How to Calculate and Solve for True Stress | Mechanical Properties

January 8, 2023 Loveth Idoko

Last Updated on June 8, 2024

The image above represents true stress. Two essential parameters, force (F) and Instantaneous Area (Ai), are needed to calculate true stress.

The formula for calculating true stress:

σ_T = ^F/_Ai

Where;

σ_T = True Stress
F = Force
A_i = Instantaneous Area

Given an example;
Find the true stress when the force is 12 and the instantaneous area is 4.

This implies that;

F = Force = 12
A_i = Instantaneous Area = 4

σ_T = ^F/_Ai
That is, σ_T = ¹²/₄
σ_T = 3

Therefore, the true stress is 3 Pa.

Calculating the Force when the True Stress and the Instantaneous Area are Given

F = σ_T x A_i

Where;

F = Force
σ_T = True Stress
A_i = Instantaneous Area

Let’s solve an example;
Find the force when the true stress is 10 and the instantaneous area is 8.

This implies that;

σ_T = True Stress = 10
A_i = Instantaneous Area = 8

F = σ_T x A_i
That is, F = 10 x 8
F = 80

Therefore, the force is 80.

Calculating the Instantaneous Area when the True Stress and Force are Given

A_i = ^F / _{σ_T}

Where;

A_i = Instantaneous Area
σ_T = True Stress
F = Force

Let’s solve an example;
Find the instantaneous area when the true stress is 5 and the force is 20.

This implies that;

σ_T = True Stress = 5
F = Force = 20

That is, A_i = ^F / _{σ_T}
A_i = ²⁰ / ₅
A_i = 4

Therefore, the instantaneous area is 4.

How to Calculate True Stress With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the true stress.

To get the answer and workings of the true stress 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 Mechanical Properties under Materials and Metallurgical

Now, Click on True Stress under Mechanical Properties

The screenshot below displays the page or activity to enter your values, to get the answer for the true stress according to the respective parameter which is the Force (F) and Instantaneous Area (A_i).

Now, enter the values appropriately and accordingly for the parameters as required by the Force (F) is 12 and Instantaneous Area (A_i) is 4.

Finally, Click on Calculate

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