The document provides the solution to problem 4-5, which involves computing various properties for a composite material given values for the properties of the fiber and matrix materials. The properties computed include: - The shear modulus of the composite G12 = 2.9111 GPa - The elastic modulus of the fiber E1 = 94.76 GPa - The elastic modulus of the matrix E2 = 7.565 GPa - The Poisson's ratio of the composite υ12 = 0.28 The solution also outlines an approach to determine the volume fraction of the fiber Vf given constraints on the elastic moduli E1 and E2.

1. Hw solution #4
Pb:4-5:
Compute E1,E2,G12 and υ12
Giveb :
Ef=230 gpa Em=Ef/50
Gm=Em/2.6 Vf=0.4 Vm=0.6
υ f=0.25 υ m= 0.3
solution :
Em=230/50=4.6 Gpa
Gm=Ef/2.6=230/2.6=1.769 Gpa
Gf=250/2.6=92 GPA
G12=(Gm*Gf)/(GmVf+GfVm)
G12=(92*1.769)/((92*0.6)+(1.769*0.4))
G12=2.9111 Gpa
E1=Ef*Vf+Em*Vm

2. 4.6*0.6+230*0.4
E1=94.76
E2=(Em*Ef)/((Em*Vf)+(Ef*Vm))
E2=7.565
υ 12 = υf*Vf+ υm*Vm
υ 12= 0.25*0.4+0.3*0.6
υ 12 =0.28
problem 4.11 :
E1>30 Gpa
E1/E2<3.5
E1= E1=Ef*Vf+Em*Vm
E2=(Em*Ef)/((Em*Vf)+(Ef*Vm))
3.5*E2 > Ef*Vf+Em*Vm > 30
3.5E2-Em*Vm > Ef*Vf > 30-Em*Vm/Ef
(3.5E2-Em*Vm)/Ef > Vf > 30-Em*Vm/Ef

3. Assume that we have E2 and Vm and Ef,Em
We can get the other one Vf and we are sure that it satisfies the
condition :
E1>30 Gpa
E1/E2<3.5