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

Abstract

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.FGMs are heterogeneous materials with the elastic and thermal properties changing continuously from one surface to the other. The material is constructed by smoothly changing the volume fraction of the constituent materials. These materials are advanced, heat resisting, erosion and corrosion resistant, and have high fracture toughness [Keles and Conker, 2011]. Nowadays, they are generally used as structural components in high temperature environments [Nayebi et al., 2015]. Recently, FGMs structures are extensively applied in various fields and are of great interest for engineers and researchers. As a kind of important structural elements, in recent decades, thick spherical shells made from FGMs are applied in an increasing number of engineering structures to satisfy special functional requirements [Ye et al., 2014]. These structures are widely used in both civilian and mechanical structures [Zhao et al., 1994]. Because of the requirements of some new manufacturing methods, the thermo-elasto-plastic behavior of spherical shells is now also of interest to engineers.Durban and Baruch [1977] studied the nonlinear behavior of a thick-walled sphere under internal and external pressure. In another work, Durban [1983] obtained an exact solution for the thermo-elastic/plastic problem of a thick-walled sphere subjected to a radial temperature gradient using linear-hardening for plastic model. Vaziri [1992] presented a semi-analytical approach to elasto-plastic analysis of hollow spheres. In this pa...

A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis

“…Moreover, both steady and unsteady asymmetric thermomechanically loaded cylinders have been examined [ 44 , 53 ]. Apart from elastic analysis, a significant amount of work is being done on elastoplastic analysis of FGM structures [ 9 , 54 , 55 ]. The stress and displacement fields of FGM are studied by Nematollahi et al [ 56 ], who investigate the influence of a magnetic field in addition to thermo-mechanical loadings on rotating FGM spheres.…”

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters

“…Furthermore, cylinders subjected to steady and unstable asymmetric thermomechanical loads have been investigated [ 27 , 35 ]. In addition to elastic analysis, elastoplastic analysis of FGM designs is a subject of substantial research [ 36 , 37 ]. Nematollahi et al [ 38 ] examine the stress and displacement fields of FGM and the impact of a magnetic field and thermo-mechanical loads on rotating FGM spheres.…”