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Konrad Herrmann
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Hardness Testing—Principles and Applications Copyright © 2011 ASM International®
Konrad Herrmann, editor All rights reserved.
www.asminternational.org
Contents
Preface � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �vii
ChaPter 1 the Fundamentals of hardness testing � � � � � � � � � � 1
The History of Hardness Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
The Term Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Interrelationship Between Material Structure and Hardness. . . . . . . . 4
Relationships Between Hardness and Other Mechanical Material
Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Hardness Unit and Traceability of the Hardness Measurement. . . . . . 9
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
EA Measurement Uncertainty Guideline for Brinell and Vickers
Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
EA Guideline for Determining Measurement Uncertainty During the
Hardness Test According to the HRC Scale. . . . . . . . . . . . . . . . 20
ChaPter 2 hardness Measurement of Metals—
Static Methods� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 25
Rockwell ISO 6508 and ASTM E 18 Procedures . . . . . . . . . . . . . . . 26
Vickers ISO 6507, ASTM E92, and ASTM E384 Procedures. . . . . . 43
Brinell ISO 6506 and ASTM E10 Procedures. . . . . . . . . . . . . . . . . . 52
Knoop ISO 4545 and ASTM E284 Procedures. . . . . . . . . . . . . . . . . 62
ChaPter 3 Dynamic test Methods � � � � � � � � � � � � � � � � � � � � � 67
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Methods to Measure the Deformation. . . . . . . . . . . . . . . . . . . . . . . . 71
Methods to Measure Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
iii
iv / Contents
ChaPter 4 hardness testing of Metals—Contactless and Other
Nondestructive Methods � � � � � � � � � � � � � � � � � � � � � � � � � � � 91
Electromagnetic Impulse Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Photothermal Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Determining Hardening Depth by Ultrasound. . . . . . . . . . . . . . . . . . 93
Scratch Hardness Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Ultrasonic Contact Impedance (UCI) Procedure. . . . . . . . . . . . . . . . 95
Checking the Hardness Testing Machines and Indenters. . . . . . . . . 100
Hardness Reference Blocks and Their Calibration . . . . . . . . . . . . . 101
Hardness Conversion According to ISO 18265. . . . . . . . . . . . . . . . .110
Capability of the Testing Equipment and Suitability of the Testing
Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
ChaPter 5 hardness Measurement of Plastics and
elastomers � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 119
Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Testing Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
ChaPter 6 Instrumented Indentation test � � � � � � � � � � � � � � 167
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Contact Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Test Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Required Checking of Test Equipment and Indenters. . . . . . . . . . . 190
Special Case: Testing of Layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Test Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Application Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Determining the True Stress-Strain Curve of Materials . . . . . . . . . 220
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
ChaPter 7 Standardization� � � � � � � � � � � � � � � � � � � � � � � � � � 235
General Comments on Standardization. . . . . . . . . . . . . . . . . . . . . . 235
Historical Development of Materials Testing Standards. . . . . . . . . 236
Status of Standardization in the Field of Hardness Testing. . . . . . . 239
Index� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 247
Hardness Testing—Principles and Applications Copyright © 2011 ASM International®
Konrad Herrmann, editor All rights reserved.
www.asminternational.org
Preface
Hardness testing is of immense importance for quality assurance in indus-
try. Although the most widely used hardness test methods for metals—
Rockwell, Brinell, and Vickers—were developed between 1900 and 1925,
in the past ten years they have experienced numerous technical innova-
tions leading to an increase in productivity and the accuracy of hardness
tests.
This publication on hardness testing provides, based on the state of stan-
dardization, an overview of the hardness testing of metals, plastics, rubber,
and other materials. It reports on technical developments such as the intro-
duction of image processing in the Brinell and Vickers methods, the adap-
tation of hardness testing machines to process-oriented testing conditions,
and the development of highly accurate and efficient calibration methods.
Most recently, guidelines have been worked out to determine the uncer-
tainty of hardness measurements as a component of the ISO standards on
hardness testing methods. With the aid of these guidelines, it is possible to
simply and directly fulfill the requirement of the international standards
that say each hardness measurement value must state its uncertainty.
In contrast to the conventional Rockwell, Vickers, and Brinell hardness
testing methods, which each produce a single hardness measurement
value, the instrumented indentation test features a great amount of infor-
mation on the elastic and plastic properties of the material. For a wide
range of applications, including the nano, micro, and macro levels, the
instrumented indentation test offers unique application possibilities. On
thin and ultrathin layers with a layer thickness in the nanometer range, it
presents a universal method for determining mechanical properties. On the
other hand, the instrumented indentation test enables the determination of
the indentation depth in the macro range, which is much more efficient
than the conventional method of micro-Vickers testing on the cross section
of the specimen.
In addition to the hardness testing of metals, the hardness testing of rub-
ber and plastics has an equally great economic importance. As in the case
of dynamic hardness testing, an essential feature is that in this area, predo-
v
vi / Preface
minantly portable hardness test devices are used. At the present time, great
efforts are being made to increase the accuracy of the rubber and plastics
hardness test as well as the dynamic hardness test by means of systematic
calibrations of the portable testing devices.
It is necessary to point out that the commercial products mentioned in
this publication do not imply any recommendation and are not necessarily
the best available products.
I give my special thanks to Mrs. U. Baier-Blott, C. Charvieux, G. Froe-
tel, and E. Jones from the PTB Translation Office for their reliable and
accurate translation of the German manuscript of this book into English.
This book, the articles of which have been written by a group of re-
nowned experts in the field of hardness testing, addresses, above all, ex-
perts in materials testing and quality control, students of materials science,
as well as technologists and design engineers in the metals and plastics
processing industries.
Konrad Herrmann
Braunschweig, March 2010
Hardness Testing—Principles and Applications Copyright © 2011 ASM International®
Konrad Herrmann, editor All rights reserved.
www.asminternational.org
1
ChaPter
the Fundamentals of
hardness testing
K. herrmann
the history of hardness testing
The Greek philosophers Democritus and Aristotle described hardness
as a defining attribute of the elements.
In ancient times and in the Middle Ages, the only way to test the hard-
ness of a material was with rough performance tests of weapons and tools
made of steel. Swords were struck on wood or stone to decide if the steel
was sufficiently hard, according to the resulting incisions. As the Middle
Ages ended, quantitative hardness testing developed step-by-step, first in
the field of mineralogy. With the construction of the railways and me-
chanical engineering, the need for testing the hardness of metals emerged
in the second half of the 19th century. Table 1 records significant stages in
the development of hardness testing.
The 10-step scratch hardness scale established by Friedrich Mohs in
1822 is still used today in mineralogy and in the assessment of grind-
ing tools. It is based on the principle that the hardness of a mineral to be
tested is determined by the two reference minerals it scratches or is not
able to scratch. Table 2 contains Mohs’s hardness values for various
materials.
Figure 1 shows the connection between Mohs hardness and Vickers
hardness, making clear the strong nonlinearity of the Mohs hardness scale.
The Mohs scale is generally used by mineralogists, yet it is not suitable
for materials other than minerals, because the hardness differentiation,
also shown in Fig. 1, is, in general, too low.
2 / hardness testing—Principles and applications
table 1 historical overview
1640 Barba scratched precious stones with a file.
1722 R.A. Réaumur scratched steel with minerals and evaluated metals with two prisms positioned crosswise,
whose edges he pressed against each other.
1747 Wallerius used fingernails, knives, files, and diamond powder to determine hardness.
1768 Kvist created a scale of hardness for minerals (diamond, 20; topaz, 15; zeolite, 13; quartz, 11; fluorite, 7;
calcite, 6; gypsum, 5; chalk, 2).
1774 Werner rubbed a mineral against a fingernail and a knife or a piece of steel to determine the amount of the
mineral powder gained in that way.
1801 Hauy created a system of four hardness classes for mineralogy.
1822 F. Mohs defined a 10-step scratch hardness scale for minerals.
1833 Seebeck developed a quasi-quantitative scratching procedure to determine hardness.
1851 Development of the drilling hardness of metals on the basis of the loss of weight during drilling with
known machining conditions.
1874 Uchatius evaluated the hardness of bronzes by means of a chisel falling from a height of 25 cm (first dy-
namic hardness testing method).
1882 TU Prague set up an 18-step scale of scratch hardness from lead to hardened steel.
H. Hertz published his theory on the elastic contact of solids.
1884 Assessment of the hardness of metals by means of the grinding hardness.
1889 A. Martens reported on a procedure of scratch hardness.
1898 A. Martens proposed a device for the instrumented indentation test with mechanical, hydraulic depth
measurement.
1900 J.A. Brinell developed the ball indentation test.
1907 P. Ludwik reported on a cone probe used both statically and dynamically.
A.F. Shore created the rebound hardness measuring method.
E. Meyer set up the power law for the ball indentation test.
1920 S.R. Rockwell developed the test force method named after him.
1925 R. Smith and G. Sandland developed the Vickers method, which allowed microhardness testing.
1926 In the U.S., the first hardness testing standard on the Brinell method was published.
1937 In Germany and Sweden, reference hardness blocks were produced.
1939 F. Knoop, C.G. Peters, and W.B.E. Emerson developed the Knoop test in the National Bureau of Stan-
dards (U.S.).
1940 First DIN standard on the Vickers method.
1943 K. Meyer built the first hardness standard measuring machine.
1950 M.M. Khrushchev and E.S. Berkovich suggested a three-sided diamond pyramid as an indenter form
(Berkovich indenter), which was later applied particularly in nanohardness testing.
1972 A.P. Ternovskij, V.P. Alechin, M.Ch. Shorshorov, M.M. Khrushchev, and V.N. Skvortsov developed the
principle of the instrumented indentation test.
1975 D. Leeb and M. Brandestini developed Equotip, the rebound hardness testing method.
table 2 Mohs hardness values
Mohs Mohs Mohs
Minerals hardness Metals hardness Various materials hardness
Talc 1 Lead 1.5 Mg(OH) 1.5
2
Gypsum 2 Tin, cadmium 2 Fingernail 2–2.5
Calcite 3 Aluminium 2.3–2.9 CuO 3.5–4
2
Fluorite 4 Au, Mg, Zn 2.5 ZnO 4–4.5
Apatite 5 Silver 2.7 MnO 5–5.5
3 4
Orthoclase 6 Antimony 3 FeO 5.5–6
2 3
Quartz 7 Copper 3 MgO 6
Topaz 8 Iron 3.5–4.5 MnO 6
2 3
Corundum 9 Nickel 3.5–5 SnO 6.5–7
2
Diamond 10 Chromium (soft) 4.5 Martensite 7
Cobalt 5 MoC 7–8
Os, Ta, W, Si, Mn 7 VC 8
2 3
Chromium (hard, electrolytic) 8 TiC 8–9
Case carburized steel 8 Sapphire (AlO) 9
2 3
MoC, SiC, VC, WC, WC 9–10
2 2
Cubic boron carbide 10
Source: Ref 1.1
Chapter 1: the Fundamentals of hardness testing / 3
Fig� 1 the connection between Mohs hardness and Vickers hardness, show-
ing the strong nonlinearity of the Mohs scale. Source: ref 2
the term Hardness
The term hardness is not a newly coined scientific word, but rather
originates from everyday language. Human fingers have sensors to assess
the hardness of objects. As a result, an unconscious association of hard-
ness with such characteristics as abrasion resistance and durability devel-
ops: an association that is not always borne out by materials science. The
classification of materials with respect to hardness starts with the degree
of deformation that can be created on a sample by hand or with a hard,
sharp object. With this everyday experience, the type of deformation
(plastic or elastic) is generally not important. What is crucial is that the
layman as well as the expert connects, with the term hardness, the ability
of a body to counter the penetration of another body with a certain resis-
tance. The larger the resistance to deformation, the harder the body ap-
pears. From this more everyday experience arises a definition of hardness
that is used generally in technology. However, only the hardness of rela-
tively soft materials can be assessed with fingers. The hardness testing of
technically more interesting, much harder materials is possible only with
testing apparatus.
The hardness also depends, besides this, on the speed with which the
object is touched. The faster the object is moved, the harder it is perceived
to be. A lead bullet that is lying on a steel plate will create no indentation
on the steel plate with gradually increasing pressure. If the lead bullet is,
however, shot at the steel plate, an indentation is then created. Even water
4 / hardness testing—Principles and applications
that appears to be soft on slow immersion can be so hard that it splits steel
when it is under high pressure.
A. Martens (Ref 3) referred to hardness, H, as the resistance with which
a body counters the penetration of another (little deformable) body. The
resistance to deformation is:
F
H = (Eq 1)
A
where F is the test force and A is the indentation surface.
This is the basis of the technical definition of hardness. The material to
be tested is, thus, subjected to stress with an indenter made of a harder
material. From the deformation of the material by the defined stress, a
hardness value is then calculated. Accordingly, these specifications have
to be made for the definition of a hardness testing method:
1. The defining equation of the hardness value under consideration of the
stress and of the material reaction
2. The form and material of the indenter
3. The force-time regime of the hardness testing method
The details of these specifications are given in Chapters 2 through 6 in
this book, where the treatment of the individual hardness testing methods
are described.
Because the plastic deformation of the sample always plays a role in
hardness testing, it follows that a hardness test cannot be repeated at the
same point.
Interrelationship Between Material
Structure and hardness
To comprehend the character of hardness, it is necessary to regard the
composition of the material. If an etched piece of steel is regarded under a
microscope, an irregular structure of the steel sample can be seen. Each
component of the structure has a different chemical composition and thus
also different physical properties. In this case, the sample has already
reached the point where the uniformity of the material properties ends.
Homogeneous crystals exhibit a space lattice in which the single atoms
are arranged at constant intervals in specific axial directions. The intera-
tomic distances amount to approximately 0.1 nm. By the bonding forces
between the atoms and the packing density inside the lattice, the structure
of the space lattices is closely connected with the hardness.
The dependence of the chemical bonding forces on the crystal structure
can be observed in the case of the reference minerals of the Mohs hard-
ness scale (Table 3).
