Question

A large-particle composite consisting of tungsten particles within a copper matrix is to be prepared. If the volume fractions of tungsten and copper are 0.90 and 0.10, respectively, estimate the upper limit for the specific stiffness of this composite given the data that follow. Specific Gravity Modulus of Elasticity (GPa)

Copper 8.9 110
Tungsten 19.3 407

Answer 1

Specific stiffness=37.95 GPa

Step-by-step explanation:

Given that

Volume fraction of tungsten V₁ = 0.9

Volume fraction of copper V₂ = 0.1

Specific gravity for tungsten S₁ = 19.3

Specific gravity for copper S₂= 8.9

Modulus of Elasticity for tungsten E₁= 407 GPa

Modulus of Elasticity for copper E₂ = 110 GPa

Modulus of Elasticity for mixture

E= E₁V₁+E₂V₂

E = 110 x 0.1 + 407 x 0.9 GPa

E=377.3 GPa

Specific gravity for mixture

S= S₁V₁+S₂V₂

S = 19.3 x 0.1 + 8.9 x 0.9

S=9.94

Specific stiffness K

`K=(E)/(S)`

`K=(377.3)/(9.94)`

K=37.95 GPa

Specific stiffness=37.95 GPa