The modulus of elasticity of composites upper bound is illustrated by the image below. To calculate modulus of elasticity of composites upper bound, four essential parameters are needed and these parameters are Modulus of Elasticity of the Matrix (Em), Modulus of Elasticity of the Particle (Ep), Volume Fraction of the Matrix (Vm) and Volume Fraction of the Particle (Vp).
The formula for calculating modulus of elasticity of composites upper bound:
Ec(u) = EmVm + EpVp
Where:
Ec(u)Â = Modulus of Elasticity of Composites Upper Bound
Em =Modulus of Elasticity of the Matrix
Also, Ep = Modulus of Elasticity of the Particle
Vm = Volume Fractions of the Matrix
Vp = Volume Fractions of the Particle
Let’s solve an example;
Find the modulus of elasticity of composites upper bound when the modulus of elasticity of the matrix is 4, the modulus of elasticity of the particle is 7, the volume fractions of the matrix is 2 and the volume fractions of the particle is 6.
This implies that;
Em =Modulus of Elasticity of the Matrix = 4
Ep = Modulus of Elasticity of the Particle = 7
Vm = Volume Fractions of the Matrix = 2
Vp = Volume Fractions of the Particle = 6
Ec(u) = EmVm + EpVp
Then, Ec(u) = (4)(2) + (7)(6)
Ec(u) = (8) + (42)
Ec(u) = 50
Therefore, the modulus of elasticity of composites upper bound is 50 Pa.
Calculating the Modulus of Elasticity of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle are Given
Em = Ec(u) – EpVp / Vm
Where:
Em =Modulus of Elasticity of the Matrix
Ec(u)Â = Modulus of Elasticity of Composites Upper Bound
Also, Ep = Modulus of Elasticity of the Particle
Vm = Volume Fractions of the Matrix
Vp = Volume Fractions of the Particle
Let’s solve an example;
Find the modulus of elasticity of the matrix when the modulus of elasticity of composites upper bound is 40, the modulus of elasticity of the particle is 10, the volume fractions of the matrix is 5 and the volume fractions of the particle is 2.
This implies that;
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Ec(u) = Modulus of Elasticity of Composites Upper Bound = 40
Ep = Modulus of Elasticity of the Particle = 10
Vm = Volume Fractions of the Matrix = 5
Vp = Volume Fractions of the Particle = 2
Em = Ec(u) – EpVp / Vm
Em = 40 – (10)(2) / 5
That is, Em = 40 – 20 / 5
Em = 20 / 5
Em = 4
Therefore, the modulus of elasticity of the matrix is 4.
Read more:Â How to Calculate and Solve for Modulus of Elasticity of Composites Lower Bound | Composites
Calculating the Modulus of Elasticity of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle are Given
Ep = Ec(u) – EmVm / Vp
Where:
Ep = Modulus of Elasticity of the Particle
Ec(u)Â = Modulus of Elasticity of Composites Upper Bound
And then, Em =Modulus of Elasticity of the Matrix
Vm = Volume Fractions of the Matrix
Vp = Volume Fractions of the Particle
Let’s solve an example;
Find the modulus of elasticity of the particle when the modulus of elasticity of composites upper bound is 50, the modulus of elasticity of the matrix is 4, the volume fractions of the matrix is 5 and the volume fractions of the particle is 10.
This implies that;
Ec(u) = Modulus of Elasticity of Composites Upper Bound = 50
Em =Modulus of Elasticity of the Matrix = 4
Vm = Volume Fractions of the Matrix = 5
Vp = Volume Fractions of the Particle = 10
Ep = Ec(u) – EmVm / Vp
Ep = 50 – (4)(5) / 10
So, Ep = 50 – 20 / 10
Ep = 30 / 10
Ep = 3
Therefore, the modulus of elasticity of the particle is 3.
Read more:Â How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties
Calculating the Volume Fraction of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Particle are Given
Vm = Ec(u) – EpVp / Em
Where:
Vm = Volume Fractions of the Matrix
Ec(u)Â = Modulus of Elasticity of Composites Upper Bound
Em =Modulus of Elasticity of the Matrix
Also, Ep = Modulus of Elasticity of the Particle
Vp = Volume Fractions of the Particle
Given an example;
Find the volume fractions of the matrix when the modulus of elasticity of composites upper bound is 30, the modulus of elasticity of the matrix is 3, the modulus of elasticity of the particle is 5 and the volume fractions of the particle is 3.
This implies that;
Ec(u) = Modulus of Elasticity of Composites Upper Bound = 30
Em =Modulus of Elasticity of the Matrix = 3
And then, Ep = Modulus of Elasticity of the Particle = 5
Vp = Volume Fractions of the Particle = 3
That is, Vm = Ec(u) – EpVp / Em
Vm = 30 – (5)(3) / 3
So, Vm = 30 – 15 / 3
Vm = 15 / 3
Vm = 5
Therefore, the volume fraction of the matrix is 5.
Calculating the Volume Fraction of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Matrix are Given
Vp = Ec(u) – EmVm / Ep
Where:
Vp = Volume Fractions of the Particle
Ec(u)Â = Modulus of Elasticity of Composites Upper Bound
Em =Modulus of Elasticity of the Matrix
Then, Ep = Modulus of Elasticity of the Particle
Vm = Volume Fractions of the Matrix
Let’s solve an example;
Find the volume fractions of the particle when the modulus of elasticity of composites upper bound is 10, the modulus of elasticity of matrix is 2, the modulus of elasticity of the particle is 4 and the volume fraction of the matrix is 3.
This implies that;
Ec(u) = Modulus of Elasticity of Composites Upper Bound = 10
Em =Modulus of Elasticity of the Matrix = 2
Also, Ep = Modulus of Elasticity of the Particle = 4
Vm = Volume Fractions of the Matrix = 3
So, Vp = Ec(u) – EmVm / Ep
Vp = 10 – (2)(3) / 4
That is, Vp = 10 – 6 / 4
Vp = 4 / 4
Vp = 1
Therefore, the volume fractions of the particle is 1.
How to Calculate Modulus of Elasticity of Composites Upper Bound Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the modulus of elasticity of composites upper bound.
To get the answer and workings of the modulus of elasticity of composites upper bound using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
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Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.
Now, Click on Composites under Materials and Metallurgical
Now, Click on Modulus of Elasticity of Composites Upper Bound under Composites
The screenshot below displays the page or activity to enter your values, to get the answer for the modulus of elasticity of composites upper bound according to the respective parameter which is the Modulus of Elasticity of the Matrix (Em), Modulus of Elasticity of the Particle (Ep), Volume Fraction of the Matrix (Vm) and Volume Fraction of the Particle (Vp).
Now, enter the values appropriately and accordingly for the parameters as required by the Modulus of Elasticity of the Matrix (Em) is 4, Modulus of Elasticity of the Particle (Ep) is 7, Volume Fraction of the Matrix (Vm) is 2 and Volume Fraction of the Particle (Vp) is 6.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia can calculate the modulus of elasticity of composites upper bound and presents the formula, workings and steps too.
