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 0.70 and 0.30, respectively, estimate the upper limit for the specific stiffness of this composite given the data that follow.

Specific Gravity Modulus of Elasticiy (GPa)

Copper 8.9 110

Tungsten 19.3 407

The upper limit for the specific stiffness of this composite is 19.6 GPa

Explanation:

Symbol for Copper is Cu while for Tungsten is W,

E = modulus of elasticity

V = Volume fraction of the materials

P = specific gravity of the materials

Let determine the combine maximum modulus of the materials using;

E = Ecu*Vcu + Ew*Vw

E = 110*0.3 + 407*0.7 = 318 GPa

Also, determine the combine specific gravity (P) of the materials

P = Pcu*Vcu + Pw*Vw

P = 8.9*0.3 + 19.3*0.7 = 16.2

The upper limit of the specific stiffness can be found by E/P = 318/16.2 = 19.6 GPa

The lower limit can be found from

{ (Ecu*Vcu) / Pcu} + { (Ew*Vw) / Pw}

{ (110*0.3) / 8.9} + { (407*0.7) / 19.3} = 18.5 GPa

The limit for the specific stiffness of this composite 18.5 to 19.6 GPa.