Toughness

Maximum energy per unit volume a material can absorb before fracture. Equal to the area under the $\sigma$-$\epsilon$ curve. Units: $\text{J/m}^3$ or $\text{MJ/m}^3$.

Measured experimentally by impact test.

Relation to Other Properties

High toughness requires both high strength and high ductility. Brittle materials fracture before significant plastic deformation, so their $\sigma$-$\epsilon$ area is small even if strength is high.

Ductile-to-Brittle Transition

Some materials (especially BCC metals like steel) transition from ductile to brittle behavior as temperature decreases. Below the transition temperature, toughness drops sharply and fracture occurs with little energy absorption.