Editing Ductility (section)

===Basic definitions===
The quantities commonly used to define ductility in a tension test are [[relative elongation]] (in percent, sometimes denoted as <math>\varepsilon_{\mathrm f}</math>) and reduction of area (sometimes denoted as <math>q</math>) at fracture.<ref name="dieter">Dieter, G. (1986) ''Mechanical Metallurgy'', McGraw-Hill, {{ISBN|978-0-07-016893-0}}</ref> Fracture strain is the [[Deformation (physics)#Engineering strain|engineering strain]] at which a test specimen fractures during a [[Index ellipsoid|uniaxial]] [[tensile test]]. Percent elongation, or engineering strain at fracture, can be written as:<ref name=DR>{{Cite web|title=Ductility Review - Strength Mechanics of Materials - Engineers Edge|url=https://www.engineersedge.com/material_science/ductility.htm|access-date=2020-07-14|website=www.engineersedge.com}}</ref><ref name=":1">{{Cite book|last=Askeland|first=Donald R.|url=https://www.worldcat.org/oclc/903959750|title=The science and engineering of materials|others=Wright, Wendelin J.|year=2016|isbn=978-1-305-07676-1|edition=Seventh|location=Boston, MA|pages=195|chapter=6-4 Properties Obtained from the Tensile Test|oclc=903959750}}</ref><ref name=":2">{{Cite book|last=Callister|first=William D. Jr.|url=https://www.worldcat.org/oclc/401168960|title=Materials science and engineering : an introduction.|others=Rethwisch, David G.|year=2010|isbn=978-0-470-41997-7|edition=8th|location=Hoboken, NJ|pages=166|chapter=6.6 Tensile Properties|oclc=401168960}}</ref>

:<math>\%\mathrm{EL} = \frac{\text{final gauge length - initial gauge length}}{\text{initial gauge length}} = \frac{l_{\mathrm f} - l_0}{l_0} \cdot 100</math>

Percent reduction in area can be written as:<ref name=":1" /><ref name=":2" />

:<math>\%\mathrm{RA} = \frac{\text{change in area}}{\text{original area}} = \frac{A_0 - A_{\mathrm f}}{A_0} \cdot 100</math>

where the area of concern is the cross-sectional area of the gauge of the specimen.

According to ''Shigley's Mechanical Engineering Design'',<ref name="Shigley2"/> 'significant' denotes about 5.0 percent elongation.