Stress and Strain

Stress

The force per unit area applied to a material is called stress. 

 \[Stress (\sigma )=\frac{Force}{Area}=\frac{F}{A}\]

Stress measured in Nm^-2 or pascals (Pa)

Strain


The ratio of extension to original length is called strain.

 \[Strain (\epsilon )=\frac{Extension}{Original \ length}=\frac{\Delta L}{L}\]

 It has no units as it is a ratio of two lengths.

 If we apply tensile force we have tensile stress and tensile strain

If we apply compressive force we have compressive stress and compressive strain.

Stress-Strain graph :

Hook’s Law: In the elastic limit, stress is proportional to strain. The gradient of the straight-line graph is the Young's modulus (Y)

 \[\therefore Y=\frac{Stress}{Strain}=\frac{\sigma }{\varepsilon }\]

 \[\Rightarrow Y=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}=\frac{FL}{A\Delta L}\]

Units of the Young modulus Y is Nm^-2 or Pa.