# How to Calculate and Solve for Ratio of Load of Fibre to Matrix | Composites

**Last Updated on August 4, 2022**

The ratio of load of fibre to matrix is illustrated by the image below.

To compute for ratio of load of fibre to matrix, four essential parameters are needed and these parameters are **Elastic Modulus of the Fibre (E _{f}), Elastic Modulus of the Matrix (E_{m}), Volume Fraction of the Fibre (V_{f})** and

**Volume Fraction of the Matrix (V**

_{m}).The formula for calculating ratio of load of fibre to matrix:

F_{(f/m)} = ^{EfVf}/_{EmVm}

Where:

F_{(f/m)} = Ratio of Load of Fibre to Matrix

E_{f} = Elastic Modulus of the Fibre

E_{m} = Elastic Modulus of the Matrix

V_{f} = Volume Fraction of the Fibre

V_{m} = Volume Fraction of the Matrix

Let’s solve an example;

Find the ratio of load of fibre to matix when the elastic modulus of the fibre is 14, the elastic modulus of the matrix is 10, the volume fraction of the fibre is 6 and the volume fraction of the matrix is 2.

This implies that;

E_{f} = Elastic Modulus of the Fibre = 14

E_{m} = Elastic Modulus of the Matrix = 10

V_{f} = Volume Fraction of the Fibre = 6

V_{m} = Volume Fraction of the Matrix = 2

F_{(f/m)} = ^{EfVf}/_{EmVm}

F_{(f/m)} = ^{(14)(6)}/_{(10)(2)}

F_{(f/m)} = ^{(84)}/_{(20)}

F_{(f/m)} = 4.2

Therefore, the **ratio of load of fibre to matrix **is **4.2.**

**Calculating the Elastic Modulus of the Fibre when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Matrix, the Volume Fraction of the Fibre and the Volume Fraction of the Matrix is Given.**

E_{f} = ^{F(f/m) x EmVm} / _{Vf}

Where:

E_{f} = Elastic Modulus of the Fibre

F_{(f/m)} = Ratio of Load of Fibre to Matrix

E_{m} = Elastic Modulus of the Matrix

V_{f} = Volume Fraction of the Fibre

V_{m} = Volume Fraction of the Matrix

Let’s solve an example;

Find the elastic modulus of the fibre when the ratio of load of fibre to matrix is 20, the elastic modulus of the matrix is 4, the volume fraction of the matrix is 2 and the volume fraction of the fibre is 12.

This implies that;

F_{(f/m)} = Ratio of Load of Fibre to Matrix = 20

E_{m} = Elastic Modulus of the Matrix = 4

V_{f} = Volume Fraction of the Fibre = 12

V_{m} = Volume Fraction of the Matrix = 2

E_{f} = ^{F(f/m) x EmVm} / _{Vf}

E_{f} = ^{20 x (4)(2)} / _{12}

E_{f} = ^{20 x 8} / _{12}

E_{f} = ^{160} / _{12}

E_{f} = 13.33

Therefore, the **elastic modulus of the fibre **is **13.33**

**Calculating the Elastic Modulus of the Matrix when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Volume Fraction of the Fibre and the Volume Fraction of the Matrix is Given.**

E_{m} = ^{EfVf} / _{F(f/m) x Vm}

Where:

E_{m} = Elastic Modulus of the Matrix

F_{(f/m)} = Ratio of Load of Fibre to Matrix

E_{f} = Elastic Modulus of the Fibre

V_{f} = Volume Fraction of the Fibre

V_{m} = Volume Fraction of the Matrix

Let’s solve an example;

Find the elastic modulus of the matrix when the ratio of load of fibre to matrix is 18, the elastic modulus of the fibre is 12, the volume fraction of the fibre is 14 and the volume fraction of the matrix is 8.

This implies that;

F_{(f/m)} = Ratio of Load of Fibre to Matrix = 18

E_{f} = Elastic Modulus of the Fibre = 12

V_{f} = Volume Fraction of the Fibre = 14

V_{m} = Volume Fraction of the Matrix = 8

E_{m} = ^{EfVf} / _{F(f/m) x Vm}

E_{m} = ^{(12)(14)} / _{18 x 8}

E_{m} = ^{168} / _{144}

E_{m} = 1.167

Therefore, the **elastic modulus of the matrix **is **1.167**

**Calculating the Volume Fraction of the Matrix when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Elastic Modulus of the Matrix and the Volume Fraction of the Fibre is Given.**

V_{f} = ^{F(f/m) x EmVm} / _{Ef}

Where:

V_{f} = Volume Fraction of the Fibre

F_{(f/m)} = Ratio of Load of Fibre to Matrix

E_{f} = Elastic Modulus of the Fibre

E_{m} = Elastic Modulus of the Matrix

V_{m} = Volume Fraction of the Matrix

Let’s solve an example;

Find the volume fraction of the fibre when the ratio of load of fibre to matrix is 7, the elastic modulus of the fibre is 20, the elastic modulus of the matrix is 4 and the volume fraction of the matrix is 6.

This implies that;

F_{(f/m)} = Ratio of Load of Fibre to Matrix = 7

E_{f} = Elastic Modulus of the Fibre = 20

E_{m} = Elastic Modulus of the Matrix = 4

V_{m} = Volume Fraction of the Matrix = 6

V_{f} = ^{F(f/m) x EmVm} / _{Ef}

V_{f} = ^{7 x (4)(6)} / _{20}

V_{f} = ^{168} / _{20}

V_{f} = 8.4

Therefore, the **volume fraction of the fibre **is **8.4**

**Calculating the Volume Fraction of the Fibre when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Elastic Modulus of the Matrix and the Volume Fraction of the Matrix is Given.**

V_{m} = ^{EfVf} / _{F(f/m) x Em}

Where:

V_{m} = Volume Fraction of the Matrix

F_{(f/m)} = Ratio of Load of Fibre to Matrix

E_{f} = Elastic Modulus of the Fibre

E_{m} = Elastic Modulus of the Matrix

V_{f} = Volume Fraction of the Fibre

Let’s solve an example;

Find the volume fraction of the matrix when the ratio of load of fibre to matrix is 10, the elastic modulus of the fibre is 16, the elastic modulus of the matrix is 6 and the volume fraction of the fibre is 8.

This implies that;

F_{(f/m)} = Ratio of Load of Fibre to Matrix = 10

E_{f} = Elastic Modulus of the Fibre = 16

E_{m} = Elastic Modulus of the Matrix = 6

V_{f} = Volume Fraction of the Fibre = 8

V_{m} = ^{EfVf} / _{F(f/m) x Em}

V_{m} = ^{(16)(8)} / _{10 x 6}

V_{m} = ^{128} / _{60}

V_{m} = 2.13

Therefore, the **volume fraction of the matrix **is **2.13**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the ratio of load of fibre to matrix.

To get the answer and workings of the ratio of load of fibre to matrix 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

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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 **Ratio of Load of Fibre to Matrix** under **Composites**

The screenshot below displays the page or activity to enter your values, to get the answer for the ratio of load of fibre to matrix according to the respective parameter which is the **Elastic Modulus of the Fibre (E _{f}), Elastic Modulus of the Matrix (E_{m}), Volume Fraction of the Fibre (V_{f})** and

**Volume Fraction of the Matrix (V**

_{m}).Now, enter the values appropriately and accordingly for the parameters as required by the **Elastic Modulus of the Fibre (E _{f})** is

**14**,

**Elastic Modulus of the Matrix (E**is

_{m})**10**,

**Volume Fraction of the Fibre (V**is

_{f})**6**and

**Volume Fraction of the Matrix (V**is

_{m})**2**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the ratio of load of fibre to matrix and presents the formula, workings and steps too.