What is established when a metal specimen begins to stretch under gradually increasing pressure?

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The main concept is the point at which a metal stops deforming elastically and starts to deform permanently under load. Under gradually increasing pressure, a metal initially stretches in a reversible, elastic manner, but at a certain stress—the yield strength—the material begins to plastically deform and will elongate even if the load is lowered. That onset of permanent, plastic deformation is what yield strength measures, so it’s the best fit for the description. Elasticity would be the reversible portion before yielding, not the threshold where permanent stretch begins. Strain is the amount of deformation, not the stress at which it starts, and hardness relates to resistance to indentation rather than tensile yielding.