Respuesta :
Answer:
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.
The upper limit for the specific stiffness of the composite from the given data is; 19.65 GPa
We are give;
Specific gravity of copper; ρ_cu = 8.9
Specific gravity of tungsten; ρ_tu = 19.3
Modulus of elasticity of copper; E_cu = 110 GPa
Modulus of elasticity of tungsten; E_tu = 407 GPa
Volume fraction of tungsten; V_tu = 0.7
Volume fraction of Copper; V_cu = 0.3
1) Upper limit for the specific stiffness;
Let us find the upper limit for the modulus of elasticity from the formula;
E_u = (E_cu × V_cu) + (E_tu × V_tu)
E_u = (110 × 0.3) + (407 × 0.7)
E_u = 317.9 GPa
Upper limit for the specific gravity is gotten from the formula;
ρ_u = (ρ_cu × V_cu) + (ρ_tu × V_tu)
ρ_u = (8.9 × 0.3) + (19.3 × 0.7)
ρ_u = 16.18
Specific stiffness = E_u/ρ_u
Specific stiffness = 317.9/16.18
Upper limit Specific stiffness = 19.65 GPa
2) Lower limit for the specific stiffness;
The lower limit is gotten from the formula;
Specific stiffness = ((E_cu × V_cu)/ρ_cu) + ((E_tu × V_tu)/ρ_tu)
Specific stiffness = (110 × 0.3/8.9) + (407 × 0.7/19.3)
Lower limit specific stiffness = 18.47 GPa
Read more about specific stiffness at; https://brainly.com/question/13979420
