General relationship between strength and hardness

By P. Zhang, Shuzhen Li, Zhefeng Zhang. 2011

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The Hall–Petch and inverse Hall–Petch relations and the hardness of nanocrystalline metals (2019, background): “Equation (1) and variants of it [2, 3] have been in use for about a century [4–8].”
Microstructure and mechanical properties of a precipitation-strengthened Al-Zr-Sc-Er-Si alloy with a very small Sc content (2018, background): “The estimated strength increments are reported in Table 4 and compared with the experimentally obtained strength increment, defined as DHV/3 [40]; DHV is the difference between the measured microhardness of the precipitation strengthened alloy and the microhardness of pure Al, 200 MPa [7,16,41].”
Extra strengthening and work hardening in gradient nanotwinned metals (2018, background): “Dislocation type GNT-4, r (1013 m–2) Homogeneous, r (1013 m–2) Ⓐ Ⓓ Ⓐ Ⓓ BCD Average BCD Average Mode I 4.3 2.9 3.0 1.4 A few near GBs .”
Extraction of mechanical properties of materials through deep learning from instrumented indentation (2020, background): “The hardness ( H ) of a material has long been used as a property from which yield strength ( σ y ) can be estimated (7, 8, 15, 16), although their connection is known to be only highly approximate (5, 16).”