Stress-strain

As a first year engineer you should expect to do a tensile test, which is explained below:

In a tensile test, a metal rod is subjected to a tensile force (A force that pulls the rod apart, as shown below).

As the force is gradually increased, the rod gradually extends. Initially the force is proportional to the extension of the rod (as dictated by hook's law). This is shown by the diagram below.

Example: The intial Length of a rod, L₀=2m, after applying a force of 500N, the length of the rod is 2.5m. Hence the extension, or change in Length, $\Delta L$ =0.5m

Stress

Even though the tensile force may only be applied at a single point on the rod, the force will spread all along the cross-section of the rod, as shown below. We assume it is distributed uniformly. This "distributed force" is something you may have referred to as pressure in the past. In the context of solid mechanics, it is known as stress,(symbol $\sigma \;$), and in this case tensile stress.

Stress is commonly defined as Force per unit area. It's formulae: $\sigma ={\frac {F}{A}}$ where: F is Tensile force, A is cross-sectional area of rod.

Stain strain, $\epsilon \;$, can be defined as the extension per unit length of the rod. Formulae: $\epsilon ={\frac {\Delta L}{L_{0}}}$

Young's modulus

Young's modulus, E, is a measure of how stiff a material is. A higher young's modulus indicates that the material is more difficult to stretch or compress. Instead of plotting Force vs extension, plot stress vs strain (shown below). The gradient of the straight line will be young's modulus of the material that the rod is made of.

Since stress is proportional to strain: $\sigma =E\cdot \epsilon$