含粘弹性界面相短纤维/弹性体复合材料的纤维临界长径比数学模型

Mathematics Model of Fiber Critical Aspect Ratio of Short-Fiber-Reinforced Elastomer Matrix Composites with Viscoelastic Interphase

建立了含粘弹性界面相短纤维/弹性体复合材料的纤维临界长径比理论模型,得到了不同界面相破坏形式下初始和长时的纤维临界长径比,并讨论了界面相剪切强度、界面相剪切松弛变量、界面相厚度等诸多参数对纤维临界长径比的影响。结果表明:纤维临界长径比和时间有关,初始时最小,长时最大;三种不同的界面相破坏形式下,纤维临界长径比计算方法也不同;纤维临界长径比和诸多力学性能和结构参数有关,它随着界面相剪切强度和厚度的增大而减小,随着纤维体积含量、弹性模量、断裂强度以及界面相剪切松弛变量的增大而增大;界面相厚度不同,纤维临界长径比差别甚大。所建模型既适合于具有一定厚度界面相的短纤维/弹性体复合材料,也适合于薄界面相或纤维没有经过表面处理的复合材料。

A Mathematics model of the fiber critical aspect ratio of short-fiber-reinforced elastomer m matrix composites with viscoelastic interphase was established, and expressions of the fiber critical aspect ratio at the initial time and long time were obtained under different failure modes of interphase. Moreover, the influence of some parameters on the fiber critical aspect ratio were discussed, such as interphase shear strength, interphase shear stress relaxation parameter and interphase thickness. Research indicates that the fiber criti- cal aspect ratio is related to the time, and it reaches to the maximum at initial time and becomes the minimum at long time. The expressions of the fiber critical aspect ratio under three different failure modes of interphase are different. The fiber critical aspect ratio depends largely on the parameters of mechanical properties and structures, it decreases with the increases of the interphase shear strength and thickness, and it increases with the increase of the fiber volume fraction, fiber fracture strength, fiber elasticity modulus and the interphase shear stress relaxation parameter. The fiber critical aspect ratio is quiet different with the variation of interphase thickness. The proposed model is not only suitable for the composite with viscoelastic interphase, but also suitable for the composite with thin- thickness interphase or fiber without surface treatment.