Plastics — Determination of fracture toughness (GIC and KIC) — Linear elastic fracture mechanics (LEFM) approach

This document specifies the principles for determining the fracture toughness of plastics in the crack-opening mode (mode I) under defined conditions. Two test methods with cracked specimens are defined, namely three-point-bending tests and compact-specimen tensile tests in order to suit different types of equipment available or different types of material. The methods are suitable for use with the following range of materials, including their compounds containing short fibres of the length ≤ 7,5 mm: — rigid and semi-rigid thermoplastic moulding, extrusion and casting materials; — rigid and semi-rigid thermosetting moulding and casting materials. In general, short fibre lengths of 0,1 mm to 7,5 mm are known to cause heterogeneity and anisotropy in the crack tip fracture process zone. Therefore, where relevant, Annex B offers some guidelines to extend the application of the same testing procedure, with some reservations, to rigid and semi-rigid thermoplastic or thermosetting plastics containing such short fibres. Certain restrictions on the linearity of the load-displacement diagram, on the specimen width and on the thickness are imposed to ensure validity (see 6.4) since the scheme used assumes linear elastic behaviour of the cracked material and a state of plane strain at the crack tip. Finally, the crack needs to be sharp enough so that an even sharper crack does not result in significantly lower values of the measured properties.

Plastiques — Détermination de la ténacité à la rupture (GIC et KIC) — Application de la mécanique linéaire élastique de la rupture (LEFM)

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Published
Publication Date
24-Jul-2018
Current Stage
6060 - International Standard published
Start Date
25-Jul-2018
Completion Date
25-Jul-2018
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INTERNATIONAL ISO
STANDARD 13586
Second edition
2018-08
Plastics — Determination of fracture
toughness (G and K ) — Linear
IC IC
elastic fracture mechanics (LEFM)
approach
Plastiques — Détermination de la ténacité à la rupture (G et K ) —
IC IC
Application de la mécanique linéaire élastique de la rupture (LEFM)
Reference number
ISO 13586:2018(E)
ISO 2018
---------------------- Page: 1 ----------------------
ISO 13586:2018(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2018

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

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Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2018 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 13586:2018(E)
Contents Page

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

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

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

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

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

4 Test specimens........................................................................................................................................................................................................ 4

4.1 Shape and size ......................................................................................................................................................................................... 4

4.2 Preparation ................................................................................................................................................................................................ 4

4.3 Notching ........................................................................................................................................................................................................ 5

4.4 Conditioning .............................................................................................................................................................................................. 6

5 Testing ............................................................................................................................................................................................................................. 6

5.1 Testing machine ..................................................................................................................................................................................... 6

5.2 Load indicator .......................................................................................................................................................................................... 6

5.3 Displacement transducer ............................................................................................................................................................... 6

5.4 Loading rigs ............................................................................................................................................................................................... 6

5.5 Displacement correction ................................................................................................................................................................ 7

5.6 Test atmosphere .................................................................................................................................................................................10

5.7 Thickness, width and crack length of test specimens ........................................................................................10

5.8 Test conditions .....................................................................................................................................................................................10

6 Expression of results .....................................................................................................................................................................................10

6.1 Determination of F .......................................................................................................................................................................10

6.2 Provisional result G ......................................................................................................................................................................11

6.3 Provisional result K ......................................................................................................................................................................11

6.4 Size criteria and validation of results ...............................................................................................................................11

6.5 Cross-check of results ....................................................................................................................................................................12

7 Precision ....................................................................................................................................................................................................................13

8 Test report ................................................................................................................................................................................................................13

Annex A (normative) Calibration factors ......................................................................................................................................................15

Annex B (informative) Testing of plastics containing short fibres .....................................................................................17

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

© ISO 2018 – All rights reserved iii
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ISO 13586:2018(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 61, Plastics, Subcommittee SC 2,

Mechanical behaviour.

This second edition cancels and replaces the first edition (ISO 13586:2000), which has been technically

revised. It also incorporates the Amendment ISO 13586:2000/Amd.1:2003, with the introduction of a

new Annex B.

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 2018 – All rights reserved
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ISO 13586:2018(E)
Introduction

This document is based on a testing protocol developed by the European Structural Integrity Society

(ESIS), Technical Committee 4, Polymers, Polymer Composites and Adhesives, who carried out the

preliminary enabling research through a series of round-robin exercises which covered a range of

material samples, specimen geometries, test instruments and operational conditions. This activity

involved nearly 10 laboratories from different countries. See References [1] and [3].

© ISO 2018 – All rights reserved v
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INTERNATIONAL STANDARD ISO 13586:2018(E)
Plastics — Determination of fracture toughness (G and
K ) — Linear elastic fracture mechanics (LEFM) approach
1 Scope

This document specifies the principles for determining the fracture toughness of plastics in the crack-

opening mode (mode I) under defined conditions. Two test methods with cracked specimens are

defined, namely three-point-bending tests and compact-specimen tensile tests in order to suit different

types of equipment available or different types of material.

The methods are suitable for use with the following range of materials, including their compounds

containing short fibres of the length ≤ 7,5 mm:
— rigid and semi-rigid thermoplastic moulding, extrusion and casting materials;
— rigid and semi-rigid thermosetting moulding and casting materials.

In general, short fibre lengths of 0,1 mm to 7,5 mm are known to cause heterogeneity and anisotropy

in the crack tip fracture process zone. Therefore, where relevant, Annex B offers some guidelines to

extend the application of the same testing procedure, with some reservations, to rigid and semi-rigid

thermoplastic or thermosetting plastics containing such short fibres.

Certain restrictions on the linearity of the load-displacement diagram, on the specimen width and on

the thickness are imposed to ensure validity (see 6.4) since the scheme used assumes linear elastic

behaviour of the cracked material and a state of plane strain at the crack tip. Finally, the crack needs

to be sharp enough so that an even sharper crack does not result in significantly lower values of the

measured properties.
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 527-1, Plastics — Determination of tensile properties — Part 1: General principles

ISO 604, Plastics — Determination of compressive properties
ISO 2818, Plastics — Preparation of test specimens by machining

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

ISO 9513, Metallic materials — Calibration of extensometer systems used in uniaxial testing

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.e lectropedia. org/
© ISO 2018 – All rights reserved 1
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ISO 13586:2018(E)
3.1
energy release rate

change in the external work δU and strain energy δU of a deformed body due to enlargement of the

ext s
cracked area δA
δU δU
exts
G=−
δA δA
Note 1 to entry: It is expressed in joules per square metre, J/m .
3.2
critical energy release rate

value of the energy release rate (3.1) in a precracked specimen under plane-strain loading conditions,

when the crack starts to grow
Note 1 to entry: It is expressed in joules per square metre, J/m .
3.3
stress intensity factor

limiting value of the product of the stress σ(r) perpendicular to the crack area at a distance r from the

crack tip and of the square root of 2πr, for small values of r
Kr=limσ × 2πr
r→0
Note 1 to entry: It is expressed in Pa × √m.

Note 2 to entry: The term factor is used here because it is common usage, even though the value has dimensions.

3.4
critical stress intensity factor

value of the stress intensity factor (3.3) when the crack under load actually starts to enlarge under a

plane-strain loading condition around the crack tip
Note 1 to entry: It is expressed in Pa × √m.

Note 2 to entry: The critical stress intensity factor K of a material is related to its critical energy release rate G

IC IC
by the formula:
GK= E
IC IC

where E is the modulus of elasticity, determined under similar conditions of loading time (up to crack initiation)

and temperature.
In the case of plane-strain conditions:
E =
1−μ
where
E is the tensile modulus (see ISO 527-1);
μ is Poisson’s ratio (see ISO 527-1).
2 © ISO 2018 – All rights reserved
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ISO 13586:2018(E)
3.5
displacement
displacement of the loading device
Note 1 to entry: It is expressed in metres, m.

Note 2 to entry: In the fracture test, the displacement of the loading device is designated as s . The displacement

of the loading device corrected as specified in 5.4, is designated as s.

Note 3 to entry: In the indentation test, the displacement of the loading device is designated as s .

3.6
stiffness
initial slope of the force-displacement diagram
dF 
S =
 
 
s→0
Note 1 to entry: It is expressed in newtons per metre, N/m.
3.7
force
applied load at the initiation of crack growth
Note 1 to entry: It is expressed in newtons, N.
Note 2 to entry: See also 6.1.
3.8
energy
input energy when crack growth initiates
Note 1 to entry: It is expressed in joules, J.
Note 2 to entry: W is based upon the corrected load-displacement curve.
3.9
crack length
crack length up to the tip of the initial crack
Note 1 to entry: It is expressed in metres, m.
Note 2 to entry: The initial crack is prepared as specified in 4.3.

Note 3 to entry: For three-point-bending test specimens, the crack length is measured from the notched face. For

compact tensile-test specimens, the crack length is measured from the load line, i.e. from the line through the

centres of the holes for the loading pins (see Figures 1 and 2).

Note 4 to entry: The crack length a is normalized by the width w of the test specimen (α = a/w).

3.10
energy calibration factor

factor to account for the crack length dependent stiffness of the test specimen, given by the formula:

 
φ aw =−S
 
 
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ISO 13586:2018(E)
where
S is the stiffness of the specimen;
α (= a/w) is the normalized crack length (see 3.9).

Note 1 to entry: Values of ϕ (a/w) are given in Annex A for both types of specimen.

3.11
geometry calibration factor
factor to account for the configuration and the dimensions of the test specimen

Note 1 to entry: Values of f (a/w) are given in Annex A for both types of specimen.

3.12
characteristic length
size of the plastic deformation zone around the crack tip

Note 1 to entry: It is required for checking fulfilment of the size criteria (see 6.4).

4 Test specimens
4.1 Shape and size

Test specimens for three-point-bending tests [also called single-edge-notch bending (SENB)] and for

compact tensile (CT) tests shall be prepared in accordance with Figure 1 and Figure 2, respectively.

It is usually convenient to make the thickness h of the test specimens equal to the thickness of a sheet

sample and to make the test specimen width w equal to 2h. The crack length a should preferably be in

the range given by 0,45 ≤ a/w ≤ 0,55.
4.2 Preparation

Test specimens shall be prepared in accordance with the relevant material International Standard for

the material under test and in accordance with ISO 2818. In the case of anisotropic specimens, take

care to indicate the reference direction on each test specimen.
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ISO 13586:2018(E)
Key
w width
l overall length l > 4,2w
h thickness w/4 < h < w/2
a crack length 0,45w ≤ a ≤ 0,55w
Figure 1 — Three-point-bending (SENB) test specimen
Key
w width
W overall width W = 1,25w ± 0,01w
l length l = 1,2w ± 0,01w
1 1
l distance between centres of two holes located l = 0,55w ± 0,005w
2 2
symmetrically to the crack plane
R radius R = 0,125w ± 0,005w
h thickness 0,4w < h < 0,6w
a crack length 0,45w ≤ a ≤ 0,55w

(The loading pins and holes shall be smooth and a loose fit to minimize friction.)

Figure 2 — Compact tensile (CT) test specimen
4.3 Notching
Method a), b) or c) can be used for notching.

a) Machine a sharp notch into the test specimen and then generate a natural crack by tapping on a

new razor blade placed in the notch (it is essential to practice this since, in brittle test specimens,

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ISO 13586:2018(E)

a natural crack can be generated by this process, but some skill is required in avoiding too long

a crack or local damage). The length of the crack thus created shall be more than four times the

original notch tip radius.

b) If a natural crack cannot be generated, as in tough test specimens, then sharpen the notch by sliding

a razor blade across the notch. Use a new razor blade for each test specimen. The length of the crack

thus created shall be more than four times the original notch tip radius.

c) Cooling tough test specimens and then performing razor tapping is sometimes successful.

Pressing the blade into the notch is not recommended because of induced residual stresses.

4.4 Conditioning

Condition test specimens as specified in the International Standard for the material under test, unless

otherwise agreed upon by the interested parties. In the absence of this information, the preferred

atmosphere is (23 ± 2) °C and (50 ± 10) % relative humidity, except when the properties of the material

are known to be insensitive to moisture, in which case humidity control is unnecessary.

5 Testing
5.1 Testing machine

The machine shall comply with ISO 7500-1 and ISO 9513, and meet the specifications given in 5.2 to 5.4.

5.2 Load indicator

The load measurement system shall comply with class 1 as defined in ISO 7500-1. The load indicator

shall show the total load carried by the test specimen. This device shall be essentially free from inertia

lag at the test speeds used. It shall indicate the load with an accuracy of at least 1 % of the actual value.

5.3 Displacement transducer

The displacement is recorded during the test. The continuously measuring displacement transducer

shall be essentially free from inertia lag at the test speeds used. It shall be able to measure the relevant

displacement within class 1 of ISO 9513 or better. The effects of the displacement transducer on the

load measurement shall be < 1 % of the load reading or they shall be corrected.
5.4 Loading rigs

A rig with moving rollers is used for three-point-bending (SENB) tests, as shown in Figure 3. Indentation

into the test specimen is minimized by the use of rollers with a large diameter (>w/2). The measurement

of the displacement shall be taken at the centre of the span L (see Figure 3).

For the compact tensile test, the test specimen is loaded by means of two pins in holes in the specimen.

The displacement of the load points during the test is measured, for example by a clip gauge near the

pins (see 5.3).
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ISO 13586:2018(E)
Key

L span between rollers L = 4w ± 0,1w 1 distance monitored by displacement transducer

R radius w/8 < R < w/2 2 bosses for rubber bands
h thickness

Figure 3 — Rig with two rollers and displacement transducer for three-point-bending

(SENB) tests
5.5 Displacement correction

The measured displacement s shall be corrected for the indentation of the loading pins, compression

of the test specimen and the machine compliance in order to determine properly the stiffness S of

the specimen and the work W at crack growth initiation. The calibration of the test system shall be

performed as follows.

The load-displacement correction curve (see Figure 4) is generated by analogy with the fracture test

but by using unnotched test specimens, as indicated in Figure 5 and Figure 6. The rollers of the three-

point-bending rig are moved together to reduce even further the small flexing of the unnotched test

specimen under load. The displacement correction shall be performed for each material and at each

different temperature and test speed since polymers are generally sensitive to temperature and test

speed. The degree of loading-pin penetration and specimen compression can vary with changes in

these variables. The indentation tests shall be performed such that the loading times are the same as

in the fracture tests. This will involve lower test speeds to reach the same load in the same time, for

example about half the speed.

In practice, a linear correction curve is usually obtained up to loads even exceeding the fracture load

of cracked test specimens (see Figure 4). Any initial nonlinearity due to penetration of the loading pins

© ISO 2018 – All rights reserved 7
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ISO 13586:2018(E)

into the specimen is observed during both the calibration test and the actual fracture test. Therefore,

the initial nonlinearity is effectively corrected for by the following proposed method.

At corresponding load, the displacement s taken from the correction curve is subtracted from the

displacement s in the actual fracture test with a notched test specimen. In this way, the corrected load-

displacement curve is constructed. The stiffness S and the energy W at crack growth initiation are

derived from this curve (see Figure 7). The corrections s of the displacements usually amount to less

than 20 % of the measured displacement s .
Key
s indentation displacement
F load
Figure 4 — Load-indentation curve determined on an unnotched test specimen

Figure 5 — Arrangement for determining the indentation displacement of a bending-test

specimen
8 © ISO 2018 – All rights reserved
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ISO 13586:2018(E)

Figure 6 — Arrangement for determining the indentation displacement of a compact tensile

specimen
Key
s displacement
F load
S stiffness
F is the load at crack growth initiation
W is the energy to break

Figure 7 — Load-displacement curve for a notched test specimen (the displacement has been

corrected for indentation effects)
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ISO 13586:2018(E)
5.6 Test atmosphere

Conduct the test in the same atmosphere as used for conditioning, unless otherwise agreed upon by the

interested parties, for example for testing at elevated or low temperatures.
5.7 Thickness, width and crack length of test specimens

Measure the thickness h and width w of each test specimen to the nearest 0,02 mm. Record an

approximate reading of the crack length a which will be corrected on completion of the test. Usually

crack tip lines are visible on the two fracture surfaces. Calculate the mean value of five readings of

the crack length taken along the original crack front. These shall be taken at the edges, the centre and

half way between. The crack length shall differ by no more than 10 % over the entire crack front. If

differences larger than 10 % are found, reject the test. Care shall be taken that it is the original crack tip

which is being observed since slow growth can occur.
5.8 Test conditions

It is recommended that (23 ± 2) °C and a test speed of (10 ± 20 %) mm/min be used as the basic test

conditions. In all cases, the loading time and the test temperature shall be measured. Speeds greater

than 0,1 m/s and loading times less than 10 ms should preferably be avoided since dynamic effects may

cause errors.

Carry out at least three tests for each set of conditions. If it is not possible to obtain valid results at 23 °C

(see 6.4), it is often possible to do so by decreasing the temperature. Usually, a reduction in the test

temperature does not change K greatly but increases the yield stress of the polymer, rendering the

fractures more brittle. If this procedure is used, both temperature and loading time shall be stated in

the test report.
6 Expression of results
6.1 Determination of F

In an ideal material, the load-displacement curve is a linear one with an abrupt drop in the load at the

instant of crack growth initiation. In such rather rare cases, F can be identified with the maximum load.

In most cases, there is some nonlinearity in the curve and this can be due to plastic deformation at the

crack tip, nonlinear elasticity, general visco-elasticity or stable crack growth after initiation but prior

to instability. The first three effects violate the linear elastic fracture mechanics (LEFM) assumption

and the fourth one means that the true initiation load is not defined by the maximum. In order to

circumvent a doubtful definition of initiation, an arbitrary rule is used here. The zero-point tangent is

drawn to the curve in Figure 7 to determine the initial stiffness S. This stiffness is reduced by 5 % and a

further line is drawn accordingly. If the maximum of the load-displacement curve falls within these two

lines, then F shall be called F (the load at crack growth initiation). If the second line intersects the

max Q

load curve at F prior to the maximum, then F shall be called F . Referring to Figure 7, the conditions of

5 5 Q
LEFM are assumed to be met if:
max
<11,
If this condition of 10 % nonlinearity is violated, the test shall be rejected.
10 © ISO 2018 – All rights reserved
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ISO 13586:2018(E)
6.2 Provisional result G

Calculate the critical energy release rate from the energy W up to the instant of crack growth initiation,

where the load is F and the original crack length is a:
G = (1)
hw××φ aw
where
W is the energy to break;
h is the test specimen thickness;
w is the test specimen width;
ϕ (a/w) is the energy calibration factor, depending on the crack length a.

Calculate ϕ as shown in Annex A. Tables with values of ϕ (a/w) for both types of test specimen are also

given in Annex A.
6.3 Provisional result K

Calculate the critical stress intensity factor K from the load F at crack growth initiation and the

Q Q
original crack length a:
Kf= aw (2)
where
F is the load at crack growth initiation;
h is the test specimen thickness;
w is the test specimen width;
f (a/w) is the geometry calibration factor, depending on the crack length a.

Calculate f as shown in Annex A. Tables with values of f (a/w) for both types of test specimen are also

given in Annex A.
6.4 Size criteria and validation of results

The test is valid only if the dimensions of the test specimen are significantly larger than the plastic zone

around the crack tip, characterized by the length r . Appropriate test specimens for plane-strain

fracture tests shall meet the following size criteria:
— thickness h
> 2,5 × r
— crack length a
> 2,5 × r
— ligament width (w – a)
> 2,5 × r

With the specimen dimensions proposed in this document, all the criteria are usually satisfied

simultaneously. The criteria cover two limitations in that h must be sufficient to ensure plane strain

but (w – a) has to be sufficient to avoid excessive pl
...

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