Toughness

In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. It is also defined as a material's resistance to fracture when stressed.

Toughness requires a balance of strength and ductility.

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:

where

Another definition is the ability to absorb mechanical energy 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,

The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to strike the specimen and deform it. 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 with the pendulum. The Charpy and Izod impact tests are typical measures of toughness.

Tensile toughness (or, deformation energy, U_T) is measured in units of joule per cubic metre (J·m⁻³) in the SI system and inch-pound-force per cubic inch (in·lbf·in⁻³) in US customary units.
1.00 N·m.m⁻³ ≃ 0.000145 in·lbf·in⁻³ and 1.00 in·lbf·in⁻³ ≃ 6.89 kN·m.m⁻³.

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