\n\nThe figure compares the stress-strain curves of a **ductile** and a **brittle** material. Which of the following statements is correct?
ABrittle materials show a long plastic region before fracture.
BDuctile materials fracture almost immediately past the elastic limit.
CDuctile materials have a large area under the curve, indicating higher toughness.
DBrittle materials always have a higher Young's modulus than ductile ones.
Answer & Solution
Correct answer: C. Ductile materials have a large area under the curve, indicating higher toughness.
Toughness is the *total* area under the $\sigma$–$\varepsilon$ curve up to fracture. Ductile materials (steel, copper) stretch far into a plastic region before failing, so their curves enclose a large area — they're tough. Brittle materials (glass, cast iron) fracture soon after the elastic limit with little plastic flow, enclosing little area. Young's modulus (slope of the elastic region) is independent of whether a material is ductile or brittle.
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