress-strain relationship in the spheres and other theories from mechanics a second-order ordinary differential equation well-known as Navier equation is obtained that represents the thermoelastic field in hollow FGM sphere. Navier equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Different results of thermoelastic field are presented across the thickness of the sphere. The analysis of the different results reveals that stress and strain in the FGM sphere are significantly depend upon variation made in temperature profile, rotation and inhomogeneity parameter on the thermoelastic field. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.

Effect of anisotropy on the large strain creep behavior of composite thick-walled spherical vessels

Effect of anisotropy on the large strain creep behavior of composite thick-walled spherical vessels

Magneto-thermal-mechanical analysis of functionally graded thick-walled spherical vessels

Magneto-thermal-mechanical analysis of functionally graded thick-walled spherical vessels

Less is better: Coated spherical vessels over-perform their entirely graded counterparts

The thermomechanical stress analysis of thick-walled spherical vessels is considered. The thickness of the vessel is assumed to be constituted of an internal functionally graded (FG) coating and an external homogeneous layer. In the graded internal layer the property variations along the thickness are linked to the constituents volume fractions by means of widely used rules of mixture. The stress behavior of these two-layered vessels is numerically assessed within the linear theory of elasticity by employing the finite difference method. A stress analysis is carried out varying the thickness of the coating and the heterogeneity index to optimize an indicator of the equivalent stress strictly linked to the load carrying capacity. In particular, it is surprisingly found that two-layered FG vessels structurally perform better than vessels that are FG in the whole thickness, leading to improved performance and nontrivial implications on the design of the coating.

Investigation of Burst Failure of a Thick-Walled Spherical Vessel with Plastic Orthotropy under Internal and External Pressures

Investigation of Burst Failure of a Thick-Walled Spherical Vessel with Plastic Orthotropy under Internal and External Pressures

Analysis of thick-walled spherical shells subjected to external pressure: Elastoplastic and residual stress analysis

When cylindrical and spherical vessels are subjected to the internal pressure, tensile tangential stresses are created throughout the thickness, the maximum of which are located at the inner surface of the vessels. To improve the performance of these vessels, autofrettage process has been devised to produce beneficial compressive residual stresses at the inner part of such vessels. The question arises whether the process such as autofrettage can be useful for vessels such as submarines or other thick walled tanks, which are used in deep sea waters and, therefore, subjected to high external hydrostatic pressure causing both radial and tangential stresses to be compressive across the thickness. On the other hand, is the residual stresses created by unloading from an external pressure beyond elastic limit beneficial and enhance their performances? In this study, elastoplastic and residual stresses in a thick-walled spherical vessel under external hydrostatic pressure has been investigated. The material behavior is considered to be elastic-perfectly plastic. Von Misses yield criterion is used to obtain initial yield point and for the ideal elastoplastic regime analytical relations are presented. It has been found that by applying external hydrostatic pressure yielding process will start from inside of the sphere. Finally after unloading, residual tensile stresses are created at the inner part of the vessel which is useful for the vessel. The residual stresses and the condition of reverse yielding is studied in this paper.

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.

Heat-Induced, Pressure-Induced and Centrifugal-Force-Induced Exact Axisymmetric Thermo-Mechanical Analyses in a Thick-Walled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material

Heat-induced, pressure-induced, and centrifugal force-induced axisymmetric exact deformation and stresses in a thick-walled spherical vessel, a cylindrical vessel, and a uniform disc are all determined analytically at a specified constant surface temperature and at a constant angular velocity. The inner and outer pressures are both included in the formulation of annular structures made of an isotropic and homogeneous linear elastic material. Governing equations in the form of Euler-Cauchy differential equation with constant coefficients are solved and results are presented in compact forms. For discs, three different boundary conditions are taken into account to consider mechanical engineering applications. The present study is also peppered with numerical results in graphical forms.

Investigation of thermo-elasto-plastic behavior of thick-walled spherical vessels with inner functionally graded coatings

Having high corrosion and thermal resistance characteristics, Functionally Graded Materials have been found wide range of applications in engineering fields. The analytical elasto-plastic solution for spherical vessels composed of outer homogenous part and inner FG coating under combined pressure and thermal loading is presented in this paper. Furthermore, the loading conditions resulted into onset of yielding from inner radius and fully plastic vessel are obtained. Material constituents in both homogenous and FG parts are assumed to be aluminum and SiC as metal matrix and ceramic particles, respectively. Although the amount of SiC particles in the homogenous part of vessel is assumed to be constant, it is varying in the radial direction of FG part based on the power law function. The results concerning two types of vessels with harder and softer FG coatings are also compared with those from homogenous vessel. Moreover, two dimensional finite element model was applied to simulate the process while the results were considered to verify the accuracy of the analytical solution. Generally, the results demonstrate that coating and grading behavior can really affect the stress distribution and yield pattern in the homogenous vessel with an inner FG coating.

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.

Об устойчивости процесса полярно-симметричного деформирования тел из разупрочняющихся материалов

Special case of continuum mechanical systems is considered. It is believed that deforming is carried out under conditions of polar symmetry of stresses and strains. Also it is assumed that material properties are described by Hencky model with softening under nonpositivity of volume deformation. Then union curve has region decreasing to zero. Aforementioned conditions are realized in such problems as expansion of spherical cavity in softening space and deforming of thick-walled spherical vessel by equable external pressure (it maybe bathyscaphe which is gradually submerged to the deep). Based on the Lagrange formalism integral quadratic functional is investigated. This functional is increment of total potential energy in the form of Lagrangian for mentioned problems. This study allows to formulate conditions of buckling for active loading which changes quasistatically. For considered problems sets of possible deformations are obtained. These possible deformations perturb the equilibrium position and do not break kinematic constraints. Obtained sets of possible deformations allow to write criterion of buckling of deformation process in explicit form for mentioned problems. It is established that only with sufficiently developed softening zone buckling of deformation process is possible.

Design of spherical vessels under steady-state thermal loading using thermo-elasto–plastic concept

Governing equilibrium equations of thick-walled spherical vessels made of material following linear strain hardening and subjected to a steady-state radial temperature gradient using elasto–plastic analysis are derived. By considering a maximum plastic radius and using the concept of thermal autofrettage for the strengthening mechanism, the optimum wall thickness of the vessel for a given temperature gradient across the wall thickness is obtained. Finally, in the case of thermal loading on a vessel, the effect of convective heat transfer on the optimum thickness is studied and a general formula for the optimum wall thickness and design graphs for several different cases are presented.

Steady-State Creep Analysis of Thick-Walled Spherical Pressure Vessels With Varying Creep Properties

Based on basic equations of steady-state creep of spherically symmetric problems, a simple and efficient iterative method is proposed in this paper to determine creep deformations and stresses in thick-walled spherical vessels with varying creep properties subjected to internal pressure. The convergence of the proposed iterative method and the influences of varying and constant material properties on stresses and equivalent strain rate are discussed. How different material parameters involved in Norton’s law affect radial and circumferential stresses together with the equivalent strain rate in thick-walled spherical vessels under internal pressure is investigated.

Evaluation of the optimum pre-stressing pressure and wall thickness determination of thick-walled spherical vessels under internal pressure

In the present study, in the first part for a spherical vessel with known dimensions and working pressure, two methods of hoop and equivalent stress optimization across the wall thickness are employed to determine the best autofrettage pressure. In the next part for a predefined working pressure the minimum wall thickness of the vessel is calculated using two other design criteria i.e. (A) optimizing the hoop stress, and (B) assuming a suitable percent for the penetration of yielding within the wall thickness. Finally, the optimum thickness and the necessary strengthening pressure are extracted and different plots are introduced for different types of structural materials under different internal pressures.

Wall thickness optimization of thick-walled spherical vessel using thermo-elasto-plastic concept

A study of thick-walled spherical vessels under steady-state radial temperature gradients using elasto-plastic analysis is reported. By considering a maximum plastic radius and using the thermal autofrettage method for the strengthening mechanism, the optimum wall thickness of the vessel for a given temperature gradient across the vessel is obtained. Finally, in the case of thermal loading on a vessel, the effect of convective heat transfer on the optimum thickness is considered, and a general formula for the optimum thickness and design graphs for several different cases are presented.

The spherical vessel with anisotropic creep properties considering large strains

The effect of material anisotropy on creep of pressurized thick-walled spherical vessel has been discussed considering the large strain theory. It is found that the creep strain varies with varying anisotropy of the material. The results obtained for the anisotropic case have been compared with those obtained for the isotropic case and it is observed that the stress and strain distribution in the wall of the vessel is strikingly different for the two cases.

A note on plastic expansion of irradiated spherical shells

Finite plastic expansion of a thick-walled spherical vessel is studied in presence of neutron radiation. Due to irradiation the yield stress and the hardening modulus vary across the shell wall. The pressure-expansion relation is obtained in case of combined linear hardening and linear attenuation.

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.