volume fraction of fibresthe epoxy material is

Question

Volume fraction of fibres:

The epoxy material is prepared to be stressed to its full strength. What must be volume fraction of fibres?

Solution

Here

σ′ = 1200 MPa, σ ′_m= 80 MPa,  E _f / E_m = 24, x = 0.25

∴          0.25 =  1200 - 80 + V _f (1 - 24) 80 /1200 + 80 (1 - 24)

                       =1120 + (- 1840) V _f/- 640

∴          V          = 640 × 0.25 - 1120 /- 1840   = 960 /1840  = 0.52