以界面不滑移条件求解单层复合材料的横向弹性模量

Solving the transverse elastic modulus of single-layer composites with interface nonslip condition

对复合材料增强体和基体交界面的受力情况进行分析。根据交界面不会滑移的基本特点,假定增强体和基体沿交界面方向发生的应变相等,用解析法直接推导出单层复合材料的横向弹性模量计算公式。研究表明:横向弹性模量不仅是增强体、基体弹性模量与体积分数的函数,而且是增强体泊松比和基体泊松比的函数,但横向弹性模量的大小与增强体和基体的尺寸与形状无关;Reuss串联公式仅是该文公式的一个特例,前者只有在增强体和基体符合柔度的对称性条件下才成立。与一组实验数据进行对比分析,结果显示计算值与实验数据相对误差保持在10%以内。

The analytical calculation of the transverse elastic modulus of single-layer composites is a classical problem. There are many calculation models for this problem, but the calculation results are quite different. In this paper, the stress state of the interface between the composite reinforcement and the matrix is analyzed. According to the basic characteristics that the interface does not slip, it is assumed that the strain of the reinforcement and the strain of the matrix along the interface are equal, and the formula for calculating the transverse elastic modulus of single-layer composite material is directly deduced by the analytical method. Studies have shown that the transverse elastic modulus is not only function of the elastic modulus and volume fraction of the reinforcement and the matrix, but also function of the Poisson’s ratio of the reinforcement and the Poisson’s ratio of the matrix, but the magnitude of the transverse elastic modulus is irrelevant with the size and shape of the reinforcement and the matrix. The Reuss series formula is only a special case of the deduced formula, and the former is only valid when the reinforcement and the matrix conform to the symmetry condition of the flexibility;the comparison results with a set of experimental data show the calculated values agree well with the experimental data.