# How to Calculate and Solve for Flexural Strength with Relation to Volume Fraction | Ceramics

**Last Updated on March 31, 2024**

The image above represents Flexural strength with relation to volume in ceramics. To calculate flexural strength with relation to volume in ceramics, three essential parameters are needed and these parameters are **Initial Stress (σ _{o}), Constant (n)** and

**Volume fraction porosity (P).**

The formula for calculating flexural strength with relation to volume:

σ_{fs} = σ_{o }exp (-nP)

Where:

σ_{fs} = Flexural Strength

σ_{o} = Initial Stress

n = Constant

P = Volume Fraction Porosity

Let’s solve an example;

Find the flexural strength when the initial stress is 11, the constant is 8 and the volume fraction porosity is 22.

This implies that;

σ_{o} = Initial Stress = 11

n = Constant = 8

P = Volume Fraction Porosity = 22

σ_{fs} = σ_{o }exp (-nP)

σ_{fr} = (11)exp(-(8)(22))

Then, σ_{fr} = (11)exp(-176)

σ_{fr} = (11)(3.665e-77)

σ_{fr} = 4.032e-76

Therefore, the **flexural strength **is **4.032e-76 Pa.**

**Calculating the Initial Stress when the Flexural Strength, the Constant and the Volume Fraction Porosity are Given**

σ_{o} = ^{σfr} / _{exp (-nP)}

Where;

σ_{o} = Initial Stress

σ_{fs} = Flexural Strength

n = Constant

P = Volume Fraction Porosity

Let’s solve an example;

Find the initial stress when the flexural strength is 20, the constant is 10 and the volume fraction porosity is 8.

This implies that;

σ_{fs} = Flexural Strength = 20

n = Constant = 10

P = Volume Fraction Porosity = 8

σ_{o} = ^{σfr} / _{exp (-nP)}

σ_{o} = ^{20} / _{exp (-10 x 8)}

That is, σ_{o} = ^{20} / _{exp (-80)}

σ_{o} = ^{20} / _{– 5.54e+34}

σ_{o} = – 3.61e-34

Therefore, the **initial stress **is **3.61e-34.**

Read more: How to Calculate and Solve for Flexural Strength for Circular Cross-section in Defects | Ceramics

**Calculating the Constant when the Flexural Strength, the Initial Stress and the Volume Fraction Porosity are Given**

n = – (In ^{σfr} / _{σo}) x ^{1} / _{P}

Where;

n = Constant

σ_{fs} = Flexural Strength

σ_{o} = Initial Stress

P = Volume Fraction Porosity

Let’s solve an example;

Find the constant when the flexural strength is 30, the initial stress is 10 and volume fraction porosity is 20.

This implies that;

σ_{fs} = Flexural Strength = 30

σ_{o} = Initial Stress = 10

P = Volume Fraction Porosity = 20

n = – (In ^{σfr} / _{σo}) x ^{1} / _{P}

n = – (In ^{30} / _{10}) x ^{1} / _{20}

That is, n = – (In 3) x 0.05

n = – 1.098 x 0.05

n = – 0.0549

Therefore, the **constant **is **– 0.0549.**

**Calculating the Volume Fraction Porosity when the Flexural Strength, the Initial Stress and Constant are Given**

P = – (In ^{σfr} / _{σo}) x ^{1} / _{n}

Where;

P = Volume Fraction Porosity

σ_{fs} = Flexural Strength

σ_{o} = Initial Stress

n = Constant

Let’s solve an example;

Find the volume fraction porosity when the flexural strength is 40, the initial stress is 2 and the constant is 12.

This implies that;

σ_{fs} = Flexural Strength = 40

σ_{o} = Initial Stress = 2

n = Constant = 12

P = – (In ^{σfr} / _{σo}) x ^{1} / _{n}

P = – (In ^{40} / _{2}) x ^{1} / _{12}

Then, P = – (In 20) x 0.05

P = – 2.99 x 0.05

P = – 0.1495

Therefore, the **volume fraction porosity **is **– 0.1495.**

**How to Calculate Flexural Strength with Relation to Volume Fraction in Ceramics Using Nickzom Calculator**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the flexural strength.

To get the answer and workings of the flexural strength 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 **for** NGN 1,500 **per** annum** 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 & Metallurgical**** **under **Engineering****.**

Now, Click on **Ceramics**** **under **Material & Metallurgical**

Now, Click on **Flexural Strength**** **under **Ceramics**

The screenshot below displays the page or activity to enter your values, to get the answer for the flexural strength according to the respective parameters which are the **Initial Stress (σ _{o}), Constant (n)** and

**Volume fraction porosity (P).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Initial Stress (σ _{o})** is

**8**,

**Constant (n)**is

**11**and

**Volume fraction porosity (P)**is

**22**.

Finally, Click on Calculate

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