How to Calculate and Solve for Fracture Toughness | Fracture

Last Updated on December 14, 2022

The image of fracture toughness is represented below.

To compute for fracture toughness, three essential parameters are needed and these parameters are Applied Load Constant (Y), Material Critical Stress (σ_c) and Length of Crack on Surface (a).

The formula for calculating fracture toughness:

K_c = Yσ_c√(πa)

Where:

K_c = Fracture Toughness
Y = Applied Load Constant
σ_c = Material Critical Stress
a = Length of Crack on Surface

Let’s solve an example;
Find the fracture toughness when the applied load constant is 9, the material critical stress is 5 and the length of crack on surface is 2.

This implies that;

Y = Applied Load Constant = 9
σ_c = Material Critical Stress = 5
a = Length of Crack on Surface = 2

K_c = Yσ_c√(πa)
K_c = (9)(5)√(π(2))
K_c = (45)√(6.283)
K_c = (45)(2.50)
K_c = 112.7

Therefore, the fracture toughness is 112.7 J/cm².

Calculating the Applied Load Constant when the Fracture Toughness, the Material Critical Stress and the Length of Crack on Surface is Given.

Y = ^K_c / _{σc √(πa)}

Where:

Y = Applied Load Constant
K_c = Fracture Toughness
σ_c = Material Critical Stress
a = Length of Crack on Surface

Let’s solve an example;
Find the applied load constant when the fracture toughness is 32, the material critical stress is 12 and the length of crack on surface is 10.

This implies that;

K_c = Fracture Toughness = 32
σ_c = Material Critical Stress = 12
a = Length of Crack on Surface = 10

Y = ^K_c / _{σc √(πa)}
Y = ³² / _{12 √(π(10))}
Y = ³² / _{12 √31.41}
Y = ³² / _67.25
Y = 0.47

Therefore, the applied load constant is 0.47.

Calculating the Material Critical Stress when the Fracture Toughness, the Applied Load Constant and the Length of Crack on Surface is Given.

σ_c = ^K_c / _{Y √(πa)}

Where:

σ_c = Material Critical Stress
K_c = Fracture Toughness
Y = Applied Load Constant
a = Length of Crack on Surface

Let’s solve an example;
Find the material critical stress when the fracture toughness is 24, the applied load constant is 14 and the length of crack on surface is 8.

This implies that;

K_c = Fracture Toughness = 24
Y = Applied Load Constant = 14
a = Length of Crack on Surface = 8

σ_c = ^K_c / _{Y √(πa)}
σ_c = ²⁴ / _{14 √(π(8))}
σ_c = ²⁴ / _{14 √25.13}
σ_c = ²⁴ / _70.18
σ_c = 0.34

Therefore, the material critical stress is 0.34.

Calculating the Length of Crack on Surface when the Fracture Toughness, the Applied Load Constant and the Material Critical Stress is Given.

a = (^K_c / _Yσc)² x ¹ / _π

Where:

a = Length of Crack on Surface
K_c = Fracture Toughness
Y = Applied Load Constant
σ_c = Material Critical Stress

Let’s solve an example;
Find the length of crack on surface when the fracture toughness is 28, the applied load constant is 8 and the material critical stress is 4.

This implies that;

K_c = Fracture Toughness = 28
Y = Applied Load Constant = 8
σ_c = Material Critical Stress = 4

a = (^K_c / _Yσc)² x ¹ / _π
a = (²⁸ / ₍₈₎₍₄₎)² x ¹ / _π
a = (²⁸ / ₃₂)² x 0.318
a = (0.875)² x 0.318
a = 0.765 x 0.318
a = 0.243

Therefore, the length of crack on surface is 0.243.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the fracture toughness.

Now, Click on Fracture under Materials and Metallurgical

Now, Click on Fracture Toughness under Fracture

The screenshot below displays the page or activity to enter your values, to get the answer for the fracture toughness according to the respective parameter which is the Applied Load Constant (Y), Material Critical Stress (σ_c) and Length of Crack on Surface (a).

Now, enter the values appropriately and accordingly for the parameters as required by the Applied Load Constant (Y) is 9, Material Critical Stress (σ_c) is 5 and Length of Crack on Surface (a) is 2.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the fracture toughness and presents the formula, workings and steps too.