Consider a carbon fiber reinforced epoxy composite. The fibers are continuous, unidirectionally aligned and 40% by volume. The tensile strength of carbon fibers is 2998 MPa, and the Young's modulus is 214 GPa. The tensile strength of the epoxy matrix is 100 MPa, and its Young's modulus is 3 GPa. Required:
a. Compute the Young's modulus and the tensile strength of the composite in the longitudinal direction.
b. What is Young's modulus in the longitudinal direction?

- the Young's modulus of the composite in the longitudinal direction  = 87.4GPa.

- The tensile strength of the composite in the longitudinal direction  = 1.26 × 10⁹.

Explanation:

The following parameters or data were given in this particular question/problem;

1. "The fibers are continuous, unidirectionally aligned and 40% by volume."

2." The tensile strength of carbon fibers is 2998 MPa, and the Young's modulus is 214 GPa."

3. " The tensile strength of the epoxy matrix is 100 MPa, and its Young's modulus is 3 GPa."

So, let us delve right into the solution to this question:

[ kindly note that part b. of this problem is the same as the part a. of the problem

Also, in point 2. above 2998MPa = 2.998 =GPa, approximately 3GPa].

40% = 40/100 = 0.4. Therefore, 1 - 0.4 = 0.6. Hence, the Young's modulus of the composite in the longitudinal direction = 3 × 0.6 + 214 × 0.4 =  1.8 + 85.6 = 87.4GPa

The tensile strength of the composite in the longitudinal direction = 100 × 10⁶ × 0.6 + 3 × 10⁹ ₓ 0.4 = 1.26 × 10⁹.

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