Space engineering - Structural materials handbook - Part 2: Design calculation methods and general design aspects

The structural materials handbook, SMH, combines materials and design information on established polymer matrix composites with provisional information on the emerging groups of newer advanced materials and their composites. Design aspects are described, along with factors associated with joining and manufacturing. Where possible, these are illustrated by examples or case studies.
The Structural materials handbook contains 8 Parts.
A glossary of terms, definitions and abbreviated terms for these handbooks is contained in Part 8.
The parts are as follows:
Part 1 Overview and material properties and applications                    Clauses 1 ‐ 9
Part 2 Design calculation methods and general design aspects    Clauses 10 ‐ 22
Part 3 Load transfer and design of joints and design of structures    Clauses 23 ‐ 32
Part 4 Integrity control, verification guidelines and manufacturing    Clauses 33 ‐ 45
Part 5 New advanced materials, advanced metallic materials, general design aspects and load transfer and design of joints    Clauses 46 ‐ 63
Part 6 Fracture and material modelling, case studies and design and integrity control and inspection    Clauses 64 ‐ 81
Part 7 Thermal and environmental integrity, manufacturing aspects, in‐orbit and health monitoring, soft materials, hybrid materials and nanotechnoligies   Clauses 82 ‐ 107
Part 8 Glossary   
NOTE: The 8 parts will be numbered TR17603-32-01 to TR 17603-32-08

Raumfahrttechnik - Handbuch Konstruktionswerkstoffe - Teil 2: Konstruktionsberechnungsverfahren und allgemeine Konstruktionsaspekte

Ingénierie spatiale - Manuel des matériaux structuraux - Partie 2 : Méthodes de calculs de conception et aspects généraux de conception

Vesoljska tehnika - Priročnik o strukturnih materialih - 2. del: Metode za izračun zasnove in splošni vidiki zasnove

Priročnik o strukturnih materialih, SMH, združuje informacije o materialih in oblikovanju uveljavljenih polimernih matričnih kompozitov z začasnimi informacijami o nastajajočih skupinah novejših naprednih materialov in njihovih kompozitov. Opisani so vidiki oblikovanja, skupaj z dejavniki združevanja in proizvodnje. Kjer je mogoče, so podani primeri ali študije primerov.
Priročnik o strukturnih materialih vsebuje 8 delov.
Slovar izrazov, opredelitve in okrajšave izrazov za te priročnike so v 8. delu.
Deli so:
1. del: Pregled in lastnosti materialov ter aplikacije                    Točke 1–9
2. del: Metode za izračun zasnove in splošni vidiki zasnove    Točke 10–22
3. del: Prenos obremenitve ter projektiranje spojev in konstrukcij    Točke 23–32
4. del: Nadzor integritete, smernice za preverjanje in proizvodnja    Točke 33–45
5. del: Novi napredni materiali, napredni kovinski materiali, splošni konstrukcijski vidiki ter prenos obremenitve in oblikovanje sklepov    Točke 46–63
6. del: Modeliranje zlomov in materialov, študije primerov, načrtovanje in nadzor integritete ter inšpekcijski pregled    Točke 64–81
7. del: Toplotna in okoljska celovitost, proizvodni vidiki, spremljanje stanja materialov v orbiti, mehki materiali, hibridni materiali in nanotehnologije   Točke 82–107
8. del: Slovar   
OPOMBA: Teh 8 delov je označenih s številkami od TR17603-32-01 do TR 17603-32-08.

General Information

Status
Published
Public Enquiry End Date
20-Oct-2021
Publication Date
09-Feb-2022
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
31-Jan-2022
Due Date
07-Apr-2022
Completion Date
10-Feb-2022

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SLOVENSKI STANDARD
SIST-TP CEN/TR 17603-32-02:2022
01-marec-2022

Vesoljska tehnika - Priročnik o strukturnih materialih - 2. del: Metode za izračun

zasnove in splošni vidiki zasnove

Space engineering - Structural materials handbook - Part 2: Design calculation methods

and general design aspects
Raumfahrttechnik - Handbuch Konstruktionswerkstoffe - Teil 2:
Konstruktionsberechnungsverfahren und allgemeine Konstruktionsaspekte

Ingénierie spatiale - Manuel des matériaux structuraux - Partie 2 : Méthodes de calculs

de conception et aspects généraux de conception
Ta slovenski standard je istoveten z: CEN/TR 17603-32-02:2022
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
SIST-TP CEN/TR 17603-32-02:2022 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/TR 17603-32-02:2022
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SIST-TP CEN/TR 17603-32-02:2022
TECHNICAL REPORT CEN/TR 17603-32-02
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
January 2022
ICS 49.140
English version
Space engineering - Structural materials handbook - Part
2: Design calculation methods and general design aspects

Ingénierie spatiale - Manuel des matériaux structuraux Raumfahrttechnik - Handbuch

- Partie 2 : Méthodes de calculs de conception et Konstruktionswerkstoffe - Teil 2:

aspects généraux de conception Konstruktionsberechnungsverfahren und allgemeine
Konstruktionsaspekte

This Technical Report was approved by CEN on 22 November 2021. It has been drawn up by the Technical Committee

CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,

Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,

Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,

Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels

© 2022 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/TR 17603-32-02:2022 E

reserved worldwide for CEN national Members and for
CENELEC Members.
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Table of contents

European Foreword ................................................................................................. 25

Introduction .............................................................................................................. 26

10 Stress-strain relationships ................................................................................ 27

10.1 Introduction ......................................................................................................... 27

10.2 Elastic property prediction for UD ply from constituent properties........................ 27

10.3 Analytical notation for elastic constant methods .................................................. 29

10.4 Calculation methods for elastic constants of UD ply ............................................ 29

10.5 Longitudinal modulus .......................................................................................... 31

10.6 Longitudinal Poisson's ratio ................................................................................. 33

10.7 Transverse modulus ............................................................................................ 34

10.7.1 General ..................................................................................................... 34

10.7.2 Jones method ........................................................................................... 34

10.7.3 Förster/Knappe method ............................................................................ 34

10.7.4 Schneider method ..................................................................................... 35

10.7.5 Puck method ............................................................................................. 35

10.7.6 Tsai method .............................................................................................. 35

10.7.7 HSB method.............................................................................................. 36

10.7.8 Graphs ...................................................................................................... 36

10.8 Transverse Poisson's ratio .................................................................................. 39

10.9 Transverse shear modulus .................................................................................. 39

10.9.1 General ..................................................................................................... 39

10.9.2 Jones method ........................................................................................... 39

10.9.3 Förster/Knappe method ............................................................................ 39

10.9.4 Schneider method ..................................................................................... 39

10.9.5 Puck method ............................................................................................. 40

10.9.6 Tsai method .............................................................................................. 40

10.9.7 HSB method.............................................................................................. 40

10.9.8 Graphs ...................................................................................................... 41

10.10 In-plane stress calculation methods .................................................................... 43

10.11 Analytical notation for in-plane methods .............................................................. 43

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10.12 Stress-strain relations for unidirectional plies ...................................................... 45

10.12.1 Fibre-oriented co-ordinate system ............................................................. 45

10.13 On axis stress strain relations ............................................................................. 45

10.13.1 General ..................................................................................................... 45

10.13.2 Compliance matrix .................................................................................... 46

10.13.3 Modulus matrix .......................................................................................... 46

10.13.4 Symmetry of compliance and modulus matrices ....................................... 46

10.14 Stress-strain relations for a ply of arbitrary orientation ......................................... 46

10.14.1 General ..................................................................................................... 46

10.14.2 Off axis stiffness of a unidirectional ply...................................................... 48

10.15 Stiffness matrix for a laminate ............................................................................. 49

10.15.1 General laminates ..................................................................................... 49

10.15.2 Symmetric laminates ................................................................................. 51

10.15.3 Flow chart ................................................................................................. 52

10.16 Calculation methods with interlaminar stresses and strains ................................. 53

10.16.1 Calculation with free-edge stresses ........................................................... 53

10.17 Qualitative evaluation of interlaminar strength for design purposes ..................... 55

10.17.1 General ..................................................................................................... 55

10.17.2 Variation of fibre direction within a [±φ°, 0°, ±φ°] laminate .......................... 57

10.17.3 Variation of the thickness of the 0° layer within the [± 30°, 0n°, ± 30°]

laminate .................................................................................................... 57

10.17.4 Variation of the sequence of layers ........................................................... 58

10.18 References ......................................................................................................... 58

10.18.1 General ..................................................................................................... 58

11 Strength prediction and failure criteria ............................................................. 60

11.1 Introduction ......................................................................................................... 60

11.1.1 Micro-mechanical strength models ............................................................ 60

11.1.2 Lamina failure models ............................................................................... 60

11.1.3 Failure criteria studies ............................................................................... 61

11.1.4 Summary of World Wide Failure Exercise (WWFE) ................................... 62

11.2 Tensile strength of UD composites in fibre direction ............................................ 64

11.2.1 General ..................................................................................................... 64

11.2.2 Weakest-link failure model ........................................................................ 64

11.2.3 Cumulative weakening failure model ......................................................... 64

11.2.4 Fibre break propagation model ................................................................. 66

11.2.5 Cumulative group mode failure model ....................................................... 66

11.2.6 Status of models ....................................................................................... 66

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11.3 Compressive strength of UD composites in fibre direction................................... 66

11.3.1 General ..................................................................................................... 66

11.3.2 Extension mode buckling .......................................................................... 67

11.3.3 Shear mode buckling ................................................................................ 67

11.3.4 Analysis of compression failure ................................................................. 68

11.4 Transverse tensile strength of UD composites .................................................... 70

11.4.1 General ..................................................................................................... 70

11.4.2 Prediction of transverse tensile strength .................................................... 71

11.4.3 Empirical analysis ..................................................................................... 71

11.5 Static strength criteria for composites ................................................................. 72

11.6 Analytical notation for static strength criteria for composites ............................... 72

11.6.1 Co-ordinate system ................................................................................... 72

11.6.2 Formulae ................................................................................................... 73

11.7 Different types of failure criteria ........................................................................... 74

11.7.1 General ..................................................................................................... 74

11.7.2 Evaluation studies ..................................................................................... 75

11.8 Overview - Failure criteria ................................................................................... 75

11.8.1 Introduction ............................................................................................... 75

11.8.2 Independent conditions ............................................................................. 76

11.8.3 Interactive conditions – Pure interpolative conditions ................................ 77

11.8.4 Interactive conditions - Physical considerations ........................................ 78

11.9 Comparison between test data and various failure criteria .................................. 87

11.9.1 Effects on failure mode ............................................................................. 87

11.10 Description of failure modes ................................................................................ 91

11.10.1 Laminates ................................................................................................. 91

11.10.2 Failure ....................................................................................................... 91

11.11 Fatigue strength of composites ........................................................................... 96

11.11.1 Background ............................................................................................... 96

11.11.2 Analytical notation ..................................................................................... 97

11.11.3 Approximation of fatigue life ...................................................................... 97

11.12 References ......................................................................................................... 99

11.12.1 General ..................................................................................................... 99

12 Calculation of thermal stress and displacement ........................................... 103

12.1 Introduction ....................................................................................................... 103

12.1.1 General ................................................................................................... 103

12.1.2 Longitudinal CTE .................................................................................... 103

12.1.3 Transverse CTE ...................................................................................... 103

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12.2 Analytical notation for thermal stress calculations ............................................. 104

12.3 Calculation of CTE from constituents ................................................................ 105

12.3.1 CTE in fibre direction ............................................................................... 105

12.3.2 CTE perpendicular to fibre direction ........................................................ 105

12.4 CTE for a laminate ............................................................................................ 106

12.5 Thermal stresses within laminate layers ............................................................ 108

12.5.1 General ................................................................................................... 108

12.5.2 Residual curing stresses ......................................................................... 108

12.6 Stress strain temperature relation ..................................................................... 109

12.6.1 General ................................................................................................... 109

12.6.2 Mechanical strains .................................................................................. 109

12.6.3 Incremental strain theory ......................................................................... 109

12.7 Microstress analysis .......................................................................................... 111

12.7.1 General ................................................................................................... 111

12.7.2 Microstresses on fibre axis ...................................................................... 111

12.7.3 Microstresses normal to fibre axis ........................................................... 111

12.8 References ....................................................................................................... 111

12.8.1 General ................................................................................................... 111

13 Moisture effects on composite properties ..................................................... 113

13.1 Introduction ....................................................................................................... 113

13.1.1 General ................................................................................................... 113

13.1.2 Moisture penetration ............................................................................... 113

13.1.3 Moisture effects ....................................................................................... 113

13.2 Analytical notation for moisture effects .............................................................. 114

13.3 Typical effects of moisture................................................................................. 115

13.3.1 General ................................................................................................... 115

13.3.2 Sample data: Effects of moisture ............................................................. 115

13.4 Approximate method for calculation of strength and modulus retention of

[0°/90°] laminates .............................................................................................. 120

13.4.1 General ................................................................................................... 120

13.4.2 Modulus retention ................................................................................... 120

13.4.3 Strength retention ................................................................................... 122

13.5 Moisture content ............................................................................................... 123

13.5.1 Fick's law ................................................................................................ 123

13.5.2 Determination of moisture content ........................................................... 124

13.5.3 Maximum moisture content ..................................................................... 125

13.5.4 Experimental determination of the diffusion coefficient ............................ 126

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13.6 Calculation of swelling coefficient from constituents .......................................... 128

13.6.1 General ................................................................................................... 128

13.6.2 Swelling coefficient β in fibre direction.................................................... 128

13.6.3 Swelling coefficient β transverse to fibres .............................................. 128

13.6.4 Swelling coefficient for a laminate ........................................................... 129

13.7 Coefficient of moisture expansion (CME) .......................................................... 131

13.7.1 Resin behaviour ...................................................................................... 131

13.7.2 Composite behaviour .............................................................................. 132

13.8 References ....................................................................................................... 133

13.8.1 General ................................................................................................... 133

14 Stress concentrations and fracture ................................................................ 135

14.1 Introduction ....................................................................................................... 135

14.1.1 General ................................................................................................... 135

14.1.2 Fracture mechanics models .................................................................... 135

14.2 Analytical notation for stress concentrations ..................................................... 136

14.3 Summary of fracture models ............................................................................. 136

14.4 Evaluation of fracture models ............................................................................ 137

14.5 WEK fracture model .......................................................................................... 138

14.5.1 General ................................................................................................... 138

14.5.2 Circular holes .......................................................................................... 138

14.5.3 Straight crack .......................................................................................... 141

14.6 WN fracture model ............................................................................................ 144

14.6.1 General ................................................................................................... 144

14.6.2 Failure criteria ......................................................................................... 144

14.6.3 Characteristics of WN fracture model ...................................................... 146

14.6.4 Circular holes .......................................................................................... 147

14.6.5 Straight cracks ........................................................................................ 151

14.6.6 Point stress criteria .................................................................................. 152

14.6.7 Average stress criterion .......................................................................... 153

14.7 Finite plate models ............................................................................................ 157

14.8 Finite width correction (FWC) ............................................................................ 157

14.8.1 General ................................................................................................... 157

14.8.2 Circular holes .......................................................................................... 159

14.8.3 Centre crack............................................................................................ 160

14.9 Calculated stress concentration factor at circular holes ..................................... 160

14.9.1 NASA results ........................................................................................... 160

14.9.2 Finite width correction (FWC) .................................................................. 162

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14.9.3 MBB/ERNO study ................................................................................... 162

14.10 Stress distribution around circular holes ............................................................ 167

14.10.1 General ................................................................................................... 167

14.10.2 Stress concentration due to tensile load .................................................. 167

14.10.3 Stress concentration due to shear load ................................................... 168

14.11 Interlaminar fracture mechanics ........................................................................ 170

14.11.1 Nomenclature .......................................................................................... 170

14.11.2 Delamination and fracture mechanics overview ...................................... 170

14.11.3 Standard test methods (static and fatigue) .............................................. 174

14.11.4 Calculation of strain energy release rate in structural analysis ................ 178

14.12 References ....................................................................................................... 184

14.12.1 General ................................................................................................... 184

15 Prediction of dynamic characteristics ............................................................ 188

15.1 Introduction ....................................................................................................... 188

15.2 Definition of damping terms ............................................................................... 188

15.2.1 General terms ......................................................................................... 188

15.2.2 Complex modulus model ......................................................................... 190

15.3 Prediction methods for damping ........................................................................ 191

15.4 Determination of damping characteristics .......................................................... 192

15.4.1 Unidirectional characteristics ................................................................... 192

15.4.2 Off axis characteristics ............................................................................ 192

15.4.3 Laminate characteristics.......................................................................... 193

15.5 Approximate data on damping .......................................................................... 193

15.6 References ....................................................................................................... 194

15.6.1 General ................................................................................................... 194

16 Computer analysis of composites .................................................................. 195

16.1 Introduction ....................................................................................................... 195

16.2 Computer programs: Analysis of composites .................................................... 195

16.2.1 General ................................................................................................... 195

16.2.2 Finite element programs.......................................................................... 197

16.2.3 Laminate analysis programs ................................................................... 198

16.2.4 Special applications programs ................................................................ 200

16.3 ESDU data for composite analysis .................................................................... 202

16.3.1 General ................................................................................................... 202

16.3.2 ESDU data items .................................................................................... 202

16.3.3 ESDUpac ................................................................................................ 204

16.4 Buckling of orthotropic plates ............................................................................ 204

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16.4.1 Title ......................................................................................................... 204

16.4.2 Usage and scope .................................................................................... 204

16.4.3 Analysis .................................................................................................. 204

16.4.4 ESDUpac A7303 ..................................................................................... 204

16.4.5 Notes ...................................................................................................... 205

16.5 Flexural stiffness of flat strips ............................................................................ 205

16.5.1 Title ......................................................................................................... 205

16.5.2 Usage and scope .................................................................................... 205

16.5.3 Analysis .................................................................................................. 205

16.6 Metallic skin stiffeners reinforced by composite - local buckling ........................ 206

16.6.1 Title ......................................................................................................... 206

16.6.2 Usage and scope .................................................................................... 206

16.6.3 Analysis and data .................................................................................... 206

16.7 Laminate stress analysis ................................................................................... 207

16.7.1 Title ......................................................................................................... 207

16.7.2 Usage and scope .................................................................................... 207

16.7.3 Analysis .................................................................................................. 207

16.8 Plate stiffnesses (In-plane) ................................................................................ 208

16.8.1 Title .................................
...

SLOVENSKI STANDARD
kSIST-TP FprCEN/TR 17603-32-02:2021
01-oktober-2021

Vesoljska tehnika - Priročnik o strukturnih materialih - 2. del: Metode za izračun

zasnove in splošni vidiki zasnove

Space engineering - Structural materials handbook - Part 2: Design calculation methods

and general design aspects
Raumfahrttechnik - Handbuch Konstruktionswerkstoffe - Teil 2:
Konstruktionsberechnungsverfahren und allgemeine Konstruktionsaspekte

Ingénierie spatiale - Manuel des matériaux structuraux - Partie 2 : Méthodes de calculs

de conception et aspects généraux de conception
Ta slovenski standard je istoveten z: FprCEN/TR 17603-32-02
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
kSIST-TP FprCEN/TR 17603-32-02:2021 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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kSIST-TP FprCEN/TR 17603-32-02:2021
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kSIST-TP FprCEN/TR 17603-32-02:2021
TECHNICAL REPORT
FINAL DRAFT
FprCEN/TR 17603-32-02
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
July 2021
ICS 49.140
English version
Space engineering - Structural materials handbook - Part
2: Design calculation methods and general design aspects

Ingénierie spatiale - Manuel des matériaux structuraux Raumfahrttechnik - Handbuch

- Partie 2 : Méthodes de calculs de conception et Konstruktionswerkstoffe - Teil 2:

aspects généraux de conception Konstruktionsberechnungsverfahren und allgemeine
Konstruktionsaspekte

This draft Technical Report is submitted to CEN members for Vote. It has been drawn up by the Technical Committee

CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,

Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,

Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,

Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are

aware and to provide supporting documentation.

Warning : This document is not a Technical Report. It is distributed for review and comments. It is subject to change without

notice and shall not be referred to as a Technical Report.
CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels

© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. FprCEN/TR 17603-32-02:2021 E

reserved worldwide for CEN national Members and for
CENELEC Members.
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Table of contents

European Foreword ................................................................................................. 25

Introduction .............................................................................................................. 26

10 Stress-strain relationships ................................................................................ 27

10.1 Introduction ......................................................................................................... 27

10.2 Elastic property prediction for UD ply from constituent properties........................ 27

10.3 Analytical notation for elastic constant methods .................................................. 29

10.4 Calculation methods for elastic constants of UD ply ............................................ 29

10.5 Longitudinal modulus .......................................................................................... 31

10.6 Longitudinal Poisson's ratio ................................................................................. 33

10.7 Transverse modulus ............................................................................................ 34

10.7.1 General ..................................................................................................... 34

10.7.2 Jones method ........................................................................................... 34

10.7.3 Förster/Knappe method ............................................................................ 34

10.7.4 Schneider method ..................................................................................... 35

10.7.5 Puck method ............................................................................................. 35

10.7.6 Tsai method .............................................................................................. 35

10.7.7 HSB method.............................................................................................. 36

10.7.8 Graphs ...................................................................................................... 36

10.8 Transverse Poisson's ratio .................................................................................. 39

10.9 Transverse shear modulus .................................................................................. 39

10.9.1 General ..................................................................................................... 39

10.9.2 Jones method ........................................................................................... 39

10.9.3 Förster/Knappe method ............................................................................ 39

10.9.4 Schneider method ..................................................................................... 39

10.9.5 Puck method ............................................................................................. 40

10.9.6 Tsai method .............................................................................................. 40

10.9.7 HSB method.............................................................................................. 40

10.9.8 Graphs ...................................................................................................... 41

10.10 In-plane stress calculation methods .................................................................... 43

10.11 Analytical notation for in-plane methods .............................................................. 43

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10.12 Stress-strain relations for unidirectional plies ...................................................... 45

10.12.1 Fibre-oriented co-ordinate system ............................................................. 45

10.13 On axis stress strain relations ............................................................................. 45

10.13.1 General ..................................................................................................... 45

10.13.2 Compliance matrix .................................................................................... 46

10.13.3 Modulus matrix .......................................................................................... 46

10.13.4 Symmetry of compliance and modulus matrices ....................................... 46

10.14 Stress-strain relations for a ply of arbitrary orientation ......................................... 46

10.14.1 General ..................................................................................................... 46

10.14.2 Off axis stiffness of a unidirectional ply...................................................... 48

10.15 Stiffness matrix for a laminate ............................................................................. 49

10.15.1 General laminates ..................................................................................... 49

10.15.2 Symmetric laminates ................................................................................. 51

10.15.3 Flow chart ................................................................................................. 52

10.16 Calculation methods with interlaminar stresses and strains ................................. 53

10.16.1 Calculation with free-edge stresses ........................................................... 53

10.17 Qualitative evaluation of interlaminar strength for design purposes ..................... 55

10.17.1 General ..................................................................................................... 55

10.17.2 Variation of fibre direction within a [±°, 0°, ±°] laminate .......................... 57

10.17.3 Variation of the thickness of the 0° layer within the [± 30°, 0n°, ± 30°]

laminate .................................................................................................... 57

10.17.4 Variation of the sequence of layers ........................................................... 58

10.18 References ......................................................................................................... 58

10.18.1 General ..................................................................................................... 58

11 Strength prediction and failure criteria ............................................................. 60

11.1 Introduction ......................................................................................................... 60

11.1.1 Micro-mechanical strength models ............................................................ 60

11.1.2 Lamina failure models ............................................................................... 60

11.1.3 Failure criteria studies ............................................................................... 61

11.1.4 Summary of World Wide Failure Exercise (WWFE) ................................... 62

11.2 Tensile strength of UD composites in fibre direction ............................................ 64

11.2.1 General ..................................................................................................... 64

11.2.2 Weakest-link failure model ........................................................................ 64

11.2.3 Cumulative weakening failure model ......................................................... 64

11.2.4 Fibre break propagation model ................................................................. 66

11.2.5 Cumulative group mode failure model ....................................................... 66

11.2.6 Status of models ....................................................................................... 66

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11.3 Compressive strength of UD composites in fibre direction................................... 66

11.3.1 General ..................................................................................................... 66

11.3.2 Extension mode buckling .......................................................................... 67

11.3.3 Shear mode buckling ................................................................................ 67

11.3.4 Analysis of compression failure ................................................................. 68

11.4 Transverse tensile strength of UD composites .................................................... 70

11.4.1 General ..................................................................................................... 70

11.4.2 Prediction of transverse tensile strength .................................................... 71

11.4.3 Empirical analysis ..................................................................................... 71

11.5 Static strength criteria for composites ................................................................. 72

11.6 Analytical notation for static strength criteria for composites ............................... 72

11.6.1 Co-ordinate system ................................................................................... 72

11.6.2 Formulae ................................................................................................... 73

11.7 Different types of failure criteria ........................................................................... 74

11.7.1 General ..................................................................................................... 74

11.7.2 Evaluation studies ..................................................................................... 75

11.8 Overview - Failure criteria ................................................................................... 75

11.8.1 Introduction ............................................................................................... 75

11.8.2 Independent conditions ............................................................................. 76

11.8.3 Interactive conditions – Pure interpolative conditions ................................ 77

11.8.4 Interactive conditions - Physical considerations ........................................ 78

11.9 Comparison between test data and various failure criteria .................................. 87

11.9.1 Effects on failure mode ............................................................................. 87

11.10 Description of failure modes ................................................................................ 91

11.10.1 Laminates ................................................................................................. 91

11.10.2 Failure ....................................................................................................... 91

11.11 Fatigue strength of composites ........................................................................... 96

11.11.1 Background ............................................................................................... 96

11.11.2 Analytical notation ..................................................................................... 97

11.11.3 Approximation of fatigue life ...................................................................... 97

11.12 References ......................................................................................................... 99

11.12.1 General ..................................................................................................... 99

12 Calculation of thermal stress and displacement ........................................... 103

12.1 Introduction ....................................................................................................... 103

12.1.1 General ................................................................................................... 103

12.1.2 Longitudinal CTE .................................................................................... 103

12.1.3 Transverse CTE ...................................................................................... 103

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12.2 Analytical notation for thermal stress calculations ............................................. 104

12.3 Calculation of CTE from constituents ................................................................ 105

12.3.1 CTE in fibre direction ............................................................................... 105

12.3.2 CTE perpendicular to fibre direction ........................................................ 105

12.4 CTE for a laminate ............................................................................................ 106

12.5 Thermal stresses within laminate layers ............................................................ 108

12.5.1 General ................................................................................................... 108

12.5.2 Residual curing stresses ......................................................................... 108

12.6 Stress strain temperature relation ..................................................................... 109

12.6.1 General ................................................................................................... 109

12.6.2 Mechanical strains .................................................................................. 109

12.6.3 Incremental strain theory ......................................................................... 109

12.7 Microstress analysis .......................................................................................... 111

12.7.1 General ................................................................................................... 111

12.7.2 Microstresses on fibre axis ...................................................................... 111

12.7.3 Microstresses normal to fibre axis ........................................................... 111

12.8 References ....................................................................................................... 111

12.8.1 General ................................................................................................... 111

13 Moisture effects on composite properties ..................................................... 113

13.1 Introduction ....................................................................................................... 113

13.1.1 General ................................................................................................... 113

13.1.2 Moisture penetration ............................................................................... 113

13.1.3 Moisture effects ....................................................................................... 113

13.2 Analytical notation for moisture effects .............................................................. 114

13.3 Typical effects of moisture................................................................................. 115

13.3.1 General ................................................................................................... 115

13.3.2 Sample data: Effects of moisture ............................................................. 115

13.4 Approximate method for calculation of strength and modulus retention of

[0°/90°] laminates .............................................................................................. 120

13.4.1 General ................................................................................................... 120

13.4.2 Modulus retention ................................................................................... 120

13.4.3 Strength retention ................................................................................... 122

13.5 Moisture content ............................................................................................... 123

13.5.1 Fick's law ................................................................................................ 123

13.5.2 Determination of moisture content ........................................................... 124

13.5.3 Maximum moisture content ..................................................................... 125

13.5.4 Experimental determination of the diffusion coefficient ............................ 126

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13.6 Calculation of swelling coefficient from constituents .......................................... 128

13.6.1 General ................................................................................................... 128

13.6.2 Swelling coefficient  in fibre direction.................................................... 128

13.6.3 Swelling coefficient  transverse to fibres .............................................. 128

13.6.4 Swelling coefficient for a laminate ........................................................... 129

13.7 Coefficient of moisture expansion (CME) .......................................................... 131

13.7.1 Resin behaviour ...................................................................................... 131

13.7.2 Composite behaviour .............................................................................. 132

13.8 References ....................................................................................................... 133

13.8.1 General ................................................................................................... 133

14 Stress concentrations and fracture ................................................................ 135

14.1 Introduction ....................................................................................................... 135

14.1.1 General ................................................................................................... 135

14.1.2 Fracture mechanics models .................................................................... 135

14.2 Analytical notation for stress concentrations ..................................................... 136

14.3 Summary of fracture models ............................................................................. 136

14.4 Evaluation of fracture models ............................................................................ 137

14.5 WEK fracture model .......................................................................................... 138

14.5.1 General ................................................................................................... 138

14.5.2 Circular holes .......................................................................................... 138

14.5.3 Straight crack .......................................................................................... 141

14.6 WN fracture model ............................................................................................ 144

14.6.1 General ................................................................................................... 144

14.6.2 Failure criteria ......................................................................................... 144

14.6.3 Characteristics of WN fracture model ...................................................... 146

14.6.4 Circular holes .......................................................................................... 147

14.6.5 Straight cracks ........................................................................................ 151

14.6.6 Point stress criteria .................................................................................. 152

14.6.7 Average stress criterion .......................................................................... 153

14.7 Finite plate models ............................................................................................ 157

14.8 Finite width correction (FWC) ............................................................................ 157

14.8.1 General ................................................................................................... 157

14.8.2 Circular holes .......................................................................................... 159

14.8.3 Centre crack............................................................................................ 160

14.9 Calculated stress concentration factor at circular holes ..................................... 160

14.9.1 NASA results ........................................................................................... 160

14.9.2 Finite width correction (FWC) .................................................................. 162

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14.9.3 MBB/ERNO study ................................................................................... 162

14.10 Stress distribution around circular holes ............................................................ 167

14.10.1 General ................................................................................................... 167

14.10.2 Stress concentration due to tensile load .................................................. 167

14.10.3 Stress concentration due to shear load ................................................... 168

14.11 Interlaminar fracture mechanics ........................................................................ 170

14.11.1 Nomenclature .......................................................................................... 170

14.11.2 Delamination and fracture mechanics overview ...................................... 170

14.11.3 Standard test methods (static and fatigue) .............................................. 174

14.11.4 Calculation of strain energy release rate in structural analysis ................ 178

14.12 References ....................................................................................................... 184

14.12.1 General ................................................................................................... 184

15 Prediction of dynamic characteristics ............................................................ 188

15.1 Introduction ....................................................................................................... 188

15.2 Definition of damping terms ............................................................................... 188

15.2.1 General terms ......................................................................................... 188

15.2.2 Complex modulus model ......................................................................... 190

15.3 Prediction methods for damping ........................................................................ 191

15.4 Determination of damping characteristics .......................................................... 192

15.4.1 Unidirectional characteristics ................................................................... 192

15.4.2 Off axis characteristics ............................................................................ 192

15.4.3 Laminate characteristics.......................................................................... 193

15.5 Approximate data on damping .......................................................................... 193

15.6 References ....................................................................................................... 194

15.6.1 General ................................................................................................... 194

16 Computer analysis of composites .................................................................. 195

16.1 Introduction ....................................................................................................... 195

16.2 Computer programs: Analysis of composites .................................................... 195

16.2.1 General ................................................................................................... 195

16.2.2 Finite element programs.......................................................................... 197

16.2.3 Laminate analysis programs ................................................................... 198

16.2.4 Special applications programs ................................................................ 200

16.3 ESDU data for composite analysis .................................................................... 202

16.3.1 General ................................................................................................... 202

16.3.2 ESDU data items .................................................................................... 202

16.3.3 ESDUpac ................................................................................................ 204

16.4 Buckling of orthotropic plates ............................................................................ 204

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16.4.1 Title ......................................................................................................... 204

16.4.2 Usage and scope .................................................................................... 204

16.4.3 Analysis .................................................................................................. 204

16.4.4 ESDUpac A7303 ..................................................................................... 204

16.4.5 Notes ...................................................................................................... 205

16.5 Flexural stiffness of flat strips ............................................................................ 205

16.5.1 Title ......................................................................................................... 205

16.5.2 Usage and scope .................................................................................... 205

16.5.3 Analysis .................................................................................................. 205

16.6 Metallic skin stiffeners reinforced by composite - local buckling ........................ 206

16.6.1 Title ......................................................................................................... 206

16.6.2 Usage and scope .................................................................................... 206

16.6.3 Analysis and data .................................................................................... 206

16.7 Laminate stress analysis ................................................................................... 207

16.7.1 Title ..................................................................
...

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