Analytical study of thermo-mechanically loaded FGM-steel/aluminum hollow spherical structures

Abstract

Particularly in recent years the behavior of spherical containers and pressure vessels of functionally graded material (FGM) has been in the focus of numerous investigations. However, in each one thereof the basic approach is subject to specific presuppositions, of course. For example, in the majority of the studies the application of an appropriate homogenization procedure is avoided by assuming independent grading indexes for each material parameter. Moreover, many investigations take only either internal pressure or heating of the structure into account, and in several cases the results are based on a numerical approach. What is more, if specific material data of a real FGM are considered at all, the available studies give numerical results specifically for a metal/ceramic-FGM. Nevertheless, nowadays also structures of metal/metal composites like steel/aluminum-FGMs are attracting more and more interest; in particular, they allow for significant weight reduction as compared to homogeneous steel devices while maintaining sufficient strength in many applications. Hence, it is the aim of the present contribution to give an in-depth discussion of spherical containers of steel/aluminum power-law graded material. The specific features of the investigation are the following ones. First, with regard to the load, both internal and outer pressure combined with elevated temperature is considered. Second, based on material data including the temperature dependence of the relevant properties of steel and aluminum (except for Poisson’s ratio), it is shown that by appropriate functional approximations analytical solutions for stresses and displacements can be found for different homogenization schemes: remarkably, this holds true not only for Voigt but also for Reuss rule, the latter leading to hypergeometric functions. Third, stresses and elastic limits – based on von Mises‘ yield criterion - are given for both full grading from steel at the inner surface to pure aluminum at the outer surface and partial grading from steel to a steel/aluminum alloy. Fourth, the achievable weight reduction in relation to the strength of the device under operating conditions is discussed thoroughly. Thus, an engineer is enabled to decide whether using a spherical steel/aluminum-FGM container may be advantageous for some applications; moreover, the results also may serve as benchmark solutions for purely numerical investigations.