Stress-Strain Graphs

A stress–strain graph is a map of how a material behaves all the way from a small load to fracture, and the named points on it each mark a change in that behaviour.

The straight section — stress is proportional to strain, and the gradient is the Young modulus.

Limit of proportionality (P) — where the line stops being straight. Beyond this the Young modulus can no longer be read from the gradient.

Elastic limit — beyond this point the material no longer returns to its original length when unloaded. It lies at or just beyond P.

Yield point — where the material begins to extend rapidly for little or no extra stress, as the internal structure gives way. Only some materials, notably mild steel, show a clear yield point.

Ultimate tensile strength (UTS) — the maximum stress on the graph. Past it the sample narrows sharply at one point, and the stress calculated from the original area appears to fall even though the true stress in the narrowed region is still rising.

Breaking point (B) — where the sample finally fractures.

The area under the graph — the energy stored per unit volume, measured in J m⁻³. This follows from the units: stress is N m⁻² and strain has no unit, so their product is N m⁻², which equals J m⁻³.

Example: note the distinction from a force–extension graph, where the area is simply energy in joules. Because stress and strain are both "per unit" quantities, their product is energy per unit volume — a property of the material rather than of the sample.

Reading the material from the shape

Brittle — a straight line to fracture, with no plastic region. Glass and ceramics.

Ductile — a straight section, then a long curved plastic region before breaking. Copper and mild steel.

Polymeric — very large strains, often with a curve that is not straight even at low stress, and loading and unloading curves that do not coincide.

Toughness — the total area under the curve to fracture: the energy per unit volume needed to break the material. A tough material absorbs a lot of energy before failing, which is a different question from how stiff it is or what stress it can withstand.