Calculate the modulus of elasticity for a composite material consisting of 60 percent
by volume of continuous E-glass fiber and 40 percent epoxy resin for the matrix when
stressed under isostress conditions. The modulus of elasticity of the E glass is 72.4 GPa and
that of the epoxy resin is 3.1GPa.
E = E1•V1 +E2•V2 = 0.6•72.4 +
0.4•3.1 =43.44 +1.24 =44.68 GPa
Oh, modulus of elasticity, such a fancy term! It's like the material's way of saying "I'm resistant to deformation, but I'll still give you a bit of flexibility." So, let's get down to business.
To calculate the modulus of elasticity for the composite material, we need to take into account the volume fraction of each component. But don't worry, I won't bore you with number crunching, I'll use my clown math instead!
First, we'll calculate the weighted average modulus, which is determined by the volume fraction of the components. So, we have 60% E-glass fiber with a modulus of 72.4 GPa and 40% epoxy resin with a modulus of 3.1 GPa.
To compute the weighted average, we'll multiply the modulus of each component by its corresponding volume fraction and then add up the results.
So, for the E-glass fiber: 72.4 GPa * 0.60 = 43.44 GPa
And for the epoxy resin: 3.1 GPa * 0.40 = 1.24 GPa
Now, let's add these two values together: 43.44 GPa + 1.24 GPa = 44.68 GPa
Ta-da! The modulus of elasticity for the composite material is approximately 44.68 GPa. Remember, this value applies under isostress conditions, meaning that the stress is evenly distributed throughout the material.
I hope you enjoyed this little math circus act!
To calculate the modulus of elasticity for the composite material, we can use the rule of mixtures. The rule of mixtures states that the composite modulus of elasticity is equal to the volume fraction of each component multiplied by its modulus of elasticity, summed together.
Given:
Volume fraction of E-glass fiber (V_f) = 0.60
Volume fraction of epoxy resin (V_m) = 0.40
Modulus of elasticity of E glass (E_f) = 72.4 GPa
Modulus of elasticity of epoxy resin (E_m) = 3.1 GPa
The modulus of elasticity for the composite material (E_composite) can be calculated as follows:
E_composite = V_f * E_f + V_m * E_m
Substituting the given values into the equation:
E_composite = (0.60 * 72.4 GPa) + (0.40 * 3.1 GPa)
Calculating this equation gives:
E_composite = 43.44 GPa + 1.24 GPa
E_composite = 44.68 GPa
Therefore, the modulus of elasticity for the composite material is 44.68 GPa.
To calculate the modulus of elasticity for a composite material, you can use the rule of mixtures. The rule of mixtures considers the individual properties of the constituents in determining the overall behavior of the composite.
The modulus of elasticity of a composite material can be calculated using the following formula:
E_composite = Vf * Ef + Vm * Em
Where:
E_composite is the modulus of elasticity of the composite material.
Vf is the volume fraction of the fiber component.
Vm is the volume fraction of the matrix component.
Ef is the modulus of elasticity of the fiber component.
Em is the modulus of elasticity of the matrix component.
In this case:
Vf = 60% = 0.6 (fiber volume fraction)
Vm = 40% = 0.4 (matrix volume fraction)
Ef = 72.4 GPa (modulus of elasticity of E-glass fiber)
Em = 3.1 GPa (modulus of elasticity of epoxy resin)
Plugging these values into the formula, we can calculate the modulus of elasticity of the composite:
E_composite = 0.6 * 72.4 GPa + 0.4 * 3.1 GPa
E_composite = 43.44 GPa + 1.24 GPa
E_composite = 44.68 GPa
Therefore, the modulus of elasticity for the composite material is 44.68 GPa.