Plastics — Determination of tension-tension fatigue crack propagation — Linear elastic fracture mechanics (LEFM) approach

ISO 15850:2014 specifies a method for measuring the propagation of a crack in a notched specimen subjected to a cyclic tensile load varying between a constant positive minimum and a constant positive maximum value. The test results include the crack length as a function of the number of load cycles and the crack length increase rate as a function of the stress intensity factor and energy release rate at the crack tip. The possible occurrence of discontinuities in crack propagation is detected and reported. The test can be also used for the purpose of determining the resistance to crack propagation failure. In this case, the results can be presented in the form of number of cycles to failure or total time taken to cause crack propagation failure versus the stress intensity factor.

Plastiques — Détermination de la propagation de fissure par fatigue en traction — Approche de la mécanique linéaire élastique de la rupture (LEFM)

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Published
Publication Date
03-Feb-2014
Current Stage
9093 - International Standard confirmed
Start Date
25-Sep-2019
Completion Date
25-Sep-2019
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INTERNATIONAL ISO
STANDARD 15850
Second edition
2014-02-15
Plastics — Determination of tension-
tension fatigue crack propagation
— Linear elastic fracture mechanics
(LEFM) approach
Plastiques — Détermination de la propagation de fissure par fatigue
en traction — Approche de la mécanique linéaire élastique de la
rupture (LEFM)
Reference number
ISO 15850:2014(E)
ISO 2014
---------------------- Page: 1 ----------------------
ISO 15850:2014(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2014

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Published in Switzerland
ii © ISO 2014 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 15850:2014(E)
Contents Page

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

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

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

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

4 Principle ........................................................................................................................................................................................................................ 5

5 Significance and use .......................................................................................................................................................................................... 5

6 Test specimens........................................................................................................................................................................................................ 6

6.1 Shape and size ......................................................................................................................................................................................... 6

6.2 Preparation ................................................................................................................................................................................................ 9

6.3 Notching ........................................................................................................................................................................................................ 9

6.4 Side grooves ............................................................................................................................................................................................10

6.5 Conditioning ...........................................................................................................................................................................................10

7 Apparatus ..................................................................................................................................................................................................................10

7.1 Test machine ..........................................................................................................................................................................................10

7.2 Grips ..............................................................................................................................................................................................................11

7.3 Crack length measurement .......................................................................................................................................................11

7.4 Test atmosphere .................................................................................................................................................................................15

8 Test procedure .....................................................................................................................................................................................................15

8.1 Measurement of specimen dimensions ..........................................................................................................................15

8.2 Specimen mounting .........................................................................................................................................................................15

8.3 Loading .......................................................................................................................................................................................................15

8.4 Out-of-plane crack propagation ............................................................................................................................................15

8.5 Discontinuous crack propagation ........................................................................................................................................15

8.6 Number of tests ...................................................................................................................................................................................15

9 Calculation and interpretation of results ................................................................................................................................16

9.1 Crack length versus number of cycles ..............................................................................................................................16

9.2 Crack curvature correction ........................................................................................................................................................16

9.3 Crack growth rate da/dN ...........................................................................................................................................................16

9.4 Stress intensity factor range ΔK ...........................................................................................................................................16

9.5 Energy release rate range ΔG .................................................................................................................................................17

10 Test report ................................................................................................................................................................................................................17

10.1 General ........................................................................................................................................................................................................17

10.2 For fatigue crack propagation test ......................................................................................................................................17

10.3 For fatigue crack propagation to failure test ..............................................................................................................18

Annex A (informative) Abnormality in the use of cyclic fatigue crack propagation test for ranking

long-term static fatigue behaviour .................................................................................................................................................19

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

© ISO 2014 – All rights reserved iii
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ISO 15850:2014(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 on the meaning of ISO specific terms and expressions related to conformity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers

to Trade (TBT) see the following URL: Foreword - Supplementary information.

The committee responsible for this document is ISO/TC 61, Plastics, Subcommittee SC 2, Mechanical

properties.

This second edition cancels and replaces the first edition (ISO 15850:2002) of which it constitutes a

minor revision.
iv © ISO 2014 – All rights reserved
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INTERNATIONAL STANDARD ISO 15850:2014(E)
Plastics — Determination of tension-tension fatigue crack
propagation — Linear elastic fracture mechanics (LEFM)
approach
1 Scope

This International Standard specifies a method for measuring the propagation of a crack in a notched

specimen subjected to a cyclic tensile load varying between a constant positive minimum and a constant

positive maximum value. The test results include the crack length as a function of the number of load

cycles and the crack length increase rate as a function of the stress intensity factor and energy release

rate at the crack tip. The possible occurrence of discontinuities in crack propagation is detected and

reported.

The test can be also used for the purpose of determining the resistance to crack propagation failure. In

this case, the results can be presented in the form of number of cycles to failure or total time taken to

cause crack propagation failure versus the stress intensity factor (see Annex A).

The method is suitable for use with the following range of materials:

— rigid and semi-rigid thermoplastic moulding and extrusion materials (including filled and short-

fibre-reinforced compounds) plus rigid and semi-rigid thermoplastic sheets;

— rigid and semi-rigid thermosetting materials (including filled and short-fibre-reinforced compounds)

plus rigid and semi-rigid thermosetting sheets.
2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable for its application. For dated references, only the edition cited applies. For undated

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

ISO 291, Plastics — Standard atmospheres for conditioning and testing
ISO 527 (all parts), Plastics — Determination of tensile properties
ISO 2818, Plastics — Preparation of test specimens by machining
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
cycle

smallest segment of a load-time or stress-time function which is repeated periodically

Note 1 to entry: The terms fatigue cycle, load cycle, and stress cycle are also commonly used.

3.2
number of cycles completed
number of load cycles since the beginning of a test
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ISO 15850:2014(E)
3.3
waveform
shape of the load-time curve within a single cycle
3.4
maximum load
max
highest value of the load during a cycle
Note 1 to entry: It is expressed in newtons.

Note 2 to entry: Only positive, i.e. tensile, loads are used in this test method.

3.5
minimum load
min
lowest value of the load during a cycle
Note 1 to entry: It is expressed in newtons.

Note 2 to entry: Only positive, i.e. tensile, loads are used in this test method.

3.6
load range
difference between the maximum and the minimum loads in one cycle, given by:
ΔP = P − P
max min
3.7
load ratio
stress ratio
ratio of the minimum to the maximum load in one cycle, i.e.:
min
max
3.8
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, as r tends to zero:
Kr=limσ() 2πr
r→0
[SOURCE: ISO 13586:2000, 3.3]
1/2
Note 1 to entry: It is expressed in pascal root metres (Pa⋅m ).

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

dimensions.
3.9
maximum stress intensity factor
max
highest value of the stress intensity factor in one cycle
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ISO 15850:2014(E)
3.10
minimum stress intensity factor
min
lowest value of the stress intensity factor in one cycle
3.11
stress intensity factor range

difference between the maximum and minimum stress intensity factors in one cycle, given by:

ΔK = K − K
max min
3.12
energy release rate

difference between the external work δU done on a body to enlarge a cracked area by an amount δA

ext
and the corresponding change in strain energy δU :
δU δU
extS
G= −
δA δA
Note 1 to entry: It is expressed in joules per square metre.

Note 2 to entry: Assuming linear elastic behaviour, the following relationship between the stress intensity factor

K and the energy release rate G holds:
where
E’ = E for plane stress;
E for plane strain conditions;
E'=
1−ν
E and ν are the tensile modulus and Poisson’s ratio, respectively.
3.13
maximum energy release rate
max
highest value of the energy release rate in one cycle
3.14
minimum energy release rate
min
lowest value of the energy release rate in one cycle
3.15
energy release rate range

difference between the maximum and minimum energy release rates in one cycle, given by:

ΔG = G − G
max min
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ISO 15850:2014(E)
3.16
notch

sharp indentation made in the specimen, generally using a razor blade or a similar sharp tool, before a

test and intended as the starting point of a fatigue-induced crack
3.17
initial crack length
length of the notch (3.16)
Note 1 to entry: It is expressed in metres.

Note 2 to entry: For compact tensile (CT) specimens, it is measured from the line joining the load-application

points (i.e. the line through the centres of the loading-pin holes) to the notch tip (see Figure 2). For single-edge-

notched tensile (SENT) specimens, it is measured from the edge of the specimen to the notch tip. Details of the

measurement procedure are given in 7.3.
3.18
crack length

total crack length at any time during a test, given by the initial crack length a plus the crack length

increment due to fatigue loading
Note 1 to entry: It is expressed in metres.
3.19
fatigue crack growth rate
da/dN

rate of crack extension caused by fatigue loading and expressed in terms of average crack extension per

cycle
Note 1 to entry: It is expressed in metres per cycle.
3.20
stress intensity calibration

mathematical expression, based on empirical or analytical results, that relates the stress intensity factor

to load and crack length for a specific specimen geometry
3.21
gauge length

free distance between the upper and lower grips after

the specimen has been mounted in the test machine
Note 1 to entry: It is expressed in metres.
3.22
number of cycles to failure

total number of load cycles from the beginning of the test to fatigue crack propagation to sample failure

3.23
time to failure

total number of load cycles from the beginning of the test to fatigue crack propagation to sample failure,

expressed in time
Note 1 to entry: It is expressed in hours.
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ISO 15850:2014(E)
4 Principle

A constant-amplitude cyclic tensile load is imposed on a specimen under suitable test conditions

(specimen shape and size, notching, maximum and minimum loads, load cycle frequency, etc.), causing a

crack to start from the notch and propagate.

The crack length a is monitored during the test and recorded as a function of the number N of load cycles

completed.

Numerical differentiation of the experimental function a(N) provides the fatigue crack growth rate

da/dN which is reported as a function of stress intensity factor and energy release rate at the crack tip.

For the case where total number of cycles to failure or time to failure is to be determined, the crack

length need not be monitored.
5 Significance and use

Fatigue crack propagation, particularly when expressed as the fatigue crack growth rate da/dN as a

function of crack-tip stress intensity factor range ΔK or energy release rate range ΔG, characterizes

a material’s resistance to stable crack extension under cyclic loading. Background information on the

fatigue behaviour of plastics and on the fracture mechanics approach to fatigue for these materials is

given in References [1] and [2].

Expressing da/dN as a function of ΔK or ΔG provides results that are independent of specimen geometry,

thus enabling exchange and comparison of data obtained with a variety of specimen configurations

and loading conditions. Moreover, this feature enables da/dN versus ΔK or ΔG data to be utilized in the

design and evaluation of engineering structures. The concept of similitude is assumed, which implies

that cracks of differing lengths subjected to the same nominal ΔK or ΔG will advance by equal increments

of crack extension per cycle.

Fatigue crack propagation data are not geometry independent in the strict sense since thickness effects

generally occur. The potential effects of specimen thickness have to be considered when generating data

for research or design.

Anisotropy in the molecular orientation or in the structure of the material, and the presence of residual

stresses, can have an influence on fatigue crack propagation behaviour. The effect can be significant

when test specimens are removed from semi-finished products (e.g. extruded sheets) or finished

products. Irregular crack propagation, namely excessive crack front curvature or out-of-plane crack

growth, generally indicates that anisotropy or residual stresses are affecting the test results.

This test method can serve the following purposes:

a) to establish the influence of fatigue crack propagation on the lifetime of components subjected to

cyclic loading, provided data are generated under representative conditions and combined with

appropriate fracture toughness data (see ISO 13586) and stress analysis information;

b) to establish material-selection criteria and inspection requirements for damage-tolerant

applications;

c) to establish, in quantitative terms, the individual and combined effects of the material’s structure,

the processing conditions, and the loading variables on fatigue crack propagation;

d) used as an accelerated test for the evaluation of service life performance of components subjected

to static fatigue loading conditions (this would also include ranking between materials — see

Annex A).
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ISO 15850:2014(E)
6 Test specimens
6.1 Shape and size
6.1.1 Standard specimens

Two different types of specimen can be used: single-edge-notched tensile (SENT) and compact tensile

(CT). Figures 1 and 2 describe their geometrical characteristics.

For the case where the test is to be carried out to sample failure for the purpose of determining the

total number of cycles to failure or time failure, and where crack propagation need not be monitored, a

[6]

full notch tensile (FNT) specimen of ISO 16770 and a cracked round bar (CRB) specimen may be also

utilized.
6.1.2 Thickness and width

When the specimen thickness h is too small compared to the width w, it is difficult to avoid lateral

deflections or out-of-plane bending of the specimen. Conversely, with very thick specimens, through-

thickness crack curvature corrections are often necessary and difficulties can be encountered in

meeting the through-thickness straightness requirement of 8.1.

On the basis of these considerations, the following limits are recommended for h and w:

a) for CT specimens, w/10 ≤ h ≤ w/2;
b) for SENT specimens, w/20 ≤ h ≤ w/4.

It should be noted that the test results are in general thickness dependent: specimens obtained from the

same material but having different thicknesses are likely to give different responses.

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

from which the specimens are cut.
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ISO 15850:2014(E)
Key
w width w/20 ≤ h ≤ w/4 (recommended)
l length l > 2,5w
1 1
h thickness
a initial crack length
The notch shall be within ±0,01w of the specimen centreline.

Figure 1 — Standard single-edge-notched tensile (SENT) specimen for fatigue crack

propagation testing
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ISO 15850:2014(E)
Key
w effective width w/10 ≤ h ≤ w/2 (recommended)
W overall width W = 1,25w ± 0,01w
l length l = 1,2w ± 0,01w
1 1
distance between centres of loading-pin holes located l = 0,55w ± 0,005w
2 2
symmetrically to the crack plane to within ± 0,005w
R radius of loading-pin hole R = 0,125w ± 0,005w
h thickness
a initial crack length a ≥ 0,2w
0 0
The notch shall be within ±0,01w of the specimen centreline.

Figure 2 — Standard compact tensile (CT) specimen for fatigue crack propagation testing

6.1.3 Size requirements

In order for the results obtained by this test method to be valid, it is required that the material behaviour

be predominantly linear elastic at all values of applied load and crack length. Deviations may arise from

either viscoelastic behaviour of the material or large-scale plasticity ahead of the crack tip. The former

may result in significant nonlinearity of the mechanical behaviour, possibly aggravated by a progressive

rise of the specimen temperature during the test. The test procedure outlined in this International

Standard is therefore recommended only for materials exhibiting very limited viscoelasticity under the

loading frequency used and for the expected test duration. Large-scale plasticity of the ligament can be

avoided by ensuring that the plastic zone around the crack tip is small compared with the size of the

[3]

uncracked ligament (w − a). On the basis of previous experience with metallic materials , it is required

that the following size limits be satisfied in order for the test results to be valid:

wa− ≥ 4 π K σ (1)
() ()
maxy
where
w − a is the uncracked-specimen ligament width;

σ is the tensile-yield stress measured in accordance with the relevant part of ISO 527.

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ISO 15850:2014(E)

The same size limits are expressed in graphical form in Figure 3, where the dimensionless quantities

Kw/ σ and a/w are plotted against each other. All combinations of specimen size, crack length,

maxy

material yield stress, and stress intensity factor which lie below the curve in Figure 3 satisfy the

specimen size requirements of this test method.

Figure 3 — Size requirements for standard fatigue crack propagation specimens (Values which

lie below the curve satisfy the specimen size requirements of this method)
6.2 Preparation

Prepare specimens in accordance with the relevant materials specification and in accordance with

ISO 2818. In the case of anisotropic materials, take care to indicate the reference direction on each

specimen.
6.3 Notching

Produce a sharp notch or, when feasible, a natural crack, intended as the starting point of the fatigue-

induced crack, in the specimen at the locations depicted in Figures 1 and 2, either in a single step or by

sharpening the tip of a blunt slot or notch made by machining.

It is required that the initial crack length a in the CT specimen be at least 0,2w so that K-calibration

is not influenced by small variations in the location and dimensions of the loading-pin holes. The notch

length in CT specimens shall be chosen accordingly (see 7.3 for details of measurement of initial crack

length a ).

The notch in both the CT and SENT specimens shall be within ±0,01w of the specimen centreline.

When sharpening a blunt notch produced by machining, the length of the sharp notch shall be more than

four times the blunt notch tip radius. Methods a), b), c), or d) can be used to create a natural crack or a

sharp notch:

a) Machine a sharp notch in the 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 specimens, a natural crack

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

damage).
© ISO 2014 – All rights reserved 9
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ISO 15850:2014(E)

b) If control is difficult or repeatability problems are experienced with method a), it is possible with

some brittle specimens to generate a sharp notch by simply pressing the razor blade against the

specimen at a temperature close to, but lower than, the glass-transition temperature of the material.

With this notching procedure, proper handling of the specimen and correct choice of temperature

are essential to avoid deformation of, or damage to, the specimen. Use a new razor blade for each

specimen.

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

razor blade across the notch. Use a new razor blade for each specimen.

d) With tough materials, cooling the specimen and then tapping with a razor blade is sometimes

successful.

It may be useful to check the effectiveness of the notching procedure by performing preliminary tests

at a constant displacement or constant loading rate on specimens notched using different methods. The

best notching method is the one which gives the lowest K-value at crack initiation.

6.4 Side grooves

Specimens may need side grooves to avoid the crack path deviating from the plane of symmetry (see 8.4)

and to promote straighter crack fronts. Side grooves may also, in some cases, improve the visibility of

the crack tip when using visual methods for crack length measurement.

The side grooves shall be equal in depth, have an included angle of 45° ± 5° and have a root radius of

0,25 mm ± 0,05 mm.

The total reduction in specimen thickness due to side grooving shall not exceed 0,2h.

When using side grooves, the specimen thickness h shall be taken as the distance between the roots of

the side grooves.
6.5 Conditioning

After notching, condition specimens as specified in the International Standard for the material tested. In

the absence of this information, select the most appropriate conditions from ISO 291, unless otherwise

agreed upon by the interested parties.
7 Apparatus
7.1 Test machine
7.1.1 General

The test machine shall be capable of imposing a prescribed load on the specimen (i.e. of operating in the

“load control” mode) and of varying the load with time in accordance with a specified waveform. The

load distribution shall be symmetrical to the specimen notch. Hydraulically driven test machines with

electronic control are generally suitable for this purpose. Mechanically driven machines can also be

used but are less versatile as regards the cycle types and frequency range available.

For the case where the load cycle frequency is lower than or equal to 0,1 Hz with load amplitude not

greater than 1 000 N, pneumatically driven test machines with electronic load-pressure feedback

control could be also suitable.
7.1.2 Load-cycle waveform

The most commonly employed waveform is a sine wave, but other types, e.g. triangular or square waves,

may be used when simulating service co
...

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