## Vickers Hardness Calculator

Hardness is a measure of the resistance of a material to plastic deformation induced by applied forces. Some materials (e.g. metals, ceramics) are harder than others (e.g. plastics, wood). Hardness is an important parameter correlating with wear resistance of the material. In applications where the wear has to be restricted, high hardness materials are typically used. See the description of the Vickers hardness test below.

## Vickers hardness test

The Vickers Hardness test (ISO 6507) is used to characterize hardness of various solid materials (metals, ceramics, etc.). A diamond pyramid is pressed against the solid with a certain normal load and the hardness is calculated based on the imprint left on the surface. Hardness may vary as a function of load, therefore, it is advised to specify applied when HV hardness is reported. A square-based pyramid indenter whose opposite sides meet at the apex at an angle of 136° is employed in Vickers hardness test. Imprint size is measured with the aid of optical microscope, see the figure below.

In contrast with Rockwell and Brinnell hardness techniques, the pyramid indenter is advantageous since the square imprints are easier to measure than the round impressions from spherical and conical indenters. Another advantage of the Vickers hardness test is absence of different scales, as compared to Rockwell and Brinnell tests. At low values (VH<~400HV), Vickers hardness was shown to be the same as Brinell hardness (see hardness conversion section).

Schematic representation of the Vickers test is shown in Figure 1. Further information regarding existing standards and procedures can be found in references [1,2].

## Vickers hardness formula

The Vickers hardness (HV) is calculated using the following Vickers hardness formula:

.

where d is the average of the two diagonals of the imprint and F is the applied load. Hardness in GPa is calculated as follows:

.

The yield stress can be approximated from the hardness (given in HV) as follows:

.

A video of a hardness test procedure is shown below:

## Hardness conversion

Different hardness scales are used for specific reasons. For non-homogeneous materials like cast iron, Brinell hardness may be used. For hard materials like steel, Rockwell hardness can be used. Comparison of the hardness values obtained using different hardness scales is shown in the graph below (source):

Exact conversion of the hardness values obtained using various hardness scales in general is not possible. However, by comparison of the hardness values at different scales, one can convert one hardness measure to another. For example, from the graph above one can convert Vickers hardness to any other hardness scale. A table with the hardness values is given below:

Brinell HBVickers HVRockwell C HRCRockwell B HRBLeeb HLD [1]
(10 mm Ball, 3000 kg load)(1 kg)(120 degree cone 150 kg)(1/16" ball 100 kg)
800-72-856
780122071-850
760121070-843
745111468-837
725106067-829
712102166-824
68294065-812
66890564-806
65286763-799
62680362-787
61477561-782
60174660-776
59072759-770
57669457-763
55264956-751
54563955-748
52960654-739
51458753120731
50256552119724
49555151119719
47753449118709
46150248117699
45148947117693
44447446116688
42746045115677
41543544115669
40142343114660
38840142114650
37539041113640
37038540112635
36238039111630
35136138111622
34635237110617
34134437110613
33133536109605
32332035109599
31131234108588
30130533107579
29329132106572
28528531105565
27627830105557
26927229104550
26126128103542
25825827102539
24925025101530
24524624100526
2402402399521
2372352399518
2292262298510
2242212197505
2172172096497
2112131995491
2062091894485
2032011794482
2001991693478
1961971592474
1911901492468
1871861391463
1851841291461
1831831190459
1801771089455
175174988449
170171787443
167168687439
165165586437
163162485434
160159384430
156154283425
154152182423
152150-82420
150149-81417
147147-80413
145146-79411
143144-79408
141142-78405
140141-77404
135135-75397
130130-72390
114120-67365
105110-62350
95100-56331
9095-52321
8185-41300
7680-37287

## References

[1] https://en.wikipedia.org/wiki/Vickers_hardness_test

[2] http://www.struers.com/en-GB/Knowledge/Hardness-testing/Vickers#

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