含非均匀界面相纤维增强复合材料热传导性能预测的递推公式

A recurrence formula for the prediction of the effective thermal conductivity of fiber reinforced composites with an inhomogeneous interphase

研究了含非均匀界面相纤维增强复合材料的宏观等效传热性能。将热导率沿径向连续变化的界面相离散为多个热导率均匀的同心圆柱层,采用广义自洽法和复变函数理论,推导了复合材料宏观等效热导率的解析递推公式,并由递推公式给出了均匀界面相和理想零厚度界面的封闭公式。理想零厚度界面复合材料的热导率与已有理论结果一致。理想零厚度界面和非均匀界面相模型的计算结果与实验数据比较表明,当纤维体积分数较小时,2种模型的预测结果与实验数据吻合均较好,当体积分数较大时,与实验数据相比,非均匀界面相模型的精度大大高于理想零厚度界面模型的精度。本文中给出的递推公式亦可用于计算多涂层纤维增强复合材料的热导率。

The thermal conductivities of fiber reinforced composites with an inhomogeneous interphase are studied. The inhomogeneous interphase with continuously varied thermal conductivity can be modeled by a multi- layer concentric cylindrical homogeneous shell. The generalized self-consistent method and complex variable technology are applied to obtain an analytical recurrence formula of the effective conductivity. In the cases of the idealized zero thickness interface and homogeneous interphase, the closed form solutions are given by the recurrence formulae. The former has been given by previous researchers. When the volume fraction of fibers is small, the predictions by both models of the idealized zero thickness interface and inhomogeneous interphase and the experiment results are in good agreement, but when the volume fraction of fiber gets large, only the model of inhomogeneous interphase leads to good predictions. The present recurrence formula can also be used to analyze the thermai conductivity of a composite with multi-coating fibers.