A statistical definition of Young's Modulus?

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Discussion Overview

The discussion revolves around the definition and understanding of Young's Modulus, particularly its statistical implications and the conditions under which it is applicable. Participants explore its theoretical framework, practical interpretations, and the limitations of its application in real-world scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant defines Young's Modulus as the ratio of stress to strain, suggesting a statistical description due to its measurement in Pascals.
  • Another participant counters that Young's Modulus can only be considered a constant for small strains, indicating that most materials do not behave elastically at larger strains.
  • A third participant corrects the initial claim, stating that strain is equal to stress divided by Young's Modulus, emphasizing that the calculated strain would be very small given the large value of Young's Modulus.
  • Some participants express that using a hypothetical scenario to illustrate Young's Modulus can be effective for teaching, despite the impracticality of extending materials to such lengths.
  • There is a repeated emphasis on the importance of ensuring that the units of force align with Young's Modulus times area, highlighting a potential misunderstanding among participants.
  • A participant questions the assumption that Young's Modulus should have a statistical description simply because it is measured in Pascals.

Areas of Agreement / Disagreement

Participants express disagreement regarding the initial definition and application of Young's Modulus, with multiple competing views on its validity and the conditions under which it can be applied. The discussion remains unresolved as differing interpretations persist.

Contextual Notes

Limitations include the dependence on the linearity of material behavior and the assumptions made about the applicability of Young's Modulus at larger strains. There is also ambiguity regarding the statistical interpretation of Young's Modulus.

Metals
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Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item and is known as the number of Newtons to extend the item by a metre.

Upon discussing with a teacher, I believe he provided me with a sufficient explanation. Although, we both want confirmation on whether this is generally accepted as true or not:

Young's Modulus = Stress/Strain
Stress = Force/Area(cross-sectional)
Strain=Δlength/length

If we make stress equal to 1, then the length of the item has been doubled due to a force extending it by its original length. This way, Young's Modulus can be defined as the amount of force across a metre squared of a material required to extend the material by its original length.

Everyone agree?
 
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Nope. Most materials are not elastic over strains that large.

Young's modulus can only be defined as a constant over strains small enough for the material response to be linear.
 
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In addition to what Dr. Courtney said, even if the linear behavior could extend to twice the original length, the algorithm you gave is still not correct. The strain is equal to the stress divided by Young's modulus, and Young's modulus is very large, so the calculated strain would be very small.
 
Yep...this is not a stupid idea I use it (FOR EFFECT) in my teaching ! For someone LEARNING about Youngs modulus the numbers are formidable..Massive forces for minute extensions.(boring sir !)
However...If you take a 1m3 of steel then the Youngs modulus represents the force needed to cause an extension of 1m (IF SUCH A THING WAS POSSIBLE WITHOUT WORRYING ABOUT WHY IT IS NOT POSSIBLE) to the cube. This certainly illustrates the high value of youngs modulus for steel and...it is interesting to stretch the imagination !
The joys of linear or non-linear behaviour can come later
 
lychette said:
Yep...this is not a stupid idea I use it (FOR EFFECT) in my teaching ! For someone LEARNING about Youngs modulus the numbers are formidable..Massive forces for minute extensions.(boring sir !)
However...If you take a 1m3 of steel then the Youngs modulus represents the force needed to cause an extension of 1m (IF SUCH A THING WAS POSSIBLE WITHOUT WORRYING ABOUT WHY IT IS NOT POSSIBLE) to the cube. This certainly illustrates the high value of youngs modulus for steel and...it is interesting to stretch the imagination !
The joys of linear or non-linear behaviour can come later
Only if the units of force are the same as Young's modulus times m^2.
 
Chestermiller said:
Only if the units of force are the same as Young's modulus times m^2.

Took you a long time to spot that :)
 
lychette said:
Took you a long time to spot that :)
I was taking a nap.o_O
 
Chestermiller said:
I was taking a nap.o_O
respect...so was I
 
Metals said:
it is measured in Pa, meaning it should have some statistical description.
Huh? Why do you think that?
 

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