Assume that a high modulus carbonepoxy reinforced plastic wi

Assume that a high modulus carbon-epoxy reinforced plastic with longitudinal fibers contain 20% high modulus carbon fibers. The elastic modulus of the epoxy matrix is 100 GPa. Determine the elastic modulus of the composite (in GPa). Determine the fraction of the load supported by the fibers (in %). Show all work clearly.

Solution

High modulus PAN based carbon fiber has modulus in the order of 400 GPa.

Given, E_m = 100 GPa, Let E_f = 400 GPa, V_f = 0.2, V_m = 0.8

So, Elastic modulus of composite, E_c = V_fE_f + V_m*E_m = 0.2*400+0.8*100 =160 GPa Ans

Let the total load is P.

Then, elongation = (P_fL/A_fE_f) = (P_mL/A_mE_m)

or, (P_f/(0.2*400)) = (P_m/(0.8*100)), P_f = P_m

So, fiber will carry 50% of the total load. Ans