 Fibre (material)

A material fibre is a long, slender physical strand: its length is large compared with its transverse dimensions. The geometry is shared by materials with different roles. Carbon fibres and glass fibres can reinforce a composite material, while an optical fibre guides light. The material's properties, the strand dimensions and the way strands are assembled all affect its response.

A single-fibre tensile test grips one strand, measures its axial force and extension over a specified gauge length, and uses its cross-sectional area to obtain stress and strain. A 2020 study used a semi-automated instrument to characterize glass fibres and carbon fibres through their stress-strain curves and inferred moduli.^[ref] Its public dataset supplies individual tensile curves at several gauge lengths, summary sheets and calculations of test-setup machine compliance.^[ref] This matters because crosshead displacement can include deformation of the apparatus as well as extension of the material fibre; its slope alone need not give the specimen's Young's modulus.

An original ideal model shows why making thinner strands changes some responses more strongly than others. Keep total material cross-sectional area $A$, length $L$ and Young's modulus $E$ fixed. Compare one solid circular rod with $N$ identical circular fibres, each of radiusFor axial loading, grip every strand so that all undergo the same extension $\Delta L$. Each supplies force $E(A/N)\Delta L/L$, and adding the forces gives the axial stiffnessindependent of $N$ under these assumptions. This is the uniform-bar linear elasticity relation applied to parallel strands.

Now make a separate pure-bending comparison of an unbonded material-fibre bundle. Allow longitudinal sliding, neglect friction, and let each strand bend about its own neutral axis with the same curvature $\kappa$. A circular strand has second moment of area $I_N=\pi r_N^4/4$ and filament bending modulus $E{I}_N$. Its bending moment is $E{I}_N\kappa$ in the small-deformation model.^[ref] Adding those moments gives the bending rigidity of an unbonded fibre bundle:Each material fibre has its own neutral axis, which is crucial to this calculation. Bonding strands together transfers shear stress and couples their axial deformation; the independent-strand sum then ceases to describe the assembly. In a reinforced composite material, that coupling is part of fibre-matrix load transfer.

For chosen $A=1{\mathrm{mm}}^2$, $L=100\mathrm{mm}$ and $E=70\mathrm{GPa}$, both axial specimens have $K_{\mathrm{ax}}=700\mathrm{N}\mathrm{m}{\mathrm{m}}^{-1}$. At $N=100$, each radius is approximately $0.0564\mathrm{mm}$, and the independent-bending value is $55.7\mathrm{N}\mathrm{m}{\mathrm{m}}^2$ compared with $5570.4\mathrm{N}\mathrm{m}{\mathrm{m}}^2$ for the solid rod. The parameters are stipulated for this model; $A$ counts material and excludes spaces between strands.

A useful mechanical comparison therefore records which material fibres are gripped, whether they can slide, their arrangement and the loading direction. Equal material quantity alone does not determine an assembly's stiffness, and small filament bending modulus does not imply small axial Young's modulus.