# What factors affect the Young's modulus of elasticity?

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 a $$1~\rm mm$$ thick steel wire the same compared to a $$10~\rm mm$$ thick wire of the same steel?

• May 26, 2020 at 4:48

• 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 $k=\large{\frac{Gd^4}{8ND^3}}$. May 17, 2016 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. May 17, 2016 at 20:30
• 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 May 17, 2016 at 22:11