Vickers Hardness

Robert Smith and George Sandland, working at Vickers Ltd, presented the test in 1922 to the Institution of Mechanical Engineers. The indenter is a square-based diamond pyramid whose opposite faces meet at 136°. Press it into the surface under a known load, remove it, and measure the two diagonals of the square mark left behind. Hardness is the load divided by the SLOPING SURFACE AREA of the impression.

The 1.8544 is exact geometry, not a fudge factor. For a pyramid of that included angle, the slant area expressed in terms of the diagonal d works out to d²/(2 sin 68°). Dividing load by that area gives HV = 2F sin(68°)/d² = 1.8543677 F/d². Note it is the sloping area and not the projected area. Vickers and Brinell both use surface area; Knoop and instrumented indentation use the projected area. That is why the scales do not agree even in principle, and why converting between them needs a table rather than a formula.

The great virtue of the pyramid is self-similarity. Impressions made at different loads are geometrically identical, only scaled, so the hardness number is independent of the load — one continuous scale from soft lead to hardened tool steel to ceramics. Brinell cannot claim that, because a ball indenter's impression changes shape with depth, which is why a Brinell result must always carry its ball diameter and load as a ratio. Rockwell cannot claim it either, since it measures depth on an arbitrary scale.

The 136° angle was not arbitrary. It was chosen so that the Vickers number would agree closely with the Brinell number over the range where Brinell is valid, because a Brinell ball's ideal impression subtends about that angle at the recommended 0.375 ratio of impression diameter to ball diameter. The scales were deliberately built to overlap, which is a piece of thoughtful metrology worth knowing about.

Hardness is conventionally quoted in kgf/mm², which genuinely IS a pressure: 1 kgf/mm² = 9.80665 MPa exactly. This site has no kgf/mm² entry in its unit picker, so the pages carry hardness in MPa and print the bare HV number alongside — divide the megapascal figure by 9.80665 to get the number a tester displays. Loads are named the same way: HV30 means a 30 kgf load, which is 294.2 N.

Three practical rules govern whether a reading means anything. Measure both diagonals and average them; a difference of more than about 5 % between them means the surface was not perpendicular to the indenter, and the result is invalid. Keep the specimen at least 1.5 diagonals thick, or the anvil underneath is part of what you measured. And space indents at least two and a half diagonals apart, because the metal around an indent is work-hardened and a neighbouring indent lands in disturbed material. Below about 1 kgf the hardness number starts to climb as the load falls — the indentation size effect, attributed to geometrically necessary dislocations — which is why a microhardness result must always be reported with its load.

Now the question this site will not answer. Everybody who finds this page wants σ_UTS ≈ 3.3 × HV, and it is not here and never will be. That relation is not physics; it is a regression, fitted separately for carbon steel, austenitic stainless, aluminium alloys, brass and cast iron, and giving a different coefficient for each. It fails outright on work-hardened, case-hardened, textured or anisotropic material, where the indenter samples a skin — roughly d/7 deep — that is nothing like the bulk. ASTM E140 and ASTM A370 publish the conversion tables and restrict them, on their own front pages, to the materials they were measured on. Reproducing a regression here would let a reader compute a tensile strength for an alloy nobody ever measured, and print it with a confident number of decimal places. Use the table for your material, or pull a tensile bar.

What hardness IS excellent for is comparison and mapping. A traverse of small indents across a case-hardened section gives the case depth. A traverse across a weld gives the hardness peak in the heat-affected zone, which is the number a welding procedure is qualified against. A traverse against holding time follows a tempering or ageing response cheaply and non-destructively. In every one of those, the hardness number is being used as an index of microstructure, which is exactly what it is.