Question

A continuous and aligned fiber-reinforced composite having a cross-sectional area of 1130 mm2 is subjected to an external tensile load. If the stresses sustained by the fiber and matrix phases are 156 MPa and 2.75 MPa, respectively, the force sustained by the fiber phase is 74,000 N and the total longitudinal strain is 1.25 x 10-3, what is the value of the modulus of elasticity of the composite material in the longitudinal direction?

Answer 1

Ec=53.7×10⁹N/m² =53.7Gpa

Step-by-step explanation:

To calculate the modulus of elasticity in the longitudinal direction. This is possible realizing Ec=σ/ε where σ=(Fm+Ff)/Ac

`Ec=Sigma/E\\Ec=((Fm+Ff)/E)/(Ac)\\ Ec=(1802+74,000)/((1.25*10^(-3))(1130)(1/1000)^(2)  )\\ Ec=53.7*10^(9)N/m^(2)\\or\\Ec=53.7GPa`