Question

Practice Problem: Large-Particle CompositesThe 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.

Answer 1

Answer: (a). Ec(μ) = 165.6 GPa

(b). Ec(∝) = 83.09 GPa

Explanation:

this is quite straightforward, so we will go step by step.

from the data we have that,

Moduli of elasticity of the metal  -(Em) is 60 Gpa

Moduli of elasticity of oxide is  (Ep) is 380 Gpa

volume Vp = 33% = 0.33

(a). To solve the upper bound-modulus of the elasticity is calculate thus;

Ec (μ) = EmVm + EpVp ----------------(1)

where E rep the modulus of elasticity

v rep the volume fraction

c rep the composite

Vm = 100% - Vp

Vm =  100% - 33% = 67%

Vm = 0.67

substituting the valus of Em, Vm, Ep, Vp  from equation (1) we have;

Ec(μ) = (60×0.67) + (380×0.33)

Ec(μ) = 40.2 + 125.4 = 165.6 GPa

Ec(μ) = 165.6 GPa

(b). The lower bound modulus of elasticity can be calculated thus;

Ec(∝) = EmVp / EpVm + EmVp -------------- (2)

substituting values Em,Vm,Ep,Vp.

Ec(∝) = 60×30 / (380×0.67) + (60 ×0.33)

Ec(∝) = 22800 / 254.6 + 19.8 = 83.09 GPa

Ec(∝) = 83.09 GPa

cheers i hope this helps!!!!