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## Homework Statement

Glass fibres in Nylon provide reinforcement. Young's modulus of glass fibre is 72.4GPa; Young's modulus of Nylon is 2.8GPa.

If the Nylon contains 30% by volume glass fibres, what fraction of the force applied parallel to the fibre axis is carried by the glass fibre?

(Assume the bonding between glass fibre and Nylon is strong enough to transfer the load, so ε

_{c}= ε

_{f}= ε

_{m}applies)

## Homework Equations

E

_{cl}= (f

_{f}⋅ E

_{f}) + (f

_{m}⋅ E

_{m})

Where

E

_{cl}= Young's modulus of composite in parallel direction

f

_{f}= Fraction of the fibre

E

_{f}= Young's modulus of the fibre

f

_{m}= Fraction of the matrix

E

_{m}= Young's modulus of the matrix

## The Attempt at a Solution

Given that Nylon is the matrix and the glass fibres are the fibre, the following can be assumed...

E

_{cl}= (0.3 ⋅ 72.4) + (0.7 ⋅ 2.8) = 41.32 MPa

With respect to the fraction of the force applied parallel to the fibre axis, is it a matter of dividing the Young's modulus of the composite by that of the fibre?

41.32 MPa / 72.4 MPa = 0.57 or 57%