Strong Influence of a Small Fiber on Shear Stress in Fiber-Reinforced Composites

TL;DR

This paper analyzes how small geometric changes in fibers within fiber-reinforced composites significantly amplify shear stress concentration, using mathematical bounds to explain the effect.

Contribution

It provides a mathematical framework establishing bounds on stress increases caused by small geometric features in fibers, highlighting their strong influence.

Findings

Small fibers or protrusions cause significant shear stress concentration.

Mathematical bounds quantify the stress amplification due to geometric changes.

The analysis explains the rapid stress growth with small particle inclusion.

Abstract

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.