# Thermoelastic Properties of Particle Reinforced Composites at the Micro and Macro Scales

## Abstract

Particle reinforced composites are widely used in tires, heat exchangers, thermal barrier coatings and many other applications, as they have good strength to weight ratio, excellent thermal insulation, ease of manufacturing and flexibility in design. During their service life, these composites are often subjected to harsh environments, which can degrade the thermo-mechanical properties of the constituents in the composites, affecting performance and lifetime of the composites. This study investigates performance of particle reinforced composites subjected to coupled heat conduction and thermo-elastic deformation at the macro and micro levels. A micromechanical model is used to determine the effective thermal and mechanical properties of the homogenized composite by incorporating microscopic characteristics of the composites. The constituent?s thermal conductivities of the composite are assumed to be functions of temperature and the elastic moduli to be functions of temperature and stress fields. The effective properties obtained from the micromechanical model represent average (macroscopic) properties. The effective heat conduction and thermo-elastic responses in the homogenized composites are compared with the responses of the composite with particles randomly distributed in the matrix (heterogeneous materials) which represent microscopic responses. For this purpose, two sets of finite element (FE) models are generated for composites with particle volume contents 12.5, 25, and 50%. The first FE model represents a homogenized composite panel and the effective responses from the micromechanical model are used as input for the material properties. The second FE model mimics composite microstructure with discontinuous particles randomly dispersed in a homogeneous matrix. Parametric studies on effects of conductivity ratio between particle and matrix, degree of nonlinearity, and volume fraction on the temperature distribution and steady state times have been studied. For lower volume fractions the temperature profiles of homogenized and heterogeneous composite models are in good agreement with each other. But for higher volume fractions, the detailed model showed a wavy profile whereas the effective model showed no signs of it. When the nonlinearity in thermal conductivity of the particle and matrix constituents is increased, the steady state time significantly deviates from the ones with constant constituent properties. When the volume fraction of particles in the composite increases, the steady state is reached in less time, since the thermal conductivity of particles are taken larger than that of the matrix. Effects of coefficient of thermal expansion (CTE) ratio of particle and matrix, temperature change, and volume fraction on the discontinuity of stress and strain fields at the interphase of matrix and particle have been studied. The stresses developed were more for higher CTE ratios and the magnitude of discontinuity also follows the same trend. As the volume fraction increases, the stresses developed and the magnitude of discontinuity also increase. Finally, sequentially coupled heat conduction and deformation analyses are performed on thermal barrier coating (TBC) systems to demonstrate the applicability of the micromechanical model in predicting overall thermo-elastic responses of the TBC.