What Fraction of Force is Carried by Glass Fibres in a Nylon Composite?

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SUMMARY

The discussion focuses on calculating the fraction of force carried by glass fibres in a Nylon composite, where the Young's modulus of glass fibre is 72.4 GPa and that of Nylon is 2.8 GPa. With 30% by volume of glass fibres, the Young's modulus of the composite in the parallel direction is determined to be 41.32 MPa. The fraction of the force applied parallel to the fibre axis is calculated as 57%, confirming that the glass fibres significantly contribute to the composite's strength.

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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 εc = εf = εm applies)

Homework Equations



Ecl = (ff ⋅ Ef) + (fm ⋅ Em)

Where
Ecl = Young's modulus of composite in parallel direction
ff = Fraction of the fibre
Ef = Young's modulus of the fibre
fm = Fraction of the matrix
Em = 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...

Ecl = (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%
 
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