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 (σ _{m}), Strength of the Fibre (σ_{f}), Volume Fraction of the Matrix (V_{m})** and

**Volume Fraction of the Fibre (V**

_{f}).The formula for calculating total composite strength:

σ_{c} = σ_{m}V_{m} + σ_{f}V_{f}

Where:

σ_{c} = Total Composite Strength

σ_{m} = Strength of the Matrix

σ_{f} = Strength of the Fibre

V_{m} = Volume Fraction of the Matrix

V_{f} = 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;

σ_{m} = Strength of the Matrix = 6

σ_{f} = Strength of the Fibre = 12

V_{m} = Volume Fraction of the Matrix = 10

V_{f} = Volume Fraction of the Fibre = 4

σ_{c} = σ_{m}V_{m} + σ_{f}V_{f}

σ_{c} = (6)(10) + (12)(4)

σ_{c} = (60) + (48)

σ_{c} = 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.**

σ_{m} = ^{σc – σfVf} / _{V}_{m}

Where:

σ_{m} = Strength of the Matrix

σ_{c} = Total Composite Strength

σ_{f} = Strength of the Fibre

V_{m} = Volume Fraction of the Matrix

V_{f} = 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;

σ_{c} = Total Composite Strength = 40

σ_{f} = Strength of the Fibre = 10

V_{m} = Volume Fraction of the Matrix = 5

V_{f} = Volume Fraction of the Fibre = 2

σ_{m} = ^{σc – σfVf} / _{V}_{m}

σ_{m} = ^{40 – (10)(2)} / _{5}

σ_{m} = ^{40 – 20} / _{5}

σ_{m} = ^{20} / _{5}

σ_{m} = 4

Therefore, the **strength of the matrix **is **4.**