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3 October, 15:56

The mechanical properties of a metal may be improved by incorporating fine particles of its oxide. Given that the moduli of elasticity of the metal and oxide are, respectively, 60 GPa and 380 GPa, what is the (a) upper-bound, and (b) lower-bound modulus of elasticity values (in GPa) for a composite that has a composition of 33 vol% of oxide particles.

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  1. 3 October, 17:38
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    A) Upper bound modulus of elasticity; E = 165.6 GPa

    B) Lower bound modulus of elasticity; E = 83.09 GPa

    Explanation:

    A) Formula for upper bound modulus is given as;

    E = E_m (1 - V_f) + E_f•V_f

    We are given;

    E_m = 60 GPa

    E_f = 380 GPa

    V_f = 33% = 0.33

    Thus,

    E = 60 (1 - 0.33) + 380 (0.33)

    E = (60 x 0.67) + 125.4

    E = 165.6 GPa

    B) Formula for lower bound modulus is given as;

    E = 1/[ (V_f/E_f) + ((1 - V_f) / E_m) ]

    E = 1/[ (0.33/380) + ((1 - 0.33) / 60) ]

    E = 1 / (0.0008684 + 0.01116667)

    E = 1/0.01203507

    E = 83.09 GPa
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