The tensile strengths MPa of Eglass fiber and graphiteHM fib

The tensile strengths (MPa) of E-glass fiber and graphite-HM fiber are 3, 450 and 2, 400 respectively. It was measured that the E-glass fiber reinforced vinyl ester, with a fiber volume fraction of 30%, has a tensile strength of 1073.5 MPa. Estimate the tensile strength of graphite-HM fiber reinforced vinyl ester with a fiber volume fraction of 40%. Note that the law of mixture says P_c = sigma_i = 1^n V_i O_i, where P_c is the property of the composite, P_i is the property of thei^th constituent, V_i is the volume of the i^th constituent, and n is the total number of constituents.

Solution

Let P_CE.P_E.P_V, are the Tensile strengths of Composite of Eglass fiber reinfoced vinyl ester, Eglass fiber, Vinyl ester respectively.

P_{CE =} 1073.5MPa

P_{E =} 3450 MPa

V_v ,V_E = volume fractions of Vinyl ester and Eglass fiber in Composite Eglass fiber and vinyl ester

V_{E =} 0.3 = 30%

V_v = 1- 0.3 = 0.7

First find the tensile stength of venyl ester by

P_cE = (P_vV_v +P_EV_E)

1073.5 = (P_v *0.7 +3450 * 0.3)

P_v = 55 MPa

The tensile stength of graphite -HM fiber reinforced venyl ester by

P_cG = (P_vV_v +P_GV_G)

where

P_G = Tensile strenth of graphite -HM fibre = 2400MPa

V_{G =} Volume fraction of graphite -HM fibre = 0.4 = 40%

V_v = volume fractions of Vinyl ester in graphite -HM fiber reinforced venyl ester = 1- 0.4 = 0.6

P_cG =tensile stength of graphite -HM fiber reinforced venyl ester

P_cG = (55*0.6 +2400*0.4) = 993MPa

The tensile stength of graphite -HM fiber reinforced venyl ester = 993MPa