How to Calculate Ductility

By Dylin Tweedie

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.



Calculating Percent Elongation

Original gauge length.

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.

Fracture length

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.

Percent elongation

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

Calculating Percent Reduction in an Area

Original diameter

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

Formula for the area of a circle

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.

Diameter at the point of fracture

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.

Percent reduction in area

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

Tip

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.

Warning

Metals tend to become more brittle as the temperature is lowered and more ductile as the temperature increases.

About the Author

Dylin Tweedie holds a Bachelor of Science in chemical engineering from the University of Connecticut and a Master of Science in mechanical engineering from Rensaleer Polytechnic Institute. Tweedie has worked in the field of power generation utilizing both conventional and renewable power sources, the environmental analytical chemistry field, water filtration devices field and food services industry. In her spare time, Tweedie is an avid enthusiast of both travel and outdoor sports and is the founder of the website petiteoutdoorgear.com.