Calculating Young's Modulus from a range of values

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Discussion Overview

The discussion revolves around calculating Young's Modulus (E) from a range of load and displacement values for different materials, specifically steel and aluminum. Participants explore the implications of material properties on the calculation, including the presence or absence of a linear stress-strain relationship.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on the best method to calculate Young's Modulus from load and displacement values, noting a decreasing trend in calculated values.
  • Another participant mentions that the method of calculation may depend on the material being tested.
  • A participant clarifies they are calculating E for both steel and aluminum and realizes they need to use the maximum load for their calculations.
  • Discussion highlights that mild steel exhibits a linear stress-strain relationship, while aluminum does not have a clear yield point, complicating the calculation for aluminum.
  • One participant asks how to calculate Young's Modulus for aluminum without a linear portion on the stress-strain graph.
  • A suggestion is made to use the formula: Force divided by area times length divided by displacement.
  • Further clarification is provided that aluminum does have a linear stress-strain relationship for small strains, but its behavior can be nonlinear at higher stress levels, affecting the calculation of Young's Modulus.
  • A reference to measured stress-strain data for aluminum and other materials is shared for additional context.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of aluminum under stress, particularly regarding its linearity and yield point. There is no consensus on the best method to calculate Young's Modulus for aluminum without a linear portion in the data.

Contextual Notes

Participants note the importance of understanding material properties and the implications of loading conditions on the calculation of Young's Modulus. The discussion reflects the complexity of determining E for materials that do not exhibit a clear linear relationship.

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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It kinda depends on what material you are testing.
 
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.
 
Mild steel will have a region where there is a linear stress-strain relationship, while there is no such region for aluminum.
 
Sorry, I misread my sheet, it just says to calculate Young's Modulus. So how would I calculate it for my aluminium data?
 
Have you studied how Young's modulus is determined for non-ferrous metals?
 
I just need to know how to calculate it without having a linear portion on the graph.
 
Last edited:
Force divided by area times length divided by displacement.
 
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
 

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