Residual strength of impact-damaged composite structures under static in-plane compressive loads

UNIVERSITA’ DEGLI STUDI DI PISA

Facolt`

a di Ingegneria

Corso di Laurea Specialistica in Ingegneria Meccanica

CENTRE NATIONAL DE ETUDES SPATIAL LAUNCHERS DIRECTORATE

Master’s Degree Thesis

Residual strength of impact-damaged

composite structures under static

in-plane compressive loads

Tutors:

Candidate:

Prof. Ing. Marco Beghini

Carlo Simoncelli

Ing. Michele Biagi

Abstract

This report outlines the work performed during the five months internship carried out at Structural,Thermal and Material department of the Launchers Directorate of the French Space Agency (CNES) in Evry - France for the achievement of the Master’s Degree in Mechanical Engineering.

The aim of the work has been to develop a simplified procedure for the prediction of the residual strength of impact-damaged composite structures.

This need starts from the will to simplify the qualification process of composite structures reducing costs and times needed for the determination of the residual properties of a damaged material, overtaking the disadvantages of the principal approaches nowadays used, like experimental tests and finite element models. An important introductionary remarks is the big difficulty that every author that confronted the problem has founded in the analysis of the impact process, char-acterized by phenomenons often very difficult and sometimes impossible to model and an elevated complexity of the whole problem.

The work started from a deep and wide literature’s review, which was also the occasion for the creation of a data-base very useful in the next phases.

A long study on the experimental data followed the state of the art analysis, and thanks to the know-how formed during the previous phase brought to the deter-mination of some experimental laws that are able, respecting the phisics of the problem, to make good prevision of many aspects of the problem.

Afterwards the main part of the work consisted in the development of a semi-analitic calculation code based on a mechanical model able to simulate the be-haviour of the damaged material subjected to a compression load and to calculate the residual resistance; this model has been implemented in Matlab code, validated and applicated to some structures of the new small european launcher Vega.

Sommario

La presente relazione riporta il lavoro effettuato durante lo stage di cinque mesi svoltosi presso la Direzione Lanciatori dell’Agenzia Spaziale Francese (CNES) a Evry (Parigi) - Francia per il conseguimento della Laurea Specialistica in Ingeg-neria Meccanica. Lo scopo del lavoro `e stato quello di sviluppare una procedura semplificata di previsione della resistenza residua di strutture in materiale compos-ito danneggiate da impatto.

Tale necessit`a partiva dalla volont`a di semplificare il processo di qualifica delle strutture in composito riducendo i costi ed i tempi necessari per la determinazione delle propriet`a residue di un materiale danneggiato superando i limiti dei principali approcci ad oggi utilizzati, come test sperimentali e modelli ad elementi finiti. Importante premessa da fare riguarda la notevole difficolt`a che ogni autore che ha affrontato il problema ha trovato nell’analisi del processo di impatto, caratteriz-zato da fenomeni spesso difficili se non impossibili da modellare e da una elevata complessit`a del problema nel suo insieme.

Il lavoro si `e quindi concretizzato partendo da una iniziale profonda e ampia analisi della letteratura tecnica sull’argomento, che `e stata pure spunto per la creazione di una base dati che si `e rivelata utilissima nelle fasi successive.

All’analisi dello stato dell’arte `e seguita una lunga fase di studio dei dati speri-mentali, che sfruttando le conoscenze sviluppate nella prima fase ha portato alla determinazione di alcune leggi sperimentali che permettono, rispettando la fisica del problema, di fare delle previsioni piuttosto efficaci di molti aspetti del prob-lema.

Successivamente la parte principale del lavoro `e consistita nello sviluppo di un codice di calcolo semi-analitico basato su un modello meccanico che fosse in grado di simulare il comportamento del materiale danneggiato sottoposto ad un carico di compressione e di calcolarne la resistenza residua; tale modello `e stato poi im-plementanto in codice Matlab, validato ed applicato ad alcune strutture del nuovo piccolo lanciatore europeo Vega.

Contents

I

Introduction

14

1 The impact problem 15

1.1 Damage Resistance, Durability and

Damage Tolerance . . . 17

1.2 Damage Tolerance approaches . . . 18

1.3 Low-velocity impact . . . 19 1.4 Quasi-static assumption . . . 22 1.5 Internal Damage . . . 25 1.6 Concept of BVID . . . 31 1.7 An innovative way: ”‘three-dimensional”’ laminates . . . 35 2 Influence of parameters 38 2.1 The indirect effect and the absorbed energy . . . 40

2.2 Mass and velocity of the impactor . . . 44

2.3 Thickness . . . 46

2.4 Stacking sequence . . . 47

2.5 Curvature of the specimen . . . 51

2.6 Shape and dimensions of the impactor . . . 54

2.7 Shape of the specimen, boundary conditions and dimensions . . . . 57

2.7.1 Shape of the specimen . . . 57

2.7.2 Dimensions . . . 57

2.7.3 Boundary conditions . . . 58

2.8 Material properties . . . 59

5

3 Approaches to the problem 61

3.1 Experimental approach . . . 61

3.1.1 Drop Weight Test (DWT) . . . 62

3.1.2 Non-Destructive Techniques for damage detection (NDT) . . 64

3.1.3 Cross-sectioning . . . 70

3.1.4 Compression After Impact test (CAI) . . . 71

3.1.5 Advantages/Disadvantages . . . 72

3.2 Finite elements approach . . . 75

3.2.1 Advantages/Disadvantages . . . 76

3.3 Industrial approaches: the qualification process . . . 77

II

Development of the

assessment method

79

4.2 First approaches . . . 81

4.3 Why a semi-analytic method . . . 81

4.4 Work phases . . . 82

5 Development of the assessment method 85 5.1 Introduction . . . 85

5.2 Contact force and deflection evaluation . . . 88

5.2.1 Contact Energy Ec . . . 90

5.2.2 Bending, Shear Energy Ebs . . . 91

5.2.3 Membrane Energy Em . . . 92

5.2.4 Solution Procedure . . . 92

5.2.5 Circular-square shape analogy . . . 94

5.3 Determination of the correlation between impact energy and delaminated area (Damage Model) . . . 96

6

5.3.2 Adimensional quantities - Introduction of the DTL . . . 97

5.3.3 Effect of stiffness . . . 98

5.3.4 Effect of stacking sequence . . . 98

5.4 Development of the successive sublaminate buckling iterative process (Failure Model) . . . 111

5.4.1 The Delamination Buckling theory . . . 112

5.4.2 The successive sublaminate buckling process . . . 116

5.4.3 Delamination distribution . . . 119

5.5 Determination of the correlation between the dent depth and the impact energy (Indenting Model) . . . 125

5.6 Development of the complete code in Matlab . . . 134

5.6.1 Implementation of the Failure Model . . . 134

5.6.2 Results . . . 138

6 Validation of the assessment method 141 6.1 Validation of the Failure Model . . . 141

6.1.1 [45, 0, −45, 90]6S Tply=0.125 mm AS4/3502 (Ref. [8]) . . . . 142

6.1.2 [45, 0, −45, 90]2S Tply=0.25 mm T300/914 (Ref. [24]) . . . . 144

6.1.3 [45, −45, 90, 0]6S Tply=0.125 mm IM7/8551-7 (Ref. [24]) . . 146

6.2 Validation of the complete assessment method . . . 149

6.2.1 [45, 0, −45, 90]6S Tply=0.125 mm AS4/3502 (Ref. [8]) . . . . 150

6.2.2 [45, 0, −45, 90]2S Tply=0.25 mm T300/914 (Ref. [24]) . . . . 151

6.2.3 [45, −45, 90, 0]6S Tply=0.125 mm IM7/8551-7 (Ref. [24]) . . 152

6.2.4 [02, 45, −45, 02, 45, −45, 0, 90]STply=0.15 mm T300/914 (Ref. [34])152 6.2.5 [02, 45, −45, 90, 45, −45, 02, 45, −45]STply=0.15 mm T300/914 (Ref. [34]) . . . 153

7 Applications of the assessment method 157 7.1 Application of the tool to complete structures . . . 157

7.2 The VEGA program . . . 159

7 8 Conclusions and Future devolopments 164

8.1 Conclusions . . . 164

8.2 Future developments . . . 166

III

Appendices

168

A.2 Functions . . . 190 A.2.1 DBcritDOWN . . . 190 A.2.2 DBcritUP . . . 197 A.2.3 DBredstiffDOWN . . . 203 A.2.4 DBredstiffUP . . . 210 A.2.5 fb . . . 217 A.2.6 fbNASA . . . 217 A.2.7 ff . . . 217 A.2.8 ffNASA . . . 218 A.2.9 ffNASAKH . . . 218 A.2.10 globbuck . . . 218 A.2.11 laminate . . . 219 A.2.12 matriceQ . . . 220 A.2.13 matrici . . . 220 A.2.14 strength . . . 221

B ”CAIAM” Tool User Manual 223

List of Figures

1.1 16 plies quasi-isotropic laminates subjected to high and low velocity

impacts with an energy of about 12 J (Ref. [7]) . . . 20

1.2 Typical surface damage in a low velocity impact . . . 21

1.3 Typical impact threat for an aircraft structure (Ref. [4]) . . . 21

1.4 Top ply cracking due to contact stresses . . . 26

1.5 Cracking through other plies due to contact stresses . . . 27

1.6 Transverse cracks in adjacent 45◦ and 0◦ plies joined via delamination 28 1.7 Schematic representation of cross-sectional view of transverse cracks and delaminations due to contact forces . . . 28

1.8 Conical shape of the delamination distribution through the thickness 30 1.9 Laser profilometer apparatus used for dent depth measurements . . 32

1.10 Dent depth profiles for different energies . . . 33

1.11 Laser profilometer dent depth plots for different energies . . . 33

1.12 Comparison of C-scan images for unpinned (left) and pinned (right) specimen . . . 37

1.13 Side view of buckling failure during CAI test for unpinned (top) and pinned (bottom) plates . . . 37

2.1 Direct (left) and indirect (right) effects scheme . . . 39

2.2 Impact energy level . . . 41

2.3 Effect of stacking sequence . . . 42

2.4 Typical load and energy vs time plot . . . 42

2.5 Normalized delamination vs impact energy with empirical relations 44 2.6 Influence of impactor mass (Ref. [8]) . . . 45

2.7 Delamination shapes and orientations (Abrate, 1998) . . . 49 8

9 2.8 Conical shape of the delamination distribution through the thickness 50 2.9 Ply by ply delamination areas for two different stacking sequence . 50

2.10 System configuration and cylindrical coordinates . . . 53

2.11 Overview of impactors . . . 54

2.12 Impact load histories obtained by different impactors . . . 55

2.13 Cross sectional observation for the impacted specimen by a) hemi-spherical, b) flat, c) conical, d) pyramid impactors . . . 56

2.14 Summary of impactor shape effects on peak load, delamination area and CAI strenght . . . 56

2.15 Recapitulation of the indirect effects . . . 60

3.1 Scheme of the test for ring filled of propellant. NASA . . . 62

3.2 (a) Drop weight impact machine (b) Standard Boeing support fix-ture . . . 63

3.3 Standard Boeing support fixture . . . 64

3.4 A, B and C-scan images . . . 66

3.5 Typical ultrasonic C-scan images . . . 67

3.6 Typical x-ray image . . . 69

3.7 Cross-sections of two different specimens with their x-rays showing where the cuts were made (Ref. [10]) . . . 71

3.8 Instrumentation of compression testing . . . 73

3.9 Position of laser and strain gauges . . . 73

3.10 CAI test equipment . . . 74

3.11 Typical FE model of an impact problem . . . 75

3.12 Scheme of the qualification process . . . 77

4.1 Flow chart of the base idea for the assessment method . . . 84

5.1 Flow chart of the assessment method . . . 87

5.2 Impact Force versus Time . . . 88

5.3 Impact Force versus Deflection . . . 89

5.4 Bending and membrane stiffness parameters . . . 93

10

5.6 Plot of Delaminated Area vs Impact Energy . . . 101

5.7 Plot of Delaminated Area vs Specific Impact Energy . . . 102

5.8 Plot of DA/T2 _{vs IE/(T · DT L) . . . 103}

5.9 Plot of DA/T2_{· w/T vs IE/(T · DT L) . . . 104}

5.10 SSF1 trend . . . 105

5.11 SSF2 trend . . . 105

5.12 SSF global trend . . . 106

5.13 Plot of DA/T2_{· w/T · 1/SSF vs IE/(T · DT L) . . . 107}

5.14 Detail of the plot with the traditional DT L . . . 108

5.15 Detail of the plot with the modified DT L . . . 108

5.16 Plot of DA/T2_{· w/T · 1/SSF vs IE/(T · DT Lmod) . . . 109}

5.17 Delamination: experimental vs calculated . . . 110

5.18 Buckling modes . . . 111

5.19 Critical strain versus damage size (Ref. [14]) . . . 113

5.20 Symbology for the delamination buckling theory . . . 114

5.21 Local Buckling modes . . . 117

5.22 C-scan image for a quasi-isotropic laminate, Ref. [30] . . . 120

5.23 C-scan image for an angle-ply laminate, Ref. [30] . . . 120

5.24 Delamination distribution through the thickness . . . 121

5.25 Method for calculation of the equivalent diameter . . . 121

5.26 Conical shape in the thickness . . . 122

5.27 Flow chart of the Failure Model (DB-LPF . . . 124

5.28 Relationship between Dent Depth and Impact Energy for different thicknesses . . . 126

5.29 Dent Depth vs Impact Energy for different thicknesses and material sets . . . 129

5.30 Dent Depth vs Impact Energy for different thicknesses and material sets with interpolation curves . . . 130

5.31 Detailed view of the zone of interest in the Dent Depth vs Impact Energy plot . . . 131

11 5.32 Plot of C fitting coefficients vs thickness T and exponential

inter-polation curve . . . 132

5.33 Operative scheme for the impact energy evaluation . . . 133

5.34 Matlab code output: delamination distribution through the thickness 140 6.1 [45, 0, −45, 90]6S Tply=0.125 mm AS4/3502 . . . 143

6.2 [45, 0, −45, 90]2S Tply=0.25 mm T300/914 . . . 145

6.3 [45, −45, 90, 0]6S Tply=0.125 mm IM7/8551-7 . . . 147

6.4 Correlation between experimental and calculated values . . . 148

6.5 Correlation between experimental and calculated values . . . 154

6.6 CAI vs Impact Energy for a specific set . . . 155

6.7 Comparison of CAI vs Impact Energy plots . . . 156

7.1 Artistic view of the VEGA launcher . . . 159

7.2 Structure of the VEGA launcher . . . 160

List of Tables

1.1 System response . . . 22

1.2 System response . . . 22

1.3 Impact duration for a woven fabric composited plate, clamped bound-ary conditions, impact energy of 24.03 J , impactor mass of 4.71 kg and impact velocity of 3.19 m/s, Ref. [19]. . . 24

1.4 Comparison of natural period and impact durations for specimen of different curvatures. Ref. [21] . . . 24

1.5 Dent depth results for different impact energies. Ref. [24] . . . 34

1.6 Dent depth results for an impact energies corresponding to a BVID damage of 0.5 mm. Ref. [24] . . . 34

1.7 Residual compressive strenght for unpinned and pinned specimens. Ref. [27] . . . 36

2.1 Parameters classification . . . 39

2.2 Duration of impact for different thicknesses and the same impact energy. Ref. [19] . . . 48

2.3 Comparison of natural period and impact durations for specimen of different curvatures. Ref. [21] . . . 53

2.4 Results for Ref. [12] . . . 59

5.1 C and n coefficients for different thicknesses . . . 127

6.1 [45, 0, −45, 90]6S Tply=0.125 mm AS4/3502 . . . 142

6.2 [45, 0, −45, 90]2S Tply=0.25 mm T300/914 . . . 144

6.3 [45, −45, 90, 0]6S Tply=0.125 mm IM7/8551-7 . . . 146

6.4 [45, 0, −45, 90]6S Tply=0.125 mm AS4/3502 . . . 150

13 6.5 [45, 0, −45, 90]2S Tply=0.25 mm T300/914 . . . 151

6.6 [45, −45, 90, 0]6S Tply=0.125 mm IM7/8551-7 . . . 152

6.7 [02, 45, −45, 02, 45, −45, 0, 90]S Tply=0.15 mm T300/914 . . . 152