Toughness

In materials science and metallurgy, toughness 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, and can be found by taking the area (i.e., by taking the integral) underneath the stress-strain curve. The explicit mathematical description is:

$energy/volume\; =\; \backslash int\_\{0\}^\{\backslash epsilon\_f\}\; \backslash sigma\backslash ,\; d\backslash epsilon$

Another Definition is "Ability to absorb mechanical (or kinetic) energy up to failure"
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 then having a sample at the bottom of its swing a measure of toughness can be found
Toughness is measured in units of joules per cubic metre (J/m³) in the SI system and pound-force per cubic inch (sometimes expressed as in-lbf/in³) in US customary units.

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