Vickers hardness test

It was decided that the indenter shape should be capable of producing geometrically similar impressions, irrespective of size; the impression should have well-defined points of measurement; and the indenter should have high resistance to self-deformation. A diamond in the form of a square-based pyramid satisfied these conditions. It had been established that the ideal size of a Brinell impression was 3⁄8 of the ball diameter. As two tangents to the circle at the ends of a chord 3d/8 long intersect at 136°, it was decided to use this as the included angle between plane faces of the indenter tip. This gives an angle from each face normal to the horizontal plane normal of 22° on each side. The angle was varied experimentally and it was found that the hardness value obtained on a homogeneous piece of material remained constant, irrespective of load.^[2] Accordingly, loads of various magnitudes are applied to a flat surface, depending on the hardness of the material to be measured. The HV number is then determined by the ratio F/A, where F is the force applied to the diamond in kilograms-force and A is the surface area of the resulting indentation in square millimeters.^{[citation needed]}

${\displaystyle A={\frac {d^{2}}{2\sin(136^{\circ }/2)}},}$

which can be approximated by evaluating the sine term to give,

${\displaystyle A\approx {\frac {d^{2}}{1.8544}},}$

where d is the average length of the diagonal left by the indenter in millimeters. Hence,^[3]

${\displaystyle \mathrm {HV} ={\frac {F}{A}}\approx {\frac {1.8544F}{d^{2}}}\quad [{\textrm {kgf/mm}}^{2}]}$,

where F is in kgf and d is in millimeters.

The corresponding unit of HV is then the kilogram-force per square millimeter (kgf/mm²) or HV number. In the above equation, F could be in N and d in mm, giving HV in the SI unit of MPa. To calculate Vickers hardness number (VHN) in kilogram-force using SI units for the input parameters, one needs to convert the force applied from N to kilogram-force by dividing by 9.806 65 (standard gravity). This leads to the following equation:^[4]

${\displaystyle \mathrm {HV} \approx {0.1891}{\frac {F}{d^{2}}}\quad [{\textrm {kgf/mm}}^{2}],}$

where F is in Newtons and d is in millimeters.

Vickers hardness numbers are reported as xxxHVyy, e.g. 440HV30, or xxxHVyy/zz if duration of force differs from 10 s to 15 s, e.g. 440HV30/20, where:

• 440 is the hardness number,
• HV names the hardness scale (Vickers),
• 30 indicates the load used in kgf.
• 20 indicates the loading time if it differs from 10 s to 15 s

When doing the hardness tests, the minimum distance between indentations and the distance from the indentation to the edge of the specimen must be taken into account to avoid interaction between the work-hardened regions and effects of the edge. These minimum distances are different for ISO 6507-1 and ASTM E384 standards.

Vickers values are generally independent of the test force: they will come out the same for 500 gf and 50 kgf, as long as the force is at least 200 gf.^[6] However, lower load indents often display a dependence of hardness on indent depth known as the indentation size effect (ISE).^[7] Small indent sizes will also have microstructure-dependent hardness values.

For thin samples indentation depth can be an issue due to substrate effects. As a rule of thumb the sample thickness should be kept greater than 2.5 times the indent diameter. Alternatively indent depth, ${\displaystyle t}$, can be calculated according to:

${\displaystyle t={\frac {d_{\rm {avg}}}{2{\sqrt {2}}\tan {\frac {\theta }{2}}}}\approx {\frac {d_{\rm {avg}}}{7.0006}},}$

To convert the Vickers hardness number to SI units the hardness number in kilograms-force per square millimeter (kgf/mm²) has to be multiplied with the standard gravity, ${\displaystyle g_{0}}$, to get the hardness in MPa (N/mm²) and furthermore divided by 1000 to get the hardness in GPa.

${\displaystyle {\text{surface area hardness (GPa)}}={\frac {g_{0}}{1000}}HV={\frac {9.80665}{1000}}HV}$

Vickers hardness can also be converted to an SI hardness based on the projected area of the indent rather than the surface area. The projected area, ${\displaystyle A_{\rm {p}}}$, is defined as the following for a Vickers indenter geometry:^[8]

${\displaystyle A_{\rm {p}}={\frac {d_{\rm {avg}}^{2}}{2}}={\frac {1.854}{2}}{A_{s}}}$

This hardness is sometimes referred to as the mean contact area or Meyer hardness, and ideally can be directly compared with other hardness tests also defined using projected area. Care must be used when comparing other hardness tests due to various size scale factors which can impact the measured hardness.

${\displaystyle {\text{projected area hardness (GPa)}}={\frac {g_{0}}{1000}}{\frac {2}{1.854}}HV\approx {\frac {HV}{94.5}}}$

If HV is first expressed in N/mm² (MPa), or otherwise by converting from kgf/mm², then the tensile strength (in MPa) of the material can be approximated as σ_u ≈ HV/c , where c is a constant determined by yield strength, Poisson's ratio, work-hardening exponent and geometrical factors – usually ranging between 2 and 4.^[9] In other words, if HV is expressed in N/mm² (i.e. in MPa) then the tensile strength (in MPa) ≈ HV/3. This empirical law depends variably on the work-hardening behavior of the material.^[10]