Does Young's Modulus Affect Volume Changes in Solid Materials?

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Discussion Overview

The discussion centers around the relationship between Young's modulus, volume changes, and the behavior of solid materials under stress, particularly focusing on whether volume remains constant when length changes in materials like iron rods. The scope includes theoretical considerations and material properties such as Poisson's ratio.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether applying stress to a solid, like an iron rod, results in volume changes or if changes in length and cross-sectional area maintain a constant volume.
  • Another participant mentions conservation of mass and introduces Poisson's ratio as a factor that describes how the cross-sectional area changes in response to stress.
  • A later post provides a formula for volume change in isotropic linear elastic materials, indicating that for no volume change, Poisson's ratio must equal 0.5, suggesting that most metals will experience some volume change under stress.
  • The same participant notes that rubbers, with Poisson's ratios close to 0.5, exhibit little to no volume change, contrasting with metals.

Areas of Agreement / Disagreement

Participants express differing views on the extent of volume change in materials under stress, with some suggesting that volume remains constant while others indicate that it does change, particularly in metals. The discussion does not reach a consensus on the impact of Young's modulus on volume changes.

Contextual Notes

Participants reference specific material properties such as Poisson's ratio and Young's modulus, but the discussion does not clarify all assumptions or definitions, leaving some aspects unresolved.

Who May Find This Useful

This discussion may be of interest to those studying material science, engineering, or physics, particularly in relation to stress-strain behavior in solid materials.

Sakha
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After a tough discussion with my friends, I opt to ask here because we aren't coming to an answer.
When stress is applied to a solid, let's say an iron rod, will the volume change, or when the length of the rod shrinks or stretches, the area of the cross sectional area will reduce or increase to maintain a constant volume?
 
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Conservation of mass... the volume is the same and poisson's ratio helps tell how much the cross sectional area will change.
 
That was exactly what I was looking for, thanks!
 
Dilatation or volume change can be given for small strains in an isotropic linear elastic material by:

[tex]\frac{dV}{V}=\frac{1-2\nu}{E}(\sigma_{x}+\sigma_{y}+\sigma_{z})[/tex]

In a uniaxial tensile test at small strains, [itex]\sigma_{y}=\sigma{z}=0[/itex]. You can see that for there to be no volume change, [itex]\nu[/itex] (Poisson's ratio) must be equal to 0.5 at which point the material is said to be incompressible, as the bulk modulus tends to infinity.

Typically, most metals exhibit Poisson's ratios of between 0.3 and 0.35, meaning you will observe some volume change at low strains. Rubbers have Poisson's ratios tending to 0.5, meaning you will exhibit little to no volume change.
 

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