How to Calculate and Solve for Critical Fibre Length | Composites

Last Updated on August 3, 2022

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 = ^{l_c x 2τ_c} / _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 = ^{l_c x 2τ_c} / _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 = ^{l_c x 2τ_c} / _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 = ^{l_c x 2τ_c} / _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.

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_c) is 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.