Hardness Testing

Why hardness testing matters

Hardness is the cheapest, fastest, and least destructive window into a metal's mechanical state. A test takes seconds, leaves a mark a fraction of a millimeter across, and needs no machined specimen — so it is the property engineers actually measure on production parts, incoming stock, weld heat-affected zones, and case-hardened surfaces. What that tiny dent tells you is the material's flow stress: the pressure needed to make it yield and flow plastically. From that one number you can infer strength, screen heat treatments, verify a specification, and catch a mixed-up alloy before it reaches assembly.

• Heat-treat verification. A quench-and-temper cycle is judged pass/fail on hardness — 58–62 HRC for a gear tooth, 28–34 HRC for a shaft.
• Case depth mapping. A traverse of Vickers microhardness indents through a carburized case defines the effective case depth (conventionally to 550 HV).
• Incoming inspection. A quick Rockwell reading confirms the right temper of aluminum or steel arrived.
• Wear and machinability. Harder surfaces resist abrasion but cut and form more reluctantly; hardness sets tooling and process windows.
• Strength estimation. When a tensile test is impractical (a finished part, a small weld bead), hardness gives a strength proxy.
• Failure analysis. An unexpectedly soft or brittle-hard region flags a missed temper, decarburization, or an overheated weld.

How indentation testing works, step by step

Every indentation test follows the same logic: press a much harder indenter into the surface with a controlled force, hold, remove it, and quantify what is left. The methods differ in indenter shape, load, and whether they read depth or projected/contact area.

1. Rockwell (depth). A minor preload (10 kgf for regular scales) seats the indenter and zeroes the reference. The major load is then applied — 60, 100, or 150 kgf depending on scale — held, and removed back to the minor load. The instrument reads the permanent increase in depth and converts it directly to a Rockwell number: HR = N − (h/0.002), where h is the residual depth in millimeters and each 0.002 mm of penetration costs one Rockwell point. HRC uses a 120° diamond Brale cone with a 150 kgf major load (hard steels); HRB uses a 1/16" (1.588 mm) ball at 100 kgf (softer steels, brass); HRA uses the diamond at 60 kgf (thin, very hard materials like carbide and case layers).
2. Brinell (ball, area). A tungsten-carbide ball of diameter D (usually 10 mm) is pressed at load P (typically 3000 kgf for steel, 500 kgf for softer metals) for 10–15 s. The impression diameter d is measured optically and the number is the load divided by the curved spherical contact area: HB = 2P / [πD(D − √(D² − d²))]. The large indent averages over grains and porosity, making Brinell ideal for castings, forgings, and coarse-grained material.
3. Vickers (diamond pyramid). A square-based diamond pyramid with a 136° included face angle is pressed at any load from a few grams (microhardness) to 100 kgf. The two diagonals of the square impression are measured and averaged to d. HV = 1.854·P/d² with P in kgf and d in mm. One continuous scale spans foil to carbide, which is why Vickers dominates research, thin coatings, and case-depth work.
4. Knoop (elongated pyramid). A close cousin of Vickers, the Knoop indenter is a rhombic pyramid with a 7:1 long-to-short diagonal ratio. Only the long diagonal is read, giving a shallow indent suited to brittle ceramics and thin plated layers: HK = 14.229·P/L².
5. Mohs (scratch). No load at all — a harder mineral scratches a softer one. The ordinal 1–10 scale places talc at 1 and diamond at 10, with quartz (7) as the field benchmark that scratches ordinary steel.

Governing equations

The two most-used indentation numbers reduce to force divided by an impression area. For Vickers, the 136° geometry fixes the constant:

HV = 1.854 · F / d²

• HV — Vickers hardness number (conventionally dimensionless; physically kgf/mm²)
• F — applied load, kgf
• d — mean of the two impression diagonals, mm
• 1.854 — geometric constant = 2·sin(136°/2) = 2·sin(68°)

In SI units (F in newtons, d in mm): HV ≈ 0.1891·F/d², and one HV point ≈ 9.807 MPa of mean contact pressure. For Brinell, the curved contact area gives:

HB = 2P / [ π·D·(D − √(D² − d²)) ]

• HB — Brinell hardness number, kgf/mm²
• P — applied load, kgf
• D — ball diameter, mm (usually 10)
• d — impression diameter, mm

The link to strength comes from Tabor's result that indentation hardness is about three times the uniaxial flow stress at a representative plastic strain of ~8%:

H ≈ 3 · σ_flow  →  UTS (MPa) ≈ 3.45 · HB (steels, per ASTM A370)

Comparing the indentation and scratch methods

Method	Indenter	Typical load	Reads	Best for	Range (approx.)
Rockwell C (HRC)	120° diamond Brale cone	150 kgf major (10 kgf minor)	Residual depth	Hardened steels	20–70 HRC
Rockwell B (HRB)	1.588 mm steel/carbide ball	100 kgf major	Residual depth	Mild steel, brass, aluminum	0–100 HRB
Rockwell A (HRA)	120° diamond cone	60 kgf major	Residual depth	Carbide, thin case, sheet	60–88 HRA
Brinell (HB)	10 mm WC ball	500–3000 kgf	Impression diameter	Castings, forgings, coarse grain	~16–650 HB
Vickers (HV)	136° diamond pyramid	1 gf–100 kgf	Mean diagonal	All materials, coatings, micro	~5–>2000 HV
Knoop (HK)	7:1 rhombic diamond	1 gf–1 kgf	Long diagonal	Brittle ceramics, thin layers	~1–>2500 HK
Mohs	Reference mineral	None (scratch)	Ordinal rank	Minerals, field geology	1–10 (ordinal)

Rough anchors on the Mohs scale: talc 1, gypsum 2, calcite 3, fluorite 4, apatite 5, orthoclase 6, quartz 7, topaz 8, corundum 9, diamond 10. The scale is ordinal, not linear — measured absolute (Vickers) hardness of diamond is several times that of corundum despite being only one Mohs step higher.

Common misconceptions and failure modes

• "Hardness is a single fundamental property." It is method-defined. The same steel yields different numbers on Rockwell, Brinell, and Vickers, and even different Vickers numbers at different loads. Always state the scale and load (e.g. 62 HRC, 650 HV0.5, 240 HB).
• "Small indents read the same as big ones." The indentation size effect makes low-load microhardness read higher because strain-gradient plasticity packs extra geometrically-necessary dislocations under a tiny indent. Micro- and macro-hardness of the same material need not agree.
• "Conversions are exact." ASTM E140 tables are empirical and material-class-specific. Applying a steel table to aluminum or austenitic stainless can be off by tens of points.
• "A single reading is enough." Surface prep dominates. Decarburized skin, work-hardened machining layers, oxide, or a lubricant film all shift the reading; take several indents on a flat, clean, properly ground surface.
• Edge and spacing errors. Indent too close to an edge or a prior impression and the plastic field is unconstrained or overlaps — readings drift. Rules of thumb: indent centers ≥ 3 diagonals apart (2.5D for Brinell) and ≥ 2.5–3 diagonals from any edge.
• Anvil and thickness effects. A specimen thinner than ~10× the indentation depth "feels" the anvil; Rockwell readings on thin stock read artificially high. The specimen must be at least 10 times the indent depth thick and rest flat with no flexing.
• Brinell on very hard steel. A steel ball flattens above ~450 HB, corrupting the reading — which is why tungsten carbide balls (HBW) replaced hardened-steel balls (the old HBS) for high-hardness work.

Worked example: Vickers reading to strength estimate

A quenched-and-tempered 4140 steel shaft is tested with a Vickers macrohardness tester at F = 30 kgf. The two measured diagonals are 0.303 mm and 0.309 mm.

1. Mean diagonal: d = (0.303 + 0.309) / 2 = 0.306 mm.
2. Vickers number: HV = 1.854 · 30 / (0.306)² = 55.62 / 0.09364 ≈ 594 HV30.
3. Approximate Rockwell C (ASTM E140 steel table): 594 HV ≈ 55 HRC — a fully hardened, moderately tempered structural steel.
4. Approximate Brinell: in the overlap range HV and HBW track closely, so HB ≈ 560 (a steel ball would flatten here, so this is a carbide-ball HBW figure).
5. Tensile strength estimate: UTS ≈ 3.45 · HB ≈ 3.45 · 560 ≈ 1930 MPa, consistent with a hard-tempered 4140 (real UTS ~1900–2000 MPa). Report the measured value (594 HV30) as primary; treat the HRC, HB, and UTS figures as table-based estimates.

The lesson: one 300-micron dent, read in seconds, brackets a part's temper, its equivalent Rockwell number, and its tensile strength to within engineering tolerance — provided you honor the scale, the load, and the surface-prep rules.