Toughness
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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.
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[edit] Mathematical definition
Toughness can be found by taking the area (i.e., by taking the integral) underneath the stress-strain curve.It's energy per unit volume prior to fracture. The explicit mathematical description is:
Where
- ε is strain
- εf 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.
If we restrict the upper limit of integration up to yield point only than the enegy absorbed per unit volume is known as modulus of resilience. Thus mathematical that would be half of the multiplication of young's modulus to that of square of yield strain.
[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.
