Question

Calculate the modulus of elasticity of carbon-epoxy composite under isostraincondition if thecomposite consists of 40% carbon fibers and 60% epoxy by volume. Also, calculate the percentageof load carried by the carbon fibers. The modulus of elasticity of the carbon fibers and the epoxyare 350 GPa and3.5 GPa, respectively.

Answer 1

Answer:

1. 142.1 GPa

2. 98.52%

Explanation:

1. The modulus of elasticity of carbon-epoxy composite is calculated using the following formula:

Ec = VmEm + VfEf

where Vm: volume of Epoxy

            Em: modulus of the elasticity of the epoxy

            Vf: volume of carbon fiber

             Ef: modulus of the elasticity of the carbon fiber

Given that :

          Vm = 0.6

            Em = 3.5 GPa

            Vf = 0.4

             Ef: 350 Gpa

Therefore Ec = (0.6 × 3.5 GPa + (0.4 × 350 GPa)

Ec = 142.1 GPa

The modulus of elasticity of carbon-epoxy composite is 142.1 GPa

2. Percentage of load carried by the carbon fibers is given by the following equation: Ff/Fc = (Ef/Ec)×Vf

where Ff is the force carried by carbon fibers, Fc is the force applied to the composite, Ec is the modulus of elasticity of the composite,  Ef is the  modulus of the elasticity of the carbon fiber and Vf  the volume of carbon fiber.

Given that:

       EF = 350 Gpa

        Ec = 142.1 GPa

         Vf = 0.4

Substituting the above values into the equation:

Ff/Fc = (350 GPa/142.1 GPa)×0.4 = 0.9852 = 98.52%

The percentage of load carried by the carbon fibers is there 98.52%