EN ISO 21432:2020

Non-destructive testing - Standard test method for determining residual stresses by neutron diffraction (ISO 21432:2019)

This document describes the test method for determining residual stresses in polycrystalline materials by neutron diffraction. It is applicable to both homogeneous and inhomogeneous materials including those containing distinct phases.
The principles of the neutron diffraction technique are outlined. Suggestions are provided on:
—          the selection of appropriate diffracting lattice planes on which measurements should be made for different categories of materials,
—          the specimen directions in which the measurements should be performed, and
—          the volume of material examined in relation to the material grain size and the envisaged stress state.
Procedures are described for accurately positioning and aligning test pieces in a neutron beam and for precisely defining the volume of material sampled for the individual measurements.
The precautions needed for calibrating neutron diffraction instruments are described. Techniques for obtaining a stress-free reference are presented.
The methods of making individual measurements by neutron diffraction are described in detail. Procedures for analysing the results and for determining their statistical relevance are presented. Advice is provided on how to determine reliable estimates of residual stresses from the strain data and on how to estimate the uncertainty in the results.

Zerstörungsfreie Prüfung - Standardprüfverfahren zur Bestimmung von Eigenspannungen durch Neutronenbeugung (ISO 21432:2019)

Dieses Dokument beschreibt das Messverfahren zur Bestimmung von Eigenspannungen in polykristallinen Werkstoffen durch Neutronenbeugung. Es ist sowohl bei homogenen als auch bei inhomogenen Werkstoffen anwendbar, einschließlich derjenigen Werkstoffe, die verschiedene Phasen enthalten.
Die Grundlagen des Verfahrens der Neutronenbeugung werden kurz dargestellt. Es werden Vorschläge bezüglich folgender Punkte bereitgestellt:
- die Auswahl geeigneter Beugungsgitterebenen, an denen Messungen für jeweils unterschiedliche Werkstoffkategorien erfolgen sollten;
- die Richtungen der Probe, in denen die Messungen durchgeführt werden sollten; und
- das untersuchte Werkstoffvolumen im Verhältnis zur Korngröße des Werkstoffs und den erwarteten Spannungszustand.
Es werden Verfahren zur genauen Positionierung und Ausrichtung von Proben in einem Neutronenstrahl sowie zur genauen Festlegung des für die einzelnen Messungen genutzten Werkstoffvolumens beschrieben.
Es erfolgt eine Beschreibung der für die Kalibrierung der zur Neutronenbeugung verwendeten Instrumente erforderlichen Vorkehrungen. Es werden Verfahren vorgestellt, mit denen eine spannungsfreie Referenzprobe hergestellt werden kann.
Die Verfahren zur Durchführung von Einzelmessungen mittels Neutronenbeugung werden ausführlich beschrieben. Es werden Vorgehensweisen zur Analyse der Ergebnisse und zur Bestimmung ihrer statistischen Relevanz vorgestellt. Es werden Hinweise gegeben, wie zuverlässige Schätzwerte von Eigenspannungen aus den Dehnungswerten bestimmt und wie die Unsicherheit der Ergebnisse bestimmt werden kann.
WARNUNG - Dieses Dokument erhebt nicht den Anspruch, dass die möglicherweise mit seiner Anwendung verbundenen Sicherheitsprobleme angesprochen werden. Es liegt in der Verantwortung des Anwenders dieses Dokumentes, geeignete Vorkehrungen für den Arbeits  und Gesundheitsschutz zu treffen und die Anwendbarkeit einschränkender Vorschriften vor der Anwendung zu bestimmen.

Essais non destructifs - Méthode normalisée de détermination des contraintes résiduelles par diffraction de neutrons (ISO 21432:2019)

AVERTISSEMENT — Le présent document n'a pas pour but de traiter des problèmes de sécurité qui sont, le cas échéant, liés à son utilisation. Il incombe à l'utilisateur du présent document de mettre en place des pratiques appropriées en matière d'hygiène et de sécurité, et de s'assurer de la conformité à la réglementation nationale en vigueur.

Neporušitvene preiskave - Standardizirana preskusna metoda za ugotavljanje zaostalih napetosti z uklonom nevtronskih žarkov (ISO 21432:2019)

General Information

• Status: Published
• Publication Date: 22-Sep-2020
• Withdrawal Date: 30-Mar-2021
• ICS: 19.100 - Non-destructive testing
• Technical Committee: CEN/TC 138 - Non-destructive testing
• Drafting Committee: CEN/TC 138/WG 1 - Ionizing radiation testing
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 23-Sep-2020
• Due Date: 11-Aug-2022
• Completion Date: 23-Sep-2020
• Ref Project: SIST EN ISO 21432:2020 - Non-destructive testing - Standard test method for determining residual stresses by neutron diffraction (ISO 21432:2019)

Relations

• Replaces: CEN ISO/TS 21432:2005/AC:2009 - Non-destructive testing - Standards test method for determining residual stresses by neutron diffraction (ISO 21432:2005/Cor 1:2008)
• Effective Date: 28-Oct-2020
• Replaces: CEN ISO/TS 21432:2005 - Non-destructive testing - Standards test method for determining residual stresses by neutron diffraction (ISO 21432:2005)
• Effective Date: 28-Oct-2020

Standards Content (Sample)

SLOVENSKI STANDARD
01-december-2020
Nadomešča:
SIST-TS CEN ISO/TS 21432:2005
SIST-TS CEN ISO/TS 21432:2005/AC:2009
Neporušitvene preiskave - Standardizirana preskusna metoda za ugotavljanje
zaostalih napetosti z uklonom nevtronskih žarkov (ISO 21432:2019)
Non-destructive testing - Standard test method for determining residual stresses by
neutron diffraction (ISO 21432:2019)
Zerstörungsfreie Prüfung - Standardprüfverfahren zur Bestimmung von
Eigenspannungen durch Neutronenbeugung (ISO 21432:2019)
Essais non destructifs - Méthode normalisée de détermination des contraintes
résiduelles par diffraction de neutrons (ISO 21432:2019)
Ta slovenski standard je istoveten z: EN ISO 21432:2020
ICS:
19.100 Neporušitveno preskušanje Non-destructive testing
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 21432
EUROPEAN STANDARD
NORME EUROPÉENNE
September 2020
EUROPÄISCHE NORM
ICS 19.100 Supersedes CEN ISO/TS 21432:2005
English Version
Non-destructive testing - Standard test method for
determining residual stresses by neutron diffraction (ISO
21432:2019)
Essais non destructifs - Méthode normalisée de Zerstörungsfreie Prüfung - Standardprüfverfahren zur
détermination des contraintes résiduelles par Bestimmung von Eigenspannungen durch
diffraction de neutrons (ISO 21432:2019) Neutronenbeugung (ISO 21432:2019)
This European Standard was approved by CEN on 31 August 2020.

This European Standard was corrected and reissued by the CEN-CENELEC Management Centre on 21 October 2020.

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, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATIO N

EUROPÄISCHES KOMITEE FÜR NORMUN G

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2020 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 21432:2020 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
The text of ISO 21432:2019 has been prepared by Technical Committee ISO/TC 135 "Non-destructive
testing” of the International Organization for Standardization (ISO) and has been taken over as
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 2021, and conflicting national standards shall
be withdrawn at the latest by March 2021.
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 CEN ISO/TS 21432:2005.
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, 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, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 21432:2019 has been approved by CEN as EN ISO 21432:2020 without any modification.

INTERNATIONAL ISO
STANDARD 21432
First edition
2019-12
Non-destructive testing — Standard
test method for determining residual
stresses by neutron diffraction
Essais non destructifs — Méthode normalisée de détermination des
contraintes résiduelles par diffraction de neutrons
Reference number
ISO 21432:2019(E)
©
ISO 2019
ISO 21432:2019(E)
© ISO 2019
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: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

ISO 21432:2019(E)
Contents Page
Foreword .v
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 5
4.1 Symbols and units . 5
4.2 Subscripts . 7
4.3 Abbreviated terms . 7
5 Summary of method . 7
5.1 General . 7
5.2 Outline of the principle — Bragg’s law . 7
5.3 Neutron sources . 7
5.4 Strain determination . 8
5.4.1 General. 8
5.4.2 Monochromatic instrument . 8
5.4.3 TOF instrument . 8
5.5 Neutron diffractometers . 9
5.6 Stress determination . 9
6 Purpose, geometry and material .14
6.1 General .14
6.2 Purpose of the measurement .14
6.3 Geometry .14
6.4 Composition .14
6.5 Thermal/mechanical history .15
6.6 Phases and crystal structures .15
6.7 Homogeneity . .15
6.8 Microstructure .15
6.9 Texture .15
7 Preparations for measurements .15
7.1 General .15
7.2 Alignment and calibration of the instrument .15
7.3 Choice of diffraction conditions .16
7.3.1 Monochromatic instruments .16
7.3.2 TOF instruments .18
7.4 Positioning procedures .19
7.5 Gauge volumes .19
7.6 Methods for establishing the macroscopically stress-free or reference lattice spacing .20
8 Measurement and recording requirements .22
8.1 General .22
8.2 Recording requirements .22
8.2.1 General.22
8.2.2 General information — instrument .22
8.2.3 General information — specimen .23
8.2.4 Specific information required for each diffraction measurement .23
8.3 Specimen co-ordinates .24
8.4 Positioning of the specimen .24
8.5 Measurement directions .24
8.6 Number and location of measuring positions .24
8.7 Gauge volume .25
8.8 Gauge volume centroid considerations .25
ISO 21432:2019(E)
8.9 Temperature .25
9 Calculation of stress .25
9.1 General .25
9.2 Normal stress determinations .25
9.3 Stress state determinations .26
9.3.1 General.26
9.3.2 The sinψ method .26
9.4 Choice of elastic constants .27
9.5 Diffraction data analysis .27
9.5.1 General.27
9.5.2 Peak fitting function .27
9.5.3 Background function .28
9.5.4 Peak to background ratio.28
9.5.5 Distorted peak profiles .28
10 Reliability .29
11 Reporting .30
11.1 General .30
11.2 Strain or stress values .30
11.2.1 General.30
11.2.2 Stress-free or reference lattice spacing .30
11.2.3 Conversion of strain to stress .30
11.2.4 Elastic constants . . .30
11.2.5 Positioning .30
11.3 Neutron source and instrument .30
11.4 General measurement procedures .31
11.5 Specimens/materials properties .31
11.6 Original data .31
11.7 Uncertainties and errors .31
Annex A (informative) Measurement and analysis methodologies .32
Annex B (informative) Determination of uncertainties in a measurand .41
Bibliography .44
iv © ISO 2019 – All rights reserved

ISO 21432:2019(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 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 135, Non-destructive testing,
Subcommittee SC 5, Radiographic Testing.
This first edition cancels and replaces ISO/TS 21432:2005, which has been technically revised. It also
incorporates the Technical Corrigendum ISO/TS 21432:2005/Cor 1:2008. Furthermore this document
replaces ISO/TTA3: 2001.
The main changes compared to ISO/TS 21432 are as follows:
— Figures 1 and 5 were replaced with updated, more suitable versions. The keys for several figures
were updated in order to better reflect and explain the content of the figures.
— 5.4 was rearranged to emphasize the distinction between monochromatic instruments and time-of-
flight instruments.
— The former Clause 7 became Clause 6 and vice versa. The new order reflects better the real order of
steps taken in the preparation of a measurement.
— 7.6 was updated to provide additional details on the determination of the stress-free reference value.
— Clause 10 was slightly modified and the references to the ISO/IEC Guides relevant to uncertainty
determination were updated.
— 11.7 was added in order to include uncertainties and errors in the reporting.
— A.5.4 was revised and amended to provide more information on grain size effects and the possibilities
to mitigate these.
— A.9 was added to explain the calculation of stresses in the case of macroscopically anisotropic
material.
— The Bibliography was updated by including a few new references.
ISO 21432:2019(E)
— Throughout the document minor revisions of the text were implemented in order to correct small
errors and to improve the clarity.
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.
vi © ISO 2019 – All rights reserved

ISO 21432:2019(E)
Introduction
Neutron diffraction is a non-destructive method that can be employed for determining residual
stresses in crystalline materials. It can also be used to determine internal stresses in samples subjected
to applied stresses. The procedure can be employed for determining stresses within the interior of
materials and adjacent to surfaces. It requires specimens or engineering components to be transported
to a neutron source. Elastic strains are derived from the measurements, which in turn are converted
into stresses. The purpose of this document is to provide an International Standard for reliably
determining stresses that are relevant to engineering applications.
INTERNATIONAL STANDARD ISO 21432:2019(E)
Non-destructive testing — Standard test method for
determining residual stresses by neutron diffraction
WARNING — This document does not purport to address the safety concerns, if any, associated
with its use. It is the responsibility of the user of this document to establish appropriate safety
and health practices and determine the applicability of regulatory limitations prior to use.
1 Scope
This document describes the test method for determining residual stresses in polycrystalline materials
by neutron diffraction. It is applicable to both homogeneous and inhomogeneous materials including
those containing distinct phases.
The principles of the neutron diffraction technique are outlined. Suggestions are provided on:
— the selection of appropriate diffracting lattice planes on which measurements should be made for
different categories of materials,
— the specimen directions in which the measurements should be performed, and
— the volume of material examined in relation to the material grain size and the envisaged stress state.
Procedures are described for accurately positioning and aligning test pieces in a neutron beam and for
precisely defining the volume of material sampled for the individual measurements.
The precautions needed for calibrating neutron diffraction instruments are described. Techniques for
obtaining a stress-free reference are presented.
The methods of making individual measurements by neutron diffraction are described in detail.
Procedures for analysing the results and for determining their statistical relevance are presented.
Advice is provided on how to determine reliable estimates of residual stresses from the strain data and
on how to estimate the uncertainty in the results.
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.
EN 13925-3:2015, Non-destructive testing — X-ray diffraction from polycrystalline and amorphous
materials — Part 3: Instruments
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at http:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
ISO 21432:2019(E)
3.1
neutron absorption
neutron capture by an atomic nucleus
Note 1 to entry: A table of nuclear capture cross-sections can be found in Reference [1].
3.2
alignment
adjustment of the specimen position and orientation and also of all the components of the instrument
such that measurements can be performed precisely at the desired location in the specimen
3.3
anisotropy
dependence of material properties on the direction with respect to the sample
3.4
attenuation
reduction of the neutron beam intensity
Note 1 to entry: Attenuation can be calculated by using the so-called “total neutron cross-section”, which
comprises neutron absorption (3.1) and different nuclear scattering processes. The attenuation length is the
distance within the material for which the primary neutron beam intensity is reduced by 1/e.
3.5
background
intensity considered not belonging to the diffraction (3.13) signal
Note 1 to entry: Background dependence on the scattering angle or time-of-flight (3.34) is not uncommon and can
have an influence on the peak position (3.11) resulting from data analysis.
3.6
beam-defining optics
arrangement of devices used to define the properties of a neutron beam such as the wavelength and
intensity distributions, divergence and shape
Note 1 to entry: These include devices such as apertures, slits, collimators, monochromators and mirrors.
3.7
Bragg edge
sharp change in the neutron intensity as a function of the wavelength or monochromator take-off angle
corresponding to the condition λ = 2d where hkl indicates an (hkl) diffracting lattice plane of the
hkl,
material under investigation
3.8
Bragg peak
intensity distribution of the neutron beam diffracted by a specific (hkl) lattice plane
3.9
peak height
maximum number of neutron counts of the Bragg peak (3.8) above the background (3.5)
3.10
peak function
analytical expression to describe the shape of the Bragg peak (3.8)
3.11
peak position
single value describing the position of a Bragg peak (3.8)
Note 1 to entry: The peak position is the determining quantity to calculate the strain.
2 © ISO 2019 – All rights reserved

ISO 21432:2019(E)
3.12
peak intensity
integrated intensity
area under the diffraction (3.13) peak above the background (3.5), normally calculated from the
associated fitted parameters of a selected peak function (3.10) and a background function
3.13
diffraction
scattering arising from coherent interference phenomena
3.14
diffraction elastic constants
E
hkl
ν
hkl
elastic constants associated with diffraction (3.13) from individual (hkl) lattice planes for a
polycrystalline material
3.15
diffraction pattern
intensity distribution of neutrons diffracted from a crystalline material over the available wavelength,
time-of-flight (3.34) and/or diffraction (3.13) angle ranges
3.16
full width at half maximum
FWHM
width of the Bragg peak (3.8) at half the peak height (3.9) above the background (3.5)
3.17
full pattern analysis
determination of the crystallographic structure and/or strain from a measured (multi-peak) diffraction
pattern (3.15) of a polycrystalline material
Note 1 to entry: In general, the full pattern analysis is termed after the method used (e.g. Rietveld refinement).
See also single peak analysis (3.31).
3.18
gauge volume
volume from which information is obtained
3.19
lattice parameters
linear and angular dimensions of the crystallographic unit cell
3.20
lattice spacing
d-spacing
lattice plane spacing
distance between adjacent parallel crystallographic lattice planes
3.21
Type I stress
macrostress
stress that self-equilibrates over a length scale comparable to the structure or component, thereby
spanning multiple grains and/or phases
3.22
Type II stress
stress that self-equilibrates over a length scale comparable to the grain size
Note 1 to entry: Stresses of Type II and Type III are collectively known as microstresses.
ISO 21432:2019(E)
3.23
Type III stress
stress that self-equilibrates over a length scale smaller than the grain size
Note 1 to entry: Stresses of Type II and Type III are collectively known as microstresses.
3.24
monochromatic instrument
instrument employing a narrow band of neutron energies (wavelengths)
3.25
monochromatic neutron beam
monochromatic beam
neutron beam with narrow band of neutron energies (wavelengths)
3.26
orientation distribution function
quantitative description of the crystallographic texture (3.32)
Note 1 to entry: The orientation distribution function is necessary to calculate the elastic constants of textured
materials.
3.27
polychromatic neutron beam
neutron beam containing a broad band of neutron energies (wavelengths)
3.28
reference point
centroid of the instrumental gauge volume (3.18)
Note 1 to entry: See 7.5.
3.29
reproducibility
closeness of agreement between indications or measured quantity values obtained under conditions of
measurement, out of a set of conditions that includes different locations, operators, measuring systems,
and replicate measurements on the same or similar objects
Note 1 to entry: A valid statement of reproducibility requires a specification of the conditions changed. These
can include the principle of measurements, method of measurements, observer, measuring instrument, reference
standard, location, conditions of use and time.
Note 2 to entry: Reproducibility can be expressed quantitatively in terms of the dispersion characteristics of the
results.
Note 3 to entry: Results are here usually understood to be corrected results.
Note 4 to entry: This definition combines ISO/IEC Guide 99:2007, 2.25, 2.15, and 2.24.
3.30
incoherent scatterer
material scattering neutrons in an uncorrelated way thus giving rise to a strong background (3.5) signal
and no Bragg peaks (3.8) or only some with low amplitude
3.31
single peak analysis
statistical procedure to determine the characteristics of a peak and the background (3.5) from the
measured diffraction (3.13) data
4 © ISO 2019 – All rights reserved

ISO 21432:2019(E)
3.32
texture
preferred orientation of crystallites, referred to as crystallographic texture, or other microstructural
features, referred to as morphological texture, within a specimen
3.33
surface scan
wall scan
intensity scan
procedure to determine the position of a specimen surface or interface with respect to the reference
point (3.28)
Note 1 to entry: The result is often called an entering curve.
3.34
time-of-flight
time needed by a neutron of a given speed to cover the distance from a defined starting point to the
detector
3.35
uncertainty in a measurement
non-negative parameter characterizing the dispersion of the quantity values being attributed to a
measurand, based on the information used
Note 1 to entry: Measurement uncertainty includes components arising from systematic effects, such as
components associated with corrections and the assigned quantity values of measurement standards, as well
as the definitional uncertainty. Sometimes estimated systematic effects are not corrected for but, instead,
associated measurement uncertainty components are incorporated.
Note 2 to entry: The parameter may be, for example, a standard deviation called standard measurement
uncertainty (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability.
Note 3 to entry: Measurement uncertainty comprises, in general, many components. Some of these may be
evaluated by Type A evaluation of measurement uncertainty from the statistical distribution of the quantity
values from series of measurements and can be characterized by standard deviations. The other components,
which may be evaluated by Type B evaluation of measurement uncertainty, can also be characterized by standard
deviations, evaluated from probability density functions based on experience or other information.
Note 4 to entry: In general, for a given set of information, it is understood that the measurement uncertainty is
associated with a stated quantity value attributed to the measurand. A modification of this value results in a
modification of the associated uncertainty.
[SOURCE: ISO/IEC Guide 99:2007, 2.26, modified — The term has been changed from "uncertainty of
measurement"; alternative terms "measurement uncertainty" and "uncertainty" have been removed.]
4 Symbols and abbreviated terms
4.1 Symbols and units
a,b,c Lengths of the edges of a unit cell, here referred to as lattice parameters nm
B Background at the peak position —
d Lattice plane spacing nm
E Macroscopic elastic modulus GPa
E Elastic modulus associated with the (hkl) diffracting lattice planes GPa
hkl
−1
g Strain gradient mm
ISO 21432:2019(E)
h Planck’s constant Js
hkl Indices of a crystallographic lattice plane
NOTE  In the remainder of the document (hkl) will be used bearing in mind
that each plane of the family {hkl} will diffract under the same conditions.
hkil Alternative Miller index notations of a crystallographic lattice plane for hexag-
onal structures
H Peak height above the background —
I Integrated neutron intensity of a Bragg peak above the background

−1
Wave vectors of the incident and diffracted neutrons nm
kk,
if
L Path length from the neutron source to the detector m
l Neutron attenuation length mm
−27
m Neutron mass (1,67 × 10 kg) kg
n
N Total number of neutrons counted
n
 

−1
nm
Q Scattering vector ( k – k )
f i
t Time of flight of neutrons from source to detectors s
T Temperature °C or K
u Standard uncertainty —
x,y,z Axes of the specimen co-ordinate system
−1
α Coefficient of thermal expansion K
Δ Variation of, or change in, the parameter that follows
ε Elastic strain —
ε Components of the elastic strain tensor —
ij
ε Normal elastic strain associated with the (hkl) diffracting lattice plane —
hkl
λ Wavelength of neutrons nm
v Poisson’s ratio
v Elastic constant corresponding to Poisson’s ratio associated with the (hkl)
hkl
diffracting lattice plane


Stress MPa
σ
σ Components of the stress tensor MPa
ij
σ Yield stress MPa
Y
2θ diffraction angle degrees
ϕ, ψ Orientation angles Degrees
6 © ISO 2019 – All rights reserved

ISO 21432:2019(E)
4.2 Subscripts
hkl, hkil Indicate relevance to crystallographic (hkl) or (hkil) lattice planes
x, y, z Indicate components of the quantity concerned along the x-, y-, z-axes
ϕ ψ Indicate the normal component, in the (ϕ ψ) − direction of the quantity concerned
0 (zero) Indicates stress-free value of the quantity concerned
ref Indicates reference value of the quantity concerned
4.3 Abbreviated terms
PSD Position sensitive detector
TOF Time-of-flight
IGV Instrumental gauge volume
NGV Nominal gauge volume
SGV Sampled gauge volume
5 Summary of method
5.1 General
This document is concerned with the determination of residual stresses that are needed in engineering
analyses. The stresses are determined from neutron diffraction measurements of lattice spacings. From
changes in these spacings, elastic strains can be derived, from which stresses can be calculated. By step-
wise translation of a specimen or component across the reference point, stresses at different locations
inside the specimen can be determined. In this clause the measurement process is summarized.
5.2 Outline of the principle — Bragg’s law
When the lattice of a crystalline material is illuminated with penetrating neutron radiation with
wavelength(s) similar to the interplanar spacings, this radiation will be diffracted as distinct Bragg
peaks. The angle at which such a peak occurs is given by Bragg’s law of diffraction, see Formula (1).
2.d sin θλ= (1)
hklhkl
where
λ is the wavelength of the neutrons;
d is the spacing of the (hkl) lattice planes responsible for the Bragg peak;
hkl
θ is the Bragg angle.
hkl
The peak will be observed at an angle 2θ from the incident beam direction, as shown schematically
hkl
in Figure 1.
5.3 Neutron sources
Neutron diffraction uses beams of neutrons generated by either fission or spallation; the former is
predominantly employed in steady-state nuclear reactors and the latter in pulsed spallation sources.
ISO 21432:2019(E)
In both cases the neutrons produced are moderated to bring their energies to the thermal range, i.e.
λ ≥ 0,09 nm. At reactor sources, a monochromatic neutron beam is usually extracted by using a crystal
monochromator to select a given narrow neutron wavelength band from the originally polychromatic
beam. At spallation sources, the neutron beam usually consists of a series of short pulses each
containing a wavelength spectrum. The velocity (and therefore wavelength in accordance with the
de Broglie principle) of each neutron can be determined by measuring the distance it has travelled to
the detector and the time it has taken to travel this distance, called the TOF. TOF measurements are,
therefore, wavelength dispersive, with the entire diffraction pattern being recorded at all available
detector positions.
5.4 Strain determination
5.4.1 General
It is evident from Bragg’s Law that if λ and θ are known experimentally, the lattice spacing, d, can be
determined. We define the lattice strain as the relative change in d with respect to the stress-free
lattice spacing, d . Thus, for the lattice planes identified by Miller Indices hkl, the lattice strain is given
by Formula (2):
d −d
Δd
hklh0, kl
hkl
ε ≡ = (2)
hkl
d d
0,hkl 0,hkl
 
By virtue of the diffraction process, the measurement direction is along the scattering vector, Qk= −k
fi
, which bisects the angle between incident and diffracted beams and is perpendicular to the diffracting
planes as shown in Figure 1.
5.4.2 Monochromatic instrument
When a specimen is illuminated by a monochromatic neutron beam of a fixed wavelength, its lattice
spacing can be determined from the observed Bragg angle, θ, by substituting Bragg’s Law [see
Formula (1)] into the strain equation [see Formula (2)]. Thus, elastic lattice strains can be determined
directly from the corresponding Bragg angles, θ , and θ , and given by Formula (3):
hkl 0,hkl
sinθ
0,hkl
ε = −1 (3)
hkl
sinθ
hkl
5.4.3 TOF instrument
At a TOF instrument the incident beam contains neutrons spanning a range of velocities (i.e.
wavelengths) arriving at the sample in pulses. In this case all lattice planes normal to the scattering
vector will diffract neutrons to the detector. The diffraction corresponding to each hkl peak is produced
by different families of grains. By using the de Broglie relationship and Bragg’s Law [see Formula (1)]
the TOF t for a particular wavelength, crystal
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