Question

A unidirectional E-Glass fiber-epoxy composite material contains 61% by volume E-Glass fibers stressed under isostrain conditions. The E-Glass fibers have a tensile modulus of 10x106 psi, and a tensile strength of 0.35x106 psi. The epoxy matrix has a tensile modulus of 0.45x106 psi, and a tensile strength of 9.0x103 psi. What is the strength of the composite material and what fraction of the load is carried by the E-Glass fibers?

Answer 1

The total load carried by the fiber will be "98%".

Step-by-step explanation:

The given values are:

`V_(f)=0.61`

`V_(m)=1-V_(f)`

`=1-0.61`

`=0.39`

`E_(f)=10 \ Mpa`

`\sigma_(f)=0.35 \ Mpa`

`E_(m)=0.45 \ Mpa` ,
`\sigma_(m)=9* 10^(-3) \ Mpa`

As we know,

⇒
`E_(e)=fE_(f)+mE_(m)`

On putting the estimated values, we get

⇒
`=0.61* 10+0.39* 0.95`

⇒
`=6.27 \ Mpa`

Now,

⇒
`\sigma_(c)=f\sigma_(f)+m\sigma_(m)`

On putting the estimated values, we get

⇒
`=0.61* 0.35+0.39* 0.009`

⇒
`=0.217 \ Mpa`

Therefore,

The load carried by fiber,

`=(f\sigma_(f))/(\sigma_(c))`

`=(0.35* 0.61)/(0.217)`

`=0.98` i.e., 98%