Stress/Strain Graphs

Stress and Strain Concepts

Stress is the amount of force that is applied to a material per unit area. It’s a measure of the intensity of the internal forces acting within a material, often resulting in deformation.
Strain is the extent of deformation of a material due to an applied force. It’s essentially the change in shape or size of a material in comparison to its original shape or size.
Stress is measured in N/m², also known as Pascals (Pa), while strain is a ratio and therefore has no units.
Strain is typically calculated as the change in dimension (such as length) divided by the original dimension.

The Relationship Between Stress and Strain

Stress and strain have a direct relationship; when stress increases, strain also increases and vice versa.
This relationship (stress = Young’s Modulus x strain) is the basis of Hooke’s Law. This law states that the strain in a solid is proportionate to the applied stress within the elastic limit of that solid.

Stress/Strain Graphs

A Stress/Strain Graph, often referred to as a ‘Hooke’s Law graph’, is a way of graphically representing the relationship between stress and strain in a material.
The graph starts at the origin (0,0) and initially shows a straight line. The slope of this line is known as the modulus of elasticity, or Young’s Modulus, which is a measure of the stiffness of a material.
The point where the straight line ends and curves is the elastic limit or the yield point. Beyond this point, the material is likely to undergo permanent deformation, which is also known as plastic deformation.
The highest point on the stress/strain graph represents the ultimate tensile strength (UTS) of the material, which is the maximum stress the material can withstand before failure.
The point of fracture or breaking of the material, when it can no longer withstand the stress, is shown on the x-axis of the graph.

Other Key Points in Stress/Strain Graph

An area under the graph line represents the energy absorbed by the material before it gets deformed plastically. This area essentially shows the material’s toughness.
A material that has an initially steep gradient on the graph has a high Young’s Modulus, meaning it’s stiffer and harder to stretch.
The straight portion of the graph is called the elastic region. If a material is deformed within this region, it will return to its original shape when the force is removed.
The curved portion of the graph is the plastic region. If a material is deformed within this region, it will not return to its original shape when the force is removed. It will be permanently deformed.