hardness Measurement of Metals— Static Methods

Hardness Testing—Principles and Applications Copyright © 2011 ASM International®

Konrad Herrmann, editor All rights reserved.www.asminternational.org

ChaPter 2

hardness Measurement of Metals—

Static Methodst. Polzin

HARDNESS MEASUREMENTS ON METALS (Ref 1) have been performed for many centuries, as the historical survey in Chap-ter 1 shows (Ref 2). Most of the hardness measuring methods stand-ardized today (Ref 3 to 13) were established before 1930 and have, in principle, remained unchanged (see Chapter 1). These procedures are exclusively static test procedures, that is, procedures in which the test force is applied to the test piece without shocks during a prescribed minimum time. Dynamic test procedures—procedures with impact force application on the test piece—have also been mentioned in earlier times in literature. They have not, however, reached the importance static procedures have. In recent years, new static, dynamic, and noncontact test procedures have been devel-oped. This chapter contains a description of the most important characteristics and specifications of all static procedures that are state of the art, commonly used, or that have the chance of being disseminated due to their advantages. In Fig. 1 the attempt is made to compile most of the procedures according to superior aspects and to arrange them systematically. The dynamic procedures are dealt with in Chapter 3 in this book, “Dynamic Test Methods,” and the noncontact procedures in Chapter 4, “Hardness Testing of Metals—Contactless and Other Nondestructive Methods.”

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26 / hardness testing—Principles and applications

rockwell ISO 6508 and aStM e 18 Procedures

Because of the simplicity of their realization and the small amount of time required for a measurement, these procedures (Ref 5 and 8, respec-tively) are the methods most widely applied in the world. The indenter is either a right circular cone with a rounded diamond tip (circular cone, 120°; radius of curvature, 0.200 mm, or 0.008 in.), shown in Fig. 2, or a sphere made of hard metal (sphere diameter, 1.5875 mm, or 0.0625 in., and 3.175 mm, or 0.125 in., and, if required by the product specifications, also 6.350 mm, or 0.25 in., and 12.70 mm, or 0.5 in.). Steel spheres, which

Fig� 2 Conical indenter according to rockwell. Source: ref 1

Fig� 1 Survey of the hardness measuring methods standardized and published in ISO 6508 and aStM e 18. Source: ref 5 and 8

Chapter 2: hardness Measurement of Metals—Static Methods / 27

formerly were used exclusively, are today used for special cases only. Compared to steel spheres, hard metal spheres lead to smaller hardness values. The principle of the procedures is shown in Fig. 3.

First, the indenter penetrates into the test piece under the preliminary test force, F0, down to a depth of penetration that is defined as the refer-ence plane for the future measurement. The depth measuring device is set to zero and the additional test force, F1, is applied. After a time of applica-tion of the additional test force defined in the standards, the maximum depth of penetration is reached. After that, the test force, F1, is withdrawn in such a way that again only the preliminary test force, F0, is acting. At the same time, the indenter moves back upward by the elastic fraction of the depth of penetration during the total test force, and the indentation persists at the remaining depth of penetration, h, with which the Rockwell hardness, HR, is defined.

The Rockwell hardness is defined as:

HR Nh

S= − (Eq 1)

where HR = Rockwell hardnessN = numerical value (constant)h = remaining depth of penetration in mm S = scale division in mm

In most cases, the hardness value is indicated directly on the hardness testing machine.

Equation 1 is explained by an example in Eq 2. For hardness measure-ments according to Rockwell C (HRC), the numerical value, N, amounts to 100 and the scale value S to 2 µm = 0.002 mm (0.00008 in.). If a re-

Fig� 3 hardness measurement according to rockwell, schematical view. Source: ref 1


maining depth of penetration, h = 80 µm = 0.08 mm (0.003 in.), is meas-ured, the hardness value is calculated as:

HRC = − = − =1000 080

0 002100 40 60

.

.(Eq 2)

Basically, the Rockwell hardness is defined arbitrarily and should, there-fore, be regarded as a material characteristic only, without any additional explication. The numerical values, N, were defined in such a way that the test result can be easily calculated and the scale division, S, can be calcu-lated in such a way that the required resolution is given. To obtain as wide a range of application of the procedure as possible, several Rockwell proce-dures, which are marked by an additional capital letter after HR (e.g., HRG), have been developed (Table 1). The individual procedures differ in:

• The indenter• Amount of the test force or preliminary test force• Numerical value, N• Scale division, S

One scale division of the Rockwell hardness corresponds to a depth of penetration of 1 or 2 µm (0.00004 or 0.00008 in.), which places corre-sponding requirements on the depth measuring device. The measurement after removal of the additional test force means that cumulative errors of the test piece are especially serious. When conical diamond indenters are used, strict care must be taken to calibrate and certify them beforehand. Different indenters may lead to strongly differing results. Presently, it has not been possible to describe the cause of this behavior in detail.

Figure 4 shows, according to Rockwell, the deviation of the hardness value from the mean value of the results of 27 indenters for 14 different conical indenters. The figure illustrates very clearly the imbalance of the deviations. All indenters complied with the prescribed tolerances of the geometric data. An assignment of the real geometric data to the deviations in Fig. 4 does not furnish any clear result. Therefore, when the indenters are tested for their usability, they should undergo a performance test (com-parison of the achieved hardness values with those of a reference standard indenter), which is also prescribed by the standards (Ref 5 and 8).

As to the use of this indenter, it must also be taken into account that, depending on the amount of the test force and the hardness of the test piece, differently shaped parts of the indenter are responsible for the for-mation of the hardness value.

Figure 5 shows the three cases to be differentiated (see Chapter 4, “Hardness Testing of Metals—Contactless and Other Nondestructive Methods,” in this book). In Fig. 5(b) and (c), the size of the conical inden-tation fractions may be different, depending on the test force and on the test piece hardness.


This may be a reason for the decreasing sensitivity of the Rockwell hardness with increasing hardness. This point is explained in more detail when the elastic and plastic deformations are addressed.

For the minimum test piece thickness, ISO 6508 (Ref 5) and ASTM E 18 (Ref 8) specify only that no deformation must be visible on the bottom side of the test piece. The values represented in the curves are based, as prescribed in ISO, on ten times the remaining depth of penetration. For the cause of this determination, see Fig. 6.

As to the distances between the indentations and from the edge, the standard specifies four times the indentation diameter, at least 2 mm (0.08

table 1 Survey of the hardness testing procedures according to rockwell, as far as they have been standardized in ISO 6508 and aStM e 18

Definition of the hardness value

Hardness scale Abbreviation

Type of the indenter

Preliminary test force, F0

Additional test, F1 Scope Example for the use

HRAh

= −1000 002.

A HRA Diamond cone 98.07 N 490.3 N 20 HRA to 88 HRA Sinter-hard metal. As HRC for low thickness of sample

HRBh

= −1300 002.

B HRB Ball 1.587 5 mm 98.07 N 882.6 N 20 HRB to 100 HRB Steel (middle or week) brass, bronze-alumi-num alloy

HRCh

= −1000 002.

C HRC Diamond cone 98.07 N 1.373 kN 20 HRC to 70 HRC Steel (hardened respec-tively tempered); hard cast iron

HRDh

= −1000 002

.

D HRD Diamond cone 98.07 N 882.6 N 40 HRD to 77 HRD Steel seldom used method

HREh

= − 1300 002.

E HRE Ball 3.175 mm 98.07 N 882.6 N 70 HRE to 100 HRE Cast iron, aluminum, and magnesium alloys, bearing metals

HRFh

= −1300 002.

F HRF Ball 1.587 5 mm 98.07 N 490.3 N 60 HRF to 100 HRF Annealed copper alloys, thin sheets

HRGh

= −1300 002.

G HRG Ball 1.587 5 mm 98.07 N 1.373 kN 30 HRG to 94 HRG Phosphor bronze, beryl-lium copper, annealed cast iron

HRHh

= −1300 002.

H HRH Ball 3.175 mm 98.07 N 490.3 N 80 HRH to 100 HRH Aluminum, zinc, lead

HRKh

= −1300 002.

K HRK Ball 3.175 mm 98.07 N 1.373 kN 40 HRK to 100 HRK Bearing metals and other metals of low hardness

HR15Nh

= −1000 001.

15N HR15N Diamond cone 29.42 N 117.7 N 70 HR15N to 94 HR15N As HRC respectively HRA, if sample is too thin or too small

HR30Nh

= −1000 001.

30N HR30N Diamond cone 29.42 N 264.8 N 42 HR30N to 86 HR30N

HR45Nh

= −1000 001.

45N HR45N Diamond cone 29.42 N 411.9 N 20 HR45N to 77 HR45N

HR15T =h

1000 001

−.

15T HR15T Ball 1.587 5 mm 29.42 N 117.7 N 67 HR15T to 93 HR15T As HRB respectively HRF, if sample is too thin or too small

HR30T =h

1000 001

−.

30T HR30T Ball 1.587 5 mm 29.42 N 264.8 N 29 HR30T to 82 HR30T

HR45Th

= −1000 001.

45T HR45T Ball 1.587 5 mm 29.42 N 411.9 N 10 HR45T to 72 HR45T

Source: Ref 5 and 8


in.). For the conical indenters, Fig. 7 shows the zones influenced by the indentation. The pile-up of the wall can be seen very clearly in the scan-ning electron microscope (SEM) image (Fig. 8).

As the figures show, only indentations that are separated from each other by ten times the remaining depth of penetration, h (center-to-center distance), should be performed.

This is why the values for the minimum test piece thickness and the center-to-center distance of two adjacent indentations can be taken in the same way from Fig. 9.

Fig� 4 Deviation of the hardness value of 14 indenters, determined on hard-ness reference blocks, from the mean value of 27 indenters. Source:

ref 1

Fig� 5 Combination possibilities in rockwell indentations with conical indenters. (a) Preliminary test force and test force indentation spherical. (b) Preliminary force indentation spherical, test force indentation conical. (c) Both

indentations conical. Source: ref 1


In this connection it is interesting for the practical selection of the test force, and thus for the selection of the procedure, to calculate which re-maining depths of penetration can be achieved as a function of the se-lected test force. Figure 10 shows this relationship for four steel test pieces of different Rockwell C hardness.

Fig� 6 rockwell C indentation with the deformed zone in an intersection laid through the indentation axis. Source: ref 1

Fig� 7 rockwell C indentation with deformed zone. Source: ref 1


To obtain as large a deformation fraction as possible with the cone of the indenter, the intersection by an HRC indention on a test piece of hard-ness 20 HRC is given as an example (Fig. 11).

Figure 12 shows the remaining deformation and the elastic fraction of the deformation during an HRC test on steel. Like the other curves of this kind, these are examples of steel. With increasing hardness of the test pieces, only the yield point changes—not the elasticity modulus.

Fig� 8 Scanning electron microscope (SeM) image of rockwell C indentation. Source: ref 1

Fig� 9 Minimum test piece thickness and center-to-center distance. Source: ref 1


The remaining deformation is obtained from this definition of the Rock-well C hardness:

HRCh

= −1000 002.

(Eq 3)

At 20 HRC, the deformation amounts to 160 µm (0.006 in.), and at 65 HRC, to 70 µm (0.003 in.). The elastic deformation increases from 13 µm

Fig� 10 remaining depth of penetration as a function of the selected test force during the hardness test according to rockwell C. Source: ref 1

Fig� 11 Profile through an hrC indentation (test piece 20 hrC). Source: ref 1


(0.0005 in.) at 20 HRC to 26 µm (0.001 in.) at 65 HRC; thus, the growth rates increase with increasing hardness. This can be explained by the in-creasing fraction of the deformation caused by the spherical end of the indenter. For practical applications, this means that the Rockwell proce-dures with the conical indenter become increasingly worse at differentiat-ing materials with increasing hardness. The real effect of this behavior is illustrated by the example of the Rockwell C hardness in Fig. 13.

In curve “a,” the Rockwell C hardness is shown as a function of the Vickers hardness, and the curve truncates with increasing hardness. The relationship becomes even clearer in curve “b.” Here, the increase in the Rockwell values has been plotted for a hardness change of 20 HV as a function of the hardness. Whereas at 250 HV (approximately 22 HRC), the Rockwell hardness still changes for HV = 20 HV by 3.7 units, this change only amounts to 0.5 units at 930 HV (approximately 68 HRC). The sensitivity has decreased to 1/7. This is shown even more clearly by Fig. 14. If the largest sensitivity of 3.7 HRC units is identified as 100%, and if other values of the sensitivity are compared to this value, a curve of the sensitivity is obtained, showing it as a percentage of to the initial sen-

Fig� 12 Plastic (remaining) and elastic deformation for the hardness test ac-cording to hrC and steel test pieces. Source: ref 1


sitivity at 20 HRC. As hardness increases, the values decrease to 13.5% of the initial sensitivity.

Having identified this phenomenon of decreasing sensitivity with in-creasing hardness in the Rockwell C procedure, the question arises: What sensitivity ratios are exhibited in the other Rockwell procedures? Figure 15 represents the changed sensitivities for seven Rockwell procedures ac-cording to curve “b” in Fig. 13.

The statement of the figure is unambiguous. To assess the measurement uncertainty of the Rockwell procedures, the information regarding the sensitivity is of significance, too.

Fig� 13 Decreasing sensitivity of the rockwell C hardness. Source: ref 1

Fig� 14 Sensitivity of the hardness test according to rockwell C, related to the initial sensitivity at 20 hrC. Source: ref 1

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hardness Measurement of Metals— Static Methods