find out the modulus of elasticitya

Question

Find out the modulus of elasticity:

A unidirectional FRP is produced with fibre volume ratio of 60%. The density of fibre is 1480 kg/m³ and that of matrix is 1200 kg/m³. Calculate the weight percentages of matrix and fibre and the density of the composite. Also find out the modulus of elasticity of composite if E_f = 70 MPa, E_m = 3 GPa.

Solution

Supposed that composite has a volume of 1 m³, so that

 V _f  = 0.6 m³               and           V_m = 0.4 m³

Mass of fibre = 1480 × 0.6 = 888 kg

And mass of matrix = 1200 × 0.4 = 480 kg

Mass of composite = 888 + 480 = 1368 kg

Density of composite = 1368 kg/1 m³ = 1368 kg/m³

Weight % of fibre = (888 /1368)  × 100 = 64.9%

Weight % of matrix = 100 - 64.9 = 35.1

Modulus of elasticity of composite

                  E = V _f E _f  + V_m  E_m

              = 0.4 × 3 + 0.6 × 70

             E = 43.2 MPa