# young's modulus factors

is young's modulus of a material different for various diameters of that material? I would assume it does, but I cannot find a reference. Is the young's modulus of 1mm thick steel the same with 10mm thick of the same steel?

## 2 Answers

The young's modulus is like the 'spring constant' for a material. It comes from treating the atoms in a material as harmonic oscillators. It is a material property that does not depend on geometry. The young's modulus for both of the materials you mention is equal.

Now the stress they feel will be different under the same applied load.

• The young's modulus isn't like the 'spring constant for a material. Spring constant for a material is defined as $\large{\frac{AE}L}$ and it depends on the geometry. Spring constant for a spring is also depends on the geometry of the spring. For example, the spring constant formula for a spiral spring is $k=\large{\frac{Gd^4}{8ND^3}}$. – lucas May 17 '16 at 20:21
• What you wrote down is just the rearrangement of the stress-strain relationship in the elastic limit $\sigma = E\epsilon$. As Young's modulus is the only geometry-independent, material-specific quantity in the spring constant it can essentially be though of as the spring constant for a material. The stress and strain allow for a relationship that is independent of geometry making the youngs modulus a far more useful quantity. – bremsstrahlung May 17 '16 at 20:30
• I know the Young's modulus is a geometry-independent quantity. All that I am saying is "it isn't like the spring constant". – lucas May 17 '16 at 20:34
• For an intuitive explanation, it is. In the elastic limit, the force felt by the material is proportional to the elongation. In that sense the modulus is like the spring constant. I never said the modulus $\emph{was}$ the spring constant. The spring constant is proportional to the modulus except for some geometric factors which are absorbed into the stress and strain anyway. You're arguing semantics – bremsstrahlung May 17 '16 at 22:11

No, Young's modulus is an intrinsic property of the material (e.g. steel) that does not depend on its form (e.g. wire diameter).

• Correct that it is an intrinsic property. A caution though - it will (particularly for steels and other engineering alloys) depend on the steel alloy, heat treatment, and any mechanical deformation (rolling, milling, etc.). So, that 1 mm sheet of steel may not have the same Young's modulus as the 10 mm sheet of the 'same' steel (particularly if the 1 mm is rolled down from the 10 mm). – Jon Custer Apr 6 '16 at 16:38