The total composite strength is illustrated by the image below. If you want to calculate the total composite strength, four essential parameters are needed and these parameters are Strength of the Matrix (σm), Strength of the Fibre (σf), Volume Fraction of the Matrix (Vm) and Volume Fraction of the Fibre (Vf).
The formula for calculating total composite strength:
σc = σmVm + σfVf
Where:
σc = Total Composite Strength
σm = Strength of the Matrix
Also, σf = Strength of the Fibre
Vm = Volume Fraction of the Matrix
Vf = Volume Fraction of the Fibre
Let’s solve an example;
Find the total composite strength when the strength of the matrix is 6, the strength of the fibre is 12, the volume fraction of the matrix is 10 and the volume fraction of the fibre is 4.
This implies that;
σm = Strength of the Matrix = 6
σf = Strength of the Fibre = 12
Vm = Volume Fraction of the Matrix = 10
Vf = Volume Fraction of the Fibre = 4
σc = σmVm + σfVf
That is, σc = (6)(10) + (12)(4)
σc = (60) + (48)
σc = 108
Therefore, the total composite strength is 108 Pa.
Calculating the Strength of the Matrix when the Total Composite Strength, the Strength of the Fibre, the Volume Fraction of the Matrix and the Volume Fraction of the Fibre are Given
σm = σc – σfVf / Vm
Where:
σm = Strength of the Matrix
σc = Total Composite Strength
Also, σf = Strength of the Fibre
Vm = Volume Fraction of the Matrix
Vf = Volume Fraction of the Fibre
Let’s solve an example;
Find the strength of the matrix when the total composite strength is 40, the strength of the fibre is 10, the volume fractions of the matrix is 5 and the volume fractions of the fibre is 2.
This implies that;
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σc = Total Composite Strength = 40
σf = Strength of the Fibre = 10
Vm = Volume Fraction of the Matrix = 5
Vf = Volume Fraction of the Fibre = 2
σm = σc – σfVf / Vm
σm = 40 – (10)(2) / 5
That is, σm = 40 – 20 / 5
σm = 20 / 5
σm = 4
Therefore, the strength of the matrix is 4.
Read more:Â How to Calculate and Solve for Total Load on Composite | Composites
Calculating the Strength of the Fibre when the Total Composite Strength, the Strength of the Matrix, the Volume Fraction of the Matrix and the Volume Fraction of the Fibre are Given
σf = σc – σmVm / Vf
Where:
σf = Strength of the Fibre
σc = Total Composite Strength
Then, σm = Strength of the Matrix
Vm = Volume Fraction of the Matrix
Vf = Volume Fraction of the Fibre
Let’s solve an example;
Find the strength of the fibre when the total composite strength is 50, the strength of the matrix is 4, the volume fractions of the matrix is 5 and the volume fractions of the fibre is 10.
This implies that;
σc = Total Composite Strength = 50
σm = Strength of the Matrix = 4
Vm = Volume Fraction of the Matrix = 5
Vf = Volume Fraction of the Fibre = 10
σf = σc – σmVm / Vf
σf = 50 – (4)(5) / 10
That is, σf = 50 – 20 / 10
σf = 30 / 10
σf = 3
Therefore, the strength of the fibre is 3.
Calculate the volume fraction of the matrix when the total composite strength, the strength of the matrix, the strength of the fibre, and the volume fraction of the fibre are given
Vm = σc – σfVf / σm
Where:
Vm = Volume Fraction of the Matrix
σc = Total Composite Strength
σm = Strength of the Matrix
Then, σf = Strength of the Fibre
Vf = Volume Fraction of the Fibre
Given an example;
Find the volume fractions of the matrix when the total composite strength is 30, the strength of the matrix is 3, the strength of the fibre is 5 and the volume fractions of the fibre is 3.
This implies that;
σc = Total Composite Strength = 30
σm = Strength of the Matrix = 3
Also, σf = Strength of the Fibre = 5
Vf = Volume Fraction of the Fibre = 3
That is, Vm = σc – σfVf / σm
Vm = 30 – (5)(3) / 3
So, Vm = 30 – 15 / 3
Vm = 15 / 3
Vm = 5
Therefore, the volume fraction of the matrix is 5.
Read more:Â How to Calculate and Solve for Modulus of Elasticity of Composites Upper Bound | Composites
Calculating the Volume Fraction of the Fibre when the Total Composite Strength, the Strength of the Matrix, the Strength of the Fibre and the Volume Fraction of the Matrix are Given
Vf = σc – σmVm / σf
Where:
Vf = Volume Fraction of the Fibre
σc = Total Composite Strength
Also, σm = Strength of the Matrix
σf = Strength of the Fibre
Vm = Volume Fraction of the Matrix
Let’s solve an example;
Find the volume fractions of the fibre when the total composite strength is 10, the strength of matrix is 2, the strength of the fibre is 4 and the volume fraction of the matrix is 3.
This implies that;
σc = Total Composite Strength = 10
σm = Strength of the Matrix = 2
That is, σf = Strength of the Fibre = 4
Vm = Volume Fraction of the Matrix = 3
Vf = σc – σmVm / σf
That is, Vf = 10 – (2)(3) / 4
Vf = 10 – 6 / 4
Then, Vf = 4 / 4
Vf = 1
Therefore, the volume fractions of the fibre is 1.
How to Calculate the Total Composite Strength Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the total composite strength.
To get the answer and workings of the total composite strength using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
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 Total Composite Strength under Composites
The screenshot below displays the page or activity to enter your values, to get the answer for the total composite strength according to the respective parameter which is the Strength of the Matrix (σm), Strength of the Fibre (σf), Volume Fraction of the Matrix (Vm) and Volume Fraction of the Fibre (Vf).
Now, enter the values appropriately and accordingly for the parameters as required by the Strength of the Matrix (σm) is 6, Strength of the Fibre (σf) is 12, Volume Fraction of the Matrix (Vm) is 10 and Volume Fraction of the Fibre (Vf) is 4.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator—The Calculator Encyclopedia can calculate the total composite strength and presents the formula, workings, and steps, too.
