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 definition

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, depsilon


  • 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 tests

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 toughness

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 also

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