Hardness Converter — HV, HRC, HRB, HBW, HRA, Knoop, UTS (ASTM E140 / ISO 18265)

Hardness conversion is one of the most frequent tasks in metals engineering: material specifications are written on one scale, the testing equipment works on another, and code limits are expressed on a third. This converter implements ASTM E140-12b lookup-table interpolation for wrought carbon and alloy steels, converting between nine scales simultaneously — Vickers (HV), Rockwell C (HRC), Rockwell B (HRB), Rockwell A (HRA), Brinell (HBW), superficial 15-N (HR15N), superficial 30-N (HR30N), Knoop (HK), and approximate tensile strength (UTS in MPa and ksi). NACE MR0175 sour-service compliance is indicated automatically. A batch conversion table accepts up to twelve values for side-by-side comparison.

Physical Basis of Indentation Hardness

Hardness is defined as resistance to permanent (plastic) deformation under a concentrated load. All indentation hardness tests share the same underlying physics: a hard indenter is pressed into the material surface under a known force, creating a plastically deformed impression whose size or depth is proportional to the material’s flow resistance. The differences between scales lie in indenter geometry, load magnitude, and whether area (Vickers, Brinell, Knoop) or depth (Rockwell) is measured.

Tabor’s Constraint Factor and the HV–UTS Relationship

The physical link between hardness and yield/tensile strength comes from Tabor’s constraint factor C (Tabor, The Hardness of Metals, 1951). For a Vickers indenter, the mean pressure under the indent p_m relates to the material’s representative flow stress σ_r (at ~8% representative strain) by:

p𝑚 = C × σ𝕣 ≈ 3.0–3.3 × σₑ  (for most structural metals)

Since HV = F/A = p𝑚 × (constant) and σₑ ≈ UTS for strain-hardening metals:

  UTS (MPa) ≈ 3.3 × HV  (Vickers, kgf/mm²; for carbon/alloy steels)
             ≈ 3.0 × HV  (more conservative, for high-strength Q&T steels)
  UTS (MPa) ≈ 3.45 × HBW (Brinell, 10mm ball, 3000 kgf load)
  UTS (MPa) ≈ 450 × HRC  (very rough, valid ~25–50 HRC only)

HV = 0.1891 × F (N) / d² (mm²)   [SI form]
   = 1.854 × F (kgf) / d² (mm²)  [traditional form]

The HV–UTS relationship holds well for wrought steels in the annealed, normalised, and Q&T condition. It fails for: cold-worked materials (hardness increases disproportionately relative to UTS because of work hardening); austenitic stainless steels (lower constraint factor due to different strain hardening exponent); cast structures (porosity and phase heterogeneity); and non-ferrous alloys. ISO 18265 Annex B provides alloy-specific HV-to-UTS conversion tables for several material categories.

The Rockwell Scales: Principle and Valid Ranges

The Rockwell test measures the net depth of penetration of the indenter under the major load relative to the depth under the preliminary minor load (10 kgf for regular Rockwell, 3 kgf for superficial Rockwell). The hardness number is a dimensionless unit calculated from the depth difference, with higher numbers indicating harder material. This depth-measurement approach makes the Rockwell test fast and suitable for production-line testing without optical measurement.

HRC = 100 − h / 0.002    (Brale diamond indenter, 150 kgf major load)
HRB = 130 − h / 0.002    (1/16” steel ball, 100 kgf major load)
HRA = 100 − h / 0.002    (Brale diamond, 60 kgf major load)

where h = net depth of indentation [mm] = depth under major load − depth under minor load

Superficial (HR_N) scales:
  HR15N: Brale indenter, 15 kgf major → valid for thin hardened cases
  HR30N: Brale indenter, 30 kgf major → medium case depths
  HR45N: Brale indenter, 45 kgf major → deeper case depths

Scale selection by material hardness range:
  HRB: 0–100 HRB (≈ 80–237 HV); soft to medium hardness
  HRC: 20–68 HRC (≈ 228–940 HV); hardened steel range
  HRA: 60–88 HRA; cemented carbide, hardened thin sections
  HR15N: 69–94 HR15N; shallow case depth (case >0.5 mm)
  HR30N: 41–86 HR30N; medium case depth (>0.75 mm)

ASTM E140 Conversion Tables: What They Are and Their Limitations

ASTM E140 hardness conversion tables were constructed empirically by testing the same specimens on multiple machines to different scales and fitting polynomials to the resulting paired data. Key points:

• Material specificity: ASTM E140 provides five separate tables. Table 1 (non-austenitic steels) is by far the most commonly used and is what this calculator implements. Using Table 1 for austenitic stainless steel introduces systematic errors of 5–10 HRC. Always verify which table applies to the material being tested.
• Microstructure dependence: Two steels at identical HRC may differ by ±15–25 HV if they have different microstructures (tempered martensite vs bainite vs pearlite), because hardness measures average resistance to plastic deformation across the indent area, which depends on microstructural uniformity and phase distribution.
• Statistical nature: Each table entry represents the mean of a dataset with scatter. ASTM E140 explicitly states that conversions accurate to ±1 HRC or ±10 HV are not always achievable, and that for critical quality assurance, measurement on the specified scale is mandatory.
• Range validity: Converting HV 85 to HRC (which would be approximately 0 HRC) is meaningless. Always confirm the target scale value falls within the valid range before reporting.

ASTM E140 Hardness Conversion Reference Table (Non-Austenitic Steels, Table 1)

NACE MR0175 / ISO 15156 Hardness Requirements

NACE MR0175 (now harmonised with ISO 15156) is the definitive standard governing materials selection for components exposed to H₂S-containing (sour) environments in oil and gas production. Sulphide stress cracking (SSC) is a hydrogen embrittlement mechanism that causes brittle fracture of high-strength steel at stresses well below the yield strength. Hardness is the primary screening criterion because SSC susceptibility correlates strongly with martensite hardness — harder martensite is more susceptible to hydrogen trapping and embrittlement.

Hardness Limits per NACE MR0175 / ISO 15156-2

Vickers Microhardness for Case Depth Profiling

For case-hardened surfaces (carburised, nitrided, induction hardened, borided), the surface and subsurface hardness distribution must be measured by Vickers microhardness (HV0.1, HV0.3, or HV1 load) at a series of positions from the surface into the core. The effective case depth (ECD) is defined as the depth at which hardness drops below a specified threshold — typically 550 HV (≈52 HRC) for carburised gears (ISO 6336-5) or 515 HV for induction hardened shafts.

Case depth rules (ISO 6336-5, AGMA 2101):
  ECD (carburising): depth to 550 HV (≈ 52 HRC)
  CHD (carburising): depth to 550 HV using HV1 per ASTM E18
  NHD (nitriding):   depth to 650 HV (≈ 58 HRC)
  SHD (induction):   depth to 550 HV (≈ 52 HRC)

Minimum indent spacing for HV microhardness traverse:
  HV0.1 (10 gf):  spacing ≥ 3× indent diagonal ≈ 15–25 μm → 50 μm min.
  HV1   (100 gf): spacing ≥ 3× indent diagonal ≈ 45–80 μm → 150 μm min.

Rockwell HRC is NOT appropriate for case depth measurement:
  HRC indentation depth ≈ 1.5 mm → averages case + transition + core
  Use HV0.3 or HV1 traverse for case profiles (per ISO 2639, ASTM E1936)

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