SiO_2/环氧(E_(44))热膨胀性渐变的梯度功能材料(FGM)设计中的数学模型极其热应力分析

Mathematical model on the design of the SiO_2/epoxy resin thermal expansion coefficient graded materials and stress analysis of FGM plates

以基体树脂环氧(E44)为连续相,SiO2颗粒为分散相,设计了一种新型的热膨胀性渐变的梯度功能材料(FGM),通过实验测定结合理论分析,确定了FGM材料组成与弹性模量、热膨胀系数及导热系数之间的关系式。应用经典层合板理论和热弹性力学理论分析了SiO2/环氧E44叠合层在稳态温度场内温度分布和热应力分布。结果表明,在稳态温度场内,FGM板的热应力分布依赖于体系的组成分布,当组成分布指数k=1时,最大热应力具有最小值。在该组成分布下,FGM板的热膨胀系数等各项性质都呈线性渐变。

In this paper, a new type functionally graded materials SiO2/epoxy resin has been designed. The thermal expansion coefficient of the FGM plate in the thickness direction was reduced gradually with the content of the SiO2 increasing. Connecting experiments results, the expressions of the thermal conductivity, thermal expansion coefficient and elasticity modulus of each layers in FGM were determined. The temperature and thermal stress distribution of the FGM were obtained for the steady states based on the classical lamination theory and thermalelastic mechanics. The results showed that in the steady states, the thermal stress and temperature distribution in the FGM strongly depended on the compositional distribution parameter, with considering the minimum thermal stress, optimum design result (the compositional distribution parameter K=1) was achieved. When K=1,the composition, thermal expansion coefficient, temperature and thermal stress distribution in the FGM were linear distribution.