INVESTIGATING FAILURE IN COMPOSITE STIFFENER RUN …...energy release rates for debonding and...

IMPERIAL COLLEGE LONDON

INVESTIGATING FAILURE IN COMPOSITE STIFFENER RUN-OUTS

Spyridon Psarras

Department of Aeronautics South Kensington Campus Imperial College London

London SW7 2AZ U.K.

This thesis is submitted for the degree of Doctor of Philosophy of Imperial College London

2013

'' Πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει.''

Αριστοτἐλης

Abstract The aim of this thesis is to improve the understanding of failure initiation and propagation, in

stractural composites featuring geometrical discontinuities. In particular, this study focuses

on stiffener run-outs as these are particularly significant in the aerospace industry. The

improved understanding achieved in this project results in a direct comparison of the

performance of different stiffener run-out configurations, and contributes towards validating

the applicability of failure models to representative structural components.

In this work, the use of a compliant web design for improved damage tolerance in stiffener

run-outs is investigated. Three different configurations were compared to establish the merits

of a compliant design: a baseline configuration, a configuration with optimised tapering and a

compliant configuration. The performance of these configurations, in terms of strength and

damage tolerance, was compared numerically using a parametric finite element analysis. The

energy release rates for debonding and delamination, for different crack lengths across the

specimen width, were used for this comparison.

The three configurations were subsequently manufactured and tested. The manufacturing

process used in this study led to sound skin-stiffener run-outs whose design was validated

against a numerical study. In order to monitor the failure process, Acoustic Emission (AE)

equipment and Digital Image Correlation (DIC) were used. AE data recorded during skin-

stiffener run-out compression tests proved useful to analyse the failure processes which take

place in these specimens.

The predicted failure loads, based on the energy release rates, showed good accuracy,

particularly when the distribution of energy release rate across the width of the specimen was

taken into account. It was shown that the compliant configuration failed by debonding and

showed improved damage tolerance compared to the baseline and tapered stiffener run-outs.

It can be concluded that the variation of the energy release rate across the width should be

considered when stiffener run-outs are designed. The results further show that, in the design

of skin-stiffener run-outs, it is important to consider the possibility of failure modes other

than debonding, and that compliant termination schemes offer the possibility of improved

damage tolerance.

Acknowledgments The author would like to acknowledge the funding of this research from the Engineering and

Physical Sciences Research Council and the Ministry of Defence under the project

EP/E023967/1 is gratefully acknowledged.

For their constant supervision, guidance and advice throughout the last four years, the author

would like to thank both his supervisors, Dr. Silvestre Pinho and Prof. Brian Falzon.

The interest, involvement and participation of Dr. Irene Guiamatsia, Dr. Jesper Arkensen, Mr.

Nikolaos Sogias, Mr. Vinoo Mohan, Mr. José M L Gutiérrez and author's research group

colleagues is acknowledged.

The author would also like to thank Mr. Gary Senior and Mr. Jon Cole for help with the

manufacturing process of specimens; and Mr. Joseph Meggyesi for help with experimental

testing.

Finally, the author would like to acknowledge his family for their constant support and

inspiration.

Declaration The work in this thesis is based on research carried out at Imperial College London and it is

all the authors own work unless referenced.

Contents

Table of contents

ABSTRACT ................................................................................................................................................... 3

1 INTRODUCTION .............................................................................................................................17

1.1 BACKGROUND AND MOTIVATION ...................................................................................................17 1.2 OBJECTIVES .....................................................................................................................................20 1.3 OUTLINE ..........................................................................................................................................21 1.4 DISSEMINATIONS AND PUBLICATIONS ...........................................................................................22

2 LITERATURE REVIEW ................................................................................................................23

2.1 COMPOSITE FRACTURE AND FAILURE MECHANISMS ....................................................................23 2.1.1 Failure in composites ...........................................................................................................23 2.1.2 Failure criteria .....................................................................................................................26

2.2 INTERACTION BETW EEN DAMAGE MECHANISMS ...........................................................................28 2.3 FAILURE MODELS ............................................................................................................................28

2.3.1 Fracture mechanics..............................................................................................................28 2.3.2 VCCT.....................................................................................................................................29 2.3.3 Damage mechanics ..............................................................................................................29 2.3.4 Cohesive models ...................................................................................................................29 2.3.5 X-FEM...................................................................................................................................32

2.4 STRESS CONCENTRATION PROBLEM ...............................................................................................33 2.4.1 Open hole problem ...............................................................................................................33 2.4.2 Adhesive Joints .....................................................................................................................34

2.5 COMPOSITE PANEL AND STIFFENER DESIGN .................................................................................36 2.6 STIFFENER BUCKLING .....................................................................................................................38 2.7 DAMAGE IN STIFFENERS .................................................................................................................41

2.7.1 Experimental state of art......................................................................................................41

Contents - Table of contents

2.7.2 Simulation state of the art ....................................................................................................45 2.8 DISCUSSION AND CONCLUSIONS .....................................................................................................47

3 MATERIAL CHARACTERIZATION .........................................................................................50

3.1 INTRODUCTION ................................................................................................................................50 3.2 STIFFNESS AND STRENGTH CHARACTERIZATION ..........................................................................50

3.2.1 Introduction ..........................................................................................................................50 3.2.2 Manufacturing ......................................................................................................................50 3.2.3 Testing ...................................................................................................................................54 3.2.4 Results ...................................................................................................................................65

3.3 FRACTURE TOUGHNESS CHARACTERIZATION ...............................................................................66 3.3.1 Introduction ..........................................................................................................................66 3.3.2 Manufacturing ......................................................................................................................66

3.4 TESTING ...........................................................................................................................................68 3.4.1 DCB .......................................................................................................................................68 3.4.2 4 ENF ....................................................................................................................................72

4 NUMERICAL DESIGN OF STIFFENER RUN-OUTS FOR DAMAGE TOLERANCE....75

4.1 INTRODUCTION ................................................................................................................................75 4.2 STRESS PROFILE AT INTERFACES WITH GEOMETRICAL AND MATERIAL DISCONTINUITIES...........76

4.2.1 Theoretical Analysis .............................................................................................................76 4.2.2 Stiffener run-out Designs .....................................................................................................82

4.3 FE MODELS .....................................................................................................................................86 4.3.1 The Model .............................................................................................................................86 4.3.2 Mesh Sensitivity Study..........................................................................................................86 4.3.3 Model analysis and results ..................................................................................................88

4.4 ENERGY RELEASE RATE FOR DEBONDING ......................................................................................94 4.4.1 The FE model........................................................................................................................95 4.4.2 The Python script................................................................................................................102

4.5 RESULTS FROM MODELLING .........................................................................................................102 4.5.1 Energy Release rate along crack.......................................................................................102 4.5.2 2nd iteration .........................................................................................................................104 4.5.3 Energy release rate along the width of the crack tip .......................................................109 4.5.4 Modelling debonding failure using VCCT........................................................................111

4.6 CONCLUSIONS ...............................................................................................................................113

5 MANUFACTURING AND TESTING PROCEDURES...........................................................114

5.1 MANUFACTURING OF STIFFENER SPECIMENS ..............................................................................114

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5.1.1 Skin ......................................................................................................................................114 5.1.2 Stiffener ...............................................................................................................................116 5.1.3 Filler....................................................................................................................................117 5.1.4 Bonding ...............................................................................................................................119

5.2 TESTING OF STIFFENER RUN-OUTS................................................................................................121 5.2.1 Digital Image Correlation .................................................................................................121 5.2.2 Acoustic Emission ..............................................................................................................121 5.2.3 Results .................................................................................................................................122

5.3 2ND ITERATION ...............................................................................................................................125 5.4 CONCLUSIONS ...............................................................................................................................129

6 DETAILED DAMAGE MODELLING FOR TAPERED RUN-OUT STIFFENERS..........130

6.1 INTRODUCTION ..............................................................................................................................130 6.2 BEBONDING OF THE TAPERED STIFFENER ....................................................................................131

6.2.1 Mode interaction ................................................................................................................134 6.2.2 Response of the Numerical Model.....................................................................................135

6.3 MODELING THE INTERLAMINAR FAILURE OF THE TAPERED STIFFENER......................................136 6.3.1 Cohesive zone damage modelling definitions...................................................................136 6.3.2 Response of the model ........................................................................................................136

6.4 MODELLING THE INTRALAMINAR FAILURE ..................................................................................137 6.5 MODELING THE EXPERIMENTAL RESULTS ....................................................................................142

6.5.1 Interaction properties ........................................................................................................143 6.5.2 Delamination investigation around the filler tip point ....................................................144 6.5.3 Delamination investigation across the filler ....................................................................144

6.6 MODELING USING XFEM .............................................................................................................147 6.7 MODELING USING LARC...............................................................................................................149 6.8 COMPARISON OF THE FAILURE MODELS .......................................................................................151 6.9 CONCLUSIONS ...............................................................................................................................152

7 CONCLUSIONS..............................................................................................................................153

7.1 NUMERICAL ANALYSIS..................................................................................................................154 7.2 THE MANUFACTURING AND TESTING PROCESSES ........................................................................154 7.3 DETAIL MODELING OF RUN-OUT STIFFENERS ...............................................................................155

8 FUTURE WORK ............................................................................................................................157

8.1 USING THIS STUDY IN OTHER STRUCTURES ..................................................................................157 8.2 OTHER PARAMETERS IN THE PARAMETRIC STUDY .......................................................................157 8.3 STUDY IN FATIGUE ........................................................................................................................157

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8.4 EXPLOITING FURTHER THE PYTHON SCRIPT, THE MANUFACTURING METHOD AND THE TEST

RESULTS .........................................................................................................................................158 8.5 OBTAIN FAILURE DATA FOR DAMAGE MODELS ............................................................................158

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Figures

Table of figures

Figure 1.1: Composites in Airbus A380 [1]...............................................................17

Figure 1.2: Premature wing-structure failure at the stiffener run-out region..

[2] ........................................................................................................18

Figure 1.3: Use of stiffeners.......................................................................................19

Figure 1.4: Stiffener run-out and its consisting parts. .................................................20

Figure 2.1: Micrograph from a kink band ..................................................................26

Figure 2.2: Intra and interlaminar failure, (0,90)s.......................................................31

Figure 2.3: DCB specimen ..........................................................................................31

Figure 2.4: Load versus displacement curve obtained from the simulation with

the analytical solution..........................................................................32

Figure 2.5: Complete failure of a composite plate with a hole [41] ...........................34

Figure 2.6: Scheme of a single lap [42] ......................................................................35

Figure 2.7: Bonded Joint Failure Scenarios ................................................................35

Figure 2.8: Stiffened plate geometry [48] ...................................................................37

Figure 2.9: I-stiffened panel. Buckling at 11 tonnes, failure at 48 tonnes [55] ..........39

Figure 2.10: Component specimen [57]......................................................................40

Figure 2.11: Summary of growth directions [60] .......................................................42

Figure 2.12: Edge view of the damaged specimens [66] ............................................44

Figure 2.13: Stringer stiffened panel subjected to shear loading [73] ........................47

Figure 3.1: Arrangement for producing laminates in Autoclave [47].........................51

Figure 3.2: Schematic of plates ...................................................................................51

Figure 3.3: The C-scans of the plates..........................................................................52

Figure 3.4: Manufacturing of compression specimen [9] ...........................................53

Figure 3.5: Specimen dimensions ...............................................................................54

Figures - Table of figures

Figure 3.6 : Compression specimens inside the rig ....................................................55

Figure 3.7: Compression specimens after testing .......................................................55

Figure 3.8: Failure strengths of longitudinal compression specimens .......................56

Figure 3.9: Bending versus strain for the longitudinal compression specimen ..........56

Figure 3.10: Stress-strain curves for the longitudinal compression specimens ..........57

Figure 3.11: Failure strengths of the transverse compression specimens ...................57

Figure 3.12: Bending versus strain for the transverse compression specimen ...........58

Figure 3.13: Stress-strain curves for the transverse compression specimens ............58

Figure 3.14: Testing of tensile specimen ....................................................................59

Figure 3.15: Tensile specimens after testing, 0o on the left and 90o on the right........60

Figure 3.16: Failure strength of the longitudinal tension specimens ..........................60

Figure 3.17: Stress-strain curves of the longitudinal tension specimens ....................61

Figure 3.18: Failure strength of the transverse tension specimens .............................61

Figure 3.19: Stress-strain curves of the transverse tension specimens .......................62

Figure 3.20: Shear specimens after testing .................................................................62

Figure 3.21: Failure strength of shear specimens ......................................................63

Figure 3.22: Stress-Strain curves of the shear specimens that were tested

without unloading ................................................................................64

Figure 3.23: Stress-Strain curves of shear specimens that were tested with

unloading .............................................................................................64

Figure 3.24: Schematic of plate for the fracture toughness specimens and the

C-scan of the plate ...............................................................................67

Figure 3.25: Precraking of a DCB specimen ..............................................................68

Figure 3.26: DCB specimen [7] ..................................................................................69

Figure 3.27: Testing a DCB specimen ........................................................................69

Figure 3.28: Load-displacement traces for DCB specimens......................................70

Figure 3.29: R-curves for DCB specimens using the Modified Beam Theory

(MBT) Method ....................................................................................70

Figure 3.30: R-curves for DCB specimens using the Compliance Calibration

(CC) Method........................................................................................72

Figure 3.31: the 4ENF test fixture ..............................................................................72

Figure 3.32: Testing a 4ENF specimen.......................................................................73

Figure 3.33: Load displacement curves for the 4ENF specimens...............................74

Figure 3.34: R-curves for 4ENF specimens ................................................................74

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Figure 4.1 : Close-form model ....................................................................................76

Figure 4.2: Free Body Diagram ..................................................................................78

Figure 4.3 : Plot of peeling stresses from analytical solution .....................................80

Figure 4.4: A study on how variables (a) and (b) affect the solution. ......81

Figure 4.5: Stiffener dimensions in mm [63] ..............................................................82

Figure 4.6 : The designs of the stiffeners that were studied. .....................................83

Figure 4.7: An example of naming code of meshing models, here a 1-10-80

model. ..................................................................................................87

Figure 4.8: Peeling stresses for different meshes along path 1 ..................................87

Figure 4.9: Max peeling stresses for different meshes................................................88

Figure 4.10: The paths where the stresses were calculated.........................................88

Figure 4.11: Peeling stresses along Path 1 ..................................................................89

Figure 4.12: Shear stresses along Path 1 .....................................................................89

Figure 4.13: Peeling stresses in Path 1 near the edge of the stiffener .........................90

Figure 4.14: Shear stresses in Path 1 near the edge of the stiffener...........................91

Figure 4.15: Peeling stresses in Path 2........................................................................92

Figure 4.16: Shear stresses in Path 2...........................................................................92

Figure 4.17: Peeling stresses in Path 3........................................................................93

Figure 4.18: Shear stresses in Path 3...........................................................................93

Figure 4.19: Designs and dimensions in mm of a) the baseline stiffener and b)

the parametric stiffener. .......................................................................94

Figure 4.20: The FE model of a specimen with the boundary conditions. .................96

Figure 4.21: Commonly used element families [4].....................................................96

Figure 4.22: Stacking sequence for the skin ...............................................................97

Figure 4.23: Course mesh for the modified design with 3D continuum elements......98

Figure 4.24: Surfaces constraints between the skin (master surface-red) and the

adhesive (slave surface-pink) ...............................................................99

Figure 4.25: Modified model with BC-1 on the left edge (clamped) and BC-2

on the right edge ( zU =1) ...................................................................100

Figure 4.26: Strain energy with composite lay-up (blue line) and with material

orientations (red line) ........................................................................101

Figure 4.27: Normalized energy release rates as a function of crack length (a)

comparison between Baseline stiffener design and selected

k 1 2/D D


Tapered stiffener with b = 3 mm, c = 10 mm and d =6.25 mm),

(b) Influence of parameter b on G, (c) Influence of parameter c

on G and (d) Influence of parameter d on G. ....................................103

Figure 4.28: (a) Front view of failed specimen; (b) Exploded view showing the

failed area; (c) Front view of Bottom part showing 00 plies ; (d)

Bottom view of the Upper part showing delaminated 450 plies ........104

Figure 4.29: Compliant Skin-Stiffener designs.........................................................105

Figure 4.30: a) Tapered stiffener after testing, b) FE model showing

delamination path, and c) FE model of a specimen with

boundary conditions. .........................................................................106

Figure 4.31: Normalized strain energy release rates as a function of crack

length showing a comparison between designs. The points were

obtained numerically and the curves are spline fits...........................107

Figure 4.32: Normalized energy release rates of the Compliant design of

different (w, h) values for (a) debonding and (b) delamination ........107

Figure 4.33: Stiffener design configurations (dimensions in mm). .........................108

Figure 4.34: Normalized strain energy release rates as a function of crack

length; comparison between Baseline stiffener design (Figure

4.33α), Tapered stiffener (Figure 4.33Figure 4.19b) and

Compliant stiffener (Figure 4.33Figure 4.19c) with dimensions

b=3 mm, c=10 mm and d=6.25 mm. .................................................109

Figure 4.35: Normalized GT/Gc across the crack tip for crack a = 1 mm for the

Baseline, Tapered and Compliant specimens....................................110

Figure 4.36: Comparing the results of the parametric study with the VCCT

method (a) along the crack and (b) along the width of the

stiffener..............................................................................................112

Figure 4.37: The refined model that was used in the VCCT method ......................113

Figure 5.1: Hand lay-up for the skin plates. ..................................................................115

Figure 5.2: Curing procedure on the Autoclave.......................................................115

Figure 5.3: The cutting schedule ..............................................................................116

Figure 5.4: Mould for the stiffener. All dimensions are in mm. ..............................117

Figure 5.5: Mould for the filler. All dimensions are in mm......................................118

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Figure 5.6: Micrographics of (a) the stiffener, (b) a zoomed area of the

stiffener, (c) filler made by stacked stripes and (d) filler made by

twisted tows. ......................................................................................118

Figure 5.7: Bonding stage with the skin, the stiffener and the adhesive film in

the wooden mould .............................................................................119

Figure 5.8: Specimens’ ends potted in epoxy resin .........................................................120

Figure 5.9: (a) Baseline stiffener specimen; (b) Tapered stiffener specimen

(identical flange geometry to Compliant type (b-i) profile of the

Tapered stiffener specimen; (b-ii) profile of the Compliant

stiffener specimen..............................................................................120

Figure 5.10: AE testing equpment ............................................................................122

Figure. 5.11: Failure loads for the baseline design and the modified design

specimens, as well as the predicted failure loads using Eq.

3.23. ...................................................................................................122

Figure 5.12: Load-Displacement and AE Amplitude-Displacement curves for

the baseline and the modified stiffener. The numbered pictures

present the displacements obtained with the DIC. ............................123

Figure. 5.13: A. (a) Baseline stiffener; (b)-(c) detail before and after failure

respectively; (d)-(e) clean debonded surfaces in the skin and

stiffener respectively. B. (a) Tapered stiffener; (b)-(c) detail

before and after failure respectively; (d)-(e) delaminated

surfaces in the skin and stiffener respectively. ..................................124

Figure.5.14: Peak frequencies versus displacement for (a) Baseline and (b)

Tapered stiffeners. .............................................................................124

Figure. 5.15: (a) Design of the Compliant stiffener (b) Normalized energy

release rates as a function of debonding and delamination length

for the three configurations (c) Load-displacement curves for the

three configurations (d) Failed surface of Compliant specimen ......125

Figure 5.16: (a) Baseline stiffener, (b) Tapered Stiffener and (c) Compliant

Stiffener after failure respectively. ....................................................126

Figure 5.17: Loads and Peak frequencies versus displacement for a) the

Baseline b) the Tapered and c) the Compliant stiffeners. A scale

on the right hand side indicates the mode of failure typically

associated with these peak frequencies [80]......................................127

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Figure 5.18: The average signal level (ASL) of the three designs.............................128

Figure 6.1: The parts of the FE model ......................................................................131

Figure 6.2: Illustration of imposed cohesive properties for debonding mode. .........132

Figure 6.3: (a) Traction-separation law for cohesive zone models (b) Modified

law to implemented in FEM ..............................................................132

Figure 6.4: Finite element model of modified specimen. ........................................133

Figure 6.5: Damage growth pattern predicted by a cohesive model for the

modified specimen compared with energy release rate

predictions using VCCT ....................................................................135

Figure 6.6: Contour plot of CSDMG at the 0o/45o interface....................................137

Figure 6.7: Delamination occurred in the Tapered stiffener....................................137

Figure 6.8: Illustration of (a) 00 plies with Hashin damage model and (b)

cohesive properties at 00/450 interface ..............................................140

Figure 6.9: Contour plot of damage variable for matrix compression ......................141

Figure 6.10: Matrix crack at right flange in the experimentally failed specimen ....141

Figure 6.11: Crack bridging in the experimentally failed specimen .........................143

Figure 6.12: Cohesive properties imposed (Pink dots) on (a) Left stringer; (b)

Right stringer .....................................................................................143

Figure 6.13 Contour plot of cohesive damage variable with crack bridging

around the filler .................................................................................144

Figure 6.14: Contour plot of cohesive damage variable with crack bridging

across the filler at lowest plane. ........................................................145

Figure 6.15: Load-displacement of crack bridging plane models.............................146

Figure 6.16: Failure sequence of the stiffener from the XFEM model. (a) the

stiffener started to debond (b) without any delamination. (c) The

debonding propagated and the first XFEM element failed.(d)

without any delamination. (e) Debonding with failed filler

XFEM elements (f) accompanied with delamination........................148

Figure 6.17: Load- displacement curve of the XFEM model ..................................149

Figure 6.18: Load-displacement of LaRC'05 model and SDV8, matrix failure

post-history. .......................................................................................150

Figure 6.19: The failure loads of different failure models ........................................151

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Tables

Table 2-1: Composite failure criteria ..................................................................................... 27

Table 3-1: Function and characteristics of the manufactured plates...................................... 52

Table 3-2: Nominal dimensions of specimens ...................................................................... 53

Table 3-3: Comparison of the material properties ................................................................. 65

Table 3-4: Function and characteristics of the manufactured plate ....................................... 66

Table 3-5: Nominal dimensions of the fracture toughness specimens................................... 67

Table 4-1 : Values [63] .......................................................................................................... 80

Table 4-2 : Lay-up details ...................................................................................................... 84

Table 4-3: Material properties of IM7/8552 ......................................................................... 85

Table 4-4: Material properties for FM300 measured in house .............................................. 95

Table 4-5: Stacking sequence for the skin and the stiffener.......................................................... 97

Table 4-6: Mesh Sensitivity Study results................................................................................. 101

Table 4-7: Predicted failure load.......................................................................................... 111

Table 5-1: Composite ply orientations ................................................................................. 116

Table 5-2: Failure loads for the different specimen types, as well as the predicted

failure loads using Eq. 3.23. .............................................................................. 126

Table 6-1: Cohesive interaction properties .......................................................................... 133

Table 6-2: Debonding loads of the Tapered stiffner ............................................................ 135

Table 6-3: Intralaminar properties of IM7/8552 .................................................................. 139

Table 6-4: Failure loads of filler crack planes compared to experimental........................... 146

Table 6-5: XFEM interaction properties ............................................................................. 147

Chapter 1

Introduction

1 Introduction

1.1 Background and motivation The increasing demand for aerostructures with high stiffness/strength to weight ratio

has resulted in the increased use of laminated composite materials for structural

components. Figure shows the many composite parts that exist on the Airbus A 380.

Figure 1.1: Composites in Airbus A380 [1]

Chapter 1 - Introduction

There is great effort in developing analytical and numerical models in order to design

composite parts for aerostructures. The relevance to the aerospace industry has to do

with the significant cost reductions that reliable virtual component testing should

allow. Also, composite components are often over-designed and thus overweight and

costly. The understanding of the damage mechanisms and failure processes drives to

further improvements and better understanding of the behaviour of aerostructures.

Research has tended to focus on specific aspects of damage modelling in order to

gain detailed insight into the various damage mechanisms; however a model that

encompasses all aspects associated with failure and that is applicable to complex

composites is still lacking.

Figure 1.2: Premature wing-structure failure at the stiffener run-out region.. [2]

Laminated carbon-fibre composite structures are susceptible to failure from any local

stress concentration which gives rise to through-thickness stresses, Figure 1.2. Stress

concentrations induced by the presence of geometrical discontinuities in components

are becoming all the more critical, since composite laminates are brittle materials and

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are very sensitive to 3-D stress fields (intralaminar and interlaminar), so requiring an

increased level of accuracy in the analysis of their behaviour during failure.

Furthermore, the lack of reliable predictive models means that qualification and

certification of composite structures is time consuming and expensive, since extensive

coupon and element testing is required. Recently there have been significant

developments in the understanding and predictive tools for composites. By exploiting

these developments, the primary objective of the EDAVCOS programme (Efficient

Design And Verification of Composite Structures) [3] was to determine a cost

efficient route to certification for composite structures. This entailed a validated

analysis-based procedure for structural verification from initial design to final

certification. The targets were a 50% reduction of the total cost for verification and

60% time scale reduction. A key aspect of the EDAVCOS programme was the

development of predictive models for stiffened structures containing defects.

The buckling characteristics of thin plates are improved considerably by using

stiffening concepts such as skin/stiffener configurations or honeycomb sandwich

configurations rather than increasing the plate thickness, Figure 1.3, which is less

structurally efficient.

Figure 1.3: Use of stiffeners

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1.2 Objectives Composite damage modelling is a vibrant area of contemporary research, fuelled by

the strategic decision of the global aerospace industry to increase the amount of

composite materials used in structural aircraft components.

The latest generation of large passenger aircraft also use mostly carbon-fibre

composite material in their primary structure and there is a trend towards the

utilization of bonding of subcomponents in preference of mechanical fastening.

Current design philosophy requires that certain stiffeners are terminated (Figure 1.4),

for example due to an intersecting structural feature or an inspection cut-out. In these

circumstances, the loading in the stiffener must be diffused into the skin, leading to

complex three-dimensional stress-states. The development and utilization of reliable

virtual component testing, in the design of composite aerostructures, can potentially

yield significant cost reductions. Such reliability requires a thorough understanding

of the damage mechanisms and failure processes in realistic aerostructures,

particularly in critical regions such as stiffener run-outs.

Figure 1.4: Stiffener run-out and its consisting parts.

The current state-of-the-art is to model the initiation of damage followed by

propagation, whether this be unstable to failure or arrested at a structural feature. The

modelling of realistic composite structures containing geometrical discontinuities,

Web

AdhesiveFillerSkin

Flange

Noodle region

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such as stiffener sun-outs, faces significant difficulties and available tools are often

not capable of simulating the complex mechanisms of crack propagation.

In this thesis numerical models of the stiffened run-outs will be created and the

capability to predict the failure mechanisms observed will be assessed. The

mechanisms of damage initiation and propagation will be investigated using acoustic

and digital imaging monitoring equipment. The overall aim of this thesis is to analyse

the mechanical response of skin-stiffener run-outs. In particular, the following

objectives are addressed:

1. To propose a reliable methodology for the design of damage tolerant skin-

stiffener run-outs.

2. To develop well-defined skin-stiffener run-out configurations with improved

damage tolerance under compressive loads.

3. To develop an accurate manufacturing procedure for skin-stiffener run-outs,

with particular emphasis on the quality of the noodle region.

4. To investigate the potential and limitations of advanced failure models in the

analysis of skin-stiffener run-outs.

1.3 Outline

This thesis is organized into the following Chapters:

Chapter 2 reviews the literature in composite stiffener run-outs; the review starts with

composite failure, where failure mechanisms and interaction between them are

reviewed. It follows with stiffened panels focusing on their behaviour and the ways of

designing them, and ends with stiffener run-outs, where the modelling and testing

procedures are presented.

Chapter 3 describes the tests that were performed in order to characterize a specific

composite material, IM7/8552 carbon epoxy, and validate the FE models that was

developed.

Chapter 4 presents a numerical investigation that was developed with the commercial

software ABAQUS [4]. A number of numerical models were developed which

enabled the investigation of stiffener run-out designs. Based on the results of this

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analysis, a new run-out design was generated and a design optimization was followed

by using the scripting computer language Python [5].

In Chapter 5 the main topics are the manufacturing of the stiffener run-out

specimens with a selection of termination schemes and the testing procedure, where

the specimens were loaded in compression until failure and monitored using Digital

Image Correlation (DIC) and Acoustic Emission (AE).

Chapter 6 outlines more detailed FE models that simulate the exact failure of the

tested stiffener run-outs. Different ways of approaching the failure are compared

giving explanations of some experimental observations and an insight into the way of

modelling the failure in composite run-out stiffeners and the problems that can arise.

Finally, the conclusions of this thesis are highlighted in Chapter 7 and possible future

work is discussed in Chapter 8.

1.4 Disseminations and Publications The work presented in this chapter resulted in the following disseminations and

publications:

1. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigating the use of compliant webs in the damage-tolerant design of stiffener run-outs, accepted to Compos. B-Eng. 2012

2. Psarras, S., S.T. Pinho, and B.G. Falzon, Damage-tolerant design of stiffener run-outs A finite element approach, in Finite Element Analysis - New Trends and Developments, InTech Publishing. Publication date: August 2012, (ISBN 980-953-307-396-0)

3. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigating the Damage Tolerance Design of Stiffener Run-outs, 15th European Conference on Composite Materials, Italy, Venice, 24th June 2012

4. Psarras, S., S.T. Pinho, and B.G. Falzon, Design of composite stiffener run-outs for damage tolerance. Finite Elements in Analysis and Design, 2011. 47(8): p. 949-954

5. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigation of Stiffener Run-out Failure, 3rd Asian-Pacific International Symposium on Aerospace Symposium and 14th Australian Aeronautical Conference, Melbourne, Australia, 28th February 2011.

6. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigation of Stiffener Run-out Failure, 14th European Conference on Composite Materials, Budapest, Hungary, 7th June 2010.

Page | 22

Chapter 2

Literature Review

2 Literature Review

2.1 Composite Fracture and Failure Mechanisms The two constituents of a composite ply, matrix and fibre, have complementary roles

within the structure: the fibres carry the majority of the load while the matrix ensures

the continuity, cohesion and to an extent, the structural integrity of the composite

structure. Composite failure happens by mechanisms involving the individual failure

of each constituent, as well as additional mechanisms created by their interaction.

2.1.1 Failure in composites

Damage in composite materials, by observing the fracture surface, can be separated

into the following failure modes

• Interface crack

• In-ply crack

• Delamination

• Crack jumping

• Fibre breakage and bridging

This separation happens because fibre strain to failure can be greater or less than the

matrix. In dealing with damage progression it is postulated that the composite loses its

Chapter 2 - Literature Review

stiffness gradually until complete failure, when composite can no longer transmit

load. The load in the composite is the sum of the load in the fibres and matrix:

c f mP P P= + (2.1)

where P is the load and the symbols c , f and m are for composite, fibre and matrix

respectively. For P Aσ= and assuming that /f f cV A A= then

( )1c f f m fV Vσ σ σ= + − (2.2)

The above equation gives a relation between the composite, matrix and fibre stresses.

In order to see how this equation works, assuming that the fibre and the matrix are

elastic materials. If the fibre’s strain to failure is bigger than matrix’s, the load will be

carried from the fibres. When the fibres break, the load will be transferred to the

matrix. But the strength of the matrix is too low to carry the load and it will result to

the failure of the matrix. So the failure will happen when

( )1c f f m fV Vσ σ σ> + − (2.3)

In case that the matrix strain is bigger, the matrix will continue to carry the load and

the fibres will break. The matrix will carry load until

( )1c m fVσ σ= − (2.4)

Page | 24


If the fibres are made of a ductile material and the matrix is brittle, when the matrix

cracks, the load is shared between the fibre and the matrix.

( )' '' 1f f f f m fV V Vσ σ σ= + − (2.5)

where 'fσ is the stress carried by the fibre and matrix just prior to matrix cracking and

''fσ is the stress on fibre segments that bridge the crack. The progression of damage,

in typical carbon-fibre structural composites, is usually in the following sequence:

i) Matrix Cracking

The number of cracks depend on the type of the load. If the load is static, the number

of cracks will be lower than that caused by fatigue load. The ply thickness and the

direction of the fibres in neighbouring plies are also factors in nature and density of

cracks. As an example, in a uniaxial tension at a [0/90/45]s composite, the cracks will

start from the 90o ply and then will appear in the 45o ply.

ii) Delamination

Delamination is a life-limiting failure mode for laminated composites. It happens

because there are no fibres normal to the plane of lamination and the thin layers of

plies are low energy failure paths. A characteristic of delamination is that it has a

tendency to grow during cyclic loading. The interlaminar stresses can be calculated

using analytical models. In order to do this it is important to remember the type of

laminate, properties of the materials and the type of loading

iii) Fibre failure and interface debonding

When there is a strong interfacial bond between the matrix and the fibre, the crack

grows into the matrix and as a result a smooth cracked surface is created. On the other

hand, when there is a weak interfacial bond the failure surface is characterized by an

irregular surface and fibre pullout. In compression, misaligned fibres micro-buckle

Page | 25


under the maximum compressive stress, usually followed by in-plane or out-of-plane

kinking and delamination from adjacent plies, as shown in Figure 2.1.

Figure 2.1: Micrograph from a kink band

2.1.2 Failure criteria

The strain energy release rates (SERR) vary tremendously from one failure

mechanism to another - Beaumont [6] derived the expressions for the SERR

associated with the micro-mechanism of composite failure - which impacts the

evolution of damage.

Several criteria, often based on the stress field within the material, are used to detect

the occurrence of each of the mechanisms previously described; these are listed in

Table 2-1.

The first criteria that were used were based on average stresses that were generated by

strength comparison and curve fitting, without taking account into the detailed

analysis of the failure processes. Most criteria reflect the interaction between failure

modes that are observed experimentally. Criteria that do not assume interaction and

predict failure are the Maximum stress and strain criteria [7, 8] . These correlate the

strength with stresses and strains respectively, having the advantage of an easy to use

model to predict failure.

It is worth noting that these are failure initiation criteria; while any structural material

is inherently flawed, it is understood that the onset of damage corresponds to the

moment when micro-defects transform into a crack, and this happens for certain

measurable stress thresholds. When all stresses are taken into account in the failure

Page | 26


process, then interaction criteria are used. This type of criteria are the Tsai-Hill and

Tsai-Wu criteria and usually are in a form of a simple equation.

Moving to micro level, criteria such as Hashin [9] and Hashin-Rotem [10] take into

account the fibre and matrix failure and distinguish the failure modes. These mode-

differentiating criteria are proven to be more accurate and reliable in reproducing the

experimental observations, and are implemented in most finite element software.

Table 2-1: Composite failure criteria

Failure Criterion Interaction Prediction

Maximum stress

Maximum strain

Tsai-Hill

Tai-Wu stress

Tsai-Wu strain

Hashin

Puck

LaRC05

Additional references of interest include the results of the world wide failure exercise

[8, 10-17], an initiative of Soden and Hinton[18], Puck [19] and failure criteria

developed in conjunction with the NASA Langley Research Centre - LaRC03, Davila

et al. [20]. Recently, Pinho et al. [21-23] developed further the criterion to LaRC’05,

an advanced failure model that relies on physical criteria at the microscopic level, that

accurately predict lamina failure when comparing experimental data to various

strength based criteria.

Page | 27


2.2 Interaction between damage mechanisms A combination of damage mechanisms that interact with each other can result in

damage development in composites. These damage mechanisms can occur separately,

but when they interact with each other can lead to local material weakening at higher

rates. Greenhalgh [24] had observed experimentally that stiffened panel configurations

loaded in different ways suffered from delamination that started from matrix cracks.

This is a design limiting factor in many cases because of the presence of matrix cracks . At

the intersection of delamination fronts with incipient matrix cracks, large gradients in

the strain energy were encountered in an analytical study by Noh and Whitcomb [25],

emphasising how matrix cracks can influence and accelerate delamination growth.

2.3 Failure models

2.3.1 Fracture mechanics

The energy absorbing micro mechanisms in composites depend on several factors

such as the formation of the fracture surface of the crack, micro cracking and

secondary cracks, and the plastic deformation of the matrix in the crack tip region. For

a cracked body this energy is:

H W U= − (2.6)

where W is the work supplied by the external forces and U is the elastic strain energy

stored in the body. The criterion for crack growth is

cH G Aδ δ≥ (2.7)

where CG is the work required to create a unit crack area and Aδ the interface in the

crack area. The strain energy release rate is

HGA

∂=

∂ (2.8)

However, the fracture mechanics approach cannot always be easily incorporated in a

direct way into a progressive failure methodology because its application requires an

Page | 28


initial flaw. A common procedure consists in using first stress- strain criterion to

predict failure initiation and then use fracture mechanics for the crack propagation.

2.3.2 VCCT

Numerical approaches based on fracture mechanics require an initial flaw and they are

used in conjunction with techniques such as the Virtual Crack Closure (VCC) method

for the determination of the strain energy release rate. The VCC method is based on

Irwin’s assumption that when a crack extends by a small amount, the energy released

in the process is equal to work required to close the crack to its original length. The

energy release rates can then be computed from the nodal forces and displacements

obtained from the solution of a finite element model and crack propagation is

simulated by advancing the crack front when the local energy release rate rises to a

critical value. The method predicts delamination growth well; however, as

aforementioned, the structure must be pre-cracked and different meshes may be

required for each delamination front as soon as the crack advances.

2.3.3 Damage mechanics

Damage mechanics is another method for representing damage in composites.. The

first Damage Mechanics concepts were presented by Kachanov [26] and Rabotnov

[27]. Later, Ladeveze [28] proposed an in-plane model based on damage mechanics

to predict matrix micro cracking and fibre/matrix debonding in unidirectional

composites. The use of damage meso-modelling allows simulating and predicting the

damage state at any point of the structure until complete failure.

2.3.4 Cohesive models

Based on fracture mechanics concepts, the area under the curve defined by a traction

vs. displacement jump constitutive law is equal to the fracture energy or energy per

unit of area, and once this energy is consumed the crack propagates. In order to

simulate mixed mode delamination, stress based criteria are typically used for

initiation and interactive mixed-mode energy release rate criteria based on

experimental evidence is used for the propagation

Page | 29


An efficient implementation of cohesive models for delamination modelling which

has been widely reported in the literature consists of interface elements (also called

cohesive or decohesion elements). Interface elements offer the possibility of coupling

stress based criteria and fracture mechanics based criteria in a unified way. Therefore,

they enable the model to predict both initiation and growth of delamination. For bi-

dimensional problems, interface elements can be defined as a one dimensional

element inserted between two adjacent layers. In a similar way, they can be extended

for three-dimensional problems, in which the one dimensional elements are replaced

by two dimensional elements connecting adjacent layers.

In elastic cases, the interface elements are very stiff in order to ensure the transference

of displacement and traction between the adjacent layers. To model delamination

growth, an interfacial material behaviour is assumed to control the relative

displacements and traction between layers and as soon as certain failure criteria are

fulfilled, the delamination is allowed to initiate and propagate.

Crisfield and Davies [29] proposed a continuous interface element for delamination

modelling in fibre composites. The interface element was embedded between two

eight-noded isoparametric plane strain elements. A bi-linear softening stress-relative

displacement relationship was assumed for the interface material model and linear and

quadratic interaction criteria were used for mixed-mode prediction. For unloading

conditions, a simple elastic damage model was adopted in which the material was

assumed to unload directly towards the origin. Daudeville and Ladeveze [30]

proposed a delamination model based on a damage mechanics approach. In their

model, connecting layers were used to represent the resin rich interface between two

adjacent layers. Excellent agreement was obtained between simulations, experimental

and closed form solutions for mode I, mode II and mixed-mode delamination,

respectively.

To the knowledge of the author, this procedure has only been applied for the study of

impact damage; however, it might be a useful tool for enabling models with both

interface and in-plane damage to simulate such situations as crack jumping from an

interface to another or to model ply-damage inducing delamination as per Figure 2.2.

Page | 30


Figure 2.2: Intra and interlaminar failure, (0,90)s

As an example, a 2-dimensional Double Cantilever Beam (DCB) model was

performed with interface elements at every layer in ABAQUS CAE [4] using

COH2D4 elements and viscous regularization (μ=2.5×10-4), Figure 2.3. The

specimen was 170 mm long, 20 mm wide, 3.6 mm thick and the pre-crack length was

50 mm. The average mode I fracture toughness registered during the test is GIC = 0.28

kJ/m2 and the flexural Young’s modulus is E = 115 GPa. The specimen had three

main parts, two were the solid parts, which represented the adherents, and the third

part consisted of interface elements with thickness 0.001 mm. The appropriate

boundary conditions were set in order to represent the test conditions.

Figure 2.3: DCB specimen

The cohesive elements are extended in order to represent crack propagation and the

main material part separation from each other. The load versus displacement curve

Delamination

Intralaminar

170

3.6

crack50

Page | 31


obtained from the simulation is presented together with the analytical solution for

propagation in Figure 2.4.

Figure 2.4: Load versus displacement curve obtained from the simulation with the analytical solution

2.3.5 X-FEM

The extended finite element method (XFEM) offers a solution to two aspects of the

crack propagation problem: refinement around the crack tip, and the discontinuous

displacement field across the crack. Regarding the refinement issue, a typical FEM

solution is the use of p-refinement or special elements such as the quarter point

element, Barsoum[31], Lim et al.[32]. A more efficient strategy recognizes that the

required refinement is only a consequence of the fact that isoparametric shape

functions are inadequate for the interpolation in regions of highly varying gradients or

discontinuities. The idea is hence to incorporate the known field variation in the

interpolation functions. The extended finite element method is really a solution to

avoid mesh refinement in regions and gives excellent results for crack propagation.

However, the added-value for problems involving cohesive crack growth in

composite materials is not obvious.

0

10

20

30

40

50

60

0 5 10 15 20

Load

(KN

)

Displacement (mm)

DCB-2

corrected beam theory

Page | 32


2.4 Stress concentration problem

2.4.1 Open hole problem

One of the simplest example of stress concentration is a hole on a composite plate.

Open hole tests are currently a part of qualification process for composite parts. The

examination of the mechanical response of a composite plate with a hole is important

for aerospace applications where bolts and rivets are used for joining purposes.

Plates with open holes have been tested in tension and compression. A finite-element

approach has been developed by Wisnom and Chang [33] for modelling the detailed

damage development in notched composites. It was designed in a way that the model

could allow the delamination between the plies. Cross ply laminates were tested in

tension and a model that predicts the development of a delamination zone was

presented.

Pierron et al [34, 35] tested open hole composite specimens in tension using full-field

strain measurements. The strains were derived from displacements using local

differentiations and polynomial fitting. Another way of monitoring the damage

process were used by Yashiro et al. [36]. Fiber Bragg Grating (FBG) sensors

confirmed myltiple types of damage (e.g., splits, transverse cracks and delamination)

near the holes of CFRP laminates.

The interlaminar stress distributions around a circular hole in symmetric composite

laminates under in-plane tensile loading investigated by Hu et al [37]. 3D finite

elements were used. The delamination location and initiation were predicted by using

the finite elements and Ko-Lin stress results [38] together with a quadratic failure

criterion.

Independent polynomial spline approximation of displacement and interlaminar

tractions is proposed by E.V Iarve [39] for stress analysis in laminates with open

holes. Excellent agreement has been observed for interlaminar stresses in a [45/-45]s

AS4/3501-6 laminate under uniaxial tension. The polynomial spline approximation,

ideally suited for problems concerned with the singular solution behaviour, has been

applied to three dimensional stress analysis. The effect of thickness, ply orientation

and hole size were examined too [38]. Large fibre reinforced composite structures can

Page | 33


give much lower strengths than small test specimens, so a proper understanding of

scaling is vital for their safe and efficient use.

The most important variables of scaling effects on the strength of composites with

open holes have been identified from experimental tests as hole size, ply and laminate

thickness. These have been scaled both independently and simultaneously over a large

range of combinations by J. Lee [40]. The laminates that were tested were

unidirectional and multidirectional and it was found that the hole size effected the

strength reduction more than the thickness and the dimensions of the specimens. The

same size effects were studied by G Green [41] with the difference that ratios of hole

diameter to width and length were kept constant, Figure 2.5. There, the delamination

was controlled by the ratio of the ply thickness to hole diameter.

Figure 2.5: Complete failure of a composite plate with a hole [41]

2.4.2 Adhesive Joints The use of adhesive bonding, Figure 2.6, rather than mechanical fasteners offers the

potential for reduced weight and cost. Their benefit is that they behave in a

predictable and reliable way, but adherend and adhesive stress distributions in the

overlap length near (and especially on) the free surface are quite different from those

occurring in the interior.

Page | 34


Figure 2.6: Scheme of a single lap [42]

The possible failure scenarios of bonded lap joints are listed below and can be seen in

Figure 2.7.

Figure 2.7: Bonded Joint Failure Scenarios

A geometrically nonlinear model for elastic adhesive joints is derived by U. Edlund

[43]. Starting from a three-dimensional problem, a linearly varying displacement

through the thickness of the adhesive is assumed and a geometrically two-dimensional

theory for the adhesive layer is obtained. P.C. Pandey and S. Narasimhan [42]

presented a 3D viscoplastic analysis of adhesively bonded single lap joint considering

material and geometric nonlinearity. The specimens were tested according the ASTM

standard. Several types of joints were examined and observations have been made in

particular on peel and shear stresses in the adhesive layer.

1

2

3

4

5

1. Damage Initiation at Adhesive/Adherend Interface2. Damage Propagation Along Weak Interface3. Secondary Damage Initiation Site4. Transverse Tension Failure in Adherend Plies5. Adherend or Adhesive Strength Failure

Page | 35


E. Oterkus et al. [44] presented a semi-analytical solution method to analyse the

geometrically nonlinear response of bonded composite lap joints with tapered and/or

non tapered adherend edges under uniaxial tension. H. Osnes and A. Andersen [45]

investigated which level of loads or prescribed end displacements led to significant

nonlinear effects. The joints examined were made of cross-ply laminates having 0 or

90 surface layers. L. da Silva and R. Adams [46] proposed techniques to reduce the

transverse stresses in the composite. They examined the effect of temperature and

they also found that, in joints with metals and composites, it is more advantageous to

have the composite as the outer adherend.

2.5 Composite Panel and Stiffener Design The collapse load of metallic stiffened panels in uniaxial tension or compression can

be determined by considering the yield strength of the material. For example, Dobbs

and Nelson [47] presented an efficient optimality criteria method for the automated

minimum weight design of structural components.

Designing composite structures is more complicated than designing metal structures

due to the increased number of possible local failures, which are usually

micromechanically governed and complex. Fibre breaking, matrix cracking, fibre

matrix debonding, and separation of individual layers can result in delaminations as

well as cracks and splits within individual layers. Microbuckling and shear failures

are also common types of failures under compressive loadings. A local damage

condition may be due to accumulation of these failures, and the final failure may be

governed by several of them.

Gόrdal and Haftka [48] used a general purpose mathematical optimization algorithm

in order to create an automated procedure for designing minimum-weight composite

panels, Figure 2.8, subject to a local damage constraint under tensile loading. Panel

fracture was predicted by using a strain based criterion and results given for both

unstiffened and stiffened plates.

Failure of a composite stiffened panel subjected to compressive loading is usually

induced by the separation failure at the skin/stiffener interface. Hyer and Cohen [49]

presented a method for computing the stress state that exists between a composite

Page | 36


skin and the flanges of a cocured composite stiffener based upon finite element

analyses and an elasticity solution. The method presented relied upon an elasticity

approach for computing the stresses in the local area of the stiffener flange edge and

the composite skin. The local analysis was based upon an eigenvalue expansion of

the stress functions that govern the stresses in the interface region. Cohen and Hyer

[50] developed this method further by including geometric nonlinearities. The

results indicated that the inclusion of geometric nonlinearities is very important for

an accurate determination of the interface stresses.

Figure 2.8: Stiffened plate geometry [48]

Kassapoglou and Dinicola [51] presented a different solution technique to a similar

problem. The solutions of the governing set of partial differential equations were

used in conjunction with an energy minimisation approach to determine unknown

constants in analytically determined stress expressions. The method presented had

the advantage of being in closed form and very efficient. This method has the

Page | 37


advantage of being less time consuming by avoiding costly finite element analysis.

Experimentation on skin/stiffener debonding has been investigated by using the four-

point bending test. Specimen edge effects in this type of test greatly influence the

skin/stiifener separation process and therefore the test does not accurately simulate

skin/stiffener debonding in actual structures.

A new method was proposed by Todoroki and Sekishiro [52] for stacking sequence

optimization to maximize the buckling load of blade-stiffened panels. A panel with

four blade-type stiffeners was adopted as a target structure for optimization. Because

of the lack of experimental data and for most practical laminated composite

structures, fibre angles were limited to a small of 0, 45, −45 and 90.

2.6 Stiffener buckling Having a very thin panel section is undesirable for two reasons. Firstly, stiffened

plates used in aircraft structures are often subject to load reversal and must be

designed to resist some compressive loads. Some panels, such as appearing skin

panels are also predominantly loaded in compression during flight. Stiffened plates

with thin panel sections might fail prematurely due to local buckling. Secondly, plates

designed to carry the applied loads mostly by the stiffeners can fail catastrophically

due to stiffener damage. To prevent thin panel sections, stress constraints with

alternative load paths or increased safety factors should be used.

Jaunky et al [53] described an approach to incorporate the effects of local skin-

stiffener interaction and presented numerical results for panel buckling. The skin-

stiffener interaction effects were introduced by computing the stiffness of the stiffener

and the skin at the stiffener region. The results from the numerical examples

considered suggest that skin-stiffener interaction effects should be included in the

smeared stiffener theory to obtain good correlation with results from detailed finite

element analyses. Hence, the smeared stiffener theory with skin-stiffener interaction

effects included is still a useful preliminary design tool and results in buckling loads

that are more accurate than the results from the traditional smeared stiffener approach.

As mentioned previously, buckling may also be a consideration in the design of

aircraft panels. Buckling resistant panels do require stiffeners with deep blades. Such

Page | 38


designs can be achieved by imposing a blade with specified width and thickness band

redesigning the plates with this new geometry. Kong et al. [54] studied the

postbuckling behaviour of graphite/epoxy panels under uniaxial compression. Their

analytical studies consisted of finite element models adopting the maximum stress

criterion. Matrix failure, shear failure and fibre failure were considered and compared

favourably with experimental result.

Stevens et al [55] investigated the post buckling behaviour of a flat stiffened, co-cured

carbon fibre composite, loaded in compression. The panel was painted white for

shadow Moiré photography. Also, a telescopic arm of an ultrasonic scanning facility

was used in order to detect the initiation of damage in the postbuckled panel and

instrumentation associated with data logging and acoustic emission sensing. The

failure mechanism was an interlaminar shear stress failure arising from the

combination of compressive loading on the postbuckled stiffener blade and the

twisting induced at the node-line of the buckled stiffener. A panel after failure can be

seen in Figure 2.9.

Figure 2.9: I-stiffened panel. Buckling at 11 tonnes, failure at 48 tonnes [55]

Page | 39


Most stiffened panel applications require some form of cutout for such purposes as

access. Nemeth et al. [56] studied the postbuckling behaviour of several graphite/epoxy

plates and several isotropic plates with central circular cutouts under compressive

loading. The experimental results indicated that the cutout size and plate orthotropy

greatly governed the change in axial stiffness of a plate at its buckling load. The results

also revealed that some of the highly orthotropic plates with cutouts exhibited greater

postbuckling stiffness than the corresponding plate without a cutout.

The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered

flanges were investigated by Falzon et al [57]. The component consisted of a stiffener

and its associated skin, as shown in Figure 2.10, loaded in uniaxial compression. The

length was chosen so that the wavelength of torsional buckling was similar to the

wavelength observed in the panel. The failure of the component was identical, i.e. a

mid-plane delamination of the stiffener web at a nodal-line.

Figure 2.10: Component specimen [57]

The failure mechanism, observed in this study, also has potential implications for the

designer. It suggests that the optimizing of stiffener flanges by tapering, to reduce the

interfacial shear and peeling stresses, may be effective enough to shift the initial

damage site to a different location— in this case on a node-line at the edge of the web.

This provides the opportunity of introducing design improvements in this region, for

Page | 40


example stitching, to further delay the onset of damage and the quick progression to

complete failure of the structure. The failure mechanism was an interlaminar shear

stress failure arising from the combination of compressive loading on the postbuckled

stiffener blade and the twisting induced at the node-line of the buckled stiffener.

Falzon and Stevens [58] presented a combined experimental and numerical buckling

and postbuckling investigation of hat-stiffened panels undergoing mode transition.

The skin bay bounded by the stiffeners was observed to buckle at a fraction of the

ultimate load supported by the panel, which contained a cut-out in the centre of their

skins. The first two specimens tested did not contain a hole in the centre of the skin.

The first panel failed earlier than the second specimen. This was accounted for by a

defect contained in the structure before testing. A mode-jump from three to five half-

waves was observed. The difference between the two panels was attributed to the

thicker skin of the second specimen. The authors concluded that the ultimate failure of

the specimens was due to interlaminar shear failure in the stiffener. This could be

deduced by inspecting the failure site. However, no photographs, microsections or

ultra sonic scans of the damaged area were provided.

2.7 Damage in Stiffeners

2.7.1 Experimental state of art

The in-plane compressive behaviour of thin-skin stiffened composite panels with a

stress concentrator in the form of an open hole were examined by Zhuk et al [59] .

Experimental studies, using ultrasonic C-scan images and X-ray radiography,

indicated that the overall damage resembles a hole. Under uniaxial compression

loading, 0 fibre microbuckling surrounded by delamination grows laterally (like a

crack) from the impact site as the applied load is increased. These local buckled

regions continued to propagate, first in discrete increments and then rapidly at failure

load. The damage pattern was very similar to that observed in laminated plates with

open holes loaded in compression. Also, the maximum stress failure criterion was

employed to estimate the residual compressive strength of the panel. The influence of

the stiffener on the compressive strength of the thin-skin panel was examined and

included in the analysis. Good agreement between experimental measurements and

predicted values for the critical failure load was obtained.

Page | 41


Greenhalgh et al [60] generated documented and controlled experimental data for

validating predictive models of stiffened panels containing defects and damage, based

on EDAVCOS [3]. Two types of defect were characterised; embedded defects

(representative of inclusions introduced into the component during fabrication) and

impact damage (representative of the damage which may be introduced by tool drop).

The damage was located at two sites; within the bay between stringers and partly

under the stringer foot. The panel failed in compression, from the impact site, before

skin/stringer debonding could initiate and a secondary mechanism occurred prior to

skin/stringer detachment developing. Parallel to that, the authors tested and analysed

the failure of stringer run-out elements that served as benchmarks for validating

predictive methods. The local geometry of the stringer run-out was varied to deduce

its effect upon the performance under tensile loading. The failure processes at the

stiffener run-out region were characterised to understand the failure mechanisms at

the run-out, and to give some guidance as to how to optimise future designs. A

summary of the fracture directions is shown in Figure 2.11. This demonstrates how

the crack growth extended along the stringer, by migrating through the skin plies until

it reached the −45/0 ply interface in which it remained.

Figure 2.11: Summary of growth directions [60]

Page | 42


Based on this work, Meeks et al [61] investigated the detailed damage mechanisms

for skin/stiffener detachment in an undamaged panel were characterised and related to

the stress conditions. This work provided an insight into the processes that control

post-buckled performance of stiffened panels 2D models and concluded that element

tests do not capture the true physics of skin/stiffener detachment: a full 3D approach

is required.

Greenhalgh and Garcia [62] deduced the failure processes in the elements, and to

characterise the effect of local geometry of the stringer run-out on the failure process,

by testing specimens in tension. The analysis showed that the critical failure

mechanism in the elements was the development of +45 ply splitting at the skin

surface, initially under mode I dominated intralaminar fracture. However, as these

splits grew beneath the stringer foot, the mode II component increased. This led to

mixed-mode delamination growth, extending parallel to the +45 ply, at the

skin/adhesive interface. Subsequently, the delamination migrated through the skin via

ply splits, ultimately reaching the interface between the second and third (−45/0)

plies, in which it remained until catastrophic failure. The conclusion of this research

was that the development and migration of delaminations via ply splits plays an

important role and needs to be modelled.

Falzon and Davies [63, 64] investigated the failure of thick-sectioned stiffener run-out

specimens loaded in uniaxial compression. The research was separated in two parts,

the experiments and the FE analysis. For all tests, failure initiated at the edge of the

run-out and propagated across the skin–stiffener interface. It was found that the

failure load of each specimen was greatly influenced by intentional changes in the

geometric features of these specimens. High frictional forces at the edge of the run-

out were also deduced from a fractographic analysis, indicating Mode II initial failure

mode, failure by skin–stiffener disbonding due to high interlaminar stresses that

develop at the end of the stiffener run-out.

Faggiani and Falzon [65] tested two run-out specimens and analyzed them

numerically. The specimens were co-cured and included an effective skin section on

top of which was mounted a tapered blade-stiffener. The sizing of the specimens was

such as to ensure that interlaminar shear stress failure occurred within the skin-flange

interfaces. The first specimen failed catastrophocaly at the 90/0 interface of the

Page | 43


closing plies, located between the bottom of the stiffener flanges and the skin top

surface. Crack initiation and propagation was almost instantaneous and highly

unstable, with the crack propagating suddenly across the whole interface. A marked

increase in activity was recorded by acoustic emission monitoring just prior to failure,

but the specimen could not be unloaded quickly enough to arrest the crack

propagation. In the second specimen, crack initiation and unstable propagation was

followed by stable crack growth allowing the test to be stopped before the crack had

propagated throughout the whole specimen. This failure behaviour was in contrast

with the sudden and completely unstable nature of the first specimen with the thinner

skin.

Hosseini-Toudeshky et al [66] investigated the damage mechanisms in a composite

bonded skin/stiffener constructions under monotonic tension loading. The approach

used experiments to identify the failure mechanisms. The tested specimens consisted

of a bonded skin and flange assembly. Typical specimens are shown in Figure 2.12.

Figure 2.12: Edge view of the damaged specimens [66]

Observations on the performed experiments show matrix crack initiation and

propagation in the skin and near the flange tip, causing the flange to almost fully

debonded from the skin in some cases, interlaminar debounding and fibre breakage up

to the failure of the components. With increasing the applied load, the matrix cracks

propagated through the thickness to reach the next layer and caused delamination

Page | 44


between the two layers. With increasing the applied load this delamination is

propagated up to the occurrence of unstable delamination.

2.7.2 Simulation state of the art

An understanding of how damage is initiated and the physics behind its progression

take priority in damage simulation. This field of research is very wide in scope, due to

the numerous configurations under which a structure can be loaded and damaged.

Several damage characterisation investigations have been undertaken by Greenhalgh

et al. [67] with specific attention to the behaviour of damaged composite stiffened

panels subjected to compressive loading. Single plane defects were embedded in the

panels at various locations during manufacture. The moving mesh technique was used

to model delamination buckling, global panel buckling and damage growth. Finite

clement models were constructed using separate layers of shell elements for the two

skin sublaminates, linked by constraint equations outside the defect. The models were

successful in representing the local buckling, damage initiation and evolution. The

technique was shown to be efficient at simulating single plane delamination growth.

The authors recommended further research to model crack migration and damage

growth beneath substructures such as stiffeners. It was noted that the damage shape

tended to be elliptical and its orientation was a function of the loading direction.

The development of an efficient three-dimensional finite element was presented by

Falzon et al. [68] It was designed for modelling composite laminates and used in a

mixed-mode fracture mechanics example. The main advantage of this formulation

is the ability to model bending of a laminated composite structure with a single 3-D

element through the thickness, thereby improving the computational efficiency of

calculating strain energy release rates.

A sophisticated finite element model was developed by Wisnom and Chang [33] in

order to approach in detail the development of damage in notched composites. Each

of the laminate's plies was represented by an element connected by interface

elements defined within ABAQUS. The interface elements introduced nonlinear

springs between the plies so that, prior to reaching a critical stress, the stiffness

between the plies is elastic and thereafter plastic. The model successfully

represented the physical processes of splitting and delamination observed in

Page | 45


experimentation. However, this model is limited by the computational power

needed to solve a structural problem since a composite structure encountered in a

real-life application will typically have twenty or more plies.

Falzon et al [69] presented an experimental and numerical study of the failure of

thick-sectioned stiffener run-out specimens loaded in uniaxial compression. The

experiments revealed that failure was initiated at the edge of the run-out and

propagated across the skin–stiffener interface. High frictional forces at the edge of the

run-out were also deduced from a fractographic analysis and it was proposed that

these forces may enhance the fracture toughness of the specimens.

The stiffeners tested in [63] were also numerically studied by Cosentino and Weaver

[70]. An nonlinear approach was developed and the results of the tests were used to

for validation purposes The correlation with the test results was fairly good and

further development of the approach was proposed, especially when the stiffeners are

non-symmetric.

Zhang et al [71] and Madhi et al [72, 73] used strain gages to investigate the

performance of repaired thin-skinned, blade-stiffened composite and the FE method

was used as a designing tool. It is thought that the failure may have initiated at a crack

in the skin, with the initial crack growing perpendicularly to the applied stress and

leading to stiffener debonds, and ultimately to collapse of the skin and the stiffeners.

The knowledge of the failure mechanisms could probably help to explain these types

of problems.

Structures under shear loading were analysed by Krueger [74]. A stringer reinforced

composite panel was modelled with shell elements, while the stringer foot, web and

noodle were modelled with a local 3D solid model and the mixed- mode strain energy

release rates were calculated. The stiffened panel that used is illustrated in Figure

2.13. It was concluded that the shear loading causes buckling on the panel, which

subsequently results in skin/stringer separation at the location of an embedded defect.

Alterations in local stiffness caused differences in the failure index distributions. The reason

for different local stiffnesses having occurred is that different modelling techniques were

used in the noodle and transition radius between the shell elements and the 3D solid

elements.

Page | 46


Figure 2.13: Stringer stiffened panel subjected to shear loading [74]

2.8 Discussion and conclusions Aerospace structures demand several constraints upon their design, most notably

strength, stiffness, weight and cost. Thin plates are usually efficient at carrying in-

plane loads. The minimum plate thickness is often governed by a stiffness constraint

in the form of buckling capacity rather than strength.

Damage tolerant structures are often designed based upon empirical data derived from

experience in earlier applications. The design cycle therefore relies quite substantially

upon a testing and validation program, which is both time consuming and prohibitively

expensive. A need arises for improved design guidelines and analysis methods to

evaluate a particular design more accurately.

A summary of research efforts into damage modelling of stiffened composite panels

subjected to tensile and compressive loads has been presented and summarized in

Appendix A. The literature indicates that the majority of damage modelling techniques

Page | 47


comprise of failure criteria, fracture mechanics and damage mechanics approaches,

although not necessarily all three. The ideal damage model for predicting the

residual strength of stiffened multidirectional composite panels, from the composite

designer's perspective should:

• Calculate the applied stress at which unstable fracture occurs

• Predict the evolution of a damaged region to assess the possibility of repair

work

• Capture the main damage modes e.g. delamination, fibre-breakage

• Be computationally inexpensive

• Be applicable to a component of any shape, stacking sequence and

subjected to any loading condition

Research has tended to focus on specific aspects of damage modelling in order to

gain detailed insight into the various damage mechanisms; however, a model that

encompasses all aspects associated with compressive failure is still lacking.

On the specific problem of skin-stiffener debonding, a large body of experimental and

analytical work carried out on the response and failure of stiffened composite

aerostructures loaded in uniaxial compression [57] has demonstrated the vulnerability

of co-cured and secondary bonded structures to interlaminar and peel stresses at the

skin-stiffener interface. The main advantage of these bonding procedures is the

significant potential weight saving over mechanically fastened structures. This

interface weakness therefore is of major concern in stiffener run-out regions where the

stiffener is terminated due to a cutout, intersecting a rib, or some other structural

feature that interrupts the load path. It is also of major concern that current design

rules are inadequate in accounting for skin-stiffener failure at these critical regions.

In a previous work [63, 64] a series of tests, with a stiffener/plate loaded in

compression, revealed high compressive through-thickness stresses which resulted in

considerable frictional shearing resistance and increased the apparent fracture

toughness needed to estimate the debonding loads. This lead to strengths that were

more than double those predicted and the need for further investigation is clear.

A set of single-stiffener panels where the stiffener is run-out, short of the loaded edge,

will be tested in compression. Testing specimens in compression can provide a

Page | 48


challenging benchmark for the developed numerical models that can use for more

complex types of failure. The loading offset induces significant through-thickness

loads which, in compression, may enhance the apparent fracture toughness. While the

mechanics is understood reasonably well, there is still considerable debate on the

details of failure initiation and propagation at these critical location Careful

observations using DIC and AE will be undertaken to deduce the nature of

delamination/debonding which will help guide the development of the analysis tools.

Page | 49

Chapter 3 - Material Characterization

Chapter 3

Material Characterization

3 Material Characterization

3.1 Introduction This section presents the characterization of strength and stiffness tests for IM7/8552

carbon epoxy. The material was supplied by Hexcel with layer thickness of 0.25 mm.

The tests were carried out in the Department of Aeronautics, Imperial College

London. The testing machines used for the tests were the Zwick testing machine and

Instron testing machine.

3.2 Stiffness and Strength Characterization

3.2.1 Introduction

The in-plane stiffness and strengths were measured, in accordance with the respective

standards. More specifically, the transverse/longitudinal tensile (ASTM D3039-76

[75]) /compressive (Imperial College method [76]) stiffnesses and strengths were

measured, as well as the non-linear in-plane shear response (ASTM D3518D-3518M

[77]).

3.2.2 Manufacturing

In order to manufacture the specimens, appropriate laminates were first needed.

Appropriate lengths were cut from the composite roll and stacked until the required

Page | 50


thickness was achieved. Each group of four plies was compacted to prevent air

entrapment, Figure 3.1. Three plates were manufactured, labelled No.1, No.2 and

No3, as can be seen in Figure 3.2.

Figure 3.1: Arrangement for producing laminates in Autoclave [47]

Figure 3.2: Schematic of plates

The dimensions of each plate and the type of specimens that they produced can be

seen in Table 3-1. When the laminates were ready, they were placed in the Autoclave

for curing, see Figure 3.1. After curing, and to ensure that there were no defects in the

laminate, the ultrasonic C-scan was used Figure 3.3, where on the upper right corner

the red circle is a coin that was used as point of reference).

Page | 51


Table 3-1: Function and characteristics of the manufactured plates

Plate Test

Dimensions

(mm)

number

of

layers layup

Thickness

(mm)

No.1 tensile 0, compression 0 300x330 8 (0o)8 2

No.2 tensile 90,compression 90 300x330 16 (0o)16 4

No.3 shear 300x300 16 (±450 )8S 4

Figure 3.3: The C-scans of the plates

End tabs were bonded on the plates using 3M Scotch-Weld. The surfaces of the

plates, where the end tabs placed, as well as the tabs, were cleaned using air pressured

sand and cleaned before the gluing of the end tabs.

The plates with the end tabs were placed on the vacuum table for curing the glue. For

the compression specimens, reverse-chamfered end tabs were used. These tabs were

bonded in two stages, first from the one side and then from the other in order to have

constant glue thickness, as seen in Figure 3.4.

Page | 52


Figure 3.4: Manufacturing of compression specimen [9]

Finally, the specimens were cut using a wet saw machine with diamond blade to the

appropriate dimensions (Table 3-2) from the respective plates. The 0o tension

specimens were cut from plate No.1 and named t0, t from tension and 0 from the 0o

direction of the fibres.

The same naming code was used for the rest of the specimens, c from compression,

90 from the 90o direction and s from shear. The c0 specimens were cut from No1

plate. From the No2 plate were cut the t90 and c90 specimens and plate No3 was

used only for the s specimens.

Table 3-2: Nominal dimensions of specimens

Test specimen end tab

width

(mm)

length (mm) thickness

(mm)

length (mm) thickness (mm)

Tension 0o 15 250 2 56 1.5

Tension 90o 25 175 4 25 1.5

Compression 0o 10 90 2 40 1.5

Compression 90o 10 90 4 40 1.5

Shear 25 250 4 56 1.5

Page | 53


Figure 3.5: Specimen dimensions

3.2.3 Testing

The testing machines used for the tests were the Zwick testing machine for the

compression tests and Instron testing machine for the tension and shear tests. The

loading rates depended on the test, 1mm/min for the compression tests and 2mm/min

for the tension and shear tests. Load and crosshead displacement were recorded

continuously by a PC data logger connected to the load cell and the testing machine.

3.2.3.1 Compression

The Imperial College method for testing composite materials in compression [76] was

used. In order to ensure that the specimens were fitted exactly in the rig, a load of

0.5 kN was applied to the specimens before the tightening of the bolts. 2 mm strain

gauges (FLA-2-11) were placed on the specimens on both sides for measuring the

strains and monitor the bending, Figure 3.6.

During the test a problem with the front gauge of the specimen c0-2 prevented the

data collection and the analysis was based only on the rear gauge data. A problem

occurred with the data collection of the specimen c90-4.

Eight specimens were tested in longitudinal compression. Figure 3.8 shows the failure

strengths of the specimens. The average strength is 1,572.9 MPa with a coefficient of

variation of 6.6%. For all tests, the bending was lower than 5%, as it can be seen in

Figure 3.9, except for specimen c0-5, where the bending is around 6%. Figure 3.10

presents the stress-strain curves of the specimens. The average longitudinal modulus

is 154.1 GPa with a coefficient of variation of 1.5%.

Page | 54


Figure 3.6 : Compression specimens inside the rig

Figure 3.7: Compression specimens after testing

In transverse compression the same number of specimens, as in longitudinal, was

tested. The only difference was that the specimens had double the thickness. Figure

3.11 presents the failure strengths; the average strength is 254.6 MPa with a

coefficient of variation of 4.6%. As it can be seen in Figure 3.12, the bending was

lower than 10%. The stress-strain curves are presented in Figure 3.13. The transverse

modulus is 9.8 GPa with a coefficient of variation of 4.4%.

specimen

rig

Strain gage

Page | 55


Figure 3.8: Failure strengths of longitudinal compression specimens

Figure 3.9: Bending versus strain for the longitudinal compression specimen

1631 1609 1639

1469

1676 1530 1484 1545

0

200

400

600

800

1000

1200

1400

1600

1800

c0-1 c0-2 c0-3 c0-4 c0-5 c0-6 c0-7 c0-8

stre

ngth

(MPa

)

specimens

0%

5%

10%

15%

20%

25%

30%

0 0.002 0.004 0.006 0.008 0.01

Bend

ing

Strain

c0-1

c0-3

c0-4

c0-5

c0-6

c0-7

c0-8

5%

Page | 56


Figure 3.10: Stress-strain curves for the longitudinal compression specimens

Figure 3.11: Failure strengths of the transverse compression specimens

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.002 0.004 0.006 0.008 0.01 0.012

Stre

ss (M

Pa)

Strain

c0-1 c0-3 c0-4 c0-5 c0-6 c0-7 c0-8

248.2 260.3

246.6 250.6 266.3 262.2

249.3 253.3

0

50

100

150

200

250

300

c90-1 c90-2 c90-3 c90-4 c90-5 c90-6 c90-7 c90-8

Stre

ngth

(MPa

)

Specimen

Page | 57


Figure 3.12: Bending versus strain for the transverse compression specimen

Figure 3.13: Stress-strain curves for the transverse compression specimens

0%

5%

10%

15%

20%

25%

30%

0 0.002 0.004 0.006 0.008 0.01

Bend

ing

Strain

c90-1

c90-2

c90-3

c90-5

c90-6

c90-7

c90-8

5%

0

20

40

60

80

100

120

140

160

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Stre

ss (M

Pa)

Strain

c90-1

c90-2

c90-3

c90-5

c90-6

c90-7

c90-8

Page | 58


3.2.3.1.1 Tensile

The tensile test method can be found as ASTM D3039-76 [75]. It is a method that

allows determination of the properties of the lamina. For longitudinal tension, three

strain gauges were placed on the first two specimens for measuring bending, as

described in ASTM D3039-76, and on the rest of them cross strain gauges FCA-3-11

were placed. On the transverse tension specimens gauges (FLA-6-11) were placed in

the loading direction Figure 3.14. Specimens t90-1 and t90-2 were destroyed

accidentally.

Figure 3.14: Testing of tensile specimen

Seven specimens were tested in longitudinal tension. Figure 3.16 shows the failure

strengths of the specimens. The average strength is 2,260 MPa with a coefficient of

variation of 7.35%. Figure 3.17 presents the stress-strain curves of the specimens. The

average longitudinal modulus is 176.6 GPa with a coefficient of variation of 6.8%.

In transverse tension, the same number of specimens, as in longitudinal, was tested.

Specimens t90-2 and t90-3 destroyed accidently from a collapse of the the testing

Page | 59


machine’s jaw. Figure 3.18 presents the failure strengths; the average strength is 62

MPa with a coefficient of variation of 7.6%. The stress-strain curves are presented in

Figure 3.19. The average transverse modulus is 8.6 GPa with a coefficient of variation

of 14.3%.

Figure 3.15: Tensile specimens after testing, 0o on the left and 90o on the right

Figure 3.16: Failure strength of the longitudinal tension specimens

2143.6 2163 2130.9 2324.5 2372 2426

0

500

1000

1500

2000

2500

t0-1 t0-2 t0-3 t0-4 t0-5 t0-7

Stre

nght

(MPa

)

Specimens

Page | 60


Figure 3.17: Stress-strain curves of the longitudinal tension specimens

Figure 3.18: Failure strength of the transverse tension specimens

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7

Load

(KN

)

Displacement (mm)

t0-1 t0-2 t0-3 t0-4 t0-5 t0-7

64.1 64.7 62

57.3 58.5

0

10

20

30

40

50

60

70

t90-3 t90-4 t90-5 t90-6 t90-7

Stre

nght

(MPa

)

Specimens

Page | 61


Figure 3.19: Stress-strain curves of the transverse tension specimens

3.2.3.2 Shear

The shear tests used in order to find shear strengths, ultimate shear strains and shear

modulus. The method that was used for measuring the in plane properties of the

material is the [ 45]s± coupon test method that is describing from the ASTM

D3518D-3518M [77].

Figure 3.20: Shear specimens after testing

0

10

20

30

40

50

60

70

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Stre

ss (M

Pa)

Strain

c90-3

c90-4

c90-5

c90-6

c90-7

Page | 62


The shear strain (γ) was computed using the longitudinal strain (εl) and transverse

strain (εtr), as:

l trγ ε ε= − (3.1)

The shear stress (τ) was computed from the applied load (P) and initial cross sectional

area (Ao) as suggested by the ASTM standard:

02

PA

τ = (3.2)

Figure 3.21: Failure strength of shear specimens

Seven specimens were tested, Figure 3.20. Strain gauges FCA-6-11 were used for the

data collection. Figure 3.21 shows the failure strengths of the specimens. Specimens

s-5, s-6, s-7 and s45-3c were loaded and unloaded. The average strength is 101.2 MPa

with a coefficient of variation of 4%. Figure 3.22 and Figure 3.23 present the stress

versus strain for straight loaded and loaded-unloaded specimens respectively. There

were problems with the data collection for specimens s-2 and s-3, s45-4 had a strain

105.3 98.3 101.2 101.6 99.8 101.5 101.7 100.1 101.5

0

20

40

60

80

100

120

s-1 s-4 s-5 s-6 s-7 s45-3c s45-5c s45-6c s45-7c

Stre

nght

(MPa

)

Specimens

Page | 63


gage misalignment. The average transverse modulus is 4.48 GPa with a coefficient of

variation of 22%.

Figure 3.22: Stress-Strain curves of the shear specimens that were tested without unloading

Figure 3.23: Stress-Strain curves of shear specimens that were tested with unloading

0

10

20

30

40

50

60

70

80

90

100

0 0.005 0.01 0.015 0.02

Stre

ss (

MPa

)

Strain

s45-1

s45-4

s45-5c

s45-7c

Page | 64


3.2.4 Results

All the test results collected in Table 3-3, which also includes a comparison with the

material manufacturer values.

Table 3-3: Comparison of the material properties

IM7/8552 Material

Properties

from Hexcel

Measured

Properties

Difference

Longitudinal Young’s

Modulus

Tension 165 GPa 177 GPa 7.0%

Compression 145 GPa 154 GPa 6.3%

Transverse Young’s

Modulus

Tension 9.4 GPa 8.6 GPa 8.5%

Compression 10.6 GPa 9.8 GPa 10.2%

Shear modulus 4.5 GPa 4.48 GPa 0.4%

Longitudinal Strength

Tension 2.6 GPa 2.2GMPa 13.0%

Compression 1.5 GPa 1.57 GPa 4.8%

Transverse Strength

Tension 60 MPa 62 MPa 3.3%

Compression 290 MPa 254.6 MPa 12.2%

Shear strength 90 MPa 101.2 MPa 12.4%

Poisson’s ratio 0.3 0.34 13 .3%

Page | 65


3.3 Fracture Toughness Characterization

3.3.1 Introduction

The energy release rate, G, is a parameter which characterizes the propensity of a

crack to grow. The critical value of this crack driving force, Gc, is called critical

energy release rate (or fracture toughness) and it is taken as a property of the material

and it is used to characterise the ability of a material to resist fracture in the presence

of cracks.

3.3.2 Manufacturing

Appropriate layers measuring 300x330 mm2 were cut from the roll and stacked over

each other. Each block of 4 plies was compacted to prevent the air entrapment. The

nominal thickness of the laminate was 3 mm, but the layup was done in two halves in

order to insert at the midplane of the laminate a non-stick, fluoroethylene polymer

film, of thickness ≈12.5 μm, and form an initiation site for the delamination, Table

3-4.

Table 3-4: Function and characteristics of the manufactured plate

Plate Test Dimensions

(mm)

number of

layers

layup Thickness

(mm)

No.4 DCB, 4ENF,

MMB

300x330 12 (0o)12 3

When the laminate was ready, it was placed in the auto-clave for curing. After curing

and to ensure that there were no defects in the laminate, the ultrasonic C-scan was

used, Figure 3.24. The dimensions of each plate and the type of specimens that were

produced can be seen in Table 3-5. The specimens were cut, using a wet saw machine

with diamond blade, to the appropriate dimensions.

Page | 66


Figure 3.24: Schematic of plate for the fracture toughness specimens and the C-scan of the plate

Table 3-5: Nominal dimensions of the fracture toughness specimens

Test specimen a

width

(mm)

length

(mm)

thickness (mm) ao

(mm)

insert lenght

(mm)

DCB 20 170 3 50 60

4 ENF 20 140 3 40 50

MMB 20 135 3 25 35

Double cantilever beam (DCB) specimens were manufactured for mode I according

to ASTM designation D5528 [78], 4 point end notch flexure for mode II [79] and

mixed mode bending tests for mixed modes I and II [80]. End tabs were bonded on

the DCB and MMB specimens. The surfaces of the specimens, where the end tabs

were placed, as well as the tabs, were cleaned using grit blasting and cleaned before

the gluing of the end tabs. The end tabs were glued with an epoxy adhesive and left

overnight under applied pressure to promote good bonding.

Page | 67


Finally, all the specimens were precracked so as to break the resin inclusion that had

been created at the end of the film and in a way that prevents the crack to propagate

extensively, as shown in Figure 3.25.

Figure 3.25: Precraking of a DCB specimen

3.4 Testing The testing machine that was used for the tests was an Instron testing machine,

equipped with a 10 KN load cell. The loading rates were 0.5 mm/min for the DCB

tests and 0.2 mm/min for the 4 ENF and MMB tests that performed for another

project [81]. Load and crosshead displacement were recorded continuously by a PC

data logger connected to the load cell and the Instron machine at a sampling rate of 2

samples per second. The crack tip was monitored using a CCD camera displaying an

enlarged image in a TV screen. An event marker was used to send a signal to the

computer as the crack tip passes through each mark on the specimen.

3.4.1 DCB

The ASTM designation D5528 [78] was used for this test method, which describes the

determination of the opening Mode I interlaminar fracture toughness, GIc, of

continuous fibre-reinforced composite materials using the double cantilever beam

(DCB) specimen with end blocks, as shown in Figure 3.26.

Page | 68


Figure 3.26: DCB specimen [7]

The specimens are painted white on one side and fine lines of 1mm increments for the

first 5mm of growth from the delamination front band, and then in 5mm increments

for a further 20mm were scribed with a height gauge to facilitate the observation of

the delamination. An example of a DCB test can be seen in Figure 3.27, where in the

inset the inserted film and the area that the interlaminar crack propagated can be

observed.

Figure 3.27: Testing a DCB specimen

The Modified Beam Theory Method [7] was used for the data analysis. Five

specimens were tested, the load-displacement curves are presented in Figure 3.28, and

Page | 69


compared very well with the corrected beam theory as in Figure 2.4. The results of the

R-curves using the Modified Beam Theory (MBT) are shown in Figure 3.29.

Figure 3.28: Load-displacement traces for DCB specimens

Figure 3.29: R-curves for DCB specimens using the Modified Beam Theory (MBT) Method

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16 18 20 22

Load

(kN

)

Displacement (mm)

DCB-1 DCB-2 DCB-3 DCB-4 DCB-5

0

50

100

150

200

250

300

350

400

450

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12

GIC

(J/

m2 )

Delamination length, a [m]

DCB-1

DCB-2

DCB-3

DCB-4

DCB-5

Page | 70


The mode I interlaminar fracture toughness is calculated according to the modified

beam theory,

32 ( )Ic

PGb

δα

=+ ∆

(3.3)

where GIc is the fracture toughness, P is the load, δ is the opening displacement, b is

the specimen width, a is the crack length and Δ is a correction term applied to the

crack length.

The latter is determined from the experimental data after generating a least square plot

of the cubic root of compliance, C1/3, as a function of delamination length, a. The

correction term Δ is the value that should be added to the crack length to make the

plot go through the origin. The compliance, C, is defined as δ/P. The average GIc is

302 J/m2 with coefficient of variation of 13.6%.

Using the Compliance Calibration (CC) Method, which generates a least squares plot

of log (d/P) versus log (a) and n is the slope,

2IcnPG

bδα

= (3.4)

the average GIc is 293 J/m2 with coefficient of variation of 16% and results of each

specimen can be seen in Figure 3.30.

Page | 71


Figure 3.30: R-curves for DCB specimens using the Compliance Calibration (CC) Method

3.4.2 4 ENF

The four point bend end-notched flexure (4ENF) test (Figure 4.32) has been proposed

as a new test to characterise mode II delamination [79]. This test has several

advantages over other tests including reduced friction, stable delamination growth and

simple fixture design. However, because it is a relatively new test, it has not been

validated on a wide range of material types. The 4ENF was also successfully used in

fatigue to characterise delamination growth and derivation of threshold values [82].

Figure 3.31: the 4ENF test fixture

0

50

100

150

200

250

300

350

400

450

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12

GIC

(J/

m2 )

Delamination length, a [m]

DCB-1 DCB-2 DCB-3 DCB-4 DCB-5

Page | 72


The specimens had a delamination starter length of 40 mm from the edge of the

specimen. One of the edges of the specimen was polished, and painted white on which

fine lines of 1 mm increments for the first 10 mm of growth from the delamination

front and then in 5 mm increments to a crack length of at least 70 mm were scribed

with a gauge height to aid the observation of the delamination (Figure 4.33).

Figure 3.32: Testing a 4ENF specimen

Data reduction for 4ENF test are in accordance with reference [83]. The results of the

4ENF test are calculated by considering the linear relationship between compliance,

C, and delamination length, a,

0 C ma C= + (3.5)

and generating a least squares fit of the experimental data to determine m and C0.

Mode II interlaminar fracture toughness IICG was calculated as [79]

2 2IIc

P mGw

= (3.6)

where w is the specimen width and P is the applied load.

The compliance calibration was performed in the 4ENF using specimens with

different initial crack lengths: The constant m is the slope of the best fit straight line

on the graph of compliance against delamination length. The average IICG is 630.9

Page | 73


N/m with coefficient of variation of 14%. The loads versus the displacement are

displayed in Figure 3.33.

Figure 3.33: Load displacement curves for the 4ENF specimens

Figure 3.34: R-curves for 4ENF specimens

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Load

(kN

)

Displacement (mm)

4ENF-2 4ENF-3 4ENF-4 4ENF-5

0

100

200

300

400

500

600

700

800

0.04 0.05 0.06 0.07 0.08 0.09 0.1

GIIC

(J/

m2 )

Delamination length, a (m)

4ENF-2

4ENF-3

4ENF-4

4ENF-5

Page | 74

Chapter 4

Numerical Design of

Stiffener Run-outs for

Damage Tolerance

4 Numerical Design of Stiffener Run-outs for

Damage Tolerance

4.1 Introduction The effect of different parameters such as material and geometry can be economically

explored by using virtual tests rather than real tests. This chapter introduces a model

that predicts the peeling stresses at bonded interfaces. The model is based on a tested

baseline design and the effect of geometrical details on the stress magnitude and

distribution are discussed. This is followed by a study of different stiffener run-out

designs models where the effects of the design parameters on the stresses between the

skin and the stiffener were investigated. The results led to the development of a

parametric approach to find an optimal run-out design for increased damage tolerance.

Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance

4.2 Stress profile at interfaces with geometrical and material

discontinuities The recent trend of incorporating more composite material in primary aircraft

structures has highlighted the vulnerability of stiffened aerostructures to through-

thickness stresses, which may lead to delamination and debonding at the skin–

stiffener interface, leading to collapse. Stiffener run-out regions are particularly

susceptible to this problem and cannot be avoided due to the necessity to terminate

stiffeners at rib intersections or at cutouts, interrupting the stiffener load path.

4.2.1 Theoretical Analysis

Previous investigations [60, 61, 63, 64] on the response of stiffened composite panels

loaded in uniaxial compression, have shown that the torsion rigidity of the stiffeners

prevents the rotation following the deformation of the buckled skin. This gives rise to

high peel stresses which result in either failure initiating at the edge of the stiffener

flange and propagating towards the stiffener centreline or failure may initiate at the

‘noodle’ region below the stiffener web and propagate out towards the edge of the

flange. For these reasons, a good understanding of the stress state at the geometric and

material discontinuity that constitutes a run-out is of paramount importance. A closed-

form model is developed that predicts peel stresses in adhesively bonded joints, as

shown in Figure 4.1.

Figure 4.1 : Close-form model

1tat

2t

2c

1E

2EaE

xNxN

Adherend 1Adhesive

Adherend 2

Page | 76


This model predicts peel stress using a beam on elastic foundation (BOEF) approach.

By accounting for the coupling of peel stress terms within the governing equation, this

model is suitable for the stress analysis of generic asymmetric joints, that is, joints

that have adherends of mismatched elastic modulus and thickness.

In order to calculate the peel stress, the lap joint is modelled by two beams connected

by a distributed elastic spring with a thickness at given by:

a

a

Ekt

= (3.1)

where aE is the Young's modulus of the adhesive as shown in Figure 4.1. These

eccentricity bending moments are responsible for the peel stress component. A fourth-

order linear differential equation for the relative vertical displacement, w, based on

BOEF interaction between the adherends, can be derived as

(3.2)

where 1 2w w w= − is the relative vertical displacement components of the adherends

1 and 2. 1 1 11 /D E I= and 2 2 21 /D E I= , where E and I are the Young modulus and

inertia respectively of the adherends 1 and 2. Equation 3.2 is solved for the relative

vertical displacement, w ; by the general solution [84]:

( ) ( )1 2 3 4( ) cos sin cos sinx xw x e C x C x e C x C xβ ββ β β β−= + + + (3.3)

where

14

1 2

1 1 12

kD D

β

= +

(3.4)

The variables 1C , 2C , 3C and 4C can be found from the boundary conditions of the

free body diagram shown in Figure 4.2.

Page | 77


Figure 4.2: Free Body Diagram

For x c= −

1( ) 0M c− = (3.5)

1( ) 0Q c− = (3.6)

1( ) 0N c− = (3.7)

2

222 2 2( ) d wM c D M

dx− = = (3.8)

3

22 2 23( ) d wQ c D Q

dx− = = (3.9)

2 ( ) xN c N− = (3.10)

For x c=

1( ) 0M c = (3.11)

1( ) 0Q c = (3.12)

1( ) 0N c = (3.13)

aE

1E

2E

c− xc

2M2M2Q 2Q

xN xN

Page | 78


2

222 2 2( ) d wM c D M

dx= = − (3.14)

2

22 2 22( ) d wQ c D Q

dx= = − (3.15)

2 ( ) xN c N= − (3.16)

From equations 3.5 and 3.8 it is extracted that

2

22

2x c

d w Mdx D=− = − (3.17)


3

23

2x c

d w Qdx D=− = − (3.18)


2

22

2x c

d w Mdx D= = (3.19)


3

23

2x c

d w Qdx D= = (3.20)

Solving equation 3.3 using as boundary conditions equations 3.17 to 3.20 leads to the

values of 1C , 2C , 3C and 4C .

The peeling stresses are finally:

p kwσ = (3.21)

Page | 79


The plot of the peeling stresses of the half section and for values in Table 4-1, that are

similar to the stiffener that is examined later, can be seen in Figure 4.3.

Table 4-1 : Values [63]

Variables Values

xN 180 kN

1t 60 mm

2t 8 mm

at 1 mm

1E 124.4 GPa

2E 102.4 GPa

aE 1 GPa

Figure 4.3 : Plot of peeling stresses from analytical solution

A study on how the solution of equation 3.21 is affected by the variables and

is presented in Figure 4.4. From Figure 4.4a can be assumed that when k is

increased, the higher the peeling stresses are closer to the end of the specimen by

decreasing the area of action. Also, when the is decreasing, as can be seen in

Figure 4.4b, the peeling stresses are getting smaller and reducing the affected area. In

real structures, as in stiffeners, the stresses can be decreased by changing 1D and as

-12-10

-8-6-4-2024

0 100 200 300 400

Peel

ing

Stre

ss [M

Pax1

03 ]

length [mm]

k

1 2/D D

1 2/D D

Page | 80


1D is geometrically dependent, the design of the stiffener run-out can play an

important role in the failure procedure. This can be used, for example, by tapering the

tip of the stiffener in order to decrease the stresses. It is clear that the modification of

the run-out design could play an important role in the stress field and this was studied

in next paragraphs by using finite element simulations.

Figure 4.4: A study on how variables (a) and (b) affect the solution.

-10-8-6-4-2024

0 100 200 300 400

Peel

ing

Stre

ss [M

Pa x

103 ]

lenght [m

D1=0.5*D2

D1=D2

D1=2*D2

(a)

(b)

-20

-15

-10

-5

0

5

0 100 200 300 400

Peel

ing

Stre

ss [M

Pa x

103 ]

lenght [m

0.5*k

k

2*k

length [mm]

length [mm]

k 1 2/D D

Page | 81


4.2.2 Stiffener run-out Designs

The current capability to use finite element simulations to predict the mechanical

response of the run-out was assessed. The objective was to investigate experimentally

how the geometry of the run-out determines the failure sequences, and how the failure

could be optimized by carefully designing the run-out. Representative structural

components were selected [63] and defined, sized as in Figure 4.5, and prediction with

nominal geometry were made using ABAQUS.

Figure 4.5: Stiffener dimensions in mm [63]

The results of these models helped in undertaking the distribution of peel stresses at the

skin-stiffener interface. Different stiffener designs, as presented in Figure 4.6, were

studied:

• Stif 0. The run-out type Stif 0 had an overall length of 440 mm and a width of

120 mm. The length of the stiffener was 400 mm, leaving an unsupported skin

section of 40 mm. The skin thickness was 8 mm.

Page | 82


Figure 4.6 : The designs of the stiffeners that were studied.

• Stif 1. This stiffener blade was tapered linearly over a distance of 200 mm, to a

height of 30 mm above the skin at the edge of the run-out. The specimen can

be seen in Figure 4.5. It can be observed that the taper does not go down to the

skin, which simplifies the manufacturing. This results in a step discontinuity in

400

40

60

120

400

40

60

120

200

20

400

40

60

120

200

400

40

60

120

200

300

40

40

120

200

100

300

40

80

120

200

100

Stif 0

Stif 4 Stif 5

Stif 3Stif 2

Stif 1

Page | 83


the cross-sectional area, which gives rise to a stress concentration at the edge

of the stiffener.

• Stif 2. This has the taper of the blade going down to the skin. This type of

design aims to minimise the discontinuity between the stiffener and the skin at

the stiffeners tip. Two different types of tapering were used, the linear and the

curved, in order to detect the effects of different tapered types of the blade.

• Based on this design, Stif 3 was studied with different tapered blade. The

blade was tapered with a curvature in order to detect any effects of a non-

linear tapared blade. The effect of the blade design was investigated in order to

determine the local notch stress distribution.

• In order to specify the role of the flange of the stiffener and the importance

that it played to the behaviour of the structure, Stif 4 was introduced. This

design is similar to Stif 2, but the flange was narrower to the tip following the

tapering of the blade.

• In addition to the previous design, Stif 5 had a widened flange targeting on the

stress distribution of the local stresses to the skin. Here the two designs, Stif 4

and Stif 5, were the design with the tapered flange and the design with the

wide flange. Also, this design could provide information about the role of the

flange in stiffener run-outs.

The lay-up for the half stiffener is quoted from the bottom flange surface to the free

surface and is shown in Table 4-2. The material used was IM7/8552 and the

properties are shown in the Table 4-3. The lay-up used in the models was similar to

skin-stiffener run-outs tested by Falzon [63]. The skin lay-up is given from the outer

to inner surfaces of the specimen with the outer layer defined as the smooth surface

which would form part of the aerodynamic surface in a wing structure and the inner

surface defined as the surface on which the stiffener is mounted.

Table 4-2 : Lay-up details

Lay-up details for specimens Lay-up

Skin [45/−45/0/90/02/−45/45/02/90/02/45/−45/0]S

Stiffener (per half section) [0/90/02/−45/45/04/−45/45/02/90/03/90/0]

Page | 84


Table 4-3: Material properties of IM7/8552

Properties IM7/8552

Longitudinal Young’s Modulus xE Tension 176.6 GPa

xE Compression 154.1 GPa

Transverse Young’s Modulus yE Tension 8.6 GPa

yE Compression 9.8 GPa

Out of plane Young’s Modulus zE Tension 10.5 GPa

zE Compression 9.4 GPa

Shear modulus xyG 4.5 GPa

Out of plane Shear modulus xzG 4.3 GPa

Out of plane Shear modulus yzG 3.2 GPa

Longitudinal Strength Tension 2.3 GPa

Compression 1.6 GPa

Transverse Strength Tension 0.06 GPa

Compression 0.25 GPa

Shear strength 0.1 GPa

Poisson’s ratio xyν 0.34

Poisson’s ratio xzν 0.31

Poisson’s ratio yzν 0.48

Mode I critical strain energy release rate IcG 0.21 kJ/m2

Mode II critical strain energy release rate IIcG

0.61 kJ/m2

Page | 85


4.3 FE Models

4.3.1 The Model

The FE models were created in ABAQUS [4]. The main model had 5 different parts,

the skin, the adhesive that was between the skin and the stiffener, the 2 parts of the

stiffener and the filler that is used in order to fill the gap that was created because of

the curvature of the stiffener parts.

All the composite parts were created using the composite module and the properties

that given were the material properties of the IM7/8552. The adhesive had the matrix

properties of IM5/8552 and the filler had elastic behaviour of a 0 ply.

All the specimens were loaded on the unsupported skin with a constant load of 180

kN, while the other side was fixed. All parts were modelled with three dimensional

hexahedral solid elements, C3D8, to accurately capture stresses in the through-

thickness direction. Also, solid elements are capable of modelling several layers of

different materials for the analysis of laminated composites. The analysis made use of

ABAQUS/Standard which well suited to quasi-static and low-speed dynamic events.

4.3.2 Mesh Sensitivity Study

The mesh sensitivity was examined by applying different meshes to the configuration

Stif 2. The region that was more critical is near the tip of the stiffener and for this

reason a finer mesh was needed there. The bias module in ABAQUS was used and the

meshes were named from the element thickness.

The naming code of meshing models was ‘mesh x1-x2-x3’, where x1 was the

‘thickness’ of the finite elements, x2 was the step of bias and x3 was the number of

elements in bias (see

Figure 4.7). There element thickness x1 was the direction in which the elements had

the specified thickness and bias x2-x3 the area where the bias module was used. The

criterion that was used in order to validate the mesh sensitivity was the maximum

peeling stress in the adhesive, because this stress plays an important role in skin-

stiffener debonding. The adhesive, which is 0.1 mm thick, was modelled with two

elements through the thickness.

Page | 86


Figure 4.7: An example of naming code of meshing models, here a 1-10-80 model.

The first mesh (mesh 5-10-80, shown in Figure 4.8) was the benchmark. By

decreasing the element thickness from 5 to 3 and then to 1, the results could be

observed to be quite different near the stiffener edge, which was the critical area

(Figure 4.8). As shown in Figure 4.8 and Figure 4.9 , the third mesh gave converged

results and was therefore used for the rest of the analysis.

Figure 4.8: Peeling stresses for different meshes along path 1

-30

-25

-20

-15

-10

-5

0

5

10

15

350 360 370 380 390 400

Stre

ss [

MPa

x103 ]

Lenght [mm]

Peeling stresses

1. mesh 5-10-80 2. mesh 3-10-80

3. mesh 1-10-80 4. mesh 1-10-120

Length [mm]

Page | 87


Figure 4.9: Max peeling stresses for different meshes

4.3.3 Model analysis and results

The peeling stresses were studied in 3 different paths in the adhesive, as can be seen

in Figure 4.10. All the paths were in the middle of the adhesive and between the 2

through-thickness elements.

Figure 4.10: The paths where the stresses were calculated

Path 1 was along the stiffener and in the middle, just beneath the blade, in order to

capture the effect of the blade design on the stresses. In addition, this path

0

2

4

6

8

10

12

1. mesh 2. mesh 3. mesh 4. mesh

Stre

ss [M

Pa x

103 ]

max peeling stresses

Page | 88


corresponds to the one used in the theoretical analysis previously shown. The peeling

stresses, copared with the analytical solution from Figure 4.3, in this path are shown

in Figure 4.11 while the shear stresses are shown in Figure 4.12.

Figure 4.11: Peeling stresses along Path 1

Figure 4.12: Shear stresses along Path 1

-60

-50

-40

-30

-20

-10

0

10

0 100 200 300 400

stres

s [M

Pa]

length [mm]

Path-1 peeling stresses

Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5Analytical

0

5

10

15

20

25

0 100 200 300 400

stres

s [M

Pa]

length [mm]

Path-1 shear stresses

Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5

Page | 89


All the designs had the same behaviour until the middle of the stiffener, where the

taper starts. The biggest differences were at the end of the stiffener, something that is

expected from the numerical analysis. Comparing the different designs with each

other, a closer look was needed, as in Figure 4.13 and Figure 4.14, in order to

determine the differences and the effects of the designs on the peeling stresses.

Figure 4.13: Peeling stresses in Path 1 near the edge of the stiffener

It is clear that reducing the geometrical discontinuity at the tip of the stiffener, the

stresses are affected. The benchmark was the design Stif 0. Comparing the stresses

with those from Stif 1, it can be inferred that the taper did not lead to a significant

decrease of the peeling stresses. In contrast, by analysing the curves for Stif 2 to Stif

5, it can be observed that alleviating the geometrical discontinuity has a significant

effect in decreasing the peel stresses as well as the shear stresses, Figure 4.13 and

Figure 4.14. By comparing the designs Stif 2 and Stif 3, it can be concluded that the

curvature of the taper does not have a significant contribution to the peel stresses and

to the shear stresses, Figure 4.13 and Figure 4.14.

-60

-50

-40

-30

-20

-10

0

10

370 375 380 385 390 395 400

stres

s [M

Pa]

length [mm]

Zoom of Path-1 peeling stresses

Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5Analytical

Page | 90


Figure 4.14: Shear stresses in Path 1 near the edge of the stiffener

By comparing designs Stif 2, Stif 4 and Stif 5, the role of the shape of the flange can

be understood – reducing the width of the flange near the tip of the stiffener will

increase the peeling and shear stresses, and conversely increasing the width of the

flange leads to a reduction in stresses. It can be concluded that design Stif 5 gave the

lower peel stresses along path 1 from all designs compared.

Path 2 was selected in order to examine the stress distribution between the centre of

the stiffener and the flanges, Figure 4.10. Path 2 intersects path 1 at the region that

showed maximum peeling stress for design Stif 0, 20 mm from run-out tip. The

results can be seen in Figure 4.15 for peeling stresses and Figure 4.16 for shear

stresses.

For Stif 1, the peeling stresses are higher close to the edge of the flange. The taper

introduced in Stif 2 can be observed to not have a significant effect on the stress

profile of the peeling stresses when there is a reduction in shear stresses. Alleviating

the geometrical discontinuity (Stif 2 to 5) does have a big effect on the profile, and

increasing the width of the flange (Stif 5) is again seen to be beneficial as it leads to a

more uniform stress distribution.

0

5

10

15

20

25

370 375 380 385 390 395 400

stres

s [M

Pa]

length [mm]

Zoom of Path-1 shear stresses


Page | 91


Figure 4.15: Peeling stresses in Path 2

Figure 4.16: Shear stresses in Path 2

The peeling and shear stresses were analysed along another path, path 3 (see Figure

4.10). Path 3 was used to investigate in more detail the peeling stresses next to the

-2

-1

0

1

2

3

4

5

-50 -30 -10 10 30 50

stres

s [M

Pa]

length [mm]



0

5

10

15

20

25

30

-50 -30 -10 10 30 50

stres

s [M

Pa]

length [mm]



Page | 92


discontinuity between the skin and the stiffener. The results for the designs

investigated are shown in Figure 4.17 and Figure 4.18.

Figure 4.17: Peeling stresses in Path 3

Figure 4.18: Shear stresses in Path 3

-45

-40

-35

-30

-25

-20

-15

-10

-5

0-50 -40 -30 -20 -10 0 10 20 30 40 50

stres

s [M

Pa]

length [mm]



0

5

10

15

20

25

30

35

40

45

-50 -40 -30 -20 -10 0 10 20 30 40 50

stres

s [M

Pa]

length [mm]



Page | 93


The results are qualitatively similar to those from path 2, with Stif 5 giving the best

performance. In conclusion, it can be stated that both the tapering of the run-out and a

widening of the flange can have a positive effect in reducing the peel and shear

stresses and obtaining a more uniform stress distribution in the width direction.

4.4 Energy release rate for debonding While the analysis of stress distributions is helpful in understanding qualitatively how

several geometrical parameters can affect the mechanical response of a run-out, a

quantitative analysis can be achieved by calculating the energy release rate for

debonding. For an FE model with 3D solid elements and assuming constant crack

length a all across the skin-stiffener interface, the total strain energy release rate can

be calculated [85]. This means that the total strain energy release rate can be

calculated from the difference in the strain energies between two same geometry FE

models, e.g. Figure 4.19a geometry, for a given debond length a in the skin- stiffener

interface. By calculating the total strain energy release rate while the debond

propagates, 𝐺 = 𝑑𝑈 𝑑𝑎⁄ , any increase of the value will indicate unstable debonding.

Figure 4.19: Designs and dimensions in mm of a) the baseline stiffener and b) the parametric stiffener.

100

10

2.5

1.25

15

2

1530

(a)

b 20

(b)

50

30

1020

d

c

aa

Page | 94


With this aim, the structural performance for debond stability of a baseline skin-

stiffener configuration under longitudinal compression, with geometry and

dimensions shown in Figure 4.19a, was compared to that of a modified parametric

configuration shown in Figure 4.19b.

The modified configuration has a widening flange towards the termination end of the

stiffener but this added material is offset by the taper of the stiffener web. This results

in a stiffener design with a similar overall weight to the baseline design.

For the parametric configuration, various values of b, c and d were analysed. The

materials used in this study are IM7/8552 carbon/epoxy pre-preg, with ply thickness

0.25 mm, for the skin and the stiffener, and FM300 adhesive film (0.15 mm thick) for

the bondline, with properties shown in Table 4-3 and Table 4-4 respectively.

Table 4-4: Material properties for FM300 measured in house

Material Exx [GPa]

Eyy [GPa]

Gxy [GPa]

vxy X

[MPa] Y

[MPa] S

[MPa] GIc

[kJ/m2] GIIc

[kJ/m2] η

FM300 2.38 - 0.68 - 61 - 49.8 0.9 2.5 8.0

In test results shown in Chapter 2.7, with geometry similar to that in Figure 4.19a, the

specimens failed by unstable debonding of the stiffener from the skin. Therefore, the

different configurations in this study were assessed by comparing the energy release

rates of the run-outs for a given displacement and for several initial debond lengths.

4.4.1 The FE model

All the FE simulations of the parametric study were carried out in ABAQUS and the

parameterized models were created using Python. The main model has five different

parts: the skin, the adhesive between the skin and the stiffener, the two parts of the

stiffener and the filler. A mesh sensitivity study was carried out to ensure that all

results presented are mesh converged. The FE model with boundary conditions is

shown in Figure 4.20.

Page | 95


Figure 4.20: The FE model of a specimen with the boundary conditions.

4.4.1.1 Assigning Element Type

The next step involves assigning element types to the various parts. Figure 4.21

shows the element families that are used most commonly in a stress analysis.

Figure 4.21: Commonly used element families [4]

In this study the 3D continuum elements (C3D8) were used, an 8-node linear brick

element, nodes at corners, and uses linear interpolation in each direction [4]. These

elements are capable of modelling several layers of different materials for the analysis

of laminated composites, which is ideal for this numerical study.

4.4.1.2 Stacking Sequence

The skin consists of eight plies and the stiffener consists of five plies. In order to keep

the same size ratio of the larger stiffeners described before, there was a limitation on

the number of plies. In particular, the stiffener thickness was chosen in order to have a

variety of ply orientations. The stacking sequences used for the skin and the stiffener are

shown in Table 4-5.

Displacement

Page | 96


Table 4-5: Stacking sequence for the skin and the stiffener

Part Stacking Sequence

Skin [45/-45/0/90]s

Stiffener (per half section) [0/90/-45/45/0]

Figure 4.22 shows the composite ply orientations for the skin. The thickness of each

ply is 0.25 mm (double thickness) and the number of integration points per ply is set to 1.

The same procedure was followed for the stiffeners.

Figure 4.22: Stacking sequence for the skin

4.4.1.3 Mesh

The number and the distribution of elements is in great importance in FE analysis. In

this analysis the “sweep” technique was used and the algorithm was specified as

“Advancing Front”. The coarse mesh of the modified design is shown in Figure 4.23 .

Page | 97


Figure 4.23: Course mesh for the modified design with 3D continuum elements

4.4.1.4 Step

Each ABAQUS model uses two steps in the analysis procedure; The first one is the

Initial step that cannot be edited, deleted, renamed, copied or replaced and it is created

by the software at the beginning of the model’s step sequence. In addition, the initial step

allows the user to define initial boundary conditions, predefined fields and interactions [4].

The second one is the Analysis step. This step defines the type of analysis to be performed

during the step, i.e. static, dynamic or transient heat transfer analysis. There are no

restrictions to the number of steps the user can define, but there are limitations to the

step sequence.

In this study, the type of analysis was “Static, General” and the time period was set to

“1”. The “Automatic Incrementation” procedure was preferred, since a general static step

analysis was performed. The maximum number of increments was set to 1000 to

reassure that the analysis will not halt if the step exceeds the number of increments.

The default value for the maximum number of increments is 100.

Page | 98


4.4.1.5 Constraints

Constraints were defined in the Assembly module for the initial positions of instances.

The type of constraint created for this model was the “tie constraint”, and as the name

suggests, ties two surfaces together for the duration of the simulation. It makes the

translational and rotational degrees of freedom equal for the two surfaces. This tie

allows the user to fuse together two regions even though the meshes created on the

surfaces of the regions may be dissimilar [8]. Figure 4.24 shows how the master and the

slave surfaces are displayed in the model.

Figure 4.24: Surfaces constraints between the skin (master surface-red) and the adhesive (slave surface-pink)

4.4.1.6 Boundary Conditions In the current study, two boundary conditions (BC) were defined. The first BC, named

DC-1, was applied on the left edge of the stiffener, Figure 4.25, and constrained all

displacements and rotations . The second BC, named BC-2 was applied on the left edge of

the stiffener and all displacements and rotations were constrained apart from the zU

which was set to zU =1. zU is the displacement in the z-direction and represents the

machine’s crosshead displacement.

Page | 99


Figure 4.25: Modified model with BC-1 on the left edge (clamped) and BC-2 on the right edge ( zU =1)

4.4.1.7 Mesh Sensitivity Study

A finite element analysis leads to an approximate solution and it can only guarantee

that equilibrium is satisfied on an average sense over an element. As a consequence,

the accuracy of the results is expected to improve when the size of the element is

decreased.

Moreover, in regions of stress concentrations, it is necessary to increase the accuracy of the

FE solution by either using elements with higher-order shape functions (p-refinement) or by

using a finer mesh of elements (h-refinement). The goal that a designer needs to achieve is

to select the best mesh density which is not prohibitively expensive to run and at the

same it will provide accurate and acceptable results [86].

In this study, three different meshes were used; the coarse mesh, the intermediate

mesh and the fine mesh. In Table 4-6, the strain energy and the running time of each

model using a standard Pentium Core 2 Duo, 2.6 GHz with 4 GB RAM computer are

presented.

Page | 100


Table 4-6: Mesh Sensitivity Study results.

Mesh Strain Energy (KJ)

Number of Elements

Running Time (minutes)

Deviation (%)

Coarse 30150 13100 25 -

Intermediate 30138 18700 35 0.039

Fine 30109 51000 90 0.096

Moreover, the partitioning technique was used. It's ply was represented as separate

material with own orientation the in order to simulate the composite lay-up. As a result,

8 partitions were created for the skin and 5 for each stiffener and material orientation

was applied.

The results obtained from both approaches were similar, Figure 4.26, and the solution can

be considered converged for all meshes. Since the running time for the intermediate

mesh was 35 minutes and the results appeared accurate and acceptable, this specific density

of elements was selected for the rest of this study.

Figure 4.26: Strain energy with composite lay-up (blue line) and with material orientations (red line)

29.829.929.930.030.030.130.130.230.230.330.3

0 10000 20000 30000 40000 50000 60000

Stra

in en

ergy

(KJ)

Number of elements

Strain energy with composite lay up

Strain energy with material orientation

Page | 101


4.4.2 The Python script

In order to perform the parametric study, a large number of models has to be created

and a script that generates these models is needed. This script was written in Python

[5] because of the advantage of using the ABAQUS scripting interface. The script

created automatically generates all models and runs them automatically. The major

advantages of the script are the automation, and reduced user time and effort required

for model generation.

The script generates parametric stiffener run-out models, generates models with

different crack lengths, and runs all models with ABAQUS. The script uses a basic

stiffener run-out configuration and changes the design each time according to the

parameter values. When a new design is generated, the script propagates the crack and

the energy release rate is calculated for every step. This procedure is repeated for all

the parameter values.

4.5 Results from modelling

4.5.1 Energy Release rate along crack

The results of the parametric study for the design presented in Figure 4.19 are shown

in Figure 4.27, where the values of GT = GΙ + GΙΙ + GΙΙΙ, the total energy release rate,

have been normalized to the GT of the reference parametric stiffener for 0.5 mm of

crack length. The variables Gi , where i = I, II, III, refer to the strain energy release

rates associated with Mode I, ‘opening mode’, II, ‘sliding shear mode’ and III,

‘scissoring mode.’

Page | 102


Figure 4.27: Normalized energy release rates as a function of crack length (a) comparison between Baseline stiffener design and selected Tapered stiffener with b = 3 mm, c = 10 mm and d =6.25 mm), (b) Influence of parameter b on G,

(c) Influence of parameter c on G and (d) Influence of parameter d on G.

Figure 4.27a compares the normalised energy release rate for the Baseline and

reference parametric stiffeners. The negative slope of the GT(a) curve for the latter

indicates stability of crack growth (assuming constant fracture toughness). The

influence of parameters b, c, and d is presented in Figure 4.27b, 3c and 3d. It is

observed that since the objective of the optimisation routine was to enhance crack

growth stability, results for the reference modified stiffener are presented since this

configuration was the derived optimum. Figure 4.27a compares the normalised energy

release rate for the baseline and selected parametric stiffeners. Given the objective of

optimising for stability of crack growth, the configuration with 3b mm= , 10c mm=

and 6.25d mm= was selected to be carried out for the following stages of this study

and named Tapered design.

(a) (b)

(c) (d)

a [mm] a [mm]

0.6

0.7

0.8

0.9

1.0

1.1

0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ized

GT

a [mm]

Baseline Stiffener

Selected Modified Stiffener

0.6

0.7

0.8

0.9

1.0

1.1

0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ized

GT

a [mm]

Parameter b

b = 1 mm

b = 2

b = 3 mm (Selected)

0.6

0.7

0.8

0.9

1.0

1.1

0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ized

GT

a [mm]

Parameter c

c = 2 mm

c = 6 mm

c = 10 mm (Selected)

0.6

0.7

0.8

0.9

1.0

1.1

0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ized

GT

a [mm]

Parameter d

d = 9

d = 6.25 mm (Selected)

d = 4 mm

Page | 103


As will be described in greater detail in the next chapter, while the Baseline

specimens did fail by debonding, the Tapered specimens did not: interlaminar and

intralaminar failures were the main failure modes of the modified run-out stiffener.

After examination of the specimens, it was observed that the specimens failed through

delamination between 0o and 45o (Figure 4.28). For this reason, a second iteration

of the models was carried out, including the modelling of delamination.

Figure 4.28: (a) Front view of failed specimen; (b) Exploded view showing the failed area; (c) Front view of Bottom part

showing 00 plies ; (d) Bottom view of the Upper part showing delaminated 450 plies

4.5.2 2nd iteration

A more detailed analysis of different configurations, which accounts for delamination,

was therefore undertaken. Three specimens were analysed. These include the Baseline

and the Tapered configuration with the parameters identified in the previous section.

The third configuration stemmed from the experience and sensibility gained during

the project. It appeared reasonable that adding a compliant region ahead of the run out

tip would reduce the stresses at the tip and thus contribute to a more stable crack

growth. Therefore, the merits of a compliant termination scheme were also

investigated.

Page | 104


4.5.2.1 Compliant skin-stiffener configurations

Four new configurations were analyzed, Figure 4.29(a)-(d). The first design, Tip-

Tapered (Figure 4.29a), was a stiffener run-out tapered down to the edge, in order to

remove the discontinuity, with a widening in the flange to avoid the delamination. By

having a widening flange, together with a tapered web, this configuration increases

the compliance of the run-out region. The second design, Notch-Tapered (Figure

4.29b), had a 45o notch (filled with an adhesive spew fillet) cut at the base of the

stiffener. The insertion of the adhesive at the base was used in order to increase the

local compliance and thus reduce the local peeling stresses. Two more designs were

developed by considering the potential benefits of local stiffness variations; one with

a step tapered blade, Step-Tapered (Figure 4.29c), and the other with a curved cut,

Curve-Tapered (Figure 4.29d).

Figure 4.29: Compliant Skin-Stiffener designs

The new FE model that was created in order to investigate these specimens is shown

in Figure 4.30b and Figure 4.30c. The different configurations in this study were

b 20

(a) Tip-Tapered stiffener configuration

50

30

1020c

a

50

30

1020

d

bc

(c) Step-Tapered stiffener configuration

20

b 20

(b) Notch-Tapered stiffener configuration

50

30

1020

d

c

a

50

30

1020

d

bc

(d) Curve-Tapered stiffener configuration

(0,0)

(15, 8)(42.5, 11.5)

(30.5, 4.2)

2nd order polynomial

a a

(w, h)

Page | 105


assessed by comparing the energy release rates of the run-outs for a given end

displacement and for several initial debond lengths, following the procedure described

previously.

Figure 4.30: a) Tapered stiffener after testing, b) FE model showing delamination path, and c) FE model of a specimen with boundary conditions.

The results of the normalised strain energy release rates are shown in Figure 4.31,

where the values of GT = GΙ + GΙΙ + GΙΙΙ, the total strain energy release rate, have been

normalized by the GT of the Tapered stiffener (Figure 4.19(b) for 0.5 mm crack

length. The negative slope of the G(a) curve indicates crack growth stability, while a

positive slope indicates instability (assuming constant fracture toughness). From a

comparison of the four designs, it can be assumed that the best performance is

expected by the Curve-tapered design. In order to optimize the design of the Curve-

tapered specimen, Figure 4.29(d), a parametric study for the parameters w and h was

assessed. The results of this study are presented in Figure 4.32, (a) for debonding and

(b) for delamination. In all cases, the energy release rate for delamination is lower

than for debonding. The designs expected to have stable debonding are the ones with

parameters (30, 9.2) and (30, 6.5). Because of the lower energy release rate of the

second, this Curve-tapered design was selected and taken forward in the rest of this

study as Compliant design.

Displacement

(a) (b)

(c)

Delamination area

Page | 106


Figure 4.31: Normalized strain energy release rates as a function of crack length showing a comparison between designs. The points were obtained numerically and the curves are spline fits.

Figure 4.32: Normalized energy release rates of the Compliant design of different (w, h) values for (a) debonding and (b) delamination

Debonding

Delamination

Tip-Tap. Notch-Tap. Step-Tap. Curve-Tap.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5

Nor

mal

ised

GT

a [mm]

(a) (b)

0.8

0.85

0.9

0.95

1

0 1 2 3 4 5

Nor

mali

sed

GT

a [mm]

Debonding

(30, 9.2)

(25, 6.5)

(30, 6.5)

(30,5.4)

(35, 6.5)

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5

Nor

mali

sed

GT

a [mm]

Delamination

(30, 9.2)

(25, 6.5)

(30, 6.5)

(30,5.4)

(35, 6.5)

Page | 107


4.5.2.2 Energy release rate along crack

The structural performance of three different skin-stiffener configurations – Baseline

(B), Tapered (T) and Compliant (C) – under longitudinal compression, with geometry

and dimensions shown in Figure 4.33, was assessed. Compared to the Baseline

stiffener (Figure 4.33a), the other two configurations have a widening flange towards

the termination end of the stiffener but this added material is offset by the taper of the

stiffener web (Tapered configuration, Figure 4.33b). The third configuration includes

taper with a curvature (Compliant, Figure 4.33c).

Figure 4.33: Stiffener design configurations (dimensions in mm).

The three different configurations were analysed for debonding and delamination

growth stability. The results of this analysis are presented in Figure 4.34, where the

100

10

2.5

1.25

15

2

20

1530

(a) Baseline stiffener configuration

50

30

1020

d

bc

a

50

30

1020

d

bc

20

(b) Tapered stiffener configuration

(c) Compliant stiffener configuration

(0,0)

(15, 8)(42.5, 11.5)

(30.5, 4.2)

2nd order polynomial

Page | 108


values of GT = GΙ + GΙΙ + GΙΙΙ, the total strain energy release rate, have been

normalized to the GT of the reference parametric stiffener for 0.5 mm of crack length.

The negative slope of the G(a) curve indicates stability of crack growth, while a

positive slope indicates instability (assuming constant fracture toughness).

Recalling the failure modes obtained experimentally [87] the Baseline stiffener

failed by debonding and the Tapered stiffener initially experienced debonding until it

finally failed by delamination. This is in agreement with the predictions in Figure

4.34. Consequently, both models were able to correctly describe these experimental

results [87]. In addition, the stability analysis for the Compliant stiffener predicts that

this design will fail stably by debonding, Figure 4.34.

Figure 4.34: Normalized strain energy release rates as a function of crack length; comparison between Baseline stiffener design (Figure 4.33α), Tapered stiffener (Figure 4.33Figure 4.19b) and Compliant stiffener (Figure 4.33Figure 4.19c)

with dimensions b=3 mm, c=10 mm and d=6.25 mm.

4.5.3 Energy release rate along the width of the crack tip

The strain energy release rate along the width of the crack tip was calculated for the

Baseline, Tapered and Compliant configurations (Figure 4.33). Fracture initiation is

Debonding

Delamination

Baseline Tapered Compliant

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5

Nor

mal

ized

GT

a [mm]

Page | 109


expected when the GT exceeds the fracture toughness Gc for a given mixed-mode ratio

GII / GT at each point along the crack tip. In other words, propagation at each point

occurs when GT / Gc >1 [74, 88]. The interlaminar fracture toughness Gc can be

calculated by using the following equation [89]:

( ) IIcc Ic IIc Ic

T

GG G G GG

η

= + −

(3.22)

where GIc and GIIc are the experimental values of fracture toughness for mode I and II

and η is determined by curve fitting (see Table 4-4). The value of Gc is normalised to

the width-average value for the Tapered specimen. Figure 4.35 shows that the trend is

similar for the Baseline and Tapered specimen types but is different in the centre of

the Compliant stiffener. This is due the difference in the web of the stiffeners.

Figure 4.35: Normalized GT/Gc across the crack tip for crack a = 1 mm for the Baseline, Tapered and Compliant specimens.

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0 2 4 6 8

Nor

mal

ised

GT / G

c

Distance across width [mm]


Page | 110


The curved taper has reduced the normalized strain energy release rate in the centre

without affecting the trend in the flange. According to equation 1 in [88] 𝐺𝐶 ∝ 𝑃2.

The maximum value of the energy release rate can be used to predict the load

corresponding to the initiation of fracture using:

c

FE T

P GP G

= (3.23)

where P is the load at initiation of fracture, PFE is the load from the FE model, Gc the

critical strain energy release rate (Equation 1.26), and GT is the strain energy release

rate predicted by the FE model as defined previously. Two different predictions for P

can be made: one using the maximum value of GT along the width, and another using

the average, Table 4-7.

Table 4-7: Predicted failure load

Predicted failure load [kN]

Based on Gavg Based on Gmax

Baseline Stiffener 19.00 16.56

Tapered Stiffener 19.17 17.45

Compliant Stiffener 19.93 18.17

4.5.4 Modeling debonding failure using VCCT

The implemented VCCT method in ABAQUS standard, developed by Boeing and

Simulia, suggested promising results, especially when the mismatched meshes had

only 3% error comparing with pairing meshes. Replacing the cohesive contact, two

surfaces (‘top’ and ‘bottom’) represented the interface plane, while the node set

‘bonded’ are those nodes on the slave surface (‘top’) behind the crack front. As can be

Page | 111


seen in Figure 4.36(a) there was good correlation between the VCCT and the

parametric study.

Figure 4.36: Comparing the results of the parametric study with the VCCT method (a) along the crack and (b) along the width of the stiffener.

On the other hand, the VCCT method could not capture the detail at the flange edge

and the weakness of the method was exposed. Generally, the discontinuities in the

geometry increase the normalised GT/GC and this trend couldn't be captured. In order

to capture the detail in the edge of the flange, the mesh resolution was increased and

was biased towards the sides, Figure 4.37, and the results can be seen in Figure

4.36(b). Despite the good results, the size of the model and the time needed for

running it prevent for further developments using VCCT.

0.5

0.7

0.9

1.1

1.3

1.5

0 1 2 3 4 5 6 7

Nor

mal

ised

GT/

GC

Distance along the crack tip [mm]

Baseline Stiffener

VCCT script results

0.9

1

1.1

1.2

0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ised

GT/

GC

a [mm]

VCCT script results

Reference Data

Baseline Stiffener

Baseline Stiffener

VCCT results

VCCT results

(a) (b)

Page | 112


Figure 4.37: The refined model that was used in the VCCT method

4.6 Conclusions A closed-form model was initially developed that predicted peel stresses in adhesively

bonded joints. The closed-form model permitted an investigation to compare the

singular stress fields at discontinuities, leading to a better understanding of the

problem.

By using FE models, similar peeling stress fields, as well as shear stress fields, were

obtained specifically for skin stiffener run-outs. The effect of the termination on the

singular stresses was examined in detail and it was hypothesised from observation of

the said fields that a tapered blade paired with a flange widening to the end of the

stiffener should reduce the peeling stresses.

Baseline, tapered and compliant stiffener run-out configurations were then analysed

using VCCT for debonding and delamination. The analyses led to predictions of the

failure modes more likely to happen for each specimen type, as well as information on

the stability of crack growth. They also led to quantitative data that can be used to

predict failure loads. This will be addressed in the following chapter, where a

comparison with experimental values will be performed.

Page | 113

Chapter 4

Manufacturing and testing

procedures

5 Manufacturing and testing procedures

5.1 Manufacturing of Stiffener Specimens All specimens were manufactured at Imperial College of London (four specimens for

each design). Each one of them consists of four main parts: the skin, the stiffener, the

adhesive and the filler. The skin and the stiffeners were manufactured using hand lay-up and

cured in the Autoclave according to Hexcel’s recommendations. The adhesive is actually a

film of 0.15mm thickness which is used in the bondline between the skin and the

stiffener and its material is FM300. Moreover, the filler was made by composite strips

of IM7/8552. The strips were gently twisted to enhance consolidation. Finally, all parts were

bonded using wooden moulds in order to ensure that the stiffeners were placed at the

exact position on the skin while pressure was applied.

5.1.1 Skin

The skin was composed of eight plies. The skin stacking sequence is shown in Table

5-1. The prepreg was removed from the freezer and was left to reach room

temperature before it was unrapped. This prevents moisture from condensing on the

Chapter 4 - Manufacturing and testing procedures

cold prepreg. Two rectangular unidirectional laminates, 300mm long and 150mm wide,

were cut and stacked. The ply by ply stacking procedure is shown in Figure 5.1.

Figure 5.1: Hand lay-up for the skin plates.

Having layed-up half of the plies (four plies), the sub-laminates were consolidated

using the vacuum table for 2 minutes. The next step for the manufacturing process was to

cure the plates in the Autoclave. According to Hexcel, the plates need to be cured at

110oC for 60 minutes and then at 180oC for 120 minutes (Figure 5.2).

Figure 5.2: Curing procedure on the Autoclave

Page | 115


The whole procedure was carried out under vacuum. The size of each skin was

110mm by 30mm. However, the plates were cut into shapes of 140mm by 30mm

since the specimens needed to be end-tabbed before they were ready to be tested. The

cutting schedule is shown in Figure 5.3.

Figure 5.3: The cutting schedule

5.1.2 Stiffener

The stiffener part is probably the most vital part of a stiffener run-out. In most studies,

failure initiates at the edge of the run-out and propagates along the skin-stiffener [60,

61] [63, 64] interface [66, 90-96]. Hence, the geometric features of these specimens

in the area of the stiffener strongly affect their failure load. As a result, a significant

effort was put on this part of the work so as to achieve the best quality of the

specimens.

Table 5-1: Composite ply orientations

Part Ply orientations

Skin [45/−45/0/90]S

Stiffener (per half section) [0/90/−45/45/0]

Page | 116


The composite lay-ups for the skin and the stiffener are shown in Table 5-1.

Aluminium blocks were machined and used as moulds in order to give the exact

geometry and dimensions to the produced stiffeners. The shape and the dimensions of

the stiffener mould can be seen in Figure 5.4.

Figure 5.4: Mould for the stiffener. All dimensions are in mm.

The stiffeners and the composite skin were manufactured using hand lay-up and cured

in an Autoclave according to Hexcel’s recommendations (60 minutes at 110C then

120 minutes at 180C under vacuum). Figure 5.4 also shows the two parts of the mould

after the lay-up and the whole stiffener after the curing (small picture top right). The curing

cycle is the same used for the skin. In this step, the stiffener was cured along with the filler

to avoid wrinkling of the fibres.

5.1.3 Filler

The filler required a particularly careful manufacture for two main reasons. Firstly, a

homogeneous filler was needed in order to avoid a weak area with potential defects in

the stiffener. Secondly, the exact shape is very important for avoiding wrinkling of the

stiffener plies. A second mould was designed and manufactured from the machined

aluminium blocks, Figure 5.5. The quality of the stiffener is illustrated in Figure 5.6.

20

3.75

32

700

5

6 10

1.25

16.5

15R 1.25

Page | 117


Figure 5.5: Mould for the filler. All dimensions are in mm.

Figure 5.6: Micrographics of (a) the stiffener, (b) a zoomed area of the stiffener, (c) filler made by stacked stripes and (d) filler made by twisted tows.

The filler was made by composite strips of IM7/8552, with two manufacturing

procedures being compared. In the first one, the strips were simply stacked in the

mould, leading to some voids (Figure 5.6c). In the second one, the strips were gently

and slightly twisted to enhance consolidation, leading to an improved quality for the

R 2.5

700

(a)

(b)

(c)

(d)

1 mm

0.25 mm

0.2 mm

0.2 mm

Page | 118


filler (Figure 5.6d). Following the manufacture (including cure) of the filler, the

stiffener was cured using the filler and the mould in Figure 5.4.

5.1.4 Bonding

The three types of stiffeners (Baseline, Tapered and Compliant) were machined to the

required shapes and dimensions, Figure 4.33, and bonded onto the skin with the

adhesive by the following procedure. Having all the parts prepared, they were bonded

together in order to create a single part, i.e. the stiffener run-out. This final step requires

the skin to be bonded on the stiffener using an adhesive. As reported before, the

material of the adhesive is FM300 and its properties are listed in Table 4-4. The

surfaces that were to be bonded were grit blasted and degreased. Wooden moulds

were used at the bonding stage in order to ensure that the stiffeners were bonded at the

exact positions on the skin while pressure was applied. Figure 5.7 shows the bonding

stage of the manufacturing process.

Figure 5.7: Bonding stage with the skin, the stiffener and the adhesive film in the wooden mould

In the final stage, the specimens’ ends were potted in epoxy resin, and subsequently

the ends were machined so as to ensure suitable load transfer during the experiments.

The specimens with the epoxy resin potted on the one end are shown in Figure 5.8. The

specimens types that were manufactured were the Baseline, the Tapered and the Compliant,

Page | 119


Figure 5.9. For the use of Digital Image Correlation (DIC), the specimens’ surface

was finally coated with a random and contrasting speckle pattern.

Figure 5.8: Specimens’ ends potted in epoxy resin

Figure 5.9: (a) Baseline stiffener specimen; (b) Tapered stiffener specimen (identical flange geometry to Compliant type (b-i) profile of the Tapered stiffener specimen; (b-ii) profile of the Compliant stiffener specimen.

(a)

(b)

(i) (ii)

Page | 120


5.2 Testing of stiffener run-outs The tests were carried out in an Instron testing machine, equipped with a 100 KN load

cell, at a loading rate of 0.2 mm/min. Load and crosshead displacement were

recorded continuously by a PC data logger connected to the load cell and the Instron

machine at a sampling rate of 2 Hz. The specimens were aligned by careful

measurement in the loading direction to avoid bending. The Imperial Data Acquisition

(IDA) program was used to record load and displacement during the tests. A high

resolution camera was used to take photos periodically in order to detect any surface

damage and debonding.

5.2.1 Digital Image Correlation

The strains and the displacements were measured with the application of DIC using

the Aramis 1.3M system developed by GOM [97]. This consisted of two pairs of

cameras that used Schneider-Kreuznach lenses (50mm) and produced images with a

resolution of 1280x1024 pixels. These were processed using the Aramis software.

5.2.2 Acoustic Emission

Acoustic Emission sensors were used to identify and investigate failures within the

specimens during testing. The AE equipment was manufactured by Physical Acoustic

Corporation (PAC) and failure was monitored by AEwin software. Broadband (WD)

sensors with an operating frequency range of 100 KHz to 1000 KHz were used and

positioned in order to obtain the best results without affecting the specimens

behaviour [81].

Figure 5.10 shows a specimen tested in compression in the Instron machine. The picture

was taken on the last seconds of the compression testing just before failure, since

bending on the skin has already occurred. Moreover, on the bottom of the picture we

can see the AE sensor.

Page | 121


Figure 5.10: AE testing equpment

5.2.3 Results

The three different stiffener run-out designs that were manufactured were tested to

failure. The Baseline stiffeners had an average failure load of 16.5 KN while the

Tapered stiffeners had an average failure load of 17.6 KN, Figure. 5.11.

Figure. 5.11: Failure loads for the baseline design and the modified design specimens, as well as the predicted failure loads using Eq. 3.23.

Baseline Stiffener Tapered Stiffener

0.00

5.00

10.00

15.00

20.00

Pred G

Pred Gmax

Spec 1 Spec 2 Spec 3 Pred G

Pred Gmax

Spec 1 Spec 2 Spec 3

Load

[KN

]

Page | 122


The same figure also shows that the predicted loads (using Eq. 3.23) match well with

the experimental values. Figure 5.12 shows the load versus displacement curves for

selected specimens of the two stiffener designs. The displacement field close to the

critical area of the expected debonding, obtained using DIC, is presented in the

same figure for different stages until final failure.

Figure 5.12: Load-Displacement and AE Amplitude-Displacement curves for the baseline and the modified stiffener. The numbered pictures present the displacements obtained with the DIC.

While the baseline stiffeners failed due to debonding of the skin-stiffener interface,

Figure. 5.13A, the modified stiffeners failed by delamination between the 0o and 45o

stiffener plies, Figure. 5.13B.

20

30

40

50

60

70

80

90

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Am

plitu

de [d

B]

Load

[KN

]

Displacement [mm]

Load Baseline Stiffener

Load Modified Stiffener

Amplitude Baseline Stiffener

Amplitude Modified Stiffener

1

1 2 3 4

2

3

4


Load Tapered Stiffener

Amplitude Baseline Stiffener

Amplitude Tapered Stiffener

Page | 123


Figure. 5.13: A. (a) Baseline stiffener; (b)-(c) detail before and after failure respectively; (d)-(e) clean debonded surfaces in the skin and stiffener respectively.

B. (a) Tapered stiffener; (b)-(c) detail before and after failure respectively; (d)-(e) delaminated surfaces in the skin and stiffener respectively.

Failure was unstable for both specimen types (Figure 5.12). The acoustic emission

signals (Figure 5.12) show that there was an increase in AE activity 0.01 mm before

catastrophic failure for the baseline specimen. For the modified specimen type, the

increase in AE emission started about 0.05 mm before catastrophic failure.

Figure.5.14 shows the peak frequency during the tests for both specimen types. A

scale on the right hand side indicates the mode of failure typically associated with

these peak frequencies [81].

Figure.5.14: Peak frequencies versus displacement for (a) Baseline and (b) Tapered stiffeners.

(a)

(b) (c)

(d) (e) (a) (e)(d)

(c)(b)

A B

Matrix cracking

Delamination

Fibre / matrix debonding

Fibre failure

Fibre pull-out

10

110

210

310

410

510

610

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak

Fre

quen

cy [K

Hz]

Displacement [mm]

10

110

210

310

410

510

610

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak

Fre

quen

sy [K

Hz]

Displacement [mm]

(a) (b)

P-FRQ Baseline Stiffener P-FRQ Tapered Stiffener

Page | 124


5.3 2nd Iteration The modified design failed by delamination, which had not been considered in the

initial numerical study (see section 4.4.1). Models including delamination were then

numerically investigated in detail (see section 4.5.2). A more detailed parametric

analysis of different configurations suggested that a compliant configuration (Figure.

5.15 a) with dimensions b=3 mm, c=10 mm and d=6.25 mm would have an improved

and stable response ( Figure. 5.15b). The response of these stiffeners is compared to

the Baseline and Tapered in this section. Figure. 5.15c shows representative load

versus displacement curves for the three specimen types, while Figure. 5.15d shows

the fracture surface of the Compliant specimen, failed by debonding.

Figure. 5.15: (a) Design of the Compliant stiffener (b) Normalized energy release rates as a function of debonding and delamination length for the three configurations (c) Load-displacement curves for the three configurations (d) Failed

surface of Compliant specimen

We recall that the Baseline stiffeners had an average failure load of 16.5 kN while the

Tapered stiffeners had an average failure load of 17.7 kN. In contrast, the Compliant

50

30

1020

d

bc

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Load

[KN

]

Displacement [mm]


Load Modified Stiffener

Load Modified-2 Stiffener

Failure initiation points

(a) (b)

(c) (d)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 1 2 3 4 5

Nor

mal

ized

GT

a [mm]

Baseline debonding

Modified Debonding

Modified-2 Debonding

Baseline Delamination

Modified Delamination

Modified-2 Delamination

Baseline Debonding

Tapered Debonding

Compliant Debonding

Baseline Delamination

Tapered Delamination

Compliant Delamination

Baseline Stiffener

Tapered Stiffener

Compliant Stiffener

Failure initiation point

Page | 125


had an average failure load of 18 kN, Table 5-2. The fracture surfaces for selected

specimens are shown in Figure Figure 5.16, and the load versus displacement curves

for selected specimens of the three stiffener designs are superposed with the

respective AE signals in Figure 5.17. The predicted loads (using Eq. 3.23) match well

with the experimental values when the maximum G across the width is used, Table

5-2.

Figure 5.16: (a) Baseline stiffener, (b) Tapered Stiffener and (c) Compliant Stiffener after failure respectively.

Table 5-2: Failure loads for the different specimen types, as well as the predicted failure loads using Eq. 3.23.

Predicted failure load [kN]

(% difference with respect to experimental)

Experimental

failure load

[kN]

Based on Gavg Based on Gmax

Baseline Stiffener

19.00

(+15.2%)

16.56

(+0.4%)

16.49 +0.34-0.39

Tapered Stiffener

19.17

(+8.2%)

17.45

(-1.5%)

17.72 +0.16-0.22

Compliant Stiffener

19.93

(+10.6%)

18.17

(+0.8%)

18.02 +0.16-0.29

(a) (b) (c)

Page | 126


Figure 5.17: Loads and Peak frequencies versus displacement for a) the Baseline b) the Tapered and c) the Compliant stiffeners. A scale on the right hand side indicates the mode of failure typically associated with these peak frequencies

[81].

Matrix cracking

Delamination


Fibre failure

Fibre pull-out

(a)

Baseline Stiffener

(b)

Tapered Stiffener

Compliant Stiffener

(c)

Matrix cracking

Delamination


Fibre failure

Fibre pull-out

Matrix cracking

Delamination


Fibre failure

Fibre pull-out

10

110

210

310

410

510

610

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak

Fre

quec

y [k

Hz]

Load

[kN

]

Dislacement [mm]

10

110

210

310

410

510

610

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak

Freq

uenc

y [kH

z]

Load

[kN

]

Displacement [mm]

10

110

210

310

410

510

610

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak

Fre

quen

cy [K

Hz]

Load

[kN

]

Displacement [mm]

Page | 127


The acoustic emission signals (Figure 5.17) show that there was an increase in AE

activity 0.01 mm before catastrophic failure for the Baseline specimen. This activity

corresponded mostly to delamination and matrix cracking according to the signal

classification from Gutkin [81]. For the Tapered specimen type, the increase in AE

emission started about 0.05 mm before catastrophic failure but more peak frequencies

detected in the fibre/matrix debonding range, which is in line with the experiments.

The Compliant specimen had an increase in AE activity (corresponding to matrix

cracking) 0.1 mm before final failure. Also, in addition to load-displacement

information, Figure 5.17 shows the peak frequency during the tests for all specimen

types. The Tapered specimen configuration promoted a combination of failure modes

including delamination and fibre bridging which preceded catastrophic failure. In

addition, the Compliant stiffener, according to AE data and as visually observed

(Figure 5.17, Figure. 5.13c), suffered only from debonding. Another parameter, that

was taken into account, was the average signal level (ASL) and the results are

presented in Figure 5.18.

.

Figure 5.18: The average signal level (ASL) of the three designs

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Am

plitu

de [d

b]

Displacement [mm]

ASL

Baseline

Tapered

Compliant

Page | 128


The Baseline design showed an increase in amplitude before the sudden and unstable

failure. On the other hand, the Tapered design registered peak frequencies 0.05 mm

before failure, indicating that the initiation of the damage started at that point.

Finally, in the Compliant design, the amplitude starts increasing 0.1mm before the

failure and increasing progressively until final failure. It is worth noting that these

peak frequencies were beyond the end-displacements at which the other two designs

failed.

5.4 Conclusions The experimental failure loads show good agreement with the predicted ones (Figure.

5.11 and Table 4.7). This indicates the FE models predicted accurately the energy

release rates for the specimens tested, and that the quality of the manufacturing,

particularly at the noodle region, (Figure 5.6) was suitable for this study. The

predictions using the maximum energy release rate across the width are in slightly

better agreement with the experiments (than using the width-average), which suggests

that it is appropriate to consider the width-variation of the energy release rate in these

studies. The load-displacement and AE amplitude-displacement curves (Figure 5.17),

as well as the peak frequency-displacement plots (Figure 5.18), show that the

Compliant design is more damage tolerant than the original one. The AE monitoring

proved to be valuable in detecting and analysing the failure modes experienced by the

specimens.

Page | 129

Chapter 6

Detailed damage

modelling for Tapered

run-out stiffeners

6 Detailed damage modelling for Tapered run-out

stiffeners

6.1 Introduction During the testing procedure, the Tapered stiffeners had an unexpected delamination

in the flange that led to an intralaminar failure in the form of a matrix crack across the

0o ply near the filler's end and continued delaminating between the filler and 0o ply.

FE models were created to numerically investigate the problem, including both

interlaminar and intralaminar fracture mechanisms with different damage modelling

techniques. Surface-based cohesive behaviour was used for Cohesive Zone Modelling

(CZM) in order to capture debonding and delamination of the stiffener. The

intralaminar fracture was captured by using Hashin [9] and LaRC [21-23] damage

criteria with a smeared crack formulation as well as XFEM. The analyses were

performed in ABAQUS 6.10.

Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners

6.2 Bebonding of the Tapered Stiffener As mentioned before, understanding and subsequently predicting debonding of the

stiffener was the primary objective of the research. In this section, debonding of the

Tapered specimen is modelled using a cohesive zone model. The results of this

analysis can be compared with the calculations made using the critical strain energy

release rate across the width of the specimen, as described in Section 4.5.3.

The unexpected delamination of the Tapered stiffener between 00 and 450 plies led to

the four part stiffener modelling: two part models corresponding to the 00 plies for left

and right sides respectively and two part models corresponding to the remaining five

plies of orientation (00/ 900/-450/450) respectively, Figure 6.1. The list of part models

are listed below:

1. Skin - single part of (450/-450/00/ 900)S laminate

2. Filler - made-up of 00 fibres

3. Left - 00 lamina of the stringer

4. Left - single part of (00/ 900/-450/450) laminate of the stringer

5. Right - 00 lamina of the stringer

6. Right - single part of (00/ 900/-450/450) laminate of the stringer

Figure 6.1: The parts of the FE model

0 plies

Rest of plies

Filler

Skin

Page | 131


The interface between the skin and the stiffener was connected by using surface-based

cohesive layer, as seen in Figure 6.2. Cohesive zone modelling is generally used for

the numerical simulation of interlaminar failure in the form of delaminations where

the damage of the cohesive zone is developed at the crack that may occur.

Figure 6.2: Illustration of imposed cohesive properties for debonding mode.

Damage initiation is driven by traction separation law and the value of the maximum

traction to, Figure 6.3. New crack surfaces are formed when the fracture toughness Gc

is equal to the area surface under the traction-separation curve. Considering the nature

of predictions made by the parametric study, the model was analysed with cohesive

interaction properties of adhesive FM 300 and listed in Table 6-1, where damage

initiation and damage evolution are based on FM300 material properties and elastic

behaviour are tuned values for the model.

Figure 6.3: (a) Traction-separation law for cohesive zone models (b) Modified law to implemented in FEM

Cohesive interaction

Page | 132


Table 6-1: Cohesive interaction properties

FM300 (adhesive)

Normal direction

First shear direction

Second shear direction

BK law η

Initial linear elastic

behaviour

Knn in Nmm-3 Kss in Nmm-3 Ktt in Nmm-3

1000000 1000000 1000000

Damage initiation

N in MPa S1 in MPa S2 in MPa 50 100 100

Damage evolution

Gn in N/mm Gs in N/mm Gt in N/mm 8

0.9 2.5 2.5 All parts were modelled using three dimensional hexahedral solid linear elements,

C3D8, to effectively capture the resulting three-dimensional stress states and provide

a better representation of the geometry. The element is fully integrated thus avoiding

potential problems associated with reduced integration. While solid elements are

capable of modelling the distinct layers of a composite with one or more elements

through the ply thickness, the formulation also allows for the representation of a

stacking sequence with a single element. This latter approach was adopted in this

present study for computational efficiency.

“Tie constraints” were used to ‘fasten’ the different parts of the finite element model

together which allows for dissimilar mesh densities between parts [4]. This facilitated the

optimisation process which required frequent changes in the geometry and dimension

design variables which could lead to a mismatch in the meshes of adjoining sections. The

FE model with boundary conditions is shown in Figure 6.4 that is similar to the

parametric study model in order comparisons to be made.

Figure 6.4: Finite element model of modified specimen.

Displacement

Page | 133


6.2.1 Mode interaction A quadratic interaction criterion was used for the traction components:

2 2 2

0 0 0 1n s t

n s t

t t tt t t

+ + =

(5.1)

where, t0n , t0

s and t0t are the peak values of the contact stress when the separation is

either purely normal to the interface or purely in the first or the second shear direction

respectively.

When the initiation criterion is met, the cohesive stiffness degrades with rate that is

defined by the damage evolution model. The overall damage of the contact point is

represented by a scalar damage variable, D. After damage initiation, the damage

varies monotonically from 0 to 1 on increasing the loading.

As mentioned before, the fracture energy is equal to the area under the traction-

separation curve Figure 6.2(b) and an energy-based damage evolution approach is

used. For the mode-mix definition of fracture energies the BK law was selected,

which is based on Benzeggagh-Kenane’s criterion [88]. The BK criterion defines the

energy dissipated as

( ) c c c cSn s n

T

GG G G GG

η

+ − =

(5.2)

with, T n sG G G= + (5.3)

S t sG G G= + (5.4)

where Gn, Gs and Gt are the fracture toughness values in the normal and two shear

directions respectively which have been measured for the material IM7/8552, Table

6-1. In this study the BK mode-mix power parameter η had the value of 1.6, a value

that corresponds to material IM7/8552 and obtained experimentally by Maimi [98,

99].

Page | 134


6.2.2 Response of the Numerical Model

The debonding failure load predicted by the model was compared with the debonding

loads predicted by using the energy release rate and the experimental results, Table

6-2.

Table 6-2: Debonding loads of the Tapered stiffner

Experiment Gavg Prediction

Gmax Prediction

Cohesive layer Prediction

Failure load [kN] 17.7 19.2 17.5 18.7

Difference from experiments

- 8.5% 1.1% 5.6%

Recalling the results from the energy release rate analysis, when the maximum energy

release rate across the width of the stiffener was used the predictions were closer to

the experimental results. In addition, when the average energy release rate was used,

the difference from the experimental results had an over-prediction of 8.5%. By using

the cohesive zone model, the difference with the experimental results was 5.6%.

Figure 6.5: Damage growth pattern predicted by a cohesive model for the modified specimen compared with energy release rate predictions using VCCT

Correlation of debonding damage growth across width of the stiffener

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0 2 4 6 8

Nor

mal

ised

GT

/ Gc

Distance across width [mm]


Page | 135


Also, the debonding growth along the width of the specimen matches with the

predictions made using strain energy release rate across the width of the stiffener as

can be seen in Figure 6.5. Comparing the FE model pattern with the Tapered curve on

the right, it is clear that there is a correlation between the crack front and the energy

release rate profile.

6.3 Modeling the interlaminar failure of the Tapered

Stiffener To investigate delamination, a model was created with a cohesive zone at the interface

of the 00 and 450 plies of the stiffener.

6.3.1 Cohesive zone damage modelling definitions

A surface-based cohesive behaviour was defined at the mentioned interface with the

penalty stiffnesses from Table 5.1 and the IM7/8552 interface properties in Table 4-3.

6.3.2 Response of the model

From the response of the model it was concluded that the damage started from the

flange interface of the stiffener and expanded to the filler area. The propagation of the

delamination stopped where the web region is starting as can be seen in Figure 6.6,

where the contour plot of the cohesive damage variable (CSDMG) can be seen. The

undamaged webs were retaining the overall stiffness of the model without affecting its

linear performance up to 19.2 kN. where the first damage next to the flange edges

starts. The damage stays there up to 17.7 kN and propagates constantly towards the

centre of the stiffener and the filler area. At 19.7 kN the damage propagates at high

rate up to 19.8 kN until the final failure.

According to the observations of the failed specimen, as can be seen in Figure 6.7, the

damage predicted follows the actual failure. The only difference is that the crack in

the actual specimen seems to jump from the 0o/45o interface to the 0o/filler interface.

This intralaminar failure is numerically investigated in the following section.

Page | 136


Figure 6.6: Contour plot of CSDMG at the 0o/45o interface.

Figure 6.7: Delamination occurred in the Tapered stiffener

6.4 Modeling the intralaminar failure In order to investigate the intralaminar failure of the specimen, that could not be

readily captured with the interface-based cohesive damage zone models, a new model

has been built using Hashin’s damage model. Hashin damage model predicts

intralaminar failures in fibre-reinforced composite materials and is available in

ABAQUS. This failure model is capable of predicting four major failure modes such

as:

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4

Load

[kN

]

displacement [mm]

Experiments

Cohesive

Page | 137


• Fibre tensile failure

• Fibre compressive failure

• Matrix tensile failure

• Matrix compressive failure

The damage initiation predictions are based on Hashin’s theory [9]. This model

considers four damage initiation criteria with respect to the four failure modes listed

above. The initiation criteria in the four damage modes are described as in the

following equations,

For fibre tension failure:

2

11 tf TF

Xσ =

(5.5)

For fibre compression failure:

2

11 cf CF

Xσ =

(5.6)

For matrix tension failure:

2 2

22 12 tm T LF

Y Sσ τ = +

(5.7)

For matrix compression failure:

22 2

22 22 12 1 2 2

Cc

m T T C LYF

S S Y Sσ σ τ = + − +

(5.8)

where σ11, σ22 and τ12 are the nominal stress components, XT is the longitudinal

tensile strength, XC is the longitudinal compressive strength, YT is the transverse

tensile strength, YC is the transverse compressive strength, SL is the longitudinal shear

strength and ST is the transverse shear strength of the composite material. According

to this criterion, when the above equations reach a value of one then damage is

assumed to initiate.

Page | 138


In the damage initiation process, an energy based damage evolution model has been

used. The scalar damage variables for each failure are calculated and they

monotonically evolve from 0 to 1 on increasing the loading after the damage

initiation. A progressive degradation of material stiffness occurs and leads to material

failure for all four damage variables of the respective failure modes.

This damage evolution model is based on the four critical energy release rates for

fibre tension, fibre compression, matrix tension and matrix compression respectively

of the material IM7/8552. In Table 6-3 the intralaminar ply properties of IM7/8552

that were used in this study are presented. These values were obtained from

experimental measurements done by Camanho et al [100].

Table 6-3: Intralaminar properties of IM7/8552

Intralaminar properties of IM7/8552 Energy [N/mm]

Fibre Tensile Fracture Energy 81.5

Fibre Compressive Fracture Energy 106.3

Matrix Tensile Fracture Energy 0.277

Matrix Compressive Fracture Energy 0.788

Hashin's damage failure model is included in ABAQUS but can only be used with

plane stress formulation elements such us shell, continuum shell and membrane

elements. The ABAQUS ability to use combined types of elements in the same model

resulted in the usage of continuum shell elements only in the area were intralaminar

fracture was expected. The 0o plies of the stiffener were modelled with eight-noded

continuum shell element (SC8R), Figure 6.8a. In order to avoid any hourglass issues

an hourglass stiffness enhanced formulation was deemed necessary. Also, cohesive

interactiona was assumed in the interface of the 00 and 450 plies of the stiffener as can

be seen in Figure 6.8b.

Page | 139


Figure 6.8: Illustration of (a) 00 plies with Hashin damage model and (b) cohesive properties at 00/450 interface

The rest of the elements of the entire model, except the 00 plies, were formulated with

fully integrated solid elements (C3D8). In order to overcome the convergence

problems caused by stiffness degradations and softening mechanisms, a viscous

stabilization coefficient of 10-5 was introduced in the analysis.

According to the numerical model's results, the failure mode predicted by the Hashin

damage model is dominant matrix failure in compression in the filler area that

correlates with the region of expected failure of the observed failed specimen (Figure

5.10). The result of this particular numerical model that incorporates the Hashin

model had greatly contributed to understanding the sequence of damage in the

experiments. The contour plots of the damage variable for the matrix compression

failure mode is illustrated in Figure 6.9. This result clearly predicts compression

failure of the matrix near the ends of filler.

From the sequence of damage plots in Figure 6.9, stiffness degradation due to matrix

failure begins slowly at a load of 17.2 kN. The matrix failure propagates parallel to

the filler at the right flange at a load of 17.6 kN. Following the matrix damage on the

right side, the matrix failure also propagates on the left side at a load of 17.9 kN. This

prediction of location of the failure initiation correlates very well with the image in

Figure 6.10. The degradation of the matrix, firstly on the right-hand flange and then

on the left side, is captured and describes the sequence of intralaminar damage up to

the failure load of 19.8 kN.

00 plies with Hashin’sdamage model

Surface with cohesive properties interaction

(a) (b)

Page | 140


Figure 6.9: Contour plot of damage variable for matrix compression

The Hashin model contributed greatly to learn more about the location of initiation of

damage and the sequence of intralaminar fracture as it happened in the sample,

Figure 6.10. The sequence of failure can be described in detail by observing the

damage fields at various intervals of displacement applied during the analysis.

Figure 6.10: Matrix crack at right flange in the experimentally failed specimen

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5

Load

[kN

]

displacement [mm]

Experiments

Hashin

Page | 141


The Hashin model helped in predicting matrix crack initiation at the right flange. It

showed an increase in propagation of crack through the 00 right ply matrix at a load

of 17.85 kN. The matrix crack initiated in the left-hand flange at a load of 17.9 kN.

The final image at the end of the analysis, Figure 6.9, shows that both sides become

greatly degraded. Although, the Hashin model has helped in the numerical

investigation on the identification of intralaminar failure modes of initiation sites and

sequences, the option to delete the element of complete degradation of a particular

failure mode between the four modes is not currently available in ABAQUS 6.10. The

function of element deletion in the current model allows the removal of the element

only when all the damage variables in each of four modes reach a value of one. A gap

is created by the deletion of elements in the model.

6.5 Modeling the experimental results As a result of the conclusions drawn by the use of the Hashin model in the previous

section, new numerical models were constructed considering the following modes of

failure:

1. Delamination at the interface of the 00 and 450 plies of the stiffener in the right

and left flanges until the appearance of the matrix cracking positions.

2. Matrix failure through the 00 plies near the ends of the filler on the left and

right sides.

3. Continuation of delamination along the 00 plies on the left and right sides.

The failure modes described above have been incorporated into numerical models by

modeling a part of the assembly with appropriate interfaces and properties of

interaction. As can be seen in Figure 6.11, the delamination between the interface of

layers 00 and the filler does not propagate vertically in the web section. In reality, the

delamination between these interfaces on both sides is joined at a certain point around

the filler by a matrix crack.

Page | 142


Figure 6.11: Crack bridging in the experimentally failed specimen

6.5.1 Interaction properties

As discussed before, the ABAQUS surface-based cohesive behaviour was used to

model the interlaminar failures. The interaction properties are as explained in Section

3.1.7 and were defined using the property assign Interaction Manager module in

ABAQUS. The definition of cohesive layer delamination between 00 and 450 plies of

reinforcement is shown in Figure 6.12.

Figure 6.12: Cohesive properties imposed (Pink dots) on (a) Left stringer; (b) Right stringer

The pink spots correspond to regions in which the interactions surface-based cohesion

is applied with the respective zone template for cohesive delamination. The skin and

0o plies with the filler were defined with the tie constraints interactions in order to

idealize the co-bonding condition in the sample. The interface between the webs of

vertical left and right stringer are tied.

Page | 143


6.5.2 Delamination investigation around the filler tip point The numerical model predicted the delamination but showed that the delamination did

not propagate until the tip of the filler but instead stopped in between the top and

bottom of the filler. This can be seen in Figure 6.13 where interlaminar and

intralaminar fracture of the interfaces is shown through the cohesive damage variable.

From the above numerical model, it was clear that the bridging of the delaminations

(00 plies/filler) did not happen around the filler and a detailed investigation across the

filler was needed. The response of the model with a crack plane across the filler was

investigated and it is presented in the next section.

Figure 6.13 Contour plot of cohesive damage variable with crack bridging around the filler

6.5.3 Delamination investigation across the filler

A numerical model was built with the crack bridging plane across the filler. The crack

bridging is parallel to the filler and 2.25mm from filler tip. In the present numerical

model the crack bridging occurred across the filler at the lowest plane. This is shown

in Figure 6.14.

Page | 144


Figure 6.14: Contour plot of cohesive damage variable with crack bridging across the filler at lowest plane.

The crack bridging between the right and the left sides of the stiffener was evaluated.

In order to carry out this study, a parametric analysis of horizontal crack planes across

the filler was performed. The models that were generated from the study are:

• Model 1 – With crack bridging plane at 0.694 mm from the filler tip point.


• Model 3 – With crack bridging plane at 1.25 mm from the filler tip point, mid

plane




• Model 7 – With crack bridging plane at 1.875 mm from the filler tip point,

3/4th plane


• Model 9 – With crack bridging plane at 2.25 mm from the filler tip point,

which is the lowest plane and it is in line with the horizontal interface of 00

and 450 plies.

In models 1, 2 and 3, there were no damage across the filler and webs and were

rejected because of an inaccurate representation of the failure process. The rest of the

Page | 145


models and the results are listed in Table 6-4. The load-displacement curves are

presented in Figure 6.15.

Table 6-4: Failure loads of filler crack planes compared to experimental

Failure load [kN]

Experime

nt Model

4 Model

5 Model

6 Model

7 Model

8 Model

9

Initiation 17.61 17.18 17.18 17.19 17.19 17.28 17.07

Maximum 17.78 18.26 18.02 18.01 17.99 17.91 17.68 Initiation Error % -2.37 -2.36 -2.32 -2.32 -1.81 -3.00

Max Error % 2.73 1.37 1.34 1.22 0.70 -0.55

Figure 6.15: Load-displacement of crack bridging plane models

Models 4 and 5 had an unstable behaviour before final failure. As the crack plane was

moving to the skin direction, the crack propagation was becoming more stable

0

2

4

6

8

10

12

14

16

18

20

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Lo

ad [k

N]

displacement [mm]

Model 4

Model 5

Model 6

Model 8

Model 8

Model 9

Experiments

Page | 146


resulting in model 8 having behaviour very close to the experimental results. The only

disadvantage was that its crack plane was far from the experimental one. this resulted

in moving to the next modelling strategy that incorporates the XFEM damage model

and described in the next section.

6.6 Modeling using XFEM A new model was built by using the XFEM method described before in paragraph

2.3.5. The mesh density of the model remained the same in order to compare this

model with the previous ones and compare with each other. In the new model, the 0o

plies of the stiffener that attach to the skin were merged with the filler in order to

create a new part. In this new part, the XFEM method was applied with the properties

that are listed in Table 6-5, where damage initiation and damage evolution are based

on IM7/8552 material properties and elastic behaviour are tuned values for the

model.

Table 6-5: XFEM interaction properties

FM300 (adhesive) Normal direction First shear

direction Second shear

direction BK

law η Initial linear

elastic behaviour

Knn in Nmm-3 Kss in Nmm-3 Ktt in Nmm-3

1000000 1000000 1000000

Damage initiation

N in MPa S1 in MPa S2 in MPa

50 50 50

Damage evolution

Gn in N/mm Gs in N/mm Gt in N/mm 1.6

0.2 0.6 0.6

Also the cohesive contact for debonding remained as well as for for delamination.

Having all the failure procedures in one model, the interaction of the failures were

investigated and the results are summarized in Figure 6.16.

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Figure 6.16: Failure sequence of the stiffener from the XFEM model. (a) the stiffener started to debond (b) without any

delamination. (c) The debonding propagated and the first XFEM element failed.(d) without any delamination. (e) Debonding with failed filler XFEM elements (f) accompanied with delamination.

According to the XFEM model the stiffener handled a maximum load of 21.5 kN

before the final failure,

Figure 6.17. In this model, failure starts with debond of the stiffener's tip

without any delamination or 0o/filler failure, Figure 6.16a,b. The debonds are the red

areas that consign the loss of contact and as can be seen they start from the centre and

the ends of the stiffener, as expected from the parametric study analysis . When the

applied load reaches 17.9 kN, the first failure of the XFEM element occurs but no

delamination failure occurs yet, Figure 6.16c,d, while the debond propagated further.

At a load of 21.5 kN, the crack in the filler reached the left side of the stiffener, while

the delamination in the filler area started, Figure 6.16e,f. From the behaviour of this

model, it can be inferred that failure started by debonding of the stiffener, that led to

a crack in/around the filler and finally coupled with delamination.

(a)

(c)

(b)

(d)

(e) (f)

Page | 148


Figure 6.17: Load- displacement curve of the XFEM model

6.7 Modeling using LaRC LaRC'05 failure model is based on failure criteria at the microscopic level with the

physical mechanics of continuous damage. Further details on the model LaRC'05 can

be found in [22, 23]. The important features of this model are summed hereinafter.

Firstly, the non-linear behaviour of the composite in the matrix-dominated directions

is taken into account, as well as the hydrostatic pressure dependence. Secondly, a

distinction is made between all the processes of possible failure, fibre tensile failure,

matrix compressive failure, matrix tensile failure and fibre kinking failure. For each

failure process, a failure index is calculated at the ply level, depending on the ply

thickness and the stacking sequence.

Once failure has started, the failure propagation is modelled by introducing a damage

variable d (as for the indices of failure, there is a damage variable for each process of

failure). The components of the tensile fracture plane were gradually and linearly

degraded.

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5

Load

[kN

]

displacement [mm]

Experiments

XFEM

Page | 149


In order to include these features in modelling, the XFEM method described in the

previous paragraph was replaced by the LaRC'05 failure model using a smeared

formulation. The values given to the code inputs and post-history outputs are listed in

Appendix B. The values in the table are a combination of values from the material

characterization performed and values proposed by Vyas et al [101].

According to the results of the numerical analysis, the failure of the stiffener started

by dedonding of the skin. The debonding procedure followed the trend that the energy

release rate study predicted, from the centre and the edges of the stiffener. Then, the

failure jumped to the 0o ply and the filler and continued from there, see Figure 6.18

where the matrix failure of the model is presented. The maximum load that this model

handled was 18.7kN, quite close to the experimental failure load. The only

disadvantage of this method is that it is time consuming.

Figure 6.18: Load-displacement of LaRC'05 model and SDV8, matrix failure post-history.

1

23 4

1

2

3

4

Page | 150


6.8 Comparison of the failure models All the models analyzed had a common mesh density in order to evaluate the

capability of capturing the damage in the stiffener and the ability to capture the real

specimen failure. Recalling the test data for the Tapered stiffener, the damage

procedure that was expected to be modeled was a combination of debonding and

delamination. In Figure 6.19, the load-displacement curves for the failure models

generated in this study are presented.

Figure 6.19: The failure loads of different failure models

All the numerical analysis results can be compared with each other as well as with the

experimental failure load. The cohesive model can give quite good predictions for the

failure load but does not properly describe the damage in/around the filler. The

Hashin damage model can fill this gap but it has to be used with the cohesive model.

The failure load when only the Hashine damage is used is 19.8 kN but when it is

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5

Load

[kN

]

displacement [mm]

Experiments

Cohesive

Hashin

Coh+Hashin

XFEM

Larc05

Page | 151


combined which cohesive elements the failure load drops to 17.9 kN. The XFEM

model captures the failure load but over-predicts the failure load by reaching 21.5 kN,

the highest in the numerical analysis. Finally, the LaRC05 has predicted accurately

the failure load, by predicting it to be 18.8 kN , as well as the damage sequence.

6.9 Conclusions

The numerical study performed in this chapter gave a good insight into the presence

of crack bridging across the filler between the filler tip point and the lowest crack

plane in line with the horizontal interface of 00 and 450 plies. The numerical models

over predicted the failure loads to different extents, but they gave another view on the

processes by which failure occurred.

Page | 152

Chapter 7

Conclusions

7 Conclusions This study led to a parametric study that resulted in an improved damage tolerant

design of stiffener run-out, the Compliant run-out. In addition, the manufacturing

process that was developed led to quality stiffener run-out specimens. The key

findings of this thesis can be categorized and highlighted as:

1. Numerical analysis

• An insight was given in the stress-design relation in stiffener run-outs

that led in the analysis of different termination schemes.

• Good prediction of failure loads were made by using the parametric

analysis that based on the strain energy release rates

• The predictions of failure load were more accurate when the maximum

strain energy release rate was taken account, which suggests that it is

appropriate to consider the width-variation of the energy release rate in

these studies.

2. Manufacturing and testing

• The manufacturing process that designed was led to sound skin-

stiffener run-outs

• The AE monitoring proved to be valuable in detecting and analysing

the failure modes experienced by the specimens.

• Compliant termination schemes offer the possibility of improved

damage tolerance.

3. Detail modelling of run-out stiffeners

Chapter 7 - Conclusions

• Compared to other modelling approaches, the parametric study gave

very good predictions.

• Other modelling techniques can be considered taking account time-

accuracy factors.

The key findings are discussed in more detail in the following three paragraphs.

7.1 Numerical analysis A closed-form model was developed that predicts peel stresses in adhesively bonded

joints and was successfully used to better understand the singularity of the stress field

at the discontinuity. Using FE models, different run-out termination schemes were

compared and the first estimations of the geometrical effects were made. It was shown

that the peeling stresses could be reduced by using stiffener run-outs with tapered web

and widened flange.

A parametric analysis based on the strain energy release rates for debonding and

delamination successfully predicted the failure loads for the three different specimen

types. The behaviour of the models was analysed for different parametric values and

the best combination was used in order to select on the best design and proceed in

manufacturing.

Also, the variation of energy release rate across the width of the stiffener was taken

into account. The predictions were more accurate when the maximum strain energy

release rate across the width was used. It can be concluded that the variation of the

energy release rate across the width should be considered when stiffener run-outs are

designed.

7.2 The manufacturing and testing processes The manufacturing process used in this study led to sound skin-stiffener run-outs

whose design was validated against a numerical study. The material characterisation

was the first step in order to obtain inputs for the FE models to be created. The

aluminium moulds led to specimens with accurate dimensions. Special attention was

given to the manufacturing of the filler, since this is a very critical region in the

Page | 154


failing procedure of the specimen. The good bonding of the stiffener on the skin was

achieved with the usage of wooden moulds that also ensured the centred positioning

of the stiffener on the skin.

DIC captured well the strain field in the area around the stiffeners tip but could not

provide significant information at the skin interface area. AE data recorded during

skin-stiffener run-out compression tests proved useful to analyse the failure processes

which take place in these specimens and detected the failure modes experienced by

the specimens. The classification of the failure modes, that the AE provided, gave an

insight into the damage that occurred and the damage tolerance for each design.

According to the AE results, it was concluded that the Compliant design exhibited the

best damage tolerance.

The experimental program provided all the appropriate data needed for failure

investigation and the FE modelling. The predicted failure loads were confirmed by

the tests, especially when the maximum release rate across the width was used for the

prediction. Also, the results show that in the design of skin-stiffener run-outs it is

important to consider the possibility of failure modes other than debonding, and that

compliant termination schemes offer the possibility of improved damage tolerance.

7.3 Detail modeling of run-out stiffeners The delamination of the Tapered stiffener as well as the debonding from the skin were

investigated by using different damage models. Firstly, this was investigated by using

the cohesive contact. This model showed that delamination at the interface of the 00

and 450 plies of the stiffener happened across the 00 plies and stopped at a point along

filler region.

Moving to the Hashin damage models, the lack of the possibility to remove elements

when one of the four failure modes is completed proved a drawback in the analysis.

Despite this, these models helped to understand the intralaminar failure modes of

initiation and the following sequence. Following the findings with the Hashin model,

the failure in/around the filler was investigated with precisely located cohesive

models for modelling intralaminar failure. A good correlation of the failure load was

Page | 155


achieved but the cracking plane in the filler at a lower location to the one observed

experimentally.

Moving to the XFEM method, the damage sequence was captured but with an over-

prediction of the failure load. The failure started by debonding of the stiffener from

the skin, moved to failure in/around the filler area that resulted in delamination

starting from the filler area. When the LaRC05 was used, the same failure sequence

was predicted but the failure load was closer to the experimental one.

Page | 156

Chapter 8

Future work

8 Future work

8.1 Using this study in other structures In this study, the failure of bonded stiffener run-outs was investigated. Considering

the complexity of the specimens, the findings of this research could also be used in

other bonded structures with simpler geometries such as bonded joints or panels with

multiple stiffeners. Also the merits of the manufacturing procedure could be used for

stiffeners with more than 5 plies.

8.2 Other parameters in the parametric study The full capabilities of laminated composites could be exploited by performing a

parametric study on the influence of different stacking sequences in the damage

procedure. A stacking sequence study could be performed by using the parametric

model described in paragraph 4.4.1. Parameters for the stacking sequence of the plies

can be added to the model, not only for the stiffener but also for the skin. Also, the

effects of different boundary conditions could be investigated.

8.3 Study in fatigue From the AE data and the test results it was concluded that the Compliant design had

increased strength and damage tolerance compared to other designs and especially to

Chapter 8 - Future work

the Baseline. It is worth testing the performance of the specimens in fatigue and

include AE monitoring. This way, a clearer view of the performance of its design can

be extracted and a comparison for each design can be made.

8.4 Exploiting further the Python script, the manufacturing

method and the test results The Python script generated can be used as part of other studies in skin stiffner run-

outs. As an example, the script was already adapted in the framework of an Airbus

funded project at Imperial College to generate multiaxial failure envelopes for runouts

and also to generate runout models for global/local analyses.

In addition, the test results of this study were used for validating alternative modelling

methods for runouts at Imperial College, and the manufacturing method was used to

manufacture runouts with different layups and termination schemes.

8.5 Obtain failure data for damage models Finally, a problem faced in this study was obtaining reliable material properties for

the different damage models. Despite the material characterization performed in this

study and the available data in the literature, a complete series of data is still missing.

The development of testing procedures to accurately measure the input required to the

failure models investigated would be a worthwhile activity.

Page | 158

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Appendix

Appendix A

Study Material stiffener

type Panel lay-up Stiffener Lay-up

Stiffener

Dimensions

(mm)

Data

Reduction Objective Comments

Z Gόrdal [48] Aluminum

2026-T3

Aluminum

7075-T6

general

purpose

mathematical

optimization

algorithm

automated procedure for designing minimum-weight composite panels subject to a local damage constraint under tensile loading

-Panel fracture

toughness was obtained

by using a strain based

criterion.

-results for both tinstiffened and stiffened plates

K. A. Stevens [55] T300/914C T (45/-45/0"2/45/

-45/90 "2) s

(45/-45/0/45/-45/

0"2/45/-45/0 "2) s

865x43/

30x32

shadow Moire

photography

FE

The postbuckling

behaviour of a flat,

stiffened, carbon

fibre composite

compression panel

delaminate under the stiffener web at points in the panel where the web bending moment is a maximum,

N. Jaunky [53] I [45/-452/45/0/90]s

[45/-45/90/0]s

[45/90/-45]s

[45/-452/45/0]s 51x0.5x5 FE approach to incorporate the effects of local skin-stiffener interaction into a smeared stiffener theory

Rayleigh-Ritz method

B.G. Falzon[58] Hy-E

3034K

Π [45/-45/0/90]s

[45/-45/0/90]s

strain gauges

linear voltage differential transducers (LVDTs)

buckling mode

transition

C.W. Kong [54] T I Π [O/90/45/0/-45] [O/90/45/- 45]s. 280x24 shadow Moire

photography

FE

The postbuckling

behavior of

graphite-epoxy

laminated stiffened

panels

The stiffeners were fabricated by the continuous plies of the skin and cocured with the skin. Therefore, separation between the stiffener

Appendix - Appendix A

and skin did not occur

even after final failure.

Zhang [71] T300/914 I uni uni 274x25 rosette strain

gauges

FE

investigations on

the performance of

repaired thin-

skinned, blade-

stiffened composite

panels in the post-

buckling range

repair scheme is

capable of restoring the

general load path as

well as recovering both

buckling and failure

loads

B. G Falzon [57] T800/924C J I Π [90/02/90/+-45/

0/90/+-45/0]s

[90/0/90/0

/+-45/90/02/90/

+45/+-45/90]s

728x55x45 strain gauge

three-point

bending test

LVDT

The postbuckling

behaviour of a

panel with blade-

stiffeners

incorporating

tapered flanges

the failure mechanism

was an interlaminar

shear stress failure

arising from the

combination of

compressive loading on

the postbuckled

stiffener blade and the

twisting induced at the

node-line of the

buckled stiffener.

Y. Zhuk et. al. [59] T800/924 T [45/−45/0/90]4s [−45/+45/0]2s

[+45/−45/0]2s ,

300x30x30 the Soutis–

Fleck fracture

model,

FE analysis

The in-plane

compressive

behaviour of thin-

skin stiffened

composite panels

with a stress

concentrator in the

form of an open

hole

The influence of the

stiffener on the

compressive strength of

the thin-skin panel is

examined and included

in the analysis

B.G Falzon [63, 64] AS4-8552 I

runout

[45/-45/0/90/

02/-45/45/02/90/

02/45/-45/0]S

[45/45/90/02/45

/-45/03/45/-45/

0/45/0/90]S

[45/-45/90/03/ -45/0/452/_45/ 90/0/45/0/45/ -45/0/90/0/ -45/45/-45/45

[0/90/02/-45/45/04/

-45/45/02/

90/03/90/0]

[_45/02/45/02/

90/02/45/0/90

/02/90/0

/-45/02/90/02

/45/02/-452/45]

[-45/02/45/02/90/

400x120x61 thick shell element is used in conjuction with the Virtual Crack Closure Technique (VCCT) to predict the crack growth characteristics of the modelled specimens

investigating the failure of thick-sectioned stiffener runout specimens loaded in uniaxial compression

-failure in itiated at the edge of the runout and propagated across the skin–stiffener interface -the failure load of each specimen was greatly influenced by intentional changes in the geometric features -some of the observed behavior was unexpected

Page | 167


/90/-45]s 02/45/0/90/02/90

/0/-45/02/90/02/

45/02/-452/45]

S. Mahdi [72, 73] T300/914C I [45/−45/0/90]4s [−45/+45/0]2s 400x30x30 Strain gauges

were used for

the

determination

of surface

strains

FE method

develop a simple

FE method that

could be used for

the design of repairs

to I-stiffened panels

-bending occurs as the

applied displacement is

increased

-failure may have

initiated at a crack in

the skin, with the init ial

crack growing

perpendicularly to the

applied stress and

leading to stiffener

debonds, and ultimately

to collapse of the skin

and the stiffeners

E. Greenhalgh [60] HTA/6376C T [+45/−45/0/90]3S [+45/−45/03/90

/03/−45/+45]

450x45x55 fractographic

analysis

the testing and

failure analysis of

wing relevant skin-

stringer panels

containing defects

-a secondary

mechanis m occurred

prior to skin/stringer

detachment developing

-the panel failed in

compression, from the

impact site, before

skin/stringer debonding

could initiate

- the effect of the

defects on the panel

strength was related to

how they influenced

skin/stiffener

debonding

E. Greenhalgh [62] AS4/8552 I

runout

[+45/−45/0/90/−45/

+45/0/+45/−45/0]S

[+45/−45/0/0/0/90]S deflections and

strains

monitored

C-scan

fractographic

analysis

deduce the failu re

processes in the

elements, and to

characterise the

effect of local

geometry of the

stringer run-out on

the failure process

-Tension

- the development and

migration of

delaminations via ply

splits plays an

important role and

needs to be modelled

C. Meeks[61] HTA/6376C T [+45/−45/0/90]3S [+45/−45/03/90

/03/−45/+45]

450x48x45 Ultrasonic

ABAQUS

The detailed

damage

mechanis ms for

skin/stiffener

detachment in an

- provides an insight

into the processes that

control post-buckled

performance of

Page | 168


undamaged panel

were characterised

and related to the

stress conditions

during post-

buckling

stiffened panels

- 2D models and

element tests do not

capture the true physics

of skin/stiffener

detachment: a fu ll 3D

approach is required

E. Greenhalgh [106] T800/M21 T [+45/0/−452/0/+45/90/

+45/0/ −452/0/+45]S

[+45/−45/0/0/90/0]S 40x40x66.5 Strain gauges evaluate two

damage tolerance

concepts; improved

toughness matrix

and Z-pinning

Hosseini-

Toudeshky[66]

ASNA 4197 skin and

flange

assembly

[0/45/90/−45/45/−45/0]s

[45/−45/0/0/45/90/−45]s

[90/45/0/0/−45/45/−45/90]s

[45/0/45/0/45/0/45/0/45]

[45/90/−45/0/90]s

[45/90/−45/0/90]s

[45/90/−45/0/90]s

[45/0/45/0/45/0/45/0/45]

50x25 a digital

camera

loads-

displacements

recorded by

the machine

FE

damage

mechanis ms in the

composite bounded

skin/stiffener

constructions under

monotonic tension

loading

- matrix crack init iation

and propagation in the

skin and near the flange

tip, causing the flange

to almost fully debound

from the skin

- interlaminar

debounding and fiber

breakage up to the

failure

A. Faggiani [65] AS4-8552 I

runout

[45/−45/0/90/02/−45 /45/02/90/02/45/−45/0]S

[45/−45/02/90/02/45/−45/

03/45/−45/0/90/02/45/−45 /0/90/02/45/−45]S

[0/90/02/−45/45/04/ −45/45/02/90/03/90/0]

[−45/02/45/02/90/

02/45/0/90/02/90

/0/−45/02/90/02

/45/ 02/−452/45]

400x120x61 strain gauges

Linear voltage differential transducers (LVDTs) fractographic analysis FE

present the experimental results of tests conducted on different stiffener runout specimens, and to show how their behaviour and failure mode can be predicted by the use of high-fidelity fin ite element (FE) analyses incorporating cohesive elements to predict delamination

-thinner skin, showed sudden crack propagation leading to collapse -thicker skin, had initially unstable crack growth followed by stable crack growth

A. Todoroki [52] AS4/3502 I 40 plies 68 plies 762X62x93 FEM analyses optimization of the

stacking sequences

in these composites

is indispensable

The new method is

applied to the buckling

load maximization of a

blade-stiffened

composite panel, in

which the strength

constraint is

demonstrated as a

feasibility study

Page | 169

Appendix - Appendix B

Appendix B

Table. A1 The list of inputs for LaRC'05 failure model

No Name Notation Value 1 Longitudinal Young's modulus (MPa) E1 171420 2 Transverse Young's modulus (MPa) E2 9080 3 Major Poisson's ratio υ12 0.34 4 Major transverse Poisson's ratio υ23 0.5 5 In-plane shear modulus (MPa) G12 4480 6 Longitudinal tensile strength (MPa) Xt 2260 7 Longitudinal compressive strength (MPa) Xc 1573 8 Transverse tensile strength (MPa) Yt 62 9 Transverse compressive strength (MPa) Yc 255 10 In-plane shear strength (MPa) SL 101.2 11 α0 53 12 φ0 0.01 13 Transverse shear strength (MPa) St 112.793 14 Slope coefficient for longitudinal shear strength ηL 0.351575 15 Slope coefficient for transverse shear strength ηt 0.286745 16 Slope coefficient for Young's modulus ηE 16 17 Slope coefficient for shear modulus ηg 0.2 18 Critical energy release rate in fibre tension (mJ/mm2) enft 97.8 19 Critical energy release rate of 2nd failure process in fibre

tension (mJ/mm2) enftii 35.5

20 Ratio strength over 2nd failure process strength rft 0.084 21 Critical energy release rate in kinking (mJ/mm2) enkink 106.3 22 Critical energy release rate of 2nd failure process in kinking

(mJ/mm2) enkinkii 20

23 Ratio strength over 2nd failure process strength rkink 0.3 24 Critical energy release rate of matrix in mode I (mJ/mm2) enb or GIc 0.256 25 Critical energy release rate of 2nd failure process matrix in

mode I (mJ/mm2) enbii 1.37

26 Ratio strength over 2nd failure process strength rb 0.0108 27 Critical energy release rate of matrix in mode II (mJ/mm2) ent or GIIc 0.7874 28 Critical energy release rate of 2nd failure process matrix in

mode II (mJ/mm2) entii 1

29 Ratio strength over 2nd failure process strength rt 0.01 30 Critical energy release rate of matrix in mode II (mJ/mm2) enl or GIIc 0.7874 31 Critical energy release rate of 2nd failure process matrix in

mode II (mJ/mm2) enlii 1

32 Ratio strength over 2nd failure process strength rl 0.01

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33 Saturation crack density crackdens 5.48008 34 Material orientation (°) beta 0 35 Flag for micro or meso scale (matrix propagation) flagscale 0 36 Flag for UD / outer / embedded ply flagplytype 1 37 Flag for bilinear or trilinear damage law for matrix flaglawmat 1 38 Flag for bilinear or trilinear damage law for fibre tension flaglawft 1 39 Flag for bilinear or trilinear damage law for kinking flaglawkink 0 40 Flag for element deletion after matrix failure delmatflag 1 41 Flag for element deletion after kinking failure delkinkflag 1 42 Flag for element deletion after splitting failure delsplitflag 1 43 Flag for element deletion after fibre tension failure delftflag 1 44 ***** delgap 2 45 ***** delsteps 100 46 Failure propagation flag faipropflag 1 47 Failure initiation flag findexflag 1 48 Non-linearity flag nlf 7 49 First order coefficient in the shear curve polynomial c1ym 5019.25 50 Second order coefficient in the shear curve polynomial c2ym -87839.9 51 Third order coefficient in the shear curve polynomial c3ym 490339 52 First order coefficient in the transverse curve polynomial c1g 9996.22 53 Scnd order coefficient in the transverse curve polynomial c2g -189894 54 Third order coefficient in the transverse curve polynomial c3g 1440960

Table A2 Post-history outputs

Post-history variable number

Name Description

1 k 2 eps1pl longitudinal plastic strain 3 eps2pl transverse plastic strain 4 eps3pl through-thickness plastic strain 5 eps12pl shear plastic strain 6 eps23pl shear plastic strain 7 eps31pl shear plastic strain 8 kfmat Matrix failure index 9 kfkink Kinking failure index 10 kfsplit Splitting failure index 11 kfft Fibre-tension failure index 12 dmat matrix failure damage variable 13 dkink kinking failure damage variable 14 dft fibre tension damage variable 15 epsmato matrix failure initiation strain 16 sigmato matrix failure initiation stress 17 epsmatf matrix failure final strain 18 epsmati matrix failure intermediate strain 19 epskinko kinking failure initiation strain 20 sigkinko kinking failure initiation stress

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21 epskinki kinking failure intermediate strain 22 epskinkf kinking failure final strain 23 epsfto fibre tension failure initiation strain 24 epsftf fibre tension failure final strain 25 epsfti fibre tension intermediate strain 26 phimem*radtodeg Φ in degrees 27 psimem*radtodeg Ψ in degrees 28 alphamem*radtodeg α in degrees 29 omega*radtodeg Ω in degrees 30 lambda*radtodeg λ in degrees 31 lmat characteristic length of matrix-failed

element 32 lkink characteristic length of kinking-failed

element 33 lftf characteristic length of fibre-tension-failed

element 34 delcount 35 eps1 longitudinal strain 36 eps2 transverse strain 37 eps3 through-thickness strain 38 eps12 shear strain 39 eps23 shear strain 40 eps31 shear strain 41 thick thickness 42 curcdens current crack density 43 failels Failed elements

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INVESTIGATING FAILURE IN COMPOSITE STIFFENER RUN …...energy release rates for debonding and...

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