Question

It is desired to produce a continuous and oriented carbon fiber-reinforced epoxy having a modulus of elasticity of at least 83 GPa in the direction of fiber alignment. The modulus of elasticity of the graphite fiber is 260 GPa, and the modulus of elasticity of the epoxy is 2.4 GPa. What is the minimum volume fraction of fibers required to meet this requirement. (this is a Chapter 16 problem) Answer: the minimum fiber volume fraction is:__________

Answer 1

Answer:

0.3129

Explanation:

Calculate The minimum fiber volume fraction using the relation below

E = x * E1 + ( 1 - x ) E2  ------ ( 1 )

given that :

E = 83 GPa , x = ?

E1 = 260 GPa ,  E2 = 2.4 GPA

Insert values back into equation 1

Then ; 80.6 = 257.6 x

∴ x ( volume fraction ) = 80.6 / 257.6  = 0.3129