# How to Calculate and Solve for Total Composite Strength | Composites

The total composite strength is illustrated by the image below.

To compute for 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
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
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 is Given.

σm = σc – σfVf / Vm

Where:

σm = Strength of the Matrix
σc = Total Composite Strength
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;

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
σm = 40 – 20 / 5
σm = 20 / 5
σm = 4

Therefore, the strength of the matrix is 4.

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 is Given.

σf = σc  – σmVm / Vf

Where:

σf = Strength of the Fibre
σc = Total Composite Strength
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
σf = 50 – 20 / 10
σf = 30 / 10
σf = 3

Therefore, the strength of the fibre is 3.

Calculating 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 is Given.

Vm = σc – σfVf / σm

Where:

Vm = Volume Fraction of the Matrix
σc = Total Composite Strength
σm = Strength of the Matrix
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
σf = Strength of the Fibre = 5
Vf = Volume Fraction of the Fibre = 3

Vm = σc – σfVf / σm
Vm = 30 – (5)(3) / 3
Vm = 30 – 15 / 3
Vm = 15 / 3
Vm = 5

Therefore, the volume fraction of the matrix is 5.

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 is Given.

Vf = σc – σmVm / σf

Where:

Vf = Volume Fraction of the Fibre
σc = Total Composite Strength
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
σf = Strength of the Fibre = 4
Vm = Volume Fraction of the Matrix = 3

Vf = σc – σmVm / σf
Vf = 10 – (2)(3) / 4
Vf = 10 – 6 / 4
Vf = 4 / 4
Vf = 1

Therefore, the volume fractions of the fibre is 1.

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:

You can also try the demo version via https://www.nickzom.org/calculator

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 (Vmis 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 solves for the total composite strength and presents the formula, workings and steps too.