Fibre-matrix load transfer

Fibre-matrix load transfer describes how interfacial shear stress transfers axial force between a reinforcing fibre and its surrounding composite matrix. For a cylindrical fibre of diameter $d$, axial force balance gives $d{\sigma }_f/dx=4\tau /d$ when $\tau$ is the appropriately signed interfacial shear stress.

The fibre stress is therefore small near a free end and builds over a transfer length. Short fibres may never reach their tensile strength before the interface slips or the matrix yields. The critical fibre length quantifies this competition in a simplified constant-shear model.

The critical fibre length is the minimum embedded fibre length needed to develop a specified tensile stress in a simple interfacial-load-transfer model. For diameter $d$, fibre strength ${\sigma }_f^{\ast }$ and constant limiting interfacial shear stress ${\tau }_i$,Each half of the fibre builds axial force from its end through interfacial shear; balancing that transferred force against the strength load gives the formula. It is a model-dependent criterion, not a universal length of the material. Nonuniform shear, imperfect bonding and fibre orientation modify actual composite behavior.