On the Fibre Pull‐out Problem

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Abstract
In this paper, the force required to pull out a long, slender fibre embedded in a semi‐infinite elastic matrix by a distance W is derived. Assuming that the fibre is slender and that there is no slip at the fibre‐matrix interface, it is shown that the nature of the inclusion depends on the parameter \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{E^* }}{E}\left({\frac{R}{l}} \right)^2 \,\ln \,\left({\frac{{2l}}{R}} \right) $\end{document} , where E, E* are the Young's moduli of the matrix and the fibre respectively. R is a typical radius of the fibre and l its length. When this parameter is large, the fibre is effectively rigid and the load transfer occurs over the entire length of the fibre. If this parameter is very much less than unity, then the inclusion is elastic in nature and the load transfer occurs in a finite neighbourhood of the embedded end of the fibre which is near the free surface of the semi‐infinite matrix.