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In materials science and
metallurgy Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the sc ...
, toughness is the ability of a material to absorb energy and plastically deform without fracturing."Toughness"
Brian Larson, editor, 2001–2011, The Collaboration for NDT Education,
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Toughness is the strength with which the material opposes rupture. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. This measure of toughness is different from that used for
fracture toughness In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a c ...
, which describes load bearing capabilities of materials with flaws. It is also defined as a material's resistance to fracture when stressed. Toughness requires a balance of
strength Strength may refer to: Physical strength *Physical strength, as in people or animals * Hysterical strength, extreme strength occurring when people are in life-and-death situations *Superhuman strength, great physical strength far above human c ...
and
ductility Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stres ...
.


Toughness and strength

Toughness is related to the area under the
stress–strain curve In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and ...
. In order to be tough, a material must be both strong and ductile. For example,
brittle A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Bre ...
materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses and high strains. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.


Mathematical definition

Toughness can be determined by integrating the stress-strain curve. It is the energy of mechanical deformation per unit volume prior to fracture. The explicit mathematical description is: : \tfrac = \int_^ \sigma\, d\varepsilon where * \varepsilon_ is strain * \varepsilon_f is the strain upon failure * \sigma is stress Another definition is the ability to absorb
mechanical energy In Outline of physical science, physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, t ...
up to the point of failure. The area under the stress-strain curve is called toughness. If the upper limit of integration up to the yield point is restricted, the energy absorbed per unit volume is known as the modulus of resilience. Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus of elasticity. That is, : Modulus of resilience =


Toughness tests

The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to deform a notched specimen of defined cross-section. The height from which the pendulum fell, minus the height to which it rose after deforming the specimen, multiplied by the weight of the pendulum, is a measure of the energy absorbed by the specimen as it was deformed during the
impact Impact may refer to: * Impact (mechanics), a high force or shock (mechanics) over a short time period * Impact, Texas, a town in Taylor County, Texas, US Science and technology * Impact crater, a meteor crater caused by an impact event * Impac ...
with the pendulum. The Charpy and
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notched impact strength tests are typical
ASTM ASTM International, formerly known as American Society for Testing and Materials, is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
tests used to determine toughness.


Unit of toughness

Tensile toughness (or, ''deformation energy'', ''U''T) is measured in units of
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
per cubic metre (J·m−3) in the SI system and inch-
pound-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-ma ...
per cubic inch (in·lbf·in−3) in
US customary units United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English uni ...
.
1.00 N·m.m−3 ≃  in·lbf·in−3 and 1.00 in·lbf·in−3 ≃ 6.89 kN·m.m−3. In the SI system, the unit of tensile toughness can be easily calculated by using area underneath the stress–strain (''σ''–''ε'') curve, which gives tensile toughness value, as given below: :''U''T = Area underneath the stress–strain (''σ''–''ε'') curve = ''σ'' × ''ε'' :''U''T P/A × ΔL/L = (N·m−2)·(unitless) :''U''T N·m·m−3 :''U''T J·m−3


See also

*
Hardness In materials science, hardness (antonym: softness) is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. In general, different materials differ in their hardness; for example hard ...
* Rubber toughening *
Shock (mechanics) A mechanical or physical shock is a sudden acceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation. Shock describes matter subject to extreme rates of force with respect to ti ...
*
Tablet hardness testing Tablet hardness testing is a laboratory technique used by the pharmaceutical industry to determine the breaking point and structural integrity of a tablet and find out how it changes "under conditions of storage, transportation, packaging and handli ...


References

{{Authority control Continuum mechanics Materials science