Load-Absorption and Interaction of Two Filaments in a Fiber-Reinforced Material

Citation

Carne, Thomas Glen (1973) Load-Absorption and Interaction of Two Filaments in a Fiber-Reinforced Material. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GDSK-RJ45. https://resolver.caltech.edu/CaltechTHESIS:02062018-115639478

Abstract

This investigation is concerned with the interaction - as far as load-absorption is concerned - of a pair of identical and parallel elastic filaments in a fiber-reinforced composite material. The filaments are assumed to have uniform circular cross-sections, are taken to be semi-infinite, and are supposed to be continuously bonded to an all­ around infinite matrix of distinct elastic properties. At infinity the matrix is subjected to uniaxial tension parallel to the filaments. Two separate but related problems are treated. In the first both filaments extend to infinity in the same direction and their terminal cross-sections are coplanar. In the second problem the filaments extend to infinity in opposite directions and their terminal cross-sections need no longer be coplanar, the two filaments being permitted to overlap partly. An approximate scheme based in part on three-dimensional linear elasticity and developed originally by Muki and Sternberg is employed in the analysis. The problems are ultimately reduced to Fredholm integral equations which characterize the distribution of the axial filament force. The integral equations are analyzed asymptotically and numerically. Results are presented which show the variation of filament force with position and the effect on this variation of various relevant geometrical and material properties.

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