# 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 = ^{Kc} / _{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 = ^{Kc} / _{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} = ^{Kc} / _{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} = ^{Kc} / _{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 = (^{Kc} / _{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 = (^{Kc} / _{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.

To get the answer and workings of the fracture toughness 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 **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.