960-

Rockwell Hardness

Measurement of

Metallic Materials

Samuel R. Low

NIST recommended

Pu
Rockwell Hardness

Measurement of

Metallic Materials

Samuel R. Low

Materials Science and 

Engineering Laboratory

January 2001

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Karen H. Brown, Acting Under Secretary of 

Commerce for Technology

National Institute of Standards and Technology

Karen H. Brown, Acting Director

UNITED STATES OF AMERICA

DEPARTMENT OF COMMERCE

Special Publication 960-5
Certain commercial entities, equipment, or materials may be identified in

this document in order to describe an experimental procedure or concept

adequately. Such identification is not intended to imply recommendation or

endorsement by the National Institute of Standards and Technology, nor is it

intended to imply that the entities, materials, or equipment are necessarily the

best available for the purpose.

National Institute of Standards and Technology

Special Publication 960-5

Natl. Inst. Stand. Technol.

Spec. Publ. 960-5

116 pages (January 2001)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2000

For sale by the Superintendent of Documents

U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone: (202) 512–1800 Fax: (202) 512–2250

Mail: Stop SSOP, Washington, DC 20402-0001
◆

FOREWORD

The Rockwell hardness test continues to be applied as a tool for assessing

the properties of a product while the tolerances on the acceptable material

hardness have become tighter and tighter. Adhering to “good practice”

procedures when performing Rockwell hardness measurements and

calibrations is a beneficial step to reducing measurement errors. The purpose

of this Guide is to explain the causes of variability in Rockwell hardness test

results and to supplement the information given in test method standards with

good practice recommendations. Although this Guide is directed more towards

the users of Rockwell hardness having the greatest concern for accuracy in

their measurements, much of the information given is also applicable for users

that only require test results to be within wide tolerance bands, where high

accuracy is not as critical.

................................

iii
ACKNOWLEDGMENTS

The author would like to thank the following persons for sharing their

experience and providing information for this Guide. Their input and review

has provided a link to the practical world of Rockwell hardness testing.*

T. Robert Shives, Consultant

Richard Antonik, SUN-TEC Corporation

Robert A. Ellis and Richard A. Ellis, David L. Ellis Co., Inc.

Thomas P. Farrell, Mitutoyo America Corporation

Giancarlo Mazzoleni and Douglas B. McGhee, Newage Testing

Instruments, Inc.

Michael L. Milalec and Richard J. Snow, Gilmore Diamond Tools, Inc.

Paul M. Mumford, United Calibration Corporation

Edward L. Tobolski, Wilson Division of Instron Corporation

The author would also like to thank present and former NIST co-workers

James L. Fink, Carole D. Flanigan, Robert J. Gettings, Walter S. Liggett, Jr.,

David J. Pitchure, John H. Smith, and John Song for their contributions towards

the Rockwell hardness standardization program at NIST.

◆

*The acknowledgements of the persons and companies listed above should

not be interpreted as an endorsement by NIST of their products or services.

...........................................................

v
Table of Contents ◆

List of Figures ..................................................................................... .....................................................................................ix

List of Tables ...................................................................................... ......................................................................................xii

1. Introduction .................................................................................... ....................................................................................1

2. Rockwell Hardness Test................................................................ ................................................................2

2.1 Significance of the test .............................................................2

2.2 Rockwell indentation test principle ............................................2

2.3 Rockwell hardness scales ........................................................4

2.4 Rockwell hardness number ......................................................4

2.5 Test method standards .............................................................6

3. Test Procedure ............................................................................... ...............................................................................9

3.1 Choosing the appropriate Rockwell scale ................................9

3.2 Test surface preparation .........................................................13

3.3 Rockwell hardness testing machine .......................................13

3.4 Hardness measurement.........................................................26

4. Reference Test Block Standards ................................................ ................................................37

4.1 Primary reference test blocks ................................................37

4.2 Secondary reference test blocks............................................40

4.3 Use of reference test block standards ...................................41

5. Verifications of Rockwell Hardness Machines ......................... .........................44

5.1 Direct verification ....................................................................44

5.2 Indirect verification..................................................................47

5.3 Correcting measurement biases ............................................49

6. Monitoring Test Machine Performance ..................................... .....................................51

6.1 Reproducibility ........................................................................51

6.2 Daily verification .....................................................................52

vii
viii

7. Reducing Measurement Differences and Errors...................... ......................53

7.1 Reduce machine component operating errors .......................53

7.2 Verify machine measurement performance ...........................53

7.3 Measurement locations ..........................................................55

8. Traceability, Error, and Uncertainty ........................................... ...........................................56

8.1 Traceability ..............................................................................56

8.2 Measurement error .................................................................58

8.3 Uncertainty .............................................................................58

9. Status of Rockwell Hardness Standardization

in the Year 2000 ............................................................................ ............................................................................63

9.1 United States ..........................................................................63

9.2 International ............................................................................65

10. Bibliography ................................................................................. .................................................................................69

Annex A: Annex A: Applied Force Effect Applied Force Effect........................................................ ........................................................71

Annex B: Annex B: Rockwell Hardness Testing Cycle Ef esting Cycle Effect ...................... ......................73

B.1 Effect of force application rate ................................................74

B.2 Effect of dwell times ................................................................78

Annex C: Annex C: Use of NIST Rockwell C Scale SRM Test Blocks.......... ..........84

C.1 Recommendations for use .....................................................84

C.2 Calculation of certified values for arbitrary locations ..............86

◆ Table of Contents
List of Figures

Figure 1: Plots of force vs. time (a) and indenter-depth vs.

time (b) for an HRC test illustrating the testing

cycle parts and the difference in indenter depth

measurements h .................................................................. 3

Figure 2: Force vs. time plot (Figure A) and indenter-depth vs.

time plot (Figure B) demonstrating the effect of an

increase in the preliminary-force for a Rockwell

HRA test ............................................................................. 16

Figure 3: Force vs. time plot (Figure A) and indenter-depth vs.

time plot (Figure B) demonstrating the effect of an

increase in the total-force for a Rockwell HRA test............ 17

Figure 4: Diagram of cross-sectional view of spheroconical

diamond indenter tip ........................................................... 24

Figure 5: Eight steps of the Rockwell test cycle ............................... 28

Figure 6: Four examples of the hardness profile across the

test surface of 25 HRC test blocks, illustrating how

the non-uniformity in hardness can vary within a

block and differs from block to block. Each line

represents a hardness change of 0.02 HRC.

Light to dark areas represent hard to soft areas. ............... 38

Figure 7: Hardness profile across the test surface of a NIST

test block. The NIST calibration measurements are

indicated by the solid circles, and the locations of

the certified values for untested locations are

indicated by the open circles .............................................. 40

Figure 8: Alternate pattern for repeatability measurements. ............. 48

Figure 9: Illustration of the three bias points corrected by a

linear fit correction curve .................................................... 50

Figure 10: Illustration of reproducibility data taken over ten days ....... 51

Figure 11: NIST Rockwell hardness standardizing machine .............. 57

Table of Contents ◆

ix
x

Figure 12: General trend of the difference between NIST and

U.S. industry Rockwell C scales. The line represents

the approximate increase in the HRC scale as

determined by NIST (for hardness levels as indicated

on the bottom axis) with respect to the HRC scale

used by U.S. industry prior to development of the

NIST scale. ....................................................................... 64

Figure 13: Results of 1999 international comparison of HRC

scale. The heavy line indicates the NIST data. ................ 67

Figure A.1: Change in the Rockwell hardness value due to a

change in the preliminary force for diamond indenter

scales (Figure A) and selected ball scales (Figure B)...... 71

Figure A.2: Change in the Rockwell hardness value due to a

change in the total force for diamond indenter scales

(Figure A) and selected ball scales (Figure B) ................. 71

Figure A.3: The possible offset in Rockwell hardness measurement

values that could be obtained for the diamond indenter

scales by varying the applied preliminary forces and

total forces within the ASTM tolerances (Figure A)

and the ISO tolerances (Figure B) .................................... 72

Figure B.1: Force and indenter depth oscillations that can

occur when the force application rate is too fast ............... 76

Figure B.2: Change in apparent HRC hardness due to changes in

the additional force application rate (indenter velocity)..... 77

Figure B.3: Expanded view of the material creep and recovery

during the dwell times of a Rockwell hardness test .......... 78

Figure B.4: Relationship between the preliminary force dwell

time and the HRC measurement value for steel

test blocks at three hardness levels ................................. 79

Figure B.5: Relationship between the total force dwell time and

the HRC measurement value for steel test blocks

at three hardness levels. .................................................. 80

Figure B.6: Relationship between the total force dwell time and the

HRB measurement value for brass test blocks at three

hardness levels. ............................................................... 81

◆ Table of Contents
Figure B.7 Relationship between the recovery dwell time and the

HRC measurement value for steel test blocks at three

hardness levels. ............................................................... 82

Figure C.1 Test block surface illustrating the locations

(letters A through K) of certified hardness values

given in Table C.2 ............................................................. 87

Figure C.2 Test surface of the Rockwell hardness SRMs

indicating the location and sequence of certification

indentations ....................................................................... 90

Table of Contents ◆

xi
xii

List of Tables

Table 1: Rockwell hardness scales with the corresponding

indenter type, applied forces and typical applications ......... 5

Table 2: Ranges of Rockwell scales given in ISO standards ......... 12

Table A.1: Specified test forces with tolerances ................................. 72

Table C.1: Hypothetical certified hardness values for the

average of six specific test block locations as

illustrated in Figure C.1 ...................................................... 87

Table C.2: Hypothetical certified hardness values for specific

test block locations. The x - y coordinate system is such

that location x = 0, y = 0 is at the block center (NIST

indentation 4), and oriented with the NIST logo at the

bottom of the block as illustrated in Figure C.1 ................. 88

Table C.3: Hypothetical semivariogram coefficients that

describe test block nonuniformity and repeatability .......... 89

Table C.4: Hypothetical NIST hardness readings for specific test

block locations................................................................... 89

Table C.5: Matrix Γ ............................................................................ 91

Table C.6: Inverse matrix Γ -1 with elements gij ................................. 91

Table C.7: Sources of uncertainty for the certified average HRC

hardness value with hypothetical values to be used

in the examples ................................................................. 92

Table C.8: The coordinates for the locations used in the

calculations of Example 2 ............................................... 100

◆ Table of Contents
1

Introduction ◆

1 INTRODUCTION

Working in a ball-bearing manufacturing plant in 1919, Stanley P. Rockwell

invented the Rockwell hardness test as a tool for obtaining a rapid and

more accurate measure of the hardness of ball races(1). Soon after,

Charles H. Wilson expanded on Rockwell’s invention, and he advanced the

Rockwell hardness test into what is today the most widely used method for

acceptance testing and process control of metals and metal products. Since

its development, the popularity of the Rockwell hardness test has steadily

grown. The Rockwell hardness test continues to be applied as a tool for

assessing the properties of a product while the tolerances on the acceptable

material hardness have become tighter and tighter. The once-thought-of

manufacturing tool has developed into a metrological instrument. To achieve

meaningful measurement results in these circumstances, it is important that

the user make every effort to reduce measurement errors. This is more easily

accomplished when the influences contributing to the error in a Rockwell

hardness test are known, and there is an understanding of what can be done to

reduce these errors. Adhering to “good practice” procedures when performing

Rockwell hardness measurements and calibrations is a crucial step to reducing

measurement errors.

The purpose of this Guide is not to specify the requirements for conducting

a Rockwell hardness test. Test method standards published by national and

international standards writing organizations, such as the American Society for

Testing and Materials (ASTM) and the International Standards Organization

(ISO), provide specific requirements and procedures for Rockwell hardness

testing. The intention of this Guide is to explain the causes of variability in

Rockwell hardness test results and to supplement the information given in test

method standards with good practice recommendations. Although this Guide

is directed more towards the users of Rockwell hardness having the greatest

concern for accuracy in their measurements, much of the information given

is also applicable for users that only require test results to be within wide

tolerance bands, where high accuracy is not as critical. It is recognized that

Rockwell hardness is often used for testing non-metallic materials such as

plastics; however, this Guide is primarily applicable to the testing of metallic

materials.

This Guide also provides recommendations for conducting verifications of

Rockwell hardness machines based on the procedures specified by the test

method standards. Some procedures recommended by this Guide exceed

current requirements of the test methods; however, they can be very useful

in helping to determine and limit sources of measurement error.
2

2 ROCKWELL HARDNESS TEST

2.1 Significance of the Test

The Rockwell hardness test is an empirical indentation hardness test. Its

worldwide adoption has likely resulted from the many advantages provided by

the test method. The test is fast, inexpensive, and relatively non-destructive,

leaving only a small indentation in the material. The simplicity in the operation

of a Rockwell hardness machine has provided the added advantage that

Rockwell hardness testing usually does not require a highly skilled operator.

By way of correlation with other material properties, the Rockwell hardness

test can provide important information about metallic materials, such as the

tensile strength, wear resistance, and ductility. The test is generally useful for

material selection, for process and quality control, and for acceptance testing

of commercial products. Consequently, in today’s manufacturing facilities,

Rockwell hardness machines can be found in use in almost every testing

environment, from the hot, oily surroundings of some manufacturing facilities,

to environmentally controlled metallographic and calibration laboratories.

2.2 Rockwell Indentation Test Principle

The Rockwell hardness test is one of several common indentation

hardness tests used today, other examples being the Brinell hardness test

and Vickers hardness test. Most indentation hardness tests are a measure of

the deformation that occurs when the material under test is penetrated with a

specific type of indenter. In the case of the Rockwell hardness test, two levels

of force are applied to the indenter at specified rates and with specified dwell

times, as illustrated for the Rockwell C scale (HRC) test in Figure 1. Unlike

the Brinell and Vickers tests, where the size of the indentation is measured

following the indentation process, the Rockwell hardness of the material is

based on the difference in the depth of the indenter at two specific times during

the testing cycle, indicated by the X marks in Figure 1. The value of hardness

is calculated using a formula that was derived to yield a number falling within

an arbitrarily defined range of numbers known as a Rockwell hardness scale.

Because the hardness value is dependent on the definition of the test method,

there are no alternative measurement systems to directly or independently

measure Rockwell hardness, nor are there intrinsic artifacts to reference.

The general Rockwell test procedure is the same regardless of the Rockwell

scale or indenter being used. The indenter is brought into contact with the

material to be tested, and a preliminary force (formally referred to as the minor

load) is applied to the indenter. The preliminary force is usually held constant

for a set period of time (dwell time), after which the depth of indentation is

measured. After the measurement is made, an additional amount of force is

◆ Rockwell Hardness Test
3

Figure 1. Figure 1.

Plots of force vs. time (a) and indenter-depth vs. time (b)

for an HRC test illustrating the testing cycle parts and

the difference in indenter depth measurements h.

(a)

(b)

Increasing Time

0

20

40

60

80

100

120

140

160

180

Force (kgf)

0

200

400

600

800

1000

1200

1400

1600

1800

Force (N)

First Depth

Measurement Final Depth

Measurement

Preliminary Force

Dwell Time

Total Force

Dwell Time

Recovery

Dwell Time

Additional Force

Application Time

F

F0

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

Indenter Depth (mm)

h

First Depth

Measurement

Final Depth

Measurement

Rockwell Indentation Test Principle ◆
4

applied at a set rate to increase the applied force to the total force level

(formally referred to as the major load). The total force is held constant for

a set time period, after which the additional force is removed, returning to the

preliminary force level. After holding the preliminary force constant for a set

time period, the depth of indentation is measured for a second time, followed

by removal of the indenter from the test material. The measured difference

between the first and second indentation depth measurements, h, (see

Figure 1) is then used to calculate the Rockwell hardness number. For many

older models of Rockwell hardness machines, the operator must manually

control most or all of the steps of the test procedure. Many of today’s newer

machines automatically perform the entire Rockwell test.

2.3 Rockwell Hardness Scales

Many manufactured products are made of different types of metals and alloys

varying in hardness, size, and thickness. To accommodate the testing of these

diverse products, several different indenter types (as discussed in 3.3.8) were

developed for the Rockwell test to be used in conjunction with a range of

standard force levels. Each combination of indenter type and applied force

levels has been designated as a distinct Rockwell hardness scale. The ASTM(2)

defines thirty different Rockwell scales, as shown in Table 1. Rockwell

hardness scales are divided into two categories: regular Rockwell scales and

superficial Rockwell scales. Both categories of tests use the same types of

indenters. The regular Rockwell scales employ the heavier force levels. For

these scales, the preliminary force level is 98.07 N (10 kgf), and the standard

total force levels may be 588.4 N (60 kgf), 980.7 N (100 kgf) or 1471 N (150

kgf). The superficial Rockwell scales employ lighter force levels, typically for

use on thinner materials. For the superficial Rockwell scales, the preliminary

force level is 29.42 N (3 kgf), and the standard total force levels may be 147.1

N (15 kgf), 294.2 N (30 kgf) or 441.3 N (45 kgf). Table 1 provides typical

applications for the different Rockwell scales as recommended by ASTM(2),

and it lists the appropriate type of indenter and force levels to be used with the

particular scale.

2.4 Rockwell Hardness Number

A Rockwell hardness measurement is reported as a Rockwell hardness

number, without units. The Rockwell hardness number is calculated from

the difference in the indentation depths before and after application of the

total force, while maintaining the preliminary test force. The difference in

indentation depths is measured as h as described above. The calculation of

the Rockwell hardness number is dependent on the specific combination of

indenter type and the forces that are used.

◆ Rockwell Hardness Test
5

For scales that use a spheroconical diamond indenter, the Rockwell hardness

number is calculated from h (in mm) as:

Scale 

Symbol 

Indenter Type 

(Ball dimensions indicate diameter.) 

Preliminary 

Force 

N (kgf) 

Total Force 

N (kgf) Typical Applications 

A Spheroconical Diamond 98.07 (10) 588.4 (60) Cemented carbides, thin steel, and shallow case 

hardened steel. 

B Ball - 1.588 mm (1/16 in.) 98.07 (10) 980.7 (100) Copper alloys, soft steels, aluminum alloys, 

malleable iron, etc. 

C Spheroconical Diamond 98.07 (10) 1471 (150) 

Steel, hard cast irons, pearlitic malleable iron, 

titanium, deep case hardened steel, and other 

materials harder than HRB 100. 

D Spheroconical Diamond 98.07 (10) 980.7 (100) Thin steel and medium case hardened steel, and 

pearlitic malleable iron 

E Ball - 3.175 mm (1/8 in.) 98.07 (10) 980.7 (100) Cast iron, aluminum and magnesium alloys, and 

bearing metals 

F Ball - 1.588 mm (1/16 in.) 98.07 (10) 588.4 (60) Annealed copper alloys, and thin soft sheet metals. 

G Ball - 1.588 mm (1/16 in.) 98.07 (10) 1471 (150) Malleable irons, copper-nickel-zinc and cupronickel alloys. 

H Ball - 3.175 mm (1/8 in.) 98.07 (10) 588.4 (60) Aluminum, zinc, and lead. 

K Ball - 3.175 mm (1/8 in.) 98.07 (10) 1471 (150) 

L Ball - 6.350 mm (1/4 in.) 98.07 (10) 588.4 (60) 

M Ball - 6.350 mm (1/4 in.) 98.07 (10) 980.7 (100) 

P Ball - 6.350 mm (1/4 in.) 98.07 (10) 1471 (150) 

R Ball - 12.70 mm (1/2 in.) 98.07 (10) 588.4 (60) 

S Ball - 12.70 mm (1/2 in.) 98.07 (10) 980.7 (100) 

Regular Rockwell Scales 

V Ball - 12.70 mm (1/2 in.) 98.07 (10) 1471 (150) 

Bearing metals and other very soft or thin materials. 

Use smallest ball and heaviest load that does not 

give anvil effect. 

15N Spheroconical Diamond 29.42 (3) 147.1 (15) 

30N Spheroconical Diamond 29.42 (3) 294.2 (30) 

45N Spheroconical Diamond 29.42 (3) 441.3 (45) 

Similar to A, C and D scales, but for thinner gage 

material or case depth. 

15T Ball - 1.588 mm (1/16 in.) 29.42 (3) 147.1 (15) 

30T Ball - 1.588 mm (1/16 in.) 29.42 (3) 294.2 (30) 

45T Ball - 1.588 mm (1/16 in.) 29.42 (3) 441.3 (45) 

Similar to B, F and G scales, but for thinner gage 

material. 

15W Ball - 3.175 mm (1/8 in.) 29.42 (3) 147.1 (15) 

30W Ball - 3.175 mm (1/8 in.) 29.42 (3) 294.2 (30) 

45W Ball - 3.175 mm (1/8 in.) 29.42 (3) 441.3 (45) 

15X Ball - 6.350 mm (1/4 in.) 29.42 (3) 147.1 (15) 

30X Ball - 6.350 mm (1/4 in.) 29.42 (3) 294.2 (30) 

45X Ball - 6.350 mm (1/4 in.) 29.42 (3) 441.3 (45) 

15Y Ball - 12.70 mm (1/2 in.) 29.42 (3) 147.1 (15) 

30Y Ball - 12.70 mm (1/2 in.) 29.42 (3) 294.2 (30) 

Superficial Rockwell Scales 

45Y Ball - 12.70 mm (1/2 in.) 29.42 (3) 441.3 (45) 

Very soft material. 

Table 1. able 1.

Rockwell hardness scales with the corresponding indenter type,

applied forces and typical applications

Regular Rockwell Hardness h

mm = − 1000 002 .

Rockwell Superficial Hardness h

mm = − 1000 001 . . 

Rockwell Hardness Number ◆
6

For scales that use a ball indenter, the Rockwell hardness number is calculated

from h (in mm) as:

2.5 Test Method Standards

The Rockwell hardness test method is specified by several national and

international standards. In North America, most Rockwell hardness testing is

performed in accordance with standards published by the ASTM(2). In other

countries throughout the world, industry testing may be in accordance with a

nationally published standard, but increasingly, countries are adopting the ISO

Rockwell hardness standards(3,4,5). The International Organization of Legal

Metrology (OIML) publishes Rockwell hardness documents referred to as

International Recommendations(6,7,8,9) for countries desiring to regulate

Rockwell hardness testing for legal purposes. Presently, use of the OIML

documents is very meager. Listed below are the document standards specifying

requirements for Rockwell hardness testing, as well as other documents related

to Rockwell hardness testing.

2.5.1 ASTM

ASTM E 18 – 2000, Standard Test Methods for Rockwell Hardness and

Rockwell Superficial Hardness of Metallic Materials

Related ASTM standards:

ASTM E 110 – 82 (Reapproved 1997), Standard Test Method for

Indentation Hardness of Metallic Materials by Portable Hardness Testers

ASTM E 140 – 97, Standard Hardness Conversion Tables for Metals

To contact or order documents:

ASTM

100 Barr Harbor Drive

West Conshohocken, PA 19428-2959

Phone: (610) 832–9585 Fax: (610) 832–9555

E-mail: service@astm.org

http://www.astm.org

Regular Rockwell Hardness h

mm = − 1300 002 .

Rockwell Superficial Hardness h

mm = − 1000 001 . . 

◆ Rockwell Hardness Test
7

ASTM standards can be purchased in the Store area of the ASTM web site.

Using a credit card, you can download standards to your own computer;

receive standards by fax, or by traditional mail. Standards vary in cost,

based on their length. Average cost for an ASTM standard is about $25.

A subscription service is also offered where subsets of standards can be

accessed for a set fee. Standards can also be purchased from ASTM by

contacting ASTM’s Customer Service Department at (610) 832–9585,

Monday through Friday, 8AM-5PM Eastern Time.

2.5.2 ISO

ISO 6508-1 Metallic Materials – Rockwell hardness test (scales A, B, C, D,

E, F, G, H, K, N, T) – Part 1: Test method, 1999-09-01

ISO 6508-2 Metallic Materials – Rockwell hardness test (scales A, B, C, D,

E, F, G, H, K, N, T) – Part 2: Verification of testing machines, 1999-09-01

ISO 6508-3 Metallic Materials – Rockwell hardness test (scales A, B, C, D,

E, F, G, H, K, N, T) – Part 3: Calibration of reference blocks, 1999-09-01

To contact or order documents:

American National Standards Institute

11 West 42nd Street

13th floor

US – New York, N.Y. 10036

Telephone: +1 212 642 49 00 Fax: +1 212 398 00 23

E-mail: info@ansi.org

http://www.ansi.org/

Electronic copies of ISO standards may be purchased from ANSI’s Electronic

Standards Store at the American National Standards Institute web site. Paper

copies of ISO standards may be purchased from Global Engineering

Documents as follows:

Global Engineering Documents

Phone: 800–854–7179 or 303–397–7956

Fax: 303–397–2740

Email: global@ihs.com

http://www.global.ihs.com

Test Method Standards ◆
8

2.5.3 OIML

OIML International Recommendation No. 11 (1974), Verification and

calibration of “Rockwell B” hardness standardized blocks

OIML International Recommendation No. 12 (1974), Verification and

calibration of “Rockwell C” hardness standardized blocks

OIML International Recommendation No. 36 (1976), Verification of

indenters for hardness testing machines (Systems: Brinell – Rockwell B, F,

and T – Vickers – Rockwell C, A, and N)

OIML International Recommendation No. 39 (1981), Verification of

hardness testing machines (Rockwell B, F, T - C, A, N systems

To contact or order documents:

OIML Publications may be purchased (in French and in English in most cases)

from the Organization’s Secretariat (BIML).

Bureau International de Métrologie Légale

11, rue Turgot

F-75009 Paris

France

Tel.: +33 (0) 1 48 78 12 82 and 42 85 27 11 Fax: +33 (0) 1 42 82 17 27

E-mail: biml@oiml.org

http://www.oiml.org/

◆ Rockwell Hardness test
9

3 TEST PROCEDURE

Numerous aspects of the Rockwell hardness test can influence the

measurement result. These include the function and calibration of individual

components of the hardness machine, variations in the indenter, the testing

cycle that is used, the testing environment, the condition of the test material,

and the operator. When considering all of these influences, it seems remarkable

that the Rockwell test has provided such a reliable test throughout its long

usage. Much of the test’s reliability may be attributed to the common practice

of performing periodic verifications of the testing machine, often several times

during a day.

When a high level of accuracy is important, it is usually necessary to put

more effort into a measurement process than is specified by test method

standards(10). As with any method of measurement, it is beneficial to identify

the significant sources of error in a Rockwell hardness measurement so that an

attempt can be made to reduce the errors and, thus, improve accuracy. Through

an understanding of how the various test influences can affect a Rockwell

hardness measurement, it becomes evident that a considerable difference in

hardness results can be obtained for the same test sample merely by varying

one or more of the test parameters. The difference in test results can be

significant, even while remaining within the individual parameter tolerances

specified by test method standards. It is also likely that many Rockwell

machines are adjusted to offset one error with another error in order to

correctly measure reference standards.

The ASTM and ISO test method standards specify the general procedures

to use when performing a Rockwell hardness test. In addition, the instruction

manual supplied with most testing machines normally provides supplementary

details on specific operational procedures. This section will discuss procedures

and precautions to be applied to general Rockwell hardness testing. It will not

cover specialized procedures for testing the vast varieties of materials and part

geometries for which Rockwell hardness may be used. It should be noted that

there are many specialized fixtures, indenters, anvils, and testing machine

configurations that are commercially available for the testing of large parts,

long parts, inner surfaces, curved surfaces, and other complex shaped

parts(1,11,12,13). This section will also discuss several of the more significant

sources of error of the Rockwell hardness test. These include the influences

of the hardness machine, indenters, testing cycle, testing environment, and

other factors that may affect the reproducibility of the test.

3.1 Choosing the Appropriate Rockwell Scale

The ASTM specifies thirty different Rockwell scales, each employing a

different combination of test forces and indenter types, which allows the testing

Test Procedure ◆
10

of most types of metallic materials and products. When Rockwell hardness is

called out by a product standard or specification, the choice of scale is usually

specified. In situations where the user must choose the appropriate Rockwell

scale, there are several factors that should be considered. These include the

type of test material, the test material thickness, the test material area or width,

the test material homogeneity, and the limitations of each Rockwell scale.

3.1.1 Type of Test Material est Material

Table 1 lists the typical types of materials that are suitable for testing on

each of the thirty Rockwell hardness scales. When deciding on an appropriate

Rockwell scale for a particular material, information in this table can assist the

user in narrowing down the number of scales to choose from.

3.1.2 Test Material Thickness

As a Rockwell hardness measurement is being made, the material surrounding

the indentation is plastically deformed with the deformation extending well

below the indentation depth. If the deformation extends completely through

the thickness of thin test material, then the deformed material will flow at the

interface with the supporting anvil. This will influence the deformation process

likely causing the test to give erroneous hardness results. Thus, the test

material must have a sufficient thickness in order to obtain a valid Rockwell

test value. Similarly, for products that are manufactured to a specific thickness,

a Rockwell scale having the appropriate combination of test forces and

indenter size must be chosen based on that thickness.

When the approximate hardness of the test material is known, the minimum

thickness needed to obtain valid Rockwell measurements may be estimated

from data tables and graphs available in the literature, such as in the ASTM

standard(2). In general, the zone of deformation extends no more than 10 times

the depth of indentation for a diamond indenter test and 15 times the depth of

indentation for a ball indenter. As a rule, there should be no deformation on the

support side of the test material following a Rockwell test, although such

markings are not always indicative of a bad test.

Testing Precautions

• Testing of too thin material can damage a steel anvil by marring the surface

or producing a small indentation. In either case, further testing should not

continue with the damaged anvil.

• Stacking one or more additional layers of metallic material together cannot

make up for an insufficient material thickness. The material flow between

the layers will produce inaccurate measurements.

×

◆ Test Procedure
11

• If the objective of the Rockwell test is to measure the hardness of a surface

feature such as a case-hardened surface, the scale chosen should be based

on the thickness of this surface feature.

3.1.3 Test Material est Material Area (or Width)

In the same way that the deformation extends below an indentation, thus

limiting the minimum material thickness, the deformation also extends outward

through the material width. If a Rockwell measurement is made near the edge

of the test material, the deformation surrounding the indentation may extend to

the edge and push out the material, thus lowering the measured hardness value.

This effect is more significant for softer materials. The general rule as

specified by the test method standards is that the distance between the center

of an indentation and the edge of the material must be at least 21⁄2 times the

diameter of the indentation. The ISO test method standard(3) also specifies that

the distance must not be less than 1 mm. Therefore, in cases where Rockwell

hardness testing is to be made on narrow width material or material having a

small area size, a Rockwell scale must be chosen that produces indentations

small enough to prevent this edge interaction.

3.1.4 Test Material Homogeneity

The size and location of metallurgical features in the test material should

be considered when choosing the Rockwell scale. For materials that are

not homogeneous, an appropriate Rockwell scale should be chosen that

would produce a sufficiently large indentation to obtain a hardness value

representative of the material as a whole. Also keep in mind that the area

surrounding a Rockwell indentation also affects the test result (see above

discussions). If the deformation zone surrounding a Rockwell indentation

extends into adjacent regions of a differing hardness, such as the heat affected

zone of a weld, the test measurement may be influenced. In such cases, a

Rockwell scale should be chosen that uses test forces and indenters that

produce a small enough indentation to avoid the influence of these areas.

3.1.5 Scale Limitations

Each Rockwell scale is an arbitrarily defined range of numbers from 0 to 100†

covering a specific range of material hardness. Although, theoretically, the

entire scale can be used for hardness testing, there are practical limitations on

the range of testing for many of the Rockwell scales. At the low hardness end

of the scales, these limits result from the indenter penetrating too deeply into

the material, possibly causing contact with the indenter cap for ball indenters.

Choosing the Appropriate Rockwell Scale ◆

†Regular Rockwell scales using a ball indenter hypothetically could obtain Rockwell values

greater than 100 up to 130.
12

In the case of diamond indenters, the sensitivity of the test diminishes as the

diamond indenter penetrates further down the conical portion of the diamond.

At the high hardness end of the scales, these limits result from the likelihood of

fracturing or significantly reducing the life of a diamond indenter. In the case of

ball indenters, the sensitivity of the test diminishes, and there is increased

possibility of flattening a steel indenter ball. The ISO standard(3) suggests the

limits given in Table 2 for some Rockwell scales.

Recommended Ranges of Rockwell Scales 

20 to 88 HRAA 70 to 94 HR15N 

20 to 100 HRBB 42 to 86 HR30N 

20 to 70 HRC 20 to 77 HR45N 

40 to 77 HRD 67 to 93 HR15T 

70 to 100 HRE 29 to 82 HR30T 

60 to 100 HRF 1 to 72 HR45T 

30 to 94 HRG 

80 to 100 HRH 

40 to 100 HRK 

A

Rockwell testing of tungsten carbide commonly produces hardness values 

above 88 HRA. 

B

Rockwell B scale testing is sometimes made on materials in the range of 0 to 

20 HRB. 

Table 2. able 2.

Ranges of Rockwell scales given in ISO standards

★ Good Practice Recommendations

• When several Rockwell scales are acceptable for testing a material,

generally, the most commonly used scale for the type of material to be

tested should be chosen. In cases where this Rockwell scale is not

appropriate for the particular application, the scale employing the highest

forces may be the best choice. The highest force will produce the largest

indentation covering more of the test material, and it will provide a Rockwell

hardness value more representative of the material as a whole. Additionally,

the highest test forces provide the most sensitivity in Rockwell hardness

testing.

◆ Test Procedure
13

• In circumstances where the user wants to compare measurements with

previously obtained Rockwell hardness data, the same scale should be

chosen as was used for the previous testing as long as a valid test can

be obtained. This is preferred to testing on one Rockwell scale and then

converting the data to another Rockwell scale by way of conversion tables.

Converted data is never as accurate as the original measurement.

• If the approximate hardness of a material is not known, a diamond indenter

scale should be tried first. A diamond indenter is not likely to be damaged

by penetrating too deeply into a soft material, whereas a ball indenter may

be flattened or damaged if the material is too hard.

3.2 Test Surface Preparation

An important feature of the Rockwell hardness test procedure is the use of

the preliminary force as part of the testing cycle. Application of the preliminary

force acts to push the indenter through minor surface imperfections and to

crush residual foreign particles present on the test surface. By establishing a

reference beneath the surface prior to making the first depth measurement, it

allows testing of materials with slight surface flaws while maintaining much of

the test accuracy. Still, as a general rule, the better a test surface is prepared,

the more likely the measurement will represent the true Rockwell hardness

value of a material.

For the best results, the test surface and the surface in contact with the

support anvil should be smooth, flat, and free of oxides, foreign matter, and

lubricants. The test surface should be prepared in a manner that will not alter

the properties of the test material such as by overheating or cold-working.

The test surface should be representative of the material under test. For that

reason, surface effects, such as carburization or decarburization, should be

removed prior to testing, unless the purpose of the test is to measure these

surface features. Similarly, other types of coatings, such as paint, galvanizing,

etc., should also be removed prior to testing.

The degree of surface roughness that can be tolerated depends on the

force levels to be applied. A finish ground surface is usually sufficient for the

Rockwell C scale and for the Rockwell ball scales that apply a force of at least

980.7 N (100 kgf). In general, lighter test forces require better surface finishes.

For the superficial scales that use a total force of 147.1 N (15 kgf), a polished

surface is usually required.

3.3 Rockwell Hardness Testing Machine

There are many designs of commercially manufactured Rockwell hardness

testing machines. The testing machines discussed in this Guide and specified

Choosing the Appropriate Rockwell Scale ◆
14

by the referenced test method standards are limited to only those types of

machines capable of performing a true “Rockwell indentation hardness test.”

Sometimes a true Rockwell test cannot be performed due to the size of the part

or its configuration. There are other devices and instruments on the market

that can be used in many of these situations, which can also report a Rockwell

hardness number. However, the measurement methods used by these devices

are not in accordance with the Rockwell indentation hardness principle. These

devices employ other test principles, such as striker rebound or eddy-current,

and make measurements to which a Rockwell number is correlated. These

devices may have some advantages, such as portability, but they cannot report

a true Rockwell hardness number.

There have been many improvements in the designs of Rockwell hardness

testers over the past 50 years. The most significant improvements have

been in the manner in which the forces are applied, the manner in which the

indentation depth is measured and the hardness value displayed, and in the

automation of the testing machine’s operation. Remarkably, many of the older

designs of Rockwell machines are still in use, so that a brief discussion of the

differences may be beneficial.

★ Good Practice Recommendation

Not all Rockwell hardness machines are equal. All machines may be capable

of performing a Rockwell hardness test in accordance with the requirements

specified in test method standards, but some may be more suitable for your

specific needs. When choosing a Rockwell hardness machine, consider factors

such as: the accuracy and measurement repeatability that is required; whether

versatility in the testing cycle may be required; the required speed of testing;

the Rockwell scales that will be used; the required resolution of the hardness

number; the size of material normally tested; and the accessories that may be

needed.

Testing Precautions

When using devices that employ measurement methods other than the

Rockwell indentation hardness principle, the type of measurement device that

was used should be reported with the correlated Rockwell numbers. This

information provides the user of the measurement data a better understanding

of how the data was obtained.

3.3.1 Scales That Can Be Tested

Because the regular Rockwell and superficial Rockwell tests use distinctly

different levels of force and two different resolutions of depth measurement,

×

◆ Test Procedure
15

most Rockwell machines in the past were designed to test only regular

scales or superficial scales. This has become less true today as new machine

development has produced many Rockwell machines designs that are capable

of testing both regular and superficial scales, sometimes referred to as “twin

testers” or “combination testers.” These machines usually can test all of the

different Rockwell scales, and, in some cases, they can also perform other

types of hardness tests.

3.3.2 Force Application Mechanism

Since its development, the most common designs of Rockwell machines

have applied the preliminary test force by compression of a helical spring,

and have applied the total force by dead weights through a force multiplying

lever system. With many years of usage, it is not unusual to find that in older

machines the preliminary force springs and the knife-edges supporting the total

force lever arms have become worn causing errors in the application of the

forces.

With the advent of reliable electronically controlled feedback systems, new

machine designs have been developed such as machines that apply the forces

with a screw-driven device controlled by a load-cell to monitor the applied

force. The new designs have the advantage that the testing cycle can be fully

controllable, and errors associated with a lever arm or preliminary force spring

are eliminated; however, different errors may be introduced associated with

the load-cell or electronics. Lever-arm/spring design machines are continually

being improved and are in common use today as reliable testing instruments,

but the trend of many Rockwell machine manufacturers is towards developing

load-cell design machines.

By varying either the preliminary force level or the total force level, different

Rockwell hardness measurement values can be obtained for the same material.

The reason for this is illustrated in Figure 2A, Figure 2B, Figure 3A, and

Figure 3B, which are plots of Rockwell A scale (HRA) test data measured at

NIST(14). Figure 2A illustrates the sequence of how the test forces are applied

during the HRA test, with the resulting indentation depth shown in Figure 2B.

Each figure shows two overlapping HRA tests; the solid line represents a test

using the standard preliminary force of 98.07 N (10 kgf), and the dashed line

represents a test where the preliminary force was increased to 103.95 N

(10.6 kgf). The test having the higher preliminary force (dashed line) resulted

in a slightly increased indentation depth at the first application of preliminary

force. Changing the preliminary force level appears to have had negligible

effect on the remaining part of the hardness test. Thus, an increase in the

level of the preliminary force causes an increase in the indentation depth at

the first application of preliminary force. This reduces the measurement value,

Rockwell Hardness Testing Machine ◆
16

h, used for the calculation of the Rockwell hardness number and results in a

higher hardness value. For the same reasons, a decrease in the level of the

preliminary force results in a lower hardness value.

◆ Test Procedure

Increasing Time 

Increasing Force 



Increasing Time 

Increasing Indenter Depth

Fig. A Fig. B

h

due to

103.95 N

(10.6 kgf)

Preliminary

Force 

h

due to

98.07 N

(10.0 kgf)

Preliminary

Force 

Figure 2. Figure 2.

Force vs. time plot (Figure A) and indenter-depth vs. time plot (Figure B)

demonstrating the effect of an increase in the preliminary-force

for a Rockwell HRA test.

Figure 3A and Figure 3B illustrate what occurs when the total force level is

increased. The test having the higher total force (dashed line) resulted in an

increased indentation depth at the application of total force. Following the

application of total force, as the additional force is removed returning to the

preliminary force level, most of the increased increment in indentation depth is

maintained. The increased indentation depth enlarges the measurement value,

h, and, thus, results in a lower hardness value. This is the opposite effect of

that discussed previously (shown in Figure 2) for an increase in the preliminary

force level. Additional tests have shown the two effects to be essentially

independent of each other and, therefore, additive in their effect.

The magnitudes of the effects that changes in the preliminary and total forces

have on the Rockwell hardness measurement value are given in Appendix A

for the Rockwell scales that use a diamond indenter and the Rockwell scales

that use a 1.588 mm (1/16 in) diameter ball indenter. Also in Appendix A,

data is presented illustrating the magnitude of measurement variation that

can be obtained for the Rockwell scales that use a diamond indenter while

maintaining the force levels within the ASTM and ISO tolerances. From this

data it is seen that a variation of ± 0.5 Rockwell units can easily be achieved

for some hardness levels simply by adjusting the force levels within the

acceptable tolerance limits.
17

3.3.3 Depth Measurement; Hardness Value Calculation and Display

The dial indicating-gage was the original method used in Rockwell machines

for measuring the indentation depth and for calculating and displaying the

Rockwell hardness number. Due to the simplicity of its operation, it continues

to be used in some of today’s Rockwell machine designs. The general principle

of its operation is to mechanically measure the movement of the indenter

through a multiplying lever system. The dial face is calibrated to indicate the

Rockwell number corresponding to the displacement of the indenter. Usually,

the dial divisions have represented whole Rockwell numbers, allowing an

estimation of the hardness number to only 1⁄2 Rockwell unit. Over years of

use, dial gages and lever systems often become worn or misaligned in many

machines, adding a component of error to the Rockwell measurement.

Many Rockwell machines produced today use one of several different types

of electronic or optical displacement-measuring instruments for directly

measuring the depth of indentation. The signal from the measuring instrument

is electronically converted to a Rockwell hardness number, which is displayed

digitally, sometimes having a resolution of 0.01 Rockwell units. Typically, these

new displacement-measuring instruments have a greater accuracy than most

dial gage/lever systems, but as often happens with digital displays, showing a

number with many decimal places may imply a greater accuracy than is

possible with the instrumentation.

The formulas for calculating Rockwell hardness, as given in 2.4 above, directly

relate the measured depth of the indenter to the Rockwell hardness number.

Increasing Time 

Increasing Force 



Increasing Time 

Increasing Indenter Depth

Fig. A Fig. B

h

due to

617.8 N

(63.0 kgf)

Total Force 

h

due to

588.4 N

(60.0 kgf)

Total Force 

Figure 3. Figure 3.

Force vs. time plot (Figure A) and indenter-depth vs. time plot (Figure B)

demonstrating the effect of an increase in the total-force

for a Rockwell HRA test.

Rockwell Hardness Testing Machine ◆
18

Consequently, an error in the depth measurement relates to an error in the

hardness measurement result as:

For regular Rockwell scales: 0.002 mm error in depth =

1 HR unit error.

For superficial Rockwell scales: 0.001 mm error in depth =

1 HR unit error.

Both the ASTM(2) and ISO(4) standards specify that the depth measuring

system have an accuracy of at least 0.5 Rockwell numbers.

3.3.4 Manual and Automatic Operation

For many years, most designs of Rockwell hardness machines required

that the operator manually apply and remove the preliminary and total forces.

This allowed the operator a great deal of control over the testing cycle;

however, consistency in the testing cycle varied between operators. The

manual operation also was considered to take too much time for production

testing.

Eventually, motors were incorporated into Rockwell machine designs to

provide an automated and repeatable testing cycle. Some machines were

fully automated to drive the application of the forces at a higher rate than was

typical for a person. The increased rate of testing is considered important for

production testing, but the automated operation removes much of the control

by the user. For many of the earlier automatic machines, the operator could not

vary the testing cycle. This was good in one respect, it retained consistency

from operator to operator; however, the testing cycle was usually set by

the manufacturer to complete a test in a relatively short time, with fast

force application rates and short dwell times. In following discussions of

the Rockwell testing cycle, it will be shown that fast force application rates

and short dwell times can lead to poor measurement repeatability.

Recognizing that many testing applications required better measurement

repeatability, as well as control of the testing cycle due to varying material

plasticity, manufacturers of automatic machines began modifying their designs

to allow the operator to adjust the testing cycle. Many of today’s Rockwell

machines can be set to a “standard” test cycle, while also allowing the testing

cycle to be adjusted to better fit the users’ needs.

3.3.5 Test Material Support (Anvils) est Material Support (Anvils)

One of the most important requirements for making a valid Rockwell

hardness test is that the test material be well supported to prevent any

movement during the test. Even the slightest movement can significantly alter

◆ Test Procedure
19

the hardness result. If the test material moves during the test, the movement

may be reflected as an error in the depth measurement. Bear in mind that for a

Rockwell superficial test, an error in the depth measurement of one-hundredth

of a millimeter will produce an error of 10 Rockwell points (see 3.3.3 above).

There are many types of material supports or anvils available for testing

different shapes and sizes of test material. The test method standards provide

some guidance for selecting an appropriate anvil. In general, flat material

should be tested on a flat anvil. Material that is curved should be tested with

the convex surface supported on a V-shaped or a double-roller style anvil.

Small or thin samples, sheet metal, or parts that do not have flat under-surfaces

should be tested on a spot anvil having a small, elevated, flat bearing surface.

There are some Rockwell machine designs that apply a clamping force to the

test material that is greater than the Rockwell test force. This type of machine

is useful when testing larger parts.

★ Good Practice Recommendations

• Often overlooked sources of error in Rockwell testing are the anvil and

anvil seat. A dirty anvil seat and almost any perceptible flaw on the anvil

and anvil seat, such as scratches or indents, can significantly affect the

hardness result. The anvils and the anvil seat should be routinely cleaned

and inspected for damage and replaced or reground when damage occurs.

• When testing large samples of test material or material with a long shape

that significantly overhangs the hardness machine’s anvil support, the

material should be additionally supported using suitable outboard fixtures.

Otherwise, the overhang may cause a cantilever or lateral force to be

applied to the indenter, resulting in measurement error or damage to the

indenter. These types of parts should not be supported by hand.

• It is very important that the method used to attach an anvil to a Rockwell

machine prevents any rocking or other movement of the anvil during the

test. Many Rockwell machine designs attach the anvil by inserting its base

into a slip fitting. This design is suitable for most purposes, although for

critical applications, it may be beneficial to rigidly affix the anvil to the

testing machine.

• Each time an anvil is installed, regardless of its design, it must be adequately

seated to the testing machine by making repeated hardness tests on a

uniform piece of material, such as a test block. Repeat the tests until there

is no increasing or decreasing trend in the measured hardness values.

• When testing curved parts, it is extremely important that the part is properly

aligned such that the indentation is made at the apex of a convex surface or

at the bottom of a concave surface. The proper alignment of a V-shaped or

Rockwell Hardness Testing Machine ◆
20

a double-roller style anvil may be checked by first making one Rockwell test

on a cylindrical piece, then, after rotating the anvil 90 ° without moving the

test piece, make a second test. If the second test falls exactly at the same

location as the first test, the alignment of the indenter is likely satisfactory.

Testing Precaution

• The anvil must present the material test surface perpendicular to the

indentation direction of the indenter. If the test surface is tested at an angle

with respect to the indentation direction, the measurement will be adversely

affected, usually lowering the measured value from the true hardness.

3.3.6 Hysteresis

Each time a Rockwell hardness test is made, the testing machine will undergo

flexure in some of the machine components including the machine frame.

If the flexure is not entirely elastic during the application and removal of the

additional force, the testing machine may exhibit hysteresis in its flexure.

Since the indenter-depth measurement systems of most Rockwell hardness

machines are directly connected to the machine frame, any hysteresis would

be reflected in the indenter-depth measurement system. A hysteresis effect

can also occur in the indenter-depth measurement system itself as the direction

of measurement reverses after applying the total force. In both cases, the

hysteresis is likely to result in an offset or bias in the test result.

Testing Precautions

• Excessive hysteresis may indicate problems with the Rockwell machine

caused by worn or dirty parts, such as in the depth measurement system,

the elevating screw and anvil seat.

3.3.7 Repeatability

The repeatability of a hardness machine is its ability to obtain the same

hardness measurement result on an ideally uniform material over a short

period of time where the test conditions (including the operator) do not vary.

Imagine a material that is perfectly uniform in hardness, which has been ideally

prepared for Rockwell hardness testing. If a small number of Rockwell tests

were made repeatedly on this material, it would be found that the measurement

results were likely not identical, but rather they varied randomly over a range

of values. The degree to which the measurement values agree provides an

indication of the repeatability of the Rockwell hardness machine. As with

most measuring devices, no matter how much effort is made to eliminate the

sources of this random variability, it is impossible to do away with completely.

×

×

◆ Test Procedure
21

All Rockwell machines exhibit some level of lack of repeatability, which

sporadically adds error to measurement values. Whereas, errors in force,

depth, and hysteresis are typically systematic errors that contribute to a bias in

the hardness measurement, lack of repeatability is a randomly occurring error.

The lack of repeatability will typically increase in instances such as when parts

of the hardness machine are worn, when excessive friction is occurring during

a test, or when the machine requires cleaning. The level of repeatability of a

hardness machine often varies between different Rockwell scales due to

variances such as the force levels and types of indenters. The repeatability

may also vary at different hardness levels within the same scale due to the

variations related to differing indentation depths.

The ASTM(2) and ISO(4) standards specify a method for assessing the lack

of repeatability of a Rockwell machine, which involves making hardness

measurements across the surface of reference test blocks (see 5.2.1). The

acceptability of the testing machine is determined from the difference between

the maximum and minimum measured hardness values. Satisfactory tolerances

on this measure of repeatability vary from 1.0 to 2.0 Rockwell units for ASTM

and from 1.2 to 6.6 units for ISO, depending on the Rockwell scale and

hardness level.

3.3.8 Indenters

The indenter is a major contributor to Rockwell hardness measurement

error. Both the spheroconical diamond indenter and the ball indenter have

characteristics that can cause significant measurement biases. In fact,

indenter measurement bias has often been used to offset other measurement

errors associated with the hardness machine. Like hardness machines, the

measurement performance of a Rockwell indenter is dependent on more than

its physical parameters. Differences in indenter performance may also be

due to the indenter’s manufacturing process. Two indenters with virtually the

same shape may produce significantly differing hardness measurements. It is

recommended that the indenters to be used be certified for performance with

respect to a higher-level master indenter. In the past, an often-used procedure

to certify Rockwell indenters was to make hardness tests on reference test

blocks, and compare the measurement to the block value. When using this

procedure, if the indenter performance did not agree with the block value,

it was difficult to determine whether the source of the error was due to the

indenter, the standardizing machine, the reference block values, or some

combination of these variables.

The test method standards state acceptability tolerances for the performance

of diamond indenters. ASTM(2) allows the performance to deviate from 0.5 to

1.0 Rockwell units from test block values, depending on the hardness level.

Rockwell Hardness Testing Machine ◆
22

ISO(4) allows the performance to deviate 0.8 Rockwell units from the

performance of a reference indenter. There are currently no requirements for

the performance of ball indenters in either ASTM or ISO standards. It should

be noted that a Rockwell indenter has formally been referred to as a

“penetrator” or “stylus.”

There are several different designs currently used for the base (opposite end

of the indentation tip) of Rockwell indenters because of the varying styles

of indenter holders found on different manufacturer’s hardness machines.

Indenters may be attached to machines using such methods as slip fittings,

threaded fixtures, or with a collet fixture. Not all indenter designs can be used

with all holder styles. Whatever method is used, it is imperative that there is

no movement of the indenter in its holder during a test.

★ Good Practice Recommendations

• Indenters should be used that are certified to be within tolerances for both

shape (geometry) and performance with respect to a reference indenter.

This applies to all types of Rockwell indenters. In the past, it was common

for diamond indenters to be certified for performance only.

• Only indenters should be used that have been verified for use with

the particular Rockwell machine, such as during an indirect verification

(see 5.2). In cases that other indenters must be used, they should be verified

in some manner for use with the testing machine. The best verification

method is to perform a full indirect verification of the applicable Rockwell

scales using the indenter in question. Other verification techniques may also

be appropriate.

• Periodically, indenters should be visually inspected for damage with the aid

of adequate magnification (20X or higher).

• Every effort should be made to keep indenters clean, particularly the

indenting portion and the surface that is seated against the testing machine.

Indenters should be cleaned periodically in a manner that will not leave

residue on the indenting portion of the tip.

• Each time an indenter is installed, regardless of its design, its seating surface

must be adequately seated against the indenter holder by making repeated

hardness tests on a uniform piece of material, such as a test block. Repeat

the tests until there is no increasing or decreasing trend in the measured

hardness values.

◆ Test Procedure
23

Testing Precaution

• If an indenter is dropped or hit with the test piece or anvil, it is imperative

that before using it further, it should be thoroughly inspected for damage and

verified for performance for each Rockwell scale that is used. Performance

verification is necessary because the measuring ability of an indenter,

particularly a diamond indenter, can change significantly without any

outward visible signs of damage.

3.3.8.1 Spheroconical Diamond Indenter

The Rockwell diamond indenter is used with the HRA, HRC, HRD, HR15N,

HR30N, and HR45N scales. The diamond indenter scales are typically used

when testing harder materials such as steel, tungsten, and cemented carbides.

Diamond is needed for testing hard materials to ensure that the indenter itself

does not deform during the indentation process. Any permanent deformation of

the indenter would adversely affect the hardness measurement of the test

material. A typical Rockwell diamond indenter consists of a metal holder into

which a diamond tip is permanently attached. The diamond tip is specified by

test method standards to have a spheroconical geometry with a 120 ° included

cone angle and a 0.2 mm radius tip, with the cone and radial tip blending in a

tangential manner as illustrated in Figure 4.

There are several error sources that can affect the measurement performance

of the Rockwell diamond indenter. Some error sources are obvious, and others

are difficult to determine. The most common error source is an incorrectly

shaped spheroconical diamond tip. In the past, this commonly occurred because

diamond is very difficult to machine into the spheroconical geometry, and, until

recently, many indenter manufacturers did not have adequate instruments to

accurately measure the diamond shape. Common practice in the manufacture

of diamond indenters was to machine the diamond shape close to nominal, and

then certify the indenter only by performance testing with little or no actual

direct verification of its geometry. Increasingly, today’s manufacturers have

developed the capabilities to accurately measure the indenter geometries and

detect variations that are out of tolerance.

Form errors in the indenter shape often translate into significant errors in the

hardness measurement. This is because a Rockwell hardness value is related

to the volume of material displaced by the indenter during the application of the

Rockwell test forces. The displaced volume is related to how deep the indenter

penetrates the material. If two Rockwell tests are made using indenters having

similar but slightly different geometries, essentially the same volume of material

will be displaced, but the depth of indentation will vary, and, thus, the calculated

Rockwell hardness value will be different.

×

Rockwell Hardness Testing Machine ◆
24

If a series of Rockwell hardness tests is made on a number of materials

ranging progressively from soft to hard, then as the material hardness

increases, less of the diamond tip penetrates the material. Therefore,

depending on the hardness of the test material, errors in the cone angle or

tip radius will cause varying degrees of error in the hardness measurement.

Because harder materials produce shallower penetration depths, the test

material is primarily in contact with the radial tip, which will have the greater

influence on measurement error. The cone angle will have a greater influence

for softer materials exhibiting deeper indentations, since the test material is

being displaced by more of the conical portion of the diamond.

Other sources of error include form error at the tangential blend, the surface

roughness of the diamond, the alignment of the indenter axis with respect to the

seating surface of the indenter to the test machine, a poorly machined seating

surface, and hysteresis in the indenter itself as it is loaded and unloaded,

possibly due to problems with the interface between the diamond and the

metal portion of the indenter. Many of these indenter problems may produce

measurement errors that will vary depending on the hardness scale used, the

hardness level of the test material, or the type of test material. Consequently,

Rockwell diamond indenters are sometimes certified for specific Rockwell

scales.

★ Good Practice Recommendation

If possible, a diamond indenter should be chosen that is certified for each

Rockwell scale that will be used or as many scales as possible. To obtain

the highest accuracy, use of more than one diamond indenter may be desired,

each certified for specific Rockwell scales. This allows an indenter to be

chosen that may agree more closely with the performance of a reference

indenter for a specific Rockwell scale, even though the performance is not

Spherical

Radius of Curvature

0.2 mm

Included Cone Angle

120 degrees

Figure 4. Figure 4.

Diagram of cross-sectional view of spheroconical diamond indenter tip.

◆ Test Procedure
25

as close (or possibly not acceptable) for other diamond scales. In the

United States, Rockwell diamond indenters are sometimes designated as being

a “C,” “N,” or “A” indenter. Usually, these designations mean the following:

a “C” indenter is appropriate for use with the regular Rockwell scales (HRA,

HRC, HRD), a “N” indenter is appropriate for the superficial Rockwell

scales (HR15N, HR30N, HR45N), and an “A” indenter usually refers to being

acceptable for testing carbides at the high end of the HRA scale. Be aware

that the ISO test method requires that each diamond indenter be performance

certified for all Rockwell scales requiring a diamond indenter.

3.3.8.2 Ball Indenters

Rockwell ball indenters are used with all Rockwell scales with the exception

of the A, C, D, and N scales for which the diamond indenter is used. Typically,

ball indenters are used when testing materials such as soft steels, copper

alloys, aluminum alloys, and bearing metals. There are four standard sizes of

ball indenters specified by ASTM(2) having diameters of 1.588 mm (1/16 in),

3.175 mm (1/8 in), 6.350 mm (1/4 in), and 12.70 mm (1/2 in). The ISO(4)

specifies only the 1.588 mm (1/16 in) and 3.175 mm (1/8 in) diameter balls.

The choice of indenter size, and, thus, hardness scale, is largely based on the

hardness and thickness of the test material. Generally, the ball size is increased

for thinner and softer materials. A typical Rockwell ball indenter consists of a

metal holder for the ball with a threaded cap to hold the ball in place.

Rockwell indenter balls can be made of either steel or tungsten carbide (WC).

In the past, most Rockwell hardness testing with ball indenters has used

steel balls, typically bearing balls; however, there is currently a general move

towards the use of tungsten carbide balls. Presently in the year 2000, ASTM

specifies steel balls as the standard indenter, and, until recently, ISO had

required that Rockwell tests be performed using only steel balls but now

allows the use of tungsten carbide balls. A problem with steel balls is that

they tend to flatten over time at the contact point with the test specimen,

particularly when testing harder materials. An indenter with a flattened ball

will not penetrate as deeply into test materials, indicating an apparent higher

hardness for the material. The tungsten carbide ball was introduced to help

overcome this problem. The harder tungsten carbide is much less susceptible

to flattening than steel balls.

Tests have indicated(14) that the use of tungsten carbide ball indenters may

result in a lower hardness measurement than when a steel ball indenter is

used. This may be partly due to differences in the compliance of the two ball

materials. Fortunately, the publishers of the ISO standard also require that the

measurement values be reported with a scale designation ending in the letter

“S” when a steel ball is used or “W” when a tungsten carbide ball is used.

Rockwell Hardness Testing Machine ◆
26

Although this designation differentiates between tests made with the two

indenters, users of the measurement data must be aware that measurement

differences may occur.

★ Good Practice Recommendation

• When steel ball indenters are used, it is important that performance

verification checks with reference test blocks be made frequently. This is

because of the tendency of the steel ball to flatten over time, particularly

when testing harder materials. Since the flattening may increase gradually,

the performance of the indenter should be consistently monitored at a rate

appropriate for the usage of the indenter and the hardness level of the

material tested.

Testing Precaution

• A steel ball can be flattened quickly if a test is mistakenly made on a

material above the appropriate hardness range (over 100 HRB) or if the

indenter is hit by the anvil or is used to test too thin material.

• When testing very soft materials, it is important to ensure that the design

of the indenter cap allows adequate protrusion of the ball. Otherwise, the

cap may contact the test material, preventing full penetration into the test

material, and result in an erroneously high hardness value. Be aware that

it is possible for the cap to contact the test material without any physical

indication on the surface of the test material.

3.4 Hardness Measurement

The Rockwell hardness test method procedure is described and specified

by the test method standards. To facilitate comparisons with other Rockwell

hardness data, the requirements of the standards should be adhered to. In

cases where the measurement of hardness is to meet a product or material

specification and must follow a particular test method standard document, the

test procedures must adhere to the requirements of the standard.

3.4.1 Set Appropriate Rockwell Scale

The Rockwell machine must be set up for testing the chosen Rockwell

scale, such that the appropriate indenter type and force levels are used. The

appropriate indenter and force levels, corresponding to each Rockwell scale,

are given in Figure 1 and by the test method standards.

×

◆ Test Procedure
27

★ Good Practice Recommendations

• The user should confirm that the indenter chosen for testing has been

previously verified for use with the particular testing machine.

• Whenever the test forces, indenters or anvils are changed, a daily check

or verification (see 6.2) of the performance of the testing machine should

be performed using reference test blocks as described by the test method

standards. In cases where the anvil to be used cannot be used for testing

a test block (e.g., a V-anvil for testing round parts), then parts or test

specimens of known hardness that can be tested with the anvil should

be maintained by the user to perform the daily check. A daily verification

should be performed at least once each day of testing regardless of whether

the indenter, anvil, or forces are changed. The daily verification tests should

be performed after the indenter and/or anvil have been seated.

Testing Precautions

• Some older designs of Rockwell machines that apply the total force by

weights acting through a lever arm may require that the proper weights be

added or removed from a hanger rod. Be aware that, in some cases, the

weights have been calibrated for a specific hardness machine and may not

produce the correct forces on other machines.

• Care must be taken to not contact the indenter when installing or removing

an anvil. Many indenters are damaged in this way. If the anvil contacts

the indenter, the indenter should be inspected and performance verified

(see 6.2) prior to further testing.

3.4.2 Testing Cycle

The Rockwell testing cycle is the sequence of operations that the hardness

machine undergoes during a measurement. The testing cycle includes the rates

at which the forces are applied and the time periods that the forces are held

constant, referred to as dwell times. The Rockwell hardness testing cycle can

be separated into eight steps, as indicated in Figure 5. These steps fall into

two categories: (1) application or removal of test forces; and (2) dwell times.

Annex B provides expanded explanations of the individual effects that each of

the testing cycle steps has on the hardness result.

When used to test most materials, particularly metals, the Rockwell

hardness test is testing cycle dependent. By using different testing cycles,

the measurement will yield different hardness results. Because the Rockwell

test is testing cycle dependent, the hardness result is not complete unless the

testing cycle that was used is also known. This dilemma of obtaining different

×

Hardness Measurement ◆
28

h

1{

2{

{

3

4

5

{

6

{

7

8

Time

Indentation Depth

Test Surface

Indentation

Direction

Total Force _____

Preliminary Force ____

_____ Preliminary Force

First depth

measurement

Second depth

measurement

h

1{

2{

{

3

4

5

{

6

{

7

8

Time

Indentation Depth

Test Surface

Indentation

Direction

Total Force _____

Preliminary Force ____

_____ Preliminary Force

First depth

measurement

Second depth

measurement

hardness values for the same material is partially solved by adhering to test

method standards, which define tolerances on the testing cycle.

3.4.2.1 Application or Removal of Test Forces

The step in the Rockwell testing cycle where the preliminary force is increased

to the total force level (step 4 in Figure 5) has been shown(15) to significantly

affect the measured hardness value. By changing the rate that the force is

applied, particularly during the last part of the force application, a range of

hardness values can be obtained. The effect may be due either to rate

sensitivity of the material under test, or to the dynamics of the hardness tester,

or a combination of both. The magnitude of the rate effect is highly dependent

on the type and hardness of the test material. It is important that the test forces

are applied at rates in accordance with the test method standards. In both the

cases of too rapid loading or loading too slowly, the test measurement can be

adversely affected.

Figure 5. Figure 5.

Eight steps of the Rockwell test cycle.

◆ Test Procedure
29

3.4.2.2 Dwell Times

Each of the three dwell time steps of the testing cycle affect the hardness

result because of creep or elastic recovery of the test material occurring during

these periods of constant force. The effects of the dwell times can be

summarized as:

1. Errors in the dwell time will produce the largest differences in hardness

measurement results when shorter dwell times are used. The user should

take this into account when choosing an appropriate test cycle. An increase

in testing speed may reduce the repeatability in measurement results.

2. In general, the Rockwell hardness number is most affected by the total

force dwell time, followed by the preliminary force dwell time, and then the

recovery dwell time. This depends somewhat on the hardness level of the

material.

★ Good Practice Recommendations

• When Rockwell hardness comparisons are to be made between two

laboratories, or two test machines, or even between two tests made on

the same hardness tester, the testing cycles that are used should agree

as closely as possible, particularly when short dwell times are used. How

close the test cycles should agree depends on the desired precision of the

hardness result. For example, in situations where the Rockwell hardness

measurement must only agree within several Rockwell hardness points,

perhaps any testing cycle within the specified ranges would be acceptable.

However, in cases where the results must have a close comparison, or there

is disagreement between laboratories, each Rockwell measurement should

be made using the same test cycle.

• When the testing machine design requires that the operator either fully or

partially perform the test procedure manually, the operator should make

every effort to operate the machine such that testing cycle requirements are

being met.

Testing Precaution

• In cases where the operator applies the preliminary force manually, such as

is common for older machines, the correct preliminary force level may be

overshot. The operator must not adjust back to the proper force. The error

to the measurement value has already occurred. In this situation, the test

should be stopped and a different location tested.

×

Hardness Measurement ◆
30

3.4.3 Seating the Anvil and Indenter

Prior to making Rockwell measurements, the hardness machine anvil and

indenter must be adequately seated. This may be accomplished by performing

standard Rockwell hardness tests on a material having a uniform hardness,

such as reference test blocks. The seating tests should be repeated until

the successive measurement values show no trend of increasing or

decreasing hardness.

3.4.4 Cleaning the Anvil and Indenter

The hardness machine anvil and indenter should be thoroughly cleaned per

manufacturer’s recommendations. In the absence of manufacturer’s cleaning

instructions, it is recommended that the anvil and indenter be cleaned with ethyl

alcohol and dried using a lint free cloth. Lastly, blow the surfaces clean of dust

using filtered air, such as from a commercial compressed air can or bottle.

Do not blow clean by mouth.

3.4.5 Placement and Removal of Test Material est Material

Usually, material to be tested with a Rockwell hardness machine is placed

on the anvil by hand by the operator. In some cases, mechanical systems are

used to automatically place and remove samples. The contact area of the test

material and anvil must be clean without the presence of dust, dirt, or lubricant.

It is extremely important that the test material be well supported to prevent any

movement during the test.

★ Good Practice Recommendation

• When a spot anvil is used that is too small to support the test material

without assistance by the operator, the operator should carefully place

the test material onto the anvil so that it is flat against the anvil surface.

The operator should hold the material steady during the application of the

preliminary force, and release it just before the preliminary force is fully

applied. This type of testing requires a skilled operator that can perform

the test without applying any added force to the test from misalignment or

movement of the test sample.

Testing Precautions

• Care must be taken to not contact the indenter when placing the test

material on the support anvil and particularly when removing the test

material. Many indenters are damaged in this way. If the test material

contacts the indenter, the indenter should be inspected and performance

verified (see 6.2) prior to further testing.

×

◆ Test Procedure
31

• The test material must be placed on the anvil such that the anvil is not

scratched, indented, or damaged in any way.

3.4.6 Making the Measurement 3.4.6 Making the Measurement

As with most testing equipment and instrumentation, the operation of Rockwell

hardness machines varies from manufacturer to manufacturer and from model

to model. Depending on the machine model, the responsibility of the operator

can vary from manually applying and controlling each of the test forces to

simply pushing a button. The user should read and follow the recommended

operating procedures found in the manufacturer’s manual.

Testing Precautions

• The test material must not be held by hand during the testing process,

except as allowed when using the spot anvil (see above). Holding the test

material by hand can cause movement of the material during a test.

• During the testing process, the operator should avoid contact with the testing

machine, the test material, and the table or stand supporting the testing

machine, except when required to operate the machine. Contact can induce

shock and vibration that can affect the test.

• When testing curved parts, special care is needed to ensure that the

specimen support correctly aligns the part and prevents movement of the

part during a test.

3.4.7 Spacing of Indentations

As a Rockwell hardness measurement is being made, the material

deformation zone extends in all directions around the indentation. This

process typically increases the hardness of the deformation zone by inducing

residual stress and cold-working the deformed material. If a second indentation

is made near an existing indentation such that the deformation zone surrounding

the new indentation overlaps the hardened material surrounding the previous

indentation, then the apparent measured hardness likely will be erroneously

elevated. This effect is increased the closer two indentations are made to

each other until the indentations become so close that the wall of the original

indentation begins collapsing, likely lowering the apparent hardness.

The general rule as specified by the ASTM(2) test method standards is that the

distance between the centers of two indentations must be at least 3 times the

diameter of the indentation. The ISO test method standard(3) specify that the

×

Hardness Measurement ◆
32

distance be at least 4 times the diameter of the indentation (but not less than

2 mm). Although these are reasonable guidelines, tests have shown(15) that

interaction with an adjacent indent can occur at these and greater distances.

Also, take into consideration that the effect will be multiplied by multiple

adjacent indents. The user should determine the appropriate distance for

the material to be tested.

3.4.8 Testing Curved Surfaces

Rockwell numbers obtained from measurements made on curved surfaces

must be corrected depending on the radius of curvature and whether the

surface is convex or concave. In the case of convex surfaces, such as the

outside of a cylinder, a correction value must be added to the test result to

increase the measured hardness value. This is because a convex surface

curves away from the indenter tip providing less surrounding material to

support the indenter than is the case for flat material. As a result, the indenter

penetrates the material more deeply and indicates a lower hardness than

the true value. Similarly, for concave surfaces, a correction value must be

subtracted from the test result to decrease the apparent hardness value. This

is because a concave surface curves towards the indenter tip, and provides

additional material to support the indenter than when testing flat material, and,

consequently, produces a shallower indentation and a higher hardness than

the true value. As the radius of curvature gets smaller, the error in the

measurement result becomes more pronounced requiring a larger correction

to be made.

The ASTM(2) and ISO(4) standards specify values for correcting tests made

on a few types of curved surfaces. The corrections given in test method

standards are to be considered approximations only. Both ASTM and ISO

give corrections for tests made on convex cylindrical surfaces. ISO also

provides limited corrections for testing on convex spherical surfaces. These

correction values are to be added to the measured hardness value to obtain an

approximation of the actual hardness of the material. If correction values for

concave surfaces are not available, the correction values given by the test

method standards for convex surfaces may be subtracted from the measured

value to provide a rough approximation of the material hardness. This

procedure for correcting tests on concave surfaces should only be used to

obtain an approximate value and not to meet a specification.

★ Good Practice Recommendation

• It is recommended that users develop their own correction values specific

for the type of material and radius of curvature that will be tested. This may

◆ Test Procedure
33

be done by testing samples of the same material in both the curved and flat

geometries, for example, by testing the curved surface and flat ends of a

cylinder. Be certain that the test surface conditions are the same for both

the curved and flat specimens.

Testing Precautions

• When testing curved parts, it is extremely important that care be taken to

ensure that the part is properly aligned such that the indentation is made

at the apex of a convex surface or at the bottom of a concave surface

(see 3.3.5). It is also extremely important to ensure that the part does not

move during testing.

• When applying correction values provided in the test method standards for

tests on curved surfaces, be certain that the corrections used are for the

same geometry as the test piece. Be aware that tests on surfaces that

curve in two axes, such as a sphere will require different corrections than

surfaces that curve in only one axis such as a cylinder.

• Depending on the hardness level, Rockwell tests should not be made on

curved surfaces below a certain radius of curvature due to the errors

associated with the large corrections that would be needed. ASTM and

ISO recommends that for Rockwell scales using a diamond indenter or a

1.588 mm (1/16 in) diameter ball indenter, regular Rockwell scale tests

should not be made on convex cylinders below 6.4 mm (1/4 in) in diameter,

and superficial Rockwell scale tests should not be made on convex cylinders

below 3.2 mm (1/8 in) in diameter. ISO also states that Rockwell tests on

the A, C, D, N, and T scales should not be made when the correction is

greater than three Rockwell units, and tests on the B scale should not be

made when the correction is greater than five Rockwell units.

3.4.9 Test Environment est Environment

The degree to which the testing environment affects the Rockwell hardness

test is generally difficult to quantify; however, three of the major environmental

factors that can contribute to measurement error are the testing temperature,

excessive vibration and general cleanliness.

★ Good Practice Recommendation

When choosing the location for installing a hardness machine, consider the

environmental conditions over the entire workday as well as seasonal changes

throughout the year.

Hardness Measurement ◆

×
34

3.4.9.1 Temperature

The test temperature can affect Rockwell hardness measurement results due

to two causes: (1) variations in the operation of the testing machine due to

temperature; and (2) temperature dependency of the test material. Variations

in the operation of the testing machine cannot be generalized for all Rockwell

testing machines. Because of the many designs of Rockwell hardness

machines having different principles of operation and instrumentation, it is

likely that each will have unique dependencies on temperature.

The temperature dependency of the test material will vary depending on

the type of material and the Rockwell scale that is used for testing. As an

indication of the typical magnitude of this effect, the following relationships

are provided. Yamamoto and Yano(16) determined that for their specific HRC

test blocks, the temperature dependence was -0.03 HRC/°C at 20 HRC,

-0.02 HRC/°C at 40 HRC and -0.01 HRC/°C at 60 HRC. W. Kersten(16)

determined a similar relationship for the material he tested of -0.0185 HRC/°C,

independent of HRC level.

★ Good Practice Recommendations

• Placement of a Rockwell hardness machine in an area that will have to

operate over a wide range of temperatures should be avoided whenever

possible. To obtain the most repeatable results, the temperature of the

hardness machine and the test material should be maintained within a

narrow temperature range. The appropriate range is dependent on the

user’s needs. The test method standards state typical testing temperatures

within the range of 10 °C to 35 °C. The ISO test method standard requires

that a test temperature of (23 ± 5) °C be used when tests are carried out

under controlled conditions.

• For some industries, it is common for a Rockwell machine to be used in an

environment that is subject to wide temperature fluctuations. In these cases,

it is important to ensure that the Rockwell machine is capable of performing

within tolerances over the range of temperatures. This may be determined

by verifying the performance of the hardness machine with reference

blocks as the temperature of the testing environment changes. When

performing these verifications, it is desirable to separate any affect due

to the temperature dependency of the reference block material. To the

extent possible, prior to and during the verifications, the blocks should

be maintained near to the temperature at which they were calibrated.

However, condensation on the test block must be avoided.

• Although the hardness machine may operate satisfactorily over a wide

temperature range, the test material may also exhibit varying hardness

◆ Test Procedure
35

values at differing temperatures. Consequently, when the temperature

dependency of the test material is not known, it is recommended to report

the test temperature with the hardness measurement results when the

temperature is suspected to be a factor.

3.4.9.2 Vibration

The Rockwell test method standards warn the user to avoid making Rockwell

hardness measurements when the testing machine is subjected to excessive

vibration or shock. As with the other environmental factors, the degree to

which vibration may affect the hardness measurement is dependent on the

design of the testing machine.

★ Good Practice Recommendation

• Rockwell hardness machines should be placed on an isolated table or

workbench, which is not shared with other equipment.

• Testing locations susceptible to excessive vibration should be avoided such

as near machinery, near worker high traffic areas, on loading docks, or

adjacent to heavily traveled roads or railroad tracks.

3.4.9.3 Cleanliness

Many designs of Rockwell hardness machines are highly susceptible to

measurement errors when dust, dirt, or oil is deposited and accumulated on

machine components. A more critical problem can occur when these types

of contaminants adhere to the specimen support anvils, elevating screw, or,

in particular, to the indenter.

3.4.10 Reporting Results

Rockwell hardness numbers should be reported as required by the test method

standards using appropriate rounding techniques. The numeric value must be

followed by the symbol HR and the scale designation. For example, 64 HRC

represents a Rockwell hardness number of 64 on the Rockwell C scale, and

81 HR30N represents a Rockwell superficial hardness number of 81 on the

Rockwell 30N scale. The ISO test method standards state the additional

requirement that when a ball indenter is used, the scale designation is followed

by the letter “S” when using a steel ball and the letter “W” to indicate the use

of a tungsten carbide ball. For example, 72 HRBW represents a Rockwell

hardness number of 72 on the B scale measured using a tungsten carbide

ball indenter.

Hardness Measurement ◆
36

3.4.11 Conversion to Other Hardness Scales or Properties

There is no general method of accurately converting the Rockwell hardness

numbers determined on one scale to Rockwell hardness numbers on another

scale, or to other types of hardness numbers, or to tensile strength values.

Nevertheless, hardness conversion tables are published by ASTM(17), in the

literature, and often by hardness equipment manufacturers. Such conversions

are, at best, approximations and, therefore, should be avoided except for

special cases where a reliable basis for the approximate conversion has been

obtained by comparison tests.

◆ Test Procedure
37

4 REFERENCE TEST BLOCK STANDARDS

Rockwell hardness test blocks are reference standards for transferring

Rockwell hardness scale values from one standardizing level to a lower level;

for example, transferring national hardness scale values directly to secondary

standardizing laboratories, or transferring the national hardness scale values

to industry through the secondary standardizing level. Rockwell hardness

test blocks are also used for verifying or comparing the performance of

Rockwell hardness machines and indenters. The test method standards

specify requirements for the preparation, size, finish, uniformity, and

standardization of reference test blocks.

Historically, Rockwell test blocks are standardized (also referred to as

calibrated) to determine the average hardness of the test surface of the block.

Normally, the calibration laboratory accomplishes this by making a number of

measurements across the block surface and then calculating the average of the

measurements. This is the usual standardization process whether the

blocks are standardized by the primary national metrology institute level or

by secondary commercial laboratories.

Because no materials are perfectly uniform in hardness, all reference test

blocks will have some hardness variation across the test surface. In most

cases, the hardness varies smoothly across the surface, but the variation is

different from block to block. The hardness variation is primarily due to the

test block manufacturing process. Figure 6 illustrates examples of the hardness

variation in four 25 HRC level test blocks.

The certified hardness value provided with a test block is an estimation of

the average hardness of the entire test surface; however, the hardness at

individual test locations will vary within a range of values extending both

above and below the certified average hardness value. This variation in

hardness across the surface is referred to as the non-uniformity of the

test block. The test method standards specify tolerances on the degree of

acceptable non-uniformity, which varies depending on Rockwell scale and

hardness level.

4.1 Primary Reference Test Blocks

Primary reference test blocks are standardized using primary standardizing

machines in accordance with the hardness definition. Usually, the National

Metrology Institute (NMI) of a country standardizes the primary reference test

blocks and maintains the national hardness scales. The National Metrology

Institute in the United States for Rockwell hardness is NIST.

Reference Test Block Standards ◆
38

4.1.1 NIST SRMs for the Rockwell C Scale

Each Rockwell hardness scale covers a range of hardness levels. To transfer

the U.S. national HRC scale values to industry requires more than one transfer

standard for the entire scale. However, production of hardness blocks at all

levels of HRC hardness is not feasible for NIST. It was determined that

industry needs test blocks at the levels specified in test method standards for

the calibration and verification of Rockwell hardness testing machines. For

the HRC scale, ASTM and ISO specify three ranges of hardness. The NIST

reference test blocks for the HRC scale reflect these ranges and are certified

at three hardness levels: 25 HRC, 45 HRC, and 63 HRC, which are available

for purchase as a Standard Reference Material (SRM® 2810, 2811, and 2812,

respectively)(18).

◆ Reference Test Block Standards

Figure 6. Figure 6.

Four examples of the hardness profile across the test surface of

25 HRC test blocks, illustrating how the non-uniformity in hardness can vary

within a block and differs from block to block. Each line represents a hardness

change of 0.02 HRC. Light to dark areas represent hard to soft areas.

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-5

0

5

10

15

20

25

30

mm

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

mm
39

Currently, NIST offers Rockwell hardness test blocks for only the Rockwell C

scale. Because the NIST SRMs are primary transfer standards, greater care in

the usage of the test blocks is recommended than for commercial test blocks

that are standardized by secondary calibration laboratories. Annex C provides

recommended procedures for the use of NIST Rockwell hardness test block

SRMs. These recommended procedures may be used as well when using

secondary standards to help improve measurement accuracy.

As a consequence of the variation in hardness across a test block, NIST

determines and provides the customer with two types of hardness certifications

with each reference test block: (1) the certified average HRC hardness across

the test surface of the block; and (2) certified HRC hardness values at specific

untested locations on the test surface(19). These two types of certifications

characterize the hardness of the test block in distinctly different ways.

4.1.1.1 Certification of the Average Surface Hardness

As discussed previously, the certified average hardness value of reference

test blocks is usually determined by calculating the simple average of several

hardness measurement values taken across the surface of the block. The

certification of the NIST SRM test blocks was partly based on the calibration

measurements; however, it was also based on a NIST derived function that

models how the hardness varies across the surface of the test block material.

In the case of the NIST blocks, the certified average hardness value is the

average of the hardness values predicted by the hardness function for all test

surface locations, and not simply the arithmetical average of the seven NIST

measurements. However, because the locations chosen for the seven NIST

measurements provide a good representation of the range in surface hardness,

the two averages are nearly identical in value.

4.1.1.2 Certification of Hardness at Untested Locations

A hardness measurement is destructive in that a specific location on a

hardness block can be measured only once. For the second type of

certification, certified HRC hardness values and the associated uncertainties

are provided for specific untested locations on the test surface of the reference

block, as illustrated by the open circles in Figure 7. Because hardness blocks

are not uniform, NIST can only predict the hardness at these untested

locations. The HRC hardness values were calculated using the surface

hardness function. Using this formula, predicted hardness values may be

calculated for any single untested location or for the average of two or more

locations. For the NIST SRMs, however, certified values of only eleven

locations are provided with the SRM test block. Section C.2 of Annex C

provides the formulas used by NIST and gives examples of how to use these

formulas.

Primary Reference Test Blocks ◆
40

This second type of NIST hardness certification provides the customer with a

valuable tool for improving the hardness comparison measurements by reducing

the influence of the test block non-uniformity. For example, the user can

combine the seven NIST calibration measurements with the eleven predicted

values to produce a profile map approximating the block surface hardness, and

then, correct measurements depending on the test location on the block. The

customer can also calculate better corrections by calculating hardness values

using the same formula NIST used to determine the hardness at the eleven

untested locations, as described in Annex C.

4.2 Secondary Reference Test Blocks

In the United States, and other countries throughout the world, the National

Metrology Institutes are usually not the sole supplier of the needed reference

standards for that country. Normally, secondary calibration laboratories

produce and calibrate the majority of test blocks for use by industry. Whereas,

NIST is planning to only provide test blocks for three hardness levels of

each Rockwell scale, the secondary calibration laboratories usually provide

reference blocks at multiple hardness levels, allowing a better verification for

a specific level of hardness.

The secondary calibration laboratories are linked to the national Rockwell

scales through the use of primary reference standards to calibrate their

standardizing machines and, often, through some form of accuracy assurance

Figure 7. Figure 7.

Hardness profile across the test surface of a NIST test block. The NIST

calibration measurements are indicated by the solid circles, and the locations

of the certified values for untested locations are indicated by the open circles.

◆ Reference Test Block Standards
41

program in connection with the primary standardization laboratory (NMI).

In the United States, this is accomplished through direct verification of the

secondary laboratories’ standardizing machines using NIST traceable

instruments and artifacts, indirect verification of the secondary laboratories’

standardizing machines using NIST SRM test block standards, and voluntary

participation in a calibration laboratory accreditation program. Because NIST

SRMs are currently available only for the Rockwell C scale, the secondary

reference test blocks of other Rockwell scales cannot be calibrated traceable

to NIST Rockwell scales.

4.3 Use of Reference Test Block Standards

Rockwell hardness reference test blocks are used primarily for the indirect

verification (see 5.2) and daily verification (see 6.2) of a Rockwell hardness

machine. Reference test blocks are also useful when comparing the relative

performance between two hardness machines by measuring the same blocks

on both machines or for comparing the performance of two indenters. Proper

care in the handling and use of reference test blocks is important to obtaining

accurate measurements. It is critical that the reference test blocks not

influence the hardness measurements due to improper use. The general

procedure for testing reference test blocks is the same as the hardness

measurement procedures discussed in 3.4. The following are additional

recommended practices for the proper use of reference test blocks.

★ Good Practice Recommendations

• Test temperature: As discussed previously, the test temperature can affect

Rockwell hardness measurement results due to the temperature dependency

of the material being tested. When using reference test blocks, it is desirable

to separate any effect due to the temperature dependency of the block

material. To the extent possible, prior to and during the verifications, the

reference test blocks should be maintained near to the temperature at

which they were calibrated.

• Anvil: When reference test blocks are being used for the verification of

a hardness machine, the same anvil must be used for the verification

(when possible) as will be used for normal testing following the verification.

In circumstances where the normally used anvil cannot be used for testing

test blocks, an initial verification of the machine should be made using an

anvil appropriate for testing reference test blocks. This anvil should then be

replaced with the anvil normally used for testing, and a second verification

should be performed. The second verification should be made on a typical

part of known hardness that is normally tested with the anvil or some other

appropriate test piece for which the correct hardness is known.

Secondary Reference Test Blocks ◆
42

• Inspection: The bottom surface of reference test blocks should be visually

inspected prior to use. The slightest dent, scratch, or spot of corrosion can

significantly affect the measurement result. Attempts to repair mechanical

damage on the bottom surface of test blocks should be avoided.

• Cleaning: Prior to use, it is recommended that the reference test block be

cleaned. A recommended method for cleaning is to gently wipe the top and

bottom test block surfaces with clean cotton or a cloth, thoroughly wetted

with ethyl alcohol. The metal surfaces should immediately be dried using a

soft lint free cloth or paper towel before the alcohol evaporates in the air.

This cleaning must be performed in a manner that prevents a residue from

remaining on the top or bottom surfaces. The cleaning should be followed

by blowing the surfaces clean of dust using filtered air. The top and bottom

surfaces should not be touched after cleaning.

• Placement on the anvil: Immediately before placing the reference test

block on the hardness machine anvil, the top surface of the anvil and the

bottom surface of the test block should be blown free of dust as before.

The reference test block should be gently and carefully placed on the anvil

before dust can return. The top test surface of the reference block should

be blown free of dust prior to testing and occasionally during the period of

use. When a flat anvil is used, the reference test block should be slid several

times back and forth over the surface of the anvil to help seat the block on

the anvil. Anytime the reference test block is lifted from and replaced on the

anvil, the procedure described above in this paragraph should be repeated.

When a spot anvil is used, extreme care should be practiced to ensure that

the test block is supported parallel to the anvil surface until the indenter

contacts the block, and the preliminary force is applied.

• Preliminary indentation: When a flat anvil is used, it is recommended that

at least one preliminary Rockwell test be performed at any location on the

test surface of the reference test block. The preliminary test will help seat

the test block on the anvil. The measured hardness value of the preliminary

test should be ignored. The user is cautioned not to make the preliminary

indentation such that it contacts a previous indentation. Doing so may

damage the indenter. A preliminary indentation is not necessary when

using a spot anvil.

• Testing cycle: Reference test blocks are typically calibrated by performing

Rockwell tests using a specific testing cycle. When reference test blocks

are used for the verification of a hardness machine, a testing cycle should

be used that replicates, as closely as possible, the testing cycle used by

the standardizing agency when the block was calibrated. Deviations in the

testing cycle dwell times or force application rate may result in measured

hardness values that are shifted from measurements made using the

◆ Reference Test Block Standards
43

standardizing testing cycle. Frequently, the testing cycle is not reported

by the standardizing agency. In this case, a testing cycle should be chosen

that is within the stated tolerances of the test method standards.

• Measurement locations: The locations for making measurements on

reference test blocks should be as specified, or recommended by the test

method standards, keeping in mind proper indentation spacing. Indentations

should be randomly distributed over the surface of the test block when

determining the measurement performance of the testing machine with

respect to the certified average hardness value of the test block. Never fill

the test surface with indentations by starting at one side of the block and

progressively moving to the other side of the block.

• Storage: It is recommended that reference test blocks be stored in an

environment that protects the blocks from mechanical damage, excessive

oxidation and corrosion. Wrapping a test block in anti-corrosion paper is

a good method for protecting the test block surface from corrosion and

oxidation when not being used. Anti-corrosion paper for ferrous and

nonferrous metals is commercially available. Although a coating of oil

can protect a block surface, it is not recommended since the oil must be

completely removed prior to testing the block. Test blocks should not be

subjected to wide variations in temperature. Elevated temperatures should

be avoided; particularly in the case of brass test blocks, which in some

cases can age-harden the block changing its overall hardness.

Testing Precautions

• The certified hardness value provided with a reference test block is

applicable only to the top test surface of the block. It does not represent

the hardness of the bottom or edge surfaces of the test block, nor the

material inside the test block. As such, NEVER make indentations on

the bottom surface of a test block. Not only will the measurement values

obtained be invalid for comparing with the block’s certified hardness value

for verification purposes, but also the reference test block can no longer be

reliably tested on the top test surface. An indentation on the bottom surface

will significantly affect subsequent hardness measurements. Any reference

test block tested on the bottom surface must never be used for verification

purposes and should be discarded.

• Once the test surface of a reference test block is filled, it should not be

machined to remove the indentations for additional testing. As stated above,

the hardness of the sub-surface material may differ from the hardness of

the original test surface. Additionally, a Rockwell indentation deforms

material well below an indentation making it difficult to determine when

sufficient affected material has been removed from the block.

×

Use of Reference Test Block Standards ◆
44

5 VERIFICATIONS OF ROCKWELL HARDNESS

MACHINES

In order to reduce the overall error in a Rockwell hardness measurement, it is

important that the different sources of error are identified and the significant

error sources be reduced if possible. This can only be accomplished by

assessing the separate parameters of the Rockwell test and verifying whether

each is within acceptable limits. The test method standards specify two

categories of methods that can be used to assess many of the aspects of the

test. They are: direct verification and indirect verification of the hardness

machine. Direct verification is a process for verifying that critical components

of the hardness machine are within allowable tolerances by directly measuring

such parameters as the test forces, depth measuring system, and machine

hysteresis. Indirect verification is a process for verifying the measurement

performance of the hardness machine by performing Rockwell hardness tests

using standardized reference blocks and indenters.

★ Good Practice Recommendations

• Although ASTM and ISO test method standards presently do not require

periodic direct verification of Rockwell machines, it is recommended that

both direct and indirect verifications be performed periodically based on the

usage and condition of the individual machine.

• When a testing machine fails to pass indirect verification of one or more

Rockwell scales, direct verification should be used as a tool to determine the

source of the problem rather than making blind adjustments of a machine

component or electronic offsets to correct errors.

• When a testing machine fails to pass direct verification of one or more of its

components, and cannot be brought within tolerances, it should be repaired

or replaced.

5.1 Direct Verification

Periodic direct verification of the individual components of a Rockwell

hardness machine is an excellent tool for determining what errors exist in the

measurement system and for indicating that a problem may be surfacing.

Unfortunately, direct verification is rarely done in practice; instead industry

primarily relies on indirect verification to assess the measurement capability of

Rockwell hardness machines. This is probably due to the difficulty and cost of

performing direct verifications, and the fact that ASTM and ISO currently only

require a limited direct verification of the hardness machine when the machine

is new or installed.

◆ Verifications of Rockwell Hardness Machines
45

5.1.1 Applied Forces Verification

The forces applied by the Rockwell machine should be verified periodically in

accordance with the test method standards and using instrumentation having

the appropriate accuracy, uncertainty, and traceability to national standards.

The forces should be verified as they are applied during a Rockwell test;

however, longer dwell times are recommended to acquire a stable

measurement.

★ Good Practice Recommendation

For hardness machines that have the capability of adjusting the applied force

levels, the forces should be adjusted as closely as possible to the center of

the tolerances. Some Rockwell hardness machines allow the applied forces

to be mechanically adjusted by the operator. Following direct verification and

adjustment, further adjustment of the forces by the operator should not be

allowed without subsequent direct verification of the adjusted force. Otherwise,

the forces can easily be adjusted out of tolerance to offset other hardness

machine problems that could have developed.

5.1.2 Depth Measuring System Verification

Direct verification of the depth measurement system should be accomplished

as outlined by the test method standards using instrumentation having the

appropriate accuracy, uncertainty and traceability to national standards.

The verification should be performed in an appropriate manner that will

verify the entire working range of the measurement device.

★ Good Practice Recommendation

• Some Rockwell machines are capable of electronically adjusting

(or correcting) the depth measurement system, or the system for

displaying the hardness value, based on comparisons with reference

blocks. If such adjustments or corrections have been made, they should

be reset or removed prior to verifying the indentation depth measuring

system. Otherwise, the verification could indicate compliance for a system

that is in fact out of tolerance.

5.1.3 Hysteresis Verification

A verification of the Rockwell machine should be made to determine the

magnitude of any hysteresis in the flexure and measurement systems of the

machine as a test is made. The goal of the hysteresis verification is to perform

a purely elastic test that results in no permanent indentation. In this way, the

Direct Verification ◆
46

level of hysteresis can be determined. The recommended method for assessing

the level of hysteresis is to perform repeated Rockwell tests with a blunt

indenter (or the indenter holder surface) acting directly onto a very hard test

piece. The tests should be conducted using the highest test force that is used

during normal testing. The hysteresis test is a somewhat difficult test to carry

out. The slightest inelastic deformation at the interface of the blunt indenter

(or holder) and the hard test piece will act to increase the apparent hysteresis.

Every effort should be made to reduce any inelastic deformation.

If there were no hysteresis in a Rockwell machine, the measurements would

indicate a hardness number of 130 Rockwell units when Rockwell ball scales

B, E, F, G, H, and K are used and a hardness number of 100 Rockwell units

when any other Rockwell scale is used. Currently, assessing the level of

hysteresis in the testing machine is not required by ASTM standards. The ISO

standards specify a test to evaluate the testing machine hysteresis allowing a

hysteresis value of 0.5 Rockwell units for machines that have a clamping

fixture for locking the test sample against the upper part of the machine frame

and 1.5 Rockwell units for machines without a locking mechanism. Allowing a

hysteresis level of 1.5 Rockwell units is excessive. Hysteresis should be limited

to less than 0.5 Rockwell units for all machines.

★ Good Practice Recommendations

• When performing the hysteresis verification tests, it is important to choose

an appropriate type of material that the blunt indenter or indenter holder

will act against. The material should have the lowest ductility possible; yet

have sufficient strength to support the test force. Metal carbides, hard

ceramics, and thick glass have been used successfully for this purpose.

Some hard metal test blocks when used for this purpose have exhibited a

small amount of plasticity, which adds to the level of hysteresis, and, thus,

are not recommended. Also, the test should be repeated in the same location

many times before the first measurement is taken. Be aware that this test

does not account for a possible hysteresis effect that could occur as a result

of a problem at the interface of the indenter and the indenter holder, or any

hysteresis due to the Rockwell indenter itself.

• For Rockwell machines that are capable of electronically adjusting

(or correcting) the depth measurement system, any adjustments or

corrections should be reset or removed prior to verifying the machine

hysteresis. Otherwise, corrections can increase or decrease the indicated

level of machine hysteresis providing an inaccurate estimate of the true

hysteresis level.

◆ Verifications of Rockwell Hardness Machines
47

5.2 Indirect Verification

Indirect verification, as specified by the test standards, involves assessing two

aspects of the hardness machine: (1) its repeatability, or how well the hardness

machine can repeatedly measure the same value on uniform material; and

(2) its error (or bias), or how well the machine’s measurement agrees with

reference standards. The methods specified by the ASTM and ISO standards

for assessing these parameters involve making hardness measurements

distributed across the surface of reference blocks. Each Rockwell scale is

evaluated in this manner usually by testing three reference blocks per scale;

the hardness levels of the three blocks are chosen to cover the hardness range

of each scale. It is important that the verifications of the hardness machine be

made with the indenter that will be used for routine testing.

The assessment of both the repeatability and error are usually based on

the same set of hardness measurements (typically five per reference block).

The range of the measured values (maximum minus minimum) of each block

provides an indication of the repeatability of the hardness machine when

testing that specific hardness level. The difference between the average of the

measured values and the certified average values of the respective reference

block provides an estimation of the measurement error or bias.

5.2.1 Measurement Repeatability

When the repeatability measurements are based on tests made across the

surface of a test block, the repeatability value will include an error contribution

due to the non-uniformity of the test block. Depending on the degree of the

hardness non-uniformity of the block, this error contribution can be significant.

When performing an indirect verification, it is best to use reference test blocks

having the highest degree of uniformity as possible.

★ Good Practice Recommendations

• The repeatability of the hardness machine should be assessed periodically

and tracked over time. An increase in the lack of repeatability may indicate

a problem with the Rockwell machine such as worn parts or the need for

cleaning and maintenance.

• A better estimate of repeatability than suggested by the test method

standards may be obtained by making a set of measurements in close

proximity to each other, adhering to indentation spacing restrictions

(see 3.4.7) such that there is no influence from a previous indentation.

A pattern such as illustrated in Figure 8 is recommended. The close

proximity of the measurements will reduce the effect of hardness

nonuniformity in the test block. This procedure must not be used for

assessing the measurement error as described below.

Indirect Verification ◆
48

5.2.2 Measurement Bias or Error

The indirect verification of the measurement error or bias is the final

indication of how all the errors in the test machine have combined together

to influence the Rockwell hardness measurement. Even when all the

parameters of a Rockwell testing machine are within specified tolerances,

the final measurement result can be outside the allowable limits for the total

error. This is because the errors associated with the separate Rockwell

hardness test parameters each have acceptability limits that are relatively wide.

If one were to combine all of the maximum allowable errors for the individual

parameters, the combination would far exceed the specified allowable total

error in measurement capability. Therefore, either the errors associated with

the individual parameters must be reduced to as small a level as possible so

that the combination of the individual errors does not exceed the total error

tolerance, or the individual parameters must be adjusted within tolerances to

produce offsetting errors so that when combined, the total error tolerance is

not exceeded. Both of these techniques rely on direct verification of the

adjustments.

Today, the most commonly used technique for handling measurement errors is

to make an adjustment to one or more machine components to reduce the total

measurement error. Unfortunately, since direct verification is rarely performed,

it is not known whether it is the problem component that is being adjusted to

reduce its error, or a within tolerance component that is being adjusted, possibly

out of tolerance, to offset the error. It is generally felt by some hardness

equipment manufacturers that, in the United States, a majority of Rockwell

hardness machines would not pass a full direct verification due to individual

parameters being out of tolerance and the associated error being offset by

Figure 8. Figure 8.

Alternate pattern for repeatability measurements.

◆ Verifications of Rockwell Hardness Machines

Closest

spacing

allowed
49

adjustments of other parameters. This practice is not recommended, and it can

lead to problems when testing materials at hardness levels other than the test

blocks levels used for the indirect verification or when testing materials other

than the test block material.

★ Good Practice Recommendation

It is recommended that the as-found condition of the testing machine be

assessed as part of an indirect verification. This is important for documenting

the historical performance of the machine. This procedure should be made

prior to any cleaning, maintenance, adjustments, or repairs. The as-found

condition of the testing machine should be determined with the user’s

indenter(s) that are normally used with the testing machine. One or more

standardized test blocks in the range of normal testing should be tested for

each Rockwell scale that will subsequently undergo indirect verification.

If the as-found condition verifications fall outside specified tolerances, it is

an indication that hardness tests made since the last indirect verification may

be suspect.

5.3 Correcting Measurement Biases

For Rockwell hardness machines that have successfully passed both direct

and indirect verifications, there will continue to be some level of measurement

error or bias with respect to the reference standards. If this bias is felt to be

significant for the user’s application, then it may be advantageous to make

mathematical corrections based on the certified values of the reference test

blocks. Presently, ASTM and ISO test methods do not address making

mathematical corrections, although, in practice, a form of mathematical

correction is commonly made for newer Rockwell machines capable of being

electronically calibrated. These machines can determine correction curves by

comparing certified test block values with values measured during an indirect

verification. The curves are electronically stored in the Rockwell machine

and correct future measurement values based of this curve. In general,

mathematical corrections should only be made in cases where the Rockwell

machine has been successfully verified.

A practical method for applying corrections for the measurement biases is to

determine a linear calibration curve for the entire hardness scale. The linear

calibration curve provides a correction value to be applied to future hardness

measurements at any hardness level of that scale. The correction value is

dependent on the Rockwell scale and hardness level of the material under test.

A linear correction curve is chosen because indirect verifications are usually

made with test blocks at only three levels of hardness for each Rockwell scale.

Indirect Verification ◆
50

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

20 25 30 35 40 45 50 55 60 65 70

Measurement Value (HRC)

Bias and Correction (HRC)

Bias Linear Fit Corrected Bias

A curvilinear fit to only three data points often can produce impractical results

at hardness levels other than the three verified levels. A separate and distinct

correction curve is required for each Rockwell scale.

Figure 9 graphically illustrates how the biases can be corrected for a single

Rockwell scale. The left axis represents the difference between testing

machine measurements made on reference test block standards and the

certified values of the reference test blocks. This is the error or bias determined

as part of an indirect verification (average of machine measurements minus

certified reference value). The bottom axis represents the hardness level that is

measured. In this example, the round points indicate the bias values determined

by testing three reference test block standards. A linear fit is made to the three

bias values. The correction to be applied to future measurements is determined

from the value at each point along the linear fit line. For example, when a

future measurement is made at 25 HRC, the correction would be to add

approximately 0.25 HRC to the measured value. The square data points and

dashed line illustrate the result of applying these corrections to the bias values.

Figure 9. Figure 9.

Illustration of the three bias points corrected by a linear fit correction curve.

◆ Verifications of Rockwell Hardness Machines
51

45.0

45.1

45.2

45.3

45.4

45.5

45.6

45.7

45.8

0 1 2 3 4 5 6 7 8 9 10 11

Test Day

HRC

6 MONITORING TEST MACHINE PERFORMANCE

6.1 Reproducibility

In the previous discussion of the repeatability of a hardness machine in 5.2.1,

it was imagined that a small number of Rockwell measurements were made

on a perfectly uniform sample of material. Now, consider that the small set of

Rockwell hardness measurements were reproduced at some periodic interval,

for example once a day over an extended period of time always using the same

test block and indenter. As before, each set of measurements would again

vary within a fairly consistent range. In addition to this within-set variation,

it also would be found that the average for each day’s measurements would

vary from day-to-day, as illustrated in Figure 10. This day-to-day variation is

known as the level of reproducibility of the hardness machine. The variation

is principally due to time dependent sources such as a change of operator or

environmental factors.

The user should monitor the performance of the hardness machine over

an extended period of time to assess the acceptable level of reproducibility.

Subsequent monitoring can provide an indication that the Rockwell machine

may be in need of maintenance or is being operated incorrectly. It is

Figure 10. Figure 10.

Illustration of reproducibility data taken over ten days.

Monitoring Test Machine Performance ◆
52

recommended that control charts, or other comparable methods, be used to

monitor the performance of the hardness machine between verifications.

Control charts provide a method for detecting lack of statistical control.

Control chart data should be interpreted by the user based on past experience.

The need for corrective action does not depend solely on data falling outside

the control limits but also on the prior data leading to this occurrence. As

a general rule, however, once the hardness machine is determined to be in

control, a single occurrence of data falling outside the control limits should

alert the user to a possible problem.

6.2 Daily Verification

The test method standards state procedures for conducting a daily verification

of the Rockwell hardness machine. The intent of the daily verification is for the

user to monitor the reproducibility of the hardness machine between indirect

verifications. At a minimum, the daily verification should be performed each

day that hardness tests are to be made for each Rockwell scale that will be

used. It is recommended that the daily verification procedures be performed

whenever the indenter, anvil, or test force is changed to ensure that these

changes to the machine have not added error to the measurement due to

occurrences such as erroneous adjustments, misalignment, or poor condition

or cleanliness of the machine components.

★ Good Practice Recommendations

• Before performing the daily verification tests, ensure that the testing

machine is working freely and that the indenter and anvil are seated

adequately. The indenter to be used for the daily verification must be the

indenter that will be used for testing.

• Whenever a Rockwell hardness machine fails a daily verification, the

hardness tests made since the last valid daily verification may be suspect.

• It is highly recommended that the results obtained from the daily verification

testing be recorded using accepted statistical process control techniques,

such as control charts. This type of monitoring can alert the user to

impending problems before the measuring capability of the hardness

machine becomes unacceptable.

◆ Monitoring Test Machine Performance
53

7 REDUCING MEASUREMENT DIFFERENCES

AND ERRORS

Consider two Rockwell hardness machines, perhaps a supplier’s machine

and a customer’s machine. Suppose both machines pass indirect verifications.

Will the two machines then measure the same hardness value for a sample

of material? In practice, there is a good chance there will be a measurable

difference in hardness values. It is even possible there could be a significant

difference, with one machine indicating that the material is within specification

tolerances and the second machine indicating the material to be out of

tolerances. Valid determinations of each machine’s measurement uncertainty

(see 8.3) should account for this discrepancy. The simple problem may be that

the uncertainties of the measurements are too large to make valid comparisons.

In this section, recommendations will be made for reducing these types of

measurement differences.

7.1 Reduce Machine Component Operating Errors

It is generally not possible to make good Rockwell hardness measurements

with a poorly operating machine. The initial consideration should be to use

a Rockwell machine capable of measuring to the required accuracy and

repeatability. As discussed previously, the errors in the operating components

of the hardness machine should be identified and assessed through the direct

verification process (see 5.1). Depending on the required level of accuracy,

simply meeting the specified operating tolerances may not be adequate.

Adjustments may be needed to bring each component to the center of

tolerance. Unfortunately, for many types of Rockwell hardness machines,

these types of adjustments are not possible in the field and, in many cases,

may not be possible at all.

It is also important to use indenters that have been certified as meeting all of

the requirements specified in the test method standards, including the shape

and alignment. Until recently, obtaining certifications of the physical dimensions

of diamond or ball indenters has been difficult. Once in use, indenters should be

inspected frequently by visual means to help determine if damage has

occurred.

7.2 Verify Machine Measurement Performance

The hardness measurement performance of a Rockwell machine does not

depend solely on the parameters assessed during a direct verification. Once

the components of the Rockwell hardness machine and indenter are considered

to be operating within acceptable limits, its overall measurement performance

Reducing Measurement Differences and Errors ◆
54

must also be verified. This is accomplished by periodic indirect verification,

coupled with daily verifications. It is important that the verifications of the

hardness machine be made together with the indenter that will be used for

routine testing.

7.2.1 Verification Frequency

The test method standards specify the maximum time allowed between indirect

verifications of Rockwell machines as well as between daily verifications.

These time intervals may not be adequate. More frequent verifications may

be necessary depending on the condition of the machine, the level of machine

usage, and the required measurement accuracy. As discussed in section 6, the

verification results should be monitored and tracked to alert the user to a drift

or erratic behavior in the machine’s performance. These types of problems

may be an indication of an escalating mechanical problem.

7.2.2 Uncertainty in the Certified Hardness Values

of Reference Test Blocks

When a high level of measurement accuracy is important, performance

verifications should be made using reference test block standards having as

low an uncertainty as is practical. This applies in the cases of both indirect

and daily verifications. The uncertainty in the certified values of the reference

standards used for machine verifications will contribute to the overall

measurement uncertainty of the hardness machine.

It is also important to consider to what standard the certified value of the

reference test block is traceable. For example, an indirect verification, or daily

verifications made with reference standards traceable to NIST standards, may

not be appropriate when testing materials that must meet the national standards

of another country or a company’s own internal standards. This will continue to

be an issue until international harmonization of the Rockwell scales is achieved.

Even when reference standards having the lowest available uncertainty are

used for machine verifications, it may not provide sufficient measurement

agreement in cases where a very high level of agreement is needed between

two Rockwell machines. Bear in mind that machine performance verifications

are normally considered acceptable when the measurement bias or error

falls within tolerance limits. The combined levels of bias of the two machines

coupled with the uncertainty of the certified values of the two test blocks

may exceed the level of measurement agreement that is required. This

measurement difference can be reduced, to a degree, by “correcting” future

measurements of each hardness machine based on the biases determined

◆ Reducing Measurement Differences and Errors
55

from the respective machine verifications. The measurement difference can

be further reduced by performing verifications of both machines using the same

test blocks, and then, determine corrections based on the total measurement

difference. When making any corrections of hardness measurements, the

discussions in 5.3 should be considered.

7.3 Measurement Locations

The characteristics of the material to be tested must be taken into

consideration when choosing appropriate measurement locations. Consider

two hypothetical Rockwell hardness machines that agree perfectly in their

measurement performance. Will the two machines then measure the same

hardness value for a sample of material? The initial response would be yes;

however, if the hardness of the material sample varies significantly from

location to location, it would be possible to obtain significant measurement

differences if the measurements were made at two different locations.

Therefore, when a high level of accuracy in measurement comparisons is

important, the same measurement locations should be tested. One solution is

to make all measurements of both machines in one test area; however, the

hardness result may not be representative of the entire sample of material.

A better solution is to choose several test locations over the entire surface

of the material to be tested by both machines. Each machine should make

measurements at each of these locations adjacent to the measurements of

the other machine. The measurement average of each machine could then

be reasonably compared and would also provide a more valid estimate of the

overall average hardness of the sample material.

Verify Machine Measurement Performance ◆
56

8 TRACEABILITY, ERROR, AND UNCERTAINTY

8.1 Traceability

Traceability is defined by the International Vocabulary of Basic and General

Terms in Metrology (VIM)(20) as “Property of the result of a measurement or

the value of a standard whereby it can be related to stated references, usually

national or international standards, through an unbroken chain of comparisons

all having stated uncertainties.” From this definition, it is clear that traceability

can only be obtained when uncertainties are determined. The traceability

hierarchy in Rockwell hardness from highest level to the hardness

measurement is the following:

(1) International definition of hardness: This is similar to a “fundamental

property value.” This definition should precisely define all aspects of the

hardness test.

(2) National definition of hardness: At this time, there is no international

agreement on a well-defined definition for any Rockwell hardness scale.

National definitions are used instead, which are based on national and

international test method standards. These definitions vary from country to

country. The U.S. national definition of Rockwell hardness, as defined by

NIST, is based on the use of the NIST primary reference standardizing

machine with a specific indenter and following a specific testing cycle(15).

(3) Primary reference standardizing machine: A primary reference

standardizing machine is usually maintained at a country’s National

Metrology Institute (NIST in the United States). The design and operation

of this machine is dependent on the hardness definition. The NIST primary

reference standardizing machine is shown in Figure 11.

(4) Primary reference test blocks: The primary reference test blocks

are calibrated using the primary reference standardizing machine in

accordance with the hardness definition.

(5) Secondary standardizing machine: The design and operation of this

machine is based on the hardness definition and calibrated using primary

reference test blocks.

(6) Secondary standardized test blocks: The secondary standardized test

blocks are calibrated using the secondary hardness machine in accordance

with the hardness definition.

(7) Laboratory hardness test machine: The design and operation of this

machine is based on the hardness definition and calibrated using

standardized test blocks.

◆ Traceability, Error and Uncertainty
57

(8) Laboratory hardness measurement: The measurement is made based

on the hardness definition, using the laboratory hardness test machine.

Two possible traceability scenarios for Rockwell hardness are: (1) to achieve

traceability to known reference standards such as reference standards

maintained at NIST; and (2) to achieve traceability based on hardness machine

Figure 11.

NIST Rockwell hardness standardizing machine.

Traceability ◆
58

errors with respect to the Rockwell hardness definition. In the first scenario,

a standardizing laboratory or a testing laboratory bases its measurement

uncertainty on measurement comparisons using standardized reference test

blocks. Traceability can then be linked to the highest reference level in the

traceability hierarchy through one or more reference levels. In the second

scenario, a standardizing laboratory’s measurement traceability is with respect

to the Rockwell hardness definition and is based on standardizing machine

errors as defined by the definition. This is the method that is used in

determining the measurement uncertainty of primary reference standardizing

machines.

8.2 Measurement Error

The Rockwell hardness test is usually thought of as a method that measures

the hardness of a material. A more accurate description might be that the

Rockwell hardness test only provides an estimate of the absolute “true”

hardness value. It is only an estimate since, like essentially all measurement

systems; there is always some level of error in a Rockwell hardness

measurement. For a hardness measurement to be useful, the level of error

must be small enough to meet the user’s needs.

The total error in a measurement is often the result of a combination of

errors from multiple sources. In the case of a Rockwell hardness machine,

errors associated with machine components, testing cycle variations, and

environmental conditions, as well as other sources, contribute in varying

degrees to the overall measurement error. When it is practical, the

measurement result should be corrected for these errors. However, in many

cases, the errors may occur randomly and cannot be corrected. In other

cases, the errors may be systematic, but there may be valid reasons for not

correcting these errors. Even when corrections are made to compensate for

the errors, there will be an additional error associated with the correction.

These uncorrected errors then account for an “uncertainty” in the accuracy

of the measurement result. To have confidence that the result of a hardness

measurement is appropriate for a particular application, some understanding

of the level of uncertainty in the measurement must be known.

8.3 Uncertainty

The determination of uncertainty associated with Rockwell hardness

measurements is a relatively new concept for many users of Rockwell

hardness as well as for laboratories engaged in hardness calibrations, such as

test block standardizing agencies. Traditionally, the acceptance criterion for

Rockwell hardness measurements has been through the use of acceptability

tolerances. This has been true for most all aspects of the Rockwell method

◆ Traceability, Error and Uncertainty
59

including measurements made as part of the direct and indirect verifications

of hardness machines and the standardization of test blocks.

Tolerance limits will continue to be used in Rockwell hardness. They provide

general criteria for determining whether a Rockwell hardness machine is

operating at an acceptable level of performance. What the acceptability

tolerance limits do not indicate is the accuracy in the measurements made

with the hardness machine. When it is important that the measurement

accuracy be known, then the uncertainty in the measurements should be

determined.

8.3.1 Uncertainty Limits

Uncertainty values are usually written as numerical limits bracketing the

measurement value. Stating a measurement value in this way tells the user

that the “true value” of the measurement would fall somewhere within these

uncertainty bounds. As an example of uncertainty as it might apply to Rockwell

hardness, consider a standardized hardness block that is certified with a value

of 25.3 HRC ± 0.4 HRC. In this example, the 25.3 HRC value is the certified

average hardness of the block, and the ± 0.4 HRC is the uncertainty in this

certified value. This means that although the standardizing agency estimated

the average hardness value of the test block to be 25.3 HRC, the “true value”

would fall somewhere within 24.9 HRC to 25.7 HRC. For a complete

understanding of this measurement and uncertainty, the values should be

accompanied with a brief statement defining what the uncertainty interval

represents. This statement should usually indicate the statistical process used

to calculate the uncertainty and state the confidence level of the uncertainty

interval.

It is important to understand the difference between uncertainty intervals,

such as given in the example above, and acceptance tolerance limits

traditionally provided with commercial test blocks. In the example above, the

± 0.4 HRC states that the standardizing agency can only estimate the “true”

average hardness of the test block and that the “true value” falls somewhere

within ± 0.4 HRC of 25.3 HRC. In contrast to these uncertainty limits, the

certified value marked on commercial test blocks in the United States has

included tolerance limits that reflect an ASTM acceptability requirement.

This requirement states that when using the test block to conduct an indirect

verification or daily check of a hardness machine, the machine’s measurement

value must fall within these limits. As a rule, the acceptance tolerances have

been stated in the same format as demonstrated above for uncertainty

statements, for example 25.3 HRC ± 1.0 HRC. These are clearly two

different concepts.

Uncertainty ◆
60

8.3.2 Highest Reference Standard

Before the level of uncertainty can be determined, the laboratory must

choose a reference standard to which the measurement value will be

compared. For example, the level of error in a Rockwell hardness machine

might be determined by comparing the result of a measurement made on a

standardized test block with the test block’s certified hardness value. It then

follows that the certified value of the test block also includes a level of error

with respect to another reference standard, typically the performance of the

hardness machine used to standardize it. The performance of the standardizing

hardness machine also includes a level of error with respect to a higher-level

reference standard, and so it goes to the highest level of reference.

The highest level of reference to which a measurement value is compared

might be referred to as the “true value.” The level of error in the measurement

is then determined with respect to this “true value” taking into account the

errors at each of the reference levels between the measurement value and the

“true value”. Ideally, the highest level of reference should be an internationally

agreed upon standard. In some cases, international agreement does not exist;

consequently national reference standards (i.e., NIST in the United States) are

typically considered the highest reference level. At present, this is the case for

Rockwell hardness.

8.3.3 Calculation of Rockwell Hardness Uncertainties

Over the past decade, there has been an increasing industry trend towards

obtaining quality program accreditation, as well as obtaining accreditation for

testing and calibration facilities. A common element of most of these programs

is the requirement for reporting the uncertainty of measurement data. As a

result, users of Rockwell hardness have struggled to develop procedures to

determine the uncertainty of Rockwell measurements.

Currently, there are no generally agreed upon U.S. or international methods

for calculating the measurement uncertainty of a Rockwell hardness machine

or the uncertainty in the certified value of standardized test blocks. A reason

for this may be that, until recently, there has been very little desire or need

by industries that use Rockwell hardness to use uncertainty values. Also, the

determination of Rockwell hardness uncertainty is not as straightforward as

it would seem.

For example, suppose the uncertainty is to be calculated by combining all of

the sources of error together. The errors associated with the hardness machine

are typically not in hardness units, but they are in other units, such as force,

length, and time. In order to determine an uncertainty in the hardness measurement,

the relationships between how these errors affect the hardness value must be

◆ Traceability, Error and Uncertainty
61

determined, often by experiment. Amplifying this problem is the fact that these

relationships vary by Rockwell scale and hardness level and are often material

dependent. In addition, the errors associated with a diamond indenter are difficult

to identify and more difficult to relate to errors in hardness. Thus, it is clear that

determining the hardness uncertainty by assessing the individual components of

the hardness machine is extremely difficult to accomplish.

A different approach to determining Rockwell hardness uncertainty is to

assume that by passing a direct and indirect verification, the errors in the

individual operating components of the hardness machine are small enough

that the indirect verification measurements are not the result of multiple large

errors offsetting each other. Thus, the individual machine components can be

considered to be operating together as a single component. The individual

operating components include the force application system, depth measuring

system, indenter, test cycle, and the remaining parts of the machine frame

and test specimen support system. By considering the hardness machine as

a single component, the uncertainties may be estimated with respect to the

overall performance of the hardness machine without having to assess the

uncertainty contributions for each of the separate machine components.

When this approach is used, the most significant sources of error have been

determined to be the following:

(1) Repeatability in the performance of the hardness machine.

(2) Reproducibility in the day-to-day performance of the hardness machine,

including operator influence.

(3) Resolution of the measurement indicating display.

(4) Uncertainty in the certified average hardness value of the reference test

block.

(5) Non-uniformity in hardness across the surface of the test block or test

material.

(6) Bias in the hardness machine measurement with respect to the reference

standard to which traceability is claimed.

(7) Determining the hardness machine measurement bias.

(8) Correcting for the measurement biases.

(9) The remaining bias in the hardness machine after a correction for bias is

made.

As this guide is being written, there are efforts both internationally and

within the United States to develop general procedures to assist Rockwell

Uncertainty ◆
62

hardness standardization laboratories and users of Rockwell hardness in

evaluating their measurement uncertainty. In the United States, the ASTM has

initiated the development of such a procedure, and the ISO is to take up this

issue at the next committee meeting of ISO TC164/SC 3 subcommittee on

hardness testing in 2001.

◆ Traceability, Error and Uncertainty
63

9 STATUS OF ROCKWELL HARDNESS

STANDARDIZATION IN THE YEAR 2000

9.1 United States

The past few years have seen significant changes to Rockwell testing in the

United States with the introduction of NIST Rockwell standards, accreditation

of Rockwell calibration laboratories, and the increased need to determine

measurement uncertainty. Although the changes may not yet have impacted

many users of Rockwell hardness, these and other proposed changes should

soon affect every level of testing and will hopefully improve the accuracy and

consistency of Rockwell measurements throughout the nation’s industries.

9.1.1 NIST Standards

In 1991, NIST began the development of a national Rockwell hardness

standardization laboratory at the urging of the ASTM and U.S. industry.

The goals of this program are to standardize the Rockwell hardness scales

for the United States and to provide industry with stable national transfer

standards in the form of reference test blocks. In standardizing the Rockwell

scales, NIST has employed instruments and procedures having the highest

metrological accuracy as practicable.

In June 1998, NIST released the first Rockwell hardness reference test block

standards for sale to industry. These blocks are for the HRC scale at three

hardness levels, nominally 25 HRC, 45 HRC, and 63 HRC. The blocks are

available to anyone wishing to purchase them; however, they are primarily

intended for use by the secondary Rockwell hardness calibration laboratories.

A significant result of the NIST standardization of the HRC scale is that the

hardness levels of the NIST HRC scale deviated from the HRC scale used by

U.S. industry at that time. The magnitude of the deviation varies by hardness

level and also depends on which calibration agency’s reference test blocks

had been used previously. Figure12 demonstrates the general trend of the

difference between NIST and U.S. industry HRC scales. The offset trend

given in Figure 12 should not be used as an absolute offset. The relationship

could possibly differ by as much as ± 0.5 Rockwell points; however, it is

generally true that the greatest offset is at the high end of the scale. Also

of interest is that the NIST HRC scale is in good agreement with other

countries worldwide (see 9.2 below).

The next Rockwell scale for which NIST will release test blocks is the

Rockwell B scale, likely followed by the HRA, HRN, and HRT scales.

Eventually NIST hopes to provide a means for traceability to all Rockwell

scales.

Status of Rockwell Hardness Standardization ◆
64

20 25 30 35 40 45 50 55 60 65 70

Nominal HRC

0.0

0.5

1.0

1.5

NIST Increase in HRC Scale

9.1.2 ASTM Test Method Standards

The ASTM Subcommittee E28.06 on Indentation Hardness Testing is always

striving to improve the Rockwell hardness test. Subcommittee members are

from industry and government, and they include manufacturers and users of

Rockwell hardness equipment. Much of the effort to improve the Rockwell

test has been through the requirements of the ASTM E18 Rockwell hardness

test method(2). A significant revision was recently made to the standard

requiring that performance verifications of Rockwell hardness indenters and

hardness machines must be made using test blocks calibrated traceable to the

Rockwell standards maintained by NIST. This can be accomplished through

the use of commercial test blocks calibrated traceable to the NIST standard

or by directly using the NIST SRMs. The new requirement will apply only to

the Rockwell scale(s) for which NIST supplies primary reference test blocks.

As NIST develops new SRMs for other Rockwell hardness scales, the same

requirement will apply for those scales.

Figure 12. Figure 12.

General trend of the difference between NIST and U.S. industry

Rockwell C scales. The line represents the approximate increase in the

HRC scale as determined by NIST (for hardness levels as indicated

on the bottom axis) with respect to the HRC scale used by

U.S. industry prior to development of the NIST scale.

◆ Status of Rockwell Hardness Standardization
65

Currently, the ASTM hardness subcommittee also is developing a major

revision of the E18 Rockwell hardness standard. The intention of the revision

is to improve E18 by: clearly specifying when traceability is achieved;

clarifying requirements and procedures; revising procedures to reflect current

practice; and adding requirements and procedures to improve the Rockwell

hardness test method.

The increasing need by industry to report uncertainties has led the ASTM

hardness subcommittee to initiate the development of a general procedure for

determining uncertainty in Rockwell hardness measurements. The procedure is

being developed to assist hardness standardization, calibration, and verification

laboratories by providing a basic approach to evaluating their uncertainty in

order to simplify and unify the interpretation of uncertainty by users of

Rockwell hardness.

9.1.3 Hardness Industry

Most U.S. secondary laboratories engaged in the manufacture and calibration

of Rockwell hardness equipment are now producing Rockwell HRC test blocks

and diamond indenters that are certified traceable to the NIST HRC reference

test block standards. This has resulted in some users having to obtain a new

Rockwell diamond indenter in order for their hardness machine to pass indirect

verification of the HRC scale using NIST traceable HRC test blocks.

9.1.4 Accreditation

An increasing number of domestic and international customers of calibration

and testing agencies are requiring that calibrations and measurements made

by these agencies be traceable to national reference standards when possible,

and, in many cases, that the laboratories be accredited to perform these

measurements. This applies to the Rockwell hardness industry as well.

Consequently, commercial and governmental programs have been developed

for accrediting laboratories engaged in Rockwell hardness testing and

calibrations.

9.2 International

International harmonization of the Rockwell hardness scales is yet to occur.

This is due to several factors, the most significant being differences in the

testing cycles used by the National Metrology Institutes (NMIs) throughout

the world and, in the case of the diamond indenter scales, differences in

the performance of the national indenters used by the NMIs(21). The need

for international harmonization is well recognized, and there are efforts to

achieve this goal currently being made under the auspices of the International

United States ◆
66

Committee for Weights and Measures (CIPM) and, to some degree, by the

ISO and OIML.

9.2.1 BIPM and CIPM

The Bureau International des Poids et Mesures (BIPM) [International

Bureau of Weights and Measures] was set up by the Convention of the

Metre, a diplomatic treaty that was signed in 1875. Under the terms of the

Metre Convention, the BIPM is financed jointly by the Member States of

the Convention and operates under the exclusive supervision of the Comité

International des Poids et Mesures (CIPM) [International Committee of

Weights and Measures]. The BIPM headquarters is located in Sèvres, France,

near Paris.

The CIPM is made up of eighteen individuals, each from a different Member

State. Its mandate is to provide the basis for a single, coherent system of

measurements throughout the world, traceable to the International System

of Units (SI). This task takes many forms, from direct dissemination of units

(as in the case of mass and time) to coordination through international

comparisons (key comparisons) of national measurement standards (as in

length, electricity, radiometry, and ionizing radiation). It operates through a

series of Consultative Committees, whose members are the national metrology

laboratories of the Member States of the Convention, and through its own

laboratory work. The CIPM meets annually at the BIPM and discusses reports

presented by its Consultative Committees. Reports of the meetings of the

CIPM, and all the Consultative Committees, are published by the BIPM.

In 1998, a new ad-hoc working group was formed under the CIPM to

investigate the present state and needs for international comparisons of

hardness standards and report to the CIPM on the most appropriate platform

for the comparison, if it is really necessary. The working group was given the

name Ad-Hoc Working Group on Hardness (AHWGH) and was comprised

of members representing ISO, OIML, the International Measurement

Confederation (IMEKO), and National Metrology Institutes having a strong

standardization program. Since its inception, the group determined that

international comparisons of hardness standards are important and necessary.

Consequently, in October 1999, the working group was officially approved as

the Working Group on Hardness (WGH) and has been placed under the

Consultative Committee on Mass (CCM).

Current efforts by the WGH include the adoption of a recent world-wide

intercomparison of Rockwell hardness scales using a diamond indenter

as an international key comparison, the initiation of a study on the shape

measurement of diamond Rockwell indenters, and the initiation of a key

comparison of Vickers hardness. An example of the results of the worldwide

◆ Status of Rockwell Hardness Standardization
67

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

HRC20 HRC25 HRC30 HRC35 HRC40 HRC45 HRC50 HRC55 HRC60 HRC62,5 HRC65

Nominal Hardness of the Reference Block 

HRC Difference from Average

NMI 1

NMI 2

NMI 4

NIST

NMI 6

NMI 7

NMI 10

NMI 11

NMI 12

intercomparison(22) is shown in Figure 13 for the Rockwell C scale. The

participants in the comparison were national metrology institutes throughout

the world, including NIST. As the figure illustrates, there continues to be

significant differences between the world’s national hardness scales.

9.2.2 ISO

The ISO technical committee on hardness testing, ISO TC164/SC3, is

comprised of hardness experts representing their nations’ standards

organizations. The schedule for review and revision of test method standards

is usually every five years; however, the committee meets each year to

discuss changes and improvements to the hardness tests, based on the latest

technical information presented by the delegations. The latest revisions of

the Rockwell hardness test method standards ISO 6508-1(3), ISO 6508-2(4),

and ISO 6508-3(5) were published in 1999.

9.2.3 OIML

The current OIML Recommendations related to hardness testing are under

revision at this time. The Recommendation R39 (1981), concerning the

verification of Rockwell hardness machines will be the initial document to

be revised.

Figure 13. Figure 13.

Results of 1999 international comparison of HRC scale.

The heavy line indicates the NIST data.

International ◆
69

10 BIBLIOGRAPHY

1. Lysaght, V.E., Indentation Hardness Testing, Reinhold Publishing Corp.,

New York, 1949, pp. 57-105.

2. ASTM E 18 – 2000, Standard Test Methods for Rockwell Hardness and

Rockwell Superficial Hardness of Metallic Materials, West Conshohocken,

PA, ASTM, 2000.

3. ISO 6508-1 Metallic Materials – Rockwell hardness test (scales A, B, C,

D, E, F, G, H, K, N, T) – Part 1: Test method, Geneva, International

Organization for Standardization, 1999.

4. ISO 6508-2 Metallic Materials – Rockwell hardness test (scales A, B, C,

D, E, F, G, H, K, N, T) – Part 2: Verification of testing machines, Geneva,

International Organization for Standardization, 1999.

5. ISO 6508-3 Metallic Materials – Rockwell hardness test (scales A, B, C,

D, E, F, G, H, K, N, T) – Part 3: Calibration of reference blocks, Geneva,

International Organization for Standardization, 1999.

6. OIML International Recommendation No. 12 (1974), Verification and

calibration of “Rockwell C” hardness standardized blocks.

7. OIML International Recommendation No. 36 (1976), Verification of

indenters for hardness testing machines (Systems: Brinell – Rockwell B, F,

and T – Vickers – Rockwell C, A, and N).

8. OIML International Recommendation No. 39 (1981), Verification of

hardness testing machines (Rockwell B, F, T – C, A, N systems).

9. OIML International Recommendation No. 11 (1974), Verification and

calibration of “Rockwell B” hardness standardized blocks.

10. Liggett, W.S., Low, S.R., Pitchure, D.J., and Song, J., “Capability in

Rockwell C Scale Hardness,” Journal of Research of the National

Institute of Standards and Technology, Volume 105, Number 4,

July–August 2000, pp. 511–533.

11. Metals Handbook, 8th Edition, Vol. 11, Nondestructive Inspection and

Quality Control, H.E. Boyer, editor, American Society for Metals, pp. 1–13.

12. Metals Handbook, Ninth Edition, Vol. 8, Mechanical Testing, Rockwell

Hardness Testing, A.R. Fee, R. Segabache, E.L. Tobolski, American

Society for Metals, pp. 74–83.

13. Metals Handbook, Desk Edition, H.E. Boyer and T.L. Gall, editors,

American Society for Metals, Hardness Testing, pp. 34–4 to 34–8, 1985.

Bibliography ◆
70

14. Low, S.R., Pitchure, D.J., Flanigan, C.D., “The Effect of Suggested

Changes to the Rockwell Hardness Test Method,” Proceedings of

XVI IMEKO World Congress, eds. Osanna, P., Durakbasa, A.,

Afjehi-Sadat, A., (2000), pp. 313–318.

15. Low, S.R, Gettings, R.J., Liggett, Jr., W.S., Song, J., Rockwell Hardness –

A Method-Dependent Standard Reference Material, Proceedings of the

1999 Workshop and Symposium (Charlotte, NC, 11–15 July 1999),

Charlotte, NC, 1999.

16. Petik, F., Factors Influencing Hardness Measurement (A Systematic

Survey of Research Results), Bureau International de Metrologie Legale,

Paris, 1983 (restricted distribution).

17. ASTM E 140 – 97, Standard Hardness Conversion Tables for Metals,

West Conshohocken, PA, ASTM, 2000.

18. NIST Standard Reference Materials Catalog 1998–99, NIST Special

Publication 260, Trahey, N.M., editor, Gaithersburg, MD, January 1998.

19. Low, S.R., Liggett, W.S., Pitchure, D.J., “A New Method of Certifying

Standardized Rockwell Hardness Test Blocks,” Proceedings of

International Symposium on Advances in Hardness Measurement,

Standards Press of China, Beijing, China, 1998, 91–96.

20. BIPM / IEC/ IFCC / ISO / IUPAC / IUPAP / OIML: International

Vocabulary of Basic and General Terms in Metrology (VIM), Clause 6.10,

1993.

21. Song, J.F., Low, S., Pitchure, D., Germak, A., Desogus, S., Polzin, T.,

Yang, H.Q., Ishida, H., Barbato, G., “Establishing a World-Wide Unified

Rockwell Hardness Scale With Metrological Traceability,” Metrologia,

1997, 34, 331–342.

22. Polzin, T., Schwenk, D., contributions from He Li, Hansen, V., Herrmann K.,

Barbato, G., Germak, A., Ishida, H., Onsinska-Karczmarek, A.,

Scartazzini, W., Borovsky, J., Elkington, D., Low, S., Song, J., Bahng, G.W.,

World-Wide Unified Scales for the Rockwell Hardness Test with Conical

Indenters, Results of the round robin test, differences between the

laboratories, Materialprüfung, (42), 2000, S. 460–467.

◆ Bibliography
71

Applied Force Effect ◆

ANNEX A: APPLIED FORCE EFFECT

The magnitude of change in the Rockwell hardness value that results from

a change in the applied force is shown in Figure A.1 for the preliminary force

and in Figure A.2 for the total force. The test method standards published

by ASTM and ISO provide tolerances for the applied Rockwell forces.

Summaries of these tolerances are given in Table A.1. Figure A.3 illustrates

the possible variation in Rockwell hardness measurement values that can be

obtained for the diamond indenter scales while maintaining the forces within

the specified tolerances.

10 20 30 40 50 60 70 80 90 100

Hardness (HR)

0.0

0.1

0.2

0.3

0.4

Hardness Change (HR)

Due To +1 N Prelim.-Force Change

HR45N HR30N

HR15N

HRC HRD

HRA

Fig. A

0 10 20 30 40 50 60 70 80 90 100 110

Hardness (HR)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Hardness Change (HR)

Due To +1 N Prelim.-Force Change

HRBW

HRGW

HRFW

Fig. B

HR15TW

HR30TW

HR45TW

10 20 30 40 50 60 70 80 90 100

Hardness (HR)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Hardness Change (HR)

Due To +1 N Total-Force Change

HRC

HRD

HRA

HR45N

HR30N

HR15N

Fig. A

0 10 20 30 40 50 60 70 80 90 100 110

Hardness (HR)

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Hardness Change (HR)

Due To +1 N Total-Force Change

HRGW

HRFW

HRBW

HR45TW

HR30TW

HR15TW

Fig. B

Figure A.1. Figure A.1.

Change in the Rockwell hardness value due to a change in the preliminary

force for diamond indenter scales (Figure A) and selected ball scales (Figure B).

Figure A.2. Figure A.2.

Change in the Rockwell hardness value due to a change in the total force

for diamond indenter scales (Figure A) and selected ball scales (Figure B).
72

Test forces 

N (kgf) 

ASTM Tolerances on 

Applied Forces 

N 

ISO Tolerances on 

Applied Forces 

N 

98.07 (10) ± 1.96 ± 1.96 

588.4 (60) ± 4.41 ± 5.88 

980.7 (100) ± 4.57 ± 9.81 

1471 (150) ± 8.83 ± 14.71 

29.42 (3) ± 0.589 ± 0.588 

147.1 (15) ± 0.981 ± 1.471 

294.2 (30) ± 1.961 ± 2.942 

441.3 (45) ± 2.943 ± 4.413 

Table A.1.

Specified test forces with tolerances

Fig. A: ASTM Fig. B: ISO

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Nominal Hardness (HR)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

± Rockwell Hardness Offset (HR)

HR45N

HRC

HRD HR30N HRA

HR15N

 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Nominal Hardness (HR)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

± Rockwell Hardness Offset (HR)

HR45N

HRC

HRD

HR30N

HRA

HR15N

Figure A.3. Figure A.3.

The possible offset in Rockwell hardness measurement values

that could be obtained for the diamond indenter scales by varying

the applied preliminary forces and total forces within the

ASTM tolerances (Figure A) and the ISO tolerances (Figure B).

◆ Applied Force Effect
73

ANNEX B: ROCKWELL HARDNESS TESTING

 CYCLE EFFECT

To better understand the Rockwell hardness testing cycle, imagine it divided

into eight parts or steps, as illustrated previously in Figure 3. These eight testing

cycle steps are defined as either a time period or an indentation velocity, each

of which can be varied. They are:

1. the contact velocity of the indenter at the point of contact with the test

material;

2. the preliminary force application rate as the preliminary force is applied;

3. the preliminary force dwell time, the time period from the onset of reaching

the preliminary force until the first baseline depth of indentation is

measured;

4. the additional force application rate as the additional force is added to the

preliminary force to obtain full application of the total force;

5. the total force dwell time, the time period during which the total force is

fully applied;

6. the additional force removal rate as the additional force is removed,

returning to the preliminary force level;

7. the recovery dwell time, the time period from when the additional force is

fully removed, until the second and final depth of indentation is measured;

and

8. the preliminary force removal rate as the preliminary force is removed.

With the exception of step 8, which has no influence on the hardness

measurement, all of the testing cycle steps can affect the hardness result to

some degree, some considerably more than others. The extent of the possible

range in hardness values depends on which steps of the testing cycle are

varied and the amount of the change, and on the hardness level and flow

properties of the material under test. Both an increase and decrease in the

hardness measurement value can occur by changing any one of the testing

cycle steps. It is also possible that by varying two or more steps of the testing

cycle, the respective effects can offset the others and result in essentially no

change in the measured hardness. The testing cycle steps that are considered

to have the greatest effect on the hardness measurement result are typically

specified by the Rockwell hardness test method standards. Also, newer

commercial hardness testers are often pre-programmed by the manufacturer

with a default testing cycle, defining two or more of these variables.

Rockwell Hardness Testing Cycle Effect ◆
74

The effect that each of the eight test-cycle steps has on the hardness result

can be divided into two categories: (1) indenter velocity or force application

rate effect; and (2) dwell time effect. Steps 1, 2, 4, 6, and 8 fall under the first

category. The effect of obtaining different measurement values by varying one

or more of these five testing cycle steps is due either to rate sensitivity of the

material under test or to the dynamics of the hardness tester. The remaining

three parts of the testing cycle, steps 3, 5, and 7, fall into the second category

defined as dwell times. Each of the three dwell time steps affect the hardness

result because of creep and elastic recovery of the test material which occurs

during these periods of constant force levels. The relative effect that each of

the eight test-cycle steps has on the Rockwell hardness result are discussed

below by presenting data from actual Rockwell hardness measurements.

The information is presented to illustrate trends only since the effect of each

testing cycle step will vary depending on the hardness scale and the specific

material tested.

B.1 Effect of Force Application Rate

For each of the five steps [1, 2, 4, 6, and 8] in this category, an excessive

indenter velocity or force application rate may adversely affect the Rockwell

measurement. The applied forces can overshoot the specified levels due

to dynamic effects, or cyclic vibration may be introduced into the force

application mechanism. Test method standards usually only specify steps 1, 2,

6, and 8 to be accomplished “without shock or vibration.” When a reasonable

testing speed is used, the magnitude that these testing cycle steps affect the

hardness result is typically negligible as compared to the effects produced by

varying the dwell time variables. In addition to the effect caused by excessive

force application rates, the measurement result may also be affected due to

rate sensitivity of the test material. For most of the five test-cycle steps, the

rate sensitivity effect is negligible with the exception of testing cycle step 4,

the additional force application velocity. For many metallic materials, variations

in the rate of applying the additional force have been shown to have a

significant measurable effect on the resultant Rockwell value.

During testing cycle steps 2, 4, 6, and 8, forces are being applied or removed

from the indenter as it produces the indentation in the test material. Because

of differences in the design and operation of hardness machines, in many cases

the indenter velocity or force application rate is not constant during the entire

period of a testing cycle step. Also, it is often difficult to accurately measure

the velocity of the indenter during a hardness test. Thus, in cases where these

testing cycle steps are specified in standards, a time period is sometimes

specified rather than indenter velocity.

◆ Rockwell Hardness Testing Cycle Effect
75

B.1.1 Step 1 – Contact Velocity of the Indenter

The effect on hardness caused by testing cycle step 1, the contact velocity

of the indenter at the point of contact with the test material, is primarily due

to dynamic effects of the indenter. An excessive contact velocity could cause

the preliminary force level to be exceeded if the indenter cannot decelerate

and stop when the preliminary force is applied, or, more likely, the indenter

may impact the test material setting up a cyclic vibration in the hardness

tester. Each of these circumstances may vary the hardness result.

B.1.2 Step 2 – Application of the Preliminary Force

The preliminary force application, testing cycle step 2, may be specified in

terms of the velocity of the indenter from initial contact of the indenter with

the test material, to the full application of the preliminary force level. It also

may be specified in terms of the period of time for applying the preliminary

force. During testing cycle step 2, the extent of indenter displacement is

relatively small, and for most commercial hardness testers, this operation

occurs fairly rapidly. An exception is that manually operated hardness testers

allow the user to easily vary the rate at which this testing cycle step occurs.

For this part of the testing cycle, any effect on the hardness result that

might be due to rate sensitivity of the test material has not been extensively

investigated. It is usually considered to be negligible in comparison with other

testing cycle steps. There is some evidence, however, that when longer time

periods are used to apply the preliminary force, significant material creep can

occur during the force application which may alter the test material creep

behavior during the preliminary force dwell time (testing cycle step 3) and,

thus, affect the hardness result.

B.1.3 Step 4 – Application of the Additional Force

The additional force application testing cycle step is defined as starting when

the additional force begins to be added to the preliminary force and ends when

the total force is achieved. Unlike the four other testing cycle steps grouped

in this category, tests have shown that the rate at which the additional force

is applied may significantly affect the Rockwell measurement. Often, neither

the indenter velocity nor the rate that the force is applied is constant during the

entire additional force application but, instead, varies during this period. In these

cases, it is typical that the velocity or rate is rapid at the onset and then slows

in the last part of the force application. It is very important that the velocity

or rate not be so fast that dynamic effects produce a momentary overshoot of

the total force level or set up oscillations in the force application mechanism.

Figure B.1 illustrates the type of force and indenter depth oscillations that

can occur when the force application rate is too fast.

Effect of Force Application Rate ◆
76

Tests have shown that by varying the indenter velocity used for the additional

force application, different Rockwell hardness results can be obtained. It is

believed that the velocity effect is more significant during the final part of

the force application. It is not clear, at this time, what mechanism causes the

change in Rockwell results when the force application rate is varied. It may

be due to the material’s ability to creep during very slow applications of force.

An example of this velocity effect is shown in Figure B.2 for a material of

50 HRC. This figure shows tests made using indenter velocities ranging from

0.5 to 70 μm/s on a test block having a hardness of approximately 50 HRC.

For this material, the largest differences in hardness measurement results

occurred for tests made with the very slowest velocities (<10 μm/s).

The measurement results were more constant as the velocity was increased.

As a point of reference, commercial hardness testers often run at velocities

of about 100 μm/s, although many slow at the last part of the force application.

B.1.4 Step 6 – Removal of the Additional Force

The magnitude of the effect that removal of the additional force (testing cycle

step 6) has on the hardness result is similar to that of testing cycle step 2. As

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Relative Time (s)

-0.03

-0.02

-0.01

0.00

Relative Indentation Depth (mm)

130

135

140

145

150

155

Force (kgf)

1300

1350

1400

1450

1500

Force (N)

Figure B.1. Figure B.1.

Force and indenter depth oscillations that can occur

when the force application rate is too fast.

◆ Rockwell Hardness Testing Cycle Effect
77

the additional force is removed, the amount of elastic recovery of the material

and, thus, indenter displacement is relatively small. For most commercial

hardness testers this operation is fixed to occur fairly rapidly, although manually

operated hardness testers may allow the user to manually vary this time period.

Again, as with testing cycle step 2, the effect that this part of the testing cycle

has on the hardness result has not been closely examined. The effect is usually

considered to be negligible, even more insignificant than any effect due to the

preliminary force application rate. However, if a very slow unloading rate were

utilized, the material would continue to creep under the higher force levels until

the additional force was completely removed. The added time under the higher

force could affect the hardness result in this case.

B.1.5 Step 8 – Removal of the Preliminary Force

Testing cycle step 8, removal of the preliminary force, occurs after the two

depth measurements have been made that are used in the determination of

the hardness result. Varying this part of the testing cycle has no effect on the

hardness result.

0 10 20 30 40 50 60 70

Constant Indenter Velocity (um/s)

50.0

50.1

50.2

50.3

50.4

50.5

50.6

50.7

HRC

Figure B.2. Figure B.2.

Change in apparent HRC hardness due to changes in the

additional force application rate (indenter velocity).

Effect of Force Application Rate ◆
78

B.1.6 Summary – Indenter Velocity and Force elocity and Force Application

 Times Effects

The testing cycle steps grouped in this category have been shown to contribute

to the resulting hardness measurement value. This is particularly true for

testing cycle step 4, the application of the additional force.

B.2 Effect of Dwell Times

As an aid to this discussion, indentation depth data will be presented for each

of the three dwell times. The data will be displayed by greatly expanding the

indenter depth axis and magnifying the area of the testing cycle of interest as

illustrated in Figure B.3.

h

Figure B.3. Figure B.3.

Expanded view of the material creep and recovery

during the dwell times of a Rockwell hardness test.

◆ Rockwell Hardness Testing Cycle Effect

B.2.1 Step 3 – The Preliminary Force Dwell Time

As stated above, the preliminary force dwell time is defined as the dwell time

from the onset of reaching the preliminary force level until the first baseline

depth of indentation is measured. In other words, during this dwell time period,

the force on the indenter is held constant at the preliminary force level. At the

end of the preliminary force dwell time, the depth of indentation is measured

which will be used in the calculation of the hardness number. While under the

constant force, if the depth of the indenter is not stable but, instead, continues
79

to creep into the test material, then the measurement value of the indentation

depth will vary with time. Thus, the first baseline depth measurement that

is used in the calculation of the HRC value will depend on how long after

reaching the preliminary force level the measurement is made (i.e., the

preliminary force dwell time). Since the calculation of Rockwell hardness is

based directly on this depth measurement, then any change in the preliminary

force dwell time will directly affect the resulting hardness value.

Tests have shown that indentation continues during the preliminary force

dwell time due to plastic flow in the test material. Figure B.4 illustrates the

creep behavior of the material for 6.5 seconds after the preliminary force is

applied. This data is for tests made on three test blocks of hardnesses 25, 45,

and 63 HRC. Since the hardness calculation is based directly on this depth

of indentation, the units of the vertical axis showing indenter depth have been

converted to an offset in HRC units by simply dividing the indenter depth in

mm by 0.002 mm per HRC unit. This was done to give the reader a sense

of how much influence the preliminary force dwell time can have on the

hardness value. Note that the Y-axis is oriented such that the hardness value

increases in the downward direction. The figure clearly shows that the shorter

the preliminary force dwell time, the more rapidly there is a change in the

HRC hardness value with time, and the lower the hardness result will be.

Effect of Dwell Times ◆

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Preliminary Force Dwell Time (s)

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

HRC Increase

25 HRC

45 HRC

63 HRC

Figure B.4. Figure B.4.

Relationship between the preliminary force dwell time and the

HRC measurement value for steel test blocks at three hardness levels.
80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Total Force Dwell Time (s)

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

HRC Decrease

63 HRC

45 HRC

25 HRC

Figure B.5. Figure B.5.

Relationship between the total force dwell time and the

HRC measurement value for steel test blocks at three hardness levels.

The data also shows that the effect of dwell time is largest at the lower

HRC levels. This is because the preliminary force dwell time effect is primarily

the result of the plasticity of the material under test. In general, the lower the

hardness of a metal, the greater is its ductility or ability to deform plastically.

B.2.2 Step 5 – The Total Force Dwell Time

The total force dwell time is defined as the dwell time during which the total

force is fully applied. Again tests have shown that the indenter continues to

penetrate into the test material during the total force dwell time. Figure B.5

and Figure B.6 show the creep behavior of the indenter for a period of

5 seconds after the total force is applied for tests made on HRC and HRB

test blocks. This data clearly shows that, as with the preliminary force dwell,

the shorter the total force dwell time, the more rapid is the change in the

hardness value with time. However, in this case, the hardness value increases

with shorter dwell times. Note that the Y-axis is oriented such that hardness

decreases in the downward direction. As with the preliminary force dwell time,

Figure B.5 and Figure B.6 also show that the effect of total force dwell time

is largest for the lower hardness levels. This effect is also due to the amount

of plasticity exhibited by the material under test. The difference in the shape

of the HRC and HRB data curves also suggests that the creep in the material

may be dependent on the type of indenter that is used.

◆ Rockwell Hardness Testing Cycle Effect
81

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Total Force Dwell Time (s)

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

HRB Increase

82 HRB

42 HRB

62 HRB

Figure B.6. Figure B.6.

Relationship between the total force dwell time and the

HRB measurement value for brass test blocks at three hardness levels.

Effect of Dwell Times ◆

B.2.3 Step 7 – The Recovery Dwell Time

The recovery dwell time is defined as beginning when the additional force

is fully removed, returning the force on the indenter to the preliminary force

level, and ending when the second and final depth of indentation is measured.

As the additional force is removed, the material under load experiences some

recovery, primarily elastic although with a small reverse-plasticity component.

If when the second and final indentation depth measurement is taken, the

material has not fully recovered, then the indenter will continue to be displaced,

again resulting in variations in indenter depth measurement with time. The

result of this second measurement of indenter depth will depend on how long

after reaching the preliminary force level was the measurement made (i.e.,

the recovery dwell time). Since the calculation of Rockwell hardness is

directly based on this depth measurement, then any change in the recovery

dwell time will directly affect the resulting hardness value.
82

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Recovery Dwell Time (s)

0.00

0.05

0.10

0.15

0.20

HRC Increase

63 HRC

45 HRC

25 HRC

Figure B.7. Figure B.7.

Relationship between the recovery dwell time and the

HRC measurement value for steel test blocks at three hardness levels.

Tests have shown that the material does continue to recover to some extent

during the recovery dwell time. Figure B.7 illustrates the recovery of the

material after the force is returned to the preliminary force level. These tests

were made on the same test blocks as discussed previously. Again, the units

of the vertical axis showing indenter depth have been converted to an offset

in HRC units. Note that the Y-axis is oriented such that hardness increases in

the upward direction. The figure shows that the shorter the preliminary force

dwell time, the more rapid is the change in the hardness value with time, and

the lower the hardness result will be. It should be noted that the data presented

here is for the elastic recovery of the test material only. In tests using a

commercial tester, there may be elastic recovery in the test machine itself,

which could add to this effect. The tests also shows that, unlike preliminary

and total force dwell times, the effect of recovery dwell time is largest for

the higher hardness levels. In this case, the displacement of the indenter during

the dwell time is due primarily to the elastic recovery in the material after the

additional force is removed. In general, the higher the hardness of a metal,

the lower is its ductility, thus the material retains a higher level of elasticity

under load.

◆ Rockwell Hardness Testing Cycle Effect
83

B.2.4 Summary – Dwell Time Effects

The above discussions demonstrate the relative effect that each of the three

dwell times has on the Rockwell hardness value. It is evident that by varying

dwell times, all else being equal, the measurement of Rockwell hardness will

be affected and will produce different results for each change in a dwell time.

The data presented show specific trends in the effects of the dwell times.

These can be summarized as follows:

• For each of the three dwell times, the rate of change in the apparent

Rockwell hardness value is most rapid during short dwell times, lessening

as the dwell times are extended.

• In general, the Rockwell hardness number is most affected by the total

force dwell time, followed by the preliminary force dwell time, and then

the recovery dwell time. This depends somewhat on the hardness level of

the material.

Effect of Dwell Times ◆
84

ANNEX C: USE OF NIST ROCKWELL

 C SCALE SRM TEST BLOCKS

The NIST SRM reference test blocks for the Rockwell C scale (HRC) are

certified at three hardness levels; 25 HRC, 45 HRC, and 63 HRC, (SRMs

2810, 2811, and 2812, respectively). Because these test blocks are often used

in situations where the highest measurement accuracy is desired, the first part

C.1 of this Annex provides recommendations for the proper use of the SRMs.

The second part C.2 of this Annex provides formulas for calculating the

certified value for any location on the SRM as well as the average hardness

of two or more arbitrary locations.

C.1 Recommendations for Use

C.1.1 Test Environment est Environment

It is recommended that the Rockwell hardness machine to be calibrated

or verified be kept in a temperature and humidity controlled environment

maintained at 23 °C ± 2 °C (73 °F ± 5 °F) and a relative humidity of 50 % or

less. The hardness machine must be in a location that is free from shock or

vibration that could affect the hardness measurements.

C.1.2 Anvil C.1.2 Anvil

It is recommended that a flat anvil (i.e., an anvil that can self support the SRM

at any test location) should be used with this SRM. However, when the SRM

is being used for the calibration or verification of a hardness machine, the same

anvil must be used with the SRM (when possible) that will be used subsequent

to the calibration or verification.

C.1.3 Seating the Anvil and Indenter

Prior to measuring the SRM, the hardness machine anvil and indenter must

be adequately seated. This may be accomplished by performing standard

Rockwell hardness tests on a material having a hardness value equal to or

higher than the stated value of the SRM. The seating tests should be repeated

until the successive measurement values show no trend of increasing or

decreasing hardness.

C.1.4 Cleaning the Anvil and Indenter

The hardness machine anvil and indenter diamond tip should be thoroughly

cleaned per manufacturer’s recommendations. In the absence of

◆ Use of NIST Rockwell C Scale SRM Test Blocks
85

manufacturer’s cleaning instructions, it is recommended that the anvil and

indenter be cleaned with ethyl alcohol and dried using a lint free cloth.

Lastly, blow the surfaces clean of dust using filtered air, such as from a

commercial compressed air can or bottle. Do not blow clean by mouth.

C.1.5 Cleaning the SRM

Prior to use, it is recommended that the SRM test block be cleaned.

A recommended method for cleaning the SRM is to gently wipe the top

and bottom SRM block surfaces with clean cotton, thoroughly wetted with

ethyl alcohol. The metal surfaces should immediately be dried using a

soft lint free cloth or paper towel before the alcohol evaporates in the air.

This cleaning must be performed in a manner that prevents a residue from

remaining on the top or bottom surfaces. The cleaning should be followed

by blowing the surfaces clean of dust using filtered air. The top and bottom

surfaces should not be touched after cleaning.

C.1.6 Placement of the SRM on the Anvil Placement of the SRM on the Anvil

Immediately before placing the SRM on the hardness machine anvil, the top

surface of the anvil and the bottom surface of the SRM should be blown free

of dust as before. The SRM should be carefully placed on the anvil before

dust can return. The top test surface of the SRM block should be blown free

of dust prior to testing and occasionally during the period of use. When a flat

anvil is used, the SRM block should be slid several times back and forth over

the surface of the anvil to help seat the block on the anvil. Any time the SRM

is lifted from and replaced on the anvil, the procedure described above in this

paragraph should be repeated. When a spot anvil is used (i.e., an anvil having

a much smaller diameter than that of the SRM block, requiring the block to be

additionally supported when testing at locations other than the block center),

extreme care should be practiced to ensure that the test block is supported

parallel to the anvil until the indenter contacts the block and the preliminary

force is applied.

C.1.7 Preliminary Indentation

When a flat anvil is used, it is recommended that at least one preliminary

Rockwell test be performed at any location on the test surface of the SRM.

The preliminary test will help seat the SRM block on the anvil. The measured

hardness value of the preliminary test should be ignored. The user is cautioned

not to make the preliminary indentation such that it contacts a previous

indentation, or the engraved circle, or NIST logo. Doing so may damage the

indenter. A preliminary indentation is not necessary when using a spot anvil.

Recommendations for Use ◆
86

C.1.8 Testing Cycle

The SRMs have been standardized by performing Rockwell tests using a

specific testing cycle. The Rockwell testing cycle may be characterized by

specifying testing cycle parameters that have been determined to have a

significant influence on the measurement results. To minimize the uncertainty

in the hardness measurement, a testing cycle should be used that replicates,

as closely as possible, the SRM standardizing testing cycle parameters as

identified in the certificate accompanying the test block SRM. Deviations

from the SRM testing cycle in dwell times or force application rate may

result in measured hardness values that are shifted from measurements

made using the SRM standardizing testing cycle.

C.1.9 Indentation Spacing

The user must recognize that a Rockwell hardness measurement may

be influenced by a nearby previously made indentation. The certificate

accompanying the test block SRM provides guidance for acceptable spacing

of indentations. In addition to avoiding making measurements too close to

previously made indents, no Rockwell measurement should be made within

1 mm of the engraved circle or the NIST logo.

C.2 Calculation of Certified Values for Arbitrary Locations

A hardness measurement is destructive in that a specific location on a

hardness block can be measured only once. Because hardness blocks are

not uniform, NIST can only predict the hardness at untested locations available

for customer measurement. The certificate that accompanies NIST Rockwell

hardness SRM test blocks provides such predictions for eleven specific

locations on the test block. This section provides the formulas used by NIST

to make these predictions. With these formulas, the user is not limited only to

the eleven locations listed in the SRM certificate but will be able to calculate

a certified hardness value for any location on the block. These formulas can

also be used for calculating various averages of the hardness values that are

obtained by averaging over two or more arbitrary locations.

Thinking of hardness as a function of location, we denote any untested

location on the block as s xy i ii = (,) and the corresponding hardness at

each location as H si ( ) . Figure C.1 shows the coordinate system for ( ) x y i i , .

Let H be the average of the hardnesses for the n locationss s 1 n , , ... .

This average is given by

(1) H . 1

n

H

k 1

n

= =

∑ ( ) sk

◆ Use of NIST Rockwell C Scale SRM Test Blocks
87

By using the methods and formulas presented in this annex, a certified

hardness value can be calculated which predicts this average hardness for

any number of arbitrary locations on an SRM block. This predicted average

hardness is denoted as $

H . As an example, consider the eleven locations

(A through K) on the block illustrated in Figure C.1. A hypothetical certified

average hardness value for a grouping of six of these eleven locations (B, D,

F, G, I, J) is given in Table C.1. When a prediction of only one location is

desired, then n=1, and $

H represents the hardness at a single location,

(i.e., $

H=H$ ( ) s1 ). As an example, for point A, we have s1 = ( ) 0, 23 .

The certified value, $

H=H$ ( ) s1 , for point A is given in Table C.2.

Locations Average Hardness Value 

B, D, F, G, I, J 64.58 ± 0.16 HRC 

Table C.1. able C.1.

Hypothetical certified hardness values for the average of

six specific test block locations as illustrated in Figure C.1

-10 0 10 20 30

-30

-20

-10

0

10

20

30

-30 -20

mm

A

B

C

D

E

F G

H

J I

K

Figure C.1. Figure C.1.

Test block surface illustrating the locations (letters A through K)

of certified hardness values given in Table C.2.

Certified Values for Arbitrary Locations ◆
88

By analyzing the hardness profile of the set of test blocks used for the

SRMs, NIST determined that the hardness is non-uniform and varies

smoothly across the surface of the block. This means that, in general, the

nearer two measurements are made to each other (limited to minimum

spacing considerations), the closer the hardness values will be. The following

method for the prediction of $

H is based on modeling hardness across the

surface of a block as a smooth random function described by a semivariogram.

The semivariogram can be thought of as a mathematical model that describes

the relationship of the spacing between any two locations on the test block

and the measured hardness difference of the two locations. In statistical

terms, this semivariogram gives you one half of the variance of the hardness

difference between any two locations on the test block. Thus, the square root

of twice the semivariogram gives the standard deviation of this difference.

For the SRM hardness block, the semivariogram is given by a simple

function of Euclidean distance. Consider two points si and sj separated by

the distance

(2)

Table C.2. able C.2.

Hypothetical certified hardness values for specific test block locations.

The x - y coordinate system is such that location x = 0, y = 0 is at the

block center (NIST indentation 4), and oriented with the NIST logo

at the bottom of the block as illustrated in Figure C.1

Location x (mm) y (mm) Hardness 

A 0 23 64.64 ± 0.17 HRC 

B 20 12 64.55 ± 0. 17 HRC 

C 20 -12 64.50 ± 0. 17 HRC 

D 0 -23 64.57 ± 0. 17 HRC 

E -20 -12 64.62 ± 0. 17 HRC 

F -20 12 64.63 ± 0. 17 HRC 

G 0 12 64.61 ± 0. 17 HRC 

H 10 6 64.55 ± 0. 17 HRC 

I 10 -6 64.51 ± 0. 17 HRC 

J -10 -6 64.60 ± 0. 17 HRC 

K -10 6 64.61 ± 0. 17 HRC 

d xx yy i j

2

i j

2 = − +− ( ) ( ) , 

◆ Use of NIST Rockwell C Scale SRM Test Blocks
89

which is given in millimeters. The semivariogram is given by

(3)

where c0, ce

, and 1/ae are given in Table C.3.

In addition to the semivariogram, calculation of certified values requires

the seven hardness readings obtained by NIST. These readings are given

in Table C.4 and illustrated in Figure C.2. The location designated as “Seat”

indicates a seating indentation that was made prior to making the seven

calibration indentations. The locations of the NIST hardness readings are

denoted by s s N1 N7 , , ... , and the readings themselves by Hs Hs N N ( ), , ( ) 1 7 ... .

γ ( ) s s i j − =

Coefficients Values 

co 0.0001 

ce 0.0025 

1/ae 0.0505 

Table C.3. able C.3.

Hypothetical semivariogram coefficients that

describe test block nonuniformity and repeatability

Table C.4. able C.4.

Hypothetical NIST hardness readings for specific test block locations

Location X Y Hardness Value 

(HRC) 

Symbol 

1 -10 17 64.676 H(sN1)

2 20 0 64.455 H(sN2)

3 -10 -17 64.636 H(sN3)

4 0 0 64.527 H(sN4)

5 10 17 64.642 H(sN5)

6 10 -17 64.508 H(sN6)

7 -20 0 64.621 H(sN7)

Certified Values for Arbitrary Locations ◆

{ co + ce [ 1 – exp (–d /a e

([

if d ≠ 0

0 if d = 0
90

Γ= − ( ( )) γ s s Ni Nj

$

H Hi i 1

7

= =

∑ λ ( ) sNi

A complete certified value involves computation of three quantities: (1) the

average hardness value itself, denoted by $

H ; (2) the standard uncertainty for

test block uniformity and repeatability, σ1 ; and (3) the combined standard

uncertainty denoted by uc . The first quantity, the average hardness prediction $

H , is calculated as a linear combination of the NIST readings given by

(4)

Figure C.2. Figure C.2.

Test surface of the Rockwell hardness SRMs indicating

the location and sequence of certification indentations.

Computation of the coefficients λi and σ1 requires four steps.

The first step is inversion of the 7 x 7 matrix Γ that has as its (i, j)-element,

the semivariogram value for the NIST indent locations sNi and sNj . We have

(5) .

Note that the diagonal elements of Γ , where i = j, will have a value of zero.

Let the elements of the inverse of Γ be denoted gij so that

(6) .

The elements of matrix Γ and the inverse matrix Γ−1 depend only on the

semivariogram for the points measured by NIST and, therefore, are constant

for all prediction calculations for this test block. The calculated values for the

two matrices are given in Table C.5 and Table C.6.

Γ− =1 ( ) gij

◆ Use of NIST Rockwell C Scale SRM Test Blocks

.

1 5

2

3 6

7 4

Seat
91

1 2 3 4 5 6 7 

1 -471.1106 38.6737 38.6737 101.4127 177.7553 38.2526 177.7553 

2 38.6737 -471.1106 38.6737 101.4127 177.7553 177.7553 38.2526 

3 38.6737 38.6737 -471.1106 101.4127 38.2526 177.7553 177.7553 

4 101.4127 101.4127 101.4127 -601.7315 101.4127 101.4127 101.4127 

5 177.7553 177.7553 38.2526 101.4127 -471.1106 38.6737 38.6737 

6 38.2526 177.7553 177.7553 101.4127 38.6737 -471.1106 38.6737 

7 177.7553 38.2526 177.7553 101.4127 38.6737 38.6737 -471.1106 

The second step is computation of the 7 elements, γ i , ,( , ,) i = ...1 7 , which

are given by

(7)

1 2 3 4 5 6 7 

1 0.000000 0.002120 0.002120 0.001643 0.001643 0.002224 0.001643 

2 0.002120 0.000000 0.002120 0.001643 0.001643 0.001643 0.002224 

3 0.002120 0.002120 0.000000 0.001643 0.002224 0.001643 0.001643 

4 0.001643 0.001643 0.001643 0.000000 0.001643 0.001643 0.001643 

5 0.001643 0.001643 0.002224 0.001643 0.000000 0.002120 0.002120 

6 0.002224 0.001643 0.001643 0.001643 0.002120 0.000000 0.002120 

7 0.001643 0.002224 0.001643 0.001643 0.002120 0.002120 0.000000 

Table C.5. able C.5.

Matrix Γ

Table C.6. able C.6.

Inverse matrix Γ -1 with elements gij

where n is the number of user chosen locations to average. Note that this

computation involves both the locations of the NIST readings and the locations

for which a certified average (or single value) is desired.

The third step is computation of three quadratic forms,

(8)

Certified Values for Arbitrary Locations ◆

γ γ i n = − =

∑

1

1

( ) s s k Ni

k

n

Q22 i ij j = = =

∑∑γ γ i j

g

1

7

1

7
92

σ1 = − − − − = =Q ∑∑ Q

Q 22

12

11

( ) ( ) 1 1

2

1 1

2

n m

n

k

n

γ s s k m

Q11 ij = = =

∑∑g i j 1

7

1

7

 (9)

(10) .

The final step is computation of the seven coefficients i λ ,( , , ) i = ...1 7 , andσ1 ,

the uncertainty due to block non-uniformity and lack of measurement

repeatability,

(11)

(12) .

The combined standard uncertainty, uc , is obtained by combining σ1 with

the uncertainties σ2 , σ3 , and σ4 from the other sources listed in the SRM

certificate. Hypothetical values for σ2 , σ3 , and σ4 are given in Table C.7.

 Uncertainty Source Standard Uncertainty 

σ1 Test Block Uniformity & Repeatability 

σ2 Day to Day Variation ± 0.02 HRC 

σ3 NIST Standardizing Tester ± 0.02 HRC 

σ4 NIST Standardizing Indenter ± 0.07 HRC 

Table C.7. able C.7.

Sources of uncertainty for the certified average

HRC hardness value with hypothetical values to be used in the examples

The formula for the combined standard uncertainties is given by

(13) .

◆ Use of NIST Rockwell C Scale SRM Test Blocks

Q12 ij j = = =

∑∑g i j

γ

1

7

1

7

λ γ i ij j

j j

= + g −

= =

∑ ∑

1

7

1

7 ( ) 1 , Q

Q g 12

11

ij

uc = +++ σσσσ 1

2

2

2

3

2

4

2
93

The formula for the expanded uncertainty is given by

(14)

where k = 2 .

The certified hardness values are reported as

(15)

C.2.1 Examples

As an aid to the user, the following two examples are provided to illustrate

how to use the procedures outlined above to calculate certified hardness

values. In the first example, the certified hardness value and uncertainty for

a single location is calculated. The second example calculates the certified

value of the average hardness of six locations as well as the uncertainty in

the average value. In both cases, the examples are based on an hypothetical

SRM test block for which seven hypothetical NIST calibration values are given

in Table C.4. Hypothetical semivariogram coefficients c0, ce

, and 1/ae used in

both examples are given in Table C.3.

EXAMPLE 1 – Certified Hardness of a Single Location

This example illustrates the steps required to calculate the certified values

of the hardness and uncertainty for a single location designated as “A” on

the test surface of this SRM. The location of “A” is defined in Table C.2 and

Figure C.1. The two values to be calculated are the certified hardness value

$

H and the uncertainty σ 1 to block non-uniformity and lack of measurement

repeatability. The symbol $

H is used to represent the certified value of the

average hardness of multiple locations. Since $

H represents the hardness at

a single location in this example, then $ $ H Hs = ( )1 where s1 is the designation

for location A.

Determination of Determination of $

H :

The formula for calculating the certified hardness value is given by Equation 4

above as

 .

Certified Values for Arbitrary Locations ◆

U ku = c , 

$

H ± c ku . 

∑

=

= 7

i 1

H = H( ) iH( ) ˆ ˆ 1 Ni s λ s
94

σ1 = − − Q Q

Q 22

12

11

( )1 2

The seven NIST measured hardness values, denoted as H( ) sNi ( , ,) i = ...1 7

in this formula, are provided above in Table C.4. Therefore, the only quantities

that need to be determined are the seven coefficients i λ ,( , , ) i = ...1 7 . The

formula for calculating these values is given by Equation 11 as

.

Determination of U: Determination of U:

The formula for calculating the certified uncertainty is

The combined standard uncertainty, uc , is obtained by combining the sources

of uncertainty σ1 , σ2 , σ3 , and σ4 listed in Table C.7 above. The formula for

combining, uc , is given by Equation 13. The uncertainties σ2 , σ3 , and σ4

remain constant for the computation of hardness for all locations of this

SRM. Thus, in order to determine U , only the uncertainty σ1 , due to block

non-uniformity and lack of measurement repeatability, must be calculated.

The formula for σ1 is given in Equation 12 as

 .

U ku = c , where k = 2 . 

Since the certified hardness of only one location is to be determined, then

n = 1 and the above equation simplifies to

 .

Calculation Steps: Calculation Steps: From these formulas, it can be seen that the

determination of the certified hardness and uncertainty values requires the

calculation of only a one dimensional array having elements γ i , ( , ,) i = ...1 7 ,

and a two dimensional array having elements gij , ( , ,) i = ...1 7 and

( , ,) j = ...1 7 . For this example, the array elements gij are provided to the

user in Table C.6. The quantities Q11 , Q12 , andQ22 are summations of the

products of the elements of these arrays.

◆ Use of NIST Rockwell C Scale SRM Test Blocks

λ γ i ij j

j j

= + g −

= =

∑ ∑

1

7

1

7 ( ) 1 Q

Q g 12

11

ij

σ1 = − − − − = =Q ∑∑ Q

Q 22

12

11

( ) ( ) 1 1

2

1 1

2

n m

n

k

n

γ s s k m
95

Note: If desired, the values Q11 , Q12 , Q22 , and λ i

 may be calculated

by matrix multiplication. The user may find it convenient to perform these

calculations using commercial spreadsheet software. Today’s spreadsheet

programs typically provide routines or functions for performing matrix

multiplication. This can simplify the task of carrying out these calculations.

Equivalent representations of these formulas are given in C.2.2.

Using the formulas for $

H and U above, the certified values are calculated

as follows.

Step 1: Determine the location coordinates

To begin, the user must first determine the coordinates of the location where

the hardness is to be determined. The x-y coordinate system that must be

used is as shown in Figure C.1 with location (0, 0) at the block center (NIST

indentation 4) and with the block rotated such that the NIST logo is positioned

at the bottom. All measurements must be in mm. For location A, Table C.2

gives the location coordinates as x mm 1 = 0 , and y mm 1 = 23 . Thus we have

s1 = ( , ) 0 23 . 

Step 2: Determine the array with elements γ i

As shown above, the array elements γ i , ( , ,) i = ...1 7 , are used in the

calculation of both the certified hardness value $

H and the uncertainty U. The

formula for calculating the values γ i is given by Equation 7 as

γ γ i . n = − =

∑

1

1

( ) s s k Ni

k

n

Since n = 1, this formula simplifies to the semivariogram

γ γ i = − ( ) s s 1 Ni .

Determination of the elements γ ( ) s s 1 Ni − , ( , ,) i = ...1 7 , is accomplished by

using a form of Equations 2 and 3. Equation 2 becomes

d xx yy i 1i

2

1 i

2 = − +− ( ) ( ) , 

Certified Values for Arbitrary Locations ◆
96

where x1 and y1 are the location coordinates, in mm, for location A on the

test surface of the SRM block. The values x1 and y1 , ( , ,) i = ...1 7 , are the

location coordinates of the seven NIST measurement indentations in numerical

order, as given above in Table C.4, and shown in Figure C.2. Thus,

By substituting the seven NIST indentation location coordinates into this

formula,

d 0x 2 y i i

2

i

2 = − +− ( ) ( 3 ) . 

Since di ≠ 0, Equation 3 becomes

γ ( ) s s 1 i − =

where c0, ce, and 1/ae are given in Table C.3 above. By substituting the values

for di into the formula, the values for the seven γ i elements are found to be

,

◆ Use of NIST Rockwell C Scale SRM Test Blocks

di = ( , ,) i = ...1 7 .

11.50

30.48

41.54

23.00

11.50

41.54

30.48

co + ce [ 1 – exp (–d i/a e

( [

γ γ i 1i = −= ( ) s s ( , ,) i = ...1 7 .

0.001154

0.002019

0.002249

0.001772

0.001154

0.002249

0.002019
97

Step 3: Determine Q Q and Q 22 12 11 , ,

The calculation of Q Q and Q 22 12 11 , , requires the values for the array

elements γ i , ( , ,) i = 1 7 K , which were calculated above in Step 2, and the

elements gij , ( , , , ,) i and j = = 17 17 K K , which are given in Table C.6.

Substituting the values for γ i and gij into the formulas yields

 ,

 , and

 .

Step 4: Determine Step 4: Determine λi

The coefficients λ i , ( , ,) i = ...1 7 , are the last quantities that are needed for

the calculation of $

H=H$ ( ) s1 . By substituting the values for γ i , gij , Q12 , and

Q11 into the formula yields

Q22 i ij j = = = =

∑∑γ γ

i j

g

1

7

1

7

0.001477

Q12 ij j = = = =

∑∑g

i j

γ

1

7

1

7

1.111513

Q11 ij = = = =

∑∑g

i 1 j

7

1

7

615.2209

Step 5: Determine the certified hardness value H$ ( ) s1

Substituting the values for the λi coefficients and the NIST hardness

values H( ) sNi , ( , ,) i = ...1 7 , yields

. $

HH H = $ i

i 1

7

() ( ) s s 1 = Ni =

∑ λ = 64.644 HRC

Certified Values for Arbitrary Locations ◆

λ γ i ij j

j j

= + g − = = =

∑ ∑

1

7

1

7 ( ) 1 Q

Q g 12

11

ij ( , ,) i = ...1 7 .

0.432567

0.024021

0.027304

0.032216

0.432567

0.027304

0.024021
98

Step 7: Determine the combined standard uncertainty Step 7: Determine the combined standard uncertainty uc

Substituting the values for σ1 , σ2 , σ3 , and σ4 into Equation 13 yields

 .

Step 6: Determine the uncertainty

Now that the certified hardness value is calculated, the associated uncertainty

in the certified value, U ku = c , must be determined. To accomplish this, the

only additional calculation needed is to determine σ1 , the uncertainty due to

block non-uniformity and lack of measurement repeatability. Substituting the

values for Q22 , Q12 , and Q11 into the formula yields

σ . 1 = − − Q = Q

Q 22

12

11

( ) 1 2

0.038165

Step 8: Determine the uncertainty Step 8: Determine the uncertainty U ku = c

Substituting the values for uc and k = 2 into equation 14 yields

64.64 ± 0.17 HRC.

◆ Use of NIST Rockwell C Scale SRM Test Blocks

uc = +++ = σσσσ 1

2

2

2

3

2

4

2 (0.04)2 + (0.02)2 + (0.02)2 + (0.07)2 = 0.085

U ku = =c 0 17 . .

Step 9: Determine the complete certified hardness value

Combining the calculated hardness value and the uncertainty yields the

certified hardness at location A as
99

EXAMPLE 2 – Certified Hardness of the Average of Six Locations

This second example expands on Example 1 above by calculating the

certified average of the hardness at multiple locations on the test surface of a

hypothetical SRM. For this example, the average hardness and the uncertainty

in this value will be calculated for a grouping of six locations (B, D, F, G, I, J)

as defined above in Table C.2 and Figure C.1. As in Example 1, the two values

to be calculated are the certified hardness value $

H and the uncertainty U.

Determination of Determination of $

H :

The formula for calculating the certified hardness value is given by Equation 4

as

 . $

HH H = $ i

i 1

7

() ( ) s s 1 = Ni =

∑ λ

The seven NIST measured hardness values, denoted as H( ) sNi ( , ,) i = ...1 7

in this formula, are given in Table C.4. Therefore, the only quantities that need

to be determined are the seven coefficients λi ,( , ,) i = ...1 7 . The formula for

calculating these values is given by Equation 11 as

. λ γ i ij j

j j

= + g −

= =

∑ ∑

1

7

1

7 ( ) 1 Q

Q g 12

11

ij

Determination of U: Determination of U:

The formula for calculating the certified uncertainty is

U ku = c , where k = 2 .

The combined standard uncertainty, uc , is obtained by combining the sources

of uncertainty σ1 , σ2 , σ3 , and σ4 listed in Table C.7 above. The formula

for combining uc is given by Equation 13. The uncertainties σ2 , σ3 , and σ4

remain constant for the computation of hardness for all locations of this

SRM. Thus, in order to determine, only the uncertaintyσ1 , due to block

non-uniformity and lack of measurement repeatability, must be calculated.

The formula for σ1 is given in Equation 12 as

σ1 = − − − − = =Q ∑∑ Q

Q 22

12

11

( ) ( ) 1 1

2

1 1

2

n m

n

k

n

γ s s k m .

Certified Values for Arbitrary Locations ◆
100

Calculation Steps: Calculation Steps: From these formulas, it can be seen that the determination

of the certified hardness and uncertainty values requires the calculation of a

one dimensional array having elements γ i , ( , ,) i = ...1 7 , a two dimensional

array having elements γ ( ) s s k m − , ( ,, k = ...1 6 and m = ...1 6 , ,) , and a two

dimensional array having elements gij , ( ,, i = ...1 7 and j = ...1 7 , ,) . For this

hypothetical SRM, the array elements gij are provided to the user in Table

C.7. The quantities Q11 , Q12 , andQ22 are summations of the products of the

elements of these arrays, as defined in Equations 8, 9, and 10.

If desired, the values Q11 , Q12 , Q22 , and λ i may be calculated by matrix

multiplication. The user may find it convenient to perform these calculations

with the assistance of commercial spreadsheet software. Today’s spreadsheet

programs typically provide routines or functions for performing matrix

multiplication. This can simplify the task of carrying out these calculations.

Equivalent representations of these formulas are given in C.2.2.

Using the formulas for $

H and U above, the certified values are calculated

as follows.

Step 1: Determine the location coordinates

To begin, the user must first determine the coordinates of the location where

the average hardness is to be determined. The x-y coordinate system that

must be used is as shown in Figure C.1 with location (0, 0) at the block

center (NIST indentation 4) and with the block rotated such that the NIST logo

is positioned at the bottom. All measurements must be in mm. The

x-y coordinates of locations B, D, F, G, I, and J are given in Table C.8.

Location X (mm) Y (mm) Symbol 

B 20 12 s1

D 0 -23 s2

F -20 12 s3

G 0 12 s4

I 10 -6 s5

J -10 -6 s6

Table C.8. able C.8.

The coordinates for the locations used in the calculations of Example 2

◆ Use of NIST Rockwell C Scale SRM Test Blocks
101

Step 2: Determine the array with elements γ i

As shown above, the array elements γ i , ( , ,) i = ...1 7 , are used in the

calculation of both the certified hardness value $

H and the uncertainty U.

The formula for calculation of the values γ i is given by Equation 7 as

γ γ i . n = − =

∑

1

1

( ) s s k Ni

k

n

Determination of the elements γ ( ) s s k Ni − ,( , ,) k = ...1 7 , for i n = ...1, , ,

where n = 6 , is accomplished by using a form of Equations 2 and 3. Equation

4 becomes

d xx yy k Ni k Ni

2

k Ni

2 = − +− ( )( ) ,

where xk and yk ( , ,) k = ...1 6 are the location coordinates in mm for the six

locations B, D, F, G, I, and J on the test surface of the SRM block. The values

xNi and yNi , ( , ,) i = ...1 7 , are the location coordinates of the seven NIST

measurement indentations in numerical order, as given in Table C.4, and shown

in Figure C.2. Thus, the values of dkNi will be a 7 6 × two dimensional array

d

k Ni =

(k = 1,... ,6)

30.47 41.54 11.33 11.33 30.72 23.32

12.00 30.48 41.76 23.32 11.66 30.59

41.95 11.50 30.98 30.98 22.98 11.32

23.32 23.00 23.32 12.00 11.66 11.66

11.33 41.54 30.47 11.33 23.32 30.72

30.98 11.50 41.95 30.98 11.32 22.98

41.76 30.48 12.00 23.32 30.59 11.66

( , ,) i = ...1 7 .

Certified Values for Arbitrary Locations ◆
102

γ ( ) s s k Ni − =

Similarly, Equation 3 becomes

where c0

, ce, and 1/ae are given in Table C.3 above. By substituting the values

for dkNi into the formula, the values of γ ( ) s s k Ni − are found to be

(k = 1,... ,6)

0.002018 0.002249 0.001142 0.001142 0.002025 0.001784

0.001189 0.002019 0.002252 0.001784 0.001166 0.002022

0.002255 0.001154 0.002032 0.002032 0.001771 0.001141

0.001784 0.001772 0.001784 0.001189 0.001166 0.001166

0.001142 0.002249 0.002018 0.001142 0.001784 0.002025

0.002032 0.001154 0.002255 0.002032 0.001141 0.001771

0.002252 0.002019 0.001189 0.001784 0.002022 0.001166

( , ,) i = ...1 7 .

Finally, each of the seven rows of γ ( ) s s k Ni − above must be summed and

divided by n = 6 to calculate the seven elements of γ i

. Thus,

γ γ i

n = −= =

∑

1

1

( ) s s k Ni

k

n

0.001727

0.001739

0.001731

0.001477

0.001727

0.001731

0.001739

( , ,) i = ...1 7 .

◆ Use of NIST Rockwell C Scale SRM Test Blocks

γ ( ) s s k Ni − = { , co + ce [ 1 – exp (–dkNi/a e

([

if dkNi ≠ 0

if dkNi 0 = 0
103

Step 3: DetermineQ22 , Q12 , and Q11

The calculation of Q22 , Q12 , and Q11 requires the values for the array

elements γ i

, ( , ,) i = ...1 7 , which were calculated above in Step 2, and the

elements gij , ( ,, i = ...1 7 and j = ...1 7 , ,) , which are given in Table C.6.

Substituting the values for γ i

 and gij into the formulas yields

Q22 i ij j = = = =

∑∑γ γ

i j

g

1

7

1

7

0.0018 ,

Q12 ij j = = = =

∑∑g

i j

γ

1

7

1

7

1.063846 , and

Q11 ij = = = =

∑∑g

i 1 j

7

1

7

615.2209 .

Step 4: Determine Step 4: Determine λ i

The coefficients λi , ( , ,) i = ...1 7 , are the last quantities that are needed for

the calculation of $

H . By substituting the values for γ i , gij , Q12 , and Q11 into

the formula yields

λ γ i ij j

j j

= + g − = = =

∑ ∑

1

7

1

7 ( ) 1 Q

Q g 12

11

ij

0.142140

0.135009

0.140579

0.164544

0.142140

0.140579

0.135009

( , ,) i = ...1 7 .

Step 5: Determine the certified hardness value Step 5: Determine the certified hardness value H$ ( ) s1

Substituting the values for the λ i coefficients and the NIST hardness values

H( ) sNi , ( , ,) i = ...1 7 yields

$

H Hi

i 1

7

= =

∑ λ ( ) sNi = 64.580 HRC .

Certified Values for Arbitrary Locations ◆
104

Step 6: Determine the uncertainty σ1

Now that the certified hardness value is calculated, the associated uncertainty

in the certified value, U ku = c , must be determined. To accomplish this, the

only additional calculation needed is to determine σ1 , the uncertainty due to

block non-uniformity, and lack of measurement repeatability. The formula for

calculating σ1 is given in Equation 12 as

σ1 = − − − − = =Q ∑∑ Q

Q 22

12

11

( ) ( ) 1 1

2

1 1

2

n m

n

k

n

γ s s k m .

Determination of the elements γ ( ) s s k m − ,( ,, k n = ...1 and m n = ...1, ,) ,

where n = 6 , is accomplished by using a form of Equations 2 and 3. Equation

2 becomes

d xx yy km k m

2

k m

2 = − +− ( )( ) ,

where ( ) x ,y k k , ( , ,) k = ...1 6 and ( ) x ,y m m , ( , ,) m = ...1 6 are the location

coordinates in mm for two of the six points of interest on the test surface of the

SRM block, in this case, the six locations B, D, F, G, I, and J. A value of dk m

must be calculated for all pairing combinations of the six locations. Thus, the

values of dk m will be a 6 6 × two dimensional array

d

km =

(k = 1,... ,6)

 0.00 40.31 40.00 20.00 20.59 34.99

40.31 0.00 40.31 35.00 19.72 19.72

40.00 40.31 0.00 20.00 34.99 20.59

20.00 35.00 20.00 0.00 20.59 20.59

20.59 19.72 34.99 20.59 0.00 20.00

34.99 19.72 20.59 20.59 20.00 0.00

(m = 1,... ,6) .

◆ Use of NIST Rockwell C Scale SRM Test Blocks
105

 ,

Similarly, Equation 3 becomes

where c0

, ce, and 1/ae are given in Table C.3 above. By substituting the values

for dk m into the formula, the values of γ ( ) s s k m − are found to be

γ ( ) s s k − = m { co + ce [ 1 – exp (–d km/a e

([

if dkm ≠ 0

if dkm 0 = 0

Finally, all of the elements of γ ( ) s s k m − above must be summed and divided

by n = 36 . Thus,

(k = 1,... ,6)

0.000000 0.002229 0.002224 0.001643 0.001670 0.002128

0.002229 0.000000 0.002229 0.002128 0.001631 0.001631

0.002224 0.002229 0.000000 0.001643 0.002128 0.001670

0.001643 0.002128 0.001643 0.000000 0.001670 0.001670

0.001670 0.001631 0.002128 0.001670 0.000000 0.001643

0.002128 0.001631 0.001670 0.001670 0.001643 0.000000

(m = 1,... ,6).

1

2

n 1 m 1

n

k

n

γ ( ) s s k m − = = =

∑∑ 0.001552 .

Substituting this value and the values for Q22 , Q12 , and Q11 into the formula

for σ1 above yields

σ1 = − − − −= = =Q ∑∑ Q

Q 22

12

11

( ) ( ). 1 1 0 015543 2

1 1

2

n m

n

k

n

γ s s k m .

γ ( ) s s k m − =

Certified Values for Arbitrary Locations ◆
106

Step 7: Determine the combined standard uncertainty uc

Substituting the values for σ1 , σ2 , σ3 , and σ4 into Equation 13 yields

Step 8: Determine the uncertainty Step 8: Determine the uncertainty U ku = c

Substituting the values for uc and k = 2 into equation 14 yields

uc = +++ = σσσσ 1

2

2

2

3

2

4

2 (0.02)2 + (0.02)2 + (0.02)2 + (0.07)2 = 0.078.

U ku = =c 0 16 . .

Step 9: Determine the complete certified hardness value

Combining the calculated hardness value and the uncertainty yields the

certified average value of the hardness at locations B, D, F, G, I, and J as

64.58 ± 0.16 HRC.

◆ Use of NIST Rockwell C Scale SRM Test Blocks
107

Q22 i ij j = = ′ = =

−

∑∑γγγ γ

i j

g

1

7

1

7

1 Γ ,

Q12 ij j = = ′ = =

−

∑∑g

i j

γ γ

1

7

1

7

1 1Γ ,

Q11 ij = = ′ = =

−

∑∑g

i 1 j

7

1

7

1 1 1 Γ , and

λγ γ γ

i ij j

j j

= + g − = + − ′

′ = =

−

−

∑ ∑ −

1

7

1

7

1

1

1

() ( ) 1 1 Q

Q g 12

11

ij Γ Γ

Γ

1

1 1 ,

C.2.2 Matrix Equivalents to Formulas of Annex C

Equivalent matrix representations of Q11 , Q12 , Q22 and λ i are

1=

1

1

1

1

1

1

1

, and

1′ = 1111111 .

Certified Values for Arbitrary Locations ◆

−1 (Γ 1 (

where Γ−1 is the matrix having gij , ( , ,) i = ...1 7 and ( , ,) j = ...1 7 as its

elements, and 1 is an n vector with 1 as elements, such that
January 2001