$2$

Multiple Choice $10$ points

A polyimide matrix with an elastic modulus of $0\mathrm{.}3{10}^6$ is to be reinforced with $80$vol$\%$ carbon fibers to give a minimum modulus of elasticity of $40{10}^6.$ Determine the Elastic modulus of the carbon fibers.

a$)49\mathrm{.}9{10}^6$;

b$)52\mathrm{.}61{10}^6$;

c$)41\mathrm{.}61{10}^6$

Hint

$E_c=E_f{V}_f+E_m{V}_m$

$E-$ Elastic modulus; V $-$ Volume fraction

Subscripts: c $-$ composite; f$-$ fiber; m $-$ matrix

a

b

c