ISO 9042:2024

International
Standard
ISO 9042
Second edition
Steels — Point counting method for
2024-04
statistically estimating the volume
fraction of a constituent with a
point grid
Aciers — Méthode d'estimation statistique de la fraction
volumique d'un constituant à l'aide de grilles de points
Reference number
© ISO 2024
All rights reserved. Unless otherwise specified, or required in the context of its implementation, 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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 1
5 Principle . 2
6 Apparatus . 2
6.1 Grid.2
6.2 Means of observation . .3
7 Sample . 3
7.1 Sampling and number of samples .3
7.2 Preparation of samples .3
8 Procedure . 4
8.1 Selection of the grid .4
8.2 Magnification selection .4
8.3 Selection of the number of observed fields .4
8.4 Array of the fields .5
8.5 Examination and estimation of the fields .5
8.6 Calculation of the volume fraction V .6
v
9 Test report . 7
Bibliography . 8

iii
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of 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 www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 17, Steel, Subcommittee SC 7, Methods of testing
(other than mechanical tests and chemical analysis).
This second edition cancels and replaces the first edition (ISO 9042:1988) which has been technically
revised.
The main changes are as follows:
— clearer definition of t multiplier and corrected values in Table 4 (formerly Table 3);
— additional grid examples;
— application to digital images;
— change of terminology: Error % is now E ;
rel
— editorial changes.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
International Standard ISO 9042:2024(en)
Steels — Point counting method for statistically estimating
the volume fraction of a constituent with a point grid
1 Scope
This document specifies a point counting method for statistically estimating the volume fraction of a
constituent through the microstructure of a steel by means of a point grid.
It applies to constituents which are clearly identifiable.
By default, counting is performed manually, but can be computer assisted or substituted by validated
computer algorithms.
NOTE In this document, the word "constituent" can designate a phase as well as a micrographic constituent
composed of two or more phases.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols and abbreviated terms
The symbols used are given in Table 1.
Table 1 — Symbols
Symbols Definition Value
n
Number of fields observed —
P Total number of points in the grid —
T
th
P Point count on the i field —
i
th
Proportion of grid points in the constituent on the i observed field,
Pi See Formula (2)
()
P
expressed as a percentage of the total number of points in the grid.
Arithmetic mean of Pi() See Formula (3)
P
P P
ˆs Estimate of the standard deviation σ of the mean See Formula (4)
CI 95 % confidence interval See Formula (5)
Student’s t-distribution for a two-sided confidence level of 95 % and
t See Table 4 for values
00,;51n−
n observed fields
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbols Definition Value
V Volume fraction of the constituent expressed as a percentage See Formula (6)
V
A Estimated area fraction of the constituent expressed as a percentage —
A,est
Relative error, a measure of the statistical precision, expressed as
E a percentage; a lower E corresponds to a lower error and thus a See Formula (7)
rel rel
higher accuracy
5 Principle
The
...