A statistical definition of Young's Modulus?

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SUMMARY

Young's Modulus is defined as the intrinsic property of a material that indicates its stiffness, calculated using the formula Young's Modulus = Stress/Strain, where Stress = Force/Area and Strain = Δlength/length. It is crucial to note that Young's Modulus is only applicable under small strains where the material's response is linear. The discussion highlights that while Young's Modulus for steel is significantly high, the concept can be challenging for learners due to the massive forces required for minute extensions. Misunderstandings about the relationship between stress, strain, and Young's Modulus can lead to incorrect interpretations of material behavior.

PREREQUISITES
  • Understanding of basic mechanics concepts such as stress and strain
  • Familiarity with the units of measurement, specifically Pascals (Pa)
  • Knowledge of linear vs. non-linear material behavior
  • Basic mathematical skills for manipulating equations
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  • Study the derivation and implications of Young's Modulus in materials science
  • Learn about the differences between elastic and plastic deformation in materials
  • Explore the concept of non-linear elasticity and its applications
  • Investigate the statistical methods for analyzing material properties
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Students and educators in materials science, mechanical engineers, and anyone interested in understanding the mechanical properties of materials, particularly in relation to elasticity and deformation.

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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