Vickers Hardness Number Calculator

This Vickers hardness number calculator uses the size of indentation to return the hardness of the material. There are different scales to measure hardness, including Brinell hardness, Rockwell hardness, Meyers hardness, and Vickers hardness test.

The Vickers hardness scale, named after the company where it was developed in 1921, is the focus of this article. This test is an alternative to Brinell hardness, and it is relatively easier to use because it does not depend on the cone diameter or size of the indenter. The article also briefly covers how to perform the Vickers hardness test.

Read on to understand how to calculate the Vickers hardness number once you have completed the indentation experiment.

Hardness tests measure the resistance of a material against plastic deformation. To perform these tests (be it Brinell, Rockwell, or Vickers), an indenter is pressed on the surface of the specimen with a specific force $F$ for a time interval of, say, 10-15 s. During this interval, the material undergoes plastic deformation, which you will measure after unloading the material specimen.

The indentation could be of different shapes depending on the type of test. For a Vickers hardness test, you'll use a diamond indenter with angle $136\degree$, and it would leave a square pyramid shaped indentation. The diagonals of the indentation are measured and averaged. Once you know the mean diagonal, you can use the Vickers hardness calculation number formula to find its value.

The Vickers hardness number, $HV$, is a function of normal force in kgf (kilogram-force), $F$, mean diagonal in mm, $d$, and, surface area of the indentation. Mathematically, Vickers hardness number in $\text{kgf/mm}^2$ is given by:

where:

• $g$ – Acceleration due to gravity, $g = 9.80665 \text{ m/s}^2$; and
• $\alpha$ – Angle of indenter, commonly taken as $\alpha = 136°$.

In order to convert the Vickers hardness number to $\text{MPa}$, you have to multiply the $HV$ value by the gravitational acceleration $g$. Such that, hardness $H$ in $\text{GPa}$ is:

The above parameter $H$ is also known as surface area hardness.

You can also estimate the tensile strength from the hardness number by dividing it with a constant $c$. Such that:

The constant $c$ depends on several factors; however, as a rule of thumb, $c$ is taken as $3$ for metallic crystalline materials.

Let's calculate the Vickers hardness number for a material specimen having an indentation with a mean diagonal of $0.5 \text{ mm}$ under a load of $50 \text{ N}$.

To calculate Vickers hardness number:

1. Enter the load value, $F = 50 \text{ N}$.
2. Fill in the value of mean diagonal as, $d = 0.5 \text{ mm}$.
3. Using the Vickers hardness calculation formula:

4. The calculator also returns the surface area hardness, and tensile strength as $370.9 \text{ MPa}$, and $126.06 \text{ MPa}$, respectively.

To calculate Vickers hardness number:

1. Divide the angle of indenter by 2.
2. Multiply force by the sine of the resultant.
3. Divide the product by gravitational acceleration.
4. Divide the quotient by square of the mean diagonal.
5. Multiply the result by 2 to obtain the Vickers hardness number.

The following equation gives the Vickers hardness formula: HV = 2 × F × sin(α/2) / (g × d²) for a given loading force F and indenter with angle, α, leaving an indentation with a mean diagonal, d, on the material specimen.

The Vickers hardness number for iron is 30-80HV5. This implies that if the test is conducted under a load value of 5 kgf, the Vickers hardness number would be 30 to 80 kgf/mm². This value is just an estimate, and the actual value depends on the composition of the iron specimen.

The Vickers hardness number for carbon steel is 55-120HV5. If the test is conducted under a load value of 5 kgf, the Vickers hardness number would be in the range of 55 to 120 kgf/mm². As an estimate, the value may vary depending on the composition of carbon steel.