Metallic materials -- Sheet and strip -- Biaxial tensile testing method using a cruciform test piece

This document specifies the method for measuring the stress-strain curves of sheet metals subject to biaxial tension using a cruciform test piece fabricated from a sheet metal sample. The applicable thickness of the sheet is 0,1 mm or more and 0,08 times or less of the arm width of the cruciform test piece (see Figure 1). The test temperature ranges from 10 °C to 35 °C. The amount of plastic strain applicable to the gauge area of the cruciform test piece depends on the force ratio, slit width of the arms, work hardening exponent (n-value) (see Annex B) and anisotropy of a test material.

Matériaux métalliques -- Tôles et bandes -- Méthode d'essai de traction biaxiale sur éprouvette cruciforme

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Publication Date
15-Jul-2021
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5060 - Close of voting Proof returned by Secretariat
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Completion Date
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INTERNATIONAL ISO
STANDARD 16842
Second edition
2021-07
Metallic materials — Sheet and strip
— Biaxial tensile testing method using
a cruciform test piece
Matériaux métalliques — Tôles et bandes — Méthode d'essai de
traction biaxiale sur éprouvette cruciforme
Reference number
ISO 16842:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO 16842:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 16842:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Principle ........................................................................................................................................................................................................................ 2

5 Test piece ...................................................................................................................................................................................................................... 2

5.1 Shape and dimensions ...................................................................................................................................................................... 2

5.2 Preparation of the test pieces..................................................................................................................................................... 3

6 Testing method ....................................................................................................................................................................................................... 4

6.1 Testing machine ..................................................................................................................................................................................... 4

6.2 Measurement method of force and strain ....................................................................................................................... 5

6.2.1 General...................................................................................................................................................................................... 5

6.2.2 Measurement method of force ............................................................................................................................. 5

6.2.3 Measurement method of strain ........................................................................................................................... 5

6.2.4 Strain measurement positions ............................................................................................................................. 5

6.3 Installation of the test piece to a biaxial tensile testing machine ......... ....................................................... 6

6.4 Testing methods ..................................................................................................................................................................................... 7

7 Determination of biaxial stress-strain curves ....................................................................................................................... 7

7.1 General ........................................................................................................................................................................................................... 7

7.2 Determination of the original cross-sectional area of the test piece ........................................................ 7

7.3 Determination of true stress ....................................................................................................................................................... 7

7.4 Determination of true strain ....................................................................................................................................................... 8

7.5 Determination of true plastic strain ..................................................................................................................................... 9

8 Test report ................................................................................................................................................................................................................11

8.1 Information in the report ............................................................................................................................................................11

8.2 Additional note ....................................................................................................................................................................................11

Annex A (informative) Method for measuring a yield surface ................................................................................................12

Annex B (informative) Factors affecting the maximum equivalent plastic strain applicable

to the gauge area of the test piece ...................................................................................................................................................16

Annex C (informative) Biaxial tensile testing machine ..................................................................................................................19

Bibliography .............................................................................................................................................................................................................................23

© ISO 2021 – All rights reserved iii
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ISO 16842:2021(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.

This second edition cancels and replaces the first edition (ISO 16842:2014), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— the font of “a” Figure 1 has been modified to “a”;
— the description in 6.1 h) has been modified for clarity;
— the title of Figure 2 b) has been modified for clarity;

— ISO 10275 has been moved from Clause 2 (Normative references) to the Bibliography;

— ISO 7500-1 has been added to Clause 2 (Normative references);
— the font of “C” Figure C.2 has been modified to “C”;
— general editorial corrections have been made.

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 © ISO 2021 – All rights reserved
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ISO 16842:2021(E)
Introduction

This document specifies the testing method for measuring the biaxial stress-strain curves of sheet

metals subject to biaxial tension at an arbitrary stress ratio using a cruciform test piece made of flat

sheet metals. The document applies to the shape and strain measurement position for the cruciform

test piece. The biaxial tensile testing machine is described in Annex C, only in terms of the typical

example of the machine and the requirements with which the machine ought to conform.

The cruciform test piece recommended in this document has the following features:

a) the gauge area of the test piece ensures superior homogeneity of stress, enabling measurement of

biaxial stress with satisfactory accuracy;

b) capability of measuring the elasto-plastic deformation behaviour of sheet metals at arbitrary stress

or strain rate ratios;

c) free from the out-of-plane deformation as is encountered in the hydrostatic bulge testing method;

d) easy to fabricate from a flat metal sheet by laser cutting, water jet cutting, or other alternative

manufacturing methods.
© ISO 2021 – All rights reserved v
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INTERNATIONAL STANDARD ISO 16842:2021(E)
Metallic materials — Sheet and strip — Biaxial tensile
testing method using a cruciform test piece
1 Scope

This document specifies the method for measuring the stress-strain curves of sheet metals subject

to biaxial tension using a cruciform test piece fabricated from a sheet metal sample. The applicable

thickness of the sheet is 0,1 mm or more and 0,08 times or less of the arm width of the cruciform test

piece (see Figure 1). The test temperature ranges from 10 °C to 35 °C. The amount of plastic strain

applicable to the gauge area of the cruciform test piece depends on the force ratio, slit width of the

arms, work hardening exponent (n-value) (see Annex B) and anisotropy of a test material.

2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 80000-1, Quantities and units — Part 1: General

ISO 7500-1, Metallic materials — Calibration and verification of static uniaxial testing machines — Part 1:

Tension/compression testing machines —Calibration and verification of the force-measuring system

3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
cruciform test piece

test piece which is recommended in the biaxial tensile test and whose geometry is specified in this

document
Note 1 to entry: See Figure 1.
3.2
gauge area

square area which is located in the middle of the cruciform test piece and is enclosed by the four arms

of the cruciform test piece
Note 1 to entry: See Figure 1.
3.3
arm
generic name for all areas other than the gauge area in the cruciform test piece

Note 1 to entry: The arms play a role of transmitting tensile forces in two orthogonal directions to the gauge area

of the cruciform test piece (see Figure 1).
© ISO 2021 – All rights reserved 1
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ISO 16842:2021(E)
3.4
biaxial tensile testing machine

testing machine for applying biaxial tensile forces to a cruciform test piece in the orthogonal directions

parallel to the arms of the test piece
Note 1 to entry: See Annex C.
3.5
yield surface

group of stress determined in a stress space, at which a metal starts plastic deformation when probing

from the elastic region into the plastic range
Note 1 to entry: See Annex A and Reference [1].
3.6
yield function

mathematical function used to generate the conditional equation (yield criterion) to which the stress

components ought to conform when the material subject to the stress is in the plastic deformation state

Note 1 to entry: See Annex A.
3.7
contour of plastic work

graphic figure derived by subjecting the material to plastic deformation along various linear stress

paths and plotting the stress points in stress space at the instance when the plastic work consumed per

unit volume along each stress path becomes identical and the plotted stress points are approximated

into either a smooth curve or curved surface
Note 1 to entry: See Annex A.
4 Principle

Measurement is made at room temperature on the yield stress and the stress-strain curves of sheet

metals under biaxial tensile stresses by measuring simultaneously and continuously the biaxial tensile

forces and strain components applied to the gauge area of a cruciform test piece while applying biaxial

tensile forces in the orthogonal directions parallel to the arms of the test piece. The test piece is made

of a flat sheet metal and has a uniform thickness. The measured biaxial stress-strain curves are used to

determine contours of plastic work of the sheet samples (see Annex A). According to the finite element

analyses of the cruciform test piece (as recommended in Clause 5) and the strain measurement position

[2][3]

(as specified in 6.2.4), the stress calculation error is estimated to be less than 2,0 % .

5 Test piece
5.1 Shape and dimensions

Figure 1 shows the shape and dimensions of the cruciform test piece recommended in document. The

test piece shall be as described as follows:

a) In principle, the thickness of a test piece, a, shall be the same as that of the as-received sheet sample,

without any work done in the thickness direction. See 5.1 b) for an exception to the rule.

b) The arm width, B, should be 30 mm or more, except where it is determined according to the

agreement between parties involved in transaction. It shall satisfy a ≤ 0,08B and should be accurate

to within ±0,1 mm for all four arms. The sheet thickness can be reduced to satisfy a ≤ 0,08B

according to the agreement between the parties involved in transaction.

c) Seven slits per one arm shall be made. Specifically, one slit shall be made on the centreline (x-axis

or y-axis) of the test piece with a positional accuracy of ±0,1 mm, and three slits shall be made at an

interval of B/8 with a positional accuracy of ±0,1 mm on each side of the centreline. All slits shall

2 © ISO 2021 – All rights reserved
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ISO 16842:2021(E)

have the same length, L, and should be accurate to within ±0,1 mm. The relationship of B ≤ L ≤ 2B

should be established. The opposing slit ends shall be made at an equal distance, B /2 and B /2,

Sx Sy
from the centreline with a positional accuracy of B/2 ± 0,1 mm.

d) The slit width, w , should be made as small as possible (see Figure B.2), preferably less than 0,3 mm.

e) The grip length, C, is considered to be sufficient if it can secure the test piece to the grips of the

biaxial tensile testing machine and can transmit the necessary tensile force to the test piece. The

standard grip length would be B/2 ≤ C ≤ B, but it can be determined arbitrarily according to the

agreement between the parties involved in the transaction.

f) An alternative test piece geometry can be used. In the use of the alternative cruciform test pieces,

the evidence of the stress measurement accuracy shall be clarified between the contractual

partners.
5.2 Preparation of the test pieces

a) The permitted variations in thickness and the permitted variations from a flat surface of the sheet

metal sample from which the cruciform test pieces are taken shall be in accordance with relevant

product standards or national standards.

b) The standard sampling direction of the test piece shall be such that the directions of arms are

parallel to the rolling (x) and transverse (y) directions of the sheet sample, respectively. The test

piece sampling direction can be determined according to the agreement between parties involved

in transaction.

c) For the fabrication of the test piece (including making of slits), any method, e.g. laser cutting, water

jet cutting, or other alternative manufacturing methods, demonstrated to work satisfactorily can

be used if agreed upon by the parties.

d) Unless otherwise specified and except for the sampling work, unnecessary deformation or heating

to the test piece shall be avoided.
© ISO 2021 – All rights reserved 3
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ISO 16842:2021(E)
Key
1 gauge area
2 arm
3 grip
4 slit
a thickness of a test piece
B arm width
B distance between opposing slit ends in the x direction
B distance between opposing slit ends in the y direction
C grip length
L slit length
R corner radius at the junctions of arms to the gauge area
w slit width
[2][3]
Figure 1 — Standard shape and dimensions of the recommended cruciform test piece
6 Testing method
6.1 Testing machine

The specifications required for the biaxial tensile testing machine (hereinafter referred to as testing

machine) are as follows (for examples of typical testing machines, see Annex C):

a) It shall have sufficient functions and durability to hold four grips of a cruciform test piece

(hereinafter referred to as test piece) in one single plane with a tolerance of ±0,1 mm during testing.

b) Two opposing grips shall move along a single straight line (hereinafter referred to as x-axis and

y-axis), and the x- and y-axes shall intersect at an angle of 90° ± 0,1° (The plane that contains the x-

and y-axes is referred to as the reference plane, while the intersection of x- and y-axes is referred to

as the centre of testing machine).

c) It shall have a function for adjusting the two opposing grips to the position at an equal distance

from the centre of the testing machine with a tolerance of ±0,1 mm before the installation of a test

piece to the grips.

d) It shall have a function for enabling the installation of a test piece to the grips while aligning the

centre of the test piece to the centre of the testing machine.
4 © ISO 2021 – All rights reserved
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ISO 16842:2021(E)

e) It shall have a function for enabling equal displacement of two opposing grips or the maintenance of

the centre of the test piece always on the centre of the testing machine with a tolerance of ±0,1 mm

during biaxial tensile test (for example, the testing machines shown in Figures C.1 and C.2 use a

link mechanism to ensure equivalent displacement of two opposing grips).

f) It shall have a capability of servo-controlled biaxial tensile testing to perform a test with a constant

nominal stress ratio (constant force ratio) and/or a test with a constant true stress ratio, and/or a

test with a constant strain-rate ratio, according to the purpose of the test (see C.2). For a link type

biaxial tensile testing machine, it shall ensure equal displacement of two opposing grips (see C.3).

g) Modern control electronics allow independent and combined control of each actuator. This is called

modal control (see C.4).

h) It shall have a function for measuring and storing the values of the tensile forces (two channels,

one for each of the two axes, x and y) and strain components (two channels, one for each of the two

axes, x and y) during biaxial tensile test with the specified accuracy and time interval agreed by the

parties concerned.
6.2 Measurement method of force and strain
6.2.1 General

This subclause specifies the method for measuring the tensile forces (F , F ) and nominal strain

x y
components (e , e ) applied to the x and y directions of a cruciform test piece.
x y
6.2.2 Measurement method of force

For measurement of F and F , load cells shall be used in the x and y directions. The force-measuring

x y

system of the testing machine shall be calibrated in accordance with ISO 7500-1, class 1, or better.

6.2.3 Measurement method of strain

For measurement of e and e , strain gauges or other methods (e.g. an optical measurement system)

x y
shall be used. Measure e and e to the nearest 0,000 1 or better.
x y
6.2.4 Strain measurement positions

Figure 2 shows the position(s) of a strain gauge (or strain gauges) for measuring e and e . e and e

x y x y

shall be measured at a position, with a distance of (0,35 ± 0,05)B from the centre of test piece, on

the centreline parallel to the maximum tensile force. The strain measurement position can also be

determined according to the agreement between parties involved in transaction.

NOTE According to the finite element analyses of the cruciform test piece as recommended in Clause 5 and

the strain measurement position as specified in Figure 2, the stress calculation error is estimated to be less than

[2][3]
2,0 % .
© ISO 2021 – All rights reserved 5
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ISO 16842:2021(E)
a1) F ≥ F a2) F ≤ F
x y x y
a) A case of measuring e and e using a biaxial strain gauge
x y,
b1) F ≥ F b2) F ≤ F
x y x y
b) A case of measuring e and e using two uniaxial strain gauges
x y,
Key
B arm width
e nominal strain in the x direction
e nominal strain in the y direction
F tensile force in the x direction
F tensile force in the y direction
[2][3]
Figure 2 — Strain measurement position
6.3 Installation of the test piece to a biaxial tensile testing machine

The test piece shall be fixed by four grips of a biaxial tensile testing machine. Care shall be taken to

ensure alignment of the centre of the test piece with the centre of the testing machine.

6 © ISO 2021 – All rights reserved
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ISO 16842:2021(E)
6.4 Testing methods

While keeping the force ratio, true stress ratio, strain-rate ratio, or the grip displacement-rate ratio

constant, biaxial tensile forces shall be applied to the test piece. F , F and e , e shall be measured with

x y x y

constant time intervals and the data shall be recorded on appropriate equipment. The test ends when

the desired strain or stress level is achieved, or should be ended when fracture or localized necking

−1 −1

occurs in the arm or gauge area. The recommended strain-rate is 0,1 s to 0,0001 s .

NOTE A similar testing method has been used for abrupt strain path changes (see Annex A.3).

7 Determination of biaxial stress-strain curves
7.1 General

Using the measured values of F , F and e , e , the stress-strain curves in the x and y directions of the

x y x y

cruciform test piece shall be determined. These curves are used to determine contours of plastic work

for the test material (see A.2).
7.2 Determination of the original cross-sectional area of the test piece

Calculate the original cross-sectional areas of the gauge area perpendicular to the x- and y-axes, A and

A , from Formulae (1) and (2):
Aa=×B (1)
SxyS
Aa=×B (2)
SyxS
where
a is the thickness of the test piece, expressed in mm;
B is the distance between opposing slit ends on the x axis, expressed in mm;
B is the distance between opposing slit ends on the y axis, expressed in mm.

Measure a to the nearest 0,01 mm or better using a micrometer with sufficient resolution. B and B

Sx Sy

shall be determined to the nearest 0,1 mm or better using a measuring device with sufficient resolution.

The calculated values of A and A shall be rounded to 0,1 mm according to ISO 80000-1.

Sx Sy
7.3 Determination of true stress

Calculate the true stress components in the x and y directions, σ and σ , from Formulae (3) and (4):

x y
σ =+()1 e (3)
x x
σ =+()1 e (4)
y y
where
© ISO 2021 – All rights reserved 7
---------------------- Page: 12 ----------------------
ISO 16842:2021(E)

A is the original cross-sectional areas of the gauge area perpendicular to the x-axes, expressed in

mm ;

A is the original cross-sectional areas of the gauge area perpendicular to the y-axes, expressed in

mm ;

e is the nominal strain in the x direction measured by the method described in 6.2;

e is the nominal strain in the y direction measured by the method described in 6.2;

F is the tensile force in the x direction, expressed in N;
F is the tensile force in the y direction, expressed in N.
7.4 Determination of true strain

Calculate the true strain components in the x and y directions, ε and ε , from Formulae (5) and (6):

x y
ε = ln(1 + e) (5)
x x
ε = ln(1 + e) (6)
y y
where

e is the nominal strain in the x direction measured by the method, as described in 6.2;

e is the nominal strain in the y direction measured by the method, as described in 6.2.

ε and ε shall be calculated to the digit of 10 from Formulae (5) and (6), and the result shall be

x y
rounded to the digit of 10 according to ISO 80000-1.

Examples of the measured biaxial true stress-true strain curves for a cold rolled ultralow carbon steel

sheet are shown in Figure 3.
8 © ISO 2021 – All rights reserved
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ISO 16842:2021(E)
a) A case of F :F = 1:1 b) A case of F :F = 2:1
x y x y
Key
X ε ε
x, y
Y σ σ / MPa
x, y

C slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, in MPa

x x x

C slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, in MPa

y y y
F tensile force in the x direction, in N
F tensile force in the y direction, in N
ε true strain in the x direction
ε true strain in the y direction
σ true stress in the x direction, in MPa
σ true stress in the y direction, in MPa
Uniaxial tensile true stress-true strain curve.

NOTE The uniaxial tensile true stress-true strain curve in the rolling direction (RD) of the same material is

also shown for comparison.

Figure 3 — Examples of true stress-true strain curves measured in the biaxial tensile test of

cold rolled ultralow carbon steel sheet
7.5 Determination of true plastic strain
p p

Calculate the true plastic strain components in the x and y directions, ε and ε , from Formulae (7)

x y
and (8):
εε=− (7)
εε=− (8)
where
© ISO 2021 – All rights reserved 9
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ISO 16842:2021(E)

C is the slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, expressed

x x x
in MPa;

C is the slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, expressed

y y y
in MPa;
ε is the true strain in the x direction;
ε is the true strain in the y direction;
σ is the true stress in the x direction, expressed in MPa;
σ is the true stress in the y direction, expressed in MPa.
p p −5

ε and ε shall be calculated to the digit of 10 from Formulae (7) and (8), and the result shall be

x y
rounded to the digit of 10 according to ISO 80000-1.

Examples of measured true stress-true plastic strain curves corresponding to Figure 3 are shown in

Figure 4.
a) A case of F :F = 1:1 b) A case of F :F = 2:1
x y x y
Key
X p p
ε , ε
x y
Y σ σ / MPa
x, y
F tensile force in the x direction, in N
F tensile force in the y direction, in N
p true plastic strain in the x direction
true plastic strain in the y direction
σ true stress in the x direction, in MPa
σ true stress in the y direction, in MPa
Uniaxial tensile true stress-true plastic strain curve.

NOTE The uniaxial tensile true stress-true plastic strain curve in the rolling direction (RD) of the same

material is also shown for comparison.
...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 16842
ISO/TC 164/SC 2
Metallic materials — Sheet and strip
Secretariat: JISC
— Biaxial tensile testing method using
Voting begins on:
2021­04­14 a cruciform test piece
Voting terminates on:
Matériaux métalliques — Tôles et bandes — Méthode d'essai de
2021­06­09
traction biaxiale sur éprouvette cruciforme
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 16842:2021(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
---------------------- Page: 1 ----------------------
ISO/FDIS 16842:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

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
CH­1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 16842:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Principle ........................................................................................................................................................................................................................ 2

5 Test piece ...................................................................................................................................................................................................................... 2

5.1 Shape and dimensions ...................................................................................................................................................................... 2

5.2 Preparation of the test pieces..................................................................................................................................................... 3

6 Testing method ....................................................................................................................................................................................................... 4

6.1 Testing machine ..................................................................................................................................................................................... 4

6.2 Measurement method of force and strain ....................................................................................................................... 5

6.2.1 General...................................................................................................................................................................................... 5

6.2.2 Measurement method of force ............................................................................................................................. 5

6.2.3 Measurement method of strain ........................................................................................................................... 5

6.2.4 Strain measurement positions ............................................................................................................................. 5

6.3 Installation of the test piece to a biaxial tensile testing machine ......... ....................................................... 6

6.4 Testing methods ..................................................................................................................................................................................... 6

7 Determination of biaxial stress-strain curves ....................................................................................................................... 7

7.1 General ........................................................................................................................................................................................................... 7

7.2 Determination of the original cross­sectional area of the test piece ........................................................ 7

7.3 Determination of true stress ....................................................................................................................................................... 7

7.4 Determination of true strain ....................................................................................................................................................... 8

7.5 Determination of true plastic strain ..................................................................................................................................... 8

8 Test report ................................................................................................................................................................................................................10

8.1 Information in the report ............................................................................................................................................................10

8.2 Additional note ....................................................................................................................................................................................10

Annex A (informative) Method for measuring a yield surface ................................................................................................11

Annex B (informative) Factors affecting the maximum equivalent plastic strain applicable

to the gauge area of the test piece ...................................................................................................................................................15

Annex C (informative) Biaxial tensile testing machine ..................................................................................................................18

Bibliography .............................................................................................................................................................................................................................22

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ISO/FDIS 16842:2021(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 non­governmental, 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.

This second edition cancels and replaces the first edition (ISO 16842:2014), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— the font of “a” Figure 1 has been modified to “a”;
— the description in 6.1 h) has been modified for clarity;
— the title of Figure 2 b) has been modified for clarity;

— ISO 10275 has been moved from Clause 2 (Normative references) to the Bibliography;

— the font of “C” Figure C.2 has been modified to “C”;
— general editorial corrections have been made.

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.
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ISO/FDIS 16842:2021(E)
Introduction

This document specifies the testing method for measuring the biaxial stress-strain curves of sheet

metals subject to biaxial tension at an arbitrary stress ratio using a cruciform test piece made of flat

sheet metals. The document applies to the shape and strain measurement position for the cruciform

test piece. The biaxial tensile testing machine is described in Annex C, only in terms of the typical

example of the machine and the requirements with which the machine ought to conform.

The cruciform test piece recommended in this document has the following features:

a) the gauge area of the test piece ensures superior homogeneity of stress, enabling measurement of

biaxial stress with satisfactory accuracy;

b) capability of measuring the elasto-plastic deformation behaviour of sheet metals at arbitrary stress

or strain rate ratios;

c) free from the out-of-plane deformation as is encountered in the hydrostatic bulge testing method;

d) easy to fabricate from a flat metal sheet by laser cutting, water jet cutting, or other alternative

manufacturing methods.
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 16842:2021(E)
Metallic materials — Sheet and strip — Biaxial tensile
testing method using a cruciform test piece
1 Scope

This document specifies the method for measuring the stress-strain curves of sheet metals subject

to biaxial tension using a cruciform test piece fabricated from a sheet metal sample. The applicable

thickness of the sheet is 0,1 mm or more and 0,08 times or less of the arm width of the cruciform test

piece (see Figure 1). The test temperature ranges from 10 °C to 35 °C. The amount of plastic strain

applicable to the gauge area of the cruciform test piece depends on the force ratio, slit width of the

arms, work hardening exponent (n-value) (see Annex B), and anisotropy of a test material.

2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 80000­1, Quantities and units — Part 1: General
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
cruciform test piece

test piece which is recommended in the biaxial tensile test and whose geometry is specified in this

document
Note 1 to entry: See Figure 1.
3.2
gauge area

square area which is located in the middle of the cruciform test piece and is enclosed by the four arms

of the cruciform test piece
Note 1 to entry: See Figure 1.
3.3
arm
generic name for all areas other than the gauge area in the cruciform test piece

Note 1 to entry: The arms play a role of transmitting tensile forces in two orthogonal directions to the gauge area

of the cruciform test piece (see Figure 1).
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ISO/FDIS 16842:2021(E)
3.4
biaxial tensile testing machine

testing machine for applying biaxial tensile forces to a cruciform test piece in the orthogonal directions

parallel to the arms of the test piece
Note 1 to entry: See Annex C.
3.5
yield surface

group of stress determined in a stress space, at which a metal starts plastic deformation when probing

from the elastic region into the plastic range
Note 1 to entry: See Annex A and Reference [1].
3.6
yield function

mathematical function used to generate the conditional equation (yield criterion) to which the stress

components ought to conform when the material subject to the stress is in the plastic deformation state

Note 1 to entry: See Annex A.
3.7
contour of plastic work

graphic figure derived by subjecting the material to plastic deformation along various linear stress

paths and plotting the stress points in stress space at the instance when the plastic work consumed per

unit volume along each stress path becomes identical and the plotted stress points are approximated

into either a smooth curve or curved surface
Note 1 to entry: See Annex A.
4 Principle

Measurement is made at room temperature on the yield stress and the stress-strain curves of sheet

metals under biaxial tensile stresses by measuring simultaneously and continuously the biaxial tensile

forces and strain components applied to the gauge area of a cruciform test piece while applying biaxial

tensile forces in the orthogonal directions parallel to the arms of the test piece. The test piece is made

of a flat sheet metal and has a uniform thickness. The measured biaxial stress-strain curves are used to

determine contours of plastic work of the sheet samples (see Annex A). According to the finite element

analyses of the cruciform test piece (as recommended in Clause 5) and the strain measurement position

[2][3]

(as specified in 6.2.4), the stress calculation error is estimated to be less than 2,0 % .

5 Test piece
5.1 Shape and dimensions

Figure 1 shows the shape and dimensions of the cruciform test piece recommended in document. The

test piece shall be as described as follows:

a) In principle, the thickness of a test piece, a, shall be the same as that of the as­received sheet sample,

without any work done in the thickness direction. See 5.1 b) for an exception to the rule.

b) The arm width, B, should be 30 mm or more, except where it is determined according to the

agreement between parties involved in transaction. It shall satisfy a ≤ 0,08B and should be accurate

to within ±0,1 mm for all four arms. The sheet thickness can be reduced to satisfy a ≤ 0,08B

according to the agreement between the parties involved in transaction.

c) Seven slits per one arm shall be made. Specifically, one slit shall be made on the centreline (x-axis

or y-axis) of the test piece with a positional accuracy of ±0,1 mm, and three slits shall be made at an

interval of B/8 with a positional accuracy of ±0,1 mm on each side of the centreline. All slits shall

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ISO/FDIS 16842:2021(E)

have the same length, L, and should be accurate to within ±0,1 mm. The relationship of B ≤ L ≤ 2B

should be established. The opposing slit ends shall be made at an equal distance, B /2 and B /2,

Sx Sy
from the centreline with a positional accuracy of B/2 ± 0,1 mm.

d) The slit width, w , should be made as small as possible (see Figure B.2), preferably less than 0,3 mm.

e) The grip length, C, is considered to be sufficient if it can secure the test piece to the grips of the

biaxial tensile testing machine and can transmit the necessary tensile force to the test piece. The

standard grip length would be B/2 ≤ C ≤ B, but it can be determined arbitrarily according to the

agreement between the parties involved in the transaction.

f) An alternative test piece geometry can be used. In the use of the alternative cruciform test pieces,

the evidence of the stress measurement accuracy shall be clarified between the contractual

partners.
5.2 Preparation of the test pieces

a) The permitted variations in thickness and the permitted variations from a flat surface of the sheet

metal sample from which the cruciform test pieces are taken shall be in accordance with relevant

product standards or national standards.

b) The standard sampling direction of the test piece shall be such that the directions of arms are

parallel to the rolling (x) and transverse (y) directions of the sheet sample, respectively. The test

piece sampling direction can be determined according to the agreement between parties involved

in transaction.

c) For the fabrication of the test piece (including making of slits), any method, e.g. laser cutting, water

jet cutting, or other alternative manufacturing methods, demonstrated to work satisfactorily can

be used if agreed upon by the parties.

d) Unless otherwise specified and except for the sampling work, unnecessary deformation or heating

to the test piece shall be avoided.
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ISO/FDIS 16842:2021(E)
Key
1 gauge area
2 arm
3 grip
4 slit
a thickness of a test piece
B arm width
B distance between opposing slit ends in the x direction
B distance between opposing slit ends in the y direction
C grip length
L slit length
R corner radius at the junctions of arms to the gauge area
w slit width
[2][3]
Figure 1 — Standard shape and dimensions of the recommended cruciform test piece
6 Testing method
6.1 Testing machine

The specifications required for the biaxial tensile testing machine (hereinafter referred to as testing

machine) are as follows (for examples of typical testing machines, see Annex C):

a) It shall have sufficient functions and durability to hold four grips of a cruciform test piece

(hereinafter referred to as test piece) in one single plane with a tolerance of ±0,1 mm during testing.

b) Two opposing grips shall move along a single straight line (hereinafter referred to as x-axis and

y-axis), and the x­ and y-axes shall intersect at an angle of 90° ± 0,1° (The plane that contains the x-

and y-axes is referred to as the reference plane, while the intersection of x- and y-axes is referred to

as the centre of testing machine).

c) It shall have a function for adjusting the two opposing grips to the position at an equal distance

from the centre of the testing machine with a tolerance of ±0,1 mm before the installation of a test

piece to the grips.

d) It shall have a function for enabling the installation of a test piece to the grips while aligning the

centre of the test piece to the centre of the testing machine.
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ISO/FDIS 16842:2021(E)

e) It shall have a function for enabling equal displacement of two opposing grips or the maintenance of

the centre of the test piece always on the centre of the testing machine with a tolerance of ±0,1 mm

during biaxial tensile test (for example, the testing machines shown in Figures C.1 and C.2 use a

link mechanism to ensure equivalent displacement of two opposing grips).

f) It shall have a capability of servo-controlled biaxial tensile testing to perform a test with a constant

nominal stress ratio (constant force ratio) and/or a test with a constant true stress ratio, and/or a

test with a constant strain­rate ratio, according to the purpose of the test (see C.2). For a link type

biaxial tensile testing machine, it shall ensure equal displacement of two opposing grips (see C.3).

g) Modern control electronics allow independent and combined control of each actuator. This is called

modal control (see C.4).

h) It shall have a function for measuring and storing the values of the tensile forces (two channels,

one for each of the two axes, x and y) and strain components (two channels, one for each of the two

axes, x and y) during biaxial tensile test with the specified accuracy and time interval agreed by the

parties concerned.
6.2 Measurement method of force and strain
6.2.1 General

This subclause specifies the method for measuring the tensile forces (F , F ) and nominal strain

x y
components (e , e ) applied to the x and y directions of a cruciform test piece.
x y
6.2.2 Measurement method of force

For measurement of F and F , load cells shall be used in the x and y directions. The force­measuring

x y

system of the testing machine shall be calibrated in accordance with ISO 7500-1, class 1, or better.

6.2.3 Measurement method of strain

For measurement of e and e , strain gauges or other methods (e.g. an optical measurement system)

x y
shall be used. Measure e and e to the nearest 0,000 1 or better.
x y
6.2.4 Strain measurement positions

Figure 2 shows the position(s) of a strain gauge (or strain gauges) for measuring e and e . e and e

x y x y

shall be measured at a position, with a distance of (0,35 ± 0,05)B from the centre of test piece, on

the centreline parallel to the maximum tensile force. The strain measurement position can also be

determined according to the agreement between parties involved in transaction.

NOTE According to the finite element analyses of the cruciform test piece as recommended in Clause 5 and

the strain measurement position as specified in Figure 2, the stress calculation error is estimated to be less than

[2][3]
2,0 % .
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ISO/FDIS 16842:2021(E)
a1) F ≥ F a2) F ≤ F
x y x y
a) A case of measuring e and e using a biaxial foil strain gauge
x y,
b1) F ≥ F b2) F ≤ F
x y x y
b) A case of measuring e and e using two uniaxial strain gauges
x y,
Key
B arm width
e nominal strain in the x direction
e nominal strain in the y direction
F tensile force in the x direction
F tensile force in the y direction
[2][3]
Figure 2 — Strain measurement position
6.3 Installation of the test piece to a biaxial tensile testing machine

The test piece shall be fixed by four grips of a biaxial tensile testing machine. Care shall be taken to

ensure alignment of the centre of the test piece with the centre of the testing machine.

6.4 Testing methods

While keeping the force ratio, true stress ratio, strain­rate ratio, or the grip displacement­rate ratio

constant, biaxial tensile forces shall be applied to the test piece. F , F and e , e shall be measured with

x y x y

constant time intervals and the data shall be recorded on appropriate equipment. The test ends when

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ISO/FDIS 16842:2021(E)

the desired strain or stress level is achieved, or should be ended when fracture or localized necking

−1 −1

occurs in the arm or gauge area. The recommended strain­rate is 0,1 s to 0,0001 s .

NOTE A similar testing method has been used for abrupt strain path changes (see Annex A.3).

7 Determination of biaxial stress-strain curves
7.1 General

Using the measured values of F , F and e , e , the stress­strain curves in the x and y directions of the

x y x y

cruciform test piece shall be determined. These curves are used to determine contours of plastic work

for the test material (see A.2).
7.2 Determination of the original cross-sectional area of the test piece

Calculate the original cross­sectional areas of the gauge area perpendicular to the x- and y-axes, A and

A , from Formulae (1) and (2):
Aa=×B (1)
Sx Sy
Aa=×B (2)
Sy Sx
where
a is the sheet thickness, expressed in mm;
B is the distance between opposing slit ends on the x axis, expressed in mm;
B is the distance between opposing slit ends on the y axis, expressed in mm.

Measure a to the nearest 0,01 mm or better using a micrometer with sufficient resolution. B and B

Sx Sy

shall be determined to the nearest 0,1 mm or better using a measuring device with sufficient resolution.

The calculated values of A and A shall be rounded to 0,1 mm according to ISO 80000­1.

Sx Sy
7.3 Determination of true stress

Calculate the true stress components in the x and y directions, σ and σ , from Formulae (3) and (4):

x y
σ =+()1 e (3)
x x
σ =+()1 e (4)
y y
where

A is the original cross­sectional areas of the gauge area perpendicular to the x-axes, expressed in mm ;

A is the original cross­sectional areas of the gauge area perpendicular to the y-axes, expressed in mm ;

e is the nominal strain in the x direction measured by the method, as described in 6.2;

e is the nominal strain in the y direction measured by the method, as described in 6.2;

F is the tensile force in the x direction, expressed in N;
F is the tensile force in the y direction, expressed in N.
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ISO/FDIS 16842:2021(E)
7.4 Determination of true strain

Calculate the true strain components in the x and y directions, ε and ε , from Formulae (5) and (6):

x y
ε = ln(1 + e) (5)
x x
ε = ln(1 + e) (6)
y y
where

e is the nominal strain in the x direction measured by the method, as described in 6.2;

e is the nominal strain in the y direction measured by the method, as described in 6.2.

ε and ε shall be calculated to the digit of 10 from Formulae (5) and (6), and the result shall be

x y
rounded to the digit of 10 according to ISO 80000­1.

Examples of the measured biaxial true stress-true strain curves for a cold rolled ultralow carbon steel

sheet are shown in Figure 3.
7.5 Determination of true plastic strain
p p

Calculate the true plastic strain components in the x and y directions, ε and ε , from Formulae (7)

x y
and (8):
εε=− (7)
x x
εε=− (8)
where

C is the slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, ex­

x x x
pressed in MPa;

C is the slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, ex­

y y y
pressed in MPa;
ε is the true strain in the x direction;
ε is the true strain in the y direction;
σ is the true stress in the x direction, expressed in MPa;
σ is the true stress in the y direction, expressed in MPa.
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ISO/FDIS 16842:2021(E)
p p

ε and ε shall be calculated to the digit of 10 from Formulae (7) and (8), and the result shall be

x y
rounded to the digit of 10 according to ISO 80000­1.
a) A case of F :F = 1:1 b) A case of F :F = 2:1
x y x y
Key
X ε ε
x, y
Y σ σ / MPa
x, y

C slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, in MPa

x x x

C slope of the elastic part of the σ − ε curve measured in the biaxial tensile test, in MPa

y y y
F tensile force in the x direction, in N
F tensile force in the y direction, in N
ε true strain in the x direction
ε true strain in the y direction
σ true stress in the x direction, in MPa
σ true stress in the y direction, in MPa

NOTE The uniaxial tensile true stress-true strain curve in the rolling direction (RD) of the same material is

also shown for comparison.

Figure 3 — Examples of true stress-true strain curves measured in the biaxial tensile test of

cold rolled ultralow carbon steel sheet

Examples of measured true stress-true plastic strain curves corresponding to Figure 3 are shown in

Figure 4.
a) A case of F :F = 1:1 b) A case of F :F = 2:1
x y x y
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ISO/FDIS 16842:2021(E)
Key
p p
ε , ε
x y
Y σ σ / MPa
x, y
F tensile force in the x direction, in N
F tensile force in the y direction, in N
true plastic strain in the x directi
...

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