Question

A continuous and aligned fiber-reinforced composite is to be produced consisting of 45 vol% aramid fibers and 55 vol% polycarbonate matrix; the mechanical characteristics of these two materials are as follows:
Modulus of Elasticity[GPa (psi)] Tensile Strength [MPa(psi)]
Aramid fiber 131 (19 × 106) 3600 (520,000)
Polycarbonate 2.4 (3.5 × 105) 65 (9425)

The stress on the polycarbonate matrix when the aramid fibers fail is 35 MPa (5075 psi). For this composite, compute the following:

(a) The longitudinal tensile strength
(b) The longitudinal modulus of elasticity

Answer 1

Answer:

Explanation:

a.) To calculate the longitudinal tensile strength of the composite as follows:

$\sigma^*_{cl}=\sigma'_m V_m+\sigma^*_fV_f$

Here $\sigma'_m$ is the stress in the matrix at fibre failure $V_m$ is the volume of matrix material $\sigma^*_f$ is the tensile strength of the fibre and $V_f$ is the volume of fibre phase.

Substituting 0.55 for $V_m$, 0.45 for  $V_f$, 35MPa for  $\sigma'_m$, 3600MPa for $\sigma^*_f$.

$\sigma^*_{cl}=(35\times0.55)+(3600\times0.45)\\=19.25+1620\\=1639.25MPa$

b.) To calculate the modulus of elasticity of the composite as follows:

$E_c=E_mV_m+E_fV_f$

Here, $E_m$ is the modulus of elasticity of matrix, $V_m$ is the volume of matrix material, $E_f$ is the modulus of elasticity of fibre, and $V_f$ is the volume of fibre material.

Substituting 0.55 for $V_m$, 0.45 for  $V_f$, 2.4MPa for  $E_m$, 131GPa for $E_f$.

$E_c=(2.4\TIMES0.55)+(131\TIMES0.45)\\=1.32+58.95\\=60.27GPa$