Converting the Scales - Leeb as a Hardness Alternative
Testing the hardness of materials is one of the oldest measuring techniques in material testing, and it is probably one of the most frequently applied measuring techniques. On one hand, this is because hardness itself is a key property of materials. On the other hand, there is a link – sometimes a very close one, sometimes less so – between material hardness and other material properties such as tensile strength and wear characteristics. In addition, discrepancies in the expected hardness can indicate undesirable structural changes – for example, in the proximity of weld seams. Another important consideration is the fact that the hardness of metals can be measured with relative ease and almost entirely without damage.
Traditional Hardness TestingThe basic question of what we mean by the hardness of a material is more difficult to answer than might be expected. The hardness of metals is usually described rather vaguely as the resistance of the material to permanent deformation. It is not, strictly speaking, a clearly defined physical variable.
Standard hardness values are obtained with the aid of accurately defined physical tests. In these tests, a hard indenter with a defined geometry and size is usually pressed with a defined force into the sample of the material, and the resulting deformation is measured. Continuous measurement and plotting of the force and indentation depth during the load exposure would approximately produce the upper of the two curves shown in Figures 1 and 2, while the lower curve shows the corresponding values after the load is released. As well as being dependent on the geometry of the indenter, the shape of the load curve is defined primarily by the yield stress, while the shape of the load-release curve is primarily a function of the elasticity of the material.
- Vickers hardness is the ratio between the maximum test load Fm and the optically measured contact area between the pyramid-shaped indenter and the material after the load is released. This area is essentially proportional to the square of the maximum indentation depth.
- On the Rockwell hardness scales, the difference in indentation depth with a comparatively small preload F0 before and after application of the main load Fm is used as a measure of hardness. The harder the material, the smaller this difference becomes. In order to obtain a scale, which increases with increasing hardness, this difference is subtracted from an arbitrarily chosen constant. In contrast to the Vickers test, this scale takes into account the shape of the load-release curve, which depends on the material and the indenter. It would, therefore, be incorrect to assume that two workpieces made of different materials that have the same Vickers hardness will also have the same Rockwell hardness and vice versa.
Dynamic Hardness TestingIt is not usually possible to perform hardness measurements according to these traditional and static methods on large workpieces such as cast or forged parts, thick plates or similar test parts. In addition, the amount of time required for testing often prevents 100% testing of testable smaller parts. The portable hardness testers developed during the last 30 years are a suitable alternative in both cases.
The hardness test according to the Leeb method is particularly quick and easy to perform. This test is performed with a tester such as the Leeb Equotip 3 from Proceq, Schwerzenbach, Switzerland (Fig. 3). The Leeb hardness is measured using a spherical indenter at the tip of a metal body that impacts on the material with a defined impact velocity and then rebounds with a lower rebound velocity. The application and release of the load take place very quickly. For this reason, the creep behavior of the material has a different effect than it does under virtually static loads. Here, it is not the maximum load Fm but the area W under the load curve (i.e. the total deformation work), which is defined. The hardness value HL is proportional to the square root of the ratio between the elastic proportion of the deformation work (We, which is the area under the load release curve) and the total deformation work W. The Leeb method is suitable for workpieces that are not too small, and it is standardized in accordance with ASTM A 956 and DIN 50156.
Creating Material-Specific Conversion CurvesIn practice, customer-acceptance testing requirements or legal directives often demand that hardness values are provided in conventional hardness scales such as Vickers or Rockwell but not in the Leeb scale. In these cases, the values need to be converted from the Leeb result of the portable tester to the specified scale. As can be seen from the above descriptions of the testing methods, there is no straightforward relationship between the hardness values obtained with the different methods – including the traditional ones – that can be justified with the laws of physics. It is fair to expect there to be conversion functions for sufficiently similar materials, however, which deliver a close enough approximation.
Most hardness testers that work according to the Leeb principle offer conversion to all common hardness scales for a number of standard materials. For some materials and applications with particularly high requirements in terms of accuracy, however, these conversions may not always be sufficient. It is recommended in these cases to create material-specific conversion curves.
In general, there are three ways to accomplish a material-specific conversion. The first two methods can be applied quickly and easily with modern equipment such as the EQUOTIP 3 by Proceq.
- Single-point method: The Leeb hardness (HL) and the hardness in the desired scale – Vickers (HV) – are determined for a large reference workpiece. A corresponding standard conversion function HV(HL) for a related material is then chosen and vertically shifted until the measured reference pair of values lies on the shifted curve. If the hardness values that are to be measured do not deviate too much from the hardness of the reference workpiece, then this is an acceptable solution.
- Two-point method: If the hardness values are scattered over a wider range, this method is recommended. Two test samples of known hardness must be tested in the scale to be reported, one as soft and one as hard as possible. The Leeb hardness is then measured for both. A straight line is then added to a suitable standard conversion curve so that both of the selected points lie on the graph of the resulting conversion function. In this way, a reliable conversion curve can be produced for a wider range (Fig. 4).
- Conversion polynomial: If a material-specific conversion needs to be applicable across a very wide range and there are several hardness values available throughout this range both in the required scale and in Leeb hardness, this method is recommended. Some of the modern test equipment enables the definition of application-specific conversion functions through the specification of the polynomial coefficients. This conversion function can also be programmed in common spreadsheet software for easy calculation of many data points. Up to fifth-order polynomials are possible. However, the required measurements and the coefficient calculations are more complex than the one or two-point calibration methods.
Documentation of All Test ResultsConversions created can be identified, for example, by the name of the material or by any practical reference label freely chosen by the user. The conversions created in this way can be fully integrated in the user manual.
In comparison to other Leeb hardness testers on the market, Equotip 3 offers full documentation of all data that influences the test results. These include:
- The date and time
- The serial numbers of the probe and electronic controllers used
- All relevant parameter settings
- The conversion function used (including application-specific functions)
- Detailed statistics for the test series
The stored measurement data are normally transferred to a PC, where they can then be archived and further processed as required. The Windows-based software application Equolink 3 is included in the package. IH
For more information: Dr. Ralph Mennicke is product manager, metal hardness testing for Proceq SA in Switzerland. Contact Tom Ott, Proceq USA, Inc., 117 Corporation Drive, Aliquippa, PA 15001; tel: 724-512-0330; fax: 724-512-0331; e-mail: firstname.lastname@example.org; web: www.proceq-usa.com
Additional related information may be found by searching for these (and other) key words/terms via BNP Media SEARCH at www.industrialheating.com: Rockwell hardness, Vickers hardness, tensile strength, hardness conversion, indenter, deformation