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.

为了准确预测三维 (3D) 编织复合材料的有效热导率 (ETC)，本工作提出了一种多尺度和多步平均场均化 (MFH) 方法。复合材料在中观尺度被认为是3D多向编织纱线作为夹杂物的复合材料，编织纱线在微观尺度被认为是单向纤维增强复合材料。编织纱线的ETCs首先使用MFH确定微观尺度的方法。根据纱线取向，将复合材料虚拟分解为多个伪晶粒，每个伪晶粒由取向的编织纱线和基体组成，然后开发了多步MFH方法来预测伪晶粒的ETC和在中尺度上按顺序进行复合，即分别对每个伪晶粒的 ETC 进行 MFH 预测，以及在两个连续步骤中由所有伪晶粒组成的复合材料。通过与多尺度有限元均匀化方法和可用的实验测试进行比较，验证了所提出的多尺度和多步 MFH 方法。建模结果表明，随着纤维体积分数和横向ETC的增加，复合材料的全厚度和面内ETCs增加，分别随着内编织角的增大而减小和增大。与多尺度有限元均质化方法相比，所提出的多尺度多步MFH方法具有计算效率更高、实现更简单的优点。