Analysis of Temperature, Displacement, and Stress in Shafts Made of Functionally Graded Materials with Various Grading Laws

Abstract

The basic understanding of the mechanics of materials, and the development of new and advanced materials have always been a key challenge over the last few decades. Recently, material scientists and engineers have recognized the potential use of innovative materials based on economic and structural performance. Functionally graded materials (FGMs) are highperforming, multifunctional, microscopically heterogeneous advanced engineering materials made of two or more constituent phases with continuous and smooth variation of composition in any predefined direction with different material gradation laws to achieve desired superior thermo-elastic material properties. Historically, Bever and Duwez [1] and Shen and Bever [2] first proposed the concept of gradation in a material composition for composites and polymeric materials in 1972. However, their works had limited impact, probably due to the lack of suitable production methods of FGMs during that time. The first practical application of FGMs was performed by Japanese material scientists to prepare advanced ultrahigh temperature-resistant structural and functional materials in 1984, and later this was reported by Koizumi. [3] FGMs were originally developed specially for aerospace structures and fusion reactors under high operating temperature. Later, applications of FGMs have been expanded widely in engineering fields and modern technology such as high-temperature environments, heat exchanger tubes, components of chemical plants, biomedical implants, and sports.There have been few works reported in literature in the broad area of design of FGMs and analysis of structures made of FGMs. Suresh and Mortensen [4] and Miyamoto et al., [5] reported a comprehensive manufacturing process based on the selection of materials, gradient patterns, and geometry of materials to fabricate FGMs and also discussed its successful applications. Naebe and Shirvanimoghaddam, [6] Markworth et al. [7] and Gupta and Talha [8] reported an overview of material selection, fabrication methods, characterization, modeling, and analysis of FGMs. Birman and Byrd [9] conducted theoretical developments of FGMs with an emphasis of studies on heat transfer issues, stress, stability, dynamic and fracture analyses, manufacturing, design, and applications. Gasik [10] performed a micromechanic study of components made of FGMs by providing the simplest model which estimated the most accurate material properties without using any vast computational methods. Niendorf [11] obtained FG alloys using additive manufacturing techniques such as selective electron beam melting and selective laser melting processes with computer-aided design. Elishakoff et al. [12] studied the manufacturing process and estimation of effective material properties of FGMs, and performed static and dynamic modeling of FG structures with variable material parameters.

Investigating the Effect of Applying Uniform Distributed Load on the Deflection of Simply Supported Axial - Functionally Graded Beam

“…When the material properties changed in thickness-direction, several studies estimated the deflection of uniform beam using analytical and numerical methods (Chakraborty et al 2003;Gayen et al 2021;Gayen 2022;Helal 2020;Li 2008;Nie et al 2013;Şimşek et al 2013;Zainy et al 2018;Zhong and Yu 2007;Zhu and Sankar 2004). On the other hand, several researchers studied the effect of crack on static or dynamic behaviors of functionally graded beams or shafts (Gayen et al 2018;.…”

“…On the other hand, several researchers studied the effect of crack on static or dynamic behaviors of functionally graded beams or shafts (Gayen et al 2018;. For example, Gayen (2022) introduced "an exact solution for thermo-elastic behavior of radially functionally graded hollow shafts" assuming different models to describe the material properties in the radial direction such as linear law, power law and exponential law models. By using a linear strain-displacement relations and steady-state Fourier equation of heat conduction, he solved analytically thermo-elastic equations to obtain displacement and stress fields as functions of radial distances, material gradient indices, and temperature gradients.…”

Special Issue on Theoretical and Applied Mechanics of Functional Materials and Structures

“…This special issue is aimed at further contributing to the understanding of theoretical and applied mechanics of functional materials and structures. It contains 18 accepted articles, including one review, with topics related to piezoelectric [1,2] , ferromagnetic [3,4] , ferroelastic [5] , advanced polymer [6][7][8] or polymer matrix composite [9][10][11][12] , and inhomogeneous [13] or functionally graded [14][15][16][17] materials. All aspects (theoretical, computational and experimental studies) of mechanics, from state-of-the-art fundamental research to applied research and applications in emerging technologies, are included.…”