Young's Modulus (Y)

Young's modulus, denoted $Y$, is the modulus of elasticity that applies to tensile (or compressive) stress and the corresponding longitudinal strain -- it is, in other words, the slope of the straight-line (Hooke's-law) part of a material's stress-strain curve when that curve is obtained by stretching (or compressing) a rod or wire along its length. By Hooke's law,

where $F$ is the applied (tensile or compressive) force, $A$ is the cross-sectional area, $L$ is the original length, and $\Delta L$ is the resulting change in length. Since strain is dimensionless, $Y$ has the same SI unit as stress: the pascal ($\text{Pa}$); because a pascal is a very small unit relative to the stresses involved in testing solids, values of $Y$ are usually quoted in gigapascals ($1\ \text{GPa} = 10^9\ \text{Pa}$).

The numerical value of $Y$ is a direct, quantitative measure of a material's stiffness along its length: a large value of $Y$ means that only a small strain is produced for a given stress -- the material is hard to stretch or compress, i.e. very stiff -- while a small value of $Y$ means the same stress produces a much larger strain -- the material is easy to stretch, i.e. comparatively soft or flexible. Steel, for example, has a very large Young's modulus (about $200\ \text{GPa}$), which is exactly why steel wires, rods, and cables are chosen wherever an engineering structure needs to resist stretching under load with only a very small, predictable elongation. Rubber, by contrast, has a Young's modulus that is smaller than steel's by a factor of several thousand, which is exactly why a rubber band stretches so easily and so noticeably for a comparatively small pulling force. …