Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

H.M. Yin^a,*, G.H. Paulino ^a, W.G. Buttlar ^a, L.Z. Sun ^b

^aDepartment of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue,  IL 61801

^bDepartment of Civil and Environmental Engineering, University of California, Irvine, 4130 Engineering Gateway, CA 92697

Abstract:

This paper proposes a new thermoelastic model for functionally graded particulate materials. Based on a representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived. For a free-standing functionally graded particulate material under a uniform temperature change, the averaged thermal strain distributed in the gradation direction is solved by considering the stress-free boundary condition. From the relation between the averaged thermal strain and the temperature change, the effective coefficients of thermal expansion are obtained, showing the weak anisotropy due to the particle interactions and microstructural gradient. When the material gradient is reduced to zero, the proposed model predicts the effective coefficients of thermal expansion for uniform composites. Parametric analyses and comparisons with other models and available experimental data are presented to demonstrate the capability of the proposed model. Furthermore, the proposed model is employed to calculate the thermal stress distributions for graded thermal barrier coatings bonded to a thick substrate and subjected to two types of thermal loading: the uniform temperature change and the steady state heat conduction in the gradation direction. However, the proposed semi-analytical scheme is general and can handle any thermal loading variation.

Keywords: A. Microstructures; B. Particulate reinforced material; B. Constitutive behavior; B. Thermal stress; C: Analytic functions; Functionally graded materials

Submitted to Journal of the Mechanics and Physics of Solids for Publication (August 11, 2005)