Multi-size unit cells to predict effective thermal conductivities of 3D four-directional braided composites

Based on the structure of the full unit cell which is formulated by three translational symmetries, three further 180° rotational symmetries of three-dimensional (3D) four-directional braided composites are clarified in this paper. It is for the first time that each rotational symmetry is used to reduce the full unit cell to a half, quarter, and eighth size. The corresponding boundary conditions for thermal analysis are derived precisely according to each rotational transformation. The effective thermal conductivities of composites with different fiber volume fractions and interior braiding angles are calculated by the full, quarter and eighth unit cells. In order to confirm the significance of accurate boundary conditions, additional comparison calculations with adiabatic boundary conditions are conducted and the result reveals that inappropriate boundary conditions may lead to an un-neglectable error in the prediction of thermal conduction behaviours. The numerical model is validated by good agreement between the numerical results and the available experimental ones.