Question

Is it possible to produce a continuous and oriented aramid fiber–epoxy matrix composite having longitudinalandtransverse moduli of elasticity of 35 GPa (5×106psi) and 5.17 GPa (7.5×105psi), respectively? Why or why not?Assume that the elastic modulus of the epoxy is 3.4 GPa (4.93×105psi).Also, the value ofEfor aramid fibers is 131GPa.

Answer 1

Not possible

Step-by-step explanation:

`E_(cl)` = longitudinal modulus of elasticity = 35 Gpa

`E_(ct)` = transverse modulus of elasticity = 5.17 Gpa

`E_m` = Epoxy modulus of elasticity = 3.4 Gpa

`V_(\rho l)` = Volume fraction of fibre (longitudinal)

`V_(\rho t)` = Volume fraction of fibre (transvers)

`E_f` = Modulus of elasticity of aramid fibers = 131 Gpa

Longitudinal modulus of elasticity is given by

`E_(cl)=E_m(1-V_(\rho l))+E_fV_(\rho l)\\\Rightarrow 35=3.4(1-V_(\rho l))+131V_(\rho l)\\\Rightarrow 35=3.4-3.4V_(\rho l)+131V_(\rho l)\\\Rightarrow V_(\rho l)=(35-3.4)/(131-3.4)\\\Rightarrow V_(\rho l)=0.24764`

Transverse modulus of elasticity is given by

`E_(ct)=(E_mE_f)/((1-V_(\rho t))E_f+V_(\rho t)E_m)\\\Rightarrow 5.17=(3.4* 131)/((1-V_(\rho t))131+V_(\rho t)3.4)\\\Rightarrow (3.4* 131)/(5.17)-131=-127.6V_(\rho t)\\\Rightarrow V_(\rho t)=((3.4* 131)/(5.17)-131)/(-127.6)\\\Rightarrow V_(\rho t)=0.35148`

`V_(\rho l)\\eq V_(\rho t)`

Hence, it is not possible to produce a continuous and oriented aramid fiber.