Leeb hardness test

Stefan Landler, winter semester 17/18

The Leeb hardness test is a method used to determine the dynamic hardness of metals. The method, which was developed by Dietmar Leeb and Marco Brandestini in the 1970s^[1], compares the velocity of an impact body before and after the collision with the test body (see Figure 1). The method is classified as a rebound hardness measurement^[2].

Fundamentals

The velocities of two bodies before and after a collision is often described with the ratio of the velocities, also known as the coefficient of restitution (COR). In the case of an impact body colliding with a stationary target, the COR is defined as follows:

$//<![CDATA[ \begin{array}{l}COR=\frac{v_2}{v_1}\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}COR\end{array} //]]>$: coefficient of restitution

• $//<![CDATA[ \begin{array}{l}v_1\end{array} //]]>$: absolute value of the velocity before the impact

• $//<![CDATA[ \begin{array}{l}v_2\end{array} //]]>$: absolute value of the velocity after the impact

The COR normally ranges from 0 to 1. A value more than 1 would imply that an energy gain occurred in the collision, which can for example happen in an explosion. A COR of 0 represents a perfect inelastic collision while a value of 1 occurs in a perfect elastic collision.

The value of the COR depends on the energy loss of the impact body in the collision. When you measure the velocity right before and right after the impact, the complete energy of the impact body is defined as:

$//<![CDATA[ \begin{array}{l}E=E_{kin}=\tfrac{1}{2}mv^2\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}E\end{array} //]]>$: complete energy of the body

• $//<![CDATA[ \begin{array}{l}E_{kin}\end{array} //]]>$: kinetic energy of the body

• $//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$: mass of the body

• $//<![CDATA[ \begin{array}{l}v\end{array} //]]>$: velocity of the body

This formula implies that the reference plane for the potential energy of the gravitaty ($//<![CDATA[ \begin{array}{l}E_{pot}\end{array} //]]>$) is on the impact area (i.e. $//<![CDATA[ \begin{array}{l}E_{pot}=0\end{array} //]]>$) and there occurs no plastic deformation of the impact body.

The difference between the energy of the body before and after the impact depends mainly on the plastic deformation of the test piece^[3][4][2]. The elastic deformation of the test body can lead to energy loss through damping and acoustic sound, but these irreversibilities are neglected. The described energy difference can be formulated as work, which can be split in a plastic and an elastic part:

$//<![CDATA[ \begin{array}{l}E_1-E_2=W=W_p+W_e\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}E_1\end{array} //]]>$: energy of the impact body after the impact

• $//<![CDATA[ \begin{array}{l}E_2\end{array} //]]>$: energy of the impact body before the impact

• $//<![CDATA[ \begin{array}{l}{W}\end{array} //]]>$: mechanical work of the deformation

• $//<![CDATA[ \begin{array}{l}W_p\end{array} //]]>$: mechanical work of the plastic deformation

• $//<![CDATA[ \begin{array}{l}W_e\end{array} //]]>$: mechanical work of the elastic deformation

The elastic part of the work is responsible for the resulting energy after the impact, while the plastic part leads to the difference of the energies^[2]. The plastic part depends on the hardness of the material and therefore the Leeb hardness test can give an indicator for this specific value. The problem is, that there are 2 unknown values ($//<![CDATA[ \begin{array}{l}W_p\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}W_e\end{array} //]]>$) but only 1 equation. Thus, the problem is underdetermined and assumptions for the elastic deformation are necessary.

Assuming you always examine the same material in the same shape with the same test conditions, the work of the elastic deformation will be the same. Thus, the resulting Leeb hardness value are directly comparable. For other cases you should consider that different Leeb hardness values are not for sure the result from different surface hardnesses. Figure 2 shows a stress-strain diagram for two exemplary materials with same yield stress but different Young’s moduli^[4][2]. The curves show a different distribution of the plastic and elastic parts of the work (same total work). This will lead to two different Leeb hardness values although the same yield stress with the same total work are indicators for a similar or an equal surface hardness. The material with the greater Young’s modulus (material 1) has a smaller part of the work as elastic deformation and can therefore give less energy to the impact body. Thus, the impact body will have a reduced velocity and the measured Leeb hardness will be smaller.

Principle

The Leeb hardness test defines the hardness HL as the quotient of the velocities before and after the impact of a well-defined impact body (mostly with a spherical contact area^[3]) and a test piece (see Figure 3):

$//<![CDATA[ \begin{array}{l}HL=\frac{v_R}{v_A}\cdot1000=COR\cdot1000\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}HL\end{array} //]]>$: Leeb hardness value

• $//<![CDATA[ \begin{array}{l}v_R\end{array} //]]>$: absolute value of the rebound velocity (after the impact)

• $//<![CDATA[ \begin{array}{l}v_A\end{array} //]]>$: absolute value of the impact velocity (before the impact)

• $//<![CDATA[ \begin{array}{l}COR\end{array} //]]>$: coefficient of restitution

Because of the strong dependence of the measured rebound velocity on the test conditions^[3] (mass, radius and impact velocity of the impact body), it is imperative to state the Leeb hardness value with the test conditions. DIN EN ISO 16859^[3][5][6] defines a few types of impact devices which give a set of parameters to give a test sequence as precise as possible. Hardness values which are determined with these parameter sets are characterized with an extended symbol to the basic symbol “HL”. The symbol for the parameter sets are among others “D”, “S” or “G” so an example for a complete Leeb hardness value would be “500 HLS”.

It is essential for the correct procedure to direct the impact normal to the test surface. In addition to that the overall direction of the impact should be observed because the gravity can have an influence on the measured result. DIN EN ISO 16859-1 shows corrections for specific test conditions. The impact should be in a certain distance from the edge of the test piece and previous impacts to suppress influences. Concrete values for the distances to be respected can be found in DIN EN ISO 16859-1. The impact area of the test piece should be clean and without contamination. The roughness of the test surface should be smooth (recommended roughness values can be found in DIN EN ISO 16859-1), whereby the requirements to the roughness rise with the decrease of the impact energy. DIN EN ISO 16859-1 advises the user to machine and polish the surface. If the test surface is curved too much (limit values in DIN EN ISO 16859-1), the measurement device should be supported for a stable connection to the surface. Furthermore, the impact should not be influenced by any vibrations or motions as well as electromagnetic fields. The test piece should be heavy and stiff therefore the DIN EN ISO 16859-1 recommends certain minimum masses and thicknesses. This condition ensures that the elastic deformation of the test piece is not a big influence on the measurement result. For light and flexible test bodies arrangements can help to increase the stiffness, for example a coupling to a support body.

Conversions to other hardness scales

DIN EN ISO 16859-1^[3] points out that there is no general way to convert Leeb hardness values to other hardness scales. Therefore, no international standard exists that gives a hint about how different scales should be compared. Nevertheless, international guidelines (ASTM E140^[7]) are published that show conversions from the Leeb hardness to other scales. Other papers, for example by Yamamoto et al.^[8], show selected relations between Leeb hardness and other scales. Other hardness scales can be easily converted by using DIN EN ISO 18265^[9].

Similar methods

The rebound hammer method is a very similar method to the Leeb hardness test. It is used to determine the surface strength of test pieces made of concrete or rock. The measurement device is a rebound hammer, often called “Schmidt hammer”, which consists of an impact plunger, a movable mass and a spring^[10]. The spring generates a force to accelerate the mass onto the plunger. The plunger generates an impact on the test surface. The rebound on the plunger produces an impulse which accelerates the mass. In contrast to the Leeb hardness test the measured parameters are not always the velocities before and after the impact but can also be the rebound distance. DIN EN 12504-2 indicates that every parameter of the rebound can be used^[10].

Two evaluation methods are used with the rebound hammer method:

• R-value: The measured parameter is the distance of the moved body after the impact
  • The R-value is measured on a scale on the round hammer
  • The R-value is not necessary a known SI unit (like mm), it is just a value on the given scale
• Q-value: The measured parameter are the velocities before and after the impact
  • The velocities are used to calculate the kinetic energy of the movable mass

  • $//<![CDATA[ \begin{array}{l}Q=100\cdot\frac{v_R^2}{v_A^2}\end{array} //]]>$

• • • $//<![CDATA[ \begin{array}{l}Q\end{array} //]]>$: Q-value

    • $//<![CDATA[ \begin{array}{l}v_R\end{array} //]]>$: absolute value of the rebound velocity (after the impact)

    • $//<![CDATA[ \begin{array}{l}v_A\end{array} //]]>$: absolute value of the impact velocity (before the impact)

    • $//<![CDATA[ \begin{array}{l}COR\end{array} //]]>$: coefficient of restitution

• Advantages of the Q-value over the R-value^[11]:
  • Lower influence of the gravity → measurement direction can be varied easier
  • Lower influence of friction
  • User-friendly because of the electronic evaluation

The conversion of the measured values of the rebound hammer method to other characteristic values shows the same problems as with the Leeb hardness values. Sometimes conversion tables for certain materials are available, but these tables should always be used carefully, because of the inaccurate relation between the measured hardness values and the strength of the test piece. A meaningful approach would be to use the measurement in comparison to a well-known test piece^[11].

Another dynamic hardness test method is the Shore hardness test. This test uses the so called sceleroscope, which is a measurement device which consists of an impact body, called hammer, and a defined tip placed on it. The hammer is dropped from a certain height and accelerates because of the gravity. The rebound distance after the collision with the test piece is measured. The Shore method is mostly replaced by other hardness test methods, like the Leeb test^[2].

The last similar test method portrayed is the Nitronic test which measures, in contrast to the other methods, the time between two impacts^[2].

Applications

Leeb hardness test

• Measurements on large and heavy pieces, for example machine tools (guide tracks), engine blocks or rollers^[2]
• Measurements on small, flexible or light metal structures possible with coupling to a heavy support piece or stiffening arrangements^[2]
• Possible measurements in every direction → access to overhead areas
• Inspection of immobile structures, for example steel bridges or pipe flanges (oil/gas)^[12]

Rebound hammer method

• Verifying the uniformity of the strength of concrete structures
• Determination of the concrete strength as a rule of thumb
• Development of own correlations between the measured hardness and the strength^[11]

Shore hardness test

• Measurements on large and heavy pieces, for example machine tools (guide tracks), engine blocks or rollers^[2]
• Most applications are historical because the Leeb hardness method is more established^[2]

Advantages and disadvantages

Advantages

• Fast measurement and evaluation
• Known influence of gravity → multiple directions for the test are possible
• Small instruments possible → measurements on areas that are difficult to reach

Disadvantages

• No international standard for conversions to other hardness values (Vickers, Brinell etc.)
• High requirements to the test surface
• Only big and heavy test pieces possible (without special arrangements)
• Standardized only for metals (but there are papers which describe the usage of the Leeb hardness test on other materials, for example rock^[13])

Literature

1. Proceq S.A. (assignee), Leeb, D., Brandestini, M. (inventor): Verfahren und Vorrichtung zur Härteprüfung von Werkstoffen. DE2452880A1 (1976).
2. Herrmann, K. (Hrsg.), Kompatscher, M.: Härteprüfung an Metallen und Kunststoffen. Grundlagen und Überblick zu modernen Verfahren. expert verlag, Renningen (2007), p 81-92.
3. DIN EN ISO 16859-1:2016-02, Metallische Werkstoffe - Härteprüfung nach Leeb - Teil 1: Prüfverfahren (ISO 16859-1:2015).
4. Kompatscher, M.: Equotip - Rebound hardness testing after D. Leeb. HARDMEKO 2004: Hardness Measurements Theory and Application in Laboratories and Industries, Washington, D.C. (2004).
5. DIN EN ISO 16859-2:2016-02, Metallische Werkstoffe - Härteprüfung nach Leeb - Teil 2: Überprüfung und Kalibrierung der Härteprüfgeräte (ISO 16859-2:2015).
6. DIN EN ISO 16859-3:2016-02, Metallische Werkstoffe - Härteprüfung nach Leeb - Teil 3: Kalibrierung von Härtevergleichsplatten (ISO 16859-3:2015).
7. ASTM E140-12be1, Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, Scleroscope Hardness, and Leeb Hardness. ASTM International, West Conshohocken, PA (2012).
8. Yamamoto, T., Yamamoto, M., Takagi, S.: Current status of rebound hardness test blocks in Japan and outlook. Proceedings of IMEKO 2010: TC3, TC5 and TC22 Conferences, Pattaya (2010), p. 379-382.
9. DIN EN ISO 18265:2014-02, Metallische Werkstoffe - Umwertung von Härtewerten (ISO 18265:2013).
10. DIN EN 12504-2:2012-12, Prüfung von Beton in Bauwerken – Teil 2: Zerstörungsfreie Prüfung – Bestimmung der Rückprallzahl (EN 12504-2:2012).
11. Proceq SA: silverschmidt Bedienungsanleitung Betonprüfhammer. Bedienungsanleitung eines Schmidt-Hammers von Proceq (19.02.2018).
12. Proceq SA: equotip. Mobile Härteprüfung Leeb - Rockwell - UCI (Equotip 550 Sales Flyer). Flyer der Webseite https://www.proceq.com/de/vergleichen/equotip-mobile-haertepruefung/ (19.02.2018).
13. Corkum, A. G., Asiri, Y., El Naggar, H., Kinakin, D.: The Leeb Hardness Test for Rock. An Updated Methodology and UCS Correlation. Rock Mechanics and Rock Engineering. Springer Vienna (2017), p. 1-11.