(N/A) Experimental observations show that for a given material,the magnitude of the strain produced is the same whether the stress is tensile or compressive.
The ratio of tensile (or compressive) stress $(\sigma)$ to the longitudinal strain $(\varepsilon)$ is defined as Young's modulus and is denoted by the symbol $Y$.
$\text{Young's modulus} = \frac{\text{Tensile stress } (\sigma)}{\text{Longitudinal strain } (\varepsilon)}$
$Y = \frac{\sigma}{\varepsilon}$
$\therefore Y = \frac{(F / A)}{(\Delta L / L)} = \frac{(F \times L)}{(A \times \Delta L)}$
Since strain is a dimensionless quantity,the unit of Young's modulus is the same as that of stress,which is $N \ m^{-2}$ or Pascal $(Pa)$.
Dimensional formula: $[M^1 L^{-1} T^{-2}]$.
Young's moduli,elastic limit,and tensile strength of some materials are given below:
| Substance | Young's Modulus $(10^9 \ N/m^2)$ | Elastic limit $(10^7 \ N/m^2)$ | Tensile strength $(10^7 \ N/m^2)$ |
| Aluminium | $70$ | $18$ | $20$ |
| Copper | $120$ | $20$ | $40$ |
| Iron (Wrought) | $190$ | $17$ | $33$ |
| Steel | $200$ | $30$ | $50$ |
| Bone (Tensile/Compressive) | $16 / 9$ | - | $12 / 12$ |
For metals,Young's moduli are large; therefore,these materials require a large force to produce a small change in length.
Steel is more elastic than copper,brass,and aluminium. It is for this reason that steel is preferred in heavy-duty machines and in structural designs.
Wood,bone,concrete,and glass have rather small Young's moduli.