Question

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, 52 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 90 vol% of oxide particles.

Answer 1

a) 347.2 GPa

b) 233.02 GPa

Step-by-step explanation:

a) To find the upper bound modulus of elasticity, we use the formula:

`E_c(u) = E_mV_m + E_pV_p`

Where,

Volume fraction= V

E = modulus

Em=52GPa

Ep=380GPa

Vp=90%=0.90

Vm= 100%-90%=10%=0.10

We now have:

`E_c(u) = (52*0.1)+(380*0.90)`

= 5.2+342

= 347.2 GPa

b) For the lower bound modulus of elasticity, we use:

`E_c(l) = (E_mE_p)/(E_pV_m+E_m+V_p)`

`=(52*380)/((52*0.90)+(380*0.10))`

=233.02 GPa