Composite engineering In a design assignment, you are asked to use continuous carbon fibres to reinforce...

Composite engineering

In a design assignment, you are asked to use continuous carbon fibres to reinforce an epoxy matrix
to achieve Young's modulus of 250 GPa along the longitudinal direction of the composite. The
epoxy matrix to use has a Young's modulus of 2 GPa and the continuous carbon fibres 400 GPa. If
the allowed maximum loading of the C fibres is 60 vol%, is the design goal achievable? You are
required to derive any equation needed in the calculation and state any assumptions made.

Expert Solution

In fibre reinforced composites, fibre material is so selected that it's Young's modulus is always more than the Young's modulus of matrix.

E_f >> E_m

E_f = Young's modulus of fibre ( Continuous carbon fibre)= 400 GPa

E_m = Young's modulus of matrix ( epoxy matrix) = 2 GPa

v_f = Volume fraction of the fibres

v_m = Volume fraction of the matrix

For longitudinal loading, the figure is as shown.

Load P, is applied parallel to the fibres. The amount of strain is equal for the matrix and fibres. However the load is ditributed among the fibres and the matrix.

Now the allowed maximum loading of C fibres is 60 vol% , i.e., v_f = 0.6, v_m = 0.4

E_c = 2 * 0.4 + 400* 0.6 = 240.8 GPa

This is the maximum value of Young's modulus of composite along the longitudinal direction, beacuse of the given limit of Carbon fibre volume%. Therefore, the design goal is not achievable.

It can be achieved if v_f = 62.31 %

samet mamat answered 2 years ago

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