SIST EN ISO 643:2024

SLOVENSKI STANDARD
01-november-2024
Nadomešča:
SIST EN ISO 643:2020
Jekla - Mikrografsko določevanje navidezne velikosti kristalnih zrn (ISO 643:2024)
Steels - Micrographic determination of the apparent grain size (ISO 643:2024)
Stahl - Mikrophotographische Bestimmung der erkennbaren Korngröße (ISO 643:2024)
Aciers - Détermination micrographique de la grosseur de grain apparente (ISO
643:2024)
Ta slovenski standard je istoveten z: EN ISO 643:2024
ICS:
77.040.99 Druge metode za Other methods of testing of
preskušanje kovin metals
77.080.20 Jekla Steels
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 643
EUROPEAN STANDARD
NORME EUROPÉENNE
September 2024
EUROPÄISCHE NORM
ICS 77.040.99 Supersedes EN ISO 643:2020
English Version
Steels - Micrographic determination of the apparent grain
size (ISO 643:2024)
Aciers - Détermination micrographique de la grosseur Stahl - Mikrophotographische Bestimmung der
de grain apparente (ISO 643:2024) erkennbaren Korngröße (ISO 643:2024)
This European Standard was approved by CEN on 2 September 2024.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye 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
© 2024 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 643:2024 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 643:2024) has been prepared by Technical Committee ISO/TC 17 "Steel" in
collaboration with Technical Committee CEN/TC 459/SC 1 “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 March 2025, and conflicting national standards shall
be withdrawn at the latest by March 2025.
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 643:2020.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 643:2024 has been approved by CEN as EN ISO 643:2024 without any modification.

International
Standard
ISO 643
Fifth edition
Steels — Micrographic determination
2024-08
of the apparent grain size
Aciers — Détermination micrographique de la grosseur de grain
apparente
Reference number
ISO 643:2024(en) © ISO 2024
ISO 643:2024(en)
© 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
ISO 643:2024(en)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Grains .1
3.2 General .2
4 Symbols . 2
5 Principle . 3
6 Selection and preparation of the specimen. 5
6.1 Test location .5
6.2 Revealing ferritic grain boundaries .5
6.3 Revealing austenitic and prior-austenitic grain boundaries .5
6.3.1 General .5
7 Characterization of grain size . 6
7.1 General .6
7.1.1 Characterization methods .6
7.1.2 Formulae .6
7.1.3 Accuracy of the methods .6
7.2 Comparison method .6
7.3 Planimetric method .9
7.4 Intercept method . 13
7.4.1 General . 13
7.4.2 Linear intercept method .14
7.4.3 Circular intercept method . 15
7.4.4 Assessment of results . 15
7.5 Other methods .16
8 Test report . 17
Annex A (informative) Methods for revealing austenitic or prior-austenitic grain boundaries in
steels .18
Annex B (normative) Determination of grain size with standard comparison charts .23
Annex C (informative) Evaluation method .35
Annex D (informative) Calculation of grain size and confidence interval .37
Annex E (informative) Grains of different size indices .40
Bibliography .46

iii
ISO 643:2024(en)
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 ISO/TC 17, Steel, Subcommittee SC 7, Methods of testing (other than
mechanical tests and chemical analysis), in collaboration with the European Committee for Standardization
(CEN) Technical Committee CEN/TC 459, ECISS - European Committee for Iron and Steel Standardization, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This fifth edition cancels and replaces the fourth edition (ISO 643:2019), which has been technically revised.
The main changes are as follows:
— the test temperature of McQuaid-Ehn method has been modified for case hardening steels to 950 °C (see A.4);
— subclause 7.2 has been modified with reference to new Annex B and amended Table 2;
— Annex B from the third edition (ISO 643:2012) has been reinstated, now with new ISO grain size charts
instead of ASTM charts;
— parts of the old Annex B (evaluation method) have been revised and moved to the main body of the
standard (subclause 7.3) and the remainder of the annex has been renumbered as Annex C;
— new Annexes D and E have been added.
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 643:2024(en)
Steels — Micrographic determination of the apparent grain size
WARNING — This document calls for the use of substances and/or procedures that may be injurious
to health if adequate safety measures are not taken. This document does not address any health
hazards, safety or environmental matters associated with its use. It is the responsibility of the user
of this document to establish appropriate health, safety and environmentally acceptable practices.
1 Scope
This document specifies micrographic methods of determining apparent ferritic or austenitic grain
size in steels. It describes the methods of revealing grain boundaries and of estimating the mean grain
size of specimens with unimodal size distribution. Although grains are three-dimensional in shape, the
metallographic sectioning plane can cut through a grain at any point from a grain corner, to the maximum
diameter of the grain, thus producing a range of apparent grain sizes on the two-dimensional plane, even in
a sample with a perfectly consistent grain size.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
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/
3.1 Grains
3.1.1
grain
closed polygonal shape with more or less curved sides, which can be revealed on a flat section through the
sample, polished and prepared for micrographic examination
[1]
Note 1 to entry: In ISO 4885 grain is defined as “space lattice formed by atoms with regular interstices".
Note 2 to entry: If any other constituent (e.g. pearlite) of similar dimensions to the grains of interest is present, that
constituent can be counted as grains of interest.
3.1.2
austenitic grain
crystal with a face-centred cubic crystal structure which may, or may not, contain annealing twins
3.1.3
ferritic grain
crystal with a body-centred cubic crystal structure which never contains annealing twins

ISO 643:2024(en)
3.2 General
3.2.1
index
positive, zero or possibly negative number G which is derived from the mean number m of grains (3.1.1)
counted in an area of 1 mm of the section of the specimen
Note 1 to entry: By definition, G = 1 where m = 16; the other indices are obtained by Formula (1).
3.2.2
intercept
N
number of grains (3.1.1) intercepted by a test line, either straight or curved
Note 1 to entry: See Figure 1.
Note 2 to entry: Straight test lines will normally end within a grain. These end segments are counted as 1/2 an
intercept. N is the average of a number of counts of the number of grains intercepted by the test line applied randomly
at various locations. N is divided by the true line length, L usually measured in millimetres, in order to obtain the
T
number of grains intercepted per unit length, N .
L
3.2.3
intersection
P
number of intersection points between grain (3.1.1) boundaries and a test line, either straight or curved
Note 1 to entry: See Figure 2.
Note 2 to entry: P is the average of a number of counts of the number of grain boundaries intersected by the test line
applied randomly at various locations. P is divided by the true line length, L usually measured in millimetres, in
T
order to obtain the number of grain boundary intersections per unit length, P .
L
4 Symbols
The symbols used are given in Table 1.
Table 1 — Symbols
Symbols Definition Value
a Mean area of grain in square millimetres
a =
m
A True area of the test box mm
B
A True area of the test circle mm
C
A Apparent area of the test figure in square millimetres —
F
d =
Mean grain diameter in millimetres
d
m
Diameter of the circle on the ground glass screen of the microscope or on a
79,8 mm
D photomicrograph enclosing the image of the reference surface of the speci-
(area = 5 000 mm )
men
g Linear magnification (to be noted as a reference) of the microscopic image In principle 100
G Equivalent index of grain size G = log m – 3
l Mean lineal intercept length, generally expressed in millimetres lN==11//P
LL
l Mean lineal intercept length for G = 0, in millimetres 0,32
L True length of the test line divided by the magnification, in millimetres —
T
a [2]
The method for designating the direction conforms to ISO 3785 .

ISO 643:2024(en)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbols Definition Value
m = n /A
Number of grains per square millimetre of specimen surface in the area
t C
m
examined
m = n /A
t B
M Number of the closest standard chart picture where g is not 100 —
n Number of grains completely inside the circle of diameter D —
e
n Number of grains intersected by the circle of diameter D —
i
n Total equivalent number of grains examined on the image of diameter D —
t
Mean number of grains intercepted per unit length L —
N
N Mean number of grains intercepted per unit length of the line
NN= /L
L
LT
a
N Number of intercepts per millimetre in the longitudinal direction —
x
a
N Number of intercepts per millimetre in the transverse direction —
y
a
N Number of intercepts per millimetre in the perpendicular direction —
z
Mean number of counts of the number of grain boundaries intersected by the
—
P
test line applied randomly at various locations
Mean number of grain boundary intersections per unit length of
P PP= /L
L
LT
test line
g
 
Q Correction factor for non-standard magnification Ql=2 og
2 
 
a [2]
The method for designating the direction conforms to ISO 3785 .
5 Principle
This document is applicable to grain structures that have a unimodal size distribution. The apparent grain
size is determined by micrographic examination of appropriately prepared sections of the specimen.
The following principal methods are available to obtain an index representing the mean value of the grain size:
a) comparison method using standard charts (see 7.2);
b) planimetric method counting grains to determine the mean number of grains per unit area, (see 7.3);
c) intercept method counting the number of grains or grain boundaries along a line of a known length
(see 7.4).
All methods give comparable results.

ISO 643:2024(en)
Figure 1 — Example of intercept, N
Intercept, N, grain counts for a straight line on a single-phase grain structure. Six intercepts and two line
segments ending within a grain equals 2 × 1/2 + 6 = 7.
Figure 2 — Example of intersection, P
Intersection, P, counts for a straight test line placed over a single-phase grain structure where the arrows
point to 7 intersection points and P = 7.

ISO 643:2024(en)
6 Selection and preparation of the specimen
6.1 Test location
If the order, or the standard defining the product, does not specify the number of specimens and the point at
which they are to be taken from the product, these are left to the manufacturer, although it has been shown
that precision of grain size determination increases the higher the number of specimens assessed. Care
shall be taken to ensure that the specimens are representative of the bulk of the product (i.e. avoid heavily
deformed material such as that found at the extreme end of certain products or where shearing has been
used to remove the specimen, etc.). The specimens shall be polished in accordance with the usual methods.
Unless otherwise stated by the product standard or by agreement with the customer, the polished surface
can be randomly selected for the specimens with equiaxial grains. The polished surface shall be parallel to
the principal axis of deformation in wrought products, for the specimens with deformed grains.
NOTE Measurements of the grain size on a transverse plane will be biased if the grain shape is not equiaxial.
6.2 Revealing ferritic grain boundaries
The ferritic grains shall be revealed by etching with nital [ethanolic 2 % to 3 % (by volume) nitric acid
solution], or with another appropriate reagent.
6.3 Revealing austenitic and prior-austenitic grain boundaries
6.3.1 General
In the case of steels having a single-phase or dual-phase mainly austenitic structure (delta ferrite grains in
an austenitic matrix) at ambient temperature, the grains shall be revealed by an etching solution. For single
phase austenitic stainless steels, the most commonly used chemical etchants are glyceregia, Kalling’s reagent
(No. 2) and Marble's reagent. The best electrolytic etch for single or two-phase stainless steels is aqueous
60 % nitric acid at 1,4 V d.c. for 60 s to 120 s, as it reveals the grain boundaries but not the twin boundaries.
Aqueous 10 % oxalic acid, 6 V d.c., up to 60 s, is commonly used but is less effective than electrolytic 60 %
nitric acid.
For other steels, one or other of the methods specified below shall be used depending on the information
required:
— “Bechet-Beaujard” method by etching with aqueous saturated picric acid solution (see A.2);
— “Kohn” method by controlled oxidation (see A.3);
— “McQuaid-Ehn” method by carburization (see A.4);
— grain boundary sensitization method (see A.7);
— other methods specially agreed upon when ordering.
NOTE The first three methods are for prior-austenitic grain boundaries while the others are for austenitic Mn or
austenitic stainless, see Annex A.
If comparative tests are carried out for the different methods, it is essential to use the same heat treatment
conditions. Results may vary considerably from one method to the other.

ISO 643:2024(en)
7 Characterization of grain size
7.1 General
7.1.1 Characterization methods
The apparent grain size can be determined by three micrographic methods: comparison method, planimetric
method and intercept method.
7.1.2 Formulae
The index is defined by Formula (1):
G
m=×82 (1)
This formula may be stated as Formula (2):
Gm=log −3 (2)
NOTE An alternative system of grain size definition is known as the ASTM grain size (see C.2).
7.1.3 Accuracy of the methods
In general, the comparison method allows for an accuracy of 0,5; the planimetric and intercept segment
methods allow for an accuracy of 0,1, see Reference [3]. For comparison between methods, the indexes
obtained are usually rounded to multiples of 0,5.
Due to the randomness of the spatial position in which each grain is cut through by the sectioning plane
and due to the measurement error, no determination of apparent grain size can be an exact measurement.
Therefore, for planimetric and intercept methods it can be of interest to calculate the 95 % confidence
interval of the grain size measurement result and adjust the number of fields inspected according to the
percentage relative accuracy, % RA, of counting corresponding to the uncertainty of ±0,25 grain size units,
taking into account that for a symmetric error of G the % RA of the measured quantity is not symmetric, see
Annex D.
The methods described in this document yield representative results for specimens with a unimodal grain
size distribution. Applying them to specimens with bimodal (or more complex) size distributions will yield
an average value that likely has no meaningful relationship with the various grain populations but may still
[4]
represent the specimen on average. ISO 14250 may be the more appropriate standard for characterizing
these specimens, see Annex E.
7.2 Comparison method
7.2.1 The image examined on the screen (or on a photomicrograph) shall be compared with a series of
standard charts presented in Annex B or overlays (using eye-piece graticules designed for grain size
measurement can be used provided these are traceable to national or international standards). The
standard charts at a magnification of 100:1 are numbered from -1 to 10 so that their number is equal to
the index G. Images for grain sizes -1 to 3 are included in the chart but when determining grain sizes in this
range it is recommended for reasons of accuracy to reduce the operating magnification of the microscope, in
combination with index conversion according to Table 2.
Using ASTM E112 charts gives substantially the same results as using the comparison charts of Annex B,
see C.2.4.
7.2.2 The standard chart with the grain size closest to that of the examined fields of the specimen can
then be determined. A minimum of three randomly selected fields shall be assessed on each specimen.

ISO 643:2024(en)
7.2.3 Where the magnification g of the image on the screen or photomicrograph is not 100:1, the index G
shall be equal to the number M of the closest standard chart, modified as a function of the ratio of the
magnifications, as given by Formula (3):
g g
GM=+2log =+Ml66, 4 g (3)
100 100
Table 2 gives the relationship between the indices for the usual magnifications.

ISO 643:2024(en)
Table 2 — Relationship between indices for the usual magnifications
Standard chart no. M 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10
Magnification of
a b
the image
Q Grain size
g
25 −4 −3 −2,5 −2 −1,5 −1 −0,5 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6
50 −2 −1 −0,5 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8
100 0 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10
200 +2 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12
400 +4 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14
500 +4,5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14 14,5
800 +6 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14 14,5 15 15,5 16
1 000 +6,5 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14 14,5 15 15,5 16 16,5
a
The values for g = 500 and g = 1 000 are rounded to the nearest multiple of 0,5.
b
EXAMPLE: At a magnification g = 50 the standard chart number M = 3 corresponds to a grain size of G = 1.

ISO 643:2024(en)
7.2.5 For the comparison method, if the difference between the maximum index G and the minimum
max
index G determined is less than three (e. g. range from G = 6 to 8,5), compute the test result as the
min
arithmetic mean of the found indices. If the indices are calculated using Formula (3), the arithmetic mean is
to be calculated after the modification for non-standard magnification. If this condition is not fulfilled, the
operator may perform an additional series of at least six determinations of the grain size. If the difference
between the maximum index and the minimum index determined in this new series is less than three, then
compute the test result as the arithmetic mean of all determinations of both the first and second series.
If this latter condition is not fulfilled, note the spread and a comment on the findings in the final report.
Alternatively, ISO 14250 should be considered. For a more elaborate discussion on specimens of non-
unimodal distribution, see Annex E.
The calculated arithmetic mean of indices shall be rounded to the nearest multiple of 0,5.
7.3 Planimetric method
7.3.1 Historically a circle measuring 79,8 mm in diameter (A = 5 000 mm ), see Figure 3, was drawn or
F
superimposed over a micrograph or a live image on a ground glass projection screen. The magnification was
then adjusted so that the circular area contained at least 50 grains in order to minimize the counting error
associated with a circular test pattern. The following procedure and formulae are magnification neutral.
NOTE The circle referenced an apparent size specifically at 100:1 magnification as perceived by an operator at a
microscope using ×10 oculars and ×10 objective. This reference also was, and still is, used in other applications such
as inclusion assessments. It is moreover a component of the recommended concentric circle grid used in the intercept
method, as well as one of the reference circles used in the comparison method.
However, more recent tools like image software allow for optimizing the combination of circle diameter and
magnification to facilitate the count and to make sure that the number of grains within the circle reach at least 50.
Therefore, it is no longer always relevant to reference a specific circle size at a specific magnification.
Figure 3 — Evaluation of the number of grains in an area enclosed by a circle

ISO 643:2024(en)
7.3.2 Two counts are made; the number of grains completely enclosed within the test circle of any given
size, n , and the number of grains intercepted by the test circle, n .
e i
The total number of equivalent grains, n , is calculated using Formula (4):
t
n
i
nn=+ (4)
te
The number of grains per mm , m, is calculated using Formula (5):
n
t
m= (5)
A
C
where A is the true area of the circle.
C
7.3.3 The planimetric approach assumes that on average, half of the grains on the test circle are within
and half are outside test circle. This assumption is only fully valid along a straight line through a grain
structure, but not for a curved line, including a circle. The bias created by this assumption increases as the
number of grains inside the test circle decreases. If the number of grains within the test circle is at least 50,
the bias becomes about 2 %.
7.3.4 A simple way to avoid this bias, irrespective of the number of grains within the test figure, is to use a
square or a rectangle (see Figure 4). However, the counting procedure then shall be modified.
First, it is assumed that the grains on each of the four corners are, on average, one fourth within the figure
and three-fourths outside. These four corner grains together equal one grain within the test box. Ignoring
the four corner grains, a count is made of the grains completely enclosed by the test box, n , and the grains
e
intercepted by the four sides of the box, n , (see Figure 4). The total number of grains is calculated as in
i
Formula (6):
n
i
nn=+ +1 (6)
te
ISO 643:2024(en)
Figure 4 — Evaluation of the number of grains in an area enclosed by a square or rectangle
7.3.5 The number of grains per mm , m , on the surface of the specimen is given by Formula (7):
n
t
m= (7)
A
B
where A is the true area of the test box used for counting.
B
7.3.6 Regardless of using a circle or a box, the mean grain area, a , in mm is calculated from Formula (8):
a= (8)
m
7.3.7 By assuming a uniform geometrical grain shape, there are several ways to calculate a mean grain
“diameter”. Assuming that all grains are square-shaped, the mean diameter, d , can be calculated with
Formula (9):
da= (9)
This is the diameter listed in Table 3.
A mean equivalent circle diameter, d , can be calculated with Formula (10):
EC
4a
d = (10)
EC
π
NOTE The mean equivalent circle diameter is often referred to in literature as ECD .

ISO 643:2024(en)
Assuming that all grains are hexagonal in a perfect honeycomb pattern, the mean vertex-to-vertex distance,
d , can be calculated with Formula (11):
v-v
8·a
d = (11)
v-v
and the mean distance between parallel sides, d , can be calculated with Formula (12):
s-s
2·a
d = (12)
s-s
7.3.8 A nominal value of m corresponds to each value of G. The values of m calculated by Formula (5) or
Formula (7) within the limits given in Table 3 are given in 0,5 steps of G.
Table 3 — Evaluation of number of grains as a function of various parameters
Mean
Mean
Number of grains, per square Mean area lineal intercept length
diameter
Mean number of
of grain
millimetre
of grain
1 intercepts on
Grain
m a l or
the
d
size indi-
P
measuring
L
ces
line, per
Nominal Limit values
G
millimetre or
Limit values
value
Nominal
N
L
value
from to from to
mm mm mm
(excl.) (incl.) (excl.) (incl.)
-1 4 3,4 4,8 0,5 0,25 0,453 0,494 0,415 2,21
-0,5 5,7 4,8 6,7 0,42 0,18 0,381 0,415 0,349 2,63
0 8 6,7 9,5 0,35 0,125 0,320 0,349 0,293 3,13
0,5 11,3 9,5 13,5 0,30 0,088 4 0,269 0,293 0,247 3,72
1 16 13,5 19,0 0,25 0,062 5 0,226 0,247 0,207 4,42
1,5 22,6 19,0 26,9 0,21 0,044 2 0,190 0,207 0,174 5,26
2 32 26,9 38,1 0,177 0,031 3 0,160 0,174 0,147 6,25
2,5 45,3 38,1 53,8 0,149 0,022 1 0,135 0,147 0,123 7,43
3 64 53,8 76,1 0,125 0,015 6 0,113 0,123 0,104 8,84
3,5 90,5 76,1 108 0,105 0,011 0 0,095 1 0,104 0,087 2 10,5
4 128 108 152 0,088 4 0,007 81 0,080 0 0,087 2 0,073 4 12,5
4,5 181 152 215 0,074 3 0,005 52 0,067 3 0,073 4 0,061 7 14,9
5 256 215 304 0,062 5 0,003 91 0,056 6 0,061 7 0,051 9 17,7
5,5 362 304 431 0,052 6 0,002 76 0,047 6 0,051 9 0,043 6 21,0
6 512 431 609 0,044 2 0,001 95 0,040 0 0,043 6 0,036 7 25,0
6,5 724 609 861 0,037 2 0,001 38 0,033 6 0,036 7 0,030 8 29,7
7 1 024 861 1 218 0,031 3 0,000 977 0,028 3 0,030 8 0,025 9 35,42
7,5 1 448 1 218 1 722 0,026 3 0,000 691 0,023 8 0,025 9 0,021 8 42,0
8 2 048 1 722 2 435 0,022 1 0,000 488 0,020 0 0,021 8 0,018 3 50,0
8,5 2 896 2 435 3 444 0,018 6 0,000 345 0,016 8 0,018 3 0,015 4 59,5
9 4 096 3 444 4 871 0,015 6 0,000 244 0,014 1 0,015 4 0,013 0 70,7
9,5 5 793 4 871 6 889 0,013 1 0,000 173 0,011 9 0,013 0 0,010 9 84,1
10 8 192 6 889 9 742 0,011 0 0,000 122 0,010 0 0,010 9 0,009 17 100
10,5 11 585 9 742 13 777 0,009 29 0,000 086 3 0,008 2 0,009 17 0,007 71 119
11 16 384 13 777 19 484 0,007 81 0,000 061 0 0,007 07 0,007 71 0,006 48 141
11,5 23 170 19 484 27 554 0,006 57 0,000 043 2 0,005 95 0,006 48 0,005 45 168
12 32 768 27 554 38 968 0,005 52 0,000 030 5 0,005 00 0,005 45 0,004 59 200
12,5 46 341 38 968 55 109 0,004 65 0,000 021 6 0,004 20 0,004 59 0,003 86 238
NOTE This table gives the values between the different parameters for equiaxed grains.

ISO 643:2024(en)
TTabablele 3 3 ((ccoonnttiinnueuedd))
Mean
Mean
Mean area lineal intercept length
Number of grains, per square
diameter
Mean number of
millimetre of grain
of grain
1 intercepts on
Grain
m l or
a
the
d
size indi-
P
L measuring
ces
line, per
Nominal Limit values
G
Limit values millimetre or
value
Nominal
N
L
value
from to from to
mm mm mm
(excl.) (incl.) (excl.) (incl.)
13 65 536 55 109 77 936 0,003 91 0,000 015 3 0,003 54 0,003 86 0,003 24 283
13,5 92 682 77 936 110 218 0,003 28 0,000 010 8 0,002 97 0,003 24 0,002 73 336
14 131 072 110 218 155 872 0,002 76 0,000 007 63 0,002 50 0,002 73 0,002 29 400
14,5 185 364 155 872 220 436 0,002 32 0,000 005 39 0,002 10 0,002 29 0,001 93 476
15 262 144 220 436 311 744 0,001 95 0,000 003 81 0,001 77 0,001 93 0,001 62 566
15,5 370 728 311 744 440 872 0,001 64 0,000 002 70 0,001 49 0,001 62 0,001 36 673
16 524 288 440 872 623 487 0,001 38 0,000 001 91 0,001 25 0,001 36 0,001 15 800
16,5 741 455 623 487 881 744 0,001 16 0,000 001 35 0,001 05 0,001 15 0,000 964 951
17 1 048 576 881 744 1 246 974 0,000 977 0,000 000 954 0,000 884 0,000 964 0,000 811 1 131
NOTE This table gives the values between the different parameters for equiaxed grains.
7.4 Intercept method
7.4.1 General
7.4.1.1 Count the number of grains intercepted, N, or the number of grain boundary intersections, P, with
a test line or a grid of test lines of known true length L . The count may be performed using a projection
T
screen, a reticle, a video monitor or a photomicrograph of the specimen.
7.4.1.2 The test line may be straight or circular. The test grid in Figure 5 shows the types of recommended
test lines.
7.4.1.3 The line or grid of lines shall be applied only once to the field examined. It is applied at random to
an adequate number of fields to obtain a valid count for N or P.
Figure 5 shows a test pattern that can be used to measure grain size by the intercept method, and which
is scaled to be convenient for g = 100. The three concentric circles have a total line length of 500 mm; their
diameters are 79,58 mm, 53,05 mm and 26,53 mm. A circular test grid averages out variations in the shape
of equiaxed grains and avoids the problem of lines ending within grains. Figure 5 also has four straight lines:
two oriented diagonally, one vertically and one horizontally. Each diagonal line has a length of 150 mm while
the horizontal and vertical lines are each 100 mm long. The straight lines will also average out variations
in the shape of equiaxed grains. Alternatively, if the degree of grain elongation is of interest, grain counts
can be made using only the vertical and horizontal lines (separately) when they are aligned so that one line
is parallel to the deformation axis (and the other line is then perpendicular to the deformation axis) on a
longitudinally-oriented polished plane [see 7.5, c)].

ISO 643:2024(en)
Figure 5 — Recommended measurement grid for the intercept segment methods
Straight lines indicate the linear intercept method (see 7.4.2) and circles indicate the circular intercept
method (see 7.4.3). These methods should be used separately.
7.4.1.5 The true total length of the grid of lines L is the measured length divided by the magnification g.
T
L can also be calculated using a scale bar or a software calibration factor.
T
7.4.2 Linear intercept method
7.4.2.1 The pattern of straight lines shown in Figure 5 is recommended. The magnification g should be
selected so that at least 50 intercepts are obtained in any one field. At least five randomly selected fields
shall be assessed with a total number of intercepts of at least 250.
NOTE If the grain size of the specimen requires the magnification to be changed in order to achieve the required
number of intercepts, the length of the measuring lines can also be varied providing that the orientation of the
measuring lines is arranged to take account of the effects of anisotropy.
7.4.2.2 The following rules apply to intercept and intersection counts of single-phase grain structures
using straight test lines:
a) when the number of intercepted grains, N, is counted:
— if a test line goes through a grain, N is 1;
— if a test line terminates within a grain, N is 0,5;
— if a test line is tangential to a grain boundary, N is 0,5.

ISO 643:2024(en)
b) when the number of grain boundary intersections, P, is counted:
— if a test line passes through a grain boundary, P is 1;
— if a test line is tangential to a grain boundary, P is 1;
— if a test line intersects a triple point, P is 1,5.
NOTE The “Snyder-Graff” method, described in C.1, Annex C, represents a linear intercept method for tool steel
(high-speed steels).
7.4.3 Circular intercept method
7.4.3.1 The pattern of circles shown in Figure 5 is recommended.
7.4.3.2 The measuring line consists either of a set of three concentric circles as shown in Figure 5 or of one
single circle.
7.4.3.3 The magnification or diameter of the circle should be selected so that there are 40 to 50 intercepts
when the measurement grid is superposed on the field to be examined. At least five randomly selected fields
shall be assessed with a total number of intercepts of at least 250.
7.4.3.4 In the case of a single circle, the largest circle is used. In this case, the magnification to be used
should enable at least 25 intercepts to be c
...