= 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.
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