What property of a material allows it to undergo large permanent strains before failure?

Ductility is the key property of a material that enables it to undergo significant permanent strains before failure. This characteristic allows materials to be stretched or deformed under tensile stress without breaking, making them ideal for applications where flexibility and the ability to absorb energy are critical.

Materials with high ductility can be shaped into complex forms and are often used in construction and manufacturing due to their ability to withstand significant deformation. Steel is a classic example of a ductile material; it can be drawn into wires or formed into beams while still maintaining structural integrity.

The other properties mentioned—brittleness, toughness, and elasticity—do not provide the same capacity for permanent strain before failure. Brittleness, for instance, describes materials that fracture without significant deformation when stress is applied. Toughness refers to a material's ability to absorb energy until failure and is a combination of strength and ductility, but it does not specifically denote the ability to undergo large permanent strains. Elasticity relates to a material's ability to return to its original shape after deforming under stress, a property more relevant to temporary deformation rather than permanent strain.