SIST EN ISO 4545-1:2018

SLOVENSKI STANDARD
01-julij-2018
1DGRPHãþD
SIST EN ISO 4545-1:2006
Kovinski materiali - Preskus trdote po Knoopu - 1. del: Preskusna metoda (ISO
4545-1:2017)
Metallic materials - Knoop hardness test - Part 1: Test method (ISO 4545-1:2017)
Metallische Werkstoffe - Härteprüfung nach Knoop - Teil 1: Prüfverfahren (ISO 4545-
1:2017)
Matériaux métalliques - Essai de dureté Knoop - Partie 1 : Méthode d'essai (ISO 4545-
1:2017)
Ta slovenski standard je istoveten z: EN ISO 4545-1:2018
ICS:
77.040.10 Mehansko preskušanje kovin Mechanical testing of metals
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 4545-1
EUROPEAN STANDARD
NORME EUROPÉENNE
March 2018
EUROPÄISCHE NORM
ICS 77.040.10 Supersedes EN ISO 4545-1:2005
English Version
Metallic materials - Knoop hardness test - Part 1: Test
method (ISO 4545-1:2017)
Matériaux métalliques - Essai de dureté Knoop - Partie Metallische Werkstoffe - Härteprüfung nach Knoop -
1: Méthode d'essai (ISO 4545-1:2017) Teil 1: Prüfverfahren (ISO 4545-1:2017)
This European Standard was approved by CEN on 30 November 2017.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 4545-1:2018 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 4545-1:2018) has been prepared by Technical Committee ISO/TC 164
“Mechanical testing of metals” in collaboration with Technical Committee ECISS/TC 101 “Test methods
for steel (other than chemical analysis)” the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by September 2018, and conflicting national standards
shall be withdrawn at the latest by September 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 4545-1:2005.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 4545-1:2017 has been approved by CEN as EN ISO 4545-1:2018 without any
modification.
INTERNATIONAL ISO
STANDARD 4545-1
Second edition
2017-12
Metallic materials — Knoop
hardness test —
Part 1:
Test method
Matériaux métalliques — Essai de dureté Knoop —
Partie 1: Méthode d'essai
Reference number
ISO 4545-1:2017(E)
©
ISO 2017
ISO 4545-1:2017(E)
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle . 1
5 Symbols and designations . 2
5.1 Symbols and designations used in this document . 2
5.2 Designation of hardness number . 3
6 Testing machine . 3
6.1 Testing machine . 3
6.2 Indenter . . 3
6.3 Diagonal measuring system . 4
7 Test piece . 4
7.1 Test Surface . 4
7.2 Preparation . 4
7.3 Thickness . 4
7.4 Support of unstable test pieces . 4
8 Procedure. 5
8.1 Test temperature . 5
8.2 Test force . 5
8.3 Periodic verification . 5
8.4 Test piece support . 5
8.5 Focus on test surface . 5
8.6 Test force application . 6
8.7 Prevention of the effect of shock or vibration . 6
8.8 Minimum distance between adjacent indentations . 6
8.9 Measurement of diagonal length . 7
8.10 Calculation of hardness value . 7
9 Uncertainty of the results . 7
10 Test report . 7
Annex A (normative) Procedure for periodic checking of the testing machine, diagonal
measuring system and the indenter by the user . 9
Annex B (informative) Uncertainty of the measured hardness values .11
Annex C (informative) Knoop hardness measurement traceability .18
Annex D (informative) CCM — Working group on hardness .22
Annex E (informative) Adjustment of Köhler illumination systems .23
Bibliography .24
ISO 4545-1:2017(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals,
Subcommittee SC 3, Hardness testing.
This second edition cancels and replaces the first edition (ISO 4545-1:2005), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— all references have been removed of indentation diagonals <0,020 mm;
— the resolution requirements have been defined for the measuring system;
— the lower test force limit of the Knoop hardness test has been expanded to 0,009 807 N;
— the requirements for the periodic (weekly or daily) verifications of the testing machine have been
defined as normative, the maximum permissible bias value has been revised, and the requirements
for the maximum permissible error in measuring a reference indentation have been revised;
— the recommendations for inspection and monitoring of the indenter have been added (moved from
ISO 4545-2);
— the requirements have been revised for the approach velocity of the indenter prior to contact with
the sample surface;
— the timing requirements for the test force application and the duration at maximum test force are
revised to indicate target time values;
— Figure 3 has been added illustrating the requirements for the minimum distance between
indentations; the distances have been stated with respect to the indentation centres rather than
the indentation limits, but the requirements have not changed;
— the requirements have been added to the test report for reporting the test date and any hardness
conversion method used;
iv © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
— Annexes C, D and E have been added concerning Knoop hardness measurement traceability, the
CCM — Working group on hardness and adjustment of Köhler illumination systems, respectively.
A list of all parts in the ISO 4545 series can be found on the ISO website.
INTERNATIONAL STANDARD ISO 4545-1:2017(E)
Metallic materials — Knoop hardness test —
Part 1:
Test method
1 Scope
This document specifies the Knoop hardness test method for metallic materials for test forces from
0,009 807 N to 19,613 N.
The Knoop hardness test is specified in this document for lengths of indentation diagonals ≥0,020 mm.
Using this method to determine Knoop hardness from smaller indentations is outside the scope of this
document as results would suffer from large uncertainties due to the limitations of optical measurement
and imperfections in tip geometry. ISO 14577-1 allows the determination of hardness from smaller
indentations.
A periodic verification method is specified for routine checking of the testing machine in service by
the user.
Special considerations for Knoop testing of metallic coatings can be found in ISO 4516.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 4545-2, Metallic materials — Knoop hardness test — Part 2: Verification and calibration of testing
machines
ISO 4545-3, Metallic materials — Knoop hardness test — Part 3: Calibration of reference blocks
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
4 Principle
A diamond indenter, in the form of a rhombic-based pyramid with angles, α and β, between opposite
edges respectively equal to 172,5° and 130° at the vertex, is forced into the surface of a test piece
followed by measurement of the long diagonal, d, of the indentation remaining in the surface after
removal of the test force, F (see Figures 1 and 2).
ISO 4545-1:2017(E)
Figure 1 — Principle of the test and indenter geometry

Figure 2 — Knoop indentation
The Knoop hardness is proportional to the quotient obtained by dividing the test force by the projected
area of the indentation, which is assumed to be a rhombic-based pyramid, and having at the vertex the
same angles as the indenter.
NOTE As applicable, this test document has adopted hardness test parameters as defined by the working
group on hardness (CCM-WGH) under the framework of the International Committee of Weights and Measures
(CIPM) Consultative Committee for Mass and Related Quantities (CCM) (see Annex D).
5 Symbols and designations
5.1 Symbols and designations used in this document
See Table 1 and Figures 1 and 2.
Table 1 — Symbols and designations
Symbol Designation
F Test force, in newtons (N)
d Length of the long diagonal, in millimetres
d Length of the short diagonal, in millimetres
s
α Angle between the opposite edges of the long diagonal at the vertex of the diamond pyramid
indenter (nominally 172,5°) (see Figure 1)
β Angle between the opposite edges of the short diagonal at the vertex of the diamond pyramid
(nominally 130°) (see Figure 1)
NOTE  Standard acceleration due to gravity, g = 9,806 65 m/s , which is the conversion factor from kgf to N.
n
To reduce uncertainty, the Knoop hardness can be calculated using the actual indenter angles α and β.
2 © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
Table 1 (continued)
Symbol Designation
V Magnification of the measuring system
c Indenter constant, relating projected area of the indentation to the square of the length of the
long diagonal
β
tan
Indenter constant, c= , for nominal angles α and β, c is approximately 0,070 28
α
2tan
HK
Test force (kgf)
Knoop hardness  =
Projected area of indentation (mm )
1 Test force (N)
=×
g
n Projected area of indentation (mm )
1 F
=×
g
n cd
For the nominal indenter constant c ≈ 0,070 28,
F
Knoop hardness ≈×1,451
d
NOTE  Standard acceleration due to gravity, g = 9,806 65 m/s , which is the conversion factor from kgf to N.
n
To reduce uncertainty, the Knoop hardness can be calculated using the actual indenter angles α and β.
5.2 Designation of hardness number
Knoop hardness, HK, is designated as shown in the following example.
640 HK 0,1 ⁄20
Duration of test force (20 s)
if not within the speciied range (10 s to 15 s)
Approximate kgf equivalent value of

applied test force where (0,1 kgf = 0,980 7 N)
Hardness symb ol
Knoop hardness valu e
6 Testing machine
6.1 Testing machine
The testing machine shall be capable of applying a predetermined force or forces within the desired
range of test forces, in accordance with ISO 4545-2.
6.2 Indenter
The indenter shall be a diamond in the shape of a rhombic-based pyramid, as specified in ISO 4545-2.
ISO 4545-1:2017(E)
6.3 Diagonal measuring system
The diagonal measuring system shall satisfy the requirements in ISO 4545-2.
Magnifications should be provided so that the diagonal can be enlarged to greater than 25 % but less
than 75 % of the maximum possible optical field of view. Many objective lenses are non-linear towards
the edge of the field of view.
NOTE A diagonal measuring system using a camera for measurement can use 100 % of the camera’s field of
view, provided it is designed to consider field of view limitations of the optical system.
The resolution required of the diagonal measuring system depends on the size of the smallest
indentation to be measured, and shall be in accordance with Table 2. In determining the resolution of
the measuring system, the resolution of the microscope optics, the digital resolution of the measuring
scale and the step-size of any stage movement, where applicable, should be taken into account.
Table 2 — Resolution of the measuring system
Diagonal length
Resolution of the measuring
d
system
mm
0,020 ≤ d < 0,080 0,000 4 mm
0,080 ≤ d 0,5 % of d
7 Test piece
7.1 Test Surface
The test shall be carried out on a polished surface, which is smooth and even, free from oxide scale and
foreign matter and, in particular, free from lubricants, unless otherwise specified in product standards.
The finish of the surface shall permit accurate determination of the diagonal length of the indentation.
7.2 Preparation
Surface preparation shall be carried out in such a way as to prevent surface damage, or alteration of the
surface hardness due to excessive heating or cold-working.
Due to the small depth of Knoop hardness indentations, it is essential that special precautions be taken
during preparation. It is recommended to use a polishing/electropolishing technique that is adapted to
the material to be measured.
7.3 Thickness
The thickness of the test piece, or of the layer under test, shall be at least 1/3 times the length of the
diagonal length of the indentation. No deformation shall be visible at the back of the test piece after
the test.
NOTE The depth of the indentation is approximately 1/30 of the diagonal length (0,033 d).
7.4 Support of unstable test pieces
For a test piece of small cross-section or of irregular shape, either a dedicated support should be used
or it should be mounted in a similar manner to a metallographic micro-section in appropriate material
so that it is adequately supported and does not move during the force application.
4 © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
8 Procedure
8.1 Test temperature
The test is normally carried out at ambient temperature within the limits of 10 °C to 35 °C. If the test
is carried out at a temperature outside this range, it shall be noted in the test report. Tests carried out
under controlled conditions shall be made at a temperature of (23 ± 5) °C.
8.2 Test force
The test forces given in Table 3 are typical. Other test forces may be used. Test forces shall be chosen
that result in indentations with a long diagonal greater than 0,020 mm.
Table 3 — Typical test forces
Test force value, F
Hardness scale
a
N Approximate kgf equivalent
HK 0,001 0,009 807 0,001
HK 0,002 0,019 61 0,002
HK 0,005 0,049 03 0,005
HK 0,01 0,098 07 0,010
HK 0,02 0,196 1 0,020
HK 0,025 0,245 2 0,025
HK 0,05 0,490 3 0,050
HK 0,1 0,980 7 0,100
HK 0,2 1,961 0,200
HK 0,3 2,942 0,300
HK 0,5 4,903 0,500
HK 1 9,807 1,000
HK 2 19,613 2,000
a
Not an SI unit.
8.3 Periodic verification
The periodic verification defined in Annex A shall be performed within a week prior to use for each test
force used but is recommended on the day of use. The periodic verification is recommended whenever
the test force is changed. The periodic verification shall be done whenever the indenter is changed.
8.4 Test piece support
The test piece shall be placed on a rigid support. The support surfaces shall be clean and free from
foreign matter (scales, oil, dirt, etc.). It is important that the test piece lies firmly on the support so that
any displacement that affects the test result cannot occur during the test.
8.5 Focus on test surface
The diagonal measuring system microscope shall be focused so that the specimen surface and the
desired test location can be observed.
NOTE Some testing machines do not require that the microscope be focused on the specimen surface.
Edge of test piece
ISO 4545-1:2017(E)
8.6 Test force application
The indenter shall be brought into contact with the test surface and the test force shall be applied in a
direction perpendicular to the surface, without shock, vibration or overload, until the applied force
attains the specified value. The time from the initial application of the force until the full test force is
+1
reached shall be 7 s .
−5
+1
NOTE 1 The requirements for the time durations are given with asymmetric limits. For example, 7 s
−5
indicates that 7 s is the nominal time duration, with an acceptable range of not less than 2 s (calculated as 7 s – 5 s)
to not more than 8 s (calculated as 7 s + 1 s).
The indenter shall contact the test piece at a velocity of ≤0,070 mm/s.
+1
The duration of the test force shall be 14 s, except for tests on materials whose time-dependent
−4
properties would make this an unsuitable range. For these tests, this duration shall be specified as part
of the hardness designation (see 5.2).
NOTE 2 There is evidence that some materials are sensitive to the rate of straining which causes changes in
the value of the yield strength. The corresponding effect on the termination of the formation of an indentation
can make alterations in the hardness value.
8.7 Prevention of the effect of shock or vibration
[6]
Throughout the test, the testing machine shall be protected from shock or vibration .
8.8 Minimum distance between adjacent indentations
The minimum distance between adjacent indentations and the minimum distance between an
indentation and the edge of the test piece are shown in Figure 3.
The minimum distance between the edge of the test piece and the centre of any indentation oriented
parallel to the edge of the test piece shall be at least 3,5 times the length of the short diagonal of the
indentation. The minimum distance between the edge of the test piece and the centre of any indentation
oriented perpendicular to the edge of the test piece shall be at least equal to the length of the long
diagonal of the indentation.
The minimum distance between the centres of two adjacent indentations, oriented side-by-side,
shall be at least 3,5 times the length of the short diagonal. For indentations oriented end-to-end, the
minimum distance between the centres of two adjacent indents shall be at least twice the length of the
long diagonal. If two indentations differ in size, the minimum spacing shall be based on the diagonal of
the larger indentation.
Edge of test piece
3,5 d
s
2 dd
3,5 d
s
d
s
d
Figure 3 — Minimum distance for Knoop indentations
6 © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
8.9 Measurement of diagonal length
The length of the long diagonal shall be measured and used for the calculation of the Knoop hardness. For
all tests, the perimeter of the indentation shall be clearly defined in the field of view of the microscope.
Magnifications should be selected so that the diagonal can be enlarged to greater than 25 %, but less
than 75 % of the maximum possible optical field of view (see 6.3).
NOTE 1 In general, decreasing the test force increases the scatter of the results of the measurements. The
accuracy of the determination of the long diagonal length is unlikely to be better than ±0,001 mm.
NOTE 2 A helpful technique for adjusting optical systems that have Köhler illumination is given in Annex E.
If the shape of the indentation appears to be nonsymmetrical, divide the long diagonal into two
segments at the point of intersection with the short diagonal, and measure the length of each segment.
If the difference between the two segments is greater than 5 % of the length of the long diagonal, check
the parallelism between the supporting plane and the measuring plane of the specimen and eventually,
the alignment of the indenter to the specimen. Test results with deviations greater than 5 % should be
discarded.
8.10 Calculation of hardness value
Calculate the Knoop hardness value using the formula given in Table 1. The Knoop hardness value can
also be determined using the calculation tables given in ISO 4545-4.
9 Uncertainty of the results
[7]
A complete evaluation of the uncertainty should be done according to JCGM 100: 2008 .
Independent of the type of sources, for hardness, there are two possibilities for the determination of the
uncertainty.
— One possibility is based on the evaluation of all relevant sources appearing during a direct calibration.
[8]
As a reference, a Euramet guideline is available.
— The other possibility is based on indirect calibration using a hardness reference block [below
abbreviated as CRM (certified reference material)] (see References [8] to [11]). A guideline for the
determination is given in Annex B.
It may not always be possible to quantify all the identified contributions to the uncertainty. In this case,
an estimate of type A standard uncertainty may be obtained from the statistical analysis of repeated
indentations into the test piece. Care should be taken if standard uncertainties of type A and B are
summarized, that the contributions are not counted twice (see JCGM 100: 2008, Clause 4).
10 Test report
The test report shall include the following information, unless otherwise agreed by the parties
concerned:
a) a reference to this document, i.e. ISO 4545-1;
b) all information necessary for identification of the test piece;
c) the date of the test;
d) the hardness result obtained in HK, reported in the format defined in 5.2;
e) all operations not specified in this document, or regarded as optional;
f) the details of any circumstances that affected the results;
ISO 4545-1:2017(E)
g) the temperature of the test, if it is outside the ambient range specified in 8.1;
h) where conversion to another hardness scale is also performed, the basis and method of this
conversion.
There is no general process of accurately converting Knoop hardness values into other scales of
hardness or into tensile strength. Such conversions, therefore, should be avoided, unless a reliable basis
for conversion can be obtained by comparison tests (see also ISO 18265).
NOTE A strict comparison of hardness values is only possible at identical test forces.
8 © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
Annex A
(normative)
Procedure for periodic checking of the testing machine, diagonal
measuring system and the indenter by the user
A.1 Periodic verification
The indenter to be used for the periodic verification shall be the same as used for testing. A hardness
reference block shall be chosen for testing that is calibrated in accordance to ISO 4545-3 on the scale
and at the approximate hardness level at which the machine will be used.
Before performing the periodic verification, the diagonal measuring system shall be indirectly verified
using one of the reference indentations on the hardness reference block. The measured indentation
length shall agree with the certified value to within the greater of 0,001 mm or 1,25 % of the indentation
length. If the diagonal measuring system fails this test, a second reference indentation may be measured.
If the diagonal measuring system fails this test a second time, the diagonal measuring system shall be
adjusted or repaired and undergo direct and indirect verification according to ISO 4545-2.
At least two hardness measurements shall be made on the calibrated surface of the hardness reference
block. The indentations shall be uniformly distributed over the surface of the reference block. The
machine is regarded as satisfactory if the maximum positive or negative percent bias, b , for each
rel
reading does not exceed the limits shown in Table A.1.
The percent bias, b , is calculated according to Formula (A.1):
rel
HH−
CRM
b =×100 (A.1)
rel
H
CRM
where
H is the hardness value corresponding to the hardness measurement taken;
H is the certified hardness of the reference block used.
CRM
If the testing machine fails this test, verify that the indenter and testing machine are in good working
condition and repeat the periodic verification. If the machine continues to fail the periodic verification,
an indirect verification according to ISO 4545-2 shall be performed. A record of the periodic verification
results should be maintained over a period of time and used to measure reproducibility and monitor
drift of the machine.
ISO 4545-1:2017(E)
Table A.1 — Maximum permissible percent HK bias
Maximum permissible percent
Mean diagonal length
HK bias, b ,
rel
d
of the testing machine,
mm
± %HK
0,02 ≤ d < 0,06 0,24/ d
0,06 ≤ d
NOTE The criteria specified in this document for the performance of the testing machine have been
developed and refined over a significant period of time. When determining a specific tolerance that the machine
needs to meet, the uncertainty associated with the use of measuring equipment and/or reference standards has
been incorporated within this tolerance, and it would therefore be inappropriate to make any further allowance
for this uncertainty by, for example, reducing the tolerance by the measurement uncertainty. This applies to all
measurements made when performing a periodic verification of the machine.
A.2 Indenter inspection
Experience has shown that a number of initially satisfactory indenters can become defective after use
for a comparatively short time. This is due to small cracks, pits or other flaws in the surface. lf such
faults are detected in time, many indenters may be reclaimed by regrinding. If not, any small defects on
the surface rapidly worsen and make the indenter useless. Therefore,
— the condition of indenters should be monitored by visually checking the aspect of the indentation on
a reference block, each day the testing machine is used,
— the verification of the indenter is no longer valid when the indenter shows defects, and
— reground or otherwise repaired indenters shall meet all of the requirements of ISO 4545-2.
10 © ISO 2017 – All rights reserved

ISO 4545-1:2017(E)
Annex B
(informative)
Uncertainty of the measured hardness values
B.1 General requirements
Measurement uncertainty analysis is a useful tool to help determine sources of error and to understand
differences in test results. This annex gives guidance on uncertainty estimation but the methods
contained are for information only, unless specifically instructed otherwise by the customer.
Most product specifications have tolerances that have been developed over the past years based
mainly on the requirements of the product but also, in part, on the performance of the machine used
to make the hardness measurement. These tolerances therefore incorporate a contribution due to the
uncertainty of the hardness measurement and it would be inappropriate to make any further allowance
for this uncertainty by, for example, reducing the specified tolerance by the estimated uncertainty of
the hardness measurement. In other words, where a product specification states that the hardness of
an item shall be higher or lower than a certain value, this should be interpreted as simply specifying
that the calculated hardness value(s) shall meet this requirement, unless specifically stated otherwise
in the product standard. However, there may be special circumstances where reducing the tolerance
by the measurement uncertainty is appropriate. This should only be done by agreement of the parties
involved.
The approach for determining uncertainty presented in this annex considers only those uncertainties
associated with the overall measurement performance of the hardness testing machine with respect
to the hardness reference blocks (abbreviated as CRM below). These performance uncertainties reflect
the combined effect to all the separate uncertainties (indirect verification). Because of this approach, it
is important that the individual machine components are operating within the tolerances. It is strongly
recommended that this procedure be applied for a maximum of one year after the successful passing of
a direct verification.
Annex C shows the four-level structure of the metrological chain necessary to define and disseminate
hardness scales. The chain starts at the international level using international definitions of the various
hardness scales to carry out international intercomparisons. A number of primary hardness standard
machines at the national level “produce” primary hardness-reference blocks for the calibration
laboratory level. Naturally, direct calibration and the verification of these machines should be at the
highest possible accuracy.
B.2 General procedure
The procedure calculates a combined uncertainty, u, by the root-squared-sum-method (RSS) out of the
different sources given in Table B.1. The expanded uncertainty, U, is derived from u by multiplying with
the coverage factor k = 2. Table B.1 contains all symbols and their designation.
The bias, b, of a hardness testing machine (also named "error"), which is derived from the difference
between
— the certified calibration value of the hardness reference block used, and
— the mean hardness value of the five indentations made in this block during calibration of the
hardness testing machine,
can be implemented in different ways into the determination of uncertainty (see ISO 4545-2).
ISO 4545-1:2017(E)
Two methods are given for determining the uncertainty of hardness measurements.
— Method 1 (M1): accounts for the systematic bias of the hardness machine in two different ways. In
one approach, the uncertainty contribution from the systematic bias is added arithmetically to this
value. In the other approach, a correction is made to the measurement result to compensate for the
systematic bias.
— Method 2 (M2): allows the determination of uncertainty without having to consider the magnitude
of the systematic bias.
Additional information on calculating hardness uncertainties can be found in the literature (see
References [7] and [8]).
NOTE 1 This uncertainty approach makes no allowance for any possible drift in the machine performance
subsequent to its last calibration, as it assumes that any such changes will be insignificant in magnitude. As such,
most of this analysis could be performed immediately after the machine’s calibration and the results included in
the machine’s calibration certificate.
NOTE 2 In this annex, the abbreviation “CRM” stands for “certified reference material”. In hardness testing
standards, certified reference material is equivalent to the hardness reference block, i.e. a piece of material with
a certified value and associated uncertainty.
B.3 Procedures for calculating uncertainty — Hardness measurement values
B.3.1 Procedure with bias (method M1)
The method M1 procedure for the determination of measurement uncertainty is explained in Table B.1.
The measurement bias, b, of the hardness testing machine can be expected to be a systematic effect.
In JCGM 100: 2008, it is recommended that a correction be used to compensate for systematic effects,
and this is the basis of M1. The result of using this method is that either all determined hardness
values x have to be reduced by b or the uncertainty, U, has to be increased by b. The procedure for the
determination of U is explained in Table B.1.
M1
The combined expanded measurement uncertainty for a single hardness measurement, x, is calculated
according to Formula (B.1):
22 2
Uk=× uu+×2 +u (B.1)
M1 HmsHTM
where
u is a contribution to the measurement uncertainty due to the lack of measurement
H
repeatability of the hardness testing machine;
u is a contribution to the measurement uncertainty due to the resolution of the hardness test-
ms
ing machine. Both the resolution of the length measurement indicating instrument and the
optical resolution of the measuring microscope shall be considered. In most cases, the overall
resolution of the measurement system should be included twice in the calculation of u due
H
to resolving the positions of both ends of the long diagonal independently;
u is a contribution to the measurement uncertainty due to the standard uncertainty of the bias
HTM
measurement, b, generated by the hardness testing machine (this value is reported as a result
of the indirect verification defined in ISO 4545-2) and is calculated according to Formula (B.2):
22 2
uu=+ uu+×2 (B.2)
HTMCRM HCRM ms
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ISO 4545-1:2017(E)
where
u is the contribution to the measurement uncertainty due to the calibration uncertainty of the
CRM
certified value of the CRM according to the calibration certificate for k = 1;
u is the contribution to the measurement uncertainty due to the combination of the lack of
HCRM
measurement repeatability of the hardness testing machine and the hardness
nonuniformity of the CRM, calculated as the standard deviation of the mean of the
hardness measurements when measuring the CRM;
u is the contribution to the measurement uncertainty due to the resolution of the hardness
ms
testing machine when measuring th
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