Question

For a fiber to be effectively reinforcing within an aligned fiber-reinforced polymer matrix composite, which of the following conditions must be met ? Select all that apply. (E = elastic modulus, l = fiber length).

1. Ef > Em2. Em > Ef3. Ef = Em4. lf > lcritical5. lf < lcritical

Answer 1

1. Ef > Em and 5. lf < lcritical

Step-by-step explanation:

The critical length of fiber is given by

`L_c=\frac {\sigma_f* d}{2\tau_c}` where d is fiber diameter,
`\sigma_f` is ultimate strength of fiber, and
`\tau_c` is fiber matrix bond strength.

When fiber length increases above critical length, the reinforcement becomes more effective since maximum fiber load is achieved by most part of the fiber hence

`L>L_c`

In matrix composite, matrix phase remains intact when fiber phase fails since the fracture strain in matrix is more than in fiber hence

`\epsilon_m>\epsilon_f`

Moreover, strain is inversely proportional to elastic modulus hence

`\frac {1}{E_m}>\frac {1}{E_f}` meaning
`E_m<E_f` or
`E_f>E_m`