Critical fibre length ($l_c$)

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.