缠绕型碳纳米管增强陶瓷基复合材料的有效刚度和应力分析

Effective stiffness and stress analysis of ceramic composites reinforced with winding carbon nano-tubes

以直线型、余弦波型和缠绕型空心碳纳米管增强陶瓷基复合材料的三维特征体积单元模型为研究对象,利用满足精确周期性边界条件的均质化法计算该模型的有效弹性模量和局部应力,分析碳纳米管的几何形状、尺寸和力学特性对碳纳米管复合材料力学性能的影响,并与经典混合法则、Halpin-Tsai法及其他数值模拟的结果进行对比.结果表明:碳纳米管的几何缠绕特性对横向变形有较好的限制作用;缠绕型复合材料的力学性能呈曲线变化,比直线型和余弦波型碳纳米管复合材料更容易受几何特性的影响:缠绕型碳纳米管的最大轴向应力和最大等效应力随碳纳米管外径的增大而增大,但碳纳米管的各向异性会降低碳纳米管的最大应力,导致缠绕型碳纳米管复合材料传递应力的能力减弱;双尺度均质化法和有限元法结合能有效反映力学性能的变化特征,是分析具有复杂微观结构力学性能的有效方法.

With three-dimensional characteristic volume element models of ceramic matrix composites reinforced by linear,cosine wave and winding hollow carbon nano-tubes(CNTs)as the research objects,this paper calculates the effective elastic modulus and local stress of the model by using the homogenization method with exact periodic boundary conditions.It also analyzes the influence of the geometrical shape,size and mechanical characteristics on the mechanical properties of CNTs composites,and compares the results show that the geometric winding characteristics of CNTs have a good limiting effect on lateral deformation.The mechanical properties of winding CNTs composites change in curve,and are more susceptible to geometric properties than linear and cosine wave carbon nanotube composites.The maximum axial stress and the maximum equivalent stress of the winding CNTs increase with the increase of the outer diameter of the CNTs,but the anisotropy of the CNTs will reduce their maximum stress,which leads to the weakening of stress transfer ability of the winding CNTs composites.The combination of two-scale homogenization method and finite element method can effectively reflect the variation characteristics of mechanical properties,which is an effective method to analyze the mechanical properties of complex microstructure.