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

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

Substituting 0.55 for [tex]V_m[/tex], 0.45 for [tex]V_f[/tex], 35MPa for [tex]\sigma'_m [/tex], 3600MPa for [tex]\sigma^*_f[/tex].

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

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

[tex]E_c=E_mV_m+E_fV_f[/tex]

Here, [tex]E_m[/tex] is the modulus of elasticity of matrix, [tex]V_m[/tex] is the volume of matrix material, [tex]E_f[/tex] is the modulus of elasticity of fibre, and [tex]V_f[/tex] is the volume of fibre material.

Substituting 0.55 for [tex]V_m[/tex], 0.45 for [tex]V_f[/tex], 2.4MPa for [tex]E_m [/tex], 131GPa for [tex]E_f[/tex].

[tex]E_c=(2.4\TIMES0.55)+(131\TIMES0.45)\\=1.32+58.95\\=60.27GPa[/tex]