The Vickers and Knoop Hardness Test Theory

INTRODUCTION

Vickers and Knoop hardness testing at a glance

When the objective is not only to understand the method but also to select a suitable instrument, users can compare ATI Vickers and Knoop hardness testers designed for microhardness testing, case depth measurement, coating evaluation and laboratory quality control.

Scope of the Vickers and Knoop hardness tests

The Vickers hardness test and the Knoop hardness test are optical indentation methods used to evaluate the hardness of metals, coatings, thin layers, welds, heat-treated components and small metallographic areas. They are widely used in quality control, material evaluation, research and development, failure analysis and laboratory testing whenever the indentation must be measured optically rather than read directly from penetration depth.

Although hardness is an empirical property, Vickers and Knoop results provide valuable information about material condition, heat treatment quality, wear resistance, local microstructural variations and, in many metallic materials, an approximate relationship with tensile strength. Their main advantage is that they can be applied over a very wide range of test forces, from microindentation testing on very small areas to macro Vickers testing on larger components.

Principle of Vickers and Knoop hardness testing

Both methods are based on the same general principle: a diamond indenter is pressed into the surface of the test specimen under a specified force, the force is held for a defined dwell time, and the residual indentation is measured after unloading. The hardness value is then calculated from the applied test force and the size of the indentation.

In the Vickers hardness test, the indenter is a square-based diamond pyramid. After the test force is removed, the two diagonals of the indentation are measured and their average value is used to calculate the Vickers hardness number, expressed as HV.

In the Knoop hardness test, the indenter is an elongated rhombic-based diamond pyramid. After the test force is removed, only the long diagonal of the indentation is measured and used to calculate the Knoop hardness number, expressed as HK. Because the Knoop indentation is longer and shallower than a comparable Vickers indentation, this method is particularly useful for thin layers, coatings, brittle materials and applications where penetration depth must be minimized.

How Vickers and Knoop hardness values are reported

Vickers and Knoop hardness values should not be reported as a number alone. The result must include the hardness symbol and the test force used, because the selected force can influence the indentation size and the practical interpretation of the result.

A Vickers result is reported with the symbol HV, while a Knoop result is reported with the symbol HK. The number following the symbol indicates the test force expressed in kilogram-force.

Examples:

• 450 HV 10 means a Vickers hardness value of 450 obtained with a test force of 10 kgf.
• 700 HV 0.1 means a Vickers hardness value of 700 obtained with a test force of 0.1 kgf, equal to 100 gf.
• 500 HK 0.5 means a Knoop hardness value of 500 obtained with a test force of 0.5 kgf, equal to 500 gf.

Microindentation hardness testing

Microindentation hardness testing extends Vickers and Knoop methods to specimens, layers or material zones that are too small or too thin for conventional macro hardness tests. It allows the evaluation of individual microstructural constituents, surface treatments, case depth profiles, weld zones, coatings and hardness gradients across a polished cross-section.

Micro Vickers and Knoop testing are especially useful when the area of interest is limited, when the indentation must remain very small, or when hardness must be measured at defined positions under microscopic observation. For this reason, these methods are commonly used in metallographic laboratories, heat treatment control, coating inspection and research applications.

Sample preparation for Vickers and Knoop hardness testing

Sample preparation is one of the most important factors in Vickers and Knoop hardness testing. Since both methods require optical measurement of the indentation, the test surface must allow the indentation edges and corners to be clearly identified by the measuring system.

The specimen should be flat, stable and properly supported. The test surface should be perpendicular to the axis of the indenter so that the force is applied normally to the surface. If the specimen is tilted, not properly mounted or insufficiently supported, the indentation may appear distorted, the diagonals may be difficult to measure and the final hardness value may be unreliable.

Surface preparation becomes more critical as the test force decreases. In micro Vickers and Knoop testing, very small indentations are measured, so scratches, polishing marks, oxide layers, etching, contamination or surface relief can strongly influence the result. For this reason, polished metallographic preparation is often required when testing thin layers, case depth profiles, weld zones or microstructural constituents.

For laboratories performing repeated microhardness measurements, sample preparation equipment, correct mounting, stable support and optical measurement quality are as important as the hardness tester itself. ATI supports complete Vickers and Knoop testing workflows, from hardness testing instruments to verification, maintenance and accredited calibration services.

Specimen preparation and support

To obtain reliable results, the test surface should be perpendicular to the axis of the indenter. If the specimen is tilted or not properly supported, the indentation may become distorted, the diagonals may appear unequal or out of focus, and the calculated hardness value may be affected.

Non-parallel or irregular specimens may require clamping, leveling fixtures or special supports to align the test surface correctly. In microindentation testing, specimens are often mounted to simplify preparation, protect edges and allow hardness traverses across surface layers, welds or heat-treated zones.

When mounting is required, the specimen must be adequately supported by the mounting medium. Excessively soft or creeping mounting compounds should be avoided, because specimen movement during force application can alter the indentation geometry and reduce measurement reliability.

Optical measurement of Vickers and Knoop indentations

In Vickers testing, both diagonals of the indentation are measured and the average diagonal length is used for the hardness calculation. In Knoop testing, the long diagonal is measured. The indentation should remain within the usable optical field of the selected objective, and the magnification should be suitable for the indentation size.

Correct focus and image quality are essential. The indentation corners must be clearly visible, sharply defined and free from surface defects that could affect the measurement. Small measurement errors can produce significant hardness errors because both Vickers and Knoop formulas depend on the square of the measured diagonal length.

As a practical rule, the smaller the indentation, the higher the required measurement accuracy. Very small indentations require careful objective selection, stable illumination, accurate focusing and, where possible, automatic image analysis to improve repeatability and reduce operator influence.

Distorted indentations can indicate problems with specimen alignment or support. In a Vickers indentation, if one half of a diagonal is significantly longer than the other half, or if the four corners are not in sharp focus, the test surface may not be perpendicular to the indenter axis. In a Knoop indentation, if the two halves of the long diagonal differ significantly or both ends are not sharply focused, the same alignment problem may be present.

Testing ambient temperature

Vickers and Knoop hardness tests are generally performed within controlled laboratory temperature conditions. Testing should normally be carried out within the temperature range specified by the applicable standard or internal procedure, commonly between 10°C and 35°C.

For high-accuracy work, reference testing, calibration activities or comparison between laboratories, it may be advisable to control the temperature within a narrower range. Stable environmental conditions help reduce measurement variability and improve the consistency of hardness results.

VICKERS AND KNOOP TEST FORCES AND HARDNESS SCALES

Vickers and Knoop hardness values must always be associated with the test force used during the measurement. The same material can produce different practical results when tested with different forces, especially in microindentation testing, thin layers, coatings or materials with hardness gradients.

The table below summarizes common Vickers and Knoop force designations. The availability of specific forces depends on the testing machine configuration, applicable standard, test method and laboratory procedure.

The selection of the test force depends on the material, expected hardness, layer thickness, indentation size and applicable standard. ATI Vickers and Knoop hardness testers cover micro, low-force and macro Vickers applications, with configurations suitable for laboratory testing, production control, CHD case depth profiles and coating evaluation.

VICKERS AND KNOOP REPEATABILITY, ERROR AND VERIFICATION

Reliable Vickers and Knoop hardness testing requires control of both the force application system and the optical measuring system. Since the hardness value is calculated from the measured indentation diagonal, errors in image quality, focus, diagonal reading, surface preparation or operator interpretation can directly affect the result.

Machine error E

The machine error E represents the difference between the hardness value measured by the machine and the certified reference value of a standardized hardness test block. It is normally evaluated at specific hardness levels and test forces during indirect verification.

In practical terms, error E indicates whether the hardness tester is reading too high or too low compared with the reference value. If the error exceeds the permitted tolerance, the machine, measuring system, indenter, test force application or calibration condition must be investigated before the results can be considered reliable.

Repeatability R

Repeatability R describes how consistently the hardness testing machine reproduces results under the same verification conditions. It is typically evaluated by making a series of indentations on a certified hardness test block and calculating the spread of the measured values.

Good repeatability means that the machine, indenter, optical system and test setup are producing stable results. Poor repeatability may indicate problems such as unstable force application, specimen movement, poor surface preparation, optical focusing errors, operator influence, dirty optics, damaged indenters or incorrect indentation measurement.

Verification using certified hardness test blocks

Vickers and Knoop hardness testing machines should be verified periodically using certified hardness reference blocks suitable for the test forces and hardness ranges normally used by the laboratory. Test blocks should be clean, properly supported and used according to the applicable standard or laboratory procedure.

For best practice, the selected reference block should be close to the expected hardness range and force level of the measurements normally performed. Using an unsuitable force, hardness range or damaged reference block may reduce the value of the verification.

In routine laboratory practice, verification is normally performed using certified Vickers and Knoop hardness test blocks with known reference values. Test blocks allow the user to check the complete testing system, including force application, indenter condition, optical measurement and software calculation.

For formal compliance, audits, maintenance programs or inter-laboratory comparison, ATI provides ISO/IEC 17025 accredited calibration services for hardness testers, measuring systems and related metrology equipment. Accredited calibration helps demonstrate traceability, verify machine performance and maintain confidence in HV and HK hardness results.

Maximum allowable repeatability and error of Vickers and Knoop hardness testing machines

The following tables summarize the maximum allowable repeatability and error limits for Vickers and Knoop hardness testing machines, according to the reference standards used for verification and calibration.

ASTM E92-23 – Table A1.4: Maximum allowable repeatability and error of testing machines

Note 1: In all cases, the repeatability is satisfactory if (d max − d min) is equal to 1 µm or less.
Note 2: In all cases, the error is satisfactory if E = 100 × |d avg − d ref| / d ref is equal to 0.5 µm or less.

ISO 6507-2:2018 – Table 4: Maximum repeatability of the Vickers testing machine

^a Or 0.001 mm, whichever is greater.
^b HV: Vickers hardness.

ISO 6507-2:2018 – Table 4: Maximum permissible percentage error E_rel of the Vickers testing machine

Note 1: Values are not given when the length of the indentation diagonal is less than 0.020 mm.
Note 2: For intermediate values, the maximum permissible error may be obtained by interpolation.
Note 3: The values for microhardness testing machines are based on a maximum permissible error of 0.001 mm or 2% of the mean diagonal length of indentation, whichever is greater.

Vickers and Knoop terminology and practical tips

Correct Vickers and Knoop hardness testing depends not only on the test force and the indenter, but also on the condition of the machine, the optical measuring system, the specimen support, the surface preparation and the verification procedure. The following terminology and practical notes summarize the main elements that influence the reliability of HV and HK hardness results.

Calibration

Calibration is the determination of the values of significant parameters by comparison with a reference instrument, certified reference material or recognized standard. In Vickers and Knoop hardness testing, calibration may involve the verification of test force application, indentation measuring system performance, indenter geometry and the overall machine performance using certified hardness reference blocks.

For laboratories working under quality systems, customer audits or accreditation requirements, calibration provides documented evidence that the hardness tester performs within the required limits and that the results are traceable to recognized standards. ATI offers ISO/IEC 17025 accredited calibration services and certified hardness test blocks for routine verification, machine checks and metrological control of Vickers and Knoop hardness testing systems.

Verification and standardization

Verification is the checking of the hardness testing machine to confirm that it conforms to the applicable specification. In practical terms, verification is normally performed using certified Vickers or Knoop hardness test blocks with known reference values.

Standardization is the process of bringing the instrument into conformity with a known standard through calibration, adjustment or verification. Regular verification is essential because small variations in force application, optical measurement, indenter condition or machine alignment can significantly affect the final hardness value, especially in low-force and microindentation testing.

Vickers and Knoop hardness testing machines should be verified periodically using certified hardness reference blocks suitable for the test forces and hardness ranges normally used by the laboratory.

Vickers and Knoop indenters

The Vickers indenter is a highly polished, square-based pyramidal diamond indenter with an angle of 136° between opposite faces. This geometry produces a symmetrical indentation with two diagonals that are measured and averaged to calculate the Vickers hardness value, expressed as HV.

The Knoop indenter is a highly polished, elongated rhombic-based pyramidal diamond indenter. Its geometry produces a long, shallow indentation, and the Knoop hardness value, expressed as HK, is calculated from the long diagonal. This makes Knoop particularly useful for thin layers, coatings, brittle materials and applications where penetration depth must be minimized.

Indenters should be inspected periodically and replaced if they become worn, chipped, cracked, dulled or separated from their mounting. A damaged indenter can produce distorted indentations, unclear corners or systematic hardness errors. Visual inspection of indentations made on certified test blocks can help identify possible indenter damage or alignment problems, but formal verification should always follow the applicable procedure.

Vickers and Knoop hardness testing machine

A Vickers or Knoop hardness testing machine must support the specimen securely and apply the selected test force in a controlled and repeatable manner. The indenter must move along an axis perpendicular to the test surface, and the machine must allow accurate optical measurement of the indentation after the force has been removed.

Because Vickers and Knoop are optical indentation methods, the measuring system is just as important as the force application system. The machine should provide suitable magnification, stable illumination, proper focusing and sufficient optical resolution for the indentation size being measured. In modern systems, automatic image analysis can reduce operator influence and improve repeatability, especially when measuring small microhardness indentations.

Specimen support and anvils

The specimen must be supported in a stable and rigid way during force application. Any movement, bending, vibration or lack of support can alter the indentation shape and reduce the reliability of the result. The support surface, fixture or anvil should be clean, smooth and free from pits, deep scratches, contamination or foreign material.

Flat specimens should be tested on a flat support surface whose bearing plane is perpendicular to the indenter axis. Cylindrical specimens, small parts or irregular components may require V-groove anvils, parallel supports, clamping fixtures or customized holding devices to keep the test area properly positioned during the test.

In microindentation testing, mounted specimens must be adequately supported by the mounting material. Soft or creeping mounting compounds should be avoided when they can allow specimen movement under load. For edge testing, coating evaluation or case depth traverses, good mounting and polishing are essential to maintain edge retention and obtain reliable indentation geometry.

Practical tips for reliable Vickers and Knoop results

Reliable Vickers and Knoop hardness results require a controlled test process. The specimen surface should be properly prepared, the test area should be flat and perpendicular to the indenter axis, the selected force should be appropriate for the material and thickness, and the indentation must be clearly visible under the measuring system.

If the machine is used for production release, heat treatment verification, case depth measurement or coating inspection, the test setup should be checked periodically with certified reference blocks. A complete control program should include suitable master hardness test blocks, regular machine verification and scheduled accredited calibration.

Before testing production parts or critical samples, it is good practice to verify the machine with certified hardness test blocks close to the expected hardness range and force level. The operator should also check that the indentation shape is regular, the corners are sharply defined and the spacing from adjacent indentations or specimen edges is sufficient.

In micro Vickers and Knoop testing, small errors have a greater influence on the final result because the indentation is very small and the hardness calculation depends on the square of the measured diagonal. For this reason, surface preparation, focusing, illumination, vibration control and automatic image measurement become especially important when working with low test forces, thin coatings, case depth profiles or microstructural constituents.

Common sources of error in Vickers and Knoop hardness testing

Most errors in Vickers and Knoop hardness testing are not caused by the hardness tester alone, but by the interaction between sample preparation, force application, optical measurement and operator procedure. Since the hardness value is calculated from the indentation size, every factor that changes or distorts the indentation can affect the result.

Unclear indentation corners
Poor polishing, surface contamination, etching or low image contrast can make the indentation tips difficult to identify and increase measurement uncertainty.

Incorrect focus
If all indentation corners are not in sharp focus, the specimen surface may not be perpendicular to the indenter axis or the optical system may not be correctly adjusted.

Insufficient spacing
Indentations placed too close to each other or too close to the specimen edge can be affected by previous plastic deformation or lack of material support.

Unstable specimen support
Movement, bending, poor mounting support or creeping mounting media can alter the indentation geometry during force application.

Damaged or contaminated indenter
A worn, chipped, contaminated or incorrectly mounted indenter can produce distorted indentations and systematic hardness errors. If indentation shapes become irregular, the indenter condition should be checked.

Wrong force selection
Using a force that is too high for a thin layer or too low for a rough surface can produce unreliable results. The selected force should be compatible with the material, thickness, surface condition and purpose of the test.

Operator influence in optical measurement
Manual diagonal measurement can be affected by focus, contrast, illumination and operator interpretation. Automatic image analysis can improve repeatability, but it still requires correct setup, calibration and image quality.