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

  • Thread starter Thread starter TyErd
  • Start date Start date
  • Tags Tags
    Modulus
Click For Summary
SUMMARY

This discussion focuses on calculating Young's Modulus from a non-linear stress-strain graph. The formula for Young's Modulus is defined as the change in stress divided by the change in strain. Participants noted that the graph's non-linearity indicates varying gradients, which complicates the calculation. It was concluded that Young's Modulus can only be accurately calculated within the elastic limit, specifically from the linear portion of the graph.

PREREQUISITES
  • Understanding of stress-strain relationships
  • Familiarity with Young's Modulus and its formula
  • Basic knowledge of graph interpretation
  • Concept of elastic limit in materials science
NEXT STEPS
  • Study the concept of elastic limit in materials
  • Learn how to identify linear regions in stress-strain graphs
  • Explore methods for calculating Young's Modulus from non-linear data
  • Investigate the significance of gradient calculations in material properties
USEFUL FOR

Students in materials science, engineers analyzing material properties, and anyone involved in mechanical testing of materials.

TyErd
Messages
297
Reaction score
0

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?
 

Attachments

  • bbbbbbb.png
    bbbbbbb.png
    7.8 KB · Views: 542
Last edited:
Physics news on Phys.org
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.
 
sorry about that, I've attached the question now.
 
TyErd said:
sorry about that, I've attached the question now.

What did you make of the statement in the first sentence?
 
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!
 
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.
 

Similar threads

Confusion Calculating Young's Modulus
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Young's Modulus from this Stress/Strain Graph
  • · Replies 29 ·
Replies
29
Views
8K
Young's Modulus and the Poisson Ratio of Aluminium
  • · Replies 1 ·
Replies
1
Views
2K
Thermal Expansion of a Wire Connected To a Rod
  • · Replies 6 ·
Replies
6
Views
3K
Traction/ Compression stress and strain exercise
  • · Replies 1 ·
Replies
1
Views
2K
Stress-strain graph-finding elastic strain energy
  • · Replies 2 ·
Replies
2
Views
2K
What is the Young's Modulus of Aluminum, Steel, and Brass?
  • · Replies 14 ·
Replies
14
Views
3K
Stress-strain (area under curve)
  • · Replies 17 ·
Replies
17
Views
4K
Stress-Strain Graphs of different materials
  • · Replies 9 ·
Replies
9
Views
7K
Different young modulus of rod - Need a proper explanation?
  • · Replies 2 ·
Replies
2
Views
2K