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.**

Continue reading How to Calculate and Solve for Critical Fibre Length | Composites