Vickers hardness test

Last updated November 19, 2023

The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure the hardness of materials.^[1] The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the indenter, and the indenter can be used for all materials irrespective of hardness. The basic principle, as with all common measures of hardness, is to observe a material's ability to resist plastic deformation from a standard source. The Vickers test can be used for all metals and has one of the widest scales among hardness tests. The unit of hardness given by the test is known as the Vickers Pyramid Number (HV) or Diamond Pyramid Hardness (DPH). The hardness number can be converted into units of pascals, but should not be confused with pressure, which uses the same units. The hardness number is determined by the load over the surface area of the indentation and not the area normal to the force, and is therefore not pressure.

Implementation

Vickers test scheme Vickers-path-2.svg — Vickers test scheme

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.

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

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

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

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

\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) using SI units one needs to convert the force applied from newtons to kilogram-force by dividing by 9.806 65 (standard gravity). This leads to the following equation:^[4]

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

where F is in N and d is in millimeters. A common error is that the above formula to calculate the HV number does not result in a number with the unit newton per square millimeter (N/mm²), but results directly in the Vickers hardness number (usually given without units), which is in fact one kilogram-force per square millimeter (1 kgf/mm²).

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

Examples of HV values for various materials^[5]
Material	Value
316L stainless steel	140HV30
347L stainless steel	180HV30
Carbon steel	55–120HV5
Iron	30–80HV5
Martensite	1000HV
Diamond	10000HV

Precautions

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.

Standard	Distance between indentations	Distance from the center of the indentation to the edge of the specimen
ISO 6507-1	> 3·d for steel and copper alloys and > 6·d for light metals	2.5·d for steel and copper alloys and > 3·d for light metals
ASTM E384	2.5·d	2.5·d

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, $t$ , can be calculated according to:

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

Conversion to SI units

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, $g_{0}$ , to get the hardness in MPa (N/mm²) and furthermore divided by 1000 to get the hardness in GPa.

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

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, $A_{\rm {p}}$ , is defined as the following for a Vickers indenter geometry:^[8]

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

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.

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

Estimating tensile strength

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]

Application

The fin attachment pins and sleeves in the Convair 580 airliner were specified by the aircraft manufacturer to be hardened to a Vickers Hardness specification of 390HV5, the '5' meaning five kiloponds. However, on the aircraft flying Partnair Flight 394 the pins were later found to have been replaced with sub-standard parts, leading to rapid wear and finally loss of the aircraft. On examination, accident investigators found that the sub-standard pins had a hardness value of only some 200–230HV5.^[11]

Related Research Articles

The Rockwell scale is a hardness scale based on indentation hardness of a material. The Rockwell test measures the depth of penetration of an indenter under a large load compared to the penetration made by a preload. There are different scales, denoted by a single letter, that use different loads or indenters. The result is a dimensionless number noted as HRA, HRB, HRC, etc., where the last letter is the respective Rockwell scale. Larger numbers correspond to harder materials.

The kilogram-force, or kilopond, is a non-standard gravitational metric unit of force. It does not comply with the International System of Units (SI) and is deprecated for most uses. The kilogram-force is equal to the magnitude of the force exerted on one kilogram of mass in a 9.80665 m/s² gravitational field. That is, it is the weight of a kilogram under standard gravity. Therefore, one kilogram-force is by definition equal to 9.80665 N. Similarly, a gram-force is 9.80665 mN, and a milligram-force is 9.80665 μN.

<span class="mw-page-title-main">Brinell scale</span> Brinell scale of hardness

The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece. It is one of several definitions of hardness in materials science.

Indentation hardness tests are used in mechanical engineering to determine the hardness of a material to deformation. Several such tests exist, wherein the examined material is indented until an impression is formed; these tests can be performed on a macroscopic or microscopic scale.

The Knoop hardness test is a microhardness test – a test for mechanical hardness used particularly for very brittle materials or thin sheets, where only a small indentation may be made for testing purposes. A pyramidal diamond point is pressed into the polished surface of the test material with a known load, for a specified dwell time, and the resulting indentation is measured using a microscope. The geometry of this indenter is an extended pyramid with the length to width ratio being 7:1 and respective face angles are 172 degrees for the long edge and 130 degrees for the short edge. The depth of the indentation can be approximated as 1/30 of the long dimension. The Knoop hardness HK or KHN is then given by the formula:

In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

In materials science, hardness is a measure of the resistance to localized plastic deformation, such as an indentation or a scratch (linear), induced mechanically either by pressing or abrasion. In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin, or wood and common plastics. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, hardness can be measured in different ways, such as scratch hardness, indentation hardness, and rebound hardness. Hardness is dependent on ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity. Common examples of hard matter are ceramics, concrete, certain metals, and superhard materials, which can be contrasted with soft matter.

Nanoindentation, also called instrumented indentation testing, is a variety of indentation hardness tests applied to small volumes. Indentation is perhaps the most commonly applied means of testing the mechanical properties of materials. The nanoindentation technique was developed in the mid-1970s to measure the hardness of small volumes of material.

<span class="mw-page-title-main">Three-point flexural test</span> Standard procedure for measuring modulus of elasticity in bending

The three-point bending flexural test provides values for the modulus of elasticity in bending $, flexural stress, flexural strain and the flexural stress-strain response of the material. This test is performed on a universal testing machine with a three-point or four-point bend fixture. The main advantage of a three-point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.$

The Shore durometer is a device for measuring the hardness of a material, typically of polymers.

A variety of hardness-testing methods are available, including the Vickers, Brinell, Rockwell, Meyer and Leeb tests. Although it is impossible in many cases to give an exact conversion, it is possible to give an approximate material-specific comparison table for steels.

Ceramography is the art and science of preparation, examination and evaluation of ceramic microstructures. Ceramography can be thought of as the metallography of ceramics. The microstructure is the structure level of approximately 0.1 to 100 µm, between the minimum wavelength of visible light and the resolution limit of the naked eye. The microstructure includes most grains, secondary phases, grain boundaries, pores, micro-cracks and hardness microindentations. Most bulk mechanical, optical, thermal, electrical and magnetic properties are significantly affected by the microstructure. The fabrication method and process conditions are generally indicated by the microstructure. The root cause of many ceramic failures is evident in the microstructure. Ceramography is part of the broader field of materialography, which includes all the microscopic techniques of material analysis, such as metallography, petrography and plastography. Ceramography is usually reserved for high-performance ceramics for industrial applications, such as 85–99.9% alumina (Al₂O₃) in Fig. 1, zirconia (ZrO₂), silicon carbide (SiC), silicon nitride (Si₃N₄), and ceramic-matrix composites. It is seldom used on whiteware ceramics such as sanitaryware, wall tiles and dishware.

The Barcol hardness test characterizes the indentation hardness of materials through the depth of penetration of an indentor, loaded on a material sample and compared to the penetration in a reference material. The method is most often used for composite materials such as reinforced thermosetting resins or to determine how much a resin or plastic has cured. The test complements the measurement of glass transition temperature, as an indirect measure of the degree of cure of a composite. It is inexpensive and quick, and provides information on the cure throughout a part.

The Meyer hardness test is a hardness test based upon projected area of an impression. The hardness, $, is defined as the maximum load, divided by the projected area of the indent, .$

Meyer's law is an empirical relation between the size of a hardness test indentation and the load required to leave the indentation. The formula was devised by Eugene Meyer of the Materials Testing Laboratory at the Imperial School of Technology, Charlottenburg, Germany, circa 1908.

The Leeb Rebound Hardness Test (LRHT) invented by Swiss company Proceq SA is one of the four most used methods for testing metal hardness. This portable method is mainly used for testing sufficiently large workpieces.

Abrasion is the process of scuffing, scratching, wearing down, marring, or rubbing away. It can be intentionally imposed in a controlled process using an abrasive. Abrasion can be an undesirable effect of exposure to normal use or exposure to the elements.

The wear coefficient is a physical coefficient used to measure, characterize and correlate the wear of materials.

<span class="mw-page-title-main">Palmqvist method</span>

The Palmqvist method, or the Palmqvist toughness test, is a common method to determine the fracture toughness for cemented carbides. In this case, the material's fracture toughness is given by the critical stress intensity factor K_Ic.

Abrasion resistant steel is a high-carbon alloy steel that is produced to resist wear and stress. There are several grades of abrasion resistant steel, including AR200, AR235, AR400, AR450, AR500 and AR600.

References

↑ R.L. Smith & G.E. Sandland, "An Accurate Method of Determining the Hardness of Metals, with Particular Reference to Those of a High Degree of Hardness," Proceedings of the Institution of Mechanical Engineers , Vol. I, 1922, p 623–641.
↑ The Vickers Hardness Testing Machine. UKcalibrations.co.uk. Retrieved on 2016-06-03.
↑ ASTM E384-10e2
↑ ISO 6507-1:2005(E)
↑ Smithells Metals Reference Book, 8th Edition, ch. 22
↑ Vickers Test Archived 21 October 2014 at the Wayback Machine . Instron website.
↑ Nix, William D.; Gao, Huajian (1 March 1998). "Indentation size effects in crystalline materials: A law for strain gradient plasticity". Journal of the Mechanics and Physics of Solids. 46 (3): 411–425. Bibcode:1998JMPSo..46..411N. doi: 10.1016/S0022-5096(97)00086-0 . ISSN 0022-5096.
↑ Fischer-Cripps, Anthony C. (2007). Introduction to contact mechanics (2nd ed.). New York: Springer. pp. 212–213. ISBN 9780387681887. OCLC 187014877.
↑ "Hardness". matter.org.uk.
↑ Zhang, P. (September 2011). "General relationship between strength and hardness". Materials Science and Engineering A. 529: 62. doi:10.1016/j.msea.2011.08.061.
↑ Report on the Convair 340/580 LN-PAA aircraft accident North of Hirtshals, Denmark on September 8, 1989 | aibn. Aibn.no. Retrieved on 2016-06-03.

External links

Video on the Vickers hardness test
Vickers hardness test
Conversion table – Vickers, Brinell, and Rockwell scales

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[1] R.L. Smith & G.E. Sandland, "An Accurate Method of Determining the Hardness of Metals, with Particular Reference to Those of a High Degree of Hardness," Proceedings of the Institution of Mechanical Engineers , Vol. I, 1922, p 623–641.

[2] The Vickers Hardness Testing Machine. UKcalibrations.co.uk. Retrieved on 2016-06-03.

[3] ASTM E384-10e2

[4] ISO 6507-1:2005(E)

[5] Smithells Metals Reference Book, 8th Edition, ch. 22

[6] Vickers Test Archived 21 October 2014 at the Wayback Machine . Instron website.

[7] Nix, William D.; Gao, Huajian (1 March 1998). "Indentation size effects in crystalline materials: A law for strain gradient plasticity". Journal of the Mechanics and Physics of Solids. 46 (3): 411–425. Bibcode:1998JMPSo..46..411N. doi: 10.1016/S0022-5096(97)00086-0 . ISSN 0022-5096.

[8] Fischer-Cripps, Anthony C. (2007). Introduction to contact mechanics (2nd ed.). New York: Springer. pp. 212–213. ISBN 9780387681887. OCLC 187014877.

[9] "Hardness". matter.org.uk.

[Journal_Article-10] Zhang, P. (September 2011). "General relationship between strength and hardness". Materials Science and Engineering A. 529: 62. doi:10.1016/j.msea.2011.08.061.

[11] Report on the Convair 340/580 LN-PAA aircraft accident North of Hirtshals, Denmark on September 8, 1989 | aibn. Aibn.no. Retrieved on 2016-06-03.

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