Answer:
Explanation:
Given that,
Mass of boron fiber in unidirectional orientation
Mb = 5kg = 5000g
Mass of aluminum fiber in unidirectional orientation
Ma = 8kg = 8000g
A. Density of the composite
Applying rule of mixing
ρc = 1•ρ1 + 2•ρ2
Where
ρc = density of composite
1 = Volume fraction of Boron
ρ1 = density composite of Boron
2 = Volume fraction of Aluminum
ρ2 = density composite of Aluminum
ρ1 = 2.36 g/cm³ constant
ρ2 = 2.7 g/cm³ constant
To Calculate fractional volume of Boron
1 = Vb / ( Vb + Va)
Vb = Volume of boron
Va = Volume of aluminium
Also
To Calculate fraction volume of aluminum
2= Va / ( Vb + Va)
So, we need to get Va and Vb
From density formula
density = mass / Volume
ρ1 = Mb / Vb
Vb = Mb / ρ1
Vb = 5000 / 2.36
Vb = 2118.64 cm³
Also ρ2 = Ma / Va
Va = Ma / ρ2
Va = 8000 / 2.7
Va = 2962.96 cm³
So,
1 = Vb / ( Vb + Va)
1 = 2118.64 / ( 2118.64 + 2962.96)
1 = 0.417
Also,
2= Va / ( Vb + Va)
2 = 2962.96 / ( 2118.64 + 2962.96)
2 = 0.583
Then, we have all the data needed
ρc = 1•ρ1 + 2•ρ2
ρc = 0.417 × 2.36 + 0.583 × 2.7
ρc = 2.56 g/cm³
The density of the composite is 2.56g/cm³
B. Modulus of elasticity parallel to the fibers
Modulus of elasticity is defined at the ratio of shear stress to shear strain
The relation for modulus of elasticity is given as
Ec = = 1•Eb+ 2•Ea
Ea = Elasticity of aluminium
Eb = Elasticity of Boron
Ec = Modulus of elasticity parallel to the fiber
Where modulus of elastic of aluminum is
Ea = 69 × 10³ MPa
Modulus of elastic of boron is
Eb = 450 × 10³ Mpa
Then,
Ec = = 1•Eb+ 2•Ea
Ec = 0.417 × 450 × 10³ + 0.583 × 69 × 10³
Ec = 227.877 × 10³ MPa
Ec ≈ 228 × 10³ MPa
The Modulus of elasticity parallel to the fiber is 227.877 × 10³MPa
OR Ec = 227.877 GPa
Ec ≈ 228GPa
C. modulus of elasticity perpendicular to the fibers?
The relation of modulus of elasticity perpendicular to the fibers is
1 / Ec = 1 / Eb+ 2 / Ea
1 / Ec = 0.417 / 450 × 10³ + 0.583 / 69 × 10³
1 / Ec = 9.267 × 10^-7 + 8.449 ×10^-6
1 / Ec = 9.376 × 10^-6
Taking reciprocal
Ec = 106.66 × 10^3 Mpa
Ec ≈ 107 × 10^3 MPa
Note that the unit of Modulus has been in MPa,
