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 0.18 and 0.82, 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

Respuesta :

Using the information provided, 19.65 GPa is the maximum specific stiffness of the composite that can be calculated.

We provide;

Copper has a specific gravity of _cu = 8.9.

Tungsten has a specific gravity of 19.3 (_tu).

Copper's elasticity modulus is 110 GPa.

E tu = 407 GPa is the tungsten's elasticity modulus.

Tungsten volume fraction: V tu = 0.7

Copper volume percent, V cu = 0.3

1) The maximum rigidity permitted;

Let's use the formula to determine the modulus of elasticity's maximum value;

E u is equal to (E cu V cu) plus (E tu V tu).

E u = (110 × 0.3) + (407 × 0.7)

E u = 317.9 GPa

The formula yields an upper bound for the specific gravity;

(_cu V cu) + (_tu V tu) = _u

ρ u = (8.9 × 0.3) + (19.3 × 0.7)

ρ u = 16.18

E/u = Specific stiffness

Stiffness specific = 317.9/16.18

Specific stiffness upper limit = 19.65GPa

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