Toughness, in materials science and metallurgy, is the resistance to fracture of a material when stressed. It is defined as the amount of energy per volume that a material can absorb before rupturing.

Mathematical definitionEdit

Toughness can be found by taking the area (i.e., by taking the integral) underneath the stress-strain curve. The explicit mathematical description is:

$ \frac \mbox{energy} \mbox{volume} = \int_{0}^{\epsilon_f} \sigma\, d\epsilon $


  • $ \epsilon $ is strain
  • $ \epsilon_f $ is the strain upon failure
  • $ \sigma $ is stress

Another definition is the ability to absorb mechanical (or kinetic) energy up to failure.

Toughness testsEdit

Tests can be done by using a pendulum and some basic physics to measure how much energy it will hold when released from a particular height. By having a sample at the bottom of its swing a measure of toughness can be found, as in the Charpy and Izod impact tests.

Unit of toughnessEdit

Toughness is measured in units of joules per cubic metre (J/m³) in the SI system and inch-pound-force per cubic inch (in·lbf/in³) in US customary units.

See alsoEdit

es:Tenacidad fa:چقرمگی gl:Tenacidade it:Tenacità ja:靭性 pt:Tenacidade sv:Seghet zh:韌性