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

1. Ef > Em and 5. lf < lcritical

Explanation:

The critical length of fiber is given by

where d is fiber diameter, is ultimate strength of fiber, and 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

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

Moreover, strain is inversely proportional to elastic modulus hence

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