# Fibre Length

The Young’s modulus of the fibre is directly proportional to the external load, which can be calculated using following equation:

Where o_{f}^{max} is the upper limit of tensile stress within the fibre, E_{f} is the fibre modulus and e_{m} is the matrix strain [72]. In softer materials, the difference between the Young’s moduli of fibre and matrix creates additional strain near their respective interface. Also, the interface area between fibre and matrix depends on the fibre diameter at a known fibre volume, which influences the homogeneity and processability of the composite. The mechanical stability of fibres within the matrix composite depends on fibre length and diameter. Substantial load must be transferred across the matrix to the fibre via interface to strengthen the composite. In general, the load transferred through shear stresses at the lateral surface of the fibre is high when compared with load transfer at the end face [63]. Fibre pull-out occurs before the fibre fracture if the fibre length is not sufficient or is small. To maximise the effect of fibres within composite material, the critical length (l_{c}) can be calculated using following equation:

Where d_{f}, c_{f3} and T_{i} represents fibre diameter, fracture strength and shear stress at the interface. To understand stress distribution with respect to fibre length along its axis a simple model has been proposed by many researchers. When the fibre length is greater than the l_{c}, then the shear stress in the fibre end is maximum and zero at the centre of the fibre [63, 72, 73].