预报纤维增强复合材料有效热导率的随机微结构胞元模型

发展了能预报复合材料有效性质的随机微结构胞元模型以预测单向纤维增强复合材料横向热导率。研究了能反映宏观有效性质的模型最小化问题, 探讨了微结构影响宏观有效热传导性能的机制。结果表明: 通过对模型指定周期边界条件并且以多个合适的小规模模型计算的平均值取代大模型计算, 可大大改进收敛性并提高计算效率, 从10×10个到30×30个子胞的模型, 所得有效热导率计算结果的最大相对变化量仅为0.6%。不同纤维排列引起热流穿过热阻大的基体的路径长度改变, 造成有效热导率不同; 纤维热导率远大于基体热导率时, 纤维随机分布造成纤维偏聚, 部分纤维接触形成"热流通道", 使得有效热导率增大, 揭示了某一体积分数下有效热导率急剧增加是由"热流通道"贯通引起。与实验结果的比较说明了微结构随机性研究的必要性和本文工作的实用价值。

A random microstructure cell model to predict the effective thermal conductivity of fiber reinforced composites

A random microstructure cell model was developed to predict the effective transverse thermal conductivity of unidirectional fiber reinforced composites.The minimization of the model that can well characterize the macroscopic effective properties was investigated,and the influence mechanism of microstructures on macroscopic effective thermal conduction properties was discussed.It is shown that convergence and computational efficiency are much improved by prescribing the periodic boundary conditions for the model together with replacing the result by a large model with the average of the results by several appropriate small models.The maximum relative variation of effective thermal conductivities is only 0.6% with the model scale ranging from 10×10 to 30×30.Different fiber distributions lead to different lengths of heat flux path with a high thermal resistance,and then result in different effective thermal conductivities.For a random fiber distribution,fibers segregate in a microscopic level.When the fiber thermal conductivity is much larger than that of the matrix,portions of the fibers come into contact and form some local "heat flow channels",which result in a higher effective thermal conductivity.At a certain fiber volume fraction,the effective thermal conductivity increases dramatically because some of the local "heat flow channels" connect and form channels across the entire composite.A comparison with experimental data demonstrates the necessity of the study on microstructural randomness and the practical value of the present work.