TALAT Lecture 2405: Fatigue an Fracture in Aluminium Structures

TALAT Lecture 2405

An Updating of TALAT Chapter 2400

Fatigue and Fracture in Aluminium Structures
(Updated from the TAS project)
TAS alu
Leonardo da Vinci program
Training in Aluminium Alloy Structural Design

40 pages, 37 Figures

Prepared by Prof. Dimitris Kosteas
Technische Universität München, Germany

Date of Issue: 1999
 EAA - European Aluminium Association

2405 Fatigue and Fracture in Aluminium Structures
(Updated from the TAS project)

Table of contents

Abstract ...............................................................................................................................3
2405.01. Fatigue Tests ........................................................................................................4
2405.01.01 Experimental Investigations .......................................................................... 4
2405.01.02 Number of Specimens Required.................................................................... 4
2405.01.03 Cost of Tests .................................................................................................. 6
2405.02 Fatigue Data Analysis and Evaluation ...............................................................7
2405.03 Fatigue Design Line ..............................................................................................8
2405.04 Safety and Reliability In Aluminium Design ...................................................10
2405.04.01 Safety Concept in Recommendations .......................................................... 10
Partial Safety Factors for Fatigue Loading ............................................................... 11
Partial Safety Factors for Fatigue Strength ............................................................... 12
2405.04.02 Safety Index and Partial Safety Factors ....................................................... 14
2405.04.03 Safety Index in Aluminium Recommendations........................................... 18
2405.04.04 Summary and Conclusions .......................................................................... 21
2405.04.05 References.................................................................................................... 22
2405.05 Unclassified Details.............................................................................................23
2405.05.01 Design by Reference to Published Data ...................................................... 23
2405.05.02 The Aluminium Data Bank (AlDaBa)......................................................... 23
2405.06 Testing for Fatigue Design ...............................................................................27
2405.07 Damage Tolerant Design....................................................................................28
2405.07.01 Outline of Provisions in ENV 1999-2, 2.3 and Annex B ............................ 29
2405.07.02 Summarizing the Life Prediction Procedure............................................... 38
2405.08 Sequence Effects ...............................................................................................39
2405.09 Strain-Life Approach .........................................................................................39
2405.10 List of Figures .....................................................................................................39

TALAT 2405 2

Abstract

Modern fatigue design standards require knowledge of fatigue data acquisition,
documentation, representation and evaluation, i.e. the background of S-N design lines
together with reliability statements. Fatigue design by testing is the next option. Finally, life
estimation based on fracture mechanics and crack propagation material characteristics is
introduced as a further option. This course material should be supplemented by the a) ENV
1999-2 (May 1998) on Fatigue Design of Aluminium Structures, b) the respective chapters in
TALAT, c) the textbook „Metal Fatigue“ by N.E.Frost, K.J.Marsh and L.P.Pook in Oxford
Engineering Science Series, 1974, and d) the book „Fatigue Testing and the Analysis of
Results“ by W. Weibull in Pergamon Press, 1961.

A compact outline of the design procedures and the respective background information for the
definition of S-N design lines for structural details for the Eurocode 9 / ENV 1999-2 has been
published in STAHLBAU Spezial „Aluminium in Practice“, 67(1998), Ernst & Sohn/Wiley,
Berlin, ISSN 0038-9145, pp 111-130. A comparison to design lines of other proposals and to
actual fatigue data is also given here. Special attention is drawn to the design proposal of the
ERAAS Fatigue Design document (1992).

This material has been utilized together with further definitions for classification of structural
details to provide a proposal supported by the European Aluminium Association as a
National Application Document, which may also be considered for introduction into the
actual standard when this will be converted from an ENV to an EN. This material is included
as a „supplement“ to this document.

TALAT 2405 3

2405.01. Fatigue Tests

2405.01.01 Experimental Investigations

The plain fatigue properties of a material will usually be determined on circular cross-section
specimens, with careful surface finish. In practice though, few parts will have highly polished,
undamaged surfaces and solely round cross-sections. Aluminium should be regarded in terms
of a product rather and so test specimens will resemble or be parts of the actual shapes in
practice, usually flat plate or sheet specimens. External corners may be mildly rounded, so that
they do not give rise to early cracks, depending on the actual detail fatigue strength to be
studied. In welded or otherwise notched specimens the crack initiation site will be rather clear
from the beginning.

Because of the inherent variation of test piece parameters (material characteristics, alloy,
product form, temper, geometrical parameters), further manufacturing parameters (joint type
and procedure, post treatment, residual stresses), and environmental parameters (load and
stress type, frequency, corrosion, temperature) a batch of nominally identical specimens is
required. About the necessary number of specimens to be tested see below. In many cases a
properly planned program, with subsequent statistical analysis of the results, may be required
in order to be able to distinguish relevant differences in fatigue behavior. Guidance is
provided in the textbooks mentioned in the abstract to this lecture for the preparation of test
pieces, the testing program itself, and there is also ample literature on the subject in many
national standards, especially in recommendations of the American Society for Testing and
Materials. General information on fatigue testing machines is to be found in the mentioned
textbooks, but information on newer models may be obtained directly from the manufacturers.

More difficult are general statements describing the preparation, set-up, and testing of full-size
structural components. These components will usually be actual parts of the structure itself,
often though will be formed and tested as H- or hollow-shape (double web, box) beams under
pure bending (so called four-point bending) or combinations of bending, shear and axial load.
Information may be obtained here from the respective reports of various laboratories
performing such tests. As one example only, the report on the extensive aluminium beam
program carried out in the eighties at the Technical University of Munich (contributing among
other results to the background data for the European Recommendations and Standards) is
mentioned: D. Kosteas and R. Ondra - Untersuchungen zum Schwingfestigkeitsverhalten
geschweißter Verbindungen in Aluminium-Großbauteilen. Bericht Nr. 897On (AIF 7331),
Laboratorium für den Konstruktiven Ingenieurbau der Techn. Univ. München, 1991.

2405.01.02 Number of Specimens Required

There are numerous literature sources dealing with the theoretical statistical aspects of fatigue
test data sample sizes required for a given probability and confidence limit. Practice will be
characterized though by the given or possible (in manufacturing, economical or time limit
terms) number of specimens. Certain general statements can be made based on the theoretical
aspects as well as on experience from actual tests - see D. Kosteas, „Einfluß des
Stichprobenumfangs bei der statistischen und regressionsanalytischen Auswertung von
Schwingfestigkeitsversuchen, insbes. bei Schweißverbindungen aus AlZnMg1“ (Influence of
sample size in the statistical and regressional analysis of fatigue test data). Aluminium,

TALAT 2405 4

50(1974), 2, 165/170. The following figures recommend number of specimens for the
estimation of an S-N line.

4-9
4 - 9 per level
if staircase
ca. 25 each
3 to 7 levels

static strength 4 - 9
LCF 4 - 9
middle range 12 - 63
HCF 25 - 50
total 45 - 131
TESTNO04.PRS

recommended < 50

alu Sample sizes on different stress levels and cycle
Training in Aluminium Application Technologies
ranges of an S-N line 2405.01.01

Recommended is a number of approximately 50 specimens if the whole range, including the
constant amplitude fatigue limit, is to be established.

TESTNO08.PRS
5,72 11 beams 5,11
7020/AlZn4.5Mg1
date points 36 beams
SFB96/D10 (1984) 7020/AlZn4.5Mg1
per beam 5083/AlMg4.5Mn
AIF 5723 (1986)
7,03 63
184
66 beams small
7020/AlZn4.5Mg1 specimens
6005A/AlMgSi0.7 464 134 7020/AlZn4.5Mg1
6005A/AlMgSi0.7
AIF 7331 (1991)
AIF 7331 (1991)

Source : Technical University of Munich
alu Example of actual number of data points generated
in some fatigue test programs with aluminium 2405.01.02
beams and small specimens

TALAT 2405 5

2405.01.03 Cost of Tests

TESTNO07.PRS

for 1 data point

approximate
cost in DM in the time
between 1980 + 1990

full-size components (beams) up to 3000

small specimens 300
influenced by detail type, weld, testing frequence or test duration,
constant or variable loading, possible crack registration, data
documentation and evaluation procedures

frequence / test duration for 2 million cycles
roughly 2 Hz full-size component roughly 14 days
6 (to 10) Hz small specimen 4 days

alu Average cost and duration of test for typical small
specimens and beams in aluminium. 2405.01.03

stress recommended
TESTNO05.PRS

range data points < 50

cycles to fracture

>100 000 DM from components
< 20 000 DM from small specimens
alu Approximate cost for an S-N line. 2405.01.04

TALAT 2405 6

2405.02 Fatigue Data Analysis and Evaluation

{from TALAT 2401.03}

The following pages give a more detailed background of the analysis of data procedures, the
common fatigue diagrams, and the linear or also, where appropriate, the non-linear
probability-stress-cycles P-S-N curves as they will be utilized in design.

This chapter 2405.02 may be regarded as informative and it is not mandatory reading for
understanding most applications mentioned in the following chapters. Important information
on the P-S-N curves is summarized in the following chapter 2405.03 „Fatigue Design Line“.

TALAT 2405 7

2405.03 Fatigue Design Line

The fatigue design line or fatigue strength curve, as defined in the ENV 1999-2 (Eurocode 9
Fatigue Design) is a multiple slope, straight line in the double logarithmic stress-life diagram
with a characteristic probability of survival, Figure 2405.03.01 and Figure 2405.03.02. The
respective partial safety factors are not included in the equations for the parts of the line since
these are, generally, assumed equal to unity, as is explained in more detail in 2405.04.1.1. The
characteristic value ∆σc is the reference value of fatigue strength at 2x106 cycles stated in
N/mm², depending on the category of the detail.

daten/texte/dim/workshopfat/lecture9.pr4

slope m 1 m 2 = m 1 +2
constant
Ds
i amplitude
fatigue
Ds C limit
Ds D
Ds L cut-off
NC N D N L
limit

1E3 1E5 N 2E6 5E6
i 1E8

 ∆σ C  1
m m2
 ∆σC   2 
m 2
m1
Ni =   ∗2∗10 N i = 
6
   ∗5∗10 6
 ∆σ i   ∆σi   5 
alu Definition of the design line for the middle 2405.03.01

and high cycle fatigue range (HCF).

TALAT 2405 8

fa / g
M2 LCF
Ds i constant
amplitude
fatigue
Ds C limit
Ds D
Ds L cut-off
NC N D N L limit

1E3 Ni 1E5 2E6 5E6 1E8

slope m0 m m 2 =m 1 +2

8
8

1

 ∆σ C  0
m
m0
Ni =   ∗ 20 1 ∗10
m 5

 ∆σ i 

alu Definition of the design line for the low 2405.03.02

cycle fatigue range (LCF)

The design line represents according to the ENV 1999-2 a 2 standard deviation level below
the mean line through experimental data. Theoretically (normal distribution assumed) this
would correspond to a probability of survival of 97,7%. Practically, assuming an average
sample size of six specimens per stress level, the mean minus 2 standard deviation level with
a probability of survival of 97,7 % would have, though, only a confidence level of γ = 0,5.

The following Figure 2405.03.03 states the k values - for the mean minus k standard
deviation levels - at some characteristic probability percentiles and respective sample sizes
together with the respective confidence levels.

Probability of survival pS
90 95 99
sample size n confidence level g
0,50 0,90 0,95 0,50 0,90 0,95 0,50 0,90 0,95
3 1,498 4,258 6,158 1,939 5,310 7,655 2,765 7,340 10,55
6 1,360 2,494 3,006 1,750 3,091 3,707 2,483 4,242 5,062
12 1,316 1,966 2,210 1,691 2,448 2,736 2,395 3,371 3,747
25 1,297 1,702 1,838 1,666 2,132 2,292 2,357 2,952 3,158
(theoretical)
Normal distribution 1,282 1,645 2,326

alu Values of k for estimations of mean minus k 2405.03.03

standard deviation levels

TALAT 2405 9

2405.04 Safety and Reliability In Aluminium Design

This chapter is based on a paper by D. Kosteas and R. Ondra presented on the 6th INALCO
Conference on Aluminium Weldments, April 3-5, 1995, in Cleveland, Ohio, USA. It has also
been published as IIW Doc. No. XIII-1586-95.

Based on the elements of the safety concept as defined in current european recommendations
an evaluation is undertaken for actual values with structural details in welded aluminium
components under fatigue loading especially. Limit values of the safety index are indicated for
conditions in practice.

2405.04.01 Safety Concept in Recommendations

A safety concept on a semi-probabilistic basis, independent from the construction type, has
been introduced in building codes and is expressed by a required value of the reliability index
in current European design recommendations, as for example the Eurocodes [1] or recently
released national codes [2]. There is a rather explicit definition for partial safety factors for
actions (for example ranging from 1.00 to 1.50 and whether favorable or unfavorable effects,
permanent or variable actions are considered [1]) and for resistance (generally 1.10 for
resistance related to the yield strength - instability - or 1.25 for resistance related to the
ultimate tensile strength [1]) to be applied to the static assessment of structures. In the case of
fatigue assessment a harmonization of assumptions has to be introduced as there are a number
of different suggestions for the actual values of the safety index or the partial safety factors to
be applied.

In the case of fatigue the assessment of the structures or parts of it can be expressed generally
by the comparison of an damage equivalent stress range ∆σe to the appropriate design stress
value ∆σR for the corresponding structural detail, whereby the respective partial safety factors
for loading γF and for resistance γM have to be taken into account, Figure 2405.04.01. The
analytical expressions are (∆σi and ni for stresses higher than ∆σD at the part of the S-N line
with slope m1 and ∆σj and nj for stresses lower than ∆σD at the part of the S-N line with slope
m2) for the equivalent stress range

1

 ∑( m
n i ∆σ i 1 ) m −m
+ ∆σ D 1 2 ∑n m2
j ∆σ j
 m1

∆σ e = 


∑n + ∑n i j




and for the fatigue assessment itself
∆σ R
γ F ∆σ e <
γM

TALAT 2405 10

σ

∆σ
∆σ
∆σ
∆σ

alu Fatigue assessment 2405.04.01

Partial Safety Factors for Fatigue Loading

The European document ENV 1991 Eurocode 1: Basis of design and actions on structures
incorporates appropriate values of γF. The Eurocode 3 for steel structures [1] states that the
fatigue assessment procedure shall incorporate a partial safety factor γF for fatigue loading to
cover uncertainties in estimating

• the applied load levels,
• the conversion into stresses and stress ranges,
• the equivalent constant amplitude stress range,
• the design life of the structure, and the evolution of the fatigue loading within the
required design life of the structure.

Especially the last point may have a significant influence on the assessment procedure and
should be taken into account accordingly. In our view the further statement of [1] that „unless
otherwise stated in other parts of the code, or in the relevant loading standard, a value of
γF=1.00 may be applied to the fatigue loading“ is somewhat irritating in this context.

The existing European Recommendations [3] do not go into any details whatsoever about the
value of γF but state rather generally that „fatigue loadings must be defined for the assessment
of the structure in accordance with its intended application“ and that „they should represent an
upper bound estimate of the fluctuating loads to be experienced by the structure or the part
during the full design life“.

The respective British document [4] places the decision upon the designing engineer but is
more specific about the values recommended. The „nominal design life“ (the period in which
the structure or component is required to perform safely) may be increased in certain
circumstances by the „fatigue life factor“, producing thus the so-called „factored design life“.

TALAT 2405 11

The fatigue life factor γL>1 (corresponding to the above-mentioned fatigue load/stress factor
γF, the relationship expressed through γL=N2/N1=(∆σ1/∆σ2)m=(1/γF)m ) accounts for

• the possibility of increasing crack growth during the later stages of the life of the
detail,
• the accuracy of the assumed loading spectrum,
• whether records of loading will be kept during the life of the detail
• the possibility of change of use of the structure in mid-life.

New aluminium standards, as the ENV 1999 Eurocode 9: Design of aluminium structures,
follow the above general recommendations. Because of the fact of the variety of loading
patterns, application fields and situations to be assessed in fatigue - especially in the case of
aluminium structures covering diverse application areas like buildings or transportation -
there is, consequently, a difficulty in defining some universal value. The ENV 1999 -
Eurocode 9 - Part 2: Design in Fatigue states with more detail that „a partial safety factor on
load intensity γFf = 1,0 may be assumed to provide an acceptable level of safety, where the
fatigue loading has been derived in accordance with the requirements“, i.e. observing specific
rules about the characteristics of load spectra and their realistic assessment over suitable
sampling periods. Where fatigue loading has been based on other confidence limits than those
stated, an acceptable level of safety may be assumed to be provided by applying the partial
safety factors on loadings given in Figure 2405.04.02. The values kF and kN describe the
multiples of standard deviations of the intensity and the number of cycles respectively of the
design load spectrum. Only in case of kF = kN = 2, or in other words when the percentile to be
used for the intensity and the percentile to be used for the number of cycles of the load
spectrum are both calculated from the respective mean value plus two standard deviations, the
partial safety factor for fatigue loading may be assumed to unity.

kF gFf
kN = 0 kN = 2
0 1,5 1,4
1 1,3 1,2
2 1,1 1,0

alu Partial safety factors gFf for fatigue load
Training in Aluminium Application Technologies 2405.04.02
intensity after ENV 1999 (EC 9)

Partial Safety Factors for Fatigue Strength

In the case of steel structures older national documents - as for instance the German DIN
15018 and DIN 4132 for cranes and crane bridges - had stated only a partial safety factor of
1.33 on material resistance calculated as the 90% probability of survival limit (without any
further details about the distribution, sample size, confidence level, etc. though) in order to
calculate allowable values of fatigue strength.

The Eurocode 3 for steel structures states that the design value of the fatigue strength shall be
obtained by dividing by a partial safety factor γM. It covers the uncertainties of the effects of

TALAT 2405 12

• the size of the detail
• the dimensions, shape and proximity of the discontinuities,
• local stress concentrations due to welding uncertainties,
• variable welding processes and metallurgical effects.

Recommended values are based on the assumption of specific quality assurance procedures
applied and relative to the consequences of failure, whereby either

• „fail-safe“ structural components may be assumed, with reduced consequences of
failure, such that the local failure of one component does not result in failure of the
structure or
• non „fail-safe“ structural components have to be assumed where local failure of one
component leads rapidly to failure of the structure.

Component assumed
Inspection and access „fail-safe“ non „fail-safe“
Periodic inspection
and maintenance. 1.00 1.25
Accessible joint
detail
Periodic inspection
and maintenance. 1.15 1.35
Poor accessibility
alu Partial safety factors gM for fatigue strength
after ENV 1993 [1]
2405.04.03

The case of no periodic inspection is apparently not considered. There is also an option of
adjustment of γM factors in cases where values of γF other than 1.00 are applied.

The British code [4] again states that „the designer may wish to apply a fatigue material factor
γM>1.00 and ist choice could be influenced by a) the need for the detail to exist in a very
hostile environment, and b) whether failure of the detail will result in failure of the entire
structure, or whether alternative load paths exist“.

A factor γM=1.00 is understood in the European Recommendations [3] for aluminium
structures. There is only an indirect statement that „the design and fabrication of details
should, as far as it is practical, allow for a) pre-service inspections in order to satisfy quality
assurance requirements, b) in-service inspections, and c) detection of fatigue cracking. A
further indirect reference is made in the provisions referring to acceptance testing where the
criterion for acceptance depends upon whether the structure is required to give a safe-life
performance or a damage tolerant performance. In the first case the design life is adjusted
through a fatigue test factor dependent upon the effective number of test results. In the second
case fracture mechanics methods lead to inspection procedures, whereby detectability of

TALAT 2405 13

cracks, rate of crack growth, critical crack length considerations, implications for the residual
safety of the structure and the cost of repair play a role.

The Eurocode 9 document ENV 1999 defines for the partial safety factor on fatigue strength a
value of γMf = 1,0 (except for adhesively bonded joints, which should be based on testing or
the safety factor will reach a higher value, approximately between 3 and 5).

As indicated the decision about the actual value depends upon specific considerations of the
structure, its joints, the attained quality and reliability in manufacturing, its purpose, its degree
of redundancy, its environment. And after all it is the combined influence of both partial
safety factors that characterizes the actual safety margin. The following information on the
safety index β and the relation to the partial safety factors γF and γM, as well as the relationship
to statistical parameters of the loading and resistance distributions (referring to the
manufacturing characteristics and quality classification of a structural detail), demonstrate the
actual situation for aluminium structural components and helps towards the definition of
appropriate values.

2405.04.02 Safety Index and Partial Safety Factors

Assuming normal distributions for loading (stresses) and fatigue strength along with the
definitions in Figure 2405.04.04 it follows that in the limit state definition R-S=0 or in the
actual design assessment on the basis of a safety margin Z=R-S>0 the variable Z itself will be
normally distributed. In this case the failure situation (when Z<0 ) can be defined according to
Figure 2405.04.05.

σ σ

µ µ

alu Distributions and parameters
2405.04.04

TALAT 2405 14

σ +σ = σ

µ

βσ

alu Distribution of the variable Z. (shaded area
corresponds to the probability of failure pf) 2405.04.05

The corresponding mathematical expressions are for the distributions of load or resistance
1  r −µ R 2 1  s −µ S 2
−   −  
1 2  σR


 1 2 σ S



fR (r) = e fS ( s ) = e
2πσ R 2πσS

the coefficients of variance
σR σS
ρR = ; ρS =
µR µS

and the percentiles
r = µ R − k R σ R = µ R (1 − k R ρ R )
s = µ S + k SσS = µ S (1 + k S ρS )
where the coefficients k account for scatter according to sample size.

The probability of failure may then - with a transformation variable U=(Z-µZ)/σZ - be
expressed as
µZ µZ
− −
u σZ σZ 1 2
 µ 
µZ − u

∫ ∫f ∫
1 2
p f = p( z ≤ 0 ) f Z ( z )dz =p( u ≤ − )= U ( u )du = e du = Φ − Z 
 
−∞
σZ −∞
2π −∞  σZ 

that means it has been transformed to a standardized normal distribution with a mean equal to
0 and a standard deviation equal to 1 and a relation may be established between the
probability of failure pf and the nominal safety factor (or the so-called global safety factor). So
according also to the definition in Figure 2405.04.04 we have

p f = Φ( − β ) = 1 − Φ( β )
β being the safety index, corresponding to the inverse coefficient of variation of the quantity Z

TALAT 2405 15

µZ µ R − µS
β= =
σZ σ R + σS
2 2

For the relationship pf - β see the following Figure 2405.04.06.

β

alu Relationship between the safety index and the
probability of failure 2405.04.06

Following the above definitions we express the safety index as shown in Figure 2405.04.07
and - Figure 2405.04.08.

∆σ
∆σ

γ ∆σ
γ

alu
Definition of safety index β 2405.04.07

TALAT 2405 16

k S sS + log γ F + log γ M + k R sR
β=
sS + sR
2 2

alu
Expression for β in practice 2405.04.08

kS=1.0 and sS=0.3 as suggested in Background to Annex 11 of the Fatigue Rules / CEN. It
should be noted here that this value for kS = kF is not as high as demanded above, Table 2, i.e.
equal to 2,0 so that a γFf = 1,0 may be assumed. Further considerations shall be needed in this.
kR=2.0 assumed in CEN/EC9 or ERAAS [3]
logγF+ logγM corresponds to „safety“ γF*γF
In this and the following formulae kS corresponds to the kF value of the spectrum load
intensity distribution, as mentioned in the text above, for instance in Table 1.

The relationship between these parameters, the partial safety factors and the standard
deviations for loading and strength, are demonstrated in the next Figure 2405.04.09.

γ ∗γ

γ ∗γ

alu Influence of scatter and partial safety factors on
the safety index 2405.04.09

TALAT 2405 17

2405.04.03 Safety Index in Aluminium Recommendations

With the above relationships we can now calculate values for the safety index β at actual
values of load scatter and for specific values of the partial safety factors. Practically in all
cases we assume the values kS=1.0 and kR=2.0 according to the suggested values of
CEN/Eurocode being also identical to the assumptions in the European Recommendations for
aluminium structures [3]. Figure 2405.04.10 demonstrates the fact that a value β=3, as
recommended in some documents, can be attained with the recommended sS=0.03 at relatively
low scatter in fatigue strength, which has been observed for some details like longitudinal
fillet welds or transverse attachments on the flange of beams, but will only reach values
around 2.5 for higher scatter in strength. A similar message is conveyed by the diagram in
Figure 2405.04.11. If the partial safety factors γF and γM are equal to 1.00 and kR=2, the
lowest curve represents the current situation in ERAAS with maxβ=2.24. Only if the design
values are defined as mean minous 3 standard deviations, that is kR=3, a value β ≅3 can be
reached for the range of possible sR values from 0.03 to 0.18 encountered with the structural
details in ERAAS. Even higher β-values, for instance 3.5 as recommended in [5], are possible
for sR < 0.1 but only if the product of the partial safety factors γF*γM reaches values >1.2. The
full spectrum of scatter in fatigue strength is shown for the ERAAS details in
Figure 2405.04.12.

γ ∗ γ = 1.1

β

Standard deviation of loading sS values at the range of actual scatter values for the
fatigue strength of details in the European Recommendations [3]

alu Values of the safety index β attained for a
γF*γM=1.10 and kS=1.0 and kR=2.0
2405.04.10

TALAT 2405 18

γ ∗γ

alu Influence of design value definition and partial safety
factors on the attainable value of the safety index 2405.04.11

standard deviation fatigue strength

alu Values of standard deviation in fatigue strength for
ERAAS structural details [3] 2405.04.12

TALAT 2405 19

In the following Figure 2405.04.13 and Figure 2405.04.14 the calculated actual β-values are
given for a number of characteristic welded structural details. Detail I: transverse attachment
with fillet welds on the beam flange non load-carrying exhibits very low values of scatter in
strength as has been established through experimental data. Detail II: the longitudinal fillet
weld between web and flange, manually welded with stops and starts or tack welds, as well as
the web stiffener welded with transverse fillet welds on web and flange. Both have a value of
0.08 in the middle range of scatter values observed. Detail III: the longitudinal attachment
welded with fillet welds on the beam flange has a similar value of 0.10, which is also in the
middle of the observed value range, but actually represents the upper limit for the greatest
number of structural details as demonstrated in Figure 2405.04.12. Detail IV: the transverse
butt weld with overfill dressed flush, naturally, exhibits a relatively big scatter with 0.18.

longitudinal
III attachment

transverse
I attachment

transverse butt
IV flush dressed

web stiffener
II transverse fillet

longitudinal
II fillet

alu Selected welded structural details on an 2405.04.13

aluminium beam

TALAT 2405 20

scatter in
fatigue k S s S + log γ F + log γ M + 2 s R k S s S + log γ F + log γ M + 3 s R
β= β=
strength s R + sS
2 2
s R + sS
2 2

sR
⇓

0.03 2.12 1.53 1.37 3.10 1.93 1.64 5.20 2.78 2.22 2.83 1.82 1.57 5.90 3.07 2.42
0.08 2.22 2.03 1.82 2.71 2.35 2.07 3.75 3.04 2.59 3.16 2.65 2.29 4.69 3.67 3.06
0.10 2.20 2.12 1.94 2.60 2.41 2.17 3.45 3.04 2.66 3.16 2.83 2.50 4.41 3.75 3.22
0.18 2.14 2.23 2.18 2.04 2.43 2.35 2.85 2.87 2.73 3.12 3.11 2.94 3.84 3.74 3.50
scatter in
loading
sS ⇒ 0.03 0.10 0.15 0.03 0.10 0.15 0.03 0.10 0.15 0.03 0.10 0.15 0.03 0.10 0.15
partial
safety
γF* γR ⇒ 1.00 1.10 1.35 1.00 1.35

The lightly shaded areas indicate values assumed in the current recommendations. The darker
areas include β-values higher than 3.5 and point out the necessary level of partial safety values
alu
Attainable values of the safety index β. 2405.04.14

2405.04.04 Summary and Conclusions

Comparing the β values to one another and for the different standard deviations of the various
details we find that
• for practical values of loading scatter sS = 0.02 to 0.06 the safety index b reaches ist
maximum value,
• in case of the ERAAS with γF = γM = 1.00 / kR = 2 / kS = 1 and mean sR = 0.07 the
maximum β-value is 2.236 ( for arbitrary loading and resistance min β = 1.60,
• a demand for very low scatter in fatigue strength is not per se a guarantee for higher
β-values, in several cases depending on the interrelation with the other parameters it
may even lead again to somewhat lower values,
• it is much more effective to have reliable information about the loading distribution
and a not so high scatter value there,
• in the case of ERAAS (which is also the case for the steel design recommendations
as well) for practical values of resistance scatter between 0.03 and 0.18 or for loading
between 0.02 and 0.06 the safety index goes not beyond ≈ 2.2,
• only in cases with partial safety factors γF* γR > 1.35 may values of β ≈ 3.5 be
reached, and this only at rather low load distribution scatter,
• the β-value may be enhanced significantly by lowering the fractile of fatigue strength
or assuming a lower design value, as demonstrated by values for kR = 3 (this
corresponds to a fractile of approximately 99% probability of survival for a sample
size of 10 and a confidence level of 0.75),
• it does not appear appropriate though to try to attain higher β-values through
magnification of kR, i.e. lower fractiles of strength or lower design values,

TALAT 2405 21

• in the BS 8118 document design values are in a number of cases lower than ERAAS,
but unless the actual mean values and the standard deviation values are reported a
direct comparison will not be possible,
• neither ERAAS nor BS 8118 assume a priori partial safety factors other than 1,
• the BS 8118 leaves an option for partial safety factors >1 „under certain
circumstances“ and as mentioned the ENV 1999 document relates the partial safety
factor for loading to certain basic conditions in the estimation of load spectra,
• these may be a) damage tolerant or redundant structures, b) satisfactory degree of
inspectability of structural components and their details, easy and not so costly repair,
d) reliability of environmental conditions and, especially, loading assumptions during
the projected lifetime of the structure, and consequently may be accounted for by the
adoption of appropriate partial safety factors.

2405.04.05 References

1. Eurocode 3: Design of steel structures. Part 1.1: General rules and rules for buildings.
European Prestandard ENV 1993-1-1, February 1992.
2. DIN 18800: Stahl im Hochbau, Teil 1: Konstruktion und Bemessung, Ausg. November
1990
3. European Recommendations for Aluminium Alloy Structures Fatigue Design, ECCS Doc.
No. 68, First Edition, 1992.
4. BS 8118:1991 - Part 1: Code of practice for design. Part 2: Specification for materials,
workmanship and protection.
5. Recommendations for the Fatigue Design of Steel Structures, ECCS Doc. No. 43, First
Edition, 1985.

TALAT 2405 22

2405.05 Unclassified Details

2405.05.01 Design by Reference to Published Data

In the case of unclassified details (§ 5.2.2 of the ENV 1999), i.e. details not covered by the
detail categories described within the ENV 1999, these should be assessed by reference to
published data where available. One such source may be the compilation of the Aluminium
Data Bank (AlDaBa). This data had its origin in the so called CAFDEE committee of the
eighties, and it has been maintained at the Technische Universität München - Light Metals
and Fatigue Section and at the Iowa State University, Ames, Iowa. It was then enhanced by
the data documented and evaluated for the purpose of the European Recommendations for
Aluminium Alloys Structures in Fatigue Design (ERAAS Fatigue, 1992), which eventually
formed the basis for the ENV 1999, as well - in this context see also IIW Doc. No. XIII-1588-
95 „Background Document to Fatigue Design Curves for Welded Aluminium Components“
by R. Jaccard, D. Kosteas, R. Ondra. The Aluminium Data Bank provides also the common
platform for the statistical and regressional evaluation of data. These procedures should be
observed whenever new data is generated for the purpose of establishing fatigue design lines
for new structural components and details not covered in the standard - in this context see next
chapter 2405.06 for more details.

2405.05.02 The Aluminium Data Bank (AlDaBa)

In the following pages a brief presentation of the main items of the „AlDaBa“, the Aluminium
Data Bank, is given. The AlDaBa was developed and is being run jointly by the Technical
University of Munich / Section of Light Metal Structures and Fatigue, Prof. D. Kosteas
(phone: +49 89 289 22521, fax: +49 89 289 22522, e-mail: kosteas@lrz.tum.de) and the Iowa
State University, Dept. of Civil Engineering, Prof. W.W. Sanders, Jr. (phone: 001 515 294
6048, fax: 001 515 294 8216).

TALAT 2405 23

2405.06 Testing for Fatigue Design

The second option to deal with unclassified details is by conducting fatigue acceptance tests in
accordance to Annex C.3 of the ENV 1999. In doing this the provisions of Annexes C.1 on
the derivation of loading data and C.2 on the derivation of stress data at critical locations of
the structural component studied should be observed.

Annex C.3 handles the derivation of endurance data, i.e. the estimation of the respective
design S-N curve. With known or estimated stress history and spectrum data specimens can be
manufactured keeping (and fully documenting) the same dimensions and procedures as
intended to be used in the final design. Any NDE and acceptance criteria should also be
documented. Loads and stresses should be recorded during the test by means of one or more
strain gages at critical locations (in appropriate distance from notches, weld toes for instance,
in order to record „nominal stresses“). A sample size of at least 8 specimens is required for the
range between 104 and 107 cycles - see here also recommendations under 2405.01.02 or
2405.03.

In the double logarithmic S-N diagram (log∆σ-logN) a mean curve shall be estimated and a
design curve, parallel to the mean, shall be obtained, either at a mean minus 2 standard
deviations level or not higher than 80% than the mean, whichever is lower.

In case that damage tolerance design is conducted a record of fatigue crack growth with cycles
should be obtained.
Similar conditions should be observed in testing full-size structural components.

When the structure is expected to give a safe life performance, then design should satisfy the
condition that
Tm ≥ TL ⋅ F
where TL is the design life in cycles
Tm is the mean (endured) life to failure in cycles
F factor defined in the table below and depending on the actual (effective) number of
specimens available

sample size = no. of specimens tested
results of tests 1 2 4 6 8 9 10 100
Identical specimens all tested 3,80 3,12 2,73 2,55 2,48 2,44 2,40 2,09
to failure. All specimens
failed.
Identical specimens all tested 3,80 2,67 2,01 1,75 1,60 1,54 1,54 0,91
simultaneously. First sample
to fail.
Population standard deviation assumed as log 0,176

alu Fatigue test factor F 2405.06.01

TALAT 2405 27

When the structure is expected to satisfy damage tolerant design then the failure criterion will
be dependent upon the life of a crack reaching a size which could be detected by a method of
inspection which can be applied in service. It also depends on the crack growth rate, critical
crack length considerations, and the implications for the residual safety of the structure and
the costs of repair.

2405.07 Damage Tolerant Design

This chapter is divided into the following parts:

• In a general introductory part from {TALAT 2403.03 Principles of Fracture
Mechanics} which gives the basic information about the fracture mechanics concept
and the assumptions and analytical expressions governing crack geometry /stress
relationships - this may be regarded as an informative part; it may be omitted in a
first reading, contains information on the basic definitions, though.

• More application oriented is the material from {TALAT 2403.05 Fracture
Mechanics Instruments for Structural Detail Evaluation and TALAT 2403.06
Calculation of an Example} which deals with proposals for treating practical cases,
and gives actually two life calculation examples.

• The last part of this chapter presents an outline of the provisions of the ENV 1999-2,
2.3 and Annex B on „damage tolerant design“ on the basis of fracture mechanics
concepts. It gives practically the procedure steps for carrying out the calculations.

Note: Further introductory information to the fatigue crack initiation and propagation
characteristics may be taken from chapter 9.9 Strain-Life Approach and the respective parts
from {TALAT 2401.02 and 2401.04 and 2401.05}.

An excellent overview of fracture mechanics applications and the fatigue crack propagation
in aluminium alloys along with life estimation calculations is presented in the paper by Dr. R.
Jaccard „Zum Bruchverhalten von Aluminiumbauteilen“ published in the STAHLBAU
Spezial „Aluminium in Practice“, 67(1998), Ernst & Sohn/Wiley, Berlin, pp 54-65.

TALAT 2405 28

2405.07.01 Outline of Provisions in ENV 1999-2, 2.3 and Annex B

Safe Life - S/N design curves
(based on component tests)
no cracks tolerated or assumed
Damage Tolerance - based on fracture
mechanics calculations
cracks assumed
Design by Testing - in lieu of standard data
alu Fatigue design methods 2405.07.01

Drawings - full details susceptible to
fatigue, required fatigue class
Manufacturing Specification
Operation Manual - assumed loads
and design life, repair methods
Maintenance Manual - methods,
locations and frequency of inspections,
max permissible crack, details of
acceptable repair methods
alu Design documents required by ENV 2405.07.02

1999

TALAT 2405 29

ni
if Dd = ∑ > 1 i. e.
Ni
if safe life Ts < design life Td
Td
i. e. = Dd > 1
Ts
and where no alternative action such as
- redesign of detail to reduce stress or
- change the detail to one with higher category
is undertaken

alu Prerequisites for damage tolerant design 2405.07.03

da/dN (m/cycle)
critical fracture length l f 1E-04
DK
depends on the "fracture Ic
criterion"
assumed minimum detectable
crack size l d ispection method DK eff
in mm visual/ liquid or
magn. penetr. R~ 0.8
aid
plain+smooth 1
surface
20 5 m i

rough Ci polygonal line
weld cap
30 10 for aluminium alloys

sharp corner DKth
1E-011
weld toe 50 15 1 10 100
DKeff (MPa m)

alu Parameter values for damage tolerant design
2405.07.04

TALAT 2405 30

Cracks Propagation Life to Failure
da/dN = C * [Ds * a * f(y)]m
m da/dN
da/dN = C * DK polygonal
line

slope m and C variable section-wise DK

alu

Damage tolerant concept 2405.07.05

a a/2c=0 Global geometry factor
B 3
Y = f(y)π-0,5
Ds Ds 2

1
crack form and size and orientation a/2c=0.2
geometry of adjacent material stress
distribution along crack path 0
a/B
Ds Ds 3 Local geometry factor Mk
a
B 2

1
adaptation factor for local stress
concentration effects (weld toe 0
notch)
a/B
3 a/2c=0 Global and local effect
2

1 a/2c=0.2

0
alu Local and Global geometry factors 2405.07.06

TALAT 2405 31

! first inspection before safe life elapses !
! subsequent inspections at regular intervals!
when measured l>l fitness-for-purpose
d
assessment and possible repair

lf critical fracture length

assumed fastest
growth curve
actual growth curve
assumed minimum detectable crack size
ld

1 i i+1 i+2 i+3 i+4 etc. inspection number
...

safe life Ts Tf calculated fracture time

alu Inspection strategy for damage tolerant design
2405.07.07

lf
assumed fastest
growth curve
multiplication by g
Ff

ld
?
actual growth curve and (in certain circumstances)
also by the fatigue test factor F
safe life Ts and by using an upper bound
Tf
calculated fracture time crack growth relationship

alu Estimation of the “fastest crack growth” curve
2405.07.08

TALAT 2405 32

by calculation and/or by testing
Nf lf

∫ dN = ∫ C ∆K
da
Tf = mi
standard test fatigue test
Nd ld i i , eff f ( g) specimens - factor F

l f = is the critical fracture crack length same material
as in crack path
l d = is the assumed min safe value of
detectable crack length
component tests
∆Ki ,eff = γ Ff ∆σ a f ( g )
correct fatigue test
m i and C i are the respective materials, factor F If
parameters of the da dN − polygon geometry and
manufacture

the inspection intervall is
with relevant
applied force
Id
Ti ≤ 0.5Tf pattern

alu Calculation of inspection intervals in damage
tolerant design 2405.07.09

Stress History Total (Design)Life Spectrum
maxs
1 2
Ds

Crack Propagation by
Cycle Integration for
each Block with
Partial Spectrum = 1/10 of the Total Spectrum Ds =const. through
same Ds - same R - descending order of stress amplitudes the da/dN-Polygon
maxs with corresponding
3 R-ratio
Ds
.....
mins

~ 10 sequences of partial spectrum = total design life spectrum

alu Integration of fatigue crack growth - accounting
for the loading spectrum 2405.07.10

TALAT 2405 33

1 overall fa γ F Fk
final = σall = σeff =
fracture γ M2 rest
Acritical

Arest
critical arest lf
see examples on following diagrams
simplifying as in ex. "b" at
critical fracture stadium with γ Fγ
plate thickness t = 2c l f = a f = a tot − a rest = a tot − F k M2

fat

Calculation of the critical fracture length lf depending on the fracture criterion (final
critical crack size such as „through thickness crack“ or reaching the critical cross
section with ultimate strength, etc.) - Fk: Load [N] - γF: partial safety factor for loading
in ENV 1999-1, 2.2, 2.3 - γM2: partial safety factor for resistance in ENV 1999-1, 5.1.1
equal to 1,25 - fa: limit value for resistance, local in net cross section, ENV 1999-1,
5.3.5 or fa = fu = characteristic value of ultimate stress of the aluminium alloy as in
Table 3.2a-d or 3.3 [N/mm²]
alu Integration of fatigue crack growth 2405.07.11

TALAT 2405 34

2 final damage in complicated crack
propagation path(s)
or
partial damage affecting serviceability
estimation of critical fracture crack length l f will have to be based upon
# computation of possible crack propagation path(s) by
integration of the da/dN line for a critical crack length a rest corresponding to a
critical cross section A rest (iterative procedure)
# definition of l f according to the overall geometry
see example "d" on following diagrams

alu Calculation of the critical fracture length lf in
complicated crack paths 2405.07.12

6 5 4 32 1 1 2
4 3
successive different geometries 5
and crack propagation 6

directions
from 1 to 2 to 3 critical
Arest
from 3 to 4
from 4 to 5
from 5 to 6

alu Successive crack geometries and Crack
propagation directions 2405.07.13

TALAT 2405 35

Parent Material weld zone
Aluminium Alloys
7020/AlZn4,5Mg1 (HAZ) t
6082/AlMgSi1 4 - 30
5083/AlMg4,5Mn Heat-Affected-Zone
5183/S-AlMg4,5Mn mm
Rolling/Extrusion Direction 5356/AlMg5
KI 4043/AlSi5
-4 -4
10 10

da/dN R = +0,5 / 0 / -1 da/dN

1,0
0,5 COR Bemessungslinie
10
-11
0 -11 mit Streubereich
DK 10 DKeff

Research program at TUMunich DFG 583-2/1 and Ph.D. thesis of U. Graf TUM 1992.
∆K-da/dN as well as ∆Keff-da/dN diagrams were derived observing the respective
crack closure effects. For a re-evaluation and statistical analysis of the ∆Keff-da/dN
curves (scatter band) see also Ph.D. thesis R. Ondra at TUM 1998.

alu An example of experimental investigations to define
da/dN curves for aluminium alloys and their weldments 2405.07.14

TALAT 2405 36

da / dN
1E-04 $
$ = +0,5
R da / dN - DK eff
1E-05 7020 / AlZn4,5Mg1
t = 8 mm
1E-06
Weld
1E-07
parent
metal HAZ
1E-08

1E-09
Weld : Dataset 17982310 (Graf) 167 data points
HAZ : Dataset 17980311 (Graf) 216 data points
PM : Dataset 17991311 (Graf) 214 data points
1E-10 $
1 10 100
eff

alu A typical measurement from the research program
of the previous figure 2405.07.15

TALAT 2405 37

2405.07.02 Summarizing the Life Prediction Procedure

Fatigue life prediction based on fracture mechanics still requires the following engineering
assumptions: (1) initial crack length, (2) residual stress distribution, and (3) fatigue crack
growth of short cracks.

Initial crack length is determined by scanning electron fractography and/or fatigue crack
calibration.

Residual stress is accounted for and short crack growth is approximated by the Kmax=const
fatigue crack growth relation.

Fatigue life is calculated by using a single phase of fatigue crack growth from the initial crack
length (usually a short crack) to the final crack length (plate thickness or any other critical
dimension) and the conservative combination of Kmax=const and R(Kmin/Kmax) curve of the
fatigue crack growth data.

Single slope fatigue crack propagation data is not recommended.

Fatigue crack propagation data is given in ENV 1999-2 as a conservative envelope of
measured values of common aluminium alloys - further upper boundary estimates for crack
propagation and scatter data are to be found in the paper by Kosteas and Ondra in the
STAHLBAU Special Issue on „Aluminium in Practice“.

Fatigue calibration is an engineering tool to allow the application of fracture mechanics at the
early stage of fatigue crack growth and to estimate the damage caused by a load spectrum.

The calibrated initial crack length is influenced by the stress field parameters, the selected
fracture mechanics model and the fatigue crack propagation. If all parameters are in agreement
with the S-N test conditions and specimen properties, the calibrated initial crack length is
identical to the physical crack length.

The fatigue crack propagation is the relevant parameter of the initial crack length calibration.
The measurement of the fatigue crack propagation is in reality nothing else than a special S-N
test of a specimen with the worst possible notch condition, a fatigue crack, and a special
loading condition. Due to the computer controlled loading and the severe (reproducible) notch
condition the fatigue crack propagation data show less scatter than respective S-N data.

Conservative fatigue crack propagation data lead to shorter initial crack length.

The S-N simulation and the initial crack length calibration must be performed using identical
fatigue crack propagation data and fracture mechanics models.

The calculation of cumulative damage due to fatigue can be performed using a fracture
mechanics evaluation of the fatigue crack growth including the early stage of fatigue crack
growth.

TALAT 2405 38

2405.08 Sequence Effects

Within this lecture series only brief information is presented in the following pages from the
material in {TALAT 2401.02}. Further details may be taken from the respective general
literature mentioned on the front page.

2405.09 Strain-Life Approach

The information in the following pages is understood as supplementary information to various
chapters of this lecture no. 9. It is optional, and actually supplements also the mentioning of
the strain-life concepts presented under lecture no. 2. It is taken from the material in {TALAT
2401.02 Fatigue Damage and Influencing Parameters} and {TALAT 2401.05 Local Stress
Concepts and Fatigue}.

2405.10 List of Figures

Figure Nr. Figure Title (Overhead)
2405.01.01 Sample sizes on different stress levels and cycle ranges of an S-N line
2405.01.02 Example of actual number of data points generated in some fatigue test
programs with aluminium beams and small specimens
2405.01.03 Average cost and duration of test for typical small specimens and beams in
aluminium
2405.01.04 Approximate cost for an S-N line

2405.03.01 Definition of the design line for the middle and high cycle fatigue range (HCF).
2405.03.02 Definition of the design line for the low cycle fatigue range (LCF)
2405.03.03 Values of k for estimations of mean minus k standard deviation levels

2405.04.01 Fatigue assessment
2405.04.02 Partial safety factors gFf for fatigue load intensity after ENV 1999 (EC 9)
2405.04.03 Partial safety factors gM for fatigue strength after ENV 1993 [1]
2405.04.04 Distributions and parameters
2405.04.05 Distribution of the variable Z. (shaded area corresponds to the probability of
failure pf)
2405.04.06 Relationship between the safety index and the probability of failure
2405.04.07 Definition of safety index β
2405.04.08 Expression for β in practice
2405.04.09 Influence of scatter and partial safety factors on the safety index
2405.04.10 Values of the safety index β attained for a γF*γM=1.10 and kS=1.0 and kR=2.0
2405.04.11 Influence of design value definition and partial safety factors on the attainable
value of the safety index
2405.04.12 Values of standard deviation in fatigue strength for ERAAS structural details
[3]

TALAT 2405 39

Figure Nr. Figure Title (Overhead)
2405.04.13 Selected welded structural details on an aluminium beam
2405.04.14 Attainable values of the safety index β.

2405.06.01 Fatigue test factor F
2405.07.01 Fatigue design methods
2405.07.02 Design documents required by ENV 1999
2405.07.03 Prerequisites for damage tolerant design
2405.07.04 Parameter values for damage tolerant design
2405.07.05 Damage tolerant concept
2405.07.06 Local and Global geometry factors
2405.07.07 Inspection strategy for damage tolerant design
2405.07.08 Estimation of the “fastest crack growth” curve
2405.07.09 Calculation of inspection intervals in damage tolerant design
2405.07.10 Integration of fatigue crack growth - accounting for the loading spectrum
2405.07.11 Integration of fatigue crack growth
2405.07.12 Calculation of the critical fracture length lf in complicated crack paths
2405.07.13 Successive crack geometries and Crack propagation directions
2405.07.14 An example of experimental investigations to define da/dN curves for
aluminium alloys and their weldments
2405.07.15 A typical measurement from the research program of the previous figure

TALAT 2405 40

TALAT Lecture 2405: Fatigue an Fracture in Aluminium Structures

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