Materials: Force-Extension Graphs

Basic Terms

The force-extension graph is a plot showing how the extension of a material varies as the applied force changes.
Extension refers to the increase in length of a material when a force is applied.
Force is measured in newtons (N) and extension is typically measured in millimetres (mm) or meters (m).

The graph usually starts at the origin (0,0) as no extension occurs without the application of force.
The initial straight-line section of the graph represents the elastic region. In this region, Hooke’s Law applies, which states that the force required to extend a spring is directly proportional to the amount it is stretched.
The end of the straight-line section signifies the limit of proportionality, beyond which Hooke’s Law ceases to apply.
Beyond the limit of proportionality, the graph continues to rise but now curves, indicating that the material is now extending more for each additional unit of force applied. This area is known as the non-linear elastic region.
The point at which the material will no longer return to its original dimensions once the load is removed is called the elastic limit.
The plastic region follows after the elastic limit. Here, the material will continue to extend with no additional force. This may result in the material becoming permanently deformed.
The ultimate tensile strength is the maximum stress a material can stand before it breaks.
The point at which the material breaks under the load is known as the breaking point.

The gradient of the graph in the linear region gives the spring constant or stiffness of the material. Materials with high spring constants are more difficult to extend.
The area under the force-extension graph up to any given point of force gives the work done in stretching the material thus far.
From the graph, we can determine various properties of the material, such as the material’s stiffness, elasticity, and tensile strength.
The force-extension graph is often used by engineers and designers to understand and predict how materials behave under load in practical applications.
Different materials have different force-extension graphs due to variations in their atomic and molecular structures, which affect the strength of the bonds between particles.