Metallic materials — Sheet and strip — Determination of biaxial stress-strain curve by means of bulge test with optical measuring systems

This document specifies a method for determination of the biaxial stress-strain curve of metallic sheets having a thickness below 3 mm in pure stretch forming without significant friction influence. In comparison with tensile test results, higher strain values can be achieved. NOTE In this document, the term "biaxial stress-strain curve" is used for simplification. In principle, in the test the "biaxial true stress-true strain curve" is determined.

Matériaux métalliques — Tôles et bandes — Détermination de la courbe contrainte-déformation biaxiale au moyen de l'essai de gonflement hydraulique avec systèmes de mesure optiques

Le présent document spécifie une méthode pour la détermination de la courbe contrainte-déformation biaxiale sur tôles métalliques d’épaisseur inférieure à 3 mm en formage en expansion pure sans influence significative des frottements. En comparaison à des résultats d’essais de traction, des valeurs plus élevées de déformation peuvent être obtenues. NOTE Dans le présent document le terme «la courbe de contrainte-déformation biaxiale» est utilisé pour simplifier la rédaction. En principe, «la courbe biaxiale contrainte vraie-déformation vraie » est déterminé dans l’essai.

General Information

Status
Published
Publication Date
09-May-2022
Current Stage
6060 - International Standard published
Start Date
10-May-2022
Due Date
13-May-2022
Completion Date
10-May-2022
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INTERNATIONAL ISO
STANDARD 16808
Second edition
2022-05
Metallic materials — Sheet and strip
— Determination of biaxial stress-
strain curve by means of bulge test
with optical measuring systems
Matériaux métalliques — Tôles et bandes — Détermination de
la courbe contrainte-déformation biaxiale au moyen de l'essai de
gonflement hydraulique avec systèmes de mesure optiques
Reference number
ISO 16808:2022(E)
© ISO 2022

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ISO 16808:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022
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
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ISO 16808:2022(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms.1
5 Principle . 2
6 Test equipment .3
7 Optical measurement system. 5
8 Test piece . 6
8.1 General . 6
8.2 Application of grid . 6
8.2.1 Type of grid . 6
8.2.2 Grid application . 6
9 Procedure .6
10 Evaluation methods for the determination of the curvature and strains at the pole.7
11 Calculation of biaxial stress-strain curves . 8
12 Test report . 9
Annex A (informative) Test procedure for a quality check of the optical measurement
system.11
Annex B (informative) Computation of the curvature on the basis of a response surface .14
Annex C (informative) Determination of the equi-biaxial stress point of the yield locus and
the hardening curve .16
Bibliography .24
iii
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ISO 16808:2022(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 16808:2014), of which it constitutes a
minor revision. The changes are as follows:
— the designation of r in Table 1 has been modified;
1_100
— the title of Figure A.4 has been modified;
— Formula (B.2) has been modified;
— Annex A has been deleted and other annexes have been renumbered accordingly;
— the status of Annex A (formerly Annex B) has been changed to informative;
— minor editorial changes have been made to align with ISO/IEC Directives Part 2, 2021.
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
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INTERNATIONAL STANDARD ISO 16808:2022(E)
Metallic materials — Sheet and strip — Determination
of biaxial stress-strain curve by means of bulge test with
optical measuring systems
1 Scope
This document specifies a method for determination of the biaxial stress-strain curve of metallic
sheets having a thickness below 3 mm in pure stretch forming without significant friction influence. In
comparison with tensile test results, higher strain values can be achieved.
NOTE In this document, the term "biaxial stress-strain curve" is used for simplification. In principle, in the
test the "biaxial true stress-true strain curve" is determined.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols and abbreviated terms
The symbols and designations used are given in Table 1.
Table 1
Symbol Designation Unit
d Diameter of the die (inner) mm
die
d Diameter of the blank holder (inner) mm
BH
R Radius of the die (inner) mm
1
h Height of the drawn blank (outer surface) mm
t Initial thickness of the sheet (blank) mm
0
t Actual thickness of the sheet mm
p Pressure in the chamber MPa
rms Standard deviation (root mean square) -
ρ Radius of curvature mm
r Surface radius for determining curvature mm
1
r Surface radius for determining strain mm
2
r Surface radius to determine curvature with a mm
1_100
diameter of 100 mm
a , b Coefficients for response surface -
i i
1
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ISO 16808:2022(E)
Table 1 (continued)
Symbol Designation Unit
σ Biaxial stress MPa
Β
e Engineering strain -
ε Major true strain -
1
ε Minor true strain -
2
ε True thickness strain -
3
ε Equivalent true strain -
Ε
l Coordinate and length of a section mm
s
dz Displacement in the z-direction mm
dz Displacement after movement correction mm
mv
5 Principle
A circular blank is completely clamped at the edge in a tool between die and blank holder. A bulge is
formed by pressing a fluid against the blank until final fracture occurs (Figure 1). During the test,
the pressure of the fluid is measured and the evolution of the deformation of the blank is recorded by
[1],[2],[3]
an optical measuring system . Based on the recorded deformation of the blank, the following
quantities near the centre of the blank are determined: the local curvature, the true strains at the
surface, and, by assuming incompressible deformation of the material, the actual thickness of the blank.
Furthermore, assuming the stress state of a thin-walled spherical pressure vessel at the centre of the
blank, the true stress is calculated from the fluid pressure, the thickness and the curvature radius.
NOTE In addition to the bulge test procedures with optical measurement systems introduced in Reference
[4] [5] [6] [7] [8] [9]
[1] and described in the following, there are also laser systems , , or tactile systems , , valid for bulge
test investigation, which are not covered in this document.
Key
h height of the drawn blank (outer surface) ρ radius of curvature
p pressure in the chamber t initial thickness of the sheet (blank)
0
ε true thickness strain (at the apex of the dome) t actual thickness of the sheet
3
d diameter of the die (inner)
die
Figure 1 — Principle of the bulge test
The coordinate origin shall be in the centre of the blank holder. The XY-plane should be parallel to the
surface of the blank holder (parallel to the clamped metal sheet before forming). Herein, the x-direction
corresponds to the rolling direction. The z-direction shall be normal to the clamped metal sheet before
forming, with the positive direction towards the optical sensor.
2
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ISO 16808:2022(E)
6 Test equipment
6.1 The bulge test shall be carried out on a machine equipped with a die, a blank holder and a fluid
chamber. The proposed equipment is illustrated in Figure 2.
Key
1 deformation measurement system 3 chamber with fluid
2 lock bead 4 pressure measurement system
Figure 2 — Proposal of a testing equipment (principle drawing)
6.2 The layout of the test equipment shall be such that it is possible to continuously measure the
outside surface of the test piece continuously during the test, i.e. to be able to determine the deformation
of the geometry by recording the evolution of X, Y, Z coordinates of a grid of points on the bulging blank
surface, in order to calculate the shape and the true strains in the central area of interest until failure
occurs.
6.3 During the test, the system shall be able to measure optically (without contact) the X, Y, Z
coordinates of a grid of points on the bulging surface of the specimen. Out of these coordinates, the true
strains ε and ε for each point of the selected area, the thickness strain ε and the curvature radius ρ
1 2 3
for the apex of the dome are calculated.
6.4 The system should be equipped with a chamber fluid pressure measurement system. An indirect
measurement system is also possible. Starting from 20 % of the maximum measured pressure value,
the precision should be 1 % of the actual measured value.
6.5 The die, the blank holder and the fluid chamber shall be sufficiently rigid to minimize deformation
during testing. The blank-holder force shall be high enough to keep the blank holder closed. Any
movement of the test piece between the blank holder and die should be prevented. Typically during the
test, the bulge pressure is acting on parts of the blank holder reducing the effective blank-holder force.
This shall be taken in consideration when defining the necessary blank-holder force.
6.6 The fluid shall be in contact with the blank surface (without any air bubbles) to prevent energy
storage during the test through compressed air bubbles which would lead to higher energy release
and greater oil splashing at failure. No fluid shall be lost through the blank holder, die and sheet or
elsewhere during the test until failure occurs.
3
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ISO 16808:2022(E)
6.7 A lock bead (or comparable geometry in the circular surface), designed to suppress any material
flow, is recommended. The lock bead shall not initiate cracks in the material. The lock bead shall be
located between blank holder and die. A location close to the die radius is recommended. The lock bead
geometry should avoid a curvature and a wrinkling of the blank when closing the tool and prevent the
sliding of the blank during the test.
6.8 It is recommended to place glass plates in front of the lenses and the illumination in order to
[7],[12]
protect the optical measuring system from oil splashing due to blank failure at the end of the test .
The plates can be fixed on the blank holder (thick glass) or near the camera lenses and illumination
(thinner glass); see Figure 3. The inserted protection shall not disturb the optical measurement quality
(see Clause 7). After each test, the glass plates shall be well cleaned without damaging or scratching
them and precisely repositioned to not alter calibration. Typically, a calibration of the optical system
including the protection increases the measurement quality.
6.9 The smallest die diameter recommended should have a ratio of die diameter to initial thickness
d / t ≥ 33 (see Figure 2). The radius of the die should not lead to cracks in the blank during the test. A
die 0
recommendation is (5 × t ) to (15 × t ) (maximum 15 mm).
0 0
a) b)
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ISO 16808:2022(E)
c)
Key
1 lamp 4 test piece
2 cameras 5 fluid
3 glass plates
Figure 3 — Examples for possible positions of oil shielding plates and lamps
7 Optical measurement system
For the determination of the radius of curvature ρ, and the true strains ε and ε , an optical-deformation
1 2
field measurement system with the following characteristics is recommended.
— Optical sensor based on two or more cameras.
— Measurement area, where d ≥ 1/2 d
measurement area die.
The used measurement area should be larger than a concentric diameter of half the diameter of the
blank holder. This area should be observable during the entire forming process for all heights of the
drawn blank.
— Local resolution (grid distance between the independent measurement points): The distance g
max
between two adjacent points on the unformed blank should follow the requirement:
d
die
g ≤
max
50
— The determination of the curvature requires an accuracy of the z-coordinates in an area with a
diameter of 1/2 d concentric to the blank holder of
die
rmsd()z ⋅100mm
rmsd()z = ≤0,015mm
n
d
die
NOTE The accuracy of the shape measurement can be checked with a test of the optical measurement system
(see Annex A).
Accuracy for strain measurement:  rms (ε ) = 0,003  rms (ε ) = 0,003
1 2
5
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ISO 16808:2022(E)
For each real strain value for the mentioned rms (ε) above, the acceptable measurement values are:
ε = 0  acceptable measurement range:  –0,003 … 0,003
real
ε = 0,5  acceptable measurement range:  0,497 … 0,503
real
— Missing measurement points: In order to avoid unbalanced curvature approximations, only the
absence of less than 5 % of the measurement points in the concentric area with a diameter = 1/2 d
die
is acceptable (without interpolation). If adjacent points are missing, the inscribed circle of this area
shall not be larger than two points.
8 Test piece
8.1 General
The test piece shall be flat and of such shape that the blank is clamped and material flow is stopped. The
use of lock beads is recommended. The edge of the blank shall be outside the lock bead.
The preparation of the blank does not influence the results as long as the surface of the test piece was
not damaged (scratches, polishing). The dimension of the outer edges can be circular (preferred) or
angular.
8.2 Application of grid
8.2.1 Type of grid
For optical full-field measurement devices, the grid shall fulfil two objectives:
a) the curvature radius determination of the specimens’ surface;
b) the strain calculation of the material deformation.
8.2.2 Grid application
Deterministic grids (e.g. squares, circles, dots) should have a strong contrast and have to be applied
without any notch effect and/or change in microstructure. Some common application techniques are:
— electrochemical etching, photochemical etching, offset printing and grid transfer;
— stochastic (speckle) patterns which can be applied by spraying paint on the surface of test piece
surfaces. Paint adherence to the surface after deformation should be checked. It is possible first to
spray a thin, matt, white base layer to reduce reflections from the test piece surfaces, then to spray
a cloud of randomly distributed black spots (e.g. black spray paint or graphite). The spray shall be
both elastic and tough enough not to crack or peel off during deformation. The random distribution
of the fine sprayed spots allows the determination of each point of the virtual grid on the specimen.
The pattern should have sufficient black/white density and appropriate size features in each point
position search area as required by the optical system used.
9 Procedure
9.1 The test shall be carried out at an ambient temperature of (23 ± 5) °C.
9.2 Determine the initial thickness of the test piece to the nearest 0,01 mm.
9.3 Clamp the test piece between blank holder and die. Avoid air bubbles between test piece and fluid
to prevent formation of compressed air during testing, leading to stronger oil splashing at failure.
6
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ISO 16808:2022(E)
−1
9.4 A constant strain rate of 0,05 s is recommended. If a constant strain rate is not possible, a
constant forming velocity of the punch or fluid should be guaranteed. In order to avoid big influences in
the biaxial stress-strain curve of temperature or strain rate sensitive materials, the bulge test should
be conducted in 2 min to 4 min. This time frame guarantees slow and acceptable strain rates and a cost-
effective testing time.
The plot of the strain rate versus time is recommended.
9.5 Measure the fluid pressure during the test.
9.6 Measure the X, Y, Z coordinates of the grid on the test piece surface during the test.
9.7 The fluid pressure data and forming data shall be measured and saved at the same time scale.
A minimum of 100 values is recommended. In order to represent the whole strain and pressure
development, at least 100 images of the bulge testing are recommended.
9.8 The failure of the test piece shall be considered as obtained when a through crack, i.e. a crack
which goes through the thickness of the test piece, has occurred. The failure is detected by decreasing
fluid pressure, which defines the end of the test.
9.9 A sufficient number of test pieces should be prepared in order to achieve at least three valid tests.
10 Evaluation methods for the determination of the curvature and strains at the
pole
For the following explanation of the calculation of the curvature and strains, a spherically shaped
surface near the pole is assumed (best-fit sphere). On the last image before failure, as defined in 9.8,
the area of the dome with the highest deformation is selected and defined as the position where to
determine the true stress and the true thickness strain ε . To obtain a stable radius of curvature of the
3
dome, a best-fit sphere can be calculated based on a selected area of points. For this selection, a radius
r is defined around the apex of the dome in the last image before bursting and the fit is performed for
1
all forming stages with the same selection of points (Figure 4).
A certain number of the first forming stages (images) are rejected, since the specimen is still too flat
for a reliable determination of the best-fit sphere, since the bending radius is very high and the fit is
not stable. For robust values of the true strain and thinning in the apex, the average value of a number
of selected points is taken. Therefore, a second area is defined by a radius r in a similar manner (see
2
Figure 4).
Based on this procedure, for every forming stage (image) the radius of curvature, the average thickness
strains, as well as the corresponding thickness and stress values at the dome apex are calculated. This
evaluation can be carried out for different r and r values (see Figure 4).
1 2
For a good convergence and robust values, the recommended range of r and r is defined:
1 2
r = (0,125 ± 0,025) × d (1)
1 die
r = (0,05 ± 0,01) × d (2)
2 die
7
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ISO 16808:2022(E)
Figure 4 — Choice of r and r for calculation of true stress and true strain for each forming
1 2
stage
An alternative proposal for the calculation of the curvature and strains is given in Annex B.
11 Calculation of biaxial stress-strain curves
For the calculation of the biaxial stress-strain curves, a simple membrane stress state of a thin-
walled spherical pressure vessel is assumed at the centre of the blank. This implies the following
simplifications:
a) equi-biaxial stress state:
σσ==σ (3)
12 B
b) representation of the curvature by the mean curvature radius:
−1
1
 
ρρ=+()11 ρ (4)
12
 
2
 
8
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ISO 16808:2022(E)
Then the biaxial true stress can be calculated according to the following equation:
ρp
σ = (5)
B
2t
using the fluid pressure p, the curvature radius ρ and the actual thickness t, with
tt= exp(ε ) (6)
03
Assuming plastic incompressible deformation of the material and neglecting elastic strains, the total
thickness strain for the calculation of the actual thickness can be approximated by the total major and
minor true strain:
εε≈− −ε (7)
31 2
Based on the plastic work principle, the biaxial stress-strain curve is a function of the plastic thickness
pl
strain:σε()− , see also Annex C. Assuming an isotropic linear elastic material behaviour and plastic
B
3
incompressibility, the plastic thickness strain is then given by:
1−ν
pl
εε=− −+ε 2 σ (8)
12 B
3
E
For the elasticity modulus E and the Poisson ratio ν, literature values are generally sufficient to subtract
the elastic contribution, e.g. E = 210 GPa and ν = 0,33 for steel, respectively E = 70 GPa and ν = 0,33 for
aluminium alloys.
The ratio of die diameter to thickness should be reasonably high to ensure a near membrane stress
state in the test piece, and a negligible influence of bending. For die diameter to thickness ratios lower
than 100, it is recommended to check if the bending strains are relatively small compared to the actual
thickness strain result ε using the following estimate for the bending strains:
3
t
 
0
ε ≈−ln 1− exp(ε ) (9)
bending  3 

 
NOTE The biaxial stress-strain curve is obtained without any assumption on the type of yield criterion. This
biaxial stress-strain curve can be used to identify the equi-biaxial stress point of the yield locus as well as to
approximate the material hardening curve beyond uniform elongation.
Annex C gives a proposal for the determination of the equi-biaxial stress point of the yield criterion and
for using the biaxial stress-strain curves of hydraulic bulge tests to extrapolate an equivalent stress-
strain curve which is based on uniaxial tension tests.
12 Test report
The test report shall contain at least the following information:
a) reference to this document i.e. ISO 16808:2022;
b) identification of laboratory that measured the bulge test values, including the name of operator;
c) identification of material;
d) initial thickness of blank;
e) grid, camera system and software used;
f) position of the protective glasses;
g) geometries of the test equipment;
9
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ISO 16808:2022(E)
h) bulge / piston speed;
i) bulge test evaluation method, respectively the parameters for identification of the curvature and
the average of strain;
j) number of replications;
k) for each bulge test, a table of values with the history of time, radius ρ, pressure p, absolute value of
plastic thickness strain and biaxial true stress;
l) biaxial stress-strain curves of all bulge tests as a plot.
10
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ISO 16808:2022(E)
Annex A
(informative)

Test procedure for a quality check of the optical measurement
system
A.1 Test procedure
Regarding the recommended quality of the optical measurement system (see Clause 7) and the
setup for example according to Figure 3, it shall be taken into account that the additional glass plates
in the optical path can have a significant influence. For a check of the final quality for the complete
experimental setup, the following procedure (see Figure A.1) is recommended.
Key
1 lamp 4 sheet metal
2 cameras 5 reference plate
3 glass plates 6 maximum height
Figure A.1 — Quality check of optical measurement system
A rigid test object (e.g. plate, 3-dimensional curved surface) with a diameter ≥ 1/2 d shall be used.
die
The object shall not to be deformed during the test procedure. The object should have an appropriate
surface for the measurement system.
The test object shall be measured on the initial sheet clamping position once without protection glass
plates (reference measurement).
The test object shall be measured with the complete measurement setup (including the protection
glass plate) in different positions (5 to 10) between initial sheet clamping position and the maximum
estimated bulge height h (see Figure A.1).
max
11
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ISO 16808:2022(E)
A.2 Post-processing
The coordinates for all measurement points in all stages shall be determined.
A rigid body movement correction shall be done by a least square fit, the 3D coordinates from each stage
are aligned to the reference measurement. For this fit, a concentric area with a diameter of 1/2 d
die
shall be used.
The remaining deviations in the z-direction (dz) describe the loss of quality. An example of a test plate
measured in nine different positions is shown in Figures A.2 and A.3.
Key
X l (in mm)
s
Y dz (in mm)
Figure A.2 — Original displacement dz of a cross section of the reference plate (d = 200 mm)
die
Key
X l (in mm)
s
Y dz (in mm)
mv
Figure A.3 — Displacement dz of a cross section of the reference plate after movement
...

NORME ISO
INTERNATIONALE 16808
Deuxième édition
2022-05
Matériaux métalliques — Tôles et
bandes — Détermination de la courbe
contrainte-déformation biaxiale
au moyen de l'essai de gonflement
hydraulique avec systèmes de mesure
optiques
Metallic materials — Sheet and strip — Determination of biaxial
stress-strain curve by means of bulge test with optical measuring
systems
Numéro de référence
ISO 16808:2022(F)
© ISO 2022

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ISO 16808:2022(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2022
Tous droits réservés. Sauf prescription différente ou nécessité dans le contexte de sa mise en œuvre, aucune partie de cette
publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique,
y compris la photocopie, ou la diffusion sur l’internet ou sur un intranet, sans autorisation écrite préalable. Une autorisation peut
être demandée à l’ISO à l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
ISO copyright office
Case postale 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Genève
Tél.: +41 22 749 01 11
E-mail: copyright@iso.org
Web: www.iso.org
Publié en Suisse
ii
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ISO 16808:2022(F)
Sommaire Page
Avant-propos .iv
1 Domaine d’application . 1
2 Références normatives .1
3 Termes et définitions . 1
4 Symboles et abréviations .1
5 Principe. 2
6 Equipement d’essai . 3
7 Système de mesure optique . 5
8 Éprouvette . 6
8.1 Généralités . 6
8.2 Application de la grille . 6
8.2.1 Type de grille . 6
8.2.2 Application de la grille . 6
9 Mode opératoire . 6
10 Méthodes d’évaluation pour la détermination de la courbure et des déformations
au niveau du dôme. 7
11 Calcul des courbes contrainte-déformation biaxiales. 8
12 Rapport d’essai . 9
Annexe A (informative) Procédure d’essai pour une vérification de la qualité du système
de mesure optique .11
Annexe B (informative) Estimation de la courbure sur la base d’une surface de réponse .14
Annexe C (informative) Détermination du point de contrainte équi-biaxiale de la zone
d’écoulement et de la courbe d’écrouissage .16
Bibliographie .24
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ISO 16808:2022(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes
nationaux de normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est
en général confiée aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude
a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,
gouvernementales et non gouvernementales, en liaison avec l'ISO participent également aux travaux.
L'ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier, de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document a
été rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir
www.iso.org/directives).
L'attention est attirée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable
de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l'élaboration du document sont indiqués dans l'Introduction et/ou dans la liste des déclarations de
brevets reçues par l'ISO (voir www.iso.org/brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion
de l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir www.iso.org/avant-propos.
Le présent document a été élaboré par le comité technique ISO/TC 164, Essais mécaniques des métaux,
sous-comité SC 2, Essais de ductilité, en collaboration avec le Comité Européen de Normalisation (CEN)
comité technique CEN/TC 459/SC 1, Méthodes d'essai des aciers (autres que les analyses chimiques),
conformément à l'accord de coopération technique entre l'ISO et le CEN (accord de Vienne).
Cette deuxième édition annule et remplace la première édition (ISO 16808:2014), dont elle constitue
une révision mineure. Les modifications sont les suivantes:
— la désignation de r dans le Tableau 1 a été modifiée;
1_100
— le titre de la Figure A.4 a été modifié;
— la Formule B.2 a été modifiée;
— l’Annexe A a été supprimée et les autres annexes ont été renumérotées en conséquence;
— le statut de l’Annexe A (ancienne Annexe B) a été changé en informatif;
— des modifications rédactionnelles mineures ont été apportées pour s'aligner sur les directives ISO/
IEC Partie 2, 2021.
Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent
document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes
se trouve à l’adresse www.iso.org/fr/members.html.
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NORME INTERNATIONALE ISO 16808:2022(F)
Matériaux métalliques — Tôles et bandes — Détermination
de la courbe contrainte-déformation biaxiale au moyen
de l'essai de gonflement hydraulique avec systèmes de
mesure optiques
1 Domaine d’application
Le présent document spécifie une méthode pour la détermination de la courbe contrainte-déformation
biaxiale sur tôles métalliques d’épaisseur inférieure à 3 mm en formage en expansion pure sans
influence significative des frottements. En comparaison à des résultats d’essais de traction, des valeurs
plus élevées de déformation peuvent être obtenues.
NOTE Dans le présent document le terme «la courbe de contrainte-déformation biaxiale» est utilisé pour
simplifier la rédaction. En principe, «la courbe biaxiale contrainte vraie-déformation vraie » est déterminé dans
l’essai.
2 Références normatives
Le présent document ne contient aucune référence normative.
3 Termes et définitions
Aucun terme n’est défini dans le présent document.
L’ISO et l’IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en
normalisation, consultables aux adresses suivantes:
— ISO Online browsing platform: disponible à l’adresse https:// www .iso .org/ obp
— IEC Electropedia: disponible à l’adresse https:// www .electropedia .org/
4 Symboles et abréviations
Les symboles et désignations utilisés sont donnés dans le Tableau 1.
Tableau 1
Symbole Désignation Unité
d Diamètre (intérieur) de la matrice mm
die
d Diamètre (intérieur) du serre-flan mm
BH
R Rayon (intérieur) de la matrice mm
1
h Hauteur du flan embouti (surface extérieure) mm
t Épaisseur initiale de la tôle (du flan) mm
0
t Épaisseur instantanée de la tôle mm
p Pression dans la chambre MPa
rms Écart-type (moyenne quadratique) —
ρ Rayon de courbure mm
r Rayon de la surface pour la détermination de la courbure mm
1
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ISO 16808:2022(F)
Tableau 1 (suite)
Symbole Désignation Unité
r Rayon de la surface pour la détermination de la déformation mm
2
Rayon de la surface pour la détermination de la courbure avec un
r mm
1_100
diamètre de 100 mm
a , b Coefficients pour la surface de réponse —
i i
σ Contrainte biaxiale MPa
B
e Déformation conventionnelle —
ε Déformation majeure vraie —
1
ε Déformation mineure vraie —
2
ε Déformation vraie dans l’épaisseur —
3
ε Déformation équivalente vraie —
E
l Coordonnées et longueur d’une section mm
s
dz Déplacement selon l’axe des z mm
dz Déplacement après correction du mouvement mm
mv
5 Principe
Un flan circulaire est complètement enserré au niveau de son bord dans un outil entre une matrice et
un serre-flan. Un dôme est formé par pression d’un fluide contre le flan jusqu’à ce que la rupture finale
survienne (Figure 1). Pendant l’essai, la pression du fluide est mesurée et l’évolution de la déformation
[1],[2],[3]
du flan est enregistrée par un système de mesure optique . Sur la base de la déformation
enregistrée du flan, les quantités suivantes sont déterminées près du centre du flan: la courbure locale,
les déformations vraies au niveau de la surface, et, en supposant une déformation incompressible du
matériau, l’épaisseur instantanée du flan. De plus, en supposant que l’état de contrainte au centre du
flan est celui d’un récipient sous pression, sphérique à paroi mince, la contrainte vraie est calculée à
partir de la pression du fluide, l’épaisseur et le rayon de courbure.
NOTE En complément des procédures d’essai de gonflement hydraulique avec des systèmes de mesure
optiques mentionnés dans la Référence [1] et décrits dans ce qui suit, il existe également des systèmes laser
[4],[5],[6] [7],[8], |9]
ou des systèmes tactiles valables pour les examens liés à l’essai de gonflement hydraulique, qui
ne sont pas couverts dans le présent document.
Légende
h hauteur du flan embouti (surface extérieure) ρ rayon de courbure
p pression dans la chambre t épaisseur initiale de la tôle (du flan)
0
ε déformation vraie dans l’épaisseur t épaisseur instantanée de la tôle
3
(au sommet du dôme)
d diamètre (intérieur) de la matrice
die
Figure 1 — Principe de l’essai de gonflement hydraulique
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ISO 16808:2022(F)
L’origine des coordonnées doit se situer au centre du serre-flan. Il convient que le plan XY soit parallèle
à la surface du serre-flan (parallèle à la tôle métallique enserrée avant formage). Ici, l’axe des x
correspond à la direction de laminage. L’axe des z doit être perpendiculaire à la tôle métallique enserrée
avant formage, les valeurs positives se trouvant du côté du capteur optique.
6 Equipement d’essai
6.1 L’essai de gonflement hydraulique doit être réalisé sur une machine équipée d’une matrice, d’un
serre-flan et d’une chambre à fluide. L’équipement proposé est illustré à la Figure 2.
Légende
1 système de mesure de la déformation 3 chambre avec fluide
2 jonc de blocage 4 système de mesure de la pression
Figure 2 — Proposition d’équipement d’essai (dessin de principe)
6.2 La disposition de l’équipement d’essai doit être telle qu’il soit possible de mesurer en continu
la surface extérieure de l’éprouvette pendant l’essai, c’est-à-dire qu’il permette de déterminer la
déformation de la géométrie en enregistrant l’évolution des coordonnées X, Y, Z d’une grille de points
à la surface du flan soumis à gonflement hydraulique, de façon à calculer la forme et les déformations
vraies dans la zone centrale examinée avant que la rupture survienne.
6.3 Pendant l’essai, le système doit être capable de mesurer par méthode optique (sans contact) les
coordonnées X, Y, Z d’une grille de points déposée sur la surface soumise à gonflement hydraulique
de l’éprouvette. À partir de ces coordonnées, les déformations vraies ε et ε pour chaque point de la
1 2
zone choisie, la déformation dans l’épaisseur ε et le rayon de courbure ρ pour le sommet du dôme sont
3
calculés.
6.4 Il convient que le système soit équipé d’un système de mesure de la pression du fluide de la
chambre. Un système de mesure indirecte est également possible. À partir de 20 % de la valeur
maximale de la pression mesurée, il convient que l’exactitude soit de 1 % de la valeur effective mesurée.
6.5 La matrice, le serre-flan et la chambre à fluide doivent être suffisamment rigides pour minimiser
la déformation pendant les essais. La force exercée par le serre-flan doit être suffisamment élevée
pour garder le serre-flan fermé. Il convient que tout mouvement de l’éprouvette entre le serre-flan et la
matrice soit empêché. Typiquement pendant l’essai de gonflement hydraulique, la pression est appliquée
sur les pièces constitutives du serre-flan réduisant la force effective du serre-flan. Cela doit être pris en
considération lors de la définition de la force nécessaire du serre-flan.
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ISO 16808:2022(F)
6.6 Le fluide doit être en contact avec la surface du flan (sans bulles d’air) pour prévenir le stockage
d’énergie pendant l’essai au travers de bulles d’air compressées qui conduiraient à une restitution
d’énergie plus grande et à une aspersion d’huile à la rupture plus importante. Du fluide ne doit pas être
perdu à travers le serre-flan, la matrice et la tôle ou en tout autre endroit pendant l’essai jusqu’à ce que
la rupture survienne.
6.7 Un jonc de blocage (ou géométrie comparable sur la surface circulaire), conçu de façon à supprimer
tout avalement du matériau, est recommandé. Le jonc de blocage ne doit pas amorcer de fissures dans le
matériau. Le jonc de blocage doit être placé entre le serre-flan et la matrice. Un positionnement proche
du rayon de la matrice est recommandé. Il convient que la géométrie du jonc de blocage évite une
courbure et une ondulation du flan lors de la fermeture de l’outillage et prévienne le glissement du flan
pendant l’essai.
6.8 Il est recommandé de placer des plaques de verre devant les lentilles et la source de lumière pour
[7],[12]
protéger le système de mesure optique de l’huile aspergée lors de la rupture . Les plaques peuvent
être fixées sur le serre-flan (verre épais) ou à proximité des lentilles et de la source de lumière (verre
plus fin); voir Figure 3. La protection insérée ne doit pas perturber la qualité du mesurage optique (voir
Article 7). Après chaque essai, les plaques de verre doivent être bien nettoyées sans les abîmer ou les
rayer et doivent être repositionnées avec précision pour ne pas modifier l’étalonnage. Typiquement, un
étalonnage du système optique incluant la protection accroît la qualité du mesurage.
6.9 Il convient que le plus petit diamètre de la matrice recommandé présente un rapport diamètre
de la matrice sur épaisseur initiale d / t ≥ 33 (voir Figure 2). Il convient que le rayon de la matrice
die 0
ne conduise pas à la formation de fissures dans le flan pendant l’essai. Une valeur de (5 × t ) à (15 × t )
0 0
(maximum 15 mm) est recommandée.
a) b)
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ISO 16808:2022(F)
c)
Légende
1 lampe 4 éprouvette
2 caméras 5 fluide
3 plaques de verre
Figure 3 — Exemples de dispositions possibles des plaques de protection contre l’huile et des
lampes
7 Système de mesure optique
Pour la détermination du rayon de courbure, ρ, et des déformations vraies ε et ε , un système optique
1 2
de mesure du champ de déformations présentant les caractéristiques suivantes est recommandé.
— Capteur optique utilisant au moins deux caméras.
— Aire de mesure avec d ≥ 1/2 d .
aire de mesure die
Il convient que l’aire de mesure utilisée soit plus grande que l’aire d’un cercle concentrique au serre-
flan et de diamètre égal à la moitié du diamètre du serre-flan. Il convient que cette aire puisse être
observée pendant la totalité du processus de formage pour toutes les hauteurs du flan déformé.
— Résolution locale (taille de grille entre les points de mesure indépendants): Il convient que
l’espacement g entre deux points adjacents du flan non déformé respecte l’exigence:
max
d
die
g ≤
max
50
— La détermination de la courbure requiert une exactitude des coordonnées sur l’axe des z dans une
zone de diamètre 1/2 d concentrique au serre-flan égale à:
die
rmsd()z ×100 mm
rmsd()z = ≤ 0,015 mm
n
d
die
NOTE L’exactitude de la mesure de la forme peut être vérifiée par un essai du système optique de mesure
(voir Annexe A).
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ISO 16808:2022(F)
Exactitude pour le mesurage de la déformation:   rms (ε ) = 0,003     rms (ε ) = 0,003
1 2
Pour chaque valeur vraie de la déformation pour la valeur rms (ε) mentionnée ci-avant, les valeurs
acceptables des mesurages sont:
ε = 0  intervalle de mesurages acceptables:   –0,003 … 0,003
real
ε = 0,5  intervalle de mesurages acceptables:   0,497 … 0,503
real
— Points de mesure manquants: De façon à éviter des approximations déséquilibrées de la courbure,
seule l’absence de moins de 5 % des points de mesure dans la zone concentrique de diamètre égal
à 1/2 d est acceptable (sans interpolation). Si des points adjacents manquent, le cercle inscrit de
die
cette zone ne doit pas être plus grand que deux points.
8 Éprouvette
8.1 Généralités
L’éprouvette doit être plane et de forme telle que le flan est maintenu et que l’avalement du matériau est
arrêté. L’utilisation de joncs de blocage est recommandée. Le bord du flan doit se situer en dehors du
jonc de blocage.
La préparation du flan n’influence pas les résultats tant que la surface de l’éprouvette n’a pas été altérée
(rayures, polissage). La forme des bords extérieurs peut être arrondie (de préférence) ou angulaire.
8.2 Application de la grille
8.2.1 Type de grille
Pour les dispositifs optiques de mesure plein champ, la grille doit remplir deux objectifs:
a) la détermination du rayon de courbure de la surface des éprouvettes;
b) le calcul des déformations du matériau.
8.2.2 Application de la grille
Il convient que les grilles déterministes (par exemple carrés, cercles, points) présentent un fort
contraste et soient appliquées sans effet d’entaille et/ou changement de la microstructure. Quelques
techniques usuelles d’application sont:
— attaque électrochimique, attaque photochimique, impression offset et transfert de grille,
— motifs stochastiques (speckle) qui peuvent être appliqués par pulvérisation de peinture à la surface
de l’éprouvette. Il convient de vérifier l’adhérence de la peinture à la surface après déformation.
Il est possible de pulvériser en premier lieu une couche fine d’apprêt blanc, mat pour réduire les
réflexions à partir de la surface des éprouvettes puis un nuage de points noirs répartis de manière
aléatoire (par exemple peinture noire pulvérisée ou graphite). Le film doit être à la fois élastique
et suffisamment résistant pour qu’il ne se fissure pas ou ne se pèle pas pendant la déformation.
La répartition aléatoire des points fins pulvérisés permet la détermination de chaque point de la
grille virtuelle sur l’éprouvette. Il convient que le motif présente une densité noir/blanc suffisante
et des caractéristiques dimensionnelles appropriées dans chaque zone de recherche de la position
des points comme requis par le système optique utilisé.
9 Mode opératoire
9.1 L’essai doit être réalisé à température ambiante de (23 ± 5) °C.
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ISO 16808:2022(F)
9.2 Déterminer l’épaisseur initiale de l’éprouvette à 0,01 mm près.
9.3 Serrer l’éprouvette entre le serre-flan et la matrice. Eviter les bulles d’air entre l’éprouvette et le
fluide pour prévenir la formation d’air comprimé pendant les essais, conduisant à une aspersion d’huile
plus conséquente lors de la rupture.
−1
9.4 Une vitesse de déformation constante de 0,05 s est recommandée. S’il n’est pas possible
d’appliquer une vitesse de déformation constante, il convient de garantir une vitesse de formage
constante du piston ou du fluide. De façon à éviter de grandes influences sur la courbe contrainte-
déformation biaxiale pour des matériaux sensibles à la température ou à la vitesse de déformation, il
convient que l’essai de gonflement hydraulique soit réalisé en 2 min à 4 min. Cet intervalle de temps
garantit de faibles et acceptables vitesses de déformation et un temps d’essai à coût maîtrisé.
Le tracé de la vitesse déformation en fonction du temps est recommandé.
9.5 Mesurer la pression du fluide pendant l’essai.
9.6 Mesurer les coordonnées X, Y, Z de la grille à la surface de l’éprouvette pendant l’essai.
9.7 Les données relatives à la pression du fluide et les données de formage doivent être mesurées et
sauvegardées avec la même échelle de temps. Un minimum de 100 valeurs est recommandé. De façon
à représenter le développement complet de la déformation et de la pression, au moins 100 images des
essais de gonflement hydraulique sont recommandées.
9.8 La rupture de l’éprouvette doit être considérée comme obtenue lorsqu’une fissure traversante,
c’est-à-dire une fissure qui se propage dans toute l’épaisseur de l’éprouvette, est apparue. La rupture
est détectée par une chute de pression du fluide ce qui définit la fin de l’essai.
9.9 Il convient de préparer un nombre suffisant d’éprouvettes pour réaliser au moins trois essais
valables.
10 Méthodes d’évaluation pour la détermination de la courbure et des
déformations au niveau du dôme
Pour l’explication suivante du calcul de la courbure et des déformations, on suppose une surface de
forme sphérique à proximité du dôme (sphère correspondant au meilleur ajustement possible). Sur la
dernière image avant la rupture telle que définie au 9.8, la zone du dôme présentant la déformation
la plus élevée est choisie et définie comme l’emplacement où déterminer la contrainte vraie et la
déformation équivalente vraie dans l’épaisseur ε . Pour obtenir un rayon de courbure stable du dôme,
3
une sphère correspondant au meilleur ajustement possible peut être calculée sur la base d’une zone
de points choisie. Pour ce choix, un rayon r est défini autour du sommet du dôme pour la dernière
1
image avant éclatement et l’ajustement est réalisé pour tous les stades de formage avec le même choix
de points (Figure 4).
Un certain nombre des premiers stades de formage (images) sont rejetés, étant donné que l’éprouvette
est encore trop plane pour une détermination fiable de la sphère correspondant au meilleur ajustement
possible, et que le rayon de cintrage est très élevé et l’ajustement n’est pas stable. Pour des valeurs
robustes de la déformation vraie et de l’amincissement au niveau du sommet, on prend la valeur
moyenne calculée à partir d’un nombre de points choisis. Par conséquent, une deuxième zone est définie
par un rayon r de manière similaire (voir Figure 4).
2
Sur la base de cette procédure, pour tous les stades de formage (images), le rayon de courbure, les
déformations moyennes dans l’épaisseur, de même que l’épaisseur correspondante et les valeurs de
la contrainte au sommet du dôme sont calculées. Cette évaluation peut être réalisée pour différentes
valeurs de r et r (voir Figure 4).
1 2
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ISO 16808:2022(F)
Pour une bonne convergence et des valeurs robustes, les intervalles recommandés pour r et r sont
1 2
définis:
r = (0,125 ± 0,025) × d (1)
1 die
r = (0,05 ± 0,01) × d (2)
2 die
Figure 4 — Choix de r et r pour le calcul de la contrainte vraie et de la déformation vraie pour
1 2
chaque étape de formage
Une proposition alternative pour le calcul de la courbure et des déformations est donnée en Annexe B.
11 Calcul des courbes contrainte-déformation biaxiales
Pour le calcul des courbes contrainte-déformation biaxiales, on suppose un état de contraintes de
membrane simple d’un récipient sous pression sphérique à paroi mince au centre du flan. Cela implique
les simplifications suivantes:
a) état de contraintes équi-biaxial:
σσ==σ (3)
12 B
b) représentation de la courbure par le rayon de courbure moyen:
−1
 
1
ρρ=+()11 ρ (4)
 
12
2
 
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ISO 16808:2022(F)
Alors, la contrainte biaxiale vraie peut être calculée conformément à l’équation suivante:
ρp
σ = (5)
B
2t
en utilisant la pression du fluide, p, le rayon de courbure, ρ, et l’épaisseur instantanée, t, avec
tt= exp(ε ) (6)
03
En supposant la déformation plastique incompressible du matériau et en négligeant les déformations
élastiques, la déformation totale dans l’épaisseur pour le calcul de l’épaisseur instantanée peut être
déterminée approximativement par les déformations totales, majeure et mineure, vraies:
εε≈− −ε (7)
31 2
Sur la base du principe du travail plastique, la courbe contrainte-déformation biaxiale est une fonction
pl
de la déformation plastique dans l’épaisseur:σε()− , voir également l’Annexe C. En supposant un
B 3
comportement élastique linéaire isotrope et une incompressibilité plastique, la déformation plastique
dans l’épaisseur est alors donnée par:
1−ν
pl
εε=− −+ε 2 σ . (8)
3 12 B
E
Pour le module d’élasticité E et le coefficient de Poisson ν, les valeurs de la littérature sont en général
suffisantes pour soustraire la contribution élastique, par exemple E = 210 GPa et ν = 0,33 pour l’acier,
respectivement E = 70 GPa et ν = 0,33 pour les alliages d’aluminium.
Il convient que le rapport diamètre de la matrice sur épaisseur soit raisonnablement élevé pour assurer
un état de contraintes proche de celui d’une membrane dans l’éprouvette, et une influence négligeable
de la flexion. Pour les rapports diamètre de matrice sur épaisseur inférieurs à 100, il est recommandé de
vérifier si les déformations en flexion sont relativement faibles comparées au résultat de la déformation
vraie dans l’épaisseur ε3 en utilisant l’estimation suivante pour les déformations en flexion:
 t 
0
ε ≈−ln 1− exp(ε ) (9)
bending 3
 

 
NOTE La courbe contrainte-déformation biaxiale est obtenue sans aucune hypothèse sur le type de critère
d’écoulement. Cette courbe contrainte-déformation biaxiale peut être utilisée pour identifier la valeur de la
contrainte équi-biaxiale correspondant à l’écoulement de même que pour déterminer
...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 16808
ISO/TC 164/SC 2
Metallic materials — Sheet and strip
Secretariat: JISC
— Determination of biaxial stress-
Voting begins on:
2021-12-14 strain curve by means of bulge test
with optical measuring systems
Voting terminates on:
2022-03-08
Matériaux métalliques — Tôles et bandes — Détermination de
la courbe contrainte-déformation biaxiale au moyen de l'essai de
gonflement hydraulique avec systèmes de mesure optiques
ISO/CEN PARALLEL PROCESSING
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/FDIS 16808:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN-
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. © ISO 2021

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ISO/FDIS 16808:2021(E)
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ISO/FDIS 16808:2021(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms.1
5 Principle . 2
6 Test equipment .3
7 Optical measurement system. 5
8 Test piece . 6
8.1 General . 6
8.2 Application of grid . 6
8.2.1 Type of grid . 6
8.2.2 Grid application . 6
9 Procedure .6
10 Evaluation methods for the determination of the curvature and strains at the pole.7
11 Calculation of biaxial stress-strain curves . 8
12 Test report . 9
Annex A (informative) Test procedure for a quality check of the optical measurement
system.11
Annex B (informative) Computation of the curvature on the basis of a response surface .14
Annex C (informative) Determination of the equi-biaxial stress point of the yield locus and
the hardening curve .16
Bibliography .24
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ISO/FDIS 16808:2021(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 16808:2014), of which it constitutes a
minor revision. The changes are as follows:
— the designation of r in Table 1 has been modified;
1_100
— the title of Figure A.4 has been modified;
— Formula (B.2) has been modified;
— Annex A has been deleted and other annexes have been renumbered accordingly;
— the status of Annex A (formerly Annex B) has been changed to informative;
— minor editorial changes have been made to align with ISO/IEC Directives Part 2:2021.
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
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 16808:2021(E)
Metallic materials — Sheet and strip — Determination
of biaxial stress-strain curve by means of bulge test with
optical measuring systems
1 Scope
This document specifies a method for determination of the biaxial stress-strain curve of metallic
sheets having a thickness below 3 mm in pure stretch forming without significant friction influence. In
comparison with tensile test results, higher strain values can be achieved.
NOTE In this document, the term "biaxial stress-strain curve" is used for simplification. In principle, in the
test the "biaxial true stress-true strain curve" is determined.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols and abbreviated terms
The symbols and designations used are given in Table 1.
Table 1
Symbol Designation Unit
d Diameter of the die (inner) mm
die
d Diameter of the blank holder (inner) mm
BH
R Radius of the die (inner) mm
1
h Height of the drawn blank (outer surface) mm
t Initial thickness of the sheet (blank) mm
0
t Actual thickness of the sheet mm
p Pressure in the chamber MPa
rms Standard deviation (root mean square) -
ρ Radius of curvature mm
r Surface radius for determining curvature mm
1
r Surface radius for determining strain mm
2
r Surface radius to determine curvature with a mm
1_100
diameter of 100 mm
a , b Coefficients for response surface -
i i
1
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ISO/FDIS 16808:2021(E)
Table 1 (continued)
Symbol Designation Unit
σ Biaxial stress MPa
Β
e Engineering strain -
ε Major true strain -
1
ε Minor true strain -
2
ε True thickness strain -
3
ε Equivalent true strain -
Ε
l Coordinate and length of a section mm
s
dz Displacement in the z-direction mm
dz Displacement after movement correction mm
mv
5 Principle
A circular blank is completely clamped at the edge in a tool between die and blank holder. A bulge is
formed by pressing a fluid against the blank until final fracture occurs (Figure 1). During the test,
the pressure of the fluid is measured and the evolution of the deformation of the blank is recorded by
[1],[2],[3]
an optical measuring system . Based on the recorded deformation of the blank, the following
quantities near the centre of the blank are determined: the local curvature, the true strains at the
surface, and, by assuming incompressible deformation of the material, the actual thickness of the blank.
Furthermore, assuming the stress state of a thin-walled spherical pressure vessel at the centre of the
blank, the true stress is calculated from the fluid pressure, the thickness and the curvature radius.
NOTE In addition to the bulge test procedures with optical measurement systems introduced in Reference
[4] [5] [6] [7] [8] [9]
[1] and described in the following, there are also laser systems , , or tactile systems , , valid for bulge
test investigation, which are not covered in this document.
Key
h height of the drawn blank (outer surface) ρ radius of curvature
p pressure in the chamber t initial thickness of the sheet (blank)
0
ε true thickness strain (at the apex of the dome) t actual thickness of the sheet
3
d diameter of the die (inner)
die
Figure 1 — Principle of the bulge test
The coordinate origin shall be in the centre of the blank holder. The XY-plane should be parallel to the
surface of the blank holder (parallel to the clamped metal sheet before forming). Herein, the x-direction
corresponds to the rolling direction. The z-direction shall be normal to the clamped metal sheet before
forming, with the positive direction towards the optical sensor.
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ISO/FDIS 16808:2021(E)
6 Test equipment
6.1 The bulge test shall be carried out on a machine equipped with a die, a blank holder and a fluid
chamber. The proposed equipment is illustrated in Figure 2.
Key
1 deformation measurement system 3 chamber with fluid
2 lock bead 4 pressure measurement system
Figure 2 — Proposal of a testing equipment (principle drawing)
6.2 The layout of the test equipment shall be such that it is possible to continuously measure the
outside surface of the test piece continuously during the test, i.e. to be able to determine the deformation
of the geometry by recording the evolution of X, Y, Z coordinates of a grid of points on the bulging blank
surface, in order to calculate the shape and the true strains in the central area of interest until failure
occurs.
6.3 During the test, the system shall be able to measure optically (without contact) the X, Y, Z
coordinates of a grid of points on the bulging surface of the specimen. Out of these coordinates, the true
strains ε and ε for each point of the selected area, the thickness strain ε and the curvature radius ρ
1 2 3
for the apex of the dome are calculated.
6.4 The system should be equipped with a chamber fluid pressure measurement system. An indirect
measurement system is also possible. Starting from 20 % of the maximum measured pressure value,
the precision should be 1 % of the actual measured value.
6.5 The die, the blank holder and the fluid chamber shall be sufficiently rigid to minimize deformation
during testing. The blank-holder force shall be high enough to keep the blank holder closed. Any
movement of the test piece between the blank holder and die should be prevented. Typically during the
test, the bulge pressure is acting on parts of the blank holder reducing the effective blank-holder force.
This shall be taken in consideration when defining the necessary blank-holder force.
6.6 The fluid shall be in contact with the blank surface (without any air bubbles) to prevent energy
storage during the test through compressed air bubbles which would lead to higher energy release
and greater oil splashing at failure. No fluid shall be lost through the blank holder, die and sheet or
elsewhere during the test until failure occurs.
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ISO/FDIS 16808:2021(E)
6.7 A lock bead (or comparable geometry in the circular surface), designed to suppress any material
flow, is recommended. The lock bead shall not initiate cracks in the material. The lock bead shall be
located between blank holder and die. A location close to the die radius is recommended. The lock bead
geometry should avoid a curvature and a wrinkling of the blank when closing the tool and prevent the
sliding of the blank during the test.
6.8 It is recommended to place glass plates in front of the lenses and the illumination in order to
[7],[12]
protect the optical measuring system from oil splashing due to blank failure at the end of the test .
The plates can be fixed on the blank holder (thick glass) or near the camera lenses and illumination
(thinner glass); see Figure 3. The inserted protection shall not disturb the optical measurement quality
(see Clause 7). After each test, the glass plates shall be well cleaned without damaging or scratching
them and precisely repositioned to not alter calibration. Typically, a calibration of the optical system
including the protection increases the measurement quality.
6.9 The smallest die diameter recommended should have a ratio of die diameter to initial thickness
d / t ≥ 33 (see Figure 2). The radius of the die should not lead to cracks in the blank during the test. A
die 0
recommendation is (5 × t ) to (15 × t ) (maximum 15 mm).
0 0
a) b)
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ISO/FDIS 16808:2021(E)
c)
Key
1 lamp 4 test piece
2 cameras 5 fluid
3 glass plates
Figure 3 — Examples for possible positions of oil shielding plates and lamps
7 Optical measurement system
For the determination of the radius of curvature ρ, and the true strains ε and ε , an optical-deformation
1 2
field measurement system with the following characteristics is recommended.
— Optical sensor based on two or more cameras.
— Measurement area, where d ≥ 1/2 d
measurement area die.
The used measurement area should be larger than a concentric diameter of half the diameter of the
blank holder. This area should be observable during the entire forming process for all heights of the
drawn blank.
— Local resolution (grid distance between the independent measurement points): The distance g
max
between two adjacent points on the unformed blank should follow the requirement:
d
die
g ≤
max
50
— The determination of the curvature requires an accuracy of the z-coordinates in an area with a
diameter of 1/2 d concentric to the blank holder of
die
rmsd()z ⋅100mm
rmsd()z = ≤0,015mm
n
d
die
NOTE The accuracy of the shape measurement can be checked with a test of the optical measurement system
(see Annex A).
Accuracy for strain measurement:  rms (ε ) = 0,003  rms (ε ) = 0,003
1 2
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ISO/FDIS 16808:2021(E)
For each real strain value for the mentioned rms (ε) above, the acceptable measurement values are:
ε = 0  acceptable measurement range:  –0,003 … 0,003
real
ε = 0,5  acceptable measurement range:  0,497 … 0,503
real
— Missing measurement points: In order to avoid unbalanced curvature approximations, only the
absence of less than 5 % of the measurement points in the concentric area with a diameter = 1/2 d
die
is acceptable (without interpolation). If adjacent points are missing, the inscribed circle of this area
shall not be larger than two points.
8 Test piece
8.1 General
The test piece shall be flat and of such shape that the blank is clamped and material flow is stopped. The
use of lock beads is recommended. The edge of the blank shall be outside the lock bead.
The preparation of the blank does not influence the results as long as the surface of the test piece was
not damaged (scratches, polishing). The dimension of the outer edges can be circular (preferred) or
angular.
8.2 Application of grid
8.2.1 Type of grid
For optical full-field measurement devices, the grid shall fulfil two objectives:
a) the curvature radius determination of the specimens’ surface;
b) the strain calculation of the material deformation.
8.2.2 Grid application
Deterministic grids (e.g. squares, circles, dots) should have a strong contrast and have to be applied
without any notch effect and/or change in microstructure. Some common application techniques are:
— electrochemical etching, photochemical etching, offset printing and grid transfer;
— stochastic (speckle) patterns which can be applied by spraying paint on the surface of test piece
surfaces. Paint adherence to the surface after deformation should be checked. It is possible first to
spray a thin, matt, white base layer to reduce reflections from the test piece surfaces, then to spray
a cloud of randomly distributed black spots (e.g. black spray paint or graphite). The spray shall be
both elastic and tough enough not to crack or peel off during deformation. The random distribution
of the fine sprayed spots allows the determination of each point of the virtual grid on the specimen.
The pattern should have sufficient black/white density and appropriate size features in each point
position search area as required by the optical system used.
9 Procedure
9.1 The test shall be carried out at an ambient temperature of (23 ± 5) °C.
9.2 Determine the initial thickness of the test piece to the nearest 0,01 mm.
9.3 Clamp the test piece between blank holder and die. Avoid air bubbles between test piece and fluid
to prevent formation of compressed air during testing, leading to stronger oil splashing at failure.
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ISO/FDIS 16808:2021(E)
−1
9.4 A constant strain rate of 0,05 s is recommended. If a constant strain rate is not possible, a
constant forming velocity of the punch or fluid should be guaranteed. In order to avoid big influences in
the biaxial stress-strain curve of temperature or strain rate sensitive materials, the bulge test should
be conducted in 2 min to 4 min. This time frame guarantees slow and acceptable strain rates and a cost-
effective testing time.
The plot of the strain rate versus time is recommended.
9.5 Measure the fluid pressure during the test.
9.6 Measure the X, Y, Z coordinates of the grid on the test piece surface during the test.
9.7 The fluid pressure data and forming data shall be measured and saved at the same time scale.
A minimum of 100 values is recommended. In order to represent the whole strain and pressure
development, at least 100 images of the bulge testing are recommended.
9.8 The failure of the test piece shall be considered as obtained when a through crack, i.e. a crack
which goes through the thickness of the test piece, has occurred. The failure is detected by decreasing
fluid pressure, which defines the end of the test.
9.9 A sufficient number of test pieces should be prepared in order to achieve at least three valid tests.
10 Evaluation methods for the determination of the curvature and strains at the
pole
For the following explanation of the calculation of the curvature and strains, a spherically shaped
surface near the pole is assumed (best-fit sphere). On the last image before failure, as defined in 9.8,
the area of the dome with the highest deformation is selected and defined as the position where to
determine the true stress and the true thickness strain ε . To obtain a stable radius of curvature of the
3
dome, a best-fit sphere can be calculated based on a selected area of points. For this selection, a radius
r is defined around the apex of the dome in the last image before bursting and the fit is performed for
1
all forming stages with the same selection of points (Figure 4).
A certain number of the first forming stages (images) are rejected, since the specimen is still too flat
for a reliable determination of the best-fit sphere, since the bending radius is very high and the fit is
not stable. For robust values of the true strain and thinning in the apex, the average value of a number
of selected points is taken. Therefore, a second area is defined by a radius r in a similar manner (see
2
Figure 4).
Based on this procedure, for every forming stage (image) the radius of curvature, the average thickness
strains, as well as the corresponding thickness and stress values at the dome apex are calculated. This
evaluation can be carried out for different r and r values (see Figure 4).
1 2
For a good convergence and robust values, the recommended range of r and r is defined:
1 2
r = (0,125 ± 0,025) × d (1)
1 die
r = (0,05 ± 0,01) × d (2)
2 die
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ISO/FDIS 16808:2021(E)
Figure 4 — Choice of r and r for calculation of true stress and true strain for each forming
1 2
stage
An alternative proposal for the calculation of the curvature and strains is given in Annex B.
11 Calculation of biaxial stress-strain curves
For the calculation of the biaxial stress-strain curves, a simple membrane stress state of a thin-
walled spherical pressure vessel is assumed at the centre of the blank. This implies the following
simplifications:
a) equi-biaxial stress state:
σσ==σ (3)
12 B
b) representation of the curvature by the mean curvature radius:
−1
1
 
ρρ=+()11 ρ (4)
12
 
2
 
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ISO/FDIS 16808:2021(E)
Then the biaxial true stress can be calculated according to the following equation:
ρp
σ = (5)
B
2t
using the fluid pressure p, the curvature radius ρ and the actual thickness t, with
tt= exp(ε ) (6)
03
Assuming plastic incompressible deformation of the material and neglecting elastic strains, the total
thickness strain for the calculation of the actual thickness can be approximated by the total major and
minor true strain:
εε≈− −ε (7)
31 2
Based on the plastic work principle, the biaxial stress-strain curve is a function of the plastic thickness
pl
strain:σε()− , see also Annex C. Assuming an isotropic linear elastic material behaviour and plastic
B
3
incompressibility, the plastic thickness strain is then given by:
1−ν
pl
εε=− −+ε 2 σ (8)
12 B
3
E
For the elasticity modulus E and the Poisson ratio ν, literature values are generally sufficient to subtract
the elastic contribution, e.g. E = 210 GPa and ν = 0,33 for steel, respectively E = 70 GPa and ν = 0,33 for
aluminium alloys.
The ratio of die diameter to thickness should be reasonably high to ensure a near membrane stress
state in the test piece, and a negligible influence of bending. For die diameter to thickness ratios lower
than 100, it is recommended to check if the bending strains are relatively small compared to the actual
thickness strain result ε using the following estimate for the bending strains:
3
t
 
0
ε ≈−ln 1− exp(ε ) (9)
bending  3 

 
NOTE The biaxial stress-strain curve is obtained without any assumption on the type of yield criterion. This
biaxial stress-strain curve can be used to identify the equi-biaxial stress point of the yield locus as well as to
approximate the material hardening curve beyond uniform elongation.
Annex C gives a proposal for the determination of the equi-biaxial stress point of the yield criterion and
for using the biaxial stress-strain curves of hydraulic bulge tests to extrapolate an equivalent stress-
strain curve which is based on uniaxial tension tests.
12 Test report
The test report shall contain at least the following information:
a) reference to this document i.e. ISO 16808:—;
b) identification of laboratory that measured the bulge test values, including the name of operator;
c) identification of material;
d) initial thickness of blank;
e) grid, camera system and software used;
f) position of the protective glasses;
g) geometries of the test equipment;
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ISO/FDIS 16808:2021(E)
h) bulge / piston speed;
i) bulge test evaluation method, respectively the parameters for identification of the curvature and
the average of strain;
j) number of replications;
k) for each bulge test, a table of values with the history of time, radius ρ, pressure p, absolute value of
plastic thickness strain and biaxial true stress;
l) biaxial stress-strain curves of all bulge tests as a plot.
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ISO/FDIS 16808:2021(E)
Annex A
(informative)

Test procedure for a quality check of the optical measurement
system
A.1 Test procedure
Regarding the recommended quality of the optical measurement system (see Clause 7) and the
setup for example according to Figure 3, it shall be taken into account that the additional glass plates
in the optical path can have a significant influence. For a check of the final quality for the complete
experimental setup, the following procedure (see Figure A.1) is recommended.
Key
1 lamp 4 sheet metal
2 cameras 5 reference plate
3 glass plates 6 maximum height
Figure A.1 — Quality check of optical measurement system
A rigid test object (e.g. plate, 3-dimensional curved surface) with a diameter ≥ 1/2 d shall be used.
die
The object shall not to be deformed during the test procedure. The object should have an appropriate
surface for the measurement system.
The test object shall be measured on the initial sheet clamping position once without protection glass
plates (reference measurement).
The test object shall be measured with the complete measurement setup (including the protection
glass plate) in different positions (5 to 10) between initial sheet clamping position and the maximum
estimated bulge height h (see Figure A.1).
max
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ISO/FDIS 16808:2021(E)
A.2 Post-processing
The coordinates for all measurement po
...

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