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基体开裂、纤维拔出、界面剥离等是碳纤维增强复合材料常出现的局部各向异性损伤现象,这些损伤逐渐扩展,削弱了材料的强度和刚度,影响材料的承载能力。对此利用宏微观摄动理论对位移进行双范围渐进展开,在微观位移中引入损伤应变,通过计算损伤应变集中因子,得到了含损伤的均质化损伤弹性常数(宏观有效刚度矩阵),用平均法和混合法检验了无损情况均质化弹性常数计算的有效性。利用经典的热动力学理论建立了相应的损伤演化方程,结合有限元法得到不同铺层方式的宏观应力-应变关系以及各向异性损伤的演化规律,所得结果与Wang等人(Wang S Z,Journal of Materials Science,1992,27:5483-5496)用相同材料做出的实验数据较为吻合,证明了利用宏微观双范围渐进展开方法分析包含各向异性损伤情况碳纤维增强复合材料力学性质的有效性。
The cracking of the matrix, fiber pull-out and interface debonding are all the phenomena of local anisotropic damage that often occurs in carbon fiber reinforced composites. These damage gradually expand, weakening the strength and stiffness of the material and affecting the load carrying capacity of the material. In this paper, the dual-range progressive expansion of displacement is introduced by using the macro-micro perturbation theory, and the damage strain is introduced into the micro-displacement. By calculating the damage strain concentration factor, the elastic damage homogeneity damage constant (macroscopic effective stiffness matrix) The average and hybrid methods test the validity of the calculation of the elastic modulus of homogenization in the non-destructive case. Based on the classical thermodynamics theory, the corresponding damage evolution equations are established, and the macroscopic stress-strain relationships of different layers and the evolution of anisotropic damage are obtained by using the finite element method. The results obtained are in good agreement with Wang et al. of Materials Science, 1992, 27: 5483-5496) is in good agreement with the experimental data of the same material. It is proved that the mechanical properties of carbon fiber reinforced composites with anisotropic damage can be analyzed by using the macro-micro dual-range progressive expansion method.