Computational Techniques for The Evaluation of Inhomogeneity Parameters on Transient Conduction in Functionally Graded Layers

Year 2019, Volume: 11 Issue: 3, 428 - 444, 13.11.2019

Mehmet Nurullah Balci , Bariş Sabuncuoğlu

https://doi.org/10.24107/ijeas.621160

Abstract

Transient thermal response of a functionally graded material (FGM) layer is considered and individual effects of inhomogeneity parameters on temperature distribution are examined. Transient conduction equation has variable coefficients controlling conductivity, mass density and specific heat capacitance due to the material property variation along the thickness of the graded layer. In order to solve the time dependent conduction equation for the unknown interior temperatures, computational methods are employed based on finite difference and finite element methods. Governing partial differential equation is discretized in space and time grids and computer codes are developed to implement explicit and implicit schemes. Results of explicit and implicit schemes are compared with those found by finite element method. A very good agreement is achieved for the applied boundary and initial conditions. Parametric study reveals the individual influences of various inhomogeneity parameters of FGM upon time dependent temperature distribution of a functionally graded layer. The results of the direct comparison study indicate that inhomogeneity parameters for specific heat and mass density have greater influence on temperature distribution than that for thermal conductivity.

Keywords

Functionally Graded Layer, Transient Heat Conduction, Computational Methods, Material Inhomogeneity

References

• Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G., Functionally Graded Materials Design, Processing and Applications. Springer Science & Business Media, New York 1999.
• Naebe, M., Shirvanimoghaddam, K., Functionally graded materials: A review of fabrication and properties. Applied Materials Today, 5, 223-245, 2016.
• Bellur-Ramaswamy, R.S., Haber, R., Sobh, N.A., Tortorelli, D.A., Modelling and process optimization for functionally graded materials. International Journal for Numerical Methods in Engineering, 62, 186-204, 2005.
• Fukui, Y., Takashima, K., Ponton, C.B., Measurement of Young’s modulus and internal friction of an in situ Al-Al3Ni functionally gradient material. Journal of Materials Science, 29(9), 2281-2288, 1994.
• Abbas, M.R., Uday, M.B., Noor, A.M., Ahmad, N., Rajoo, S., Microstructural evaluation of a slurry based Ni/YSZ thermal barrier coating for automotive turbocharger turbine application. Materals & Design, 109, 47-56, 2016.
• Dhineshkumar, S.R., Duraiselvam, M., Natarajan, S., Panwar, S.S., Jena, T., Khan, M.A., Enhancement of strain tolerance of functionally graded LaTi2Al9O19 thermal barrier coating through ultra-short pulsed based laser texturing. Surface & Coatings Technology, 304, 263-271, 2016.
• Naga, S.M., Awaad, M., El-Maghraby, H.F., Hassan, A.M., Elhoriny, M., Killinger, A., Gadow, R., Effect of La2Zr2O7 coat on the hot corrosion of multi-layer thermal barrier coatings. Materials & Design, 102, 1-7, 2016.
• Daikh, A.A., Megueni, A., Thermal behavior of Functionally Graded Materials. In: 5th International Conference on Welding Non Destructive Testing and Materials and Alloys Industry, Oran, Algeria, 2016.
• Kuroda, Y., Kusaka, K., Moro, A., Togawa, M., Evaluation tests of ZrO2/Ni functionally gradient materials for regeneratively cooled thrust engine applications. Holt J.B., Koizumi M., Hirai T., Munir Z.A. (Eds.), Ceramic Transactions, 34, Functionally Gradient Materials, American Ceramic Society, Westerville, Ohio, 289-296, 1993.
• Reddy, J.N., Chin, C.D., Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, 21(6), 593-626, 1998.
• Yang, Y., Temperature Dependent Thermoelastic Analysis of Multi-dimensional Functionally Graded Materials, Ph.D. Dissertation, University of Pittsburgh, USA, 2015.
• Hosseini, S.M., Akhlaghi, M., Shakeri, M., Transient heat conduction in a functionally graded thick hollow cylinders by analytical method. Heat and Mass Transfer, 43, 669-675, 2007.
• Bahtui, A., Eslami, M.R., Generalized coupled thermoelasticity of functionally graded cylindrical shells. International Journal for Numerical Methods in Engineering, 69, 676-697, 2007.
• Zhao, X., Liew, K.M., An element-free analysis of mechanical and thermal buckling of functionally graded conical shell panels. International Journal for Numerical Methods in Engineering, 86, 269-285, 2011.
• Sharma, R., Jadon, V.K., Singh, B., Analysis of temperature field in a composite functionally graded material plate by finite element method. International Journal of Advances in Materials Science and Engineering (IJAMSE), 4(4), 41-47, 2015.
• Cho, J.R., Oden, J.T., Functionally graded material: a parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme. Computer Methods in Applied Mechanics and Engineering, 188, 17-38, 2000.
• Nemat-Alla, M., Reduction of thermal stresses by composition optimization of two-dimensional functionally graded materials. Acta Mechanica, 208, 147-161, 2009.
• Sladdek, J., Sladdek, V., Zhang, C., Transient heat conduction analysis in a functionally graded materials by the meshless local boundary integral equation method. Computational Materials Science, 28, 494-504, 2003.
• Sadowski, T., Nakonieczny, K., Thermal shock response of FGM cylindrical plates with various grading patterns. Computational Materials Science, 43: 171-178, 2008.
• Nakonieczny, K., Sadowski, T., Modelling of ‘thermal shocks’ in composite materials using meshfree FEM. Computational Materials Science, 44, 1307-1311, 2009.
• Li, G., Guo, S., Zhang, J., Li, Y., Han, L., Transient heat conduction analysis of functionally graded materials by a multiple reciprocity boundary face method. Engineering Analysis with Boundary Elements, 60, 81-88, 2015.
• Li, M., Wen, P.H., Finite block method for transient heat conduction analysis in functionally graded media. International Journal for Numerical Methods in Engineering, 99, 372-390, 2014.
• Olatunji-Ojo, A.O., Boetcher, S., Cundari, T.R., Thermal conduction analysis of layered functionally graded materials. Computational Materials Science, 54, 329-335, 2012.
• Jin, Z., Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution. Materials, 4(12), 2108-2118, 2011.
• Chan, Y-S., Paulino, G.H., Fannjiang, A.C., Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials – Part II: Crack Parallel to the Material Gradation. ASME Journal of Applied Mechanics, 75(0611015), 1-11, 2008.
• Balci, M.N., Dag, S., Yildirim, B., Subsurface stresses in graded coatings subjected to frictional contact with heat generation. Journal of Thermal Stresses, 40(4), 517-534, 2017.
• Chen, P., Chen, S., Thermo-mechanical contact behavior of a finite graded layer under a sliding punch with heat generation. International Journal of Solids and Structures, 50, 1108-1119, 2013.
• Fujimoto, T., Noda, N., Influence of the compositional profile of functionally graded material on the crack path under thermal shock. Journal of the American Ceramic Society, 84(7), 1480-1486, 2001.
• ANSYS, ANSYS Basic Analysis Procedures Guide, release 15.1, ANSYS Inc., Canonsburg, PA, USA, 2015.
• Burlayenko, V.N., Altenbach, H., Sadowski, T., Dimitrova, S.D., Bhaskar, A., Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements. Applied Mathematical Modelling, 45,422-438, 2017.
• Fuchiyama, T., Noda, N. Analysis of thermal stresses in a plate of functionally gradient material. JSAE Review, 16, 373-387, 1995.
• Anlas, G., Santare, N.H., Lambros, J., Numerical calculation of stress intensity factors in a functionally graded materials. International Journal of Fracture, 104, 131-143, 2000.