What is Brinell Hardness?
The Brinell Hardness Number (BHN) is one of the oldest and most widely used methods for quantifying the hardness of a material. Developed by Swedish engineer Johan August Brinell in 1900, the test works by pressing a hardened steel or tungsten carbide ball into the surface of a specimen under a controlled load and then measuring the diameter of the impression left behind. The resulting number tells you how resistant the material is to permanent deformation.
Understanding hardness is critical in engineering, metallurgy, and manufacturing. When you select a steel for a gear, choose an aluminium alloy for an aircraft skin, or specify a casting for a pump housing, the hardness value helps predict wear resistance, machinability, and suitability for the intended service conditions. The Brinell test is particularly valued because its large indentation samples a broad area of the material surface, averaging out local variations caused by grain boundaries, inclusions, or uneven microstructure.
The test is governed by international standards including ASTM E10 and ISO 6506, which define the permissible ball sizes, applied loads, and measurement procedures. A standard Brinell test uses a 10 mm diameter ball and a 3,000 kgf load for ferrous metals, though lighter loads and smaller balls are specified for softer materials and thinner sections.
The BHN Formula
The Brinell Hardness Number is calculated from the applied force and the geometry of the indentation using the following formula:
[\text{BHN} = \frac{2F}{\pi \times D \times \left(D - \sqrt{D^2 - d^2}\right)}]
Where:
- F is the applied force in kilogram-force (kgf). If the force is measured in newtons, divide by 9.80665 to convert to kgf.
- D is the diameter of the ball indenter in millimeters.
- d is the diameter of the indentation measured on the material surface, in millimeters.
The denominator represents the curved surface area of the spherical indentation. The term inside the parentheses, D minus the square root of D squared minus d squared, corresponds to the depth of the impression expressed through the ball geometry. Multiplying by pi and D converts this depth into the contact area of the curved impression, giving a result in square millimeters. Dividing twice the applied force by this area yields the hardness in kgf/mm2.
Calculation Example
Let us work through a standard test scenario step by step.
Given:
- Applied force: 3,000 kgf
- Ball diameter: 10 mm
- Indentation diameter: 4 mm
Step 1: Calculate the expression under the square root.
[D^{2} - d^{2} = 10^{2} - 4^{2} = 100 - 16 = \text{84}]
Step 2: Take the square root.
[\sqrt{84} \approx 9.165]
Step 3: Calculate the parenthetical term.
[D - \sqrt{D^2 - d^2} = 10 - 9.165 = 0.835]
Step 4: Calculate the denominator.
[\pi \times D \times 0.835 = 3.14159 \times 10 \times 0.835 = 26.233]
Step 5: Calculate the numerator.
[2F = 2 \times 3{,}000 = 6{,}000]
Step 6: Compute the BHN.
[\text{BHN} = \frac{6{,}000}{26.233} \approx 228.70]
The Brinell Hardness Number for this specimen is approximately 228.70 BHN. This value is typical of a medium-carbon steel in the normalised condition.
Quick Reference: Common BHN Values
| Material | Typical BHN Range |
|---|---|
| Pure aluminium | 15 - 25 |
| Brass | 60 - 120 |
| Mild steel | 120 - 180 |
| Medium-carbon steel | 200 - 300 |
| Tool steel (hardened) | 350 - 600 |
| White cast iron | 400 - 650 |
How the Brinell Test Works in Practice
A standard Brinell hardness test follows a well-defined procedure. The test specimen is placed on the anvil of the hardness testing machine. The indenter, a polished ball made of hardened steel (for materials up to 450 BHN) or tungsten carbide (for harder materials), is brought into contact with the surface. The full test load is applied gradually and held for a dwell time, typically 10 to 15 seconds for ferrous metals and 30 seconds or more for non-ferrous alloys.
After the load is removed, the diameter of the indentation is measured at two perpendicular directions using a low-power microscope or optical measurement system. The two readings are averaged to account for any slight asymmetry, and this average diameter is used in the BHN formula.
The choice of load and ball size follows a load-to-diameter ratio principle. For a 10 mm ball, common loads are 3,000 kgf for steel and iron, 1,500 kgf for copper alloys, and 500 kgf for soft metals. This ratio ensures that indentations across different test configurations produce comparable hardness numbers.
Converting Between Force Units
The BHN formula requires force in kilogram-force. If your testing machine reads in newtons, you need to convert before calculating:
[F_{\text{kgf}} = \frac{F_{\text{N}}}{9.80665}]
For example, a 29,420 N load converts to:
[\frac{29{,}420}{9.80665} \approx 3{,}000 \text{ kgf}]
The calculator handles this conversion automatically when you select newtons as the force unit.
Practical Tips for Accurate Brinell Testing
Getting reliable BHN values requires attention to several practical details:
- Surface preparation. The test surface should be smooth and free of scale, oxide, or coatings. A rough surface leads to irregular indentation edges that are difficult to measure accurately. Grinding or polishing the test area before testing improves measurement consistency.
- Specimen thickness. The specimen must be thick enough that the indentation does not cause a visible bulge on the opposite face. As a rule of thumb, the specimen thickness should be at least 10 times the depth of the indentation. For a 10 mm ball with a typical indentation, this means a minimum thickness of roughly 8 to 10 mm.
- Spacing between indentations. The centre of each indentation should be at least 2.5 times the indentation diameter from the edge of the specimen and at least 3 times the indentation diameter from the centre of any adjacent indentation. Indentations placed too close together produce artificially high readings because the material has already been work-hardened by the previous test.
- Dwell time consistency. Always hold the load for the full specified dwell time. Releasing too early results in a smaller indentation and an artificially high BHN. For non-ferrous metals that creep under load, the longer 30-second dwell is essential.
- Measure at two perpendicular diameters. Indentations are rarely perfectly circular. Measuring at 90 degrees and averaging the two readings compensates for any asymmetry caused by material anisotropy or slight misalignment.
Limitations and When to Use Other Tests
The Brinell test excels for softer to medium-hard materials and for specimens with coarse microstructures. However, it has some limitations:
- Very hard materials. Above approximately 650 BHN, even tungsten carbide balls can deform, leading to inaccurate results. For materials this hard, the Vickers or Rockwell C tests are more appropriate.
- Thin or small parts. The large indentation requires a substantial specimen. For thin sheet metal, coatings, or small components, micro-hardness tests such as Vickers or Knoop are better suited.
- Case-hardened surfaces. If only a thin hardened layer exists on a softer substrate, the Brinell ball may penetrate through the hard case, producing a reading that reflects the softer core rather than the surface hardness. Superficial Rockwell or Vickers tests at low loads are preferred for case depth evaluation.
Despite these limitations, the Brinell test remains the standard method for incoming material inspection, foundry quality control, and any application where a single number needs to represent the bulk hardness of a large section of material. Its simplicity, reproducibility, and long history of correlation with mechanical properties make it an indispensable tool in the engineer's kit.
Relationship Between BHN and Tensile Strength
One of the most practically useful properties of the Brinell Hardness Number is its well-established correlation with ultimate tensile strength (UTS). For many common engineering materials, you can estimate tensile strength directly from a hardness measurement without performing a destructive tensile test. This makes the Brinell test a powerful quality control tool on the factory floor, where tensile testing requires expensive equipment and destroys the test specimen.
For carbon and low-alloy steels, the approximate relationship is:
[\text{UTS (MPa)} \approx 3.45 \times \text{BHN}]
Or in imperial units:
[\text{UTS (psi)} \approx 500 \times \text{BHN}]
Using the earlier example where we calculated a BHN of 228.70:
[\text{UTS} \approx 500 \times 228.70 = 114{,}350 \text{ psi}]
[\text{UTS} \approx 3.45 \times 228.70 = 789 \text{ MPa}]
This correlation holds reasonably well for BHN values between 120 and 450 in carbon steels. Outside this range, or for materials like stainless steel, cast iron, and non-ferrous alloys, the relationship changes and material-specific conversion factors should be used.
| Material Group | Approximate UTS Factor |
|---|---|
| Carbon and low-alloy steel | 500 psi/BHN or 3.45 MPa/BHN |
| Austenitic stainless steel | 490 psi/BHN or 3.38 MPa/BHN |
| Grey cast iron | 450 psi/BHN or 3.10 MPa/BHN |
| Aluminium alloys | 500 psi/BHN or 3.45 MPa/BHN |
| Copper alloys | 475 psi/BHN or 3.27 MPa/BHN |
These conversion factors are empirical approximations derived from large datasets of paired hardness and tensile measurements. They are published in standards such as ASTM A370 and SAE J417. While they are not substitutes for formal tensile testing in critical applications -- pressure vessels, aerospace components, or load-bearing structural members still require direct tensile data -- they provide valuable screening information for incoming material inspection, process control, and quick field assessments.
The practical implication is significant: a single Brinell test takes minutes to perform on a portable hardness tester and gives you both a hardness value and a tensile strength estimate. For a foundry receiving incoming bar stock, this means every heat of steel can be verified against the material certificate before it enters production, catching out-of-specification material before it becomes a costly defective part.