## 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.