A stress-strain graph shows how a material deforms as stress is applied. It reveals important material properties, including stiffness, yield strength, ultimate tensile strength, ductility and toughness.
How the graph is constructed
The vertical axis represents stress, meaning the applied force per unit original cross-sectional area:
Stress is normally measured in pascals, although megapascals, , are often more practical. The horizontal axis represents strain, which is the extension divided by the original length:
Strain has no unit because it is a ratio.
What the curve shows
| Feature | Meaning on the graph |
|---|---|
| Linear elastic region | Stress is proportional to strain. The material returns to its original dimensions when unloaded. |
| Gradient | The gradient in the linear elastic region is Young's modulus, . A steeper gradient indicates a stiffer material. |
| Yield point | Permanent, plastic deformation begins. The material will not fully recover when unloaded. |
| Ultimate tensile strength | The maximum engineering stress reached by the material. |
| Fracture point | The point at which the specimen breaks. |
| Strain at fracture | Indicates ductility: a ductile material undergoes more plastic deformation before fracture. |
| Area under the curve | Represents , or the energy absorbed per unit volume before fracture. |
After the ultimate tensile strength, a ductile specimen may undergo necking, where its cross-sectional area decreases locally before fracture. Brittle materials typically fracture after little plastic deformation, while ductile materials have a longer plastic region.
IB exam technique
In A3.2 structural systems, label both axes and identify the elastic region, yield point, plastic region, ultimate tensile strength and fracture point. A common misconception is that the steepest material is the strongest: gradient measures stiffness, whereas strength concerns the stress a material can withstand before yielding or failing.