The critical fibre length is illustrated by the image below.

To compute for critical fibre length, three essential parameters are needed and these parameters are **Critical Fibre Stress (σ* _{f}), Fibre Diameter (d)** and

**Shear Yield Strength (τ**

_{c}).The formula for calculating critical fibre length:

l_{c} = ^{σ*fd}/_{2τc}

Where:

l_{c} = Critical Fibre Length

σ*_{f} = Critical Fibre Stress

d = Fibre Diameter

τ_{c} = Shear Yield Strength

Let’s solve an example;

Find the critical fibre length when the critical fibre stress is 15, the fibre diameter is 3 and the shear yield strength is 10.

This implies that;

σ*_{f} = Critical Fibre Stress = 15

d = Fibre Diameter = 3

τ_{c} = Shear Yield Strength = 10

l_{c} = ^{σ*fd}/_{2τc}

l_{c} = ^{(15)(3)}/_{2(10)}

l_{c} = ^{(45)}/_{(20)}

l_{c} = 2.25

Therefore, the **critical fibre length **is **2.25 cm.**

**Calculating the Critical Fibre Stress when the Critical Fibre Length, the Fibre Diameter and the Shear Yield Strength is Given.**

σ*_{f} = ^{lc x 2τc} / _{d}

Where:

σ*_{f} = Critical Fibre Stress

l_{c} = Critical Fibre Length

d = Fibre Diameter

τ_{c} = Shear Yield Strength

Let’s solve an example;

Given the critical fibre length as 24, the fibre diameter as 12 and the shear yield strength as 4. Find the critical fibre stress?

This implies that;

l_{c} = Critical Fibre Length = 24

d = Fibre Diameter = 12

τ_{c} = Shear Yield Strength = 4

σ*_{f} = ^{lc x 2τc} / _{d}

σ*_{f} = ^{24 x 2(4)} / _{12}

σ*_{f} = ^{24 x 8} / _{12}

σ*_{f} = ^{192} / _{12}

σ*_{f} = 16

Therefore, the **critical fibre stress **is **16.**

**Calculating the Fibre Diameter when the Critical Fibre Length, the Critical Fibre Stress and the Shear Yield Strength is Given.**

d = ^{lc x 2τc} / _{σ*f}

Where:

d = Fibre Diameter

l_{c} = Critical Fibre Length

σ*_{f} = Critical Fibre Stress

τ_{c} = Shear Yield Strength

Let’s solve an example;

Find the fibre diameter when the critical fibre length is 20, the critical fibre stress is 32 and the shear yield strength is 12.

This implies that;

l_{c} = Critical Fibre Length = 20

σ*_{f} = Critical Fibre Stress = 32

τ_{c} = Shear Yield Strength = 12

d = ^{lc x 2τc} / _{σ*f}

d = ^{20 x 2(12)} / _{32}

d = ^{20 x 24} / _{32}

d = ^{480} / _{32}

d = 15

Therefore, the **fibre diameter **is **15 cm.**

**Calculating the Shear Yield Strength when the Critical Fibre Length, the Critical Fibre Stress and the Fibre Diameter is Given.**

τ_{c} = ^{σ*fd} / _{lc x 2}

Where:

τ_{c} = Shear Yield Strength

l_{c} = Critical Fibre Length

σ*_{f} = Critical Fibre Stress

d = Fibre Diameter

Let’s solve an example;

Given that the critical fibre length is 14, the critical fibre stress is 8 and the fibre diameter is 6. Find the Shear Yield Strength?

This implies that;

l_{c} = Critical Fibre Length = 14

σ*_{f} = Critical Fibre Stress = 8

d = Fibre Diameter = 6

τ_{c} = ^{σ*fd} / _{lc x 2}

τ_{c} = ^{(8)(6)} / _{14 x 2}

τ_{c} = ^{48} / _{28}

τ_{c} = 1.714

Therefore, the **shear yield strength **is **1.714.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the critical fibre length.

To get the answer and workings of the critica fibre length 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 **Critical Fibre Length** under **Composites**

The screenshot below displays the page or activity to enter your values, to get the answer for the critical fibre length according to the respective parameter which is the **Critical Fibre Stress (σ* _{f}), Fibre Diameter (d)** and

**Shear Yield Strength (τ**

_{c}).Now, enter the values appropriately and accordingly for the parameters as required by the **Critical Fibre Stress (σ* _{f})** is

**15**,

**Fibre Diameter (d)**is

**3**and

**Shear Yield Strength (τ**is

_{c})**10**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the critical fibre length and presents the formula, workings and steps too.