How to Calculate Young's Modulus from a Non-Linear Stress-Strain Graph

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In summary, the conversation discusses calculating Youngs modulus, with the question attached. The formula for Youngs modulus is given, and the attempt at a solution involves finding the gradient between each of the points on the graph. However, it is noted that Youngs modulus can only be calculated for stress-strain that remains below the elastic limit. The conversation then concludes with a clarification on the first data point and the gradients between data points.
  • #1
TyErd
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Homework Statement


Question simply asks to calculate the Youngs modulus. I've attached the question.



Homework Equations


Youngs Modulus = (change in stress)/(change in strain)


The Attempt at a Solution


okay, what i did was simply find the gradient between each of the points. However they were all different gradients, which means the graph isn't linear (i think). So then how do i solve it?
 

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  • #2
TyErd said:

Homework Statement


Question simply asks to calculate the Youngs modulus. I've attached the question.

Homework Equations


Youngs Modulus = (change in stress)/(change in strain)

The Attempt at a Solution


okay, what i did was simply find the gradient between each of the points. However they were all different gradients, which means the graph isn't linear (i think). So then how do i solve it?

I believe Youngs modulus can only be calculated for stress-strain that remains below the elastic limit - ie the first straight part of the graph.

EDIT: btw, I don't see the question attached, but hopefully this will help anyway.
 
  • #3
sorry about that, I've attached the question now.
 
  • #4
TyErd said:
sorry about that, I've attached the question now.

What did you make of the statement in the first sentence?
 
  • #5
Oh i get it, the first data point would be 0 stress 0 strain and the gradient between 0,0 and the 1st data point is the same as the gradient between the first data point and the second data point but different from the 2nd and 3rd. I get it, thank you!
 
  • #6
TyErd said:
Oh i get it, the first data point would be 0 stress 0 strain and the gradient between 0,0 and the 1st data point is the same as the gradient between the first data point and the second data point but different from the 2nd and 3rd. I get it, thank you!

well done.
 

FAQ: How to Calculate Young's Modulus from a Non-Linear Stress-Strain Graph

What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It describes how much a material will deform under a given amount of stress.

How do you calculate Young's modulus?

Young's modulus is calculated by dividing the stress applied to a material by the strain it experiences. In other words, it is the ratio of stress to strain. This value is typically represented by the letter E and has units of force per area (such as N/m² or Pa).

What is the significance of Young's modulus?

Young's modulus is an important property of materials as it helps engineers and scientists understand how a material will behave under different conditions. It can also be used to compare the stiffness or strength of different materials.

What factors can affect Young's modulus?

The Young's modulus of a material can be affected by various factors such as temperature, the presence of impurities, and the material's microstructure. Additionally, the way a material is processed or manufactured can also impact its Young's modulus.

How is Young's modulus used in real-world applications?

Young's modulus is used in various fields such as engineering, materials science, and physics. It is used to design and analyze structures, predict material behavior under different conditions, and select appropriate materials for specific applications. For example, it is crucial in designing bridges, buildings, and other structures to ensure their safety and stability.

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