Airbus

Technical Manual MTS 005 Iss. B

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prior authorisation from AEROSPATIALE and its contents cannot be disclosed. © AEROSPATIALE - 1998

3page 1

Fatigue Manual

Subject Tool for calculating the crack initiation life of a metallic structural item of a civil aircraft subjected to cyclic loading.

Fields of application All programs.

Structure design speciality.

Computer based tools supporting this manual

Contents Detailed summary Foreword Field of validity Explanations on the method Appendices Bibliography

1

4

5

4

5

21

2

Structure Design

Manuals

Fatigue Manual - Appendices

© AEROSPATIALE - 1998 MTS 005 Issue. B 3page Ann.

Reference documents Refer to "Bibliography" chapter

Documents to consult

Terminology Refer to chapter I.1.3 "Rotation"

Table of revisions

Revision Date Pages modified Reason for changes made A 02/98 All New document.

Supersedes technical note No. 436.0112/88. B 07/98 Paragraph 3.3.6 Revisions

Fatigue Manual - Informations de gestion

© AEROSPATIALE - 1998 MTS 005 Issue. B page IG1

DO NOT DISTRIBUTE THIS PAGE

List of approval

Logo Function Name/Christian name A/BTE/CC/CM Head of Department CAZET G.

Key words Calculation

Bibliography -

Distribution list

Logo Function Name/Christian name (if necessary)

A/BTE/QN A/BTE/QN Library SIBADE Alain A/BTE/QN Diderot archives SIBADE Alain

A/BTE/SM/MG A/BTE Technical Library BOUTET Fernand

Distribution list managed in real time by A/POI/D - (Didocost application)

CONTENTS P. 1/4

© AEROSPATIALE 1998 FATIGUE MANUAL Revision B (July1998)

CONTENTS

Revision B (July 1998)

I FOREWORD..........................................................................................................

1 DEFINITIONS....................................................................................................

1.1 Reminder: the fatigue phenomenon.................................. Rev. A (Jan. 1998)

1.2 Conventional definition of crack initiation ........................... Rev. A (Jan. 1998)

1.3 Notations ............................................................................ Rev. A (Jan. 1998)

2 GOALS ..............................................................................................................

2.1 Reporting and valorising AS experience ............................ Rev. A (Jan. 1998)

2.2 Multi-user tool..................................................................... Rev. A (Jan. 1998)

3 APPROACH PRINCIPLES ................................................................................

3.1 Systematic processing of AS tests ..................................... Rev. A (Jan. 1998)

3.2 Global analysis ................................................................... Rev. A (Jan. 1998)

CONTENTS P. 2/4


II FIELD OF VALIDITY.............................................................................................

1 EXTERNAL PARAMETERS..............................................................................

1.1 Loading / stress spectrum .................................................. Rev. A (Jan. 1998)

1.1.1 Tension or shear uniaxial loading .......................................................

1.1.2 "Civil aircraft" type spectra ..................................................................

1.1.3 No frequency effect .............................................................................

1.2 Environment ....................................................................... Rev. A (Jan. 1998)

1.2.1 No temperature effect .........................................................................

1.2.2 No fatigue - corrosion interaction ........................................................

2 INTRINSIC PARAMETERS OF THE PART ......................................................

2.1 Material .............................................................................. Rev. A (Jan. 1998)

2.2 Surface condition after machining...................................... Rev. A (Jan. 1998)

2.2.1 Part finishing .......................................................................................

2.2.2 Roughness..........................................................................................

2.2.3 Residual stresses................................................................................

2.3 Technological treatments ................................................... Rev. A (Jan. 1998)

2.3.1 Surface treatments..............................................................................

2.3.2 Mechanical treatments ........................................................................

2.3.3 Fastener installation ............................................................................

3 LIFE...................................................................................................................

3.1 Average / application of a safety factor .............................. Rev. A (Jan. 1998)

3.2 Field of application ............................................................. Rev. A (Jan. 1998)

CONTENTS P. 3/4


III DESCRIPTION OF THE METHOD

1 GENERAL MATHEMATICAL FORMULATION .................................................

1.1 Calculation under a monotonic load ................................... Rev. A (Jan. 1998)

1.1.1 Uniaxial tension loading ......................................................................

1.1.2 Extension to uniaxial shear loading.....................................................

1.2 Spectrum calculation.......................................................... Rev. A (Jan. 1998)

1.2.1 Miner's rule..........................................................................................

1.2.2 Rain-Flow principle..............................................................................

1.2.3 Example of application........................................................................

1.3 Fundamental properties ..................................................... Rev. A (Jan. 1998)

1.3.1 Monotonic loading equivalent to the spectrum....................................

1.3.2 Spectrum coefficient (Cs)....................................................................

1.4 Consequences on practical application.............................. Rev. A (Jan. 1998)

1.4.1 Fundamental parameters....................................................................

1.4.2 Use in sizing........................................................................................

1.4.3 Use in substantiation...........................................................................

2 DETERMINATION OF THE EQUIVALENT MONOTONIC LOAD.....................

2.1 Basic calculation with the computerised system ................ Rev. A (Jan. 1998)

2.2 High speed calculation using the spectrum calculation ..... Rev. A (Jan. 1998)

3 DETERMINATION OF THE INTRINSIC QUALITY OF THE PART (IQF) .........

3.1 General IQF law ................................................................. Rev. A (Jan. 1998)

3.2 Effect of material ................................................................ Rev. A (Jan. 1998)

3.3 Influence of scale effect ..................................................... Rev. A (Jan. 1998)

3.4 Effect of technological process .......................................... Rev. A (Jan. 1998)

3.4.1 Surface treatments..............................................................................

CONTENTS P. 4/4


3.4.2 Mechanical treatments ........................................................................

3.4.3 Fastener installation ............................................................................

3.5 Kt in cylindrical shafts......................................................... Rev. A (Jan. 1998)

3.6 Kt in notched plates............................................................ Rev. B (July 1998)

3.7 Kt in drilled plates............................................................... Rev. A (Jan. 1998)

3.8 Kt in yokes.......................................................................... Rev. A (Jan. 1998)

3.9 Kt in bolted and riveted assemblies.................................... Rev. A (Jan. 1998)

APPENDIX 1 / Substantiation of the general mathematical model ....................

A1.1 Demonstration by an elastic-plastic approach ................. Rev. A (Jan. 1998)

A1.2 Examples of use .............................................................. Rev. A (Jan. 1998)

APPENDIX 2/ Substantiation of the general IQF law ...........................................

A2.1 Law on notches................................................................ Rev. A (Jan. 1998)

A2.2 Law on yokes ................................................................... Rev. A (Jan. 1998)

A2.3 Law on bolted and riveted assemblies............................. Rev. A (Jan. 1998)

APPENDIX 3/ Simplified modelling of a fastener.................................................

A3.1 Determination of flexibility ................................................ Rev. A (Jan. 1998)

A3.2 Determination of the equivalent section........................... Rev. A (Jan. 1998)

BIBLIOGRAPHY......................................................................................................

................................................................................................. Rev. A (Jan. 1998)

Ch. I FOREWORD P. 1/1

© AEROSPATIALE 1998 FATIGUE MANUAL Revision A (Jan. 1998)

I FOREWORD

This document supersedes the first edition (Ref. 1).

Nonetheless, the general approach is globally the same which should facilitate, for potentialusers, the use of this new version after having used the former version.

As far as possible, this new manual takes into account the remarks made by users:- during the 1992-93 audit;- during the proofing phase (July-December 1997);- over the last few years, through the Stress Office Support.

This document remains "open-ended" and later may be completed (or modified if the occasionarises) by means of new partial editions (with a new revision index).

Ch. I.1.1 REMINDER: THE FATIGUE PHENOMENON P. 1/2


1 DEFINITIONS

1.1 REMINDER: THE FATIGUE PHENOMENON

Damage to a metallic part, under cyclic loading, can be summarised by 3 phases of developmentof the damage, called "fatigue":

- a "crack initiation" period which is generally on the surface for 2 main reasons:. the dislocations in the crystal structure, responsible for material plasticity, are more easily

formed on the surface than in the heart of the part and travel more easily;. the surface is exposed to adverse environmental conditions;

in general, this entails (when examined under an scanning electron microscope) the following:. initially, formation of surface slide bands, that can be removed by very light polishing;. then the slide bands multiply and persist;. formation of intrusions and extrusions;. lastly, the appearance of micro-cracks along these geometrical defects; one of these

defects then becomes more significant than the others;

- a stable "growth" period of this crack characterised by a generally smooth and shiny fractureappearance in which lines of arrested growth make it possible to approximately date whencrack initiation started;

- an abrupt growth entailing a "static fracture" in the part characterised by a rougher and dullerappearance.

The following figure illustrates this phenomenon:

Ch. I.1.1 REMINDER: THE FATIGUE PHENOMENON P. 2/2


Number of cycles

Length of crack

Initiation Growth

Static fracture

formation of a micro-crack

acrack

progress

a

Ch. I.1.2 CONVENTIONAL DEFINITION OF CRACK INITIATION P. 1/1


1.2 CONVENTIONAL DEFINITION OF CRACK INITIATION

Considering the difficulty in measuring the initiation phase of a crack, the corresponding definitioncan only be conventional.

Often, the definition depends on the inspection method implemented to detect the phase.Generally in reference documentation, the phase corresponds to a 0.5 mm long crack.

In this "Fatigue Manual" considering that laws are defined using the results from tests on small testspecimens until they break, the approximate corresponding length of cracks is, as anaverage:

3 to 5 mm

Fatigue cracks in test

specimen just before

abrupt fracture

Also, this corresponds to the length of the crack that can be reasonably detected on aircraft usingnon-destructive testing techniques, such as eddy currents, ultrasonic, etc.

Ch. I.1.3 NOTATIONS P. 1/2


1.3 NOTATIONS

The following notations shall be systematically used to facilitate document understanding:

Smin

Smax

SaverageSa

Reference cross-section

σmin

σmax

σaverageσa

Example of a notched tension

test specimen

S rated stress (in a reference cross-section) in elastic stateSmax maximum rated stress in a loading cycleSmin minimum rated stress in a loading cycleSave average rated stress in a loading cycleSaalternating rated stress in a loading cycle

R ratio: Smin / SmaxKtstress concentration coefficient equal to the ratio:

local elastic stress at crack initiation point / S

σσσσ local stress (at crack initiation point) in elastic-plastic stateσσσσmax maximum local stress in a loading cycleσσσσmin minimum local stress in a loading cycleσσσσave average local stress in a loading cycleσσσσa alternating local stress in a loading cycle

Ch. I.1.3 NOTATIONS P. 2/2


monotonic loading: succession of identical stress cycles

complex or spectrum loading:succession of different stress cycles

N average life until crack initiation, as defined in the previous paragraph and given as:. cycles for a part subject to monotonic loading. generally in flights for a part subject to complex or spectrum loading

Ch. I.2.1 REPORTING AND VALORISING AS EXPERIENCE P. 1/1


2 GOALS

2.1 REPORTING AND VALORISING AS EXPERIENCE

The essential goal of the Fatigue Manual, which was edited for the first time in 1988, is to record allAS know-how in the field involved, in the same manner as the other A/BTE/CC manuals:

- Design Manual;- Static Manual (Metallic);- Composite Manual.

These manuals satisfy the same concerns which can be summarised by the following 4 actions:

"collect""preserve"

"synthesise""make available"

Ch. I.2.2 MULTI-USER TOOL P. 1/1


2.2 MULTI-USER TOOL

The Fatigue Manual has been designed so as to be of a sufficient level of user friendliness for:- designers during the sizing phase;

essential goal: minimise the risk of the occurrence of cracks especially in typical areas; thisgoal can be translated by the following principle:

"prevent rather than cure"

- designers in the aircraft certification and follow-up phase;essential goal: substantiation:

. of new structures;

. of modifications following non-conformities detected during production;

. in-service repair following the discovery of a cracked area or an accidentally damagedarea.

Ch. I.3.1 SYSTEMATIC PROCESSING OF AS TESTS P. 1/1


3 APPROACH PRINCIPLES

3.1 SYSTEMATIC PROCESSING OF AS TESTS

The Fatigue Manual is practically a rule of the thumb method based on overall analysis andsynthesis of AS tests conducted over approximately the last 20 years.

The approach is summarised in the following graph:

Statistically processable tests

==> direct processing pour

for the manual

PP

PP

Elementary test specimens (process + material data)

Structural items ("design" data)

Subassembly

Test airframe

Level1

Level 2

Level 3

Level 4

P

PP

Limited tests (generally

certification) ==>

verification and validation of the manual

Ch. I.3.2 GLOBAL ANALYSIS P. 1/1


3.2 GLOBAL ANALYSIS

The main difficulty consists in finding the right compromise between method simplicity andreliability.

To this end, the following sentences may be considered as key points to the approach:

- 1st step: identify the essential parameters, naturally drawing upon available tests and alsotheoretical analysis, in particular the numerical methods showing certain mechanicalbehaviours governing crack initiation in metallic structures;

- 2nd step: as far as possible, make the parameters independent, one from the other;

- 3rd step: quantify the effect of parameters in a friendly manner:. simple analytical formulas;. charts.

Ch. II FIELD OF VALIDITY P. 1/1


II FIELD OF VALIDITY

The purpose of this chapter is to define as precisely as possible the field of application of thismanual, taking into account that:

- this document does not cover the entire metallic material fatigue field which is extremely vast,taking into account a great number of parameters involved;

- the laws set forth in this document concern technological processes specific to AS andpossibly to its subcontractors or partners.

Consequently, reference is made for information purposes to AS standards documentsdetailing the field of application of these processes.

Ch. II.1.1 LOADING / STRESS SPECTRUM P. 1/2


1 EXTERNAL PARAMETERS

1.1 LOADING / STRESS SPECTRUM

1.1.1 Tension or shear uniaxial loading

The local stress state at the crack initiation point (refer to III.1.1) induced by the rated loading ofthe part involved must be:

- in tension direction (or practically), the matrix of stress that can be formulated as follows:

00000000S

- or in shear direction (or practically), the matrix of stress that can be formulated as follows:

00000S0S0

1.1.2 "Civil aircraft" type spectra

The law for calculating damage under complex loading (refer to III.1.2) was built using correlationsbetween calculations / tests conducted under civil aircraft type spectra, i.e. using a known averagemission to which perturbations are randomly added (gusts, manoeuvres, taxiing, etc...).

As an example, some statistical stress records are given on the following page.

1.1.3 No frequency effect

The effect due to frequency may be considered negligible, knowing that there is (see nextparagraph):

- no creep;- no corrosion.

Ch. II.1.1 LOADING / STRESS SPECTRUM P. 2/2


Upper wing surface Lower wing surface

Fuselage roof Engine pylon

Ch. II.1.2 ENVIRONMENT P. 1/1


1.2 ENVIRONMENT

1.2.1 No temperature effect

The results of the fatigue tests, carried out in a laboratory at room temperature, are assumed to beapplicable in a temperature field between:

- the "low" temperatures, where, generally speaking, an increase to the allowable tensile stressis found; however, on the other hand, a reduction in ductility (embrittlement) is found;

- the "high" temperatures, where there is a risk of appearance of the creep phenomenoncombined with conventional fatigue; for this reason, the following recommended temperaturesmust not be exceeded:

. 80 to 100°C approx. for aluminium alloys, except 2618 (≈150°C);

. 350°C for steels as well as TA6V (200°C for other titanium alloys);

. 650°C for nickel alloys.

1.2.2 No fatigue - corrosion interaction

It is assumed that there is no corrosion due to an aggressive environment which deterioratesthe fatigue strength of the studied parts, i.e.:

- either the material is selected correctly: for example, titanium alloys and stainless steels arehighly corrosion "resistant";

- a metallic or organic coating is selected, avoiding contact between the part and the aggressiveenvironment (refer to II.2.3.1);

- or sealing compounds are used (interlay, added beads, filling of cavities, wet installation orcovering of fasteners, filling of countersunk holes).

It is assumed that there is no galvanic corrosion due to the bad association of two materials incontact. Consequently, generally speaking:

- concerning fastener installation, it is prohibited to use:. aluminium rivets in titanium or steel parts;. untreated fasteners, made of titanium, nickel or steel in aluminium parts;

- it is prohibited to install, at the interfaces of parts:. untreated, unpainted, titanium, nickel, steel or composite parts without interlay of sealant

with aluminium parts.

Refer to the following documents for assembly recommendations:- ASDT 029: "Protection";- ASDT 072: "Anti-corrosion protection (long-range aircraft)".

Ch. II.2.1 MATERIAL P. 1/5


2 INTRINSIC PARAMETERS OF THE PART

2.1 MATERIAL

The following tables list the typical AS qualified materials used and, for reference, purposes theirminimum required static characteristics (R: allowable tensile stress / R0,2: allowable tensile yieldstress at which permanent strain equals 0,2% / A: elongation at rupture).

The fatigue characteristics of the materials underlined are known (therefore, tests have beencarried out on these materials).

ALUMINIUM ALLOYS (ASN-B 10000)density around 2,8

Young's modulus E≈72000 MPa(approximately 70% of an aircraft structure)

Semi-finished product Heat treatment R min.

(MPa)

R0,2 min.

(MPa)

A min.

(in %)

2014 Thin sheet T4 / T42 400 255 15

T6 / T62 440 390 7

Extruded bar T6 / T651 460 415 7

Drawn bar T6 / T651 450 380 8

Extruded shape T6 / T 62 / T651 415 370 7

2014 Pl Thin sheet T4 / T42 385 240 15

T6 / T62 420 345 9

2024 Thin sheet T3 410 290 14

T42 430 265 15

T351 445 290 14

Thick sheet T351 430 290 12

Structure tube T3 / T351 / T42 440 290 10


Drawn bar T3 / T351 440 315 12

Extruded shape T3 / T351 440 330 12

T42 420 280 14

2024 Pl Thin sheet T3 390 260 12

T42 380 230 13



2124 Thick sheet T351 440 290 12

2214 Thick sheet T451 400 250 12

T651 460 410 7

2618A Thin sheet T 62 400 325 7

T 8 400 335 7

Thick sheet T 851 430 385 5

Extruded bar T 851 415 360 6

Extruded shape T 62 400 335 7

2618A Pl Thin sheet T62 390 310 7

T8 395 325 7

6061 Thin sheet T4 / T42 210 110 16

T6 / T62 290 240 10



T6 / T62 270 245 8

Drawn bar T6 290 245 8

7010 Thin sheet T6 560 500 7


T7451 495 430 6

T7651 525 450 5

Extruded shape T6510 560 510 5

7050 Thick sheet T7451 510 440 8

T7651 525 455 6

7075 Thin sheet T6 540 470 8

T76 490 410 9


T7351 480 370 7

T7651 490 410 6

Extruded bar T6 550 480 7

Drawn bar T6 530 450 8

T73 / T7351 470 385 11

Extruded shape T6 540 480 7

T6510 / T6511 560 490 7

T73511 / T76511 485 420 8

7075 Pl Thin sheet T6 505 440 10

7175 Thick sheet T7351 480 390 7



7475 Thin sheet T76 490 410 9


T7651 490 410 6

7475 Pl Thin sheet T76 470 390 8

TITANES ET ALLIAGES DE TITANE (ASN-B20000)density around 4,4

Young's modulus E≈110000 MPa

(less than 10% of an aircraft structure)


(MPa)

R0,2 min.

(MPa)

A min.

(in %)

T40 Thin sheet Annealed 390 280 22

Rolled/forged bar Annealed 390 280 20

T60 Thin sheet Annealed 570 460 15

Rolled / forged bar Annealed 540 440 16

T-U2 Thin sheet Annealed 540 460 18

Hardened 690 550 10

Rolled/forged bar Annealed 540 400 16

TA6V Thin sheet Annealed 920 870 8

Thick sheet Annealed 890 820 8

Rolled / forged bar Annealed 900 800 10

Hardened 1100 1040 8

NICKEL ALLOYS (ASN-A 3271/3360/3361)density around 8,2

module de Young E≈200000 MPa

(in engine areas of an aircraft)


(MPa)

R0,2 min.

(MPa)

A min.

(in %)

Inconel 625 Thin sheet Annealed 830 410 30

(NC22DNb)

Inconel 718 Thin sheet / Hardened 1270 1030 12

(NC19FeNb) Rolled / forged bar + ageing



STEELS (ASN-B 01000/05000)density around 7,8

Young's modulus E≈200000 MPa

(approximately 10% of an aircraft structure)


(MPa)

R0,2 min.

(MPa)

A min.

(in %)

XC18 Sheet Annealed 392 235 25

Bar / forged part WH+Tempered 440 270 21

XC38 Bar / forged part WH+Tempered 620 400 17

XC65 Bar / forged part WH+Tempered 900 750 12

15CDV6 Sheet / Structure AH+Te.>620 980 780 10

tube / Bar / forged part OH+Te.>600 1080 930 10

25CD4 Sheet OH+Tempered 880 690 10

Structure tube OH+Te.>? 660 470 15

OH+Te.>520 880 690 10

Bar / forged part OH/TE+Te.>520 880 690 12

OH/TE+Te.>550 780 590 14

OH/TE+Te.>580 640 470 15

30CD12 Bar / forged part OH+Tempered 930 780 14

30CDV13 Bar / forged part OH+Tempered 1080 880 12

35CD4 Structure tube OH+Te.>540 1080 960 10

OH+Te.>410 1350 1230 8

40CDV20 Bar / forged part AH+Tempered 1500 1300 9

12NC12 Bar / forged part OH+Tempered 930 730 11

16NCD13 Bar / forged part OH+Tempered 1030 740 11

16NCD17 Bar / forged part Cem.+Te. 1270 880 8

30NCD16 Bar / forged part OH+Te.>525 1220 1020 8

OH+Te.>540 1080 880 10

OH+Te.>580 1080 880 10

35NC6 Bar / forged part OH+Te.>550 880 740 14

OH+Te.>580 780 640 15

35NCD16 Bar / forged part AH+Te.>200 1760 1420 6

AH+Te.>550 1230 1030 8

AH+Te.>550 1080 880 10



40CAD6.10 Bar / forged part OH+Tempered 930 780 12

E-Z1CND12-09

(Marval X12)

Bar / forged part AH+Tempered 1300 1200 9

Z2CN18-10 Sheet Over-hardened 440 180 45

Work hardened 800 700 10

Structure tube Over-hardened 500 210 40

Work Hardened 800 700 10

Bar / forged part Over-hardened 440 180 45

E-Z3NCT25 Sheet MS+AC 640 200 40

MS+AC+A+AC 850 550 20

Z6CND15-07

(PH15.7MO)

Sheet / Bar / forged part Treated+Temper

ed

1220 1100 6

E-Z6CNU15-05 Bar / forged part Treated 1310 1170 10

(15-5 PH) H 1025 1070 1000 11

E-Z6NCT25 Bar / forged part OH/WH+Temper

ed

960 660 10

Z8CND17-04 Bar / forged part OH+Te.>380 1100 900 14

(17.4 PH) OH+Te.>580 900 700 16

Z10CNT18-11 Sheet / Structure tube /

Bar /

Over-hardened 490 220 40

forged part Work Hardened 800 700 10

Z10CNW17 Sheet / Bar / forged part MS+AC 540 220 35

Z12CN13 Sheet / Bar / forged part AH/TH+Re. 590 410 16

Z12CN17-07 Sheet Work hardened 885 600 17

Z12CND16-04 Bar / forged part Treated 1400 1150 9

Z15CN17-03 Bar / forged part OH+Te.>300 1350 1050 10

OH+Te.>600 880 690 12

Z30CN13 Bar / forged part AH/OH+Te. 880 690 10

Ch. II.2.2 SURFACE CONDITION AFTER MACHINING P. 1/1


2.2 SURFACE CONDITION AFTER MACHINING

2.2.1 Part finishing

Finishing of metallic parts, excluding bores: prior to any treatment, edges must systematically bedeburred to obtain:

0,2 mm ≤ deburring depth (or finish radius) < 0,5 mm.

Edges of bores shall be slightly deburred at the top and bottom of the assembly involved toprovide a good mating plane for fasteners. The same applies to interfaces if this joint can bedisassembled.

Refer to the following documents for complementary information on the general directivesconcerning dimensions:

- NSA 2110: "General manufacturing tolerances";- A/DET 0031: "Finishing of aluminium alloy parts by deburring, breaking sharp edges or

radiusing";- A/DET 0164: "Finishing of edges on hard metallic parts";- A/DET 0029: "Installation of shear bolts";- A/DET 0085: "Installation of tension bolts".

2.2.2 Roughness

The following rule is mandatory satisfied:

Ra ≤ 1,6 for bores Ra ≤ 3,2 outside bores.

2.2.3 Residual stresses

Inherent residual stresses always remain, they are:- difficult to quantify;- depend on machining conditions and also the material.

The laws proposed in this manual integrate the existence of this type of stress as these lawsare built using the results from fatigue tests on test specimens that are generally machined duringAS production work

Caution: this is no longer the case if, for example, stress relieving is carried out (in particularfor titanium alloys). In this case, the fatigue strength may be considerably modified.

Ch. II.2.3 TECHNOLOGICAL TREATMENTS P. 1/18


2.3 TECHNOLOGICAL TREATMENTS

2.3.1 Surface treatments

The following table lists the typical processes used and qualified by AS. Fatigue characteristicsare available for the treatments underlined (therefore the treatments for which the test resultsare available).

ALUMINIUM ALLOYS

Scope of use Functions Standard

CAA Non-conducting layer Adherence base before A/DET 0072

(Chromic No abrasion and wear painting

Acid resistance Good corrosion

Anodising) (2 to 5 micron layer) resistance (if sealed)

SAA Prohibited on fatigue load- Adherence base before A/DET 0091

(Sulphuric carrying parts, cast, riveted, painting

Acid bonded, welded Good corrosion resistance

Anodising) (8 to 12 micron layer) Wear protection

HA Prohibited on fatigue load- Adherence base before A/DET 0097

(Hard carrying parts, cast, painting

Anodising riveted, bonded, welded Good corrosion resistance

(30 to 40 micron layer) Wear protection

ALODINE Parts where CAA is not Adherence base before A/DET 0079

(chromating possible, touch-up painting A/DET 0175

treatment) No abrasion and wear Good corrosion resistance

resistance (if painted)

(< 1 micron layer) Conducting layer

NICKEL Prohibited on parts in Adherence base before A/DET 0147

PLATING + fuel area painting

CADMIUM (30 to 50 micron layer) Good corrosion resistance

PLATING Conducting layer

WITH SWAB Protection against galvanic

coupling

(carbon composite)



TITANIUM AND TITANIUM ALLOYS


SAA Parts subject to risks Adherence base before A/DET 0084

(Sulphuric of external aggression painting

Acid (< 1 micron layer) Protection against

Anodising) galvanic coupling

IVD Hardware only Adherence base before A/DET 0012

(Ion (4 to 12 micron layer painting

Vapour or 7 to 20 micron layer) Conducting layer

Deposit) Heat resistant

STEELS


CADMIUM Embrittling process Adherence base before A/DET 0073

(1 de-embrittlement painting A/DET 0167

operation necessary) Good corrosion resistance

Touch-up Conducting layer

Non-stainless steels Protection against

Rm<145 hb galvanic coupling

(10 to 20 micron layer)

CHROMAGE Embrittling process Good corrosion resistance A/DET 0027

(1 de-embrittlement Protection against wear

operation necessary) Decorative


PHOSPHA- Prohibited on tight Adherence base before A/DET 0081

TING tolerance parts painting

(with magne- Non-stainless steels (zinc phosphating)

sium or zinc) Rm<145 hb Protection against wear

(2 to 5 micron layer) (magnesium phosphating)



STEELS (continued)

SILVER (10 to 15 micron layer) Adherence base before A/DET 0163

PLATING painting

Protection against wear

conducting layer

ALUMINIUM Used when conventional Adherence base before A/DET 0180

SPRAYING processes cannot be used painting

(large size parts, high service Good corrosion resistance

temperature) Conducting coat




2.3.2 Mechanical treatments

The following tables list the standard use processes qualified at AS. The fatigue characteristicsare known for the underlined treatments (therefore the test results are available for thesetreatments). The purpose of all these treatments is to improve the fatigue strength of a metallicstructure.

ALUMINIUM ALLOYS

Scope of use Standard

COLD Prohibited on cast parts with low A/DET 0020

WORKING elongation at rupture, in short transverse

(of bores) direction (S-T), at temperatures greater

than 100°C

BUSHLOC Prohibited on cast parts with low A/DET 0201

(process elongation at rupture, in short transverse

similar to direction (S-T), at temperatures greater

FORCEMATE) than 100°C

SHOT-PEENING Prohibited on parts treated against A/DET 0018

(with balls) corrosion, at temperatures greater than

100°C

TITANIUM AND TITANIUM/STEEL ALLOYS

Scope of use Standard

BUSHLOC Prohibited on cast parts with low A/DET 0201

(process elongation at rupture, in short transverse

similar to direction (S-T), at temperatures greater

FORCEMATE) than 245°C (steels) and 425°C

(titanium alloys)

SHOT-PEENING Prohibited on parts treated against A/DET 0052

(with balls) corrosion, at temperatures greater than

245°C (steels) and 425°C (titanium alloys)



2.3.3 Fastener installation

a) Types

The diameters of nominal fasteners are defined as follows:

ITEM 1 2 3 4 5 6 7

in. 1/8 5/32 3/16 1/4 5/16 3/8 7/16

mm 3,17 3,96 4,76 6,35 7,94 9,52 11,11

8 9 10 12 14 16 18 20

1/2 9/16 5/8 3/4 7/8 1 9/8 5/4

12,7 14,29 15,88 19,05 22,22 25,4 28,58 31,75

The diameters of repair fasteners are defined as follows:

ITEM R1 R2

in. +1/64 +1/32 for a given nominal diameter

mm +0,4 +0,8

The following tables list the most frequently used fastener systems, which are also recommendedin the following documents:

- ASDT 017: "Selection and instructions for use of assembly items (single aisle aircraft),"- ASDT 040: "Selection and instructions for use of assembly items (commuter aircraft),- ASDT 064: "Selection and instructions for use of assembly items (long-range aircraft).".

The corresponding repair fastener systems are also given in compliance with standard:- ASN-A 2180: "Repair dimensions, oversize holes.".

The installation conditions and the associated nuts are indicated in the following paragraph.



Standards between parentheses correspond to countersunk heads. For example: NSA 5351(50) -> 5351 for protruding heads and 5350 for countersunk heads.

SNAP RIVETS

No Material Protection Dia. D Standard

ALUMINIUM 1 2117 T4 Alodine 1,6 to 3,6 ASN-A 2050(51/49) DCJ

2 2017 T4 " 4 to 8 " DEJ

3 7050 T73 " " " DKJ

4 2117 T4 " 1,6 to 3,6 NSA 5413(12) DCJ

5 2017 T4 " 4 to 8 " DEJ

"SLUG" 6 2117 T4 " 4 to 8 ASN-A 2047

TITANIUM 7 T40 IVD 2,4 to 5,6 ASN-A 2020(19)

8 " - " NSA 5407(06)

MONEL 9 NU30 Cadmium 2,4 to 5,6 NSA 5415(14)

10 " - " NSA 5415N(14N)

BOLTS

No Material Protection Dia. D Standard

HI-LOK 11 Steel Cadmium 2 to 12 NSA 5041(40)

12 TA6V IVD " NSA 5041V(40V)

13Stainless

steel Passivation " NSA 5041C(40C)

14 TA6V IVD " ASN-A 2004V(03V)

HI-LOK 15 Steel Cadmium 3 to 10 NSA 5351(50)

"BULL NOSE" 16 TA6V SAA " NSA 5351V(50V)

17 " IVD " ASN-A 2009V(08V)

18 Steel Cadmium " NSA 5357(56) [R1]

19 " " " NSA 5359(58) [R2]

HI-LITE 20 Steel Cadmium " ASN-A 2027(26)

21 TA6V IVD " ASN-A 2027V(26V)

22 " SAA " ASN-A 2027T(26T)

23 " HI-KOTE 1 " ASN-A 2027K(26K)



BOLTS (continued)

n° Material Protection Dia. D Standard

RECESS 24 Steel Cadmium 1 à 8 NAS 1151 à 1158

COUNTERSUN

K

25 TA6V IVD " NAS 1151V à 1158V

HEAD 26 " IVD 3 à 8 ASN-A 2001V

27 " SAA " ASN-A 2001T

28 Steel Cadmium 3 à 8 ASN-A 2314/15 [R1/R2]

29 Stainless

steel

Passivation 1 à 8 NAS 1151E à 1158E

30 " - 3 à 8 ASN-A 2314C/15C [R1/R2]

31 Steel Cadmium 3 à 10 NSA 5168

32 " " 7 / 10 NSA 5401/02 [R1/R2]

33 Steel Cadmium 6 / 10 NSA 5452

34 " " 10 ASN-A 2060/62 [R1/R2]

35 Inco. 718 IVD 3 à 10 ASN-A 0092

36 " " " ASN-A 0095/97 [R1/R2]

37 Inco. 718 Passivation 3 à 10 ASN-A 0124

38 " " " ASN-A 0141/142 [R1/R2]

HEXAGONAL 39 Stainless

steel

Passivation 3 à 20 NAS 6303 à 6320

HEAD 40 " " " NAS 6303X/Y à 6320X/Y [R1/R2]

41 Steel Cadmium 3 à 20 NAS 6603 à 6620

42 " " " NAS 6603X/Y à 6620X/Y [R1/R2]

43 Stainless

steel

Passivation 3 à 20 NSA 6703 à 6720

44 " " " NAS 6703X/Y à 6720X/Y [R1/R2]

45 TA6V IVD 3 à 20 NAS 6403 à 6420

46 Steel Cadmium " NSA 1303 à 1320

47 TA6V IVD 3 à 12 ASN-A 2000V

48 " SAA " ASN-A 2000T

49 " IVD " ABS 0114V

50 " SAA " ABS 0114T

51 Steel Cadmium " ASN-A 2318/19 [R1/R2]



BOLTS (continued)


TORQ-SET 52 Steel Cadmium 1 à 8 NAS 1131 à 1138

ROUND 53 TA6V IVD " NAS 1131V à 1138V

HEAD 54 " IVD 3 à 8 ASN-A 2016V

55 " SAA " ASN-A 2016T

56 Steel Cadmium " ASN-A 2316/17 [R1/R2]

57 Stainless

steel

Passivation 1 à 8 NAS 1131C à 38C

58 " " 3 à 8 ASN-A 2316C/17C [R1/R2]

12-POINT 59 Steel Cadmium 3 à 10 NSA 5170/72

SHEAR BOLT 60 " " 3 / 5 / 8/

10 / 12

NSA 5403/04 [R1/R2]

61 Steel Cadmium 6 à 10 NSA 5453

62 " " " ASN-A 2061/63 [R1/R2]

63 Inco. 718 IVD 3 à 10 ASN-A 0093

64 ASN-A 0096/98 [R1/R2]


66 " " 3 à 10 ASN-A 0139/140 [R1/R2]

12-POINT 67 Steel Cadmium 4 à 14 MS 21250

TENSION BOLT 68 Inco. 718 IVD 4 à18 NSA 5378A

69 " " 4 à 14 NSA 5398A/99A [R1/R2]


71 " " 4 à 18 NSA 5378

72 " " 4 à 14 NSA 5398/99 [R1/R2]

TAPERLOCK 73 TA6V SAA 3 à 10 NSA 5093V(92V)

74 " " " NSA 5154V(53V) [R1]

75 " IVD " ASN-A 2013V(12V)

76 " " " NSA 5154VA(53VA) [R1]

77 " HI-KOTE 1 " ASN-A 2013K(12K)

78 " " " NSA 5154K(53K) [R1]



BOLTS (continued)

SOULDERED 79 Steel Cadmium 4 à 16 NSA 5042

BOLT 80 " " 5 à 9 NSA 5118/19 [R1/R2]

(for yokes) 81 Stainless

steel

- 4 à 16 NSA 5042C

82 " " 5 à 9 NSA 5118C/19C [R1/R2]

83 Stainless

steel

- 4 à 16 NSA 5042E

84 " " 5 à 9 NSA 5118E/19E [R1/R2]

CAPTIVE BOLT (LOCKBOLT)


GPL 85 TA6V SAA 2 / 6 ASN-A 2042(41)

86 Steel Cadmium 3 / 6 ASN-A 2054(40)

87 " " " ASN-A 2171(70) [R1]

88 Stainless

steel

Passivation " ASN-A 2054C(40C)

89 " " " ASN-A 2171C(70C) [R1]

LGPL4 90 TA6V IVD 3 / 6 ASN-A 2392(91)

LGPS4 91 " " " ASN-A 2392S(91S)

LGPL2 92 TA6V IVD 2 / 4 ASN-A 2048(43)

93 " " " ASN-A 2048S(43S)

LGPS2 94 " " " ASN-A 2048X(43X) [R1]



BLIND RIVETS


VISU-LOK 95 Steel Cadmium ASN-A 0082(81)

CHERRY-MAX 96 Alu. SAA ASN-A 0078A(77A)

97 Monel - ASN-A 0078E(77E)

98 " IVD ASN-A 0078F(77F)

CHERRY-NUT 99Stainless

steel - ABS 112P

10

0

" Cadmium ABS 112C

HUCK MLS 10

1

Monel - NAS 1921M(19M)

10

2

" Cadmium NAS 1921MW(19MW)

BPT 10

3

Stainless

steel

Passivation MS 21141(40)



b) Assembly conditions

Bolt fits are those proposed by NSA 2010/2012: the tightening torques correspond to A/DET 0030.

SNAP RIVETS

n° Type of riveting D(upset head) / D

ALUMINIUM 1 Hand / Squeeze / Auto. 1,5 / 1,8

2 Hand / Squeeze "

3 Auto. "

4 Hand / Squeeze / Auto. 1,4 / 1,8

5 Hand / Squeeze "

SLUG 6 Auto. 1,4 / 1,8

TITANIUM 7 Hand / Squeeze / Auto. 1,25 / 1,4 (for aluminium parts)

8 " 1,3 / 1,5 (for titanium and steel parts)

MONEL 9 Hand / Squeeze / Auto. 1,25 / 1,4 (for aluminium parts)

10 " 1,3 / 1,5 (for titanium and steel parts)

BOLTS

n° Fit Tightening Nut mat. Nut standard

HI-LOK 11 (1)

12 (4) (1) Steel NAS 1726E/27E

13 (5) (2) Alu. or NSA 5182

14

HI-LOK 15 (1) (3) Steel NAS 1726E/27E

"BULL NOSE" 16 (4) (1) Steel NAS 1726E/27E

17 (5) (2) Alu. or NSA 5182

18 (3) Steel NAS 1726E/27E

19 (3) " "

HI-LITE 20 (1) (1) Steel ASN-A 2531/32/36/38

21 (4) (4) Alu. or ASN-A 2028/29

22 (5) (5) Alu. or ASN-A 2037

23 (swivel end)



BOLTS (continued)


RECESS 24 (6) Steel/Stainle

ss steel

NAS 1726E/27E / 26CSE/27CE

COUNTERSUN

K

25 " Stainless or NSA 5457CE

HEAD 26 " steel or ASN-A 2021CE

27 " Steel/Stain or MS 21042/43

28 (7) less steel or NAS 509/9C

29 (8) " or NAS 5059/59C

30 (1) (9) " or NSA 5060/60C

31 (5) (10) Steel/Stainle

ss steel

NAS 1726E/27E / 26CSE/27CE

32 (10)/(12) Steel or NSA 5094 or NSA 5171/74

33 (10) Steel/Stainle

ss steel

NAS 1726E/27E / 26CSE/27CE

34 " Steel or NSA 5094

35 " Stainless NAS 1726CSE/27CE

36 " steel "

37 " " "

38 " " "

HEXAGONAL 39

HEAD 40


ss steel

NAS 1726E/27E / 26CSE/27CE

42 " " or NSA 5457CE

43 " Stainless

steel

or ASN-A 2021CE

44 (1) " Steel/Stainle

ss steel

or MS 21042/43

45 (5) (7) " or NAS 509/9C

46 (8) " or NAS 5059/59C

47 (9) " or NSA 5060/60C

48

à

51



BOLTS (continued)


TORQ-SET 52 (6) Steel/Stainle

ss steel

NAS 1726E/27E / 26CSE/27CE

ROUND 53 " " or NSA 5457CE

HEAD 54 (1) " " or ASN-A 2021CE

55 (5) " Steel/Stainle

ss steel

or MS 21042/43

56 (7) " or NAS 509/9C

57 (8) " or NAS 5059/59C

58 (9) " or NSA 5060/60C

12-POINT 59 (10) Steel/Stainle

ss steel

NAS 1726E/27E / 26CSE/27CE

SHEAR BOLT 60 (10)/(12) Steel or NSA 5094 or NSA 5171/74


ss steel

NAS 1726E/27E / 26CSE/27CE

62 (1) " " "

63 (5) " Stainless

steel

NAS 1726CSE/27CE

64 " " "

65 " " "

66 " " "

12-POINT 67 (13) Steel NSA 5057

TENSION BOLT 68 (14) Inconel ASN-A 0094

69 (6) (14) " "

70 (14) " NSA 5373

71 (13) " "

72 (14) " "

TAPERLOCK 73 Steel NAS 1726E/27E

74 " "

75 See See " "

76 NSA 2010 A/DET 030 " "

77 " "

78 " "



BOLTS (continued)

SOULDERED 79

BOLT 80

(for yokes) 81 (8) " NAS 5059/59C

82 (9) " or NSA 5060/60C

83

84

CAPTIVE BOLT (LOCKBOLT)


GPL 85 TA6V ASN-A 2045

86 Pre-

87 tensioning Monel ASN-A 2044

88 (1) ≈

89 (2) 50%

LGPL4 90 (3) fastener

LGPS4 91 (4) rupture Alu. ASN-A 2045

LGPL2 92 load

93

LGPS2 94

Fits and torques indicated in the previous tables by () are explained on the following pages.



Fit

The following tables indicate, for each type of fit in the previous table and for each nominal fastenerdiameter, in compliance with NSA 2010/2012:

- on the left-hand scale:the clearance or interference values (in µm): min./max. values (thin line) and averagevalue (thick line),

- on the right-hand scale:the clearance or interference percentage (in %): min./max. values (light grey) and averagevalue (dark grey):

100.ondia.fixati

on)dia.fixatige(dia.alésaInt −= (in %)

-40

-20

0

20

40

60

80

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

22,2 25,4 28,6 31,75

-0,8%

-0,6%

-0,4%

-0,2%

0,0%0,2%

0,4%

0,6%

0,8%(1) Clearance fit hardware in aluminium

0

10

20

30

40

50

60

70

4,8 6,35 7,9 9,50,0%

0,2%

0,4%

0,6%

0,8%

1,0%

1,2%

1,4%

1,6%(2) Clearance fit harware (auto installa.) in alu.

-70

-60

-50

-40

-30

-20

-10

0

4,8 6,35 7,9 9,5-1,6%

-1,4%

-1,2%

-1,0%

-0,8%

-0,6%

-0,4%

-0,2%

0,0%(3) Low interference fit hardware (auto installa.) in alu.



-140

-120

-100

-80

-60

-40

-20

0

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9-2,0%-1,8%-1,6%-1,4%-1,2%-1,0%-0,8%-0,6%-0,4%-0,2%0,0%

(4) High interference fit hardware in aluminium

0

10

20

30

40

50

60

70

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

22,2

0,0%0,1%0,2%0,3%0,4%0,5%0,6%0,7%0,8%0,9%1,0%

(5) Cleareance fit hardware in titanium/steel

050

100150200250300350400450500

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

22,2 25,4 28,6 31,75

0,0%

2,0%

4,0%

6,0%

8,0%

10,0%

12,0%(6) Tension bolts



Tightening

The following tables indicate, for each type of tightening in the previous table and for each nominalfastener diameter, in compliance with A/DET 0030:

- on the left-hand scale: the tightening torque (in daN.m): minimum/maximum values (lightgrey) and average value (dark grey),

- on the right-hand scale: the pretightening stress (in hb): minimum/maximum values (thinline) and average value (thick line).

0123456789

10

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9

0

10

20

30

40

50

60Tightening (1)

012345678

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9

0

10

20

30

40

50

60Tightening (2)

0123456789

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9

051015202530354045

Tightening (3)

012345678

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9

0

10

20

30

40

50

60Tightening (4)

02468

1012141618

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0102030405060708090

Tightening (5)

0

1

2

3

4

5

6

4,8 6,35 7,9 9,5 11,1 12,701020304050607080

Tightening (6)



0123456789

10

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0

10

20

30

40

50

60Tightening (7)

012345678

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0

5

10

15

20

25

30

35Tightening (8)

012345678

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0

5

10

15

20

25

30

35Tightening (9)

0

5

10

15

20

25

30

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0

20

40

60

80

100

120

140Tightening (10)

0

5

10

15

20

25

30

35

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

020406080100120140160180

Tightening (11)

02468

101214161820

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,9

0102030405060708090

Tightening (12)

05

101520253035404550

4,8 6,35 7,9 9,5 11,1 12,7 14,3 15,919

0

50

100

150

200

250Tightening (13)

0102030405060708090

100

4,8 6,357,9 9,5 11,112,714,315,919

22,225,4

050100150200250300350400450500

Tightening (14)

Ch. II.3.1 AVERAGE/APPLICATION OF A SAFETY FACTOR P. 1/1


3 LIFE

3.1 AVERAGE/APPLICATION OF A SAFETY FACTOR

The life calculated using the Fatigue Manual is an average life.

Therefore, it is necessary to apply a safety factor to take the significant scatter inherent to thefatigue phenomenon and also calculation precision into account.

Generally, this factor is:

5=αααα

for non-inspectable or non-repairable areas,

or:

3=αααα

for inspectable and repairable areas,i.e. the areas to which the Damage Tolerance Rules can be applied.

Also, it would be more precise to associate a given rupture probability with the safety factor.However, this makes it necessary to know, in a statistically reliable manner, the scatter (standarddeviations) associated with the fatigue phenomenon and the scatter related to external parameters(loading, environment, etc.).

However, today, there is not sufficient data of this type to be able to apply this approachsystematically.

Ch. II.3.2 FIELD OF APPLICATION P. 1/1


3.2 FIELD OF APPLICATION

The calculation is valid above 103 cycles (or flights) approximately, i.e. for fatigue after a greatnumber of cycles.

As the life targets of our aircraft are relatively ambitious, it is all the more logical to positionourselves in this domain. Consequently, they are:

- between 20000 and 48000 flights for the AIRBUS family;- 70000 flights for the ATR family.

This results in at least 2.104 ground-air-ground cycles that the structure has to be capable ofsupporting.

Aircraft Target (in flights)

ATR42 / 72 70000

A300 B2 48000

A300 B4-100 40000

A300 B4-200 34000

A300-600 30000

A310-200 40000

A310-300 (short mission) 35000

A310-300 (long mission) 17500

A319 / A320 / A321 48000

A330 40000

A340 20000

Ch. III DESCRIPTION OF THE METHOD P. 1/1


III DESCRIPTION OF THE METHOD

The simplest and the most conventional method to appraise fatigue crack initiation in a metallicstructural item consists in experimentally building a complete system of Wohler curves. This wouldhowever require a very great quantity of test specimens making the cost totally prohibitive.

Consequently, the most industrial method consists in "imagining" the most generalmathematical model possible to reduce the number of tests appreciably. For example, BOEINGand CETIM use the same approach..

Modelling proposed in the next paragraph has been correlated in a very satisfactory manner undermonotonic loading and also under complex loading representing civil aircraft missions (Ref. 2).

An interesting analogy is made with the elastic-plastic approach (much less frequently found in theindustry) in Appendix 1 to further validate the model presented below.

Ch. III.1.1 CALCULATION UNDER A MONOTONIC LOAD P. 1/7


1 GENERAL MATHEMATICAL FORMULATION

1.1 CALCULATION UNDER A MONOTONIC LOAD

1.1.1 Uniaxial tension loading

--> General formulation:

The average life is expressed in the following form:

( )( )

p

maxq

5

.S/0,9R-1IQF10N

.=

in which:

the IQF (Fatigue Quality Index) is the maximum stress at R=0.1 making it possible to obtain an

average life of 105 cycles.

Smax(0.1) =IQF

log( N)R=0.1 R

10 5

log(Smax)

Smax(R)

This point was chosen as a reference as the AS fatigue tests carried out up to today were

essentially conducted at R=0.1, and in a life domain between approximately 104 and 106 cycles.



--> p and q values:

Material p q

Aluminium alloys 4,5 0,6

Titanium and titanium alloys 6,5 0,6

Nickel alloys / Steels 7,5 0,6



--> Consequences:

The following table summarises all equations that can be formulated using the previous life law:

Variables:

Smax / R / IQF / N

Variables:

Sa / Saverage/ IQF / N

( )( )

p

maxq

5

S/0,9R-1IQF.10N

=

. ( ) ( )p

q)-(1amoy

qa

5

S+S./0,92.SIQF.10N

=

( )( )

1/p5

qmax N10.

/0,9R-1IQFS

= ( ) ( ) * 0IQF

10NS+S./0,92.S

1/p

5q)-(1

amoyq

a =−

.

1/p

5max

q

10N..S

0,9R-1IQF

= ( ) ( )1/p

5q)-(1

amoyq

a 10NS+S./0,92.SIQF

= .

1/(p.q)51/q

max N10.

SIQF0,9.-1=R

( ) a

q)-1/(11/p5

qa

moy S-N

10./0,92.S

IQFS

=

* This equation has to be solved to determine Sa as a function of Saverage, N and IQF.

The Wohler and the Haigh curves are given consecutively on the following page for an aluminiumalloy with:

- an allowable tensile yield stress of 300 MPa,- and IQF of 150 MPa for the structural item involved.



N (number of cycles)

0

50

100

150

200

250

10000 100000 1000000 10000000

R=-10R=-6R=-3R=-1

R=0,1

R=0,4

R=0,7

Save (MPa)

0

50

100

150

200

250

300

-300 -200 -100 0 100 200 300

N=100.000

N=10.000

N=3.000

N=1.000.000

N=10.000.000

R=0,1

R=-10



1.1.2 Extension to uniaxial shear loading

In this case, the stress matrix at the initiation site can be formulated as follows:

00000S0S0

For example, this is the case of a solid or hollow shaft in torsion.

--> General formulation:

The average life is expressed in the following form:

( )

p

aq

5

.S3.2/0,9IQF10N

.=

or even:

( )( )

p

max

5

.S/0,9R-1IQF'.10N

=

where:

( )0,79.IQF

/2).0,93.(2/0,9IQFIQF' q == (as q=0,6)

is the maximum stress (shear) at R=0.1, making it possible to obtain an average life of 105 cycles(shear fatigue quality index).

Therefore, this formulation is of the same type as the tension one and only incorporates a slightdifference in the f(R) law (no q coefficient).

This equation has not be checked on AS tests; however, it satisfies the two properties commonlyfound in reference documents (in particular, Sinès criterion):

- N is independent of the average stress;- at R=0.1, for the same life N, there is:

Smax ( tension) ==== 3 .Smax (shear)



--> p and q values: (same values as for tension)

Material p q

Aluminium alloys 4,5 0,6

Titanium and titanium alloys 6,5 0,6

Nickel alloys / Steels 7,5 0,6

--> Consequences:

The following table summarises all equations that can be found using the previous life law:

Variables:

Smax / R / IQF / N

Variables:

Sa / Saverage / IQF / N

( )( )

p

max

5

S/0,9R-1IQF'.10N

=

. ( )

p

a

5

.S2/0,9IQF'.10N

=

( )( )1/p5

max N10.

/0,9R-1IQF'S

= ( )

1/p5

a N10.

2/0,9IQF'S

=

1/p

5max 10N..S

0,9R-1IQF'

= ( )1/p

5a 10N..S2/0,9IQF'

=

1/p5

max N10.

SIQF'0,9.-1=R

-

The Wohler and the Haigh curves are given consecutively on the following page for an aluminiumalloy with:

- an allowable tensile yield stress of 300 MPa;- and IQF of 150 MPa for the structural item involved.



N (number of cycles)

0

20

40

60

80

100

120

140

160

180

200

1E+04 1E+05 1E+06 1E+07

R=-10R=-6R=-3R=-1

R=0,1

R=0,4

R=0,7

Save (MPa)

0

50

100

150

200

-200 -150 -100 -50 0 50 100 150 200

N=100.000

N=10.000

N=3.000

N=1.000.000

N=10.000.000

R=0,1

R=-10

Ch. III.1.2 SPECTRUM CALCULATION P. 1/5


1.2 SPECTRUM CALCULATION

1.2.1 Miner's rule

Damage to a structural item subjected to monotonic stress loading characterised by (Smax, Ri) isassumed to accumulate linearly. Consequently, if Ni is the life corresponding to this loading, thedamage after ni cycles is defined as:

i

ii N

nd =

Miner's rule then advances that the total spectrum damage is equal to the sum of the damagerelated to each cycle:

=i i

i

N

nD

failure is then reached when:

1D =

1

NNfailure

D

Nonetheless, to improve calculation reliability, Miner's rule on the stress spectrum previouslyprocessed by the Rain-Flow counting method, has to be applied.



1.2.2 Rain-Flow principle

This method can be described metaphorically as consisting in allowing a fluid to flow along theprocessed stress spectrum.

Processing is as follows:

- the stress sequence is rearranged so that the first value corresponds to the minimum (ormaximum) peak of the sequence;

- the first flow starts at the first peak; the second flow starts at the next minimum (or maximum)peak; this is continued up to the end of the sequence;

- each flow is stopped in compliance with one of the following rules; it provides a half cyclewhich is associated with its complement to provide a complete cycle;

Stop

Previous flow

Initial peak

1S

time



StopPeak less than

initial peak

2S

time

Initial peak

StopEnd of record

3S

time

Initial peak

- all cycles defined in this manner constitute the new spectrum to be taken into account in thedamage calculation (same number of cycles).



1.2.3 Example of application

This method can be described metaphorically as consisting in allowing a fluid to flow along theprocessed stress spectrum, as follows:

0

50

100

150

200

t

(MPa)

1

2 3

4

5

1

2 3 4 5

smax

Simplified flight

All that remains is to calculate the damage related to cycles 1 to 5 as shown in the following figure:



1

2 3 4 5

10 4N

10 5 10 6 (cycles)

1 235

4

D=10 -4 D=10 -5 D=10 -5

D(total)=1,2.10 -4

N = 8333 flights

3.10 4 3.10 5

R=2/3

R=1/3

R=0

(MPa)smax

Ch. III.1.3 FUNDAMENTAL PROPERTIES P. 1/2


1.3 FUNDAMENTAL PROPERTIES

1.3.1 Monotonic loading equivalent to the spectrum

On a given structural item, a monotonic cycle (Smax = Seq , R=0,1) is equivalent or gives the same

life N, to the stress spectrum of a flight or a sequence of flights (previously subjected to Rain-Flowprocessing) if:

D(spectre))D(monotone =

or:

=i i

N1

N1

or (for uniaxial tension loading):

( )( )

=

i

.SR-1

IQF.10

1

SIQF.10

1p

maxiq

i

5

p

éq

5

9,0/

or:

( )( )[ ]1/p

i

pmaxi

qiéq .S/0,9R-1=S

therefore:- Seq is independent from IQF;- if the stress spectrum is modified in a given K ratio (cross-section changed, etc.), Seq is

modified by the same ratio K;

these two properties facilitate iteration, especially during the sizing phase.

Consequently, N may be formulated simply as:

p

éq

5

SIQF10N

.=

(demonstration the same as for shear, replacing IQF by IQF' and q by 1)

Ch. III.1.3 FUNDAMENTAL PROPERTIES P. 2/2


1.3.2 Spectrum coefficient (Cs)

Consider Sref : a reference stress arbitrarily selected from the stress spectrum suffered by a given

structural item (for example, the average stress during cruise). Then the spectrum coefficient isdefined by:

ref

éq

SS

=Cs

or (for uniaxial tension loading):

( )( )1/p

i

p

ref

maxiqi

ref

éq

SS./0,9R-1

SS

=Cs

=

therefore:- Cs is independent from IQF;- if the stress spectrum is modified in a given ratio K (cross-section loading, etc.) Cs is not

modified and becomes an intrinsic characteristic of the studied structural item..

Consequently, N can be formulated simply as::

p

ref

5

Cs.SIQF10N

.=

(demonstration identical to shear, replacing IQF by IQF' and q by 1).

Ch. III.1.4 CONSEQUENCES ON PRACTICAL APPLICATION P. 1/2


1.4 CONSEQUENCES ON PRACTICAL APPLICATIONS

1.4.1 Fundamental parameters

IQF, Seq, N are the main parameters of the calculation model; the method is summarised on graph

following:

STRUCTURAL ITEM

FLIGHT LOADING

INITIATION LAW

MATERIAL

TECHNOLOGY

GEOMETRY

IQF

N

seq.

PP

Monotonic fatigue test

FLIGHTS NUMBER UNTILL INITIATION

Ch. III.1.4 CONSEQUENCES ON PRACTICAL APPLICATION P. 2/2


1.4.2 Use in sizing

The following is known during structural item sizing:

- Ngoal, the life;

- Seq characterising the severity of the stress spectrum suffered by this part;

therefore it is possible to deduce IQFallowable by:

1/p

5objectif

éqadmissible 10N

.SIQF

=

then all that remains is to prove that:

admissibleIQFIQF ≥

1.4.3 Use in substantiation

The following is known when substantiating a structural item:

- IQF characterising the intrinsic quality of the part under fatigue stress;

- Seq characterising the severity of the stress spectrum suffered by this part;

therefore it is possible to deduce the average life for:

p

éq

5

SIQF.10N

=

therefore, all that remains is to prove that:

objectifNN ≥

αααα

α being the selected safety factor.

Ch. III.2.1 BASIC CALCULATION WITH THE COMPUTERISED SYSTEM P. 1/2


2 DETERMINATION OF THE EQUIVALENT MONOTONIC LOAD

2.1 BASIC CALCULATION WITH THE COMPUTERISED SYSTEM

A list of calculation procedures to be used is given below:

PSF6: "Composition of fatigue load statistical records"composition of the statistical records of stresses based on the assumption that a flight is asuccession of steps each characterised by overlaying:

. an average stress (balancing) characterising the aircraft and its mission independentlyfrom the environment;

. one or more dynamic stresses created by the environment (gusts, manoeuvres, taxiing,etc.).

PSF9: "Analysis of the statistical record of stresses (main spectrum)"breakdown of the statistical record of stresses, derived from PSF6, into "main and residual";breakdown of the statistical record of stresses, derived from PSF6, into main and residual.

PSF10: "Simulation by independent flights/random sorting"generation of a theoretical spectrum of stresses in the form of a random sequence of flightseach comprising a random succession of cycles complying with the main/residual proportiongiven by PSF9.

PSF11: "Analysis and breakdown of the stress spectrum/Rain-Flow"generation of a new stress spectrum, using the one obtained from PSF10 or PSF12, andusing the Rain-Flow counting method;

PSF12: "Analysis/filtering and validation of discrete spectra"conversion of a theoretical stress spectrum obtained by PSF10 into a "filtered" spectrum(therefore with fewer cycles) to enable the performance of fatigue tests; for example, it mayalso be used for a PSF11/PSF8 calculation sequence.

PSF8: "Calculation of the fatigue life (crack initiation)"application of the crack initiation law given in this manual on the stress spectrum obtainedfrom PSF11.

Ch. III.2.1 BASIC CALCULATION WITH THE COMPUTERISED SYSTEM P. 2/2


The entire approach is summarised in the following diagram:

PSF6

PSF9

PSF10

PSF11

PSF12

N

"Statistical" record of stresses

"Statistical" record broken down into main / residual

"Theoretical" stress spectrum

"Filtered" spectrum

Spectrum processed by "Rain-Flow"

PSF8

Life calculation

Ch. III.2.2 HIGH-SPEED CALCULATION USING THE SPECTRUM COEFFICIENT P. 1/3


2.2 HIGH-SPEED CALCULATION USING THE SPECTRUM COEFFICIENT

These spectrum coefficients are given for information purposes for:- typical areas of ATR and AIRBUS aircraft families (parts under the responsibility of AS),- theoretical fatigue missions.

For more information, in particular:- in more complex areas (e.g.: load take-up areas, landing gear bays),;- for aircraft versions different from those mentioned in this document;

it is strongly recommended to speak with the experts in charge of these areas.

These coefficients only correspond to aluminium alloy structures (essentially to 2XXX and 7XXXtype series).

-----------------

In the first table below, the reference Sref corresponds to the stress encountered in the cruisephase (without any environmental disturbance).

The mission involved is a short 45 minute mission.

ATR Type CsWing

Lower surface panels and spars ATR 1,9 / 2,1



In the second table below, the reference stress Sref corresponds to the stress encountered during

the highest "cruise" phase (but without any environmental disturbance) but which nonethelessincorporates the pressurisation effect.

The mission involved is:- a mission lasting between 90 minutes and 265 minutes for the A310, 200dev and 300 versions

(Ref. 3);- a 75 minute mission for the A319/A320/A321, versions 100 and 200;- a 90 minute mission for the A330, version 300 (Ref. 4 & 5);- a mission lasting between 75 minutes and 405 minutes for the A340, versions 200, 300 and

300WV020 (Ref. 4 & 5).

AIRBUS Type CsSections 11 / 12

Pure pressurisation area A310 / A319 /A320 / 1,065A321 / A330 / A340

Sections 13 / 14

Pressurisation area + fuselage bending A319 / A320 /A321 1,065 /1,15

Section 15

A310 1,1 / 1,4Pressurisation area + fuselage bending A330 1,1 / 1,4

A340 1,2 / 1,5



AIRBUS (continued) Type CsSection 21

Lower surface panels and spars A310 1,6 / 2A319 / A320 /A321 1,3 / 1,5

A330 / A340 1,5 / 1,8

Lower surface tee fitting A310 1,8 / 2,2A319 / A320 /A321 1,4 / 1,6

A330 / A340 1,7 / 2

Ch. III.3.1 GENERAL IQF LAW P. 1/3


3 DETERMINATION OF THE INTRINSIC QUALITY OF THE PART(IQF)

3.1 GENERAL IQF LAWThe following rule-of-thumb law obtained by processing a great number of tests (approximately1000 cases --> refer to the overall substantiation in Appendix 2 and the reference documents)proposes a simple formulation for the average IQF value depending on assumed independentpreponderant parameters:

KtC..T3.T4.T5)M.E.(T1.T2IQF =

(in MPa)

where:

MEANING OF COEFFICIENTS

Definition See chapter

M Effect of material 3.2

E Influence of scale effect 3.3

T1 Effect of surface treatment 3.4T1=1 if no treatment

T2 Effect of mechanical treatment 3.4T2=1 if no treatment

T3 Effect of the type of fasteners used 3.4for bolted and riveted assemblies only

T3=1 if no fasteners

T4 Effect of fastener installation conditions 3.4for bolted assemblies only

T4=1 if no fasteners



T5 Effect of countersinking 3.4for bolted and riveted assemblies only

T5=1 if no countersink

Kt Effect of the geometry 3.5(stress concentration effect) à

3.9C Effect of the type of structural configuration See next

page

Notches C=510

Yokes C=430

Bolted or riveted assemblies C=630



Remarks on the C coefficient:- C is greater for assemblies than for notches (+24%) as neither the Kt nor the technological

coefficients T1, T2, T3, T4, T5 take into account the beneficial effects in fatigue:

of clamping for bolts, or residual interference created by rivet cold working,but at the same time, the possible load transfer by friction (friction between sheets),

- C is less for yokes than for notches (-15%) as:clevis pins are considered being without any clamping effect and therefore do notincorporate the previous beneficial effect;the very high fretting in pins facilitates the initiation of micro-cracks except:

if fretting is eliminated by interference fitting of a bush in the bore (FORCEMATE orBUSHLOC process);if residual compression stress is created around the bore (COLD WORKING).

The following figure illustrates the role of C for M=T1=T2=T3=T4=T5=1:

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10 11

ASSEMBLIES

NOTCHES

YOKES

Kt

IQF

Ch. III.3.2 EFFECT OF MATERIAL P. 1/2


3.2 EFFECT OF MATERIAL

The characteristics are valid for:- non-cast materials,- parts stressed in the "long" and "long transverse" direction but not in the "short

transverse" direction, in which a deterioration of crack initiation characteristics, not quantifiedhere, can be seen.

ALUMINIUM ALLOYS

Materials M2014 - 2114 - 2214 0,95

T4XX / T6XX

2024 - 2124 - 2224 1with copper T3XX / T4XX

2618T6XX 1T8XX 0,95

with lithium 2091 1T8XX

with zinc 7010 - 7050 - 7075 - 7175 - 7475 0,9T6XX / T7XX


Materials Mnon T40 1,2

alloyed

TU2 1,4alloyed

TA6V 1,8

Ch. III.3.2 EFFECT OF MATERIAL P. 2/2


NICKEL ALLOYS

Materials MINCONEL 625 2,3

INCONEL 718 2,6

STEELS

Materials Mlow alloy 35NCD16 2,6materials 40CDV12

E-Z1CND12-09 2,6Z3CNDA13-8

high alloy Z6CND15-07materials E-Z6CNU15-05

Z8CND17-04

Ch. III.3.3 INFLUENCE OF SCALE EFFECT P. 1/1


3.3 INFLUENCE OF SCALE EFFECT

The scale factor is calculated using the following simple formula (r is the notched radius given inmm).

0,08

r1=E

r

r=d/2

0,70

0,75

0,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

0,1 1 10 100

E

r

Ch. III.3.4 EFFECT OF TECHNOLOGICAL PROCESS P. 1/9


3.4 EFFECT OF TECHNOLOGICAL PROCESS

3.4.1 Surface treatments

ALUMINIUM ALLOYS

T1No treatment 1

CAA. on mechanical machining 0,75

. on chemical milling 0,85(Ref. 6)

ALODINE. with sulphur-chromic 0,9

acid stripping

. without sulphur-chromic 1acid stripping:

touch ups, etc.

(Ref. 7)


T1No treatment 1

SAA (1)

( ): according to our "material" experts at Toulouse and Suresnes

(no fatigue tests available)



STEELS

T1No treatment 1

CADMIUM PLATING 0,9(Ref. 8)

PHOSPHATING (1)

( ): according to our "material" experts at Toulouse and Suresnes

(no fatigue tests available)



3.4.2 Mechanical treatments

ALUMINIUM ALLOYS

T2No treatment 1

COLD WORKING(excluding yokes)

. reduced (2%) 1,1. conventional (4%) 1,2

COLD WORKING(yokes)

1,5

reduced (2%)

FORCEMATE (yokes) 1,7

SHOT-PEENING 1,15(Ref. 9)


T2No treatment 1





STEELS

T2No treatment 1





3.4.3 Fastener installation

a) Type of fasteners

ALUMINIUM ALLOY

T3BLIND RIVET (0,8)

ALU. RIVET. hand riveting 1

. Ce / auto. riveting 1,05

SLUG RIVET 1,2auto. riveting

TITANIUM RIVET. hand riveting 1,15

. Ce / auto. riveting 1,2

MONEL RIVET 1,25hand riveting

BOLT 1(slight clearance /

nominal torquing)

( ): use 0.7 to cover all types of blind rivets




T3TITANIUM RIVET 1,15

hand riveting

MONEL RIVET 1,25hand riveting

BOLT 1(slight clearance /

nominal torquing)

NICKEL ALLOYS/STEELS

T3BOLT 1

(slight clearance /

nominal torquing)



b) Fastener installation conditions (for bolts only)

By definition, the interference percentage is:

100.ondia.fixati

on)dia.fixatige(dia.alésaInt −= (in %)

ALUMINIUM ALLOYS

T4INTERFERENCEFIT ASSEMBLY

(interference given in %)

=1-0,44.Int-0,12.Int2

1

1,05

1,1

1,15

1,2

1,25

1,3

1,35

1,4

-2,0% -1,5% -1,0% -0,5% 0,0%

T4

Int



c) Countersink effect

Hole fitted with a countersunk fastener(Ref. 11)

ep

0,85

0,90

0,95

1,00

1,05

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

T5

e-p

(in mm)



Countersink incorrectly filled with a fastener(Ref. 12)

ep

T5INCORRECTLY

FILLED COUNTERSINK 0,85

Ch. III.3.5 KT IN CYLINDRICAL SHAFTS P. 1/17


3.5 KT IN CYLINDRICAL SHAFTS

The equations used to plot the following graphs are from the CETIM (Ref. 13) and comply with theresults given in the PETERSON (Ref. 14) and the ESDU 89048 (Ref. 15).

Processed models:

A111 Solid shaft with half round shoulderA112 Solid shaft with angled flank shoulderA113 Solid shaft with 2 shouldersA121 Solid shaft with a half round bottom grooveA122 Solid shaft with an angled flank grooveA131 Solid shaft with transverse hole

A211 Hollow shaft with half round bottom external grooveA212 Hollow shaft with angled flank external grooveA221 Hollow shaft with transverse holeA231 Hollow shaft with internal groove

Remark:

in the case of nominal tension + bending loading, covered by the convention:

. Stension is the nominal reference stress used to express the Kt: Kt=Smax/Stension

. Sbending is assumed to be proportional to Stension:Sbending =λλλλ.Stension

by overlaying, the following is deduced:Smax=Kttension.Stension+Ktbending.( λλλλ.Stension)

or:Smax=(Kttension + λλλλ.Ktbending).Stension

therefore:

Kt=(Kttension + λλλλ.Ktbending)



A111) Solid shaft with half round shoulder

F Fde Mt MfMtMf d

r

2traction d4.F=S.π 3flexion d

32.Mf=S.π 3torsion d

16.Mt=S.π

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d)0,01 0,020,03

0,05

0,07

0,1

0,2

0,5

1

10

Kt tension



d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d)0,01 0,020,03

0,05

0,07

0,1

0,2

0,5

1

10

Kt bending

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d) 0,01 0,02

0,03

0,05

0,07

0,1

0,2

0,5

1

10

Kt torsion



A112) Solid shaft with angled flank shoulder

F Fde Mt MfMtMf d

r

αααα

2traction d4.F=S.π

Sflexion = 32.Mfπ.d 3 3torsion d

16.Mt=S.π

)cosA111modèledutractionKttractionKt αααα() (=)(

)cosA111modèleduflexionKtflexionKt αααα() (=)(

)cosA111modèledutorsionKttorsionKt αααα() (=)(



A113) Solid shaft with 2 shoulders

Mf

r

F Fde Mt MfMtd

r

L

2traction d4.F=S.π


16.Mt=S.π

1. Two shoulders spaced L>2d apart:

refer to case A111 for a half round shoulder;

refer to case A112 for an angled flank shoulder.

2. Two shoulders less than L≤2d apart:

calculate an equivalent height:

deq = d +0,3.L

and replace "de" by "deq":

refer to case A111 for a half round shoulder;

refer to case A112 for an angled flank shoulder.



A121) Solid shaft with a half round bottom groove

F Fde Mt MfMtMf d

r

2traction d4.F=S.π


16.Mt=S.π

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d)0,01 0,02 0,03 0,05 0,1

0,2

0,5

1

4

10

Kt tension



d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d)0,01 0,02 0,03 0,05

1

0,1

0,2

0,5

4

10

Kt bending

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

2r/(de-d) 0,01 0,030,02

0,05

0,2

0,1

0,5

1

410

Kt torsion



A122) Solid shaft with an angled flank groove

F Fde Mt MfMtMf d

r

αααα

2traction d4.F=S.π


16.Mt=S.π

)2

cosA121modèledutractionKttractionKt

αααα() (=)(

)2

cosA121modèleduflexionKtflexionKt

αααα() (=)(

)2

cosA121modèledutorsionKttorsionKt

αααα() (=)(



A131) Solid shaft with transverse hole

F Fde Mt MfMtMf d

(hole centreline in the bending plane)

2traction de4.F=S.π 3flexion de

32.Mf=S.π 3torsion

de16.Mt=S

.π

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Kt tension



d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Kt bending

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Kt torsion



A211) Hollow shaft with half round bottom external groove

F Fde di Mt MfMtMf d

r

)di-(d4.F=S 22traction .π )di-(d

32.Mf.d=S 44flexion .π )di-(d16.Mt.d=S 44torsion .π

only valid if 2d/(de-d)>20; if 2d/(de-d)< 20 refer to case A121.

(de-d)/(d-di)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

103

1

0,5

0,2

0,1

0,3

2r/(de-d)Kt tension



(de-d)/(d-di)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

103

1

0,5

0,2

0,1

0,3

2r/(de-d)Kt bending

(de-d)/(d-di)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

1010,50,2

0,1

0,05

0,03

0,02

2r/(de-d)Kt torsion



A212) Hollow shaft with angled flank external groove


r

αααα

)di-(d4.F=S 22traction .π )di-(d

32.Mf.d=S 44flexion .π )di-(d16.Mt.d=S 44torsion .π

)2

cosA211modèledutractionKttractionKt

αααα() (=)(

)2

cosA211modèleduflexionKtflexionKt

αααα() (=)(

)2

cosA211modèledutorsionKttorsionKt

αααα() (=)(



A221) Hollow shaft with transverse hole


(hole centreline in the bending plane)

)di-(de4.F=S 22traction .π )di-(de

32.Mf.de=S 44flexion .π )di-(de16.Mt.de=S 44torsion .π

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

0 0,6 0,8 0,9 di/deKt tension



d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

0,90,6

0di/deKt bending

d/de

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

0,4 00,5

0,6

0,7

0,8

0,9

di/deKt torsion



A231) Hollow shaft with transverse groove


r

)d-(de4.F=S 22traction .π )d-(de

32.Mf.d=S 44flexion .π )d-(de16.Mt.d=S 44torsion .π

(d-di)/(de-d)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

103210,5

0,3

0,2

0,1

2r/(d-di)Kt tension



(d-di)/(de-d)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

103210,50,3

0,2

0,1

2r/(d-di)Kt bending

(d-di)/(de-d)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

1021

0,50,30,2

0,1

0,05

0,03

2r/(d-di)Kt torsion

Ch. III.3.6 KT IN NOTCHED PLATES P. 1/36


3.6 KT IN NOTCHED PLATES

The equations used to plot the following graphs are from CETIM (Ref. 13), unless otherwiseindicated and are in compliance with the results given in the PETERSON (Ref. 14) and ESDU69020 (Ref. 15).

Processed models:

B111 Plate with 1 filletB112 Plate with 1 fillet (chemical milling)B121 Plate with 2 symmetrical filletsB122 Plate with 2 symmetrical angled flank filletsB123 Plate with 2x2 symmetrical fillets

B211 Plate with 1 half round bottom notchB212 Plate with 1 notch with an angled flank half round bottomB221 Plate with 2 notches with half round bottomB222 Plate with 2 notches with angled flank half round bottom

B311 "Infinite" plate with 1 elliptical reworkB312 "Semi-infinite" plate with 1 semi-elliptical reworkB313 "Infinite" plate with 1 elliptical rework and 1 centred round hole

Remark:

in the case of nominal tension + bending loading, covered by the convention:

. Stension is the nominal reference stress used to express the Kt:Kt=Smax/Stension

Sbending is assumed to be proportional to Stension:Sbending = λ λ λ λ.Stension

by overlaying, the following is deduced:Smax=Kttension.Stension+Ktbending.(λλλλ.Stension)

or:Smax=(Kttension + λ λ λ λ.Ktbending).Stension

therefore:

Kt=(Kttension + λ λ λ λ.Ktbending)



B111) Plate with 1 fillet

FE e

rl

w : plate width

e.wF=S

Assumptions:

* These calculations were made using a 3D finite element model, taking into account:- a non-linear geometric behaviour.

e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

4210,7

0,30,2

0,5

r/e

Kt tension l/e=1



e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

4210,7

0,30,2

0,5

r/e

Kt tension l/e=5

e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

421

0,7

0,3

0,2

0,5

r/e

Kt tension l/e=10



e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

421

0,7

0,3

0,2

0,5

r/e

Kt tension l/e=20

e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

421

0,7

0,3

0,2

0,5

r/e

Kt tension l/e=40



e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

421

0,7

0,3

0,2

0,5

r/e

Kt tension l/e=60

e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

421

0,7

0,3

0,2

0,5

r/e

Kt tension l/e=80



e/E

1

2

3

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

42

10,7

0,3

0,2

0,5

r/eKt tension l/e=infinite



B112) Plate with 1 fillet (chemical milling)

FE e

rl

w : plate width

e.wF=S

Assumptions:

* The bath temperature is between 90° and 103°.

* It is difficult to define the geometrical profile of the fillet precisely. Nonetheless, it was checkedthat the radius increases when e/E decreases. The method proposed here is therefore based on alaw (IQF law) corrected as a result of tests (Ref. 6) which included:

- e between 1 and 3 mm,- e/E between 0.4 and 0.85.

* In this field, the IQF is relatively constant and equal to:

IQF=215.M

which corresponds to "Ktequivalent" of around 2.4.



B121) Plate with 2 symmetrical fillets

F FE MfMf e

r

w : plate width

e.wF=Straction .we

6.Mf=S 2flexion

e/E

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,01 0,02 0,03

0,05

0,07

0,1

0,2

0,5

1

10

2r/(E-e)Kt tension



e/E

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,01 0,02 0,030,05

0,07

0,1

0,2

0,5

1

10

2r/(E-e)Kt bending



B122) Plate with 2 symmetrical angled flank fillets

F FE MfMf e

r

αααα

w : plate width

e.wF=Straction .we

6.Mf=S 2flexion

)cosB121modèledutractionKttractionKt αααα() (=)(

)cosB121modèleduflexionKtflexionKt αααα() (=)(



B123) Plate with 2x2 symmetrical fillets

F FE MfMf e

r

l

w : plate width

e.wF=Straction .we

6.Mf=S 2flexion

1. Two shoulders spaced L>2d apart:

refer to case B121 for a half round shoulder;

refer to case B122 for an angled flank shoulder.

2. Two shoulders less than L ≤ 2d apart:

calculate an equivalent height:

Weq = d +0,3.L

and replace "W" by "Weq":

refer to case B121 for a half round shoulder;

refer to case B122 for an angled flank shoulder.



B211) Plate with 1 half round bottom notch

r

W wF F MfMf =

=

e : plate thickness

e.wF=Straction 2flexion e.w

6.Mf=S

w/W

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,02 0,03 0,05 0,07 0,1 0,2

0,3

0,5

1

3

10

r/(W-w)Kt tension



w/W

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,030,02 0,05 0,07 0,1

0,2

0,3

0,5

1

3

10

r/(W-w)Kt bending



B212) Plate with 1 notch with an angled flank half round bottom

Mf

αααα

W wF F Mf

r

e : plate thickness


6.Mf=S

)2

cosB211modèledutractionKttractionKt

αααα() (=)(

)2

cosB211modèleduflexionKtflexionKt

αααα() (=)(



B221) Plate with 2 notches with half round bottom

W wF F MfMf

r

e : plate thickness


6.Mf=S

w/W

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,02 0,03 0,05 0,07 0,1

0,2

0,3

0,5

1

3

10

2r/(W-w)Kt tension



w/W

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0,02 0,03 0,05 0,07 0,1

0,2

0,3

0,5

1

3

10

2r/(W-w)Kt bending



B222) Plate with 2 notches with angled flank half round bottom

W wF F MfMf

r

αααα

e : plate thickness


6.Mf=S

)2

cosB221modèledutractionKttractionKt

αααα() (=)(

)2

cosB221modèleduflexionKtflexionKt

αααα() (=)(



B311) "Infinite" plate with 1 elliptical rework

S Sba

q

q

ep

Section A-A

A A

The rework slope is defined by:

min(a;b)p .

Assumptions:

* These calculations were made using a 3D finite element model (Ref. 22), taking into account:- a linear geometrical behaviour (non-linear results only very slightly different);- a variable radius at the bottom of the rework:

from 0,6.a according to the axis a of the ellipse;to 0,6.b according to the axis b of the ellipse.--> use r=min(0,6.a;0,6.b) to calculate the influence scale effect E.

* Charts are provided for the 2 types of configurations:- tension loading:

creation of a tension overstress in the same direction at the bottom of the rework (thereis also a tension stress perpendicular to the previous one but it remains negligible);

- shear loading:creation of a shear overstress at the bottom of the rework.



b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%

10%15%20%25%30%

35%

40%

45%

50%

Kt tension p/e55%60%min(a;b)/p=3

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%10%15%20%25%30%

35%

40%

45%

50%




b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%10%15%20%25%30%

35%

40%

45%

50%


b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%30%

35%

40%

45%

50%




b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%10%15%20%25%

30%

35%

40%

45%

Kt shear min(a;b)/p=3 60% p/e55% 50%

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%

30%

35%

40%

45%

50%Kt shear min(a;b)/p=10 60% p/e55%



b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%

Kt shear min(a;b)/p=15 60% p/e55%

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%

Kt shear min(a;b)/p=20 60% p/e



B312) "Semi-infinite" plate with 1 semi-elliptical rework

S S

ba

e

View from the side of the rework

p


min(a;b)p .

Assumptions:


from 0,6.a according to the axis a of the ellipse;to 0,6.b according to the axis b of the ellipse.--> use r=min(0,6.a;0,6.b) to calculate the influence of scale effect E.

* Charts are provided for one type of configuration:- tension loading (parallel to the edge):

creation of a tension overstress in the same direction at the bottom of the rework (thereis also a tension stress perpendicular to the previous but remains negligible).



b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%

10%

15%

20%

25%

30%

35%

40%80%70%60%50%Kt tension min(a;b)/p=0,5p/e

45%

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%

10%

15%

20%

25%

30%

35%

40%80%70%60%50%Kt tension min(a;b)/p=1p/e

45%



b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%

5%

10%

15%

20%

25%

30%

35%

40%80%70%60%50%Kt tension min(a;b)/p=3

p/e

45%

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%

25%

30%

35%

40%

45%80% 70% 60% 50%Kt tension min(a;b)/p=10

p/e



b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%

30%

35%

40%

45%

80% 70% 60% 50%Kt tension min(a;b)/p=15 p/e

b/a

1

2

3

4

5

6

7

8

9

10

0,01 0,1 1 10 100

0%5%10%15%20%25%

30%

35%

40%

45%

80% 70% 60% 50%Kt tension min(a;b)/p=20p/e



B313) "Infinite" plate with 1 elliptical rework and 1 centred round hole

ba

q

q

ep

Section A-A

A A

S1 S1

S2=λλλλ .S1

S2=λλλλ .S1

d


min(a - d / 2; b - d / 2)p .

Assumptions:


from 0,8.(a-d/2) according to the axis a of the ellipse;to 0,8.(b-d/2) according to the axis b of the ellipse.--> use r=d/2 to calculate the influence of scale effect E;--> calculate IQF as for an assembly (C=630 in particular) if a fastener is installed into

the hole (without transferred load).

* Charts are provided for the 2 types of configurations:- biaxial loading with different λ values:

creation of a tension overstress at the bottom of the rework, tangent to the hole;- shear loading:

creation of a tension overstress at the bottom of the rework, tangent to the hole.



(b-d/2)/(a-d/2)

4

5

6

7

8

9

10

0,1 1 10

0%5%10%15%20%25%30%35%

40%

45%

50%

55%

60%

Ktp/e

min(a-d/2; b-d/2)/p=3

λ=−1λ=−1λ=−1λ=−1 (q=0)Biaxial tension with:

(b-d/2)/(a-d/2)

4

5

6

7

8

9

10

0,1 1 10

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%

60%

Ktp/e

min(a-d/2; b-d/2)/p=10




(b-d/2)/(a-d/2)

4

5

6

7

8

9

10

0,1 1 10

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%

60%Kt

p/e

min(a-d/2; b-d/2)/p=15


(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%25%30%35%40%

45%50%

55%60%

Ktp/e

min(a-d/2; b-d/2)/p=3

λ=−0,5λ=−0,5λ=−0,5λ=−0,5 (q=0)Biaxial tension with:



(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%25%30%

35%

40%

45%

50%

55%

60%Ktp/e

min(a-d/2; b-d/2)/p=10

λ=−0,5λ=−0,5λ=−0,5λ=−0,5 (q=0)Biaxial tension with:

(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%Ktp/e

min(a-d/2; b-d/2)/p=15

λ=−0,5λ=−0,5λ=−0,5λ=−0,5 (q=0)Biaxial tension with: 60%



(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%25%30%35%40%45%50%55%60%

Ktp/e

min(a-d/2; b-d/2)/p=3

λ=0λ=0λ=0λ=0 (q=0)Uniaxial tension with:

(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%25%

30%

35%

40%

45%

50%

55%

60%

Ktp/e

min(a-d/2; b-d/2)/p=10




(b-d/2)/(a-d/2)

3

4

5

6

7

8

9

0,1 1 10

0%5%10%15%20%

25%

30%

35%

40%

45%

50%

55%

60%Kt

p/e

min(a-d/2; b-d/2)/p=15


(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%35%40%45%50%55%60%

Ktp/e

min(a-d/2; b-d/2)/p=3

λ=0,5λ=0,5λ=0,5λ=0,5 (q=0)Biaxial tension with:



(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%

35%

40%

45%

50%

55%

60%Kt

p/emin(a-d/2; b-d/2)/p=10

λ=0,5λ=0,5λ=0,5λ=0,5 (q=0)Biaxial tension with:

(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%

5%10%15%20%25%

30%

35%

40%

45%

50%

55%Ktp/e

min(a-d/2; b-d/2)/p=15

λ=0,5λ=0,5λ=0,5λ=0,5 (q=0)Biaxial tension with: 60%



(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%35%40%45%50%55%60%

Ktp/e

min(a-d/2; b-d/2)/p=3

λ=1λ=1λ=1λ=1 (q=0)Biaxial tension with:

(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%

35%

40%

45%

50%

55%

60%

Ktp/e

min(a-d/2; b-d/2)/p=10

λ=1λ=1λ=1λ=1 (q=0)Biaxial tension with:



(b-d/2)/(a-d/2)

2

3

4

5

6

7

8

0,1 1 10

0%

5%10%15%20%25%30%

35%

40%

45%

50%

55%

Ktp/e

min(a-d/2; b-d/2)/p=15

λ=1λ=1λ=1λ=1 (q=0)Biaxial tension with: 60%

(b-d/2)/(a-d/2)

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%35%40%45%50%55%

Ktp/e

min(a-d/2; b-d/2)/p=3

(S1=S2=0)Pure shear q:

60%



(b-d/2)/(a-d/2)

4

5

6

7

8

0,1 1 10

0%5%10%15%20%25%30%35%

40%

45%

50%

55%

Ktp/e

min(a-d/2; b-d/2)/p=10

(S1=S2=0)Pure shear q:

60%

(b-d/2)/(a-d/2)

4

5

6

7

8

0,1 1 10

0%

5%10%15%20%25%30%35%

40%

45%

50%

55%

Ktp/e

min(a-d/2; b-d/2)/p=15

(S1=S2=0)Pure shear: 60%

Ch. III.3.7 KT IN DRILLED PLATES P. 1/19


3.7 KT IN DRILLED PLATES

The equations used to plot the following graphs are from ESDU 67023/75007/80027 (Ref. 15) andROARK (Ref. 16).

Processed models:

C111 "Infinite" plate with 1 round holeC112 "Infinite" plate with n round holesC113 "Infinite" plate with 2 different round holesC121 "Finite" plate with 1 round hole

C211 "Infinite" plate with 1 elliptical holeC221 "Finite" plate with 1 elliptical hole

C311 "Infinite" plate with 1 rectangular hole

Remark:

in the case of a biaxial nominal load (S1;S2), by convention:

. S1 is the maximum nominal stress; it is used as a reference to express Kt, except when itis nil:

Kt=Smax/S1. S2 is assumed to be proportional to S1 when it is not nil:

S2=λλλλ.S1therefore with λ≤ λ≤ λ≤ λ≤1

in the case of nominal shear loading q, and when S1 is not nil:

. q is used as the reference to express the Kt:Kt=Smax/q

. q is assumed to be proportional to S1:S1=λλλλ'.q



C111) "Infinite" plate with 1 round hole

S1 S1

S2=λλλλ.S1

d

AB

S2=λλλλ .S1

AB

Kt= SA

S1= (3 - λλλλ ) for information:

SB

S1= (3.λ -1)

λλλλ

1

2

3

4

5

6

-1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1

Kt



C112) "Infinite" plate with n round holes

S1 S1

w

S2=λλλλ .S1

S2=λλλλ .S1

A

B

Ad

A A

d/w

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

-1

-0,5

0

0,5

1

____ Kt (2 holes)

_ _ _ Kt (infinity of holes)

Kt

λλλλ



S1 S1

S2=λλλλ .S1

S2=λλλλ .S1

wB

d

A

A

d/w

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

____ Kt (2 holes)

_ _ _ Kt (infinity of holes)

-0,5

0

0,5

1

-1

Kt

λλλλ



w

A

B

A

d

q

q

d/w

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Kt (in relation to q)

____ Kt (2 holes)



C113) "Infinite" plate with 2 different round holes

S1 S1

D

d

αααα

S2=λλλλ .S1

S2=λλλλ.S1

q

q

w

d/(2w-D)

0

0,5

1

1,5

2

2,5

3

3,5

4

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ____ Kt (small hole)

D/d

1,52,5

1,251

2,5

1,5

_ _ _ Kt (large hole)

3

10

5

Uniaxial tension S1 (S2=0;q=0)αααα = 0°Kt



d/(2w-D)

2

3

4

5

6

7

8

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ____ Kt (small hole)

D/d

1,252,5 1,25

1

5

2,5


10

105

Uniaxial tension S2 (S1=0;q=0)αααα = 0°Kt (in relation to S2)

d/(2w-D)

3

3,5

4

4,5

5

5,5

6

6,5

7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ____ Kt (small hole)

D/d

2,51,5

1

2


2,5

105

Pure shear q (S1=S2=0)

1,5

10

= 0°ααααKt (in relation to q)



d/(2w-D)

2

3

4

5

6

7

8

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ____ Kt (small hole)

D/d

2,5

1

4,5


2,5

105

Uniaxial tension S1 (S2=0;q=0)

2,5

5

= 45°αααα

5

10Kt

d/(2w-D)

3

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ____ Kt (small hole)

D/d

1


2,5

10

Pure shear q (S1=S2=0)2,5

5

= 45°αααα510Kt (in relation to q)



C121) "Finite" plate with 1 round hole

w F F

b

d MfMf


6.Mf=S

d/(2.b)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

0,5 0,35 0,10,20

b/w

Kt tension



d/(2.b)

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

b/w

0,5

0,35

0,10

0,2

Kt bending



C211) "Infinite" plate with 1 elliptical hole

S1 S1b

a

q

q

A

B

S2=λλλλ.S1

S2=λλλλ.S1

Biaxial tension (q=0)

S1)S;max(S=Kt BA

with: SA = S1. 1+ 2. b

a- λλλλ

and:

SB = S1. λλλλ.... 1+ 2.a

b

-1

λλλλ

0

2

4

6

8

10

-1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1

a/b0,25

0,33

0,4

0,5

Kt

12

2,5

3

4



Uniaxial tension S1 (S2=0) + shear q

λλλλ

0

5

10

15

20

25

30

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

'=S1/q

Kt 0,25 0,3

0,4

4

0,520,751,51

a/b

General case: biaxial loading (S1;S2) + shear q

the result is drawn up from the following overlaying:

1st case: biaxial tension (a/b.S2; S2); in this case, the maximum stress is uniform allaround the hole and equal to:

Smax1 = (1+a/b).S2

2nd case: uniaxial tension (S1-a/b.S2; 0) + shear q; the maximum stress indicated Smax2 isdefined using the product of the stress concentration coefficient (from the chart above) andfrom q;

Kt is deduced by:

qSmax2+Smax1=Kt



C221) "Finite" plate with 1 elliptical hole

wF F

b

MfMf

cd


6.Mf=S

2c/w

0

5

10

15

20

25

30

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

c/d10

5

2

10,5

Kt tension

3

6

8b/w = 0,5



2c/w

0

5

10

15

20

25

30

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

c/d10

5

2

10,5

Kt tension

3

6

8

b/w = 0,35

2c/w

0

5

10

15

20

25

30

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

c/d

10

5

210,5

Kt tension

3

6

8

b/w = 0,2



2c/w

0

5

10

15

20

25

30

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

c/d

10

5

210,5

Kt tension

3

6

8

b/w = 0,1

2c/w

0

5

10

15

20

25

30

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

c/d

10

5

210,5

Kt tension

3

6

8

b/w = 0

During bending, only for b/w=0.5:



2b/w

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

1

2

c/d

Kt bending

Other possible application:

Kt may be relatively well approximated for other geometrical notches, length 2c and radiusr, using an equivalent ellipse with:

r.c=d

r

2c



C311) "Infinite" plate with 1 rectangular hole

S1 S1b

ar

q

q

S2=λλλλ.S1

S2=λλλλ.S1

a/b

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6

Uniaxial tension (S2=0;q=0)

r/b

0,1

0,05

0,2

0,30,40,60,81

- - - a = r

Kt



a/b

1

2

3

4

5

6

7

8

9

10

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Equal biaxial tension (S2=S1;q=0)r/b

0,1

0,05

0,15

0,2

0,40,3

0,5

- - - a = r

Kt

a/b

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6

Unequal biaxial tension (S2=S1/2;q=0)r/b

0,1

0,05

0,2

0,3

0,60,4

0,8 - - - a = r 1

Kt



a/b

3

5

7

9

11

13

15

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Pure shear (S2=S1=0)r/b

0,1

0,05

0,15

0,2

0,5

0,3

- - - a = r

Kt (in relation to q)

Ch. III.3.9 KT IN BOLTED AND RIVETED ASSEMBLIES P. 1/44


3.8 KT IN YOKES

A

A

wF

F

w/2A

A



F

w/2A

A

e.wF=S

(e : thickness)

The Kt at points marked A is determined using the general formula below:

.GKt=Kt ETglobal

. KtET: Kt due to the transferred load (calculated in 2D);

. G: correction coefficient of KtET (calculated in 3D) to take into account:

- the deformation of the fastener and therefore of the bore;- possible bending due to the flanges of the yoke.



KtET (square yoke)

wFd

h

Ω

Assumptions:

* These calculations were made using a 2D finite element model (Ref. 17), considering:- zero clearance (bore/fastener);- negligible effect of the Young's modulus of the metallic materials used.

* If the ratio R of loading is negative, take into account:

R=0.

* The charts are given for Ω included between 0° and 90°.If Ω is always greater than 90°, plot F as shown on the figure below and only take into accountcomponent F1 (at 90°) knowing that component F2 is in pure compression:

F F1

F2



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3 0,35

0,4

0,5

0,45

0,550,7

h/wΩΩΩΩ = 0°

d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,5

0,45

0,55

0,7

h/wΩΩΩΩ = 30°



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45

0,5 0,55

0,7

h/wΩΩΩΩ = 60°

d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5 0,55

0,7

h/wΩΩΩΩ = 90°



KtET (rounded yoke)

F

d

h

ββββΩΩΩΩ

w/2

Assumptions:

* These calculations were made using a 2D finite element model (Ref. 17) considering:- zero clearance (bore/fastener);- negligible effect of the Young's modulus of the metallic materials used.

* If the ratio R of loading is negative, consider that:

R=0.



* The graphs are given for Ω between 0° and 90°.If Ω is always greater than 90°, plot F as indicated on the figure below and only take into accountthe component F1 (at 90°) knowing that component F2 is in pure compression.

F F1

F2



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,35

0,4

0,3

0,45

0,5 0,55

0,7

h/wΩΩΩΩ = 0°ββββ = 0°

d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,450,50,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,450,5

0,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45

0,5 0,55

0,7h/w

ΩΩΩΩ = 90°ββββ = 0°



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,35

0,4

0,3

0,450,5

0,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4 0,45 0,5 0,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,40,450,50,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45 0,5

0,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45 0,5

0,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4 0,45 0,50,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45 0,50,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45 0,5

0,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7

h/w


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,40,45 0,5

0,55

0,7




d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,450,5

0,55

0,7


d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,450,5

0,55

0,7

h/w




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4 0,45 0,5

0,55

0,7




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,450,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45

0,5

0,55

0,7




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,40,45

0,5

0,55

0,7




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45

0,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,40,45

0,5

0,55

0,7

h/w




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3

0,35

0,4

0,45

0,5

0,55

0,7




d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7


d/w

3

4

5

6

7

8

9

10

11

12

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4 0,45

0,5

0,55

0,7




d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,40,45

0,5

0,55

0,7

h/w


d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,40,45

0,5

0,55

0,7

h/w

ΩΩΩΩ = 30°ββββ = 105°



d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,40,45

0,5

0,55

0,7


d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4

0,45

0,5

0,55

0,7




d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35

0,4 0,45

0,5

0,55

0,7


d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3 0,35 0,40,45

0,5

0,55

0,7




d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,30,35 0,4 0,45

0,5

0,55

0,7


d/w

2

3

4

5

6

7

8

9

10

11

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt

0,3 0,35

0,4

0,45

0,50,550,7




KtET (eye-end yoke)

Fd

w/2

r

b

Assumptions:

* These calculations were carried out using the 2D finite element model (Ref. 17) considering:- zero clearance (bore/fastener);- negligible effect of the Young's modulus of the metallic materials used.

* If the ratio R of loading is negative, consider that:

R=0.

* The graphs are only given for a tension load as this type of yoke is only used with rods.

* In the following graphs, b is assumed to be known. Consequently, r is deduced as being equal to:

a)-(w4

)a-(w-br

222

=



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt0,7

0,4

0,510,6 0,8

0,9 a/wb/w=0,5

d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt 0,7

0,5 10,6

0,80,9 a/wb/w=1



d/w

4

5

6

7

8

9

10

11

12

13

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Kt 0,7

0,5 10,6

0,80,9 a/wb/w=1,5



G coefficient

Assumptions:

* These calculations were made using a 3D finite element model (ref. 17), considering:- zero clearance (bore/fastener);- negligible effect from shape and direction of the load.

* Graphs are given for two types of configuration:- yokes with symmetrical double shear (male and female parts studied);- yokes with single shear which is an infrequent configuration as it is more detrimental in

fatigue than the previous configuration.



Yoke with symmetrical double shear (male part):

F/2

F e'

e

e F/2

d

The maximum stress is at the interface of the studied plate, thickness e (quantified by G).

e'/d

1

2

3

0 0,5 1 1,5 2 2,5 3

G

3

1

2,5

1,5

0,5

3,5

Ef/Ep

2

Notation:

- Ef: Young's modulus of the fastener;- Ep: Young's modulus of the plate.



Yoke with symmetrical double shear (female parts):

F/2

F e'

e

e F/2

d

The maximum stress is at the interface of the 2 studied plates, thickness e (quantified by G).

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=0,521,510,50,25

Notation:- Ef: Young's modulus of the fastener;- Ep: Young's modulus of the plate.



e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=1

21,510,50,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=1,5

21,510,50,25



e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=2

21,510,50,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=2,5

21,510,50,25



e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=3

21,510,50,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=3,5

21,5

10,50,25



Yoke with single shear:

F

e

e'

d

F

The maximum stress is at the lower part (interface) of the studied plate, thickness e (quantified byG).

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=0,5

210,25




e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=1

210,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=1,5

210,25



e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=2

210,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=2,5

210,25



e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=3

210,25

e/d

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3

G e'/eEf/Ep=3,5

210,25



3.9 KT IN BOLTED AND RIVETED ASSEMBLIES

Schematic examples of the configuration:(the studied plate is shaded)

Assemblies of 2 plates under tension

F

F

F

F

Study of a line of fasteners

ee'

ee'

"Total" load transfert

"Partial" load transfert

Generally, the critical fatigue line in the studied plate corresponds to the first load transfer line,except possibly for:

- variable thickness plates;- when fasteners or assembly methods of different types are used in the assembly.



Assemblies of 3 plates under tension

F

F1

ee2

e1

F2

F1

F

e1e2

e

F2

F

F

e e2

e1


"Total" load transfert

"Partial" load transfert

Same remarks as previously concerning the most critical locations.




f S.e.w

Definition of the transfert rate αper fastener:S B

dAb

w

f

The Kt at points A (close to an edge) and B (between bores) is determined using the followinggeneral formula:

FETEPglobal K.Kt+.G.Kt).Kt-(1=Kt αααααααα +

. (1-αααα): load rate not transferred by the fastener;

. KtEP: Kt due to the non-transferred load (calculated in 2D);

. αααα: load rate transferred by the fastener;

. KtET: Kt due to the transferred load (calculated in 2D);

. G: correction coefficient of KtET to take deformation of the fastener and

consequently of the bore (calculated in 3D) into account;

.K: ratio between the bending stress Sf at the studied line and the referencestress S;

. KtF: Kt in bending mode (calculated in 3D).

This overlaying of the various mechanical effects is illustrated on the following page by a explodedview on a given bore:



Smax = ((1- αααα).KtEP + αααα.KtET.G + KtF.SF).S

(1-αααα).S

αααα.S

Smax (ET) = αααα.KtET.G.S

Smax (EP) = (1-αααα).KtEP.S

S+SF

+

=

SF

Smax (F) = KtF.SF

+

Smax = Smax(EP) + Smax (ET) + Smax (F)

S



KtEP _ KtET

S B

dAb

f

S B

dAb

w

S

KtEP KtET

w

Assumptions:

* These calculations were made using a 2D finite element model, considering:- zero clearance (bore/fastener);- zero clamping of the fastener;- negligible effect of the Young's modulus of the metallic materials used;- negligible effect of the longitudinal pitch l (interline distance) for l/w greater than 0,7;- negligible effect from staggering q (distance of staggering between bores) for q/w less than

1.

* Calculate with:- d/w is b is greater than w/2;- d/(w/2+b) is b is less than w/2.



d/w

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

10,00

0,1 0,2 0,3 0,4 0,5 0,6

Kt EP (A)

Kt EP (B)

Kt ET (A)

Kt ET (B)

Kt

Remarks:

- with an oversizing (increased from d to d'), consider that d'/w instead of d/w with areassessment of the transfer rate for the studied bore;

- with oversizing and fitting of an intermediate bush with an external diameter d (same fastener),take into account d'/w instead of d/w.



KtF

e

wd

Sf Sf

Assumptions:

These calculations were made using a 3D (simplified) finite element model (Ref.17) considering:- Sf as the average bending stress at the fastener (see paragraph below: "simplified analysis

of an assembly") related to the overall cross-section:

.we6.MfSf

2=

Mf being the average bending moment at the fastener.



e/d

1

2

3

4

0 0,5 1 1,5 2 2,5

Kt

0,1

0,4

0,5

d/w

0,30,250,2

0,45

0,35

0,550,6



G coefficient

Assumptions:

* These assumptions were made using a 3D finite element model (Ref. 17), considering:- zero clearance (bore/fastener);- zero clamping of the fastener;- negligible effect of d/w.

* Graphs are provided for 4 types of configurations:- 2-plate assembly;- 3-plate assembly (external and internal parts studied);- assembly with more than 3 plates (external and internal parts studied) being an extrapolation

of the previous case.



2-plate assembly:

F

F e

e'

d

The maximum stress is at the top part (interface) of the studied plate, thickness e (quantified by G).


e/d

1

2

3

4

0 0,5 1 1,5 2 2,5 3

G

3

12,5

1,50,5

3,5

Ef/Ep 2



3-plate assembly (external part):

1st possibility: F1/F2 considered positive

F

F1 e1

e

e2F2

d

The maximum stress is on the lower part (interface) of the studied plate, thickness e (quantified byG).

2nd possibility: F1/F2 considered as negative

F

F1 e1

e

e2 F2

d

The maximum stress is on the lower part (interface) of the studied plate, thickness e (quantified byG).




F1/F2=-4

FF1

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,25

3

1



F1/F2=-2

FF1

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,25

3

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5 1,25

3

1



F1/F2=-1,6

FF1

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,25

3

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,51,25

3

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2

1,5

4 e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,25

3

1



F1/F2=-1,3

FF1

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,51,25

3

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

21,5

4 e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,25

3

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2

1,5

4 e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,25

3

1



F1/F2=-1,2

FF1

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G 2 1,54 e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,25

3

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G 2

1,5

4 e1/d

0,4

0,80,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,25

3

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2

1,5

4 e1/d

0,4

0,80,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,25

3

1



F1/F2=-0,8

FF1 F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8 0,62,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

3 1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G 2 1,54 e1/d

0,4

0,8 0,62,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

3 1

0,25

0,15

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8 0,62,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

3 1



F1/F2=-0,7

FF1 F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8 0,62,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253 1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8 0,62,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253 1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,253 1



F1/F2=-0,4

F

F1 F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253 1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253 1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,253 1



F1/F2=0

F

F2

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253 1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253 1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,2531



F1/F2=0,5

F

F2F1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253 1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,2531

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,253

1



F1/F2=2

F

F2F1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,2531



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,253

1



F1/F2=+(-)infinite

FF1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=0,5

- - Ef/Ep=1,5

1,253

1



e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=1,5

- - Ef/Ep=2,5

1,253

1

e/e1

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4

G

0,25

2 1,54

0,15

e1/d

0,4

0,8

0,6

2,5

___ Ef/Ep=2,5

- - Ef/Ep=3,5

1,253

1



3-plate assembly (internal part):

1st possibility: F1/F2 considered positive

F1

F e

e1

e2 F2

d

If F1>F2:- the maximum stress is on the top part of the studied plate, thickness e (quantified by Gmax),- the minimum stress on the lower part (quantified by Gmin).

If F1<F2, the opposite occurs.



2nd possibility: F1/F2 considered negative

F1

F e

e1

e2F2

d

In this case:- the maximum stress is on the top part of the studied plate, thickness e (quantified by Gmax),- the minimum stress on the lower part (quantified by Gmin).




e/d

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmax -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4

___ Ef/Ep=0,5

- - - Ef/Ep=1,5

0,5/2

e/d

0

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmin -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4___ Ef/Ep=0,5

- - - Ef/Ep=1,5

0,5/2



e/d

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmax -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4

___ Ef/Ep=1,5

- - - Ef/Ep=2,5

0,5/2

e/d

0

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmin -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4___ Ef/Ep=1,5

- - - Ef/Ep=2,5

0,5/2



e/d

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmax -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4

___ Ef/Ep=2,5

- - - Ef/Ep=3,5

0,5/2

e/d

0

1

2

3

4

5

6

7

8

9

10

0 0,5 1 1,5 2

Gmin -0,8/-1,25

0/±

-0,75/-1,33-0,9/-1,1

1

F1/F2

-0,25/-4

-0,5/-2

-0,6/-1,66

-0,66/-1,5

-0,71/-1,4___ Ef/Ep=2,5

- - - Ef/Ep=3,5

0,5/2



Assembly of more than 3 plates (external part):

G is equal to that of 3 plates, considering:- as the 2nd plate, the plate directly in contact with e1 and F1 as influencing parameters;- as the 3rd plate, the equivalent plate built using plates e2 to en, with F2+ ...+Fn (algebraic

sum) as the influencing parameter.

F

F1 e1e

e2F2

d

enFn

F

F1 e1

e

e2+...+enF2+...+Fn

d

équivalent to



Assembly of more than 3 plates (external part):

G is equal to that of the 3 plates, considering:- as the first plate, the equivalent plate built using plates e1 to ei, with F2+...+Fn (algebraic

sum) as the influencing parameter;- as the 3rd plate, the equivalent plate built using plates e(i+1) to en, with F(i+1)+...+Fn

(algebraic sum) as the influencing parameter.

F

F1 e1

e

d

enFn

F

F1+...+Fi e1+...+ei

e(i+1)+...+enF(i+1)+...+Fn

d

e

équivalent to



Simplified mechanical analysis of an assembly(Ref. 18 & 19)

To apply the previous principle, it is necessary to develop a simplified 3D model capable of takinginto account the global mechanical effects, i.e.:

. the distribution of load flows, especially the part of the load transferred at each fastener (αααα);

. general bending due to possible displacement of the neutral fibre, more especially at eachfastener (K).

Therefore, these models must be capable of:- estimating the load transferred at each fastener and also the bending at this fastener;- not integrating local effects due to fasteners as such effects are taken into account in the

stress concentration coefficients (Kt).

--> The first point above means that this global model must replace both:- the "spring" model (plates and attachments modelled by springs operating in direction of load)

often used to estimate only the transferred loads; nonetheless, it is sufficient when thegeneral bending is negligible (e.g.: symmetrical double shear joint, joints stiffened againstbending with solid parts, etc.);

Example

- the "beam" model (assembly modelled as a single beam) which is often used to estimate onlygeneral bending (e.g.: formulas proposed by Schijve for single shear assemblies).

Example



The following problem can be solved:

- in the case of an assembly that can be simply represented by an interfastener pitch:. by modelling plates and fasteners by beams;. by introducing interplate contact conditions (between facing nodes).

Example

Node

- in the case of a more complex assembly:. by modelling the plates using thin shells and fasteners by beams;. by introducing interplate contact conditions (between facing nodes).

Example

--> The second point may be observed by simply modelling the fasteners with beams, incorporatingcharacteristics adapted to provide a good relative displacement of plates. To this end, anequivalent reduced section (shear) Sr may be used, calculated using flexibility C (refer to themethod in Appendix 3).

The latter-mentioned were assessed using a 3D F.E. model representing 2 plates. They aresimilar to the Douglas and Boeing formulas indicated in reference documents.

Also, they were calculated on a 3-plate F.E. model which provided very similar results.Consequently, the results defined using the former can be extrapolated to any stack-up.

A1 APPENDIX 1 P. 1/1


APPENDIX 1Substantiation

of the general mathematical model

A1.1 DEMONSTRATION BY AN ELASTIC-PLASTIC APPROACH P. 1/6


A1.1 Demonstration by an elastic-plastic approach

A1.1.1 Advantages offered by this approach

Historically, two types of approach have been used to forecast fatigue crack initiation metallicstructures.

The first and most widely used approach is based upon "imposed stress" tests using testspecimens (different Kt) subjected only to local plasticity and therefore concerns a life range

covering approximately 103 cycles up to the fatigue limit, around 107 cycles. The Fatigue Manual iswithin this framework.

The other approach, generally used for parts subjected to high plasticity (elastic-plastic approach)is based on an "imposed deformation" test on a smooth test specimen (Kt=1) and therefore

concerns a life range covering 1 to 106 cycles approximately.

Nonetheless, this second approach makes it possible to explicate the first. To this end, the followingstatement is sufficient:

in a notched part subjected to cyclic loading, as long as the structure globally reacts in elasticmode, the plastic area confined to the bottom of the notch works under imposed deformation(not stress) as illustrated on the following figure:



Elastic area

Plastic area

σσσσεεεε

S

σ

ε

σσσσmax

"Imposed" deformation

field

Smax

Sminεεεεmaxεεεεmin

σσσσmin

note the following evolution of the maximum stress as a function of time:

σ

N

Stabilisation (major part of the life)

Accomodation Cracking



It is possible, when performing the basic imposed deformation test at Rε=-1, at each deformation

level, to determine the characteristic stabilised stress of the major portion of the life of the testspecimen;

like this, a graph, called "cyclic tension" comparable to that of the "monotonic tension", is obtained,which is often modelled by the "Ransberg-Osgood" formula, formulated as follows:

n'K'E σ+σ=ε .

σ

ε

Example of stabilised loop

"Monotonic" tension curve

"Cyclic" tension curve

with regards to the life curve, the formula frequently used to represent the results at Rε=-1 is the

"Manson-Coffin" curve:

cf

'bf'

a.(2.N).(2.N)E ε+σ=ε

which is schematically represented by:



log εa

log N

εεεεe=

εεεεp=

εεεεa

σ

'f

E .(2.N)b

ε'f .(2.N)c

in order to integrate any ratio Rε, the general "Smith-Topper-Watson" seems more appropriate:

c)+(bf

'f

'2.bf'

maxa.(2.N)..(2.N)E σε+σ=σε

2

.

A1.1.2 Consequence of the “elastic-plastic” approach

For a notched part, subjected to uniaxial monotonic loading, the "Neuber" energy criterion may beapplied:

E.SKt max

22

maxe

maxe

maxmax=.εσ=.εσ

E.SKt a

22

ae

ae

aa=.εσ=.εσ

In the long life domain (greater than 103 cycles), the Smith-Topper-Watson formula mayapproximately be reduced to:

2.bf'

maxa.(2.N)E

2

. σ≈σε

using the second Neuber formula, the following can be formulated as:

2.bf'

a

maxa22

.(2.N)EE.SKt 2

. σ≈σ

σ

knowing that:

S

a=

(1 −R)2

.Smax



and that for relatively low plasticity:

σmax

σa

≈S

max

Sa

=2

(1−R)

the following is deduced:

1/b-

max

0,5

0,5)+(b

.SR)-(1

Ktf'2

N

σ

≈

.

therefore the general form:

p

f(R).SKtC

Nmax

≈

where:

C (and possibly p) characterises the effect of the material, the surface condition (related topossible heat, mechanical or chemical treatment) as well as the influence of scale (staticeffect related to the size of the critical area concerned by crack initiation);Kt characterises the significance of local stress related to the geometrical notch effect;f(R).Smax that from monotonic cyclic loading.



A1.1.3 Consequence on the “Fatigue Manual “approach

The previous formulation, even though approximate, enables us to better understand themathematical model proposed in this manual.

In addition to the form of the equation, we can also deduce that the life can reasonably beexpressed as a function of two independent parameters:

- a parameter intrinsic to the part through the expression C/Kt;- a parameter external to the part through the expression f(R).Smax for which a (1-R)q.Smax

form seems more appropriate with q close to 0.5;this is also confirmed by MIL-HDBK-5F, which models all life curves (on aluminium, titaniumand nickel alloys as well as steels) using a function of a similar type.

A1.2 EXAMPLES OF USE P. 1/2


A1.2 Examples of use

Two correlations between calculations/tests under monotonic loading are presented as examples:- the theoretical structure shown by curves;- the experimental structure shown by dots.

2024 T3511 EXTRUDED / KT=3,3

Number of cycles

0

50

100

150

200

250

300

350

400

450

500

1E+03 1E+04 1E+05 1E+06 1E+07 1E+08

-10

-6

-3

-1

0,1

0,4

0,7

R=-1

R=0,1

R=0,7

IQF=155Smax

A1.2 EXAMPLES OF USE P. 2/2


7010 T6511 EXTRUDED / KT=2,3

0

100

200

300

400

500

600

1E+03 1E+04 1E+05 1E+06 1E+07 1E+08

-10

-6

-3

-1

0,1

0,4

0,7

R=-6

R=-3

R=-1

R=0,1

R=0,7

IQF=210Smax

Number of cycles



APPENDIX 2Substantiation

of the general IQF law

A2.1 LAW ON NOTCHES P. 1/5


A2.1 Law on notches

On the following graphs, the experimental results are collected from:- MIL-HDK (Ref. 20) --> black dots on the graphs;- Aerospatiale data bank (Ref. 21) (only for the larger samples, statistically more suitable for

processing) --> white dots on the graphs;

are presented in the following form:

f(Kt).T3.T4.T5)M.E.(T1.T2

IQF =

(T1.T2.T3.T4.T5 equal to 1 generally,and 1.1 for certain polished test specimens)

using the coefficients presented in the table in Chapter III.3.

Statistically (the least squares method), the average law is formulated as:

Kt510

M.EIQF =

it is represented by a continuous line on the graphs with a scatter of about:

± 10% (dotted lines on the graphs).



0

100

200

300

400

500

600

1 2 3 4 5 6 7

2014 T6XX

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

2618 TXXX

Kt

IQF/(E.M)



0

100

200

300

400

500

600

1 2 3 4 5 6 7

7XXX T6XX / T7XXX

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

T40

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

TU2

Kt

IQF/(E.M)



0

100

200

300

400

500

600

1 2 3 4 5 6 7

TA6V

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

INCONEL 625

Kt

IQF/(E.M)

0

100

200

300

400

500

600

1 2 3 4 5 6 7

INCONEL 718

Kt

IQF/(E.M)



0

100

200

300

400

500

600

1 2 3 4 5 6 7

High strength steels

Kt

IQF/(E.M)

A2.2 LAW ON YOKES P. 1/3


A2.2 Law on yokes

The experimental results collected using the AS data bank are given on the following graphs andare presented in the following form:


IQF =

(T1.T2.T3.T4.T5 will be called T to simplify)

using the coefficients presented in the tables in Chapter III.3.

Statistically (least squares method), the average law is formulated as:

Kt430

M.E.TIQF =

it is represented by a continuous line on the graphs, with a scatter of approximately:




0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Clearance • Cold workingo Forcemate

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)

- Clearance

0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

- Clearance • Cold working

o Forcemate



0

100

200

300

3 4 5 6 7 8 9 10

TA6V

Kt

IQF/(E.M.T)

- Clearanceo Forcemate

0

100

200

300

3 4 5 6 7 8 9 10


Kt

IQF/(E.M.T)

- Clearanceo Forcemate

A2.3 LAW ON BOLTED AND RIVETED ASSEMBLIES P. 1/10


A2.3 Law on bolted and riveted assemblies

Experimental results collected from the AS data bank on the following graphs are presented in theform:


IQF =

(T1.T2.T3.T4.T5 called T to simplify)

using the coefficients presented in Chapter III.3.

Statistically (least squares method), the average law is formulated as:

Kt630

M.E.TIQF =

t is represented by a continuous line on the graphs with an approximate scatter of about:




0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Clearance

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)

- Clearance

0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

- Clearance



0

100

200

300

3 4 5 6 7 8 9 10

Ta6V

Kt

IQF/(E.M.T)

- Clearance

0

100

200

300

3 4 5 6 7 8 9 10


Kt

IQF/(E.M.T)

- Clearance



0

100

200

300

3 4 5 6 7 8 9 10

2214 T6XX

Kt

IQF/(E.M.T)

- Interference

0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Interference

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)

- Interference



0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

- Interference



0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

o Cold working

- Cold working + Int.

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)


0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

o Cold working




0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Alu. riveto "Slug" rivet

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)

- Alu. riveto "Slug" rivet

0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

- Alu. rivet



0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Titanium riveto Monel rivet

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)


0

100

200

300

3 4 5 6 7 8 9 10

7XXX T6XX / T7XX

Kt

IQF/(E.M.T)

- Titanium rivet



0

100

200

300

3 4 5 6 7 8 9 10

T40

Kt

IQF/(E.M.T)

- Titanium rivet

0

100

200

300

3 4 5 6 7 8 9 10

TU2

Kt

IQF/(E.M.T)

- Titanium rivet

0

100

200

300

3 4 5 6 7 8 9 10

TA6V

Kt

IQF/(E.M.T)




0

100

200

300

3 4 5 6 7 8 9 10

2024 T3XX / 2091 T8XX

Kt

IQF/(E.M.T)

- Blind rivet

0

100

200

300

3 4 5 6 7 8 9 10

2618 T6XX / T8XX

Kt

IQF/(E.M.T)

- Blind rivet



APPENDIX 3Simplified modelling of a fastener

A3.1 DETERMINATION OF FLEXIBILITY P. 1/4


A3.1 Determination of flexibility

Flexibility C (in mm/N) of a fastener, diameter d, between 2 plates, thickness e and e' is deducedfrom the following formula:

Ep

74000d

4,8.C=C MPa 74000=Epmm; 4,8=d .

e

e'

d

Cd=4,8 mm; Ep=74000 MPa (en mm/N ) is given in the following graphs:

e/d

1,9

2,1

2,3

2,5

2,7

2,9

3,1

3,3

3,5

3,7

3,9

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=0,5

1

1,2

1,6

d=4,8 mm

Ep=74000 Mpa



e/d

1,8

2

2,2

2,4

2,6

2,8

3

3,2

3,4

3,6

3,8

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=1

1

1,2

1,6

Ep=74000 MPa

d=4,8 mm

e/d

1,6

1,8

2

2,2

2,4

2,6

2,8

3

3,2

3,4

3,6

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=1,5

1

1,2

1,6

d=4,8 mm

Ep=74000 MPa



e/d

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

3,2

3,4

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=2

1

1,2

1,6

d=4,8 mm

Ep=74000 MPa

e/d

1,3

1,5

1,7

1,9

2,1

2,3

2,5

2,7

2,9

3,1

3,3

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=2,5

1

1,2

1,6

d=4,8 mm

Ep=74000 MPa



e/d

1,2

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

3,2

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=3

1

1,2

1,6

d=4,8 mm

Ep=74000 MPa

e/d

1

1,2

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

0 0,4 0,8 1,2 1,6 2

C(x100000)

5

2

e'/e

3

Ef/Ep=3,5

1

1,2

1,6

d=4,8 mm

Ep=74000 MPa

A3.2 DETERMINATION OF THE EQUIVALENT SECTION P. 1/2


A3.2 Determination of the equivalent section

Considering a simplified model of a fastener clamping 2 plates:

e

e'l

l= (e+e')2

F

Beam balance

d

FMfA

MfB

A

B

The deformed shape at the end of the beam representing the fastener is formulated as:

2.Ef.IflMf.

Gf.Srl

3.Ef.IflF.

23

−

+=∆

knowing that:

2lF.=Mf

If=fastener inertiaSr=reduced shear section

Gf = Ef

2.(1+ υ) (fastener shear modulus)

A3.2 DETERMINATION OF THE EQUIVALENT SECTION P. 2/2


A study has been conducted to compare the simplified method described here with 3D finiteelement calculations fully modelling usual assemblies.

The results show that the best way of representing an equivalent fastener consists in consideringthe fastener as infinitely rigid in bending and therefore take into account only deformationdue to shear;

consequently, the deformed shape is formulated as:

=∆Ef.Sr

).l+2.(1F. υ

giving the following equation:

C =

∆F

(flexibility given in the assembly chapter)

finding the equivalent fastener is therefore the same as taking::

If="infinite"

Ef.C).l+2.(1Sr υ=

BIBLIOGRAPHY P. 1/4


BIBLIOGRAPHY

BIBLIOGRAPHY P. 2/4


Ref. (1): "Manuel de fatigue - Endurance" (Fatigue Manual - Endurance)Aerospatiale technical note n° 436.0112/88A.GALLIOTH.LEMAN

Ref. (2): "Amorçage en fatigue sous chargement complexe uniaxial: proposition d'un nouveaumodèle intégrant les fortes compressions" (Crack initiation and fatigue mode under a uniaxialcomplex load: proposal for a new model incorporating high compression)Aerospatiale technical note n° 573.0027/97D.CAMPASSENS

Ref. (3): "Coefficient de spectre pour les tronçons 15 et 21 de l'A310" (Spectrum coefficient forsections 15 and 21 of the A310)Aerospatiale technical note n° 453.0681/91A.BALEIX

Ref. (4): "Coefficients de spectre de fatigue pour le tronçon 15 des avions de type Long Range"(Fatigue spectrum coefficients for section 15 of long range type aircraft)Internal memorandum 528.1037/97P.BRUNI

Ref. (5): "A330/340: analyses pour Maintenance Review Board" (A330/340: analysis for theMaintenance Review Board)Internal memorandum 528.1129/97M.SENECHAL

Ref. (6): "Influence de l'oxydation anodique chromique et de l'usinage chimique sur lecomportement en fatigue des alliages d'aluminium aéronautiques" (Effect of chromic acid anodisingand chemical milling on the fatigue behaviour of aeronautical aluminium alloys)ThesisF.SANCHEZ

Ref. (7): "Influence des traitements de surface sur la tenue en fatigue des alliages d'aluminium"(Effect of surface treatments on the fatigue strength of aluminium alloys)PV 47732 (Suresnes)JM.CUNTZ

BIBLIOGRAPHY P. 3/4


Ref. (8): "Remplacement du cadmium phase 3 / Caractérisation approfondie du revêtement zinc-nickel" (Replacement of phase 3 cadmium / In-depth characterisation of zinc-nickel coating)DCR/I 04867/97D.MARCHANDISE

Ref. (9): "Grenaillage de précontraintes des alliages d'aluminium" (Aluminium alloy prestressingshot-peening)Internal memorandum 564.0509/97E.HERBAY

Ref. (10): "Synthèse d'essais sur le procédé de grenaillage de précontrainte des métaux durs(TA6V, 40CDV12, Marval X12)" (Summary of tests on the hard metallic prestressing shot-peeningprocess (TA6V, 40CDV12, Marval X12))Aerospatiale technical note n° 564.0310/97E.SENGES

Ref. (11): "Aging aircraft / Repair assessment program"AIRBUS INDUSTRIE / Product support directorate

Ref. (12): "Essais de fatigue sur éprouvettes type réparations de peau" (Fatigue tests on skin repairtype test specimens)Aerospatiale technical note n° 450.0238/96M.ARNAL

Ref. (13): "Guide du dessinateur / Les concentrations de contraintes" (Draftsman guide / Stressconcentation)CETIM

Ref. (14): "Stress concentration factor"R.E.PETERSON

Ref. (15): "Engineering Sciences Data Unit"The Royal Aeronautical SocietyInstitution of Mechanical Engineers

Ref. (16): "Formulas for stress and strain" (édition 5)R.J.ROARKW.C.YOUNG

Ref. (17): "Application Fatigue" (catalogue ASFAT) (Fatigue application (ASFAT catalog))C.GRASSIN

BIBLIOGRAPHY P. 4/4


Ref. (18): "Comportement des assemblages: principe de modélisation" (Assembly behaviour:modelling principle)Aerospatiale technical note n° 530.0008/98P.ROBERT

Ref. (19): "Etude en fatigue des réparations "feuilletées" / Corrélations calculs-essais" (Fatiguestudy of "stack-up" repairs / Calculation-test correlations)Aerospatiale technical note n° 528.0207/98D.CAMPASSENS

Ref. (20): "MILITARY HANDBOOK" (édition MIL-HDBK-5G du 1/11/94)R.J.ROARKW.C.YOUNG

Ref. (21): "Manuel des données de base des matériaux métalliques / Endurance en fatigue"(Manual of basic metallic material data / Fatigue endurance)Aerospatiale technical note n° 437.0264/90JC.ROGOS

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