Question

The mechanical properties of some metals may be improved by incorporating fine particles of their oxides. If the moduli of elasticity of a hypothetical metal and its oxide are, respectively, 55 GPa and 430 GPa, what is the upper-bound modulus of elasticity value for a composite that has a composition of 31 vol% of oxide particles

Answer 1

Answer:

171.2 GPa

Explanation:

I explained every step in the attached file, please kindly go through it.

But the answer is 171.2 GPa

Answer 2

The upper bound modulus will be "163 GPa".

According to the question:

Modulus elasticity,

• Metal, $E_m = 55 \ GPa$
• Oxide, $E_o = 430 \ GPa$

Volume fraction,

• Metal = 53% or 0.53
• Oxide = 31% or 0.31

By using the rules of mixture,

The upper bound will be:

→ $E_u= E_mV_m+E_o V_o$

By putting the values, we get

        $= (55\times 0.53)+(430\times 0.31)$

        $= 29.15+133.3$

        $= 163 \ GPa$

Thus the above answer is right.

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