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Hardness is resistance to permanent plastic deformation by indentation; it is measured by Brinell, Rockwell, Vickers, or Knoop methods based on load, indenter geometry, and indent size. Hardness approximately correlates with tensile yield strength (σ_y ≈ H/C where H is hardness and C is a constant ≈ 0.1), making hardness a quick, nondestructive proxy for strength. However, hardness and ductility are often inversely related.
From your study of strengthening mechanisms, you know that yield strength measures the stress at which a material begins to deform plastically — when dislocations move irreversibly through the lattice. Hardness measures the same underlying resistance to plastic deformation, but probed locally: a hard indenter is pressed into the material surface under a controlled load, and the size of the resulting indent (or the depth, depending on the method) is measured. A material that resists indentation requires a higher stress to flow around the indenter tip, which is the same microstructural resistance that gives it a high yield strength. This is why the two properties correlate.
The three major hardness scales differ in indenter geometry and measurement convention. Brinell hardness (HB) uses a large hardened steel or tungsten carbide ball (typically 10 mm diameter) pressed with a heavy load (500–3000 kg) and measures the diameter of the remaining indent. The large ball averages over multiple grains, making Brinell useful for coarse-grained or heterogeneous materials. Vickers hardness (HV) uses a diamond pyramid indenter with a square base and measures both diagonals of the indent — it works at a wide range of loads (from milligrams to kilograms) and gives a consistent scale from very soft to very hard materials. Rockwell hardness (HR) is the fastest method: it measures indent depth under a minor preload plus a major load, and reads directly off a dial or display. Different Rockwell scales (HRA, HRB, HRC, etc.) use different indenter types and loads, suited to different material hardness ranges. HRC is the standard for hardened steels.
The empirical correlation σ_y ≈ H/C (with H in MPa, C ≈ 0.1 for many metals) arises because both properties depend on the same microstructural barriers to plastic flow — dislocation density, grain size, precipitates, and solid-solution atoms. The correlation is approximate: it works best for strain-hardened metals, less well for ceramics or polymers. In steels, a rough rule is that ultimate tensile strength (UTS) ≈ 3.45 × HB (in MPa) or UTS ≈ 500 × HB (in psi). This means you can estimate the strength of a steel component from a portable hardness tester on the shop floor, without machining tensile specimens.
The hardness-ductility tradeoff reflects a fundamental microstructural reality: the same mechanisms that impede dislocation motion (raise yield strength and hardness) also limit the total plastic strain before fracture. A quenched-and-tempered high-strength steel is much harder than an annealed mild steel, but it also has far less elongation. This tradeoff is central to materials selection: a hardened steel cutting tool needs maximum hardness to resist wear, even at the cost of brittleness; a structural steel must balance adequate strength with sufficient ductility to absorb impact without catastrophic fracture. Understanding this relationship lets you use a quick hardness test not just to read a number, but to infer the full mechanical character of a material.