What characteristic allows tough cutting tools to withstand sudden stresses?

Tough cutting tools are designed to endure sudden stresses primarily due to their toughness. Toughness refers to a material's ability to absorb energy and deform without fracturing. It is a critical property for cutting tools, as they often encounter unexpected loads or impact during operation.

When a cutting tool experiences a sudden stress, such as during an interrupted cut or when it encounters an obstruction in the material being cut, a tough material can absorb and dissipate that energy instead of breaking or chipping. This characteristic helps maintain the integrity of the cutting edge and prolongs the lifespan of the tool.

While flexibility, density, and hardness are important material properties, they do not confer the same level of resistance to sudden stresses as toughness does. Flexibility might allow a tool to bend but not necessarily to withstand abrupt forces without breaking. Density and hardness contribute to the tool's ability to cut well and resist wear but do not directly address the challenge of sudden impacts or stress. Thus, toughness is the key characteristic that enables cutting tools to perform reliably under unpredictable conditions.