论文标题
短纤维增强复合材料的弹性张量的相关结构
Correlation structure in the elasticity tensor for short fiber-reinforced composites
论文作者
论文摘要
目前的工作对SFRC在中尺度上的材料特性以及所得的相关结构进行了深入的分析和数值分析，并考虑了纤维几何形状的概率特征。这是通过使用Tandon和Weng以及Halpin和Tsai的分析框架来计算工程常数来完成的。在纤维长度，直径和方向等输入参数相对于其概率密度函数选择。结果表明，它们受到纤维长度，纤维方向和纤维体积分数的显着影响。分析获得的值的验证是在数值的基础上进行的。因此，生成二维微观结构并将其转移到数值模型中。该过程的优点是，在预设区域中有几种具有不同几何特性的纤维。数值分析的结果符合分析获得的结论。此外，数值模拟的结果分别与平面应变和平面应力状态的假设无关。最后，研究了弹性张量的相关结构。弹性张量的对称特性不仅表征了相关结构，而且还确认了总体横向异分材料行为。与影响参数相反，平面应变和平面应力状态的相关函数各不相同。
The present work provides a profound analytical and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.
