Why do Brinell hardness values often relate to ultimate tensile stress?

Brinell hardness values correlate with ultimate tensile stress (UTS) because both measurements are fundamentally linked to a material's resistance to permanent deformation, or yielding.12

In the Brinell hardness test, a hardened ball is pressed into a surface under a specific load, and the resulting hardness value is calculated by dividing that load by the spherical area of the indentation. Because this process forces the material to undergo plastic strain, the resistance encountered by the indenter reflects the same mechanical properties that govern how a material behaves when subjected to the maximum load in a tensile test.231

While the tensile test measures the stress at which a material reaches its maximum load before necking occurs, the Brinell test provides a practical, related indicator of that strength. Consequently, these hardness values serve as a reliable and efficient proxy for estimating the UTS of metals in industrial and engineering applications.2