In an aligned and continuous carbon fiber-reinforced nylon 6,6 composite, the fibers are to carry 97% of a load applied in the longitudinal direction.(a) using the data provided, determine the volume fraction of fibers that will be required.(b) what will be the tensile strength of this composite? assume that the matrix stress at fiber failure is 50 mpa (7250 psi

0.258

Explanation:

The equation below can be used to calculate the volume fraction of the fiber,

Ff/Fm = Ef*Vf/(Em*Vm)

Since Vm + Vf = 1, the above equation can be rewritten as,

Ff/Fm = Ef * Vf/Em(1-Vf)

Taking,

Ff = Fraction of fiber

Fm = fraction of matrix

Em = elastic modulus of matrix

Vm = volume of matrix

EF = elastic modulus of fiber

Vf = volume of fiber.

Substituting given values,

0.97/0.03 = 260 x Vf/2.8(1-Vf)

Making Vf the subject,

The volume fraction of the fiber, Vf is obtained as 0.258.

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