SIST EN ISO 12004-2:2021

SLOVENSKI STANDARD
01-junij-2021
Nadomešča:
SIST EN ISO 12004-2:2009
Kovinski materiali - Določevanje krivulj preoblikovalnosti za pločevino in trakove -
2. del: Določevanje krivulj preoblikovalnosti v laboratoriju (ISO 12004-2:2021)
Metallic materials - Determination of forming-limit curves for sheet and strip - Part 2:
Determination of forming-limit curves in the laboratory (ISO 12004-2:2021)
Metallische Werkstoffe - Bestimmung der Grenzformänderungskurve für Bleche und
Bänder - Teil 2: Bestimmung von Grenzformänderungskurven im Labor (ISO 12004
2:2021)
Matériaux métalliques - Détermination des courbes limites de formage pour les tôles et
bandes - Partie 2: Détermination des courbes limites de formage en laboratoire (ISO
12004-2:2021)
Ta slovenski standard je istoveten z: EN ISO 12004-2:2021
ICS:
77.040.10 Mehansko preskušanje kovin Mechanical testing of metals
77.140.50 Ploščati jekleni izdelki in Flat steel products and semi-
polizdelki products
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 12004-2
EUROPEAN STANDARD
NORME EUROPÉENNE
March 2021
EUROPÄISCHE NORM
ICS 77.040.10 Supersedes EN ISO 12004-2:2008
English Version
Metallic materials - Determination of forming-limit curves
for sheet and strip - Part 2: Determination of forming-limit
curves in the laboratory (ISO 12004-2:2021)
Matériaux métalliques - Détermination des courbes Metallische Werkstoffe - Bestimmung der
limites de formage pour les tôles et bandes - Partie 2: Grenzformänderungskurve für Bleche und Bänder -
Détermination des courbes limites de formage en Teil 2: Bestimmung von Grenzformänderungskurven
laboratoire (ISO 12004-2:2021) im Labor (ISO 12004 2:2021)
This European Standard was approved by CEN on 15 January 2021.

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.

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Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
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United Kingdom.
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COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12004-2:2021 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 12004-2:2021) has been prepared by Technical Committee ISO/TC 164
"Mechanical testing of metals" 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 September 2021, and conflicting national standards
shall be withdrawn at the latest by September 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 EN ISO 12004-2:2008.
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 12004-2:2021 has been approved by CEN as EN ISO 12004-2:2021 without any
modification.
INTERNATIONAL ISO
STANDARD 12004-2
Second edition
2021-02
Metallic materials — Determination
of forming-limit curves for sheet and
strip —
Part 2:
Determination of forming-limit curves
in the laboratory
Matériaux métalliques — Détermination des courbes limites de
formage pour les tôles et bandes —
Partie 2: Détermination des courbes limites de formage en laboratoire
Reference number
ISO 12004-2:2021(E)
©
ISO 2021
ISO 12004-2:2021(E)
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
ii © ISO 2021 – All rights reserved

ISO 12004-2:2021(E)
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Principle . 2
6 Test pieces and equipment . 3
6.1 Test pieces . 3
6.1.1 Thickness of test pieces . 3
6.1.2 Test piece geometry . 3
6.1.3 Test piece preparation in test area . 4
6.1.4 Number of different test piece geometries . 4
6.1.5 Number of tests for each geometry . 4
6.2 Application of grid . 4
6.2.1 Type of grid . 4
6.2.2 Grid application . 5
6.2.3 Accuracy of the undeformed grid . 5
6.3 Test equipment . 5
6.3.1 General. 5
6.3.2 Strain determination . 7
6.3.3 Nakajima test . 7
6.3.4 Marciniak test . 9
7 Analysis of strain profile and measurement of ε – ε pairs .11
1 2
7.1 General .11
7.2 Evaluation using section lines (position-dependent measurement) .11
7.2.1 General.11
7.2.2 Position and processing of measurements .12
7.2.3 Extraction of the “bell-shaped curve” and determination of the inner
limits for the best-fit curve through experimental points .13
7.2.4 Definition of outer limits for best-fit windows and evaluation of the
inverse best-fit parabola on the “bell-shaped curve” .14
8 Documentation .15
9 Test report .16
Annex A (normative) Second derivative and “filtered” second derivative .17
Annex B (normative) Calculation of the width of the fit window.18
Annex C (normative) Evaluation of the inverse best-fit parabola on the “bell-shaped curve” .19
Annex D (normative) Application/Measurement of grid —
Evaluation with magnifying glass or microscope .21
Annex E (informative) Tables of experimental data for validation of calculation programme .22
Annex F (normative) Representation and mathematical description of FLC .23
Annex G (informative) Examples of critical section line data .24
Annex H (normative) Flowchart from measured strain distributions to FLC values .25
Bibliography .27
ISO 12004-2:2021(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 164, Mechanical testing of metals,
Subcommittee SC 2, Ductility testing, in collaboration with the European Committee for Standardization
(CEN) Technical Committee CEN/TC 459/SC 1, Test methods for steel (other than chemical analysis), in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 12004-2:2008), which has been
technically revised.
The main changes compared to the previous edition are as follows:
1) The title was changed to have three elements.
2) Clause 2 and Clause 3 were added from the previous edition, and the subsequent clauses were
renumbered.
3) The descriptions of when to use ISO 12004-1 or ISO 12004-2 (this document) was revised in the
Introduction.
4) Permissions and requirements were clarified in 6.1.3, 6.1.5, 6.2.2, 6.2.3, 6.3.2, 6.3.3.3, 6.3.4.3, 7.2.2,
and 7.2.3.
5) In 6.3.1, the punch velocity range was expanded and permission for exceptional cases in aluminium
alloys, as well as steel, was added.
6) Clarification was added that although the Nakajima method is known to have non-linear strain
paths (6.3.3.1), it is still acceptable. Clarification as to why the failure is required to be near the
apex of the dome was added to 6.3.3.3. In 6.3.3.3, the “validity of test” requirement for the Nakajima
test was made explicit in a similar format to that shown for the Marciniak test in 6.3.4.4. In 6.3.3.3
and 6.3.4.4, a statement regarding rejection of specimens not meeting the valid test requirements
was added.
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ISO 12004-2:2021(E)
7) The “Measuring instrument” clause (4.3.5 in the previous edition) was removed since it is
a repetition of the “Measurement instrument” section of 6.3.2 but had a different accuracy
requirement. The required accuracy is now shown as originally described in 6.3.2.
8) The requirement on the second derivative range was clarified in 7.2.3(c), and the requirements in
the keys of Figures 8 and 9 were changed to match 7.2.3(c).
9) The permission to use other methods of measurement was moved from 7.2.1 to 7.1 and was
clarified.
10) The statement regarding the “time-dependent method” was removed from 7.1 but now a statement
admitting the use of other methods including both the “time-dependent method” or “time and
position dependent methods” appears in Clause 5.
11) In 7.2.2, the method of selecting the section line locations based on the crack position was clarified,
and permission was added to use the maximum strain location, as long as the test validity
requirements are still met.
12) The use of the procedure in 7.2.3 when extracting the “bell-shaped curve” for use in evaluating the
section lines using the position-dependent method has been changed to being required rather than
just suggested. This seems to be consistent with the original intent.
13) In Annex A, the method was changed to be required rather than proposed. Annex C was clarified
to show that the procedure is required. Clarification to the text of Annex D was added, and its use
is explicitly permitted. In Annex F, explicit permission to use a regression using in-house functions
was added, as well as the requirement that the function be reported.
14) Editorial changes and clarifications were made throughout the document.
A list of all parts in the ISO 12004 series can be found on the ISO website.
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.
ISO 12004-2:2021(E)
Introduction
A forming-limit diagram (FLD) is a diagram containing major/minor strain points.
An FLD can distinguish between safe points and necked or failed points. The transition from safe to
failed points is defined by the forming-limit curve (FLC).
To determine the forming limit of materials, two different methods are possible.
1) Strain analysis on failed press shop components to determine component and process
dependent FLCs.
In the press shop, the strain paths followed to reach these points are generally not known. Such an
FLC depends on the material, the component, and the chosen forming conditions. This method is
described in ISO 12004-1 and is not intended to determine one unique FLC for each material.
2) Determination of FLCs under well-defined laboratory conditions.
For evaluating formability, one unique FLC for each material in several strain states can be
measured. The determination of the FLC must be specific and uses multiple linear strain paths.
This document, i.e. ISO 12004-2, is intended for this type of material characterization.
For this document (concerning determination of forming-limit curves in laboratory), the following
conditions are also of note.
— Forming-limit curves (FLCs) are determined for specific materials to define the extent to which
they can be deformed by drawing, stretching or any combination of drawing and stretching. This
capability is limited by the occurrence of localized necking and/or fracture. Many methods exist to
determine the forming limit of a material; but results obtained using different methods cannot be
used for comparison purposes.
— The FLC characterizes the deformation limit of a material in the condition after a defined thermo-
mechanical treatment and in the analysed thickness. For a judgement of formability, the additional
knowledge of mechanical properties and the material’s history prior to the FLC-test are important.
To compare the formability of different materials, it is important to judge not only the FLC but also the
following parameters:
a) mechanical properties at least in the main direction;
b) percentage plastic extension at maximum force, according to ISO 6892-1;
c) r-value with given deformation range, according to ISO 10113;
d) n-value with given deformation range, according to ISO 10275.
vi © ISO 2021 – All rights reserved

INTERNATIONAL STANDARD ISO 12004-2:2021(E)
Metallic materials — Determination of forming-limit
curves for sheet and strip —
Part 2:
Determination of forming-limit curves in the laboratory
1 Scope
This document specifies testing conditions for use when constructing a forming-limit curve (FLC) at
ambient temperature and using linear strain paths. The material considered is flat, metallic and of
thickness between 0,3 mm and 4 mm.
NOTE The limitation in thickness of up to 4 mm is proposed, giving a maximum allowable thickness to the
punch diameter ratio.
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 terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbol English French German Unit
e Engineering strain Déformation conventionnelle Technische Dehnung %
True strain Déformation vraie Wahre Dehnung
ε (logarithmic strain) (déformation logarithmique) (Umformgrad, —
Formänderung)
ε Major true strain Déformation majeure vraie Grössere Formänderung —
ε Minor true strain Déformation mineure vraie Kleinere Formänderung —
ε True thickness strain Déformation vraie en épaisseur Dickenformänderung —
σ Standard deviation Ecart-type Standardabweichung —
D Punch diameter Diamètre du poinçon Stempeldurchmesser mm
Carrier blank hole Diamètre du trou du contre-flan Lochdurchmesser
D mm
bh
diameter des Trägerblechs
X(0), X(1)
X-position Position en X X-Position mm
X(m) .X(n)
ISO 12004-2:2021(E)
Table 1 (continued)
Symbol English French German Unit
f(x) = Best-fit parabola Parabole de meilleur fit Best-Fit-Parabel
—
ax + bx + c
f(x) = Best-fit inverse parabola Parabole inverse de meilleur fit Inverse Best-Fit-Parabel
—
1/(ax + bx + c)
S(0), S(1).S(5) Section Section Schnitt —
n Number of X-positions Nombre de points en X Nummer der X-Positionen —
Number of the X-posi- Numéro du point en X Nummer der X-Position am
m tion at the failure/crack correspondant à la rupture Riss —
position
w Width of the fit window Largeur de la fenêtre de fit Breite des Fit-Fensters mm
t Initial sheet thickness Épaisseur initiale de la tôle Ausgangsblechdicke mm
Plastic strain ratio Coefficient d'anisotropie Senkrechte Anisotropie
r —
plastique
Table 2 gives a comparison of the symbols used in different countries.
Table 2 — Comparison of symbols used in different countries
English International German Format Unit
symbol symbol
Engineering strain e ε — %
True strain
ε φ Decimal —
(logarithmic strain)
ε = ln(1 + e) — — — —
The symbol typically used for true strain is “ε”, but in German-speaking countries the symbol “φ” is used
for true strain. Additionally, in German-speaking countries the symbol “ε” is used to define engineering
strains.
The notation for true strain used in this text is “ε” following the typical international definition.
5 Principle
The FLC is intended to represent the almost intrinsic limit of a material in deformation assuming a
linear strain path. To determine the FLC accurately, it is necessary to have as nearly linear a strain path
as possible.
A deterministic grid of precise dimensions or a stochastic pattern is applied to the flat and undeformed
surface of a blank. This blank is then deformed using either the Nakajima or the Marciniak procedure
until failure, at which point the test is stopped.
The FLC determination from the measurements should be performed using the “position-dependent”
method described in 7.2.
Other methods (e.g. “time-dependent” or “time and position dependent” methods) of FLC determination
from the measurements exist. If agreed to by the interested parties, one of the other methods may be
used and, if used, shall be indicated in the test report.
The deformation (strain) across the deformed test piece is determined and the measured strains are
processed in such a way that the necked or failed area is eliminated from the results. The maximum
strain that can be imposed on the material without failing is then determined through interpolation.
This maximum of the interpolated curve is defined as the forming limit.
2 © ISO 2021 – All rights reserved

ISO 12004-2:2021(E)
The forming limits are determined for several strain paths (different ratios between ε and ε ). The
1 2
determined strain paths range from uniaxial tension to biaxial tension (stretch drawing). The collection
of the individual forming limits in different strain states is plotted as the forming-limit curve. The
curve is expressed as a function of the two true strains ε and ε on the sheet surface and plotted in a
1 2
diagram, the forming-limit diagram. The minor true strains ε are plotted on the X-axis and the major
principal true strains ε on the Y-axis (see Figure 1).
Standard conversion formulae permit the calculation of major (ε ) and minor true strains (ε ) from
1 2
measured length changes or engineering strains. In the following, the word "strain" implies the true
strain, which is also called logarithmic strain.
Key
X minor true strain, ε
Y major true strain, ε
F FLC
a
Uniaxial tension, ε = −[r/(r + 1)] ε .
2 1
b
Intermediate tensile strain.
c
Plane strain.
d
Intermediate stretching strain state.
e
Intermediate stretching strain state.
f
Equi-biaxial tension (= stretching strain state) ε = ε .
2 1
Figure 1 — Six different strain paths
6 Test pieces and equipment
6.1 Test pieces
6.1.1 Thickness of test pieces
This procedure is intended for flat, metallic sheets with a thickness between 0,3 mm and 4 mm.
For steel sheets a maximum thickness of 2,5 mm is recommended.
6.1.2 Test piece geometry
The following geometries are recommended: waisted blanks with a central, parallel shaft longer than
25 % of the punch diameter (for a 100 mm punch: preferable shaft length 25 mm to 50 mm; fillet radius
20 mm to 30 mm) (see Figure 2).
ISO 12004-2:2021(E)
a
Shaft length.
b
Remaining blank width.
c
Fillet radius.
Figure 2 — Waisted test piece geometry with parallel shaft length (dog bone shape)
For ε > 0, blanks with semi-circular cut-outs with different radii are possible.
For steel (mainly soft steel grades), rectangular strips with different widths are sufficient if test pieces
do not fail at the die radius; otherwise use the test piece geometry as described above.
With an outer circular shape of the blanks, a more uniform distribution of the experimental forming-
limit points is attainable than when rectangular strips are used.
6.1.3 Test piece preparation in test area
Milling, spark-erosion or other methods that do not cause cracks, work hardening or microstructure
changes may be used ensuring that fracture never initiates from the edges of test pieces.
6.1.4 Number of different test piece geometries
At least five geometries for the description of a complete FLC are necessary. A uniform allocation of the
FLC from uniaxial to equi-biaxial tension is recommended.
If the description of a complete FLC is not necessary, then a lower number of geometries is allowed, but
this shall be mentioned in the test report.
6.1.5 Number of tests for each geometry
As many test pieces as are necessary shall be tested to achieve at least three valid samples for each test
piece geometry.
6.2 Application of grid
6.2.1 Type of grid
The recommended grid size is approximately one times the material thickness (grid size is related to
the material thickness due to necking width), a maximum grid size of 2,5 times the material thickness
is allowed and the largest grid dimension allowed for a 100 mm punch is 2,54 mm (0,1 in). In general,
grid sizes of 1 mm or 2 mm are used. Small grid sizes are often limited because of their lack of accuracy
(if the undeformed grid is not measured before beginning of test).
For a stochastic pattern, the “virtual” grid size should correspond to the recommended grid size. A
smaller “virtual” grid size may be used.
4 © ISO 2021 – All rights reserved

ISO 12004-2:2021(E)
6.2.2 Grid application
Deterministic grids (e.g. squares, circles, dots) should have a rich contrast and shall be applied
without any notch effect and/or change in microstructure. Some common application techniques are
electrochemical, photochemical, offset print and grid transfer.
Stochastic (speckle) patterns can be applied by spraying paint onto the test piece surfaces. It is possible
to spray a thin, matt, white base layer to reduce back reflections from the test piece surfaces. Following
this, a cloud of randomly distributed black spots can be sprayed (e.g. black spray paint or graphite).
Grid/pattern adherence to the surface should be checked after deformation for both the deterministic
grids and stochastic patterns.
6.2.3 Accuracy of the undeformed grid
To achieve the required total system accuracy of 2 % (see 6.3.2), the initial grid accuracy should be
measured to an accuracy better than 1 % based on one times the standard deviation (1σ). This
recommendation only applies for systems where the local undeformed condition is not measured as
part of the evaluation.
6.3 Test equipment
6.3.1 General
The following parameters are valid for both Nakajima and Marciniak tests.
Punch velocity: 0,5 mm/s to 2 mm/s.
Prevention of material’s draw-in: Draw-in shall be prevented as much as possible to ensure near-
ly linear strain paths. Possible methods of mitigation are: using
draw beads, suitable blank holder forces, serrated or knurled tools
(providing that the two last methods do not involve risk of strain
localization or fracture).
Blank holder force, in kN: Draw-in shall be prevented as much as possible.
Test temperature: (23 ± 5) °C.
Test direction: For a given FLC, the main orientation of all test pieces shall be the
direction of lowest limit strain e and the same orientation rela-
tive to the rolling direction, see Figure 3.
Aluminium alloys: Longitudinal (shaft orientation parallel to rolling direction);
exceptional cases are allowed but shall be reported.
Steel: Transverse (shaft orientation perpendicular to rolling direction);
exceptional cases are allowed but shall be reported.
In the case that the preferred failure direction is not known, it should be checked using a biaxial strain
test or any other suitable method.
ISO 12004-2:2021(E)
a)  Steel b)  Aluminium alloys

a Rolling direction (RD).
Figure 3 — Shaft orientation with respect to the rolling direction (RD)
Surface roughness of punch: The contacting area of the punch surface should be polished.
Die material and hardness: Hardened steel.
Blank holder shape: Full circular blank holder or blank holder with cut-out; see Figure 4.

Key
D cut-out width, equal to punch diameter
a
Serrated blank holder with cut-out.
b
Blank.
c
Punch.
NOTE To come closer to ideal linear strain paths and to reach a more uniform distribution of true strain
values, a circular blank holder with a cut-out can be useful (recommended width of cut-out = punch diameter).
Figure 4 — Blank holder with cut-out
Test stop criterion: Crack occurrence.
Crack detection: Visual or force drop.
6 © ISO 2021 – All rights reserved

ISO 12004-2:2021(E)
6.3.2 Strain determination
6.3.2.1 Total system accuracy
The total accuracy of the strain measurement system should be better than 2 % based on one times the
standard deviation (1σ) (accuracy depends on grid accuracy/resolution, camera resolution, measuring
field, calculation algorithm, etc.).
6.3.2.2 Accuracy of the undeformed grid
Initial grid spacing accuracy should be better than 1 % based on one times the standard deviation (1 σ)
of the grid used (this recommendation only applies for systems where the undeformed condition is not
used in evaluation).
6.3.2.3 Measurement instrument
Any convenient grid-spacing measuring device may be used; the uncertainty of the measurement device
shall be less than 1 % of the measured length.
Cameras and software allowing total system accuracy of strain measurement better than 2 % based on
one times the standard deviation (1 σ) are recommended.
6.3.2.4 Strain measurement
Strain measurement may be performed either by measurement of only the final grid dimension, where
the accuracy of the initial grid spacing is known (<1 %), or by comparison of the final grid dimension
relative to the initial one, or using an incremental method, which refers to the initial grid size for the
strain calculation.
6.3.3 Nakajima test
6.3.3.1 General
The Nakajima forming method uses a hemispherical punch; see Figure 5.
The Nakajima test is known to result in an initially non-linear strain path, but is still an acceptable test
method, and may be used to determine the FLC. The Marciniak test, described in 6.3.4, is known to have
a more linear strain path than the Nakajima test.
NOTE To determine a more accurate FLC, some authors (for example, see Reference [4]) propose a process to
correct the effects of the non-linear strain path, bending, and contact pressure.
If a process is applied to correct for the effects of non-linear strain path, bending, or contact pressure,
then it shall be indicated in the test report.
ISO 12004-2:2021(E)
Dimensions in millimetres
a
Lubrication layer.
b
Test piece.
Figure 5 — Cross section of the tool used for Nakajima testing
6.3.3.2 Tool
Punch diameter: (100 ± 2) mm.
Die diameter: Preferably 105 mm and greater than or equal to the punch diameter plus
2,5 times the material thickness.
Die radius: Preferably 8 mm with a minimum of either 5 mm or 2 times the material
thickness, whichever is the greater value.
6.3.3.3 Test conditions
The “position dependent” method described in 7.2 prefers a single symmetric peak in the strain profile
[see 7.2.1 and Annex G 1)]. In the case of the Nakajima test, this can only be achieved with low friction
between the test piece and the punch to result in a single neck and failure near the apex of the dome.
Therefore, a lubrication system is required.
For the test to be valid, the fracture shall occur within a distance less than 15 % of the punch diameter
away from the apex of the dome. Specimen not meeting this requirement shall be rejected. The
lubrication system should be adjusted so that the test meets this validity requirement.
NOTE With an optimal lubrication system, it is possible to induce fracturing very near to the apex of the
dome. In this case, the problem of pronounced double necking [Annex G 2)] symmetrical to the apex of the dome
(where afterwards one of the two necked zones is fractured) is drastically reduced. The strong double peaks in
the strain profile section line are reduced. This makes automatic evaluation of ε – ε pairs more accurate.
1 2
The lubrication system may not be changed during the measurement of one specific FLC.
8 © ISO 2021 – All rights reserved

ISO 12004-2:2021(E)
Recommended lubrication systems are:
a) for low punch forces (thinner sheets or materials with relatively low tensile strength, e.g. for Al-
sheets <2 mm):
1) oil or grease (e.g. lanolin);
2) circular blanks of PE or PTFE foil (e.g. 0,05 mm thick);
3) oil or grease.
b) for high punch forces (thicker sheets or materials with higher tensile strength):
1) simple:
as in a) but with soft PVC instead of PTFE.
2) complex:
i) oil or grease (e.g. lanolin);
ii) circular blanks of PE or PTFE foil (0,05 mm to 0,1 mm thick);
iii) oil or grease;
iv) soft PVC sheet (2 mm to 5 mm thick);
v) oil or grease;
vi) circular blanks of PE or PTFE foil (0,05 mm to 0,1 mm thick);
vii) oil or grease.
Layers i) and vii) are optional.
With these two lubrication systems, most of the tests can meet the condition of a fracture on the top of
the dome. From previous testing experience on different material types, no general lubrication system
(suitable for all materials and all thickness ranges) can be recommended. The most difficult conditions
are encountered during the testing of high strength materials of large thickness. Alternative lubrication
systems may be used based on personal practice and experience. In such cases, it is recommended that
the lubrication systems be tested in advance during hemispherical punch stretching. The lubrication
system providing the largest limiting dome height, while still meeting the condition of a fracture on the
top of the dome, should be considered the most suitable.
The diameter of the foil blank (part of the lubrication system) should be smaller than the punch
diameter to prevent the foil wrinkling.
6.3.4 Marciniak test
6.3.4.1 General
The Marciniak forming method uses a flat punch, see Figure 6.
ISO 12004-2:2021(E)
Dimensions in millimetres
a
Test piece.
b
Carrier blank.
Figure 6 — Cross section of the tool used for Marciniak testing
6.3.4.2 Tool
Punch diameter: Flat punch of diameter (100 ± 25) mm.
Punch nose radius: Suggested 10 % of punch diameter.
Die diameter: Suggested 120 % of punch diameter.
Die radius: Between 10 % and 20 % of punch diameter.
6.3.4.3 Carrier blanks
In order to prevent contact between the test piece and the plane surface of the punch, it is necessary to
use carrier blanks. This helps to ensure fracture occurs in the correct position (see the validity of test
in 6.3.4.4) and helps to ensure a homogeneous applied deformation.
Carrier blanks should be cut out of a material at least as ductile as the material being tested. Rupture of
the carrier blank should not occur before the fracture of the sheet material being studied.
The minimum thickness of the carrier blank should be around 0,8 times the thickness of the blank
tested; one or more carrier blanks may be used to achieve the recommended thickness.
The carrier blank size should be equal to the tested specimen or to the size of the blank used for the
biaxial strain path (facilitating the manufacture and storage of carrier blanks).
The carrier blank shall have a central hole of diameter D (for example 32 mm to 34 mm for 1 mm thick
bh
sheets) centred relative to the punch. This hole shall have an edge quality sufficient to avoid premature
cracking. The final diameter of the hole at the time of test piece rupture shall remain smaller than
the diameter of the plane zone of the punch. If necessary, the carrier blank may be cut in two parts
(perpendicular to strain direction).
It can be useful to have a higher surface roughness of the carrier blank towards the specimen’s surface
(e.g. sand blasting) to enhance the frictional force between the carrier blank and the test piece.
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ISO 12004-2:2021(E)
6.3.4.4 Test conditions
Lubrication is not permitted between the carrier blank and specimen, but it is often necessary between
the punch and the carrier blank.
For the test to be valid, the rupture shall start in the plane zone above the hole of the carrier blank.
Specimen not meeting this requirement shall be rejected.
7 Analysis of strain profile and measurement of ε – ε pairs
1 2
7.1 General
The measurement using camera(s) can be done in various ways using different analysis methods (AM)
by evaluation of section line data.
— AM1: evaluation of the cracked sample (offline)
Analyse an image set just after the deformation but not directly on the forming machine.
— AM2: evaluation of the cracked sample with grid calibrated from starting dimensions
(offline)
Analyse an image set before and just after the deformation but not directly on the forming machine.
— AM3: evaluation of the situation directly before the crack will happen (online)
With the camera(s) fixed directly on the forming machine, record the starting image and the image
sequence during the last steps of deformation before failure. This is used for position-dependent
measurement online. Define the section line positions perpendicular to the crack on the image with
fracture and then transfer them back to the last image before the crack becomes visible, in order to
get the section line for selecting pairs of ε – ε values without crack opening.
1 2
These three cases use the concept of selecting pairs of ε – ε values from sections approximately
1 2
perpendicular to the crack and are described in 7.2.
Other methods (automatic or manual) may be used if the measurement accuracy is sufficient. Annex D
shall be used for the accuracy requirements for magnifying glasses or microscopes.
7.2 Evaluation using section lines (position-dependent measurement)
7.2.1 General
The basic concept of this method is the analysis of the measured strain distribution along predefined
section lines. By removing the strain points in the necked area, the strain distribution just before the
onset of necking is reconstructed in this region by curve fitting of the remaining part of the strain
distribution on both sides of the neck. The following steps can be identified:
— defining the relevant sections containing the neck (described in 7.2.2);
— marking of the neck region by an objective mathematical criterion; in this way the inner limits of the
curve fit window are defined (described in 7.2.3);
—
...