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A carbon fibre is a slender reinforcement made predominantly of carbon, used to carry tension along its length. Its axial Young's modulus, tensile strength and mass density are especially useful when comparing how much elastic load a lightweight component can carry. A fibre's measured tensile strength also depends on defects and the length tested, so one strength value does not characterize every specimen.

Embedding carbon fibres in a polymer produces carbon-fibre-reinforced polymer. The composite matrix supports the fibre arrangement and permits fibre-matrix load transfer; the axial performance of an aligned assembly does not imply equal transverse performance. Tensile testing of single fibres measures the reinforcement response, while testing composite strips at different orientations measures how that response survives assembly into a composite material.

Carbon-fibre-reinforced polymer is a composite material in which carbon fibres reinforce a polymer composite matrix. The fibres carry axial tension efficiently, while the composite matrix maintains their arrangement and transfers load through interfacial shear stress. A component's response therefore depends on fibre direction, fibre volume fraction and bonding as well as the constituent properties.

For continuous aligned reinforcement, the longitudinal rule of mixtures predicts the initial axial Young's modulus. A stack with fibres in several directions trades some axial performance for reinforcement in those directions. Such an arrangement can reduce in-plane anisotropy, but does not automatically make the through-thickness response identical. Comparing tensile testing along the fibres, across them and through the assembled layers reveals different possible failure mechanisms, including fibre fracture and loss of fibre-matrix load transfer.

A composite material contains distinguishable constituent phases whose arrangement contributes to the bulk properties. In a fibre-reinforced example, strong fibres carry much of the axial load while a composite matrix holds them together and transmits shear stress between them. Carbon-fibre-reinforced polymer combines carbon fibres with a polymer composite matrix; glass fibres provide another reinforcement.

The constituent proportions alone do not determine the result. Aligned fibres produce anisotropy, whereas changing their orientations changes which directions are reinforced.^[ref] In an ideal long-fibre composite, the longitudinal rule of mixtures estimates the axial Young's modulus. A comparison of tensile testing along and across the fibres exposes the importance of geometry and fibre-matrix load transfer. The same idea of combining phase properties with geometry appears in effective conductivity, although the relevant constitutive equations differ.

The course examples connect material performance index values to materials selection charts; the shaft and flywheel examples identify carbon-fibre-reinforced polymers among candidates with high specific strength. Their numerical properties concern specified examples and should not be treated as universal beam compression allowables.