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Hardness is the mechanical resistance that a material opposes the mechanical penetration of another body. Depending on the type of action, a distinction is made between different types of hardness. Hardness is not only the resistance to harder bodies, but also to softer and equally hard bodies. The definition of hardness differs from that of strength , which is the resistance of a material to deformation and separation.

Hardness is also a measure of the wear behavior of materials. Hard glasses scratch less, hardened gears wear less. When choosing tool cutting edges such as milling heads or turning tools , the hardness is of particular importance; hard cutting edges stay sharp longer, but break faster.

Hardness and its testing are important focal points in the areas of solid state physics , materials science and the analysis of materials as well as in geosciences for the characterization of rocks and minerals . Hardness, along with its fracture toughness , strength , ductility , stiffness , density and melting temperature, is one of the material properties .

Hardness test on a roller around 1900

Hardness and strength

The hardness of a material only has something to do with the strength of the material to a limited extent , even if the strength influences the test methods for hardness measurement, which are based on the penetration depth of various test specimens . The influence of strength can be reduced by measuring on thin films , but it cannot be completely avoided.

In certain cases, however, the hardness of a material has a convertible relationship to the material strength. The relatively inexpensive hardness test can then replace a tensile test, which is usually much more complex . The possibility of converting the Brinell or Vickers hardness to the tensile strength of structural steels is of practical importance. In this way, for example, material mix-ups can be detected when inspecting steel structures.

Most materials of great hardness are also very brittle , so they can hardly be plastically deformed and suddenly break. The technique of cutting glass is based on this, among other things .

For the construction of components, hardness and toughness must be sensibly balanced: A hard, brittle component breaks easily if a peak load occurs. Tough (i.e. less hard) material would survive this without damage or with only minor consequences. However, the latter would wear out quickly. It is therefore often sought to provide a large inner area (core) made of tough, solid material with a very hard surface layer. This has two advantages: the resistance to wear increases and cracks can form much more poorly. The actual loads are absorbed inside.

Hardness test and hardness scales

In materials science, especially in the case of metals, test methods are mainly used that measure the indentation hardness. Standardized test specimens are pressed into the workpiece under specified conditions. The surface or depth of the permanent impression is then measured. In principle, a distinction is made between static and dynamic hardness testing methods. The dynamic test methods suddenly apply the load on the part to be tested; with the static methods the load is constant or gradually increasing.

Martens (universal hardness)

The name universal hardness is misleading about its real use in everyday industrial life. There, and also in the laboratory, this procedure is used extremely rarely.

The Martens hardness test method was named after the German physicist Adolf Martens (1850–1914) and is also known as an instrumented penetration test. In 2003, the universal hardness was renamed Martens hardness. The procedure is standardized in DIN EN ISO 14577 (Metallic materials - Instrumented penetrant test to determine hardness and other material parameters).

With this method, the force and the penetration depth are measured continuously during the loading and unloading phase . Martens hardness (HM) is defined as the ratio of the maximum force to the associated contact area and is given in the unit Newton per square millimeter.

In contrast to the Vickers or Brinell method, not only the plastic behavior of the material is determined, but also other material parameters such as the penetration modulus (elastic penetration modulus - E IT ), penetration creep (C IT ) and plastic can be determined from the measurement curve obtained and elastic deformation work can be determined.

The most common indenters are: the Vickers pyramid (see Vickers method), a hard metal ball, a spherical diamond indenter and the Berkovich indenter. The Berkovich indenter has a point like a regular tetrahedron with a flank angle of 65 °. The outline of the impressions is typically roughly triangular.

The conversion of the penetration depth to the contact surface must be determined for each indenter shape. The contact area for Vickers and Berkovich bodies is calculated from the product of the square of the penetration depth and the constant 26.43.

Rockwell (HR)

Rockwell hardness principle (B scale, steel ball)

There are several hardness testing methods developed by the American engineer and company founder Stanley P. Rockwell in 1920, which are specialized for certain areas of application. The different methods are identified with the unit HR and a subsequent identifier; Examples of a Rockwell designation are HRA, HRB, HRC or HR15N, for hardness tests on sheet metal up to a thickness of 0.20 mm HR15T and beyond that HR30Tm.

The Rockwell hardness of a material results from the penetration depth of a test body when a certain pre- and test force is applied. Test specimens , forces, duration and unit calculation formulas are specified in the standard DIN EN ISO 6508-1 (formerly DIN EN 10109). The test body is preloaded into the surface of the workpiece to be tested with a specified test force. The depth of the penetration of the test body with preload serves as a reference plane. The indenter is then subjected to the main load for a period of at least two seconds and a maximum of six seconds. This is then removed again so that only the preload is effective. The difference in the penetration depths before and after the main load is applied is the measure of the Rockwell hardness of the material. The Rockwell units are calculated according to a (depending on the applied Normskale different) from the penetration depth formula. The penetration depth of the test body is determined with a dial gauge connected to the test probe.

In the procedure according to scale C (unit HRC) a conical test piece made of diamond with a point angle of 120 ° and a rounded point with a radius of 0.2 mm is used. This test method is mainly used for very hard materials. According to scale B, steel balls with a diameter of 1.5875 mm (HRB, HRF, HRG) or 3.175 mm (HRE, HRH and HRK) are used as further rock wave penetrators.

Test procedure:

  1. Give up pre-force - with HRA, HRB, HRC etc .: 10 kp (≈98 N); for HRN and HRT: 3 kp (≈29.4 N)
  2. Zero the dial gauge
  3. Give up main force in addition, z. B. HRB = 90 kp (≈882.6 N), HRC = 140 kp (≈1372.9 N)
  4. The duration of action depends on the creep
    behavior of the substance: 2–3 s: for metals without time-dependent plastic behavior
    3–6 s: for metals with time-dependent plastic behavior
  5. Pick up main force
  6. Read the hardness value on the dial gauge
  7. Cancel pre-force

The Rockwell test is very fast, but places high demands on the clamping of the test object in the test device. It is unsuitable for test items that yield elastically in the test device, for example pipes .

Examples of Rockwell hardnesses:

Measuring range: HRC hardness values ​​permitted for the procedure must be between 20 and 70.


Brinell hardness test

The hardness test method developed by the Swedish engineer Johan August Brinell in 1900 and presented at the World Exhibition in Paris is used for soft to medium-hard metals ( EN ISO 6506-1 to EN ISO 6506-4) such as unalloyed structural steel, aluminum alloys and wood (ISO 3350) and for materials with an uneven structure such as cast iron. A hard metal ball is pressed into the surface of the workpiece to be tested with a specified test force F.

In the past, steel balls (specification HBS or HB) were used as indenters in addition to hard metal balls. Since 2006, the standard has stipulated balls made of cemented carbide for all materials , for example tungsten carbite (HBW specification). The balls used have diameters of 10 mm, 5 mm, 2.5 mm and 1 mm.

The thickness of the specimen is chosen so that no deformation is visible on the underside after the test. This is given from a thickness of 8-10 times the indentation depth h. The test load is chosen so that 0.24 D <d <0.6 D applies. The distance between the center of the impression and the edge of the sample should be greater than 3d, the distance between two impressions greater than 6d. The test force is applied at right angles to the test surface without impacts or vibrations and is increased within 5 to 8 seconds. After a period of constant loading of 10 to 15 seconds for steels and cast iron and 10 to 180 seconds for non-ferrous metals and their alloys, the diameter of the permanent indentation in the workpiece is measured and the surface of the indentation is determined from this.

The diameter d to be determined is the mean value of two diameters d 1 and d 2 of the permanent impression lying at right angles to one another . In the case of anisotropic deformation, the diameter required to calculate the hardness is averaged from the largest d 1 and the smallest diameter d 2 .

The Brinell hardness is defined as the ratio of the test force for impression surface. The test force in Newtons is multiplied by the value 0.102 (i.e. the reciprocal of 9.81) in order to convert the force unit Newton into the older unit, kilopond . This ensures that hardness measurements using modern units give the same result as historical values ​​based on units that are outdated today.

In the above formula, the force in N , the ball diameter and the mean indentation diameter in mm. The value in the denominator results from the formula for the surface of the round side of a spherical segment, a so-called spherical cap .

With unalloyed and low-alloy steels, the Brinell hardness can be used to derive the tensile strength ( ) of the material with a certain tolerance :


The usual range of application for Brinell hardnesses between 100 HBW and 400 HBW for unhardened steels.

Standard specification of the Brinell hardness

According to EN ISO 6506-1, the method used, the ball diameter and the test force must always be specified in addition to the hardness value.

Example: 345 HBW 10/3000

in which:

  • 345 = hardness value in kp / mm²
  • HBW = test method (W stands for the material of the test ball: tungsten carbide hard metal)
  • 10 = ball diameter D in mm
  • 3000 = test force in kp

If the load is longer than 15 s, the load time must also be specified. Example: 210 HBW 5/10/60

Hardness test with the Poldi hammer

Test device ( Poldihammer ) with comparison rod for measuring the ball impact hardness

A modification of the Brinell test is the test with the Poldi hammer, in which the impression of the ball is created by hand with an undefined hammer blow. Because of the sudden load, it is a dynamic hardness test method. The ball penetrates the back of a metal rod with a defined hardness. The hardness of the test piece can then be calculated from the ratio of the two indentation diameters. The method has the advantage that it can be used to test any stored test items and built-in components on site. Although the hardness values ​​determined in this way do not exactly match the statically determined hardness values, they are sufficient in most cases for the demands made in industry. The name "Poldi" comes from the steel works of the same name in Kladno , Czech Republic , where this test method was developed.

Vickers (HV)

Vickers hardness test
A non-standard impression (crooked) of a Vickers tester in etched case-hardening steel

The Brinell test is very similar to the hardness test developed by Smith and Sandland in 1925 and named after the British armaments company Vickers , which is used to test homogeneous materials and is also used to test the hardness of thin-walled or surface-hardened workpieces and edge zones. It is regulated in the standard according to DIN EN ISO 6507-1: 2018 to -4: 2018. In contrast to the Rockwell test, an equilateral diamond pyramid with an opening angle (measured between the side surfaces, not the edges of the pyramid) of 136 ° is pressed into the workpiece under a specified test force. The impression surface is calculated from the length of the diagonals of the permanent impression determined by means of a measuring microscope. The ratio of test force in the unit Newton to the indentation surface ( d in millimeters) multiplied by the factor 0.1891 results in the Vickers hardness (HV, VHN = Vickers Hardness Number ). When this hardness test was developed, it was still common practice to specify the test force in the unit kilopond, and the factor was 1.8544 (= 2 * sin 136 ° / 2).

is there

The number 0.102 is the conversion factor from Newtons to Kilopond.

The Vickers hardness test can be divided into three areas:

  1. Vickers hardness test: F ≥ 49.03 N
  2. Vickers small force hardness test: 1.961 N ≤ F <49.03 N
  3. Vickers micro hardness test: 0.0098 N ≤ F <1.961 N

Standard specification of Vickers hardness

In addition to the hardness value, the test method used, the holding time of the test force and the test force must always be specified.

Example: 610 HV 10

in which:

  • 610 = hardness value
  • HV = procedure
  • 10 = test force F in kilopond

If the load does not last between 10 and 15 s, the load time must also be specified. Example: 610 HV 10/30

The Vickers test is usually carried out on a fixed test device which cannot wobble or be disturbed. For tests on very large and / or solid components, there are also portable hardness testers that are magnetically or mechanically attached to or on the test piece.

The Vickers hardness test is versatile and is one of the quasi-non-destructive tests, as only minor damage to the component occurs, which can often be accepted. In the case of components that must not show any damage after the test, it is considered a destructive test method, as the component is damaged by the Vickers hardness test.

The Vickers hardness is used, for example, in the specification "45H" for set screws with hexagon socket or "14H" and "22H" for set screws with slot and in dental technology for dental alloys . The strength classes 14H, 22H, 33H and 45H are obtained by dividing the hardness values ​​by 10, i.e. they correspond to Vickers hardnesses HV (min.) Of 140, 220, 330 and 450.

Dental alloys

The hardness of dental metals is measured according to Vickers for precious metal alloys with the test force HV5 (5 kp corresponds to 49.03 N) and for non- precious metal alloys with HV10.

There are three hardness values ​​for dental alloys:

  • w = soft; Hardness of the alloy in the delivery condition or after soft annealing
  • a = hardened; Hardness of the alloy after targeted heat treatment = "tempering"
  • g / b = self-tempering: hardness of the alloy, which can be achieved by slow cooling after casting

When performing the test, make sure that the holding time of the test force is 10–15 s. The specimen must be firmly clamped and the test surface must be absolutely perpendicular to the test direction. Soiling etc. must be removed. The test was successful if the edges of the impression are even and the pyramid tip is pressed in in the middle. In practice, it is recommended to make several impressions, the max. and min. Disregard the value of these measurements and determine the mean of the remaining ones.


A modification of the Vickers hardness test is the Knoop hardness test (DIN EN ISO 4545-1 to -4: Metallic materials - Knoop hardness test), which was developed in 1939 by the American physicist and engineer Frederick Knoop (1878–1943). The diamond tip, which is equilateral in the Vickers test, has a rhombic shape in the Knoop test. The point angles are 172.5 ° for the long and 130 ° for the short side. Only the long diagonal of the impression is measured. The Knoop test is often used for brittle materials such as ceramics or sintered materials ; When measuring hardness on layer systems, it is the most precise measuring method.


Hand-held device for testing the hardness of elastomers: the needle for penetration at the bottom right
6 mm thick rubber plate in the measuring device, above it the penetrating needle of the Shore hardness tester

For elastomers

The Shore hardness, developed in 1915 by the American Albert Shore , is a material parameter for elastomers and plastics and is specified in the standards DIN EN ISO 868 , DIN ISO 7619-1 and ASTM D2240-00 .

The core of the Shore hardness tester (durometer) consists of a spring-loaded pin made of hardened steel. Its depth of penetration into the material to be tested is a measure of the Shore hardness, which is measured on a scale from 0 Shore (2.5 millimeter penetration depth) to 100 Shore (0 millimeter penetration depth). So a high number means great hardship. With a Shore hardness tester, an additional device can be used that presses the sample to be measured with a force of 12.5 Newtons for Shore-A, or 50 Newtons for Shore-D on the measuring table. When determining the Shore hardness, the temperature plays a greater role than when determining the hardness of metallic materials. Therefore, the target temperature of 23 ° C to the temperature range of ± 2 is here  K limited. The material thickness should be at least 6 millimeters. The hardness of the rubber is determined by the crosslinking (weakly crosslinked = soft rubber, strongly crosslinked = hard rubber). But the content of fillers is also decisive for the hardness of a rubber article.

  • Shore-A is indicated for soft elastomers after measurement with a needle with a blunt tip. The end face of the truncated cone has a diameter of 0.79 millimeters, the opening angle is 35 °. Application weight: 1 kg, holding time: 15 s. Hand-held measuring devices usually have to be read immediately when the sample is pressed; the displayed value decreases with longer holding times.
  • Shore-D is specified for tough elastomers after measurement with a needle that tapers at a 30 ° angle and has a spherical tip with a diameter of 0.2 millimeters. Application weight: 5 kg, holding time: 15 s

Measurements according to Shore-B and Shore-C can also be found, but they are only rarely used. These test methods combine the truncated cone of the Shore-A and Shore-D test methods with the other test force.

A metrological similar method is to determine the IRHD = "International Rubber Hardness Degree", the German also microhardness called.

For metals

This process is based on the principle that a ball falling on the workpiece (or a shaft with a ball point) will rebound more or less, depending on the hardness of the workpiece and the height of fall. It is rarely used because, although it is a very simple process, the precision depends both on the mass of the workpiece (small workpieces can easily slip) and on the perfect perpendicular of the fall axis. The hardness measurement is expressed in Shore points and is only standardized for large, ground cylinders.


The Barcol hardness is a hardness scale for glass fiber reinforced plastics (GRP). According to the DIN EN 59 standard, it is determined, like the Shore hardness, with the aid of a handheld measuring device and a truncated cone with a flat tip.


The Buchholz hardness is used for lacquers and can only be used for smooth, at least (10 µm + impression depth) thick, non-elastic lacquers. To determine the Buchholz hardness according to DIN 53 153, ISO 2815, the Buchholz hardness tester, which consists of a round, pointed wheel (= double truncated cone) and a weight, is placed on the horizontal surface for 30 seconds and then the indentation length with a 20 -fold magnifying microscope measured. The Buchholz hardness results from the following formula:

For better visibility of the length, the indentation point is illuminated with a lamp at an angle of 30 ° to the plane perpendicular to the indentation point, whereby the indentation point stands out very brightly from the rest of the paint.


The Leeb hardness test was first used in 1978 and measures the energy introduced via the rebound.


Memorial plaque for Friedrich Mohs in Vienna

This hardness value can only be determined by comparing several materials or material conditions.

Hard fabrics scratch soft ones. This insight is the basis of the hardness test according to Friedrich Mohs (1773–1839), which is mainly used in mineralogy . Mohs, a geologist, scratched various minerals against each other and arranged them according to their hardness. The exemplary assignment of numerical values ​​for widespread and thus easily accessible minerals resulted in an ordinal scale , the Mohs scale, which is still widely used in mineralogy and geology today. The hardness differences between the individual reference minerals are not linear. Information on the hardness of minerals always refer to the Mohs scale, unless otherwise stated. For comparison, the grinding hardness according to Rosiwal , also referred to as absolute hardness, is shown , which characterizes the grinding effort of the respective material and gives a better impression of the actual hardness conditions. Both hardness scales have no units. In addition, the hardness according to the Vickers method is given in the table. It gives the best reference to the hardness measurement methods commonly used today.

With regard to the usability and need for care of minerals as gemstones , a somewhat coarser classification is often given. Minerals with a Mohs hardness of 1 to 2 are considered soft, from 3 to 5 as medium-hard, and all minerals above the Mohs hardness of 6 are called hard.

Reference mineral hardness Remarks
Mohs Rosiwal
Talc mutnikSVK01.JPG Talk 01 000.000.03 00.002.4 with fingernail schabbar
Gypsum-40102.jpg Plaster of paris or
02 000.001.25 00.036 scratchable with fingernail
Calcite-sample2.jpg Calcite
03 000.004.5 00.109 scratchable with copper coin
Fluorite with Iron Pyrite.jpg Fluorite
04th 000.005.0 00.189 easily scratchable with a pocket knife
Apatite 2.jpg Apatite 05 000.006.5 00.536 still scratchable with pocket knife; the hardest human tissue, tooth enamel, has this degree of hardness, as does the well-known jewelry material rhinestone
Orthoclase-t07-43b.jpg Orthoclase
06th 000.037 00.795 scratchable with steel file
Quartz-137772.jpg quartz 07th 000.120 01,120 scratches window glass
Topaz cut.jpg topaz 08th 000.175 01,427  
Cut Ruby.jpg corundum 09 001,000 02,060 Types of corundum include ruby and sapphire .
Diamond-39513.jpg diamond 10 140,000 10,060 Hardest naturally occurring mineral next to silicon carbide ; scratchable only by itself and (under the influence of heat) by boron nitride . In the meantime, a few artificially produced, harder materials are known, including: ADNR .

Other special hardness testing methods

In addition, some special hardness testing methods are common:

  • The universal hardness test was renamed the Martens hardness test in 2003 and specified in the DIN EN ISO 14577 standard (Metallic materials - Instrumented penetrant test to determine hardness and other material parameters)
  • The ball indentation test in accordance with EN ISO 2039-1 for plastics uses balls with a diameter of 5.0 mm, a preload of 9.8 N and test loads of 49.0, 132, 358 or 961 N. The measured penetration depth must be in the range between 0.15 mm and 0.35 mm. From this, a reduced test force and finally the ball indentation hardness HB in N / mm² are calculated or read from a table.
  • The Hardgrove Index indicates the hardness of coal .
  • The Janka hardness test checks the hardness of wood.
  • To study nanomechanical properties of materials: nanoindentation


The Mohs hardness and the absolute hardness are units without units.

From a physical point of view, the correct unit for the Vickers and Brinell hardness test would be 1 N / m² or 1 N / mm². It must be noted, however, that these test methods were developed at the beginning of the 20th century and have since been standardized and internationalized in ever more detailed standards. For the physicist, this results in a somewhat abstract notation for hardness values ​​and units. The abbreviation of the test method and the test conditions are specified as the unit of hardness. Both Vickers and Knoop hardness can be converted into physical quantities by multiplying by a factor, whereby the true hardness H (true) is obtained in kp / mm². For the Vickers hardness this factor is 1.618, for the Knoop hardness it is 1.500.

Some examples of common hardness indications are given below:

  • Vickers hardness test:   610 HV 10   with
    • 610: hardness value
    • HV: procedure
    • 10: Test force in kilopond
  • Brinell hardness test:   345 HBW 10/3000   with
    • 345: hardness value
    • HBW: test procedure (information such as HB, HBS is out of date.)
    • 10: Ball diameter D in mm
    • 3000: test force in kilopond
    • In the case of a load that lasts longer than 15 s, the load time must also be specified: Example: 210 HBW 5/750/60
  • Rockwell hardness test:   58 HRC   with
    • 58: hardness value
    • HRC: test method


  • The force used to be measured in kilopond. A kilopond corresponds to the weight of one kilogram at the standard location. The conversion of the unit of force from Pond to the unit Newton resulted in a correction of the formulas for calculating the hardness values. This correction is already taken into account in the article. If the newton unit of force and the correction factor are used to determine the hardness value, the result is the same as when the kilopond unit of force is used. This has the advantage that old hardness values ​​determined at “kilopond times” are still valid.
  • For practical reasons, kilopond is still used when specifying the test method, since whole numbers can be used.


When dealing with the various hardness test methods, it is often necessary to convert the measured hardness value of one method into that of another method or the tensile strength. For this reason, empirical values ​​were determined on the basis of a large number of comparative measurements, conversion tables were created and standardized in the corresponding standard (EN ISO 18265 (formerly DIN 50150)).

Important: different tables apply for different materials and different heat treatment stages. The grades included are also listed in EN ISO 18265.

The following conversion tables can therefore only be viewed as a guide. The corresponding standard must be used for a standard-compliant conversion. However, if one goes to the limits of what is possible when designing components, the approximations and assumptions made in the standardization are often insufficient to ensure correct design and testing.

Hardening and machining

The hardness of steels can be influenced during production - see also hardening .

Above 65 HRC, the possibilities for machining with geometrically defined cutting edges of surfaces (turning, drilling, milling) usually end . Harder surfaces have to be ground (cutting with a geometrically undefined cutting edge). For some years now it has been possible to use surface-coated hard metal tools to machine hardened steels up to a hardness of 68 HRC. For this purpose, high-speed precision milling and turning machines are used, which can create the desired shapes with an accuracy of 5 µm. For this purpose, a different infeed technique is used: high speed, high feed, but very low cutting depth.

Hardness classes

Various guidelines and standards provide for hardness classes. Hardness classes are sometimes also referred to as (pressure) strength classes or confused with them.


  • DIN EN ISO 898 - "Mechanical properties of connecting elements made of carbon steel and alloy steel " defines in part 5 " Grub screws and similar connecting elements with threads in defined hardness classes - regular thread and fine thread"
  • DIN 267 - "Mechanical connecting elements" defines in part 24 "Technical delivery conditions - hardness classes for nuts without specified test forces"
  • DIN EN 13813 defines hardness classes IC 10, IC 15, IC 40 and IC 100 for mastic asphalt , depending on the penetration depth of the stamp (according to DIN EN 12697-20). The higher the number, the softer the screed. For cement screed , it defines surface hardness classes SH30 SH40 SH50 SH70 SH100 SH150 SH200 and specifies minimum nominal thicknesses for floating screeds depending on the hardness class (for vertical loads ≤ 2 kN / m²).

Web links

Wiktionary: hardness  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. Federal Institute for Material Testing: Micro hardness measurement ( Memento of the original from July 31, 2013 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. . @1@ 2Template: Webachiv / IABot / www.bam.de
  2. ^ Alfred Böge (Ed.): Vieweg manual mechanical engineering: Basics and applications of mechanical engineering . 18th edition. Vieweg & Sohn-Verlag, Wiesbaden 2007, ISBN 978-3-8348-9092-4 , p. E93 ( limited preview in Google Book Search).
  3. metallograf.de: Information about steel for metallographers - test forces in the hardness test according to Brinell
  4. Bremen University of Applied Sciences Internship hardness test
  5. ^ University of Regensburg
  6. Information such as HB or HBS is no longer permissible according to the current standard (see DIN EN ISO 6506-1: 2005 as at: 03/2006 Chapter 4.1 "Symbols and abbreviations")
  7. DIN German Institute for Standardization eV: Metallic materials - Vickers hardness test - Part 1: Test method ( Memento from March 19, 2013 in the Internet Archive ) (PDF; 56 kB)
  8. Railsback's: Some Fundamentals of Mineralogy and Geochemistry (English, PDF 20 kB)
  9. Frederick Knoop (1878–1943)
  10. Tire Lexicon - Shore hardness (English)
  11. Hardness test - introduction ( Memento of the original of July 31, 2013 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF 635.6 kB; p. 2).  @1@ 2Template: Webachiv / IABot / www.igz.ch
  12. Hardness tester for metallic materials (PDF 99 kB; p. 1)
  13. Diamanten-Kontor - The hardness of precious stones
  14. ^ A b Walter Schumann: Precious stones and gemstones. All species and varieties in the world. 1600 unique pieces . 13th revised and expanded edition. BLV Verlags-GmbH., Munich et al. 2002, ISBN 3-405-16332-3 , p. 20 .
  15. Rudolf Graubner: Lexicon of Geology, Minerals and Rocks . Emil Vollmer Verlag GmbH, Munich 1980, ISBN 3-87876-327-1 , p. 158 .
  16. ^ Ulrich Lehmann: Paleontological Dictionary . 4th edition. Enke Verlag , Stuttgart, 1996. Page 213
  17. Valid for unalloyed and low-alloy steels. Use the other tables of the EN ISO 18265 standard for heat-treatable steels, cold-work steels, high-speed steels and various types of carbide. High deviations are to be expected, especially with high-alloy or work-hardened steels.
  18. The diameter specification for the Brinell hardness refers to a 10 mm test ball.
  19. Modern cutting materials - area of ​​application for materials of different hardness ( Memento of January 19, 2012 in the Internet Archive ), (PDF 328.6 kB; p. 4).