 | Khattad I.A. A novel numerical approach and experimental study on the waviness defects in composite structures: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Faserverbundleichtbau und Adaptronik, Braunschweig. - Köln: Deutsches Zentrum für Luft- und Raumfahrt, 2013. - vii, 220 p.: ill. - (Forschungsbericht; 2013-14). - Ref.: p.215-220. - ISSN 1434-8454
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1 Introduction
1.1 Rationale and Motivation ................................ 1
2 Hypotheses and outline
2.1 Hypotheses of the present work .......................... 5
2.2 Outline of the thesis ................................... 7
3 The State of the Art of the Effects of Fibres and Plies
Undulations on the Stiffness and Strength
3.1 The State of the Art ................................... 11
4 Stiffness Analysis of Lamina and Laminate with Waviness
4.1 jritroduction .......................................... 19
4.2 Analytical Approach .................................... 20
4.2.1 Theoretical Basis and Concepts .................. 20
4.2.2 Theoretical Analysis of the Stiffness of
Lamina with In-plane Fibre Waviness ............. 26
4.2.3 Theoretical Analysis of the Stiffness of
Laminate with Out-of-plane Waviness ............. 32
4.2.4 Represent the Waviness Geometry by Fourier
Series Function ................................. 38
4.2.5 Theoretical Analysis for Stiffness of Laminate
with 3D Surface Out-of-plane Ply Waviness ....... 39
4.2.6 Parametric Studies on Analytical Approach ....... 44
4.3 Finite Element Approach ................................ 51
4.3.1 The Principle of the FE Approach ................ 55
4.3.2 Finite Element Modelling ........................ 57
4.3.3 Extension of FE Model for Fibre Volume
Fraction Effect ................................. 61
4.3.4 The capability of EF Approach ................... 63
4.3.5 Awoctation Between the FE Approach and the CLT
Analysis ........................................ 67
4.4 Parametric case studies on FE approach ................. 71
4.4.1 Comparison Case Studies Between Analytical and
FE Approaches ................................... 71
4.4.2 Case Studies on the Limitation of E-CLT ......... 76
4.4.3 Parametrical Studies on the Finite Element
Approach ........................................ 82
4.5 The Conclusion of the Stiffness Analysis of Lamina
and Laminate with Waviness ............................. 94
5 Strength Analysis of Lamina and Laminate with Waviness
5.1 Introduction ........................................... 95
5.2 Strength Analysis of Lamina and Laminate with
Waviness ............................................... 96
5.2.1 The Conceptual Framework ........................ 98
5.2.2 Hashin Failure Criterion ....................... 100
5.2.3 A 3D Hashin Failure Criteria in Strain Terms ... 103
5.3 A 3D Damage Model Based on Continuum Damage
Mechanics (CDM) ....................................... 107
5.3.1 Damage Variable ................................ 107
5.3.2 Damage Threshold ............................... 109
5.3.3 Multidimensional Damage and Effective Spaces ... 110
5.4 Applications on Strength of Laminate with Waviness .... 115
5.5 The Discussion of the Results ......................... 117
5.6 Application of Strength in × Direction of UD Tension
Specimen with Planar Out-of-plane Ply Waviness ........ 119
5.6.1 Problem Description and Material
Characteristics ................................ 120
5.6.2 The considerations of finite element model ..... 121
5.6.3 The Discussion of the Results on the Tension
Specimen with Waviness ......................... 124
6 Experimental Works to Fabricate Tension Specimens with
Controlled Out-of-plane Wavy plies
6.1 Introduction .......................................... 139
6.2 Literature Review on the Experimental Works ........... 140
6.3 The principle of RTM technology ....................... 149
6.4 The Process of Manufacturing Tension Specimens ........ 151
6.4.1 Coupon Specimens Geometry and Materials ......... 151
6.4.2 Two-step method (co-curing) (TSM) for
HTA40/LY564 .................................... 152
6.4.3 The Advantages of TSM Approach ................. 156
6.4.4 Constrains on Specimen Dimensions and
Fabrication .................................... 158
6.4.5 Quality Assurance Testing ...................... 161
6.4.6 Tension Tests and Evaluations .................. 164
6.4.7 Discussion of the Results ...................... 169
6.5 The Manufacturing Methodology of Thin Specimens ....... 173
6.5.1 Step.1 ......................................... 174
6.5.2 Step.2 ......................................... 174
6.5.3 Step.3 ......................................... 175
6.6 Experimental Tension Test of Thin Specimen ............ 178
6.6.1 The Principle of ARAMIS [105] .................. 179
6.6.2 Strain Computation by ARAMIS ................... 179
6.6.3 Discussion of the Results of the Tension Test
of Thin Specimens .............................. 180
6.6.4 The Comparesion between the FE Model and the
Experimental Test of the Tension Specimen ...... 185
7 Conclusion and outlook
7.1 The Conclusion ........................................ 189
7.2 Outlook ............................................... 192
Appendix A .................................................... 195
Appendix В .................................................... 202
Appendix С .................................................... 204
References .................................................... 214
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