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Toughness, in materials science
Materials science

Materials science or materials engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering....
 and metallurgy
Metallurgy

Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic Chemical element, their intermetallics, and their mixtures, which are called alloys....
, is the resistance to fracture
Fracture

A fracture is the separation of an object or material into two, or more, pieces under the action of stress .The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal....
 of a material when stressed
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
. It is defined as the amount of energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 per volume that a material can absorb before rupturing
Rupture (engineering)

Rupture, or ductile rupture describes the ultimate failure of toughness ductility materials loaded in tension. Rupture describes a failure mode in which, rather than cracking, the material "pulls apart", generally leaving a rough surface....
.

hness can be found by taking the area (i.e., by taking the integral) underneath the stress-strain curve
Stress-strain curve

File:Metal yield.svgDuring testing of a material sample, the stress?strain curve is a graphical representation of the relationship between Stress , derived from measuring the load applied on the sample, and Strain , derived from measuring the deformation of the sample, i.e....
. The explicit mathematical description is:



Where

Another definition is the ability to absorb mechanical (or kinetic) energy up to failure.

s 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.






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Toughness, in materials science
Materials science

Materials science or materials engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering....
 and metallurgy
Metallurgy

Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic Chemical element, their intermetallics, and their mixtures, which are called alloys....
, is the resistance to fracture
Fracture

A fracture is the separation of an object or material into two, or more, pieces under the action of stress .The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal....
 of a material when stressed
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
. It is defined as the amount of energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 per volume that a material can absorb before rupturing
Rupture (engineering)

Rupture, or ductile rupture describes the ultimate failure of toughness ductility materials loaded in tension. Rupture describes a failure mode in which, rather than cracking, the material "pulls apart", generally leaving a rough surface....
.

Mathematical definition

Toughness can be found by taking the area (i.e., by taking the integral) underneath the stress-strain curve
Stress-strain curve

File:Metal yield.svgDuring testing of a material sample, the stress?strain curve is a graphical representation of the relationship between Stress , derived from measuring the load applied on the sample, and Strain , derived from measuring the deformation of the sample, i.e....
. The explicit mathematical description is:



Where
  • is strain
  • is the strain upon failure
  • 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
Charpy impact test

The Charpy impact test, also known as the Charpy v-notch test, is a Wiktionary:standardized high strain -rate test which determines the amount of energy absorbed by a material during fracture....
 and Izod impact tests
Izod impact strength test

Izod impact strength testing is an ASTM standard method of determining impact strength. A notched sample is generally used to determine impact strength....
.

Unit of toughness

Toughness is measured in units of joule
Joule

The joule is the SI derived unit of energy in the International System of Units. It is defined as:One joule is the amount of energy required to perform the following actions:...
s per cubic metre
Cubic metre

The cubic metre is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with SI prefix, was the st?re....
 (J/m³) in the SI
Si

Si, si, or SI may refer to :...
 system and inch-pound-force
Pound-force

The pound-force or simply pound is a Units of measurement of force....
 per cubic inch
Cubic inch

A cubic inch is a non-International System of Units Units of measurement of volume, equal to the volume of a cube with sides of one inch.Cubic inches are still sometimes used as a unit of measurement in the United States and Canada, although SI is continuing to gradually displace non-SI usage....
 (in·lbf/in³) in US customary units.

See also

  • Affie
  • Fracture toughness
    Fracture toughness

    In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications....
  • Graph toughness
    Graph toughness

    In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t-tough if, for every k > 1, G cannot be split into k different connected components by the removal of fewer than tk vertices....
  • Hardness