Question

for a continuous and aligned Kevlar-29 fiber-reinforced composite, the modulus elasticity in the longitudinal direction is 19 GPa and the modulus of elasticity in the transverse direction is 7.7 GPA​. if the volume fraction of fibers is 0.40, what is the modulus of elasticity for the fiber phase?

Answer 1

This problem asks for us to compute the modulas elasticity of fiber and matrix phases for acontinuous and aligned Kevlar-29 fiber-reinforced composite.We can write expressions for the longitudinal moduli using Equations

Ecl=Em(1−Vf)+Ef*Vf

Here Ecl = 19 GPa,Vf = 0.40

19 GPa =Em(1−0.40) +Ef(0.40) ______________(1)

Now We can write expressions for the transverse elastic moduli using Equations

Ect=(EmEf)/((1−Vf)Ef+VfEm)

Here Ect = 7.7 GPa,Vf = 0.40

7.7 GPa =EmEf / (1−0.40)Ef+0.40Em   ______________(2)

Solving these two expressions simultaneously for Em and Ef leads to

Em = 12.09 GPa

Ef = 29.36 GPa =modulas elasticity of fiber phase.