# How to Calculate Ductility

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Ductility is a mechanical property of materials that refers to the degree of plastic deformation a material can sustain prior to fracture. If little or no plastic deformation can occur, the material is termed "brittle." Ductility can be quantitatively expressed in terms of either "percent elongation" or "percent reduction in an area." The values for percent elongation and percent reduction in area, however, will not necessarily be the same for the same material.

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## Calculating Percent Elongation

• Measure the original gauge length (Lo) of the material around the point of intended fracture. This value is commonly 2 inches or 50 millimeters.

• Apply a tensile force to the material slowly until fracture occurs.

• Fit the broken parts back together and measure the fracture length (Lf), using the same endpoints on the material as the initially measured gauge length.

• Calculate the percent elongation using the following equation: 100(Lf-Lo)/Lo.

## Calculating Percent Reduction in an Area

• Measure the diameter of the solid cylindrical material to be tested (d).

• Calculate the original cross-sectional area (Ao) of the rod by using the diameter into the following equation: pi*(d/2)^2

• Apply a tensile force to the material slowly until fracture occurs.

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• Measure the diameter of the cylinder at the point of fracture (df) then calculate the cross-sectional area at the point of fracture (Af), using the same equation.

• Calculate the percent reduction in area using the following equation: 100(Ao-Af)/Ao.

## Tips & Warnings

• The magnitude of percent elongation will depend on specimen gauge length and therefore it is customary to specify the initial gauge length when reporting the percent elongation.
• Metals tend to become more brittle as the temperature is lowered and more ductile as the temperature increases.

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