Multi-scale and multi-step modeling of thermal conductivities of 3D braided composites

To accurately predict the Effective Thermal Conductivities (ETCs) of Three-Dimensional (3D) braided composites, this work proposes a multi-scale and multi-step Mean-Field Homogenization (MFH) method. The composites are considered as the composites with 3D multi-directional braiding yarns as inclusions at the meso-scale, and the braiding yarns are viewed as unidirectional fibers reinforced composites at the micro-scale. The ETCs of the braiding yarns are firstly determined using the MFH method at the micro-scale. According to the yarn orientation, the composites are virtually decomposed into several pseudo-grains, each of which consists of the oriented braiding yarns and matrix, and the multi-step MFH method is then developed to predict the ETCs of the pseudo-grains and the composites sequentially at the meso-scale, i.e. the MFH prediction of the ETCs of each pseudo-grain individually and the composites consisting of all the pseudo-grains in two sequential steps. The proposed multi-scale and multi-step MFH method is validated by comparing with the multi-scale FE homogenization method and the available experimental test. The modeling results show that the through-thickness and in-plane ETCs of the composites increase with the increase of fiber volume fraction and transverse ETC, and decrease and increase with the increase of interior braiding angle, respectively. The proposed multi-scale and multi-step MFH method possesses the advantages of better computational efficiency and simpler implementation compared with the multi-scale FE homogenization method.