Question

a chopped-fiber composite is to use an e-glass fiber with peek. the fiber has a modulus of 73 gpa, and the matrix has a modulus of 3.7 gpa. what is the modulus of a composite with a fiber volume fraction of 60%? the fibers are aligned, and we want the modulus in the fiber direction.

Answer 1

The modulus of the chopped-fiber composite using E-glass fiber with PEEK and a fiber volume fraction of 60% is calculated using the rule of mixtures, resulting in a modulus of approximately 45.28 GPa in the fiber direction.

Step-by-step explanation:

The question concerns the determination of the modulus of a chopped-fiber composite using E-glass fiber with PEEK (polyether ether ketone) matrix in the fiber direction. Given the modulus of E-glass fiber as 73 GPa and the modulus of the PEEK matrix as 3.7 GPa, along with a fiber volume fraction of 60%, we can use the mixture rule to calculate the modulus of the composite in the fiber direction.

To calculate the composite modulus (Ec) in the direction of the fibers, the rule of mixtures is typically used:
Ec = Vf * Ef + Vm * Em

Where Vf is the volume fraction of the fibers, Ef is the modulus of the fibers, Vm is the volume fraction of the matrix, and Em is the modulus of the matrix.

By substituting the given values:
Ec = 0.60 * 73 GPa + 0.40 * 3.7 GPa

Therefore:
Ec = 43.8 GPa + 1.48 GPa

Ec = 45.28 GPa

Thus, the modulus of the composite in the fiber direction is approximately 45.28 GPa.