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

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Answer:

171.2 GPa

Explanation:

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But the answer is 171.2 GPa

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The upper bound modulus will be "163 GPa".

According to the question:

Modulus elasticity,

  • Metal, [tex]E_m = 55 \ GPa[/tex]
  • Oxide, [tex]E_o = 430 \ GPa[/tex]

Volume fraction,

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

By using the rules of mixture,

The upper bound will be:

→ [tex]E_u= E_mV_m+E_o V_o[/tex]

By putting the values, we get

        [tex]= (55\times 0.53)+(430\times 0.31)[/tex]

        [tex]= 29.15+133.3[/tex]

        [tex]= 163 \ GPa[/tex]

Thus the above answer is right.

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