A statistical definition of Young's Modulus?

In summary: Huh?The Spring Constant is the stiffness of an item and is known as the number of Newtons to extend the item by a metre.
  • #1
Metals
48
2
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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  • #2
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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Likes Dale
  • #3
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.
 
  • #4
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
 
  • #5
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.
 
  • #6
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 :)
 
  • #7
lychette said:
Took you a long time to spot that :)
I was taking a nap.o_O
 
  • #8
Chestermiller said:
I was taking a nap.o_O
respect...so was I
 
  • #9
Metals said:
it is measured in Pa, meaning it should have some statistical description.
Huh? Why do you think that?
 

Related to A statistical definition of Young's Modulus?

1. What is Young's Modulus?

Young's Modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It describes the relationship between stress (force per unit area) and strain (change in length per unit length) in a material when it is subjected to tension or compression.

2. How is Young's Modulus calculated?

Young's Modulus is calculated by dividing the stress by the strain in a material under linear elastic deformation. This value is typically expressed in units of pressure, such as Pascals (Pa) or Megapascals (MPa).

3. What is the importance of Young's Modulus in materials science?

Young's Modulus is an important property in materials science because it allows us to compare the stiffness of different materials. It is also used to predict how a material will behave under different loads and stresses, making it crucial for engineering and design applications.

4. How does temperature affect Young's Modulus?

Temperature can have a significant effect on Young's Modulus. In general, as temperature increases, the modulus decreases due to the increased thermal motion of atoms within the material. This can cause the material to become more flexible and less stiff.

5. Can Young's Modulus vary for a single material?

Yes, Young's Modulus can vary for a single material depending on factors such as temperature, strain rate, and the direction of the applied force. For example, some materials may have different moduli in tension and compression, or may exhibit non-linear behavior at high strains.

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