Investigating the Effect of Cyclic Thermal Load Frequency on the Thermo-elastic Stress Distribution in FGM Spheres Using Semi-analytical Method

Functionally Graded (FG) materials are inhomogeneous composites, usually made from a mixture of metals and ceramics, providing the specific benefits of both the constituents. These materials have some unique properties such as high strength under thermomechanical stresses, lack of stress concentration and delamination. Present study is concerned with determining the alternating temperature, stress and strain fields in an FG hollow sphere subjected to cyclic thermal loading and internal pressure. The inner surface of the sphere is considered to be made of alumina grading with power law up to the outer surface made from aluminum. Duhamel's principle is utilized to calculate the temperature field in the sphere since it is appropriate in analyzing the behavior of structures with alternating boundary conditions. By considering a quasi-static condition, the governing differential equation is solved by using discretization method. The results are compared with those obtained using finite element method and good agreement is observed. The effect of frequency of the thermal load on the amplitude of the stresses is also investigated. The results show that, there is a critical range of the frequency in which the amplitude of stresses become maximum and beyond this range, the stress and strain domain vanish. It has been shown that by increasing the thickness of the sphere, the critical frequency decreases significantly.