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Materials Testing Simulator

Brinell Hardness Test Simulator — HBW and Indent Diameter

Visualize plastic indentation by a tungsten-carbide ball. Compute HBW, indent depth and the validity of d/D and F/D² in real time from load, ball diameter and indent diameter.

Parameters
Load F
N
Ball diameter D
mm
Indent diameter d
mm
Material (F/D² class)
—

Material code: 0 = steel/cast iron (F/D²≈30), 1 = Cu/Al alloys (F/D²≈10), 2 = soft metals (F/D²≈5). Keep d < D.

While paused, move the sliders to update the result instantly.

Results
—
Applied load F
—
Ball diameter D
—
Indentation diameter d
—
Brinell hardness HBW
Brinell hardness test animation

The ball indenter descends under load F, the indent diameter d grows → HBW is measured → the load is released, looping smoothly.

Theory & Key Formulas

Brinell hardness is the load divided by the spherical cap area of the plastic indent left by a ball indenter.

HBW (traditional kgf/mm²). F in N, D in mm, d in mm; the 0.102 = 1/9.81 factor converts N → kgf:

$$\mathrm{HBW} = \frac{0.102 \cdot 2F}{\pi D \left(D - \sqrt{D^2 - d^2}\right)}$$

Indent depth h and spherical cap area A:

$$h = \frac{D - \sqrt{D^2 - d^2}}{2}, \qquad A = \pi D h$$

Load constant F/D² and validity band:

$$\frac{F}{D^2} \approx 30,\ 10,\ 5\ [\mathrm{kgf/mm^2}], \qquad 0.24 \le \frac{d}{D} \le 0.60$$

Same F/D² allows HBW values obtained with different D to be compared (geometric similarity). For elastic contact theory see hertz-contact.html, hertz-line-contact.html, contact-ellipse-hertz.html and bearing-life.html.

What is the Brinell hardness test simulator?

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There are Vickers and Rockwell too — what makes Brinell different?
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Brinell uses a big ball and a big load. A 10 mm tungsten-carbide ball, 3000 kgf (about 29.4 kN), and a few-millimetre crater that you measure under a microscope. The default values here (F=29420 N, D=10 mm, d=4 mm) are a typical steel test, and the result is HBW ≈ 229. That's a fairly hard structural steel.
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When I move the indent diameter d the HBW changes a lot. d = 3 mm gives a much higher hardness.
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Right — smaller indent under the same load means a harder material. The denominator in $\mathrm{HBW}=0.102\cdot 2F/(\pi D(D-\sqrt{D^2-d^2}))$ is the spherical cap area. Shallower indent, smaller area, larger "stress". Watch the lower chart: as d/D grows, HBW drops sharply.
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There's a green band at 0.24–0.60 on the curve. What does that mean?
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That's the valid d/D window. Below 0.24 the indent is so shallow that elastic recovery dominates measurement error. Above 0.60 plastic flow piles up around the ball and HBW falls. Inside the band, HBW is essentially load-independent — that's why both ISO 6506 and JIS Z 2243 pin you to this range.
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If I switch the material to "soft metals", the validity card says "F/D² off". Why?
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The load constant F/D² needs to match the material class. Steel needs about 30 kgf/mm², copper/aluminium 10, soft metals 5. Push 3000 kgf with a 10 mm ball into pure aluminium and the indent gets way too deep. In practice you pick F/D² first, then back-calculate the load. Same F/D² across different D gives the same HBW — that's the geometric similarity behind the method.

FAQ

The indent is part of a sphere and its surface area is exactly πDh. That choice — not the projected circle πd²/4 — is what defines Brinell. Because the depth h is hard to measure directly, you measure d and use h = (D−√(D²−d²))/2 to convert.
Older standards used hardened steel balls (HBS), but above about 450 HB the ball itself flattens and gives biased results. Tungsten carbide balls (HBW) stay essentially rigid up to about 650 HB. Modern ISO 6506 and JIS Z 2243 specify the WC ball and the HBW notation.
A reading microscope measures the diameter on two perpendicular axes and the average is taken as d. If the two values differ too much (tilted surface or strong anisotropy), the specimen must be re-prepared. Modern automatic stations use edge detection on a captured image for the same result.
Yes. Specimen thickness must be at least 10·h, otherwise the rigid backing or an elastic floor distorts the reading. Indent centre must be at least 2.5·d from any edge and 3·d (4·d for steel) from any neighbouring indent. Violating these spacings causes plastic-zone interference and shifts HBW.

Real-world applications

Cast iron and cast steel quality control: The large indent averages over the coarse, inhomogeneous microstructure of castings. Crankshafts, engine blocks and railway wheels are routinely accepted against HBW specifications such as "FC250 cast iron: 180–250 HBW".

Heat-treatment verification on rolled and forged stock: Large forgings need a representative average rather than a single surface point. The 10 mm ball is insensitive to surface roughness and decarburised layers, which is why it dominates QC of forged rolls and gear blanks after normalising or annealing.

Material specifications and acceptance tests: JIS, ISO and ASTM material standards list allowed HBW ranges, and mill certificates always include them. "SS400 ≤ 120 HBW", "S45C Q&T 217–277 HBW" — designers use HBW as a quick proxy for mechanical properties.

Estimating tensile strength: For steels the empirical relation σ_B [MPa] ≈ 3.45 · HBW holds well (HBW 200 ⇒ about 690 MPa). When tensile testing a large part is impractical, HBW gives a fast non-destructive estimate. Coefficients differ for cold-worked or non-ferrous metals.

Common misconceptions and pitfalls

The most common mistake is to think HBW is load divided by the projected circle. It is divided by the spherical cap area πDh. Push d/D from 0.5 to 0.8 in the lower chart: as d approaches D the cap area explodes and HBW collapses, far more sharply than a projected-area definition would predict. Always remember which area is in the denominator.

The second pitfall is treating the 0.24–0.60 d/D band as a soft guideline. Outside the band, HBW for the same material can swing by tens of units when you change the load. Setting d = 1 mm (d/D = 0.1) in the simulator returns thousands of HBW — that is the elastic seating of the ball, not a hardness number. Using such values for acceptance testing makes acceptable parts fail and vice versa.

The last pitfall is ignoring the F/D² load constant. Using the steel 3000 kgf load on a soft copper alloy gives d/D > 0.7 and a biased low HBW. Conversely, a 187.5 kgf load on a 2.5 mm ball (F/D² = 30) on small cast-iron specimens yields the same HBW as the 10 mm test — that is the geometric similarity at work. Switch the material slider and confirm that the validity card turns "Valid": steels accept roughly 7500 N – 30000 N, soft metals only around 1500 N.

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How to Use

  1. Select material from dropdown (steel, aluminum, cast iron, or copper alloy) to auto-populate reference hardness ranges.
  2. Set applied load (F) in kgf using slider—typical range 500–3000 kgf for industrial testing; 187.5 kgf for soft metals.
  3. Input tungsten-carbide ball diameter (D) in mm—standard sizes are 1, 2, 5, or 10 mm; smaller balls suit thin sections.
  4. Enter measured indent diameter (d) in mm after physical impression; simulator calculates HBW, indent depth, and ratio validity.
  5. Verify d/D ratio displays 0.24–0.60 (ASTM E10 compliance); if outside range, retest with adjusted load.

Worked Example

Steel specimen tested with 3000 kgf load, 10 mm tungsten-carbide ball. Measured indent diameter d = 4.8 mm. HBW = (2 × 3000) / [π × 10 × (10 − √(100 − 23.04))] = 6000 / [π × 10 × 2.64] ≈ 72.1 HBW. Indent depth h ≈ 1.3 mm. Ratio d/D = 0.48 (valid, within 0.24–0.60). Result acceptable per ISO 6506-1.

Practical Notes

  1. Light alloys (aluminum 6061-T6, ~95 HBW) require 500 kgf load; high-strength steel (hardened tool steel, ~650 HBW) needs 3000 kgf to avoid sub-scale errors.
  2. d/D below 0.24 indicates underload; above 0.60 indicates overload—both invalidate ISO certification; retest immediately.
  3. Tungsten-carbide balls resist deformation better than hardened steel; use WC for materials exceeding 450 HBW to prevent ball flattening and measurement drift.
  4. Indent depth h must clear surface roughness; for Ra > 3.2 µm surfaces, apply 10–15 second dwell before removing load to stabilize plastic flow.