What does toughness indicate in a material?

Toughness in a material is defined as its ability to absorb energy before failure, which is represented by the total area under the stress-strain curve. This area provides a measurement of how much energy a material can withstand during loading until it fractures. Toughness combines aspects of both strength and ductility, indicating that a tough material can endure both high stress and significant deformation without breaking. This property is crucial in applications that require materials to withstand impacts or shocks, as it reflects the material’s performance under actual conditions rather than just during a simple tensile test.

The other options relate to different properties of materials. For instance, resistance to cutting relates more to hardness, while flexibility and ductility pertain to a material's ability to deform without breaking, but don't fully encapsulate toughness. Resistance to impact and deformation, while somewhat related to toughness, does not directly define it in the same comprehensive manner as the total area under the stress-strain curve does.