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.