Thermo-Elastic Response of Thin Functionally Graded Beams Under Various Heat Loads – Theoretical Studies and Experimental Validation

Abstract

Suitability of functionally graded materials (FGMs) as structural members in modern industrial applications such as mechanical, aerospace, nuclear engineering and reactors are being explored vehemently. Considering the potential applications in thermal environment, functionally graded material structures may undergo various types of heat loads such as sudden heating or step heating, moving heat load, gradual heating, point heat load and or shock load, periodic and aperiodic thermal loads. The research related to fabrication of FGM structures and their theoretical modeling is very scarce. Researchers are exploring the manufacturing techniques to produce FGM structures with varying percentages of constituent materials. In the view of this fact, present work attempts to study the static deflection, free vibration and response to thermal loads of functionally graded beams numerically and validate them experimentally. The functionally graded SUS316-Al2O3 beams with ceramic content varying from 0 to 40% are prepared by plasma spraying technique while the functionally graded Al-Al2O3 beams with ceramic content varying from 0 to 50% are prepared using powder metallurgy process. A microstructure study is carried out using SEM to understand the distribution of various elements in the plasma sprayed and powder metallurgy process FGM beam samples. Nonlinear finite element analysis accounting the von Kármán strain is used to obtain static deflection and free vibration of a clamped free and clampsimple support functionally graded beam. The results are experimentally validated with the functionally graded SUS316-Al2O3 and Al-Al2O3 beam. The numerical results had an error of 4.05-12.91% for the deflection and 2.02 to 14.31 % for the fundamental frequency in case of SUS316-Al2O3 beam and more than 50% for deflection and fundamental frequency in case of Al-Al2O3 beam with respect to experimental results. The porosity plays an important role and governs the Young’s modulus of the sintered material which directly effects the deflection and free vibration frequency results. The commonly used and accepted theoretical models for Young’s modulus with porosity effect available in the literature were used to obtain the theoretical results. 24-31% reduction in error was observed for pure aluminium beam while the error reduced byiv 13% for Al-Al2O3 FGM beam. ANSYS 3D 20 noded structural solid element is used to study the role of shear deformation of the FGM samples on displacements and natural frequencies. The first mode of vibration obtained from numerical approach and ANSYS 3D element are much closer to experimental results. However, the nonlinear finite element FGM code provide poor results for higher modes compared to ANSYS 3D element. The nonlinear thermo-elastic analysis of thin functionally graded SUS316-Al2O3 beam accounting the von-Kármán strain and temperature dependent material properties under different heat loads and structural boundary conditions is also attempted. A two dimensional Lagrangian rectangular finite element is used to obtain the temperature distribution on the transverse plane of the beam. The significance of geometric nonlinearity is illustrated through numerical exercise. As the thermal load increases, the thermal deflection of FG beam are higher compared to linear analysis. Furthermore, the power law index also has a pronounced role. The numerical results of the static deflection of FG beam, in general, depends on power law index. Apart, the deflection produced by linear and nonlinear approach are considerably different. Thermo-elastic deflection and thermal stresses are evaluated for various structural and thermal boundary conditions. Thermo-elastic oscillations along with deflection are observed in case of beams subjected to step, concentrated line and shock heat load whereas thermoelastic deflection is observed for beams subjected to moving heat load. In case of shock heat load, irrespective of the power law index, the time for maximum temperature rise of the beam material is same, whereas the maximum elastic deflection occurs either after or before the maximum temperature rise depending on the power law index. The thermo-elastic deflection increase continuously irrespective of the power law index for line heat source. When FGM beams are subjected to moving heat source the time for maximum deflection depends on the power law index whereas the time for maximum temperature rise is independent of the power law index. In general, temperature dependency of material properties influence the amplitude of thermal oscillations. High thermal stresses are induced in beams with pin-pin and clamp-pin boundary condition as compared to hinge-hinge beam.v Thermal analysis is carried out on SUS316-Al2O3 and Al-Al2O3 FGM beam with heat source at one end. The temperature distribution is simulated using ANSYS and is validated with the experimental results. The temperature profile from ANSYS simulation results are in good agreement with experiment the with an error of 17% near the heat source while the maximum error 5.65% is observed 50mm away from heat source. Thermal vibration and induced thermal deflection studies have been carried out on the SUS316-Al2O3 FGM beam sample under clamp free boundary condition with heat applied at clamp end using electric heating coil. The response of the 2 FGM beams and pure SUS316 beam are studied at various heat loads varying from 2.925 W to 23.9 W. Theoretical model is validated with experimental results for SUS316-Al2O3 FGM beam sample-1. The experimental results are in close comparison with the theoretical results.