Metallic materials — Principles and designs for multiaxial fatigue testing

ISO/TR 12112:2018 discusses the general principles of multiaxial fatigue testing and the design recommendations for specific classes of multiaxial testing machines and test specimens.

Matériaux métalliques — Principes et conceptions associés aux essais de fatigue multiaxiale

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Publication Date
24-Apr-2018
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6060 - International Standard published
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25-Apr-2018
Completion Date
25-Apr-2018
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TECHNICAL ISO/TR
REPORT 12112
First edition
2018-04
Metallic materials — Principles and
designs for multiaxial fatigue testing
Matériaux métalliques — Principes et conceptions associés aux essais
de fatigue multiaxiale
Reference number
ISO/TR 12112:2018(E)
ISO 2018
---------------------- Page: 1 ----------------------
ISO/TR 12112:2018(E)
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Published in Switzerland
ii © ISO 2018 – All rights reserved
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ISO/TR 12112:2018(E)
Contents Page

Foreword ..........................................................................................................................................................................................................................................v

Introduction ................................................................................................................................................................................................................................vi

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

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

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

4 General principles ............................................................................................................................................................................................... 2

4.1 Methodology ............................................................................................................................................................................................. 2

4.2 Historical development ................................................................................................................................................................... 2

4.3 Specific multiaxial test methods .............................................................................................................................................. 6

[6]

4.3.1 Bending + torsion ........................................................................................................................................... .......... 6

[7]

4.3.2 Axial + torsion ............................................................................................................................................................. 6

[8]

4.3.3 Axial + internal pressure ................................................................................................................................... 6

[9]

4.3.4 Axial + internal + external pressure ......................................................................................................... 6

[10]

4.3.5 Axial + internal + external pressure + torsion .............................................................................. 6

[11]

4.3.6 Cruciform — LCF ................................................................................................................................................... 6

[12]

4.3.7 Cruciform — Crack growth ........................................................................................................................... 7

4.4 Multiaxial fatigue analysis ............................................................................................................................................................. 7

4.4.1 Computer aided design .............................................................................................................................................. 7

4.4.2 Fatigue life prediction ........................................................................................................................................... ....... 7

4.5 Multiaxial fatigue failure criteria ............................................................................................................................................. 8

5 Axial + torsion testing systems and specimen design.................................................................................................... 9

5.1 Historical development ................................................................................................................................................................... 9

5.2 Specimen design .................................................................................................................................................................................11

5.2.1 Design considerations ..............................................................................................................................................11

5.2.2 Design recommendations .....................................................................................................................................11

[4]

5.2.3 Comparison with ASTM E2207 .................................................................................................................11

5.3 Machine design ....................................................................................................................................................................................12

5.3.1 Frame ......................................................................................................................................................................................12

5.3.2 Loadcells ..............................................................................................................................................................................12

5.3.3 Strain measurement...................................................................................................................................................12

5.3.4 Control ...................................................................................................................................................................................12

5.3.5 Data acquisition .............................................................................................................................................................12

5.3.6 Software................................................................................................................................................................................12

6 Cruciform testing systems and specimen design .............................................................................................................13

6.1 Historical development ................................................................................................................................................................13

6.2 Specimen design .................................................................................................................................................................................13

6.3 Machine design ....................................................................................................................................................................................14

6.3.1 Frame ......................................................................................................................................................................................14

6.3.2 Loadcells ..............................................................................................................................................................................14

6.3.3 Strain measurement...................................................................................................................................................15

6.3.4 Crack growth monitoring ......................................................................................................................................15

6.3.5 Control ...................................................................................................................................................................................15

6.3.6 Data acquisition .............................................................................................................................................................15

6.3.7 Software................................................................................................................................................................................15

7 Axial + differential pressure systems and specimen design ................................................................................16

7.1 Historical development ................................................................................................................................................................16

7.2 Specimen design .................................................................................................................................................................................19

7.2.1 Design considerations ..............................................................................................................................................19

7.2.2 Design recommendations .....................................................................................................................................19

7.2.3 Axial stress due to pressure ................................................................................................................................20

7.3 Machine design ....................................................................................................................................................................................20

7.3.1 Frame ......................................................................................................................................................................................20

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ISO/TR 12112:2018(E)

7.3.2 Pressure containment ..............................................................................................................................................20

7.3.3 Differential pressure ..................................................................................................................................................20

7.3.4 Force measurement ....................................................................................................................................................20

7.3.5 Pressure measurement ...........................................................................................................................................20

7.3.6 Strain measurement...................................................................................................................................................20

7.3.7 Control ...................................................................................................................................................................................20

7.3.8 Data acquisition .............................................................................................................................................................20

7.3.9 Software................................................................................................................................................................................21

Annex A Historical analysis of specimen geometry .........................................................................................................................22

Bibliography .............................................................................................................................................................................................................................29

iv © ISO 2018 – All rights reserved
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ISO/TR 12112:2018(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.

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World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following

URL: www .iso .org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals,

Subcommittee SC 4, Fatigue, fracture and toughness testing.
© ISO 2018 – All rights reserved v
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ISO/TR 12112:2018(E)
Introduction

Structural components in industry are frequently subject to some form of multiaxial stressing. Fatigue

cracks generally initiate from surface defects or discontinuities and are thus primarily influenced by

the surface biaxial stress system. This can vary from equibiaxial, where surface principal stresses are

equal in magnitude and sign (present under conditions of pressurization, rotation and thermal loading)

to pure shear where surface stresses are equal in magnitude, opposite in sign (as in shafts and shear

panels).

The majority of fatigue test data gathered worldwide have been and will continue to be under uniaxial

conditions for reasons of simplicity and cost. A secondary goal of multiaxial testing is therefore to

develop behavioural models which relate failure under specified multiaxial conditions to established

uniaxial cases.

This document utilizes data gathered from the past 80 years spanning most multiaxial fatigue research.

It can be of interest to new researchers in the field and form a basis for full International Standards as

the need arises.
vi © ISO 2018 – All rights reserved
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TECHNICAL REPORT ISO/TR 12112:2018(E)
Metallic materials — Principles and designs for multiaxial
fatigue testing
1 Scope

This document discusses the general principles of multiaxial fatigue testing and the design

recommendations for specific classes of multiaxial testing machines and test specimens.

2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

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

— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
3.1
biaxial strain ratio
ratio of the surface principal strains, smaller/larger
3.2
biaxial stress ratio
ratio of the surface principal stresses, smaller/larger
3.3
principal strains
ε > ε > ε
1 2 3
principal direct strains at a point in a multiaxial strain field
3.4
principal stresses
σ > σ > σ
1 2 3
principal direct stresses at a point in a multiaxial strain field
3.5
Poisson’s ratio

negative ratio of transverse to longitudinal strain under uniaxial tensile stressing

3.6
specimen diameter
diameter of a cylindrical tubular specimen

Note 1 to entry: The symbols d , d and d are used to express outside, inside and mean diameters, respectively.

0 i m
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ISO/TR 12112:2018(E)
3.7
parallel length
parallel length of a cylindrical tubular specimen
3.8
fillet radius
fillet radius of a cylindrical tubular specimen
3.9
directional suffix
suffix identifying a direction in a cylindrical tubular specimen

Note 1 to entry: The suffixes z, r and θ are used to express axial, radial and circumferential directions,

respectively.
3.10
strain component suffix
suffix identifying a strain component

Note 1 to entry: The suffixes e, p and t are used for elastic, plastic and total strain components, respectively.

3.11
internal pressure
internal pressure within a cylindrical tubular specimen
4 General principles
4.1 Methodology

Multi-axial fatigue testing sets out to simulate the dynamic stress-strain conditions at key locations on

components, on test specimens of constant geometry for a given test series, and to determine the cyclic

stress-strain history, crack initiation and propagation behaviour, fatigue life and failure mode.

Dependent on the level of geometric constraint in the real component, it can be more useful to

test specimens under stress or strain control, e.g. a test specimen representative of a relatively

unconstrained gas turbine blade can be tested in stress control whereas it can be more relevant to

utilize strain control for a test specimen simulating part of a steam turbine disc subject to thermal

straining during start-up.

Further, where stress amplitudes are sufficient to take test specimen materials well into the region

of cyclic plasticity (LCF), it can be preferable to employ strain control in order to better control cyclic

amplitude during the test and failure at end of test.
4.2 Historical development

Multiaxial fatigue has been addressed since the 1930s. Initially, testing machine and specimen designs

were created to address specific biaxial stress conditions, e.g. torsion, bending + torsion, cantilever

bending, anticlastic bending and plate pressurization. However, a criticism of much of the early research

was that specimen design had to change in order to change the biaxial stress or strain ratio, leading to

uncertainty in the interpretation of results.

The benefit of being able to test a single specimen design over a wide range of biaxiality led to the

choice of two generic specimen types, tubular and cruciform, together with associated multi-axis

testing machine designs.
2 © ISO 2018 – All rights reserved
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ISO/TR 12112:2018(E)
[5]

Table 1 summarizes the attributes of the different test methods applicable to tubular and plate

specimens.

Biaxiality is shown in terms of the range of surface strains with ε held constant. Only cruciforms

and systems employing axial force plus internal and external pressure are capable of applying fully

reversed fatigue cycles over the full range of biaxiality (−1 ≤ ϕ ≤ +1) to test specimens.

Buckling is a key concern in the design of effective LCF specimens.
A reasonable gauge area of essentially constant strain is beneficial.
Ideally, strain should be constant through the thickness.

If all the applied forces are carried by the gauge area, then all stresses and strains can be determined;

otherwise, only total (not plastic) strains can be measured.

The ability to visually observe the specimen is useful especially for surface crack monitoring.

Some designs are suitable for high temperature and thermo-mechanical fatigue (TMF) testing.

Systems involving torsion cause the principal axes to rotate up to 45°.

System cost can be scaled by the number of actuators, and therefore closed servo-loops, in the design.

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ISO/TR 12112:2018(E)
4 © ISO 2018 – All rights reserved
Table 1 — Multiaxial test methods for tubular and plate specimens

Biaxial Range of Single Immune Invariant Min. Moni- Speci- Crack High tem- TMF Rota- No. of

specimen surface geome- to buck- σ and ε ε-gra- toring men ob- growth perature studies tion of actuators

schemat- principal try ling on gauge dient biaxial σ servation studies capability principal propor-

ics and strains area through and ε stresses tional to
modes of thickness cost
loading
Bending
√ √ √ √ √ 1
+ torsion
Axial
√ √ √ √ √ √ √ √ √ 2
+ torsion
Axial
√ √ √ √ √ √ 2
+ P
int
Axial
+ P
int
+ con- √ √ √ √ √ 2
stant
+ P
ext
Axial
+ P
int
√ √ √ √ √ 4
+ P
ext
+ torsion
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ISO/TR 12112:2018(E)
© ISO 2018 – All rights reserved 5
Table 1 (continued)

Biaxial Range of Single Immune Invariant Min. Moni- Speci- Crack High tem- TMF Rota- No. of

specimen surface geome- to buck- σ and ε ε-gra- toring men ob- growth perature studies tion of actuators

schemat- principal try ling on gauge dient biaxial σ servation studies capability principal propor-

ics and strains area through and ε stresses tional to
modes of thickness cost
loading
Cantile-
√ √ √ √ 1
ver bend
Anticlas-
√ √ √ √ √ 1
tic bend
Plate
pressuri- √ √ 1
zation
Cruci-
√ √ √ √ √ 4
form LCF
Cruci-
form
√ √ √ √ √ √ √ √ 4
crack
growth
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ISO/TR 12112:2018(E)
4.3 Specific multiaxial test methods
[6]
4.3.1 Bending + torsion

This was the first technique used to apply combined stresses in high cycle fatigue (HCF) at room

temperature. Oscillating vertical forces were applied to a horizontally clamped cylindrical specimen

which could be rotated by up to 90° in the horizontal plane so as to introduce bending, bending

+ torsion, or torsion in the waisted centre section. Specimens were either solid or hollow. A number of

these electro-mechanical testing machines were built between 1930 and 1950 to investigate fatigue of

aero-engine steels, especially for crankshaft applications.
[7]
4.3.2 Axial + torsion

This popular technique employs a single tubular specimen design with a gauge length over which stress

and strain are substantially invariant and access for strain measurement and crack monitoring. The

principal stress and strain directions progressively rotate through 45° as the test moves from uniaxial

to torsion. Elevated temperature testing and thermo-mechanical fatigue (TMF) are achievable with

relevant accessories and control software. Despite a limited range of strain biaxiality (–ν ≥ ϕ ≥ −1),

this approach is widespread and standard testing machines with dual servo-hydraulic actuators are

available from commercial manufacturers.
[8]
4.3.3 Axial + internal pressure

This approach permits a single tubular specimen design with essentially invariant stress and strain

over the gauge length. Crack studies are difficult as maximum stress occurs at the bore, so cracks can

only be visible after penetration of the wall shortly prior to failure. In addition, cyclic plasticity results

in strain ratchetting as external radial compression cannot be applied to fully reverse the stress —

strain cycle. Hence this approach is essentially restricted to elastic HCF studies. The testing machine

typically utilizes a dual actuator servo-hydraulic design.
[9]
4.3.4 Axial + internal + external pressure

This design enables fully reversed cycling without ratchetting because radial compression can be

applied. Axial and circumferential stresses and strains are measurable, enabling LCF hysteresis loops

on both surface axes, which makes the approach suitable for fundamental behavioural studies. Because

a pressure vessel is located around the specimen, visual observations are difficult. Also elevated

temperature testing above about 200 °C requires gas pressurization which presents safety issues. By

employing variable internal pressure and fixed external pressure, a design with just 2 servo-hydraulic

actuators is achievable.
[10]
4.3.5 Axial + internal + external pressure + torsion

The addition of torsion introduces rotation of principal stress or strain axes which allows, in principle,

material anisotropy and the effects of the different symmetries (in the axial and circumferential

directions) to be investigated. The mechanical design is complex with 4 servo-hydraulic actuators, but

has been successfully achieved.

NOTE Multiaxial testing machines featuring axial force and differential pressure are typically used for

academic research or specific R&D applications and are usually designed and manufactured to order.

[11]
4.3.6 Cruciform — LCF

Four orthogonal loading arms apply biaxial strain to a central circular gauge area on the specimen. This

area is usually spherically recessed on both sides in order to resist buckling and ensure that cracks

initiate near the centre. In consequence, the gauge area does not support all the applied forces, i.e.

some of the force is shunted around the outside. As a result, stresses and plastic strains are not readily

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ISO/TR 12112:2018(E)

determinable. However, visual observation of developing fatigue cracks is straightforward and elevated

temperature testing, including TMF, is readily achievable.
[12]
4.3.7 Cruciform — Crack growth

The four orthogonal arms are slotted to minimize grip constraint. A central square, constant thickness,

gauge area typically features a central hole stress raiser to initiate fatigue cracks. There is a large

region of essentially constant biaxial strain ideal for crack initiation and propagation studies. Elevated

temperature testing, including TMF, is achievable. Maximum compressive strains are limited to avoid

buckling in the gauge area and arms.

NOTE Cruciform designs provide the opportunity for testing single geometry plate specimens with dual

symmetry over the range of surface biaxiality. Testing systems employ 4 servo-hydraulic actuators within an

annular frame and are typically specified according to application and manufactured to order.

4.4 Multiaxial fatigue analysis
4.4.1 Computer aided design

In the design of structural components subject to multiaxial fatigue, it is common to use finite element

analysis (FEA) to determine stresses and strains. For elastic behaviour, such analyses are useful to

predict stress concentrations and local yield in order to evolve specimen designs.

4.4.2 Fatigue life prediction

Yield criteria such as Tresca (maximum shear), Von Mises or octahedral shear strain, coupled with the

Palmgren-Miner linear damage hypothesis, are frequently employed to predict “multiaxial fatigue life”.

However, research evidence does not necessarily support this approach.
[13][14]

Multiaxial LCF fatigue studies on specimens capable of being tested over the full biaxial range

showed that Tresca and Von Mises did not correlate all the fatigue life data, especially over the range

between uniaxial and torsion, i.e. (0 ≥ ψ ≥ −1) and (−ν ≥ ϕ ≥ −1).

For example, in Figure 1, Mohr’s strain circles drawn with principal strain (ε ) constant and Poisson’s

ratio = 0,5, show that the maximum shear strain (γ ) is the lowest in the uniaxial stress (ϕ = −ν) case.

max

However, ranking these biaxial fatigue cases from most to least damaging, the order was equibiaxial

strain (ϕ = +1), plane strain (ϕ = 0), uniaxial stress (ϕ = −ν) and pure shear (ϕ = −1).

[15]

Current consensus indicates that a critical shear plane analysis including, as a modifier, the direct

stress or strain acting normal to that plane, offers the best approach to correlating multiaxial fatigue

behaviour across the complete range of applied biaxial surface stresses or strains.

© ISO 2018 – All rights reserved 7
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ISO/TR 12112:2018(E)
a) Pure shear (ϕ = −1) b) Uniaxial stress (ϕ = −ν)
c) Equibiaxial strain (ϕ = +1) d) Plane strain (ϕ = 0)
Figure 1 — Mohr’s strain circles, ε constant, for Poisson’s Ratio (ν) = 0,5
4.5 Multiaxial fatigue failure criteria

The definition of fatigue failure criteria can have a significant effect on attempts to correlate theoretical

analysis with experimental results.

Axial force + torsion (without pressurization) results in the gauge area seeing all the applied stresses.

...

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