Calculating Young's Modulus from a range of values

In summary, to calculate Young's modulus for a non-ferrous metal such as aluminum, one must consider whether the material has a linear stress-strain relationship or not. For aluminum, there is a region of linear relationship for small strains, but it does not have a clear yield point like mild steel. Depending on the application, the maximum allowable stress for aluminum may be in the nonlinear region, or it may be assumed to be a linear elastic material with a lower stress limit.
  • #1
MegaDeth
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Homework Statement

I don't need to give any information, I just need to know the best way to calculate E from a range of values for load and displacement given the length and diameter. I've calculate it for a few values and the value appears to decrease so I'm not sure where to take the value for E from.
 
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  • #2
It kinda depends on what material you are testing.
 
  • #3
I'm doing it for both steel and aluminium, though I've just realized I have to calculate it for the maxiumum load so everything is fine now.
 
  • #4
Mild steel will have a region where there is a linear stress-strain relationship, while there is no such region for aluminum.
 
  • #5
Sorry, I misread my sheet, it just says to calculate Young's Modulus. So how would I calculate it for my aluminium data?
 
  • #6
Have you studied how Young's modulus is determined for non-ferrous metals?
 
  • #7
I just need to know how to calculate it without having a linear portion on the graph.
 
Last edited:
  • #8
Force divided by area times length divided by displacement.
 
  • #9
SteamKing said:
Mild steel will have a region where there is a linear stress-strain relationship, while there is no such region for aluminum.

Aluminum does have a linear stress-strain relationship for small strains, but unlike mild steel it doesn't have an obvious "yield point" where the linear relationship ends.

For some structural applications the maximum allowable stress for aluminum is in the nonlinear region. If the material is loaded up to that stress level, its behavior is not elastic and it does not return to its original length when unloaded. But for other applications aluminum is assumed to be a linear elastic material, with a lower stress limit.

Some measured stress strain data for Al and other materials here: http://fp.optics.arizona.edu/optomech/references/OPTI_222/OPTI_222_W4.pdf
 

What is Young's Modulus?

Young's Modulus, also known as the elastic modulus or modulus of elasticity, is a measure of a material's stiffness or resistance to deformation. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) in a material under load.

Why is it important to calculate Young's Modulus?

Calculating Young's Modulus allows us to understand and compare the mechanical properties of different materials. It is a fundamental parameter in material science and engineering, as it helps us predict how a material will behave under stress and strain, and determine its suitability for specific applications.

What is the formula for calculating Young's Modulus?

The formula for Young's Modulus is:
E = σ / ε
Where E is the Young's Modulus, σ is the stress, and ε is the strain.

How do you calculate Young's Modulus from a range of values?

To calculate Young's Modulus from a range of values, you need to plot a stress-strain curve for the material and determine the slope of the linear region. The slope of the curve represents the Young's Modulus, as it is the ratio of stress to strain. You can then use the formula E = σ / ε to calculate the value of Young's Modulus.

What are the limitations of calculating Young's Modulus from a range of values?

There are several limitations to calculating Young's Modulus from a range of values. Firstly, the material must exhibit a linear relationship between stress and strain, which is not always the case. Additionally, the calculated value may vary depending on the testing conditions and the accuracy of the measurements. It is also important to note that Young's Modulus is only one measure of a material's mechanical properties and does not account for other factors such as fatigue and creep.

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