Paper and board -- Determination of bending stiffness -- General principles for two-point, three-point and four-point methods

This document specifies three test methods for determining the bending stiffness of paper and paperboard. The test methods differ in the type of loading mode, thus giving rise to the two-point, three-point and four-point bending test methods. For paper and paperboard in a low thickness range, the two-point bending method and the three-point bending method are suitable. For corrugated fibreboard and board with a higher thickness, the four-point bending method is recommended. The measurement conditions are defined in such a way that the test piece is not subjected to any significant permanent deformation during the test, nor is the range of validity of the formulae for calculating the bending stiffness exceeded. In these bending tests, the test pieces of paper and board are regarded as "beams" as defined by the science of the strength of materials, see Reference [2].

Papier et carton -- Détermination de la rigidité à la flexion -- Principes généraux pour les méthodes à deux points, à trois points et à quatre points

Papir, karton in lepenka - Ugotavljanje upogibne togosti s statično metodo - Splošna načela za dvo-, tri- in štiritočkovne metode

General Information

Status
Published
Publication Date
13-May-2019
Current Stage
6060 - International Standard published
Start Date
17-Apr-2019
Completion Date
14-May-2019

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SLOVENSKI STANDARD
SIST ISO 5628:2020
01-november-2020
Papir, karton in lepenka - Ugotavljanje upogibne togosti s statično metodo -
Splošna načela za dvo-, tri- in štiritočkovne metode

Paper and board -- Determination of bending stiffness -- General principles for two-point,

three-point and four-point methods

Papier et carton -- Détermination de la rigidité à la flexion -- Principes généraux pour les

méthodes à deux points, à trois points et à quatre points
Ta slovenski standard je istoveten z: ISO 5628:2019
ICS:
85.060 Papir, karton in lepenka Paper and board
SIST ISO 5628:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST ISO 5628:2020
---------------------- Page: 2 ----------------------
SIST ISO 5628:2020
INTERNATIONAL ISO
STANDARD 5628
Third edition
2019-05
Paper and board — Determination of
bending stiffness — General principles
for two-point, three-point and four-
point methods
Papier et carton — Détermination de la rigidité à la flexion —
Principes généraux pour les méthodes à deux points, à trois points et à
quatre points
Reference number
ISO 5628:2019(E)
ISO 2019
---------------------- Page: 3 ----------------------
SIST ISO 5628:2020
ISO 5628:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

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

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

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

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
---------------------- Page: 4 ----------------------
SIST ISO 5628:2020
ISO 5628:2019(E)
Contents Page

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

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

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

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

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

4 Symbols and units ............................................................................................................................................................................................... 2

5 Theory ............................................................................................................................................................................................................................. 2

6 Different bending test methods ............................................................................................................................................................ 3

6.1 Two-point bending method ......................................................................................................................................................... 3

6.2 Three-point bending method ..................................................................................................................................................... 4

6.3 Calculation of bending stiffness using the two-point and three-point methods ............................ 5

6.3.1 Bending stiffness determination ........................................................................................................................ 5

6.3.2 Geometrical requirement ......................................................................................................................................... 5

6.3.3 Allowable deflections and angles ...................................................................................................................... 5

6.4 Four-point bending method ........................................................................................................................................................ 6

6.4.1 Geometry ................................................................................................................................................................................ 6

6.4.2 Calculation of bending stiffness .......................................................................................................................... 7

6.4.3 Measurement conditions .......................................................................................................................................... 7

6.4.4 Geometrical and practical considerations ................................................................................................. 7

7 Apparatus ..................................................................................................................................................................................................................... 8

8 Sampling and preparation of test pieces ..................................................................................................................................... 8

8.1 Sampling ....................................................................................................................................................................................................... 8

8.2 Conditioning .............................................................................................................................................................................................. 8

8.3 Preparation of test pieces .............................................................................................................................................................. 8

9 Procedure..................................................................................................................................................................................................................... 8

10 E valuation and calculation ......................................................................................................................................................................... 9

11 Test report ................................................................................................................................................................................................................... 9

Bibliography .............................................................................................................................................................................................................................10

© ISO 2019 – All rights reserved iii
---------------------- Page: 5 ----------------------
SIST ISO 5628:2020
ISO 5628:2019(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso

.org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 6, Paper, board and pulps, Subcommittee

SC 2, Test methods and quality specifications for paper and board.

This third edition cancels and replaces the second edition (ISO 5628:2012), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— in 6.4.2, a Note has been added to clarify the measurement of F.

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 2019 – All rights reserved
---------------------- Page: 6 ----------------------
SIST ISO 5628:2020
ISO 5628:2019(E)
Introduction

Bending stiffness is regarded as an important property of paper and board, and a large number of test

methods have been used for its determination. This is a result, in part at least, of the wide range in the

bending stiffness of paper and board. For paper and board in the grammage range 50 g/m to 500 g/

m , bending stiffness might vary by a factor of over 1 000. This wide variation is reflected in the design

of instruments intended for the measurement of this property.

A second factor to be taken into account is that, in general terms, bending stiffness (as defined here)

can only be determined with accuracy within certain limits with regard to the degree of deformation

imposed upon the test piece. These limits depend on the dimensions of the test piece and on the test

method used.

This document is intended to enable the bending stiffness (as defined here) to be measured and

described in a consistent way, despite the variations in material type and instrument design. It will be

found that many commercially available instruments can be regarded as giving results in accordance

with this document for only part of the range of bending stiffness, or for only some of the materials for

which they were originally designed. It is intended, therefore, that this document will be used as the

basis for preparing detailed methods for determining bending stiffness, using particular instruments.

© ISO 2019 – All rights reserved v
---------------------- Page: 7 ----------------------
SIST ISO 5628:2020
---------------------- Page: 8 ----------------------
SIST ISO 5628:2020
INTERNATIONAL STANDARD ISO 5628:2019(E)
Paper and board — Determination of bending stiffness
— General principles for two-point, three-point and four-
point methods
1 Scope

This document specifies three test methods for determining the bending stiffness of paper and

paperboard. The test methods differ in the type of loading mode, thus giving rise to the two-point,

three-point and four-point bending test methods.

For paper and paperboard in a low thickness range, the two-point bending method and the three-point

bending method are suitable.

For corrugated fibreboard and board with a higher thickness, the four-point bending method is

recommended.

The measurement conditions are defined in such a way that the test piece is not subjected to any

significant permanent deformation during the test, nor is the range of validity of the formulae for

calculating the bending stiffness exceeded.

In these bending tests, the test pieces of paper and board are regarded as “beams” as defined by the

science of the strength of materials, see Reference [2].
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 186, Paper and board — Sampling to determine average quality

ISO 187, Paper, board and pulps — Standard atmosphere for conditioning and testing and procedure for

monitoring the atmosphere and conditioning of samples

ISO 534, Paper and board — Determination of thickness, density and specific volume

ISO 3034, Corrugated fibreboard — Determination of single sheet thickness
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/
© ISO 2019 – All rights reserved 1
---------------------- Page: 9 ----------------------
SIST ISO 5628:2020
ISO 5628:2019(E)
3.1
bending stiffness

resistance that a test piece offers to bending, in the region of elastic deformation

Note 1 to entry: The theories used for the determination of bending stiffness are derived under the condition that

the test piece is perfectly flat at the beginning of the test. In a real situation, the test piece always deviates from

flatness. It is, however, not possible to give recommendations on the magnitude of such deviations (such as curl,

twist, cockle or other deviations) that can be present and still produce a valid test.

4 Symbols and units
The following symbols are used for the formulae in this document.
Symbol Unit Meaning
b mm test piece width in the direction of the bending axis
E MPa (N/mm ) modulus of elasticity
f mm linear deflection
F N force
f mm maximum linear deflection
max
I mm second moment of inertia
l mm bending length
l mm distance in the four-point method
l mm bending length in the four-point method
S N·mm bending stiffness
t mm test piece thickness
α ° (degree) bending angle
α ° (degree) maximum bending angle
max
ε % (mm/mm) strain
ε % (mm/mm) maximum strain
max
5 Theory

For a beam of a homogeneous material, with equal thickness and a constant modulus of elasticity in

the plane of the paper or board, the bending stiffness S (per unit width b) may be derived from the

product of the modulus of elasticity, E, and the second moment of inertia, I, of the test piece, divided by

the width, b, of the test piece as shown in Formula (1):
EI⋅
S = (1)

From a testing point of view, the bending stiffness, S , may be evaluated in three principally

different ways:
a) From the
...

SLOVENSKI STANDARD
oSIST ISO 5628:2020
01-oktober-2020
Papir, karton in lepenka - Ugotavljanje upogibne togosti s statično metodo -
Splošna načela za dvo-, tri- in štiritočkovne metode

Paper and board -- Determination of bending stiffness -- General principles for two-point,

three-point and four-point methods

Papier et carton -- Détermination de la rigidité à la flexion -- Principes généraux pour les

méthodes à deux points, à trois points et à quatre points
Ta slovenski standard je istoveten z: ISO 5628:2019
ICS:
85.060 Papir, karton in lepenka Paper and board
oSIST ISO 5628:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
oSIST ISO 5628:2020
---------------------- Page: 2 ----------------------
oSIST ISO 5628:2020
INTERNATIONAL ISO
STANDARD 5628
Third edition
2019-05
Paper and board — Determination of
bending stiffness — General principles
for two-point, three-point and four-
point methods
Papier et carton — Détermination de la rigidité à la flexion —
Principes généraux pour les méthodes à deux points, à trois points et à
quatre points
Reference number
ISO 5628:2019(E)
ISO 2019
---------------------- Page: 3 ----------------------
oSIST ISO 5628:2020
ISO 5628:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

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

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

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

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
---------------------- Page: 4 ----------------------
oSIST ISO 5628:2020
ISO 5628:2019(E)
Contents Page

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

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

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

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

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

4 Symbols and units ............................................................................................................................................................................................... 2

5 Theory ............................................................................................................................................................................................................................. 2

6 Different bending test methods ............................................................................................................................................................ 3

6.1 Two-point bending method ......................................................................................................................................................... 3

6.2 Three-point bending method ..................................................................................................................................................... 4

6.3 Calculation of bending stiffness using the two-point and three-point methods ............................ 5

6.3.1 Bending stiffness determination ........................................................................................................................ 5

6.3.2 Geometrical requirement ......................................................................................................................................... 5

6.3.3 Allowable deflections and angles ...................................................................................................................... 5

6.4 Four-point bending method ........................................................................................................................................................ 6

6.4.1 Geometry ................................................................................................................................................................................ 6

6.4.2 Calculation of bending stiffness .......................................................................................................................... 7

6.4.3 Measurement conditions .......................................................................................................................................... 7

6.4.4 Geometrical and practical considerations ................................................................................................. 7

7 Apparatus ..................................................................................................................................................................................................................... 8

8 Sampling and preparation of test pieces ..................................................................................................................................... 8

8.1 Sampling ....................................................................................................................................................................................................... 8

8.2 Conditioning .............................................................................................................................................................................................. 8

8.3 Preparation of test pieces .............................................................................................................................................................. 8

9 Procedure..................................................................................................................................................................................................................... 8

10 E valuation and calculation ......................................................................................................................................................................... 9

11 Test report ................................................................................................................................................................................................................... 9

Bibliography .............................................................................................................................................................................................................................10

© ISO 2019 – All rights reserved iii
---------------------- Page: 5 ----------------------
oSIST ISO 5628:2020
ISO 5628:2019(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso

.org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 6, Paper, board and pulps, Subcommittee

SC 2, Test methods and quality specifications for paper and board.

This third edition cancels and replaces the second edition (ISO 5628:2012), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— in 6.4.2, a Note has been added to clarify the measurement of F.

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 2019 – All rights reserved
---------------------- Page: 6 ----------------------
oSIST ISO 5628:2020
ISO 5628:2019(E)
Introduction

Bending stiffness is regarded as an important property of paper and board, and a large number of test

methods have been used for its determination. This is a result, in part at least, of the wide range in the

bending stiffness of paper and board. For paper and board in the grammage range 50 g/m to 500 g/

m , bending stiffness might vary by a factor of over 1 000. This wide variation is reflected in the design

of instruments intended for the measurement of this property.

A second factor to be taken into account is that, in general terms, bending stiffness (as defined here)

can only be determined with accuracy within certain limits with regard to the degree of deformation

imposed upon the test piece. These limits depend on the dimensions of the test piece and on the test

method used.

This document is intended to enable the bending stiffness (as defined here) to be measured and

described in a consistent way, despite the variations in material type and instrument design. It will be

found that many commercially available instruments can be regarded as giving results in accordance

with this document for only part of the range of bending stiffness, or for only some of the materials for

which they were originally designed. It is intended, therefore, that this document will be used as the

basis for preparing detailed methods for determining bending stiffness, using particular instruments.

© ISO 2019 – All rights reserved v
---------------------- Page: 7 ----------------------
oSIST ISO 5628:2020
---------------------- Page: 8 ----------------------
oSIST ISO 5628:2020
INTERNATIONAL STANDARD ISO 5628:2019(E)
Paper and board — Determination of bending stiffness
— General principles for two-point, three-point and four-
point methods
1 Scope

This document specifies three test methods for determining the bending stiffness of paper and

paperboard. The test methods differ in the type of loading mode, thus giving rise to the two-point,

three-point and four-point bending test methods.

For paper and paperboard in a low thickness range, the two-point bending method and the three-point

bending method are suitable.

For corrugated fibreboard and board with a higher thickness, the four-point bending method is

recommended.

The measurement conditions are defined in such a way that the test piece is not subjected to any

significant permanent deformation during the test, nor is the range of validity of the formulae for

calculating the bending stiffness exceeded.

In these bending tests, the test pieces of paper and board are regarded as “beams” as defined by the

science of the strength of materials, see Reference [2].
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 186, Paper and board — Sampling to determine average quality

ISO 187, Paper, board and pulps — Standard atmosphere for conditioning and testing and procedure for

monitoring the atmosphere and conditioning of samples

ISO 534, Paper and board — Determination of thickness, density and specific volume

ISO 3034, Corrugated fibreboard — Determination of single sheet thickness
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/
© ISO 2019 – All rights reserved 1
---------------------- Page: 9 ----------------------
oSIST ISO 5628:2020
ISO 5628:2019(E)
3.1
bending stiffness

resistance that a test piece offers to bending, in the region of elastic deformation

Note 1 to entry: The theories used for the determination of bending stiffness are derived under the condition that

the test piece is perfectly flat at the beginning of the test. In a real situation, the test piece always deviates from

flatness. It is, however, not possible to give recommendations on the magnitude of such deviations (such as curl,

twist, cockle or other deviations) that can be present and still produce a valid test.

4 Symbols and units
The following symbols are used for the formulae in this document.
Symbol Unit Meaning
b mm test piece width in the direction of the bending axis
E MPa (N/mm ) modulus of elasticity
f mm linear deflection
F N force
f mm maximum linear deflection
max
I mm second moment of inertia
l mm bending length
l mm distance in the four-point method
l mm bending length in the four-point method
S N·mm bending stiffness
t mm test piece thickness
α ° (degree) bending angle
α ° (degree) maximum bending angle
max
ε % (mm/mm) strain
ε % (mm/mm) maximum strain
max
5 Theory

For a beam of a homogeneous material, with equal thickness and a constant modulus of elasticity in

the plane of the paper or board, the bending stiffness S (per unit width b) may be derived from the

product of the modulus of elasticity, E, and the second moment of inertia, I, of the test piece, divided by

the width, b, of the test piece as shown in Formula (1):
EI⋅
S = (1)

From a testing point of view, the bending stiffness, S , may be evaluated in three principally

different ways:
a) From th
...

INTERNATIONAL ISO
STANDARD 5628
Third edition
2019-05
Paper and board — Determination of
bending stiffness — General principles
for two-point, three-point and four-
point methods
Papier et carton — Détermination de la rigidité à la flexion —
Principes généraux pour les méthodes à deux points, à trois points et à
quatre points
Reference number
ISO 5628:2019(E)
ISO 2019
---------------------- Page: 1 ----------------------
ISO 5628:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

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

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

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

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 5628:2019(E)
Contents Page

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

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

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

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

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

4 Symbols and units ............................................................................................................................................................................................... 2

5 Theory ............................................................................................................................................................................................................................. 2

6 Different bending test methods ............................................................................................................................................................ 3

6.1 Two-point bending method ......................................................................................................................................................... 3

6.2 Three-point bending method ..................................................................................................................................................... 4

6.3 Calculation of bending stiffness using the two-point and three-point methods ............................ 5

6.3.1 Bending stiffness determination ........................................................................................................................ 5

6.3.2 Geometrical requirement ......................................................................................................................................... 5

6.3.3 Allowable deflections and angles ...................................................................................................................... 5

6.4 Four-point bending method ........................................................................................................................................................ 6

6.4.1 Geometry ................................................................................................................................................................................ 6

6.4.2 Calculation of bending stiffness .......................................................................................................................... 7

6.4.3 Measurement conditions .......................................................................................................................................... 7

6.4.4 Geometrical and practical considerations ................................................................................................. 7

7 Apparatus ..................................................................................................................................................................................................................... 8

8 Sampling and preparation of test pieces ..................................................................................................................................... 8

8.1 Sampling ....................................................................................................................................................................................................... 8

8.2 Conditioning .............................................................................................................................................................................................. 8

8.3 Preparation of test pieces .............................................................................................................................................................. 8

9 Procedure..................................................................................................................................................................................................................... 8

10 E valuation and calculation ......................................................................................................................................................................... 9

11 Test report ................................................................................................................................................................................................................... 9

Bibliography .............................................................................................................................................................................................................................10

© ISO 2019 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 5628:2019(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso

.org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 6, Paper, board and pulps, Subcommittee

SC 2, Test methods and quality specifications for paper and board.

This third edition cancels and replaces the second edition (ISO 5628:2012), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— in 6.4.2, a Note has been added to clarify the measurement of F.

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 2019 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 5628:2019(E)
Introduction

Bending stiffness is regarded as an important property of paper and board, and a large number of test

methods have been used for its determination. This is a result, in part at least, of the wide range in the

bending stiffness of paper and board. For paper and board in the grammage range 50 g/m to 500 g/

m , bending stiffness might vary by a factor of over 1 000. This wide variation is reflected in the design

of instruments intended for the measurement of this property.

A second factor to be taken into account is that, in general terms, bending stiffness (as defined here)

can only be determined with accuracy within certain limits with regard to the degree of deformation

imposed upon the test piece. These limits depend on the dimensions of the test piece and on the test

method used.

This document is intended to enable the bending stiffness (as defined here) to be measured and

described in a consistent way, despite the variations in material type and instrument design. It will be

found that many commercially available instruments can be regarded as giving results in accordance

with this document for only part of the range of bending stiffness, or for only some of the materials for

which they were originally designed. It is intended, therefore, that this document will be used as the

basis for preparing detailed methods for determining bending stiffness, using particular instruments.

© ISO 2019 – All rights reserved v
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INTERNATIONAL STANDARD ISO 5628:2019(E)
Paper and board — Determination of bending stiffness
— General principles for two-point, three-point and four-
point methods
1 Scope

This document specifies three test methods for determining the bending stiffness of paper and

paperboard. The test methods differ in the type of loading mode, thus giving rise to the two-point,

three-point and four-point bending test methods.

For paper and paperboard in a low thickness range, the two-point bending method and the three-point

bending method are suitable.

For corrugated fibreboard and board with a higher thickness, the four-point bending method is

recommended.

The measurement conditions are defined in such a way that the test piece is not subjected to any

significant permanent deformation during the test, nor is the range of validity of the formulae for

calculating the bending stiffness exceeded.

In these bending tests, the test pieces of paper and board are regarded as “beams” as defined by the

science of the strength of materials, see Reference [2].
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 186, Paper and board — Sampling to determine average quality

ISO 187, Paper, board and pulps — Standard atmosphere for conditioning and testing and procedure for

monitoring the atmosphere and conditioning of samples

ISO 534, Paper and board — Determination of thickness, density and specific volume

ISO 3034, Corrugated fibreboard — Determination of single sheet thickness
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/
© ISO 2019 – All rights reserved 1
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ISO 5628:2019(E)
3.1
bending stiffness

resistance that a test piece offers to bending, in the region of elastic deformation

Note 1 to entry: The theories used for the determination of bending stiffness are derived under the condition that

the test piece is perfectly flat at the beginning of the test. In a real situation, the test piece always deviates from

flatness. It is, however, not possible to give recommendations on the magnitude of such deviations (such as curl,

twist, cockle or other deviations) that can be present and still produce a valid test.

4 Symbols and units
The following symbols are used for the formulae in this document.
Symbol Unit Meaning
b mm test piece width in the direction of the bending axis
E MPa (N/mm ) modulus of elasticity
f mm linear deflection
F N force
f mm maximum linear deflection
max
I mm second moment of inertia
l mm bending length
l mm distance in the four-point method
l mm bending length in the four-point method
S N·mm bending stiffness
t mm test piece thickness
α ° (degree) bending angle
α ° (degree) maximum bending angle
max
ε % (mm/mm) strain
ε % (mm/mm) maximum strain
max
5 Theory

For a beam of a homogeneous material, with equal thickness and a constant modulus of elasticity in

the plane of the paper or board, the bending stiffness S (per unit width b) may be derived from the

product of the modulus of elasticity, E, and the second moment of inertia, I, of the test piece, divided by

the width, b, of the test piece as shown in Formula (1):
EI⋅
S = (1)

From a testing point of view, the bending stiffness, S , may be evaluated in three principally

different ways:

a) From the maximum slope of the curve achieved from recording force versus linear deflection (F/f ),

[2]

or force versus angular deflection (F/α), see Figure 1 . The rate of testing shall be reported.

[5]

b) Applying a linear deflection or angular deflection and recording the force after a specified time .

This document gives suggestions for maximum allowable deflections for the various beam-bending

methods. The time of application shall be reported.
c) Applying a force and recording the linear deflection or angular deflec
...

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