Question

For an aligned carbon fibre-epoxy matrix composite having a 0.25 volume fraction of fibres, compute the critical fibre length = Assuming the following: 1) an average fiber diameter of 7.80 x 10 mm 2) an average fiber length of 9.3 mm 3) a fiber fracture strength of 4.5 GPa 4) a fiber-matrix bond strength of 75 MPa 5) a matrix stress at composite failure of 6.0 MPa 6) a matrix tensile strength of 60 MPa. Express answers with three significant figures.

Answer 1

The critical fibre length lc depends on parameters like nature of fibre, matrix, interfacial strength etc.

It can be found using the following equation,

$l_c = \frac{\sigma_f^{*}d}{2\tau_c}$

Where $\sigma_f^{*}$ is the fibre fracture strength , d is the average fiber diameter, $\tau_c$ is fibre matrix bond strength

$l_c = \frac{4500*7.80*10^{-3}}{2*75}$

$l_c = 0.234 mm$

Therefore critical length of fibre is 0.234 mm.