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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.

[edit] 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:

Where

• ε is strain
• ε_f is the strain upon failure
• σ is stress

Another definition is the ability to absorb mechanical (or kinetic) energy up to failure. Area covered under stress strain curve is called toughness.

[edit] 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.

[edit] 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.

[edit] Toughness and strength

Strength and toughness are related. A material may be strong and tough if it ruptures under high forces, exhibiting high strains; on the other hand, brittle materials may be strong but with limited strain values, so that they are not tough. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupture.

[edit] See also

• Fracture toughness
• Graph toughness
• Hardness