Question

2. Consider unidirectionally reinforced glass/epoxy composites. The fibers are continuous and 60% by volume. The tensile strength of glass fibers is 1 GPa and the Young's modulus is 70 GPa. The tensile strength of the epoxy matrixis 60 MPa and its Young's modulus is 3GPa. Compute the Young's modulus and the tensile strength of the composite in the longitudinal direction.

Answer 1

ANSWER:

Young's modulus for mixture is defined as:

E = Ef Vf + Em Vm

   Here: f = fiber ; m = epoxy matrix ; v = volume fraction;

From the given data:

Ef = 70Gpa ,  $\sigma$f = 1Gpa , Vf = 0.6

Em = 3Gpa , $\sigma$ m = 60mpa , Vm = 0.4  

Then,

Young's modulus E = (70) (0.6) + (3)(0.4)

E = 43.2Gpa

For Lognitudinal strain:-

fiber ---> Ef  =  $\sigma$f / Ef = 1/70 = 0.0142

epoxy matrix ---> Em =  $\sigma$m / Em = 60(106) / 3(109) = 0.2

So, from fiber and epoxy matrix we can write as

Ef  < Em

So, $\sigma$ m' = Em  *   Ef = (3) (0.0142) = 0.0426Gpa

From tensile strength:-

$\sigma$ = $\sigma$ f Vf   + $\sigma$ m'  Vm

$\sigma$ = (0.6)+(1) + (0.4) (0.0426)

$\sigma$ = 0.6 + 0.01704

  $\sigma$ = 0.61704Gpa

$\sigma$= 617.04Mpa