横观各向同性基体复合材料的等效弹性常数

Effective Elastic Properties of Transversely Isotropic Matrix Based Composites

细观力学的一个主要研究内容是求复合材料的等效弹性性能.常见的细观力学模型解析公式一般假定基体各向同性且只存在纤维和基体两相材料,实际复合材料的基体和纤维之间往往存在一个横观各向同性的界面相,该三相复合材料的等效性能可由两个两相复合材料性能的组合得到,这就需要求出横观各向同性基体复合材料的等效弹性常数.该文基于两相同心圆柱模型,首先导出了横观各向同性基体内应力与增强纤维内应力之间桥联矩阵的解析公式,与基于数值积分Eshelby张量得到的Mori-Tanaka桥联矩阵相符,再进一步获得了横观各向同性基体复合材料的5个弹性常数显式表达式.文中还给出了扩展的桥联模型显式公式.选用适当的桥联参数,两种模型所得结果十分接近.

One of the main objectives of micromechanics is to predict the effective elastic properties of composites. Most existent explicit micromechanics models are based on an assumption of isotropic matrices and on that only 2-phase constituent materials are involved. In reality,a composite may possess a 3 rd interphase between the fiber and the matrix,which is generally transversely isotropic. Accordingly,the prediction of the elastic properties of a 3-phase composite can be achieved through the combination of 2 kinds of 2-phase composites,to which a micromechanics model with transversely isotropic matrix should be applicable.The explicit bridging tensor elements to correlate the internal stresses of a transversely isotropic matrix with those of a reinforcing fiber in a concentric cylinder assemblage（ CCA） model were derived firstly. Then this obtained bridging tensor was used to deduce analytical formulae for all the 5 effective elastic moduli of the composite made with the transversely isotropic matrix. An extension of the bridging model applicable to fiber reinforced transversely isotropic matrix composites was achieved as well. With properly chosen bridging parameters,the predicted elastic moduli of the composite with the 2 models are quite close to each other.