ductility
Ductility is how much a material can be stretched or bent out of shape before it finally breaks — its 'give', its willingness to deform rather than snap. Gold is the champion: a gram can be drawn into a wire hundreds of metres long. Chalk, glass, and cast iron are the opposite; they have almost no ductility and shatter with little warning. Ductility is why you can bend a copper pipe by hand but a ceramic tile just cracks.
It is measured in two common ways from a tensile test. Percent elongation is the permanent stretch at fracture: EL = 100 x (L_f - L0) / L0, where L_f is the length of the broken pieces fitted back together. Reduction of area is how much the cross-section shrank at the break: RA = 100 x (A0 - A_f) / A0. A ductile structural steel might elongate 20 to 30 percent; a brittle grey cast iron under 1 percent. Both numbers grow with the amount of plastic flow the material can sustain before it cracks.
Ductility is prized not because parts are meant to deform, but because a ductile material bends, sags, and gives visible warning before failing, and it tolerates overloads, stress concentrations, and rough handling. A brittle material offers no such grace. The honest catch runs through metallurgy: the very treatments that raise strength (cold work, quenching, adding carbon) usually LOWER ductility, so a large part of engineering is buying enough strength without spending all the ductility — the strength-ductility trade-off.
Drop a wrench on a ductile steel bracket and it may dent; drop it on a grey cast-iron one and it can crack clean through — same job, but the cast iron's near-zero ductility gives no warning.
Ductility is stretch before fracture, measured as percent elongation or reduction of area.
Ductility is not strength — a soft annealed copper is very ductile but weak, a hardened steel very strong but less ductile. Strengthening treatments almost always eat into ductility (the strength-ductility trade-off).