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Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis

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Abstract

This paper presents a method for optimisation of the material composition of functionally graded materials (FGMs) for thermal stress relaxation. This method consists of a multiscale thermoelastic analysis and a genetic algorithm. In the presented method, location-dependent unit cells representing the microstructures of two-phase FGMs are created using morphology description functions, and the homogenised material properties and microscale thermal stresses are computed using the asymptotic expansion homogenisation method. Thermal stress relaxation effects at the microscale in the FGMs are quantitatively evaluated, being reflected for the optimisation computation of the material composition. Numerical calculations are performed for a functionally graded infinite plate subjected to prescribed surface temperatures, and it is demonstrated that the optimisation with the knowledge of specific microstresses in FGMs results in not only a different trend of material composition distribution but also a different critical location for material failure from those obtained by conventional optimisation without the knowledge of the microstresses.

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References

  1. Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G.: Functionally Graded Materials: Design, Processing and Applications. Kluwer, Boston (1999)

    Book  Google Scholar 

  2. Watanabe, R., Takahashi, H., Tamura, M., Shiota, K., Yoshida, T., Kurino, T. (eds): Functionally Gradient Materials. Kogyo Chosakai, Tokyo (1993)

    Google Scholar 

  3. Wang M., Pan N.: Predictions of effective physical properties of complex multiphase materials. Mater. Sci. Eng. R Rep. 63, 1–30 (2008)

    Article  Google Scholar 

  4. Chen B., Tong L.: Thermomechanically coupled sensitivity analysis and design optimization of functionally graded materials. Comput. Methods Appl. Mech. Eng. 194, 1891–1911 (2005)

    Article  MATH  Google Scholar 

  5. Bobaru F.: Designing optimal volume fractions for functionally graded materials with temperature-dependent material properties. Trans. ASME J. Appl. Mech. 74, 861–874 (2007)

    Article  Google Scholar 

  6. Vel S.S., Pelletier J.L.: Multi-objective optimization of functionally graded thick shells for thermal loading. Compos. Struct. 81, 386–400 (2007)

    Article  Google Scholar 

  7. Boussaa D.: Optimization of temperature-dependent functionally graded material bodies. Comput. Methods Appl. Mech. Eng. 198, 2827–2838 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goupee A.J., Vel S.S.: Transient multiscale thermoelastic analysis of functionally graded materials. Compos. Struct. 92, 1372–1390 (2010)

    Article  Google Scholar 

  9. Pindera M.J., Aboudi J., Arnold S.M.: Thermomechanical analysis of functionally graded thermal barrier coatings with different microstructural scales. J. Am. Ceram. Soc. 81, 1525–1536 (1998)

    Article  Google Scholar 

  10. Dao M., Gu P., Maewal A., Asaro R.J.: A micromechanical study of residual stresses in functionally graded materials. Acta Mater. 45, 3265–3276 (1997)

    Article  Google Scholar 

  11. Tsukamoto H.: Analytical method of inelastic thermal stresses in a functionally graded material plate by a combination of micro- and macromechanical approaches. Compos. B Eng. 34, 561–568 (2003)

    Article  Google Scholar 

  12. Khan K.A., Muliana A.H.: A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials. Compos. B Eng. 40, 511–521 (2009)

    Article  Google Scholar 

  13. Cannillo V., Montorsi M., Siligardi C., Sola A., de Portu G., Micele L., Pezzotti G.: Microscale computational simulation and experimental measurement of thermal residual stresses in glass-alumina functionally graded materials. J. Eur. Ceram. Soc. 26, 1411–1419 (2006)

    Article  Google Scholar 

  14. Vena P.: Thermal residual stresses in graded ceramic composites: a microscopic computational model versus homogenized models. Meccanica 40, 163–179 (2005)

    Article  MATH  Google Scholar 

  15. Terada K., Hori M., Kyoya T., Kikuchi N.: Simulation of the multi-scale convergence in computational homogenization approaches. Int. J. Solid Struct. 37, 2285–2311 (2000)

    Article  MATH  Google Scholar 

  16. Takano N., Zako M.: Integrated design of graded microstructures of heterogeneous materials. Arch. Appl. Mech. 70, 585–596 (2000)

    Article  MATH  Google Scholar 

  17. Ootao Y., Tanigawa Y., Ishimaru O.: Optimization of material composition of functionally graded plate for thermal stress relaxation using a genetic algorithm. J. Therm. Stress. 23, 257–271 (2000)

    Article  Google Scholar 

  18. Xianfan C., Shutian L.: Topology description function based method for material design. Acta Mechanica Solida Sinica 19, 95–102 (2006)

    Google Scholar 

  19. Goupee A.J., Vel S.S.: Multiscale thermoelastic analysis of random heterogeneous materials: Part II: Direct micromechanical failure analysis and multiscale simulations. Comput. Mater. Sci. 48, 39–53 (2010)

    Article  Google Scholar 

  20. Vel S.S., Goupee A.J.: Multiscale thermoelastic analysis of random heterogeneous materials: Part I: Microstructure characterization and homogenization of material properties. Comput. Mater. Sci. 48, 22–38 (2010)

    Article  Google Scholar 

  21. Gurdal Z., Haftka R.T., Hajela P.: Design and Optimization of Laminated Composite Materials. Wiley, New York (1999)

    Google Scholar 

  22. Shabana Y.M., Noda N.: Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method. Int. J. Solid Struct. 45, 3494–3506 (2008)

    Article  MATH  Google Scholar 

  23. Schapery R.A.: Thermal expansion coefficients of composite materials based on energy principles. J. Compos. Mater. 2, 380–404 (1968)

    Article  Google Scholar 

  24. Tanaka K., Watanabe H., Sugano Y., Poterasu V.F.: A multicriterial material tailoring of a hollow cylinder in functionally gradient materials: Scheme to global reduction of thermoelastic stresses. Comput. Methods Appl. Mech. Eng. 135, 369–380 (1996)

    Article  MATH  Google Scholar 

  25. Guinovart-Diaz R., Bravo-Castillero J., Rodriguez-Ramos R., Martinez-Rosado R., Serrania F., Navarrete M.: Modeling of elastic transversely isotropic composite using the asymptotic homogenization method. Some comparisons with other models. Mater. Lett. 56, 889–894 (2002)

    Article  Google Scholar 

  26. Na K.S., Kim J.H.: Optimization of volume fractions for functionally graded panels considering stress and critical temperature. Compos. Struct. 89, 509–516 (2009)

    Article  Google Scholar 

  27. Hasselman D.P.H., Johnson L.F.: Effective thermal conductivity of composites with interfacial thermal barrier resistance. J. Compos. Mater. 21, 508–515 (1987)

    Article  Google Scholar 

  28. Halpin J.C., Tsai S.W.: Effects of environmental factors on composite materials. Report AFML-TR 67, 423 (1969)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Systems Engineering, Asahikawa National College of Technology, 2-2-1-6 Shunkodai, Asahikawa, 071-8142, Japan

    Ryoichi Chiba

  2. Department of Mechanical Systems Engineering, Iwate University, 4-3-5 Ueda, Morioka, 020-8551, Japan

    Yoshihiro Sugano

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  1. Ryoichi Chiba
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  2. Yoshihiro Sugano
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Correspondence to Ryoichi Chiba.

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Chiba, R., Sugano, Y. Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis. Acta Mech 223, 891–909 (2012). https://doi.org/10.1007/s00707-011-0610-z

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  • DOI: https://doi.org/10.1007/s00707-011-0610-z

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