Definitions

# Toughness

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:

$frac mbox\left\{energy\right\} mbox\left\{volume\right\} = int_\left\{0\right\}^\left\{epsilon_f\right\} sigma, depsilon$

Where

• $epsilon$ 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.