Hardness methods and sensitivity coefficients
Hardness is an unusual physical property in that it is the result of a defined measurement procedure and not an intrinsic materials property susceptible to precise definitions in terms of fundamental units of mass, length, and time. In practice, hardness is measured in terms of the size of an impression made on a specimen by an indenter of a specified shape when a specified force is applied for a specified time, the indent being measured after the force has been removed. There are three principal standard methods for expressing the relationship between hardness and the size of the impression, these being Brinell, Rockwell, and Vickers. For practical and calibration reasons, each of these methods is divided into a range of scales, defined by a combination of applied load and indenter morphology, to cover the range of hardness. Recently, with the introduction of instrumented indentation hardness, it has become possible to measure the indent under the applied force.
These background notes provide information on the following hardness methods:
- Brinell Hardness
- Instrumented Indentation
- Knoop Hardness
- Rockwell Hardness
- Rubber Hardness
- Vickers Hardness
The hardness of a metallic material can be defined as its resistance to plastic deformation caused by a force applied through an indenter. It is an unusual property in that it is the result of a defined measurement procedure and not an intrinsic property which can be defined in terms of fundamental SI units.
In practice, hardness is measured in terms of the size of an impression made in a specimen by an indenter of a specified shape when a specified force is applied for a specified time, the indent being measured after the force has been removed. There are three principal standard methods for expressing the relationship between hardness and the size of the impression, these being Brinell, Vickers, and Rockwell. For practical and calibration reasons, each of these methods is divided into a range of scales, defined by a combination of applied load and indenter geometry.
The determination of a hardness value depends on the results of measurements of a large number of different parameters, such as force, diameter, depth, time, radius, and angle. Each of these measurements has an associated uncertainty, and these uncertainties will each contribute to the overall uncertainty of the hardness value.
The relationship between the uncertainty associated with the parameter and the uncertainty associated with the resultant hardness value is given by a sensitivity coefficient ci, defined as the change in hardness H, resulting from a change in the input parameter xi:
ci = ΔH/Δxi
Sensitivity coefficients can also be used to make corrections to hardness values in situations in which the measured value of an input parameter differs from the value specified within the relevant Standard or, where a range of values is permitted within the Standard, to correct the hardness to a nominal input parameter value.
Some sensitivity coefficients can be calculated by taking partial derivatives of the equation defining the hardness value. Others, such as the effect of tip radius and length of line of junction, can be evaluated from geometrical considerations. Many sensitivity coefficients, however, can only be determined by practical experiment – this is done by varying the parameter of interest, while keeping all other inputs as constant as possible, and seeing what the effect is on the measured hardness. As the hardness of a particular specimen cannot be measured more than once in the same location, good quality hardness reference blocks need to be used, and a number of indentations need to be made at each value of the input parameter. Sensitivity coefficients determined by such practical work are generally only applicable to the particular material of the reference block.
The following sections give details of sensitivity coefficients, obtained in the ways described above, for the three principal hardness methods:
- Geoff Stanbury and Francis Davis, The uncertainty evaluation of NPL's hardness facility, Proceedings of XVI IMEKO World Congress in Vienna, Austria, 2000
- Geoff Stanbury and Francis Davis, UK's provision of primary hardness standards, Proceedings of XVI IMEKO World Congress in Vienna, Austria, 2000
- NPL Report CMAM 31: Proposed future research for hardness standards
- NPL Report CMAM 53: Provision of hardness standards - final report
- NPL Report CMAM 69: Results of a survey of the priorities for an increased range of UK traceable hardness scales
- NPL Report CMAM 87: Uncertainty in hardness measurement
- Force, Torque, Hardness, and Extensometry: Andy Knott
- Establishment and maintenance of standards of force: Andy Knott
- Development of standards of torque: TBC
- Brinell, Vickers, and Rockwell hardness standards: Laurence Brice
- Extensometry standards: Andy Knott
- Force, Torque, and Hardness Special Interest Group: Hannah Carter
- ASTM D2240-00, Standard Test Method for Rubber Property—Durometer Hardness (Types A, B, C, D, DO, E, M, O, OO, OOO, OOO-S, and R).
- ASTM E18-05e1, Standard Test Methods for Rockwell Hardness and Rockwell Superficial Hardness of Metallic Materials.
- BS 903-A26:1995 and ISO 48:1994, Physical testing of rubber - Part A26: Method for determination of hardness (hardness between 10 IRHD and 100 IRHD).
- BS EN ISO 868:2003, Plastics and ebonite - Determination of indentation hardness by means of a Durometer (Shore hardness).
- ISO 4545 Parts 1, 2, 3, and 4 : 2005, Metallic materials - Knoop hardness test.
- BS EN ISO 6506 Parts 1, 2, 3, and 4 : 2005, Metallic materials - Brinell hardness test.
- BS EN ISO 6507 Parts 1, 2, and 3 : 2005, Metallic materials - Vickers hardness test.
- BS EN ISO 6508 Parts 1, 2, and 3 : 2005, Metallic materials - Rockwell hardness test (scales A, B, C, D, E, F, G, H, K, N, T).
- BS EN ISO 14577 Parts 1, 2, and 3 : 2002, Metallic materials - Instrumented indentation test for hardness and materials parameters.
We operate a user group within the Engineering Measurement Awareness Network (EMAN) called the Force, Torque, and Hardness Special Interest Group