纤维增强复合材料中小纤维对剪切应力的强烈影响
Strong Influence of a Small Fiber on Shear Stress in Fiber-Reinforced Composites
摘要：
在刚性纤维增强材料中，高剪切应力集中发生在纤维之间的狭窄区域。通过增加横截面的小的几何变化，例如细纤维或纤维的悬垂部分，浓度显著增加。本文用数学分析的方法解释了横截面上的小颗粒引起的应力的迅速增长。为此，我们考虑两个关键的情况下，一个薄的纤维之间存在一对纤维，和两个纤维中的一个有一个突出的小肿块的横截面。对于每一种情况下，最佳的下限和上界的应力与纤维的几何因素的建立来解释强烈增加的增长的应力由一个小颗粒。
英文摘要：
In stiff fiber-reinforced material, the high shear stress concentration occurs in the narrow region between fibers. With the addition of a small geometric change in cross-section, such as a thin fiber or a overhanging part of fiber, the concentration is significantly increased. This paper presents mathematical analysis to explain the rapidly increased growth of the stress by a small particle in cross-section. To do so, we consider two crucial cases where a thin fiber exists between a pair of fibers, and where one of two fibers has a protruding small lump in cross-section. For each case, the optimal lower and upper bounds on the stress associated with the geometrical factors of fibers is established to explain the strongly increased growth of the stress by a small particle.
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