Numerical simulations and experimental investigations on quasi-static and cyclic mixed mode delamination of multidirectional CFRP laminates [Elektronische Ressource] / Parya Naghipour. Betreuer: Heinz Voggenreiter
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Numerical simulations and experimental investigations on quasi-static and cyclic mixed mode delamination of multidirectional CFRP laminates [Elektronische Ressource] / Parya Naghipour. Betreuer: Heinz Voggenreiter

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Numerical Simulations and ExperimentalInvestigations on Quasi-Static and Cyclic MixedMode Delamination of Multidirectional CFRPLaminatesA thesis accepted by the Faculty of Aerospace Engineering and Geodesy of theUniversität Stuttgart in partial fulfilment of the requirements for the degree ofDoctor of Engineering Sciences (Dr.-Ing.)byParya Naghipourborn in Tabriz, Iranmain referee : Prof. Dr.-Ing. H. Voggenreiterco-referee : Prof. Dr. rer. nat. Siegfried Schmauderco-referee : Prof. Dr. rer. nat. Hans-Peter RöserDate of defence : 03.05.2011Institute of Aircraft Design, University of Stuttgart2011 AcknowledgmentsFirst of all, I would like to express my profound gratitude to the GermanAerospace Center (DLR), specifically to the Institute of Material Research, whereI conducted this research, for making this work possible and for supporting mefinancially throughout the time of the doctorate.I offer my thanks to my committee members: to the main referee Prof. Dr.-Ing. Heinz Voggenreiter, Director of the Institute of Material Research (at DLR,Cologne) and Institute of Structures and Design (at DLR, Stuttgart), and theco-referee Prof. Dr. rer. nat. Siegfried Schmauder, at the Institute for MaterialsTesting, Materials Science and Strength of Materials (IMWF) at University ofStuttgart, for supporting this work.I am grateful to my supervisor, Prof. Dr.-Ing.

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Published 01 January 2011
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Numerical Simulations and Experimental
Investigations on Quasi-Static and Cyclic Mixed
Mode Delamination of Multidirectional CFRP
Laminates
A thesis accepted by the Faculty of Aerospace Engineering and Geodesy of the
Universität Stuttgart in partial fulfilment of the requirements for the degree of
Doctor of Engineering Sciences (Dr.-Ing.)
by
Parya Naghipour
born in Tabriz, Iran
main referee : Prof. Dr.-Ing. H. Voggenreiter
co-referee : Prof. Dr. rer. nat. Siegfried Schmauder
co-referee : Prof. Dr. rer. nat. Hans-Peter Röser
Date of defence : 03.05.2011
Institute of Aircraft Design, University of Stuttgart
2011 Acknowledgments
First of all, I would like to express my profound gratitude to the German
Aerospace Center (DLR), specifically to the Institute of Material Research, where
I conducted this research, for making this work possible and for supporting me
financially throughout the time of the doctorate.
I offer my thanks to my committee members: to the main referee Prof. Dr.-
Ing. Heinz Voggenreiter, Director of the Institute of Material Research (at DLR,
Cologne) and Institute of Structures and Design (at DLR, Stuttgart), and the
co-referee Prof. Dr. rer. nat. Siegfried Schmauder, at the Institute for Materials
Testing, Materials Science and Strength of Materials (IMWF) at University of
Stuttgart, for supporting this work.
I am grateful to my supervisor, Prof. Dr.-Ing. Marion Bartsch, whose never end-
ing support, detailed and constructive comments, guidance, understanding and
encouragement provided the basis for the present dissertation. Moreover, our dis-
cussions beyond the daily work contributed greatly to my personal life views and
attitudes as a researcher. I would also like to sincerely thank her for supporting
me and giving me the opportunity to attend several conferences for presenting my
work and networking, and to attend University of Delaware as a research scholar
and spend 3 months of my PhD overseas in USA.
During this work I had the opportunity to collaborate and make useful discus-
sions with Dr.-Ing. Joachim Hausmann, to conduct the required experiments
with Dipl.-Ing Janine Schneider, and perform microscopical investigations with
Dipl.-Phys Ludmila Chernova at DLR. I express thanks to them for enabling a
perfect collaboration and for their valuable support. Thanks are also to the col-
leagues at the Institute of Structures and Design at DLR Stuttgart for producing
the test specimens during the whole work.
Finally I would like to give special thanks to my lovely mother and father who
have always been a source of inspiration and encouragement and provided me
with their unconditional support and confidence throughout the whole work.
Cologne, September 2010
i Contents
Acknowledgments i
Abbreviations iii
Abstract vi
Kurzfassung ix
1 Introduction 1
1.1 Motivation............................... 1
1.2 ObjectiveandStructureoftheThesis...... 3
2 Experimental Study of Delamination in Fiber Reinforced Com-
posites under Quasi-Static Loading 6
2.1 Fracture Mechanical Definitions for Describing Delamination in
FiberReinforcedComposites..................... 6
2.1.1 ModeITestProcedure.......... 7
2.1.2 ModeITestProcedure................... 9
2.1.3 MixedModeBending(MMB)TestProcedure....... 1
2.2 MMB test: Data Reduction, Kinematics, Critical Loads, Failure
Criteria ................................ 12
2.2.1 DataReductionandKinematics..... 12
2.2.2 Specification of Critical Load, Delamination Length and
Crack Length for the Calculation of Fracture Toughness . 18
2.2.3 FailureCriteria........................ 19
ii2.3 MMBtest,ExperimentalProcedure................. 20
2.3.1 TestSpecimens.............. 20
2.3.2 MMBExperimentalProcedure ..... 2
2.3.3 MMB Experimental Results and Data Reduction . . . . . 24
2.4 ComparisonofFractureSurfacesinDifferentLayups ....... 28
3 Numerical Simulations of Quasi-Static MMB Tests and Experi-
mental Validations 35
3.1 TheNumericalModel:Ply+Interface............... 35
3.2 PlyDamageModel................ 36
3.3 InterfaceElement...... 39
3.3.1 KinematicFormulation.................... 40
3.3.2 Constitutive Equations: Bilinear Softening Response . . . 43
3.3.3 Constitutive Equations: Exponential Softening Response . 47
3.4 Description of the Numerical FE Model and Identification of Ma-
terialProperties............................ 49
3.5 ResultsandDiscussiononFESimulations... 52
3.5.1 Comparison of Load-Displacement Responses in Numerical
SimulationsandMMBExperiments............. 52
3.5.2 Comparison of Damage Initiation Profiles in Different
Layups .................. 56
3.5.3 Comparison of Crack Tip Failure Stresses in Different Layups 58
3.5.4 Effect of Interface Parameters on Numerical Load-
DisplacementResponse.................... 61
4 Analytical Crack Tip Element/ Non Singular Field Approach for
Estimation of MMB Fracture Toughness and Effect of Thermal
Residual Stresses on Calculation of Toughness Values 65
4.1 ObjectiveoftheAnalyticalApproach................ 65
4.2 Analytical Crack Tip Element/ Non Singular Field (CTE/NSF)
Approach for Estimation of MMB Fracture Toughness in Multidi-
rectionalLaminates.......................... 6
4.3 Evaluation of Mixed Mode Interfacial Fracture Toughness of Mul-
tidirectional Laminates with Residual Thermal Stresses . . . . . . 72
iii5 Simulation and Experimental Evaluation of Mixed Mode Delam-
ination in Multidirectional CF/PEEK Laminates under Fatigue
Loading 76
5.1 TheFatiguePhenomenoninCFRP................. 76
5.2 ModelsforAnalyzingFatigueBehaviour.... 7
5.2.1 FatigueLifeModels...................... 7
5.2.2 FractureMechanicsModels ....... 78
5.2.3 DamageMechanicsModels.................. 79
5.3 One Element Tests with the Implemented Cyclic Damage Model . 94
5.4 MMB Specimen under Cyclic Loading: Experiment and Numerical
Simulation............................... 97
5.4.1 CyclicMMBExperiments........ 97
5.4.2 Numerical Simulations of Cyclic MMB Experiments . . . . 100
5.5 Microstructure Analysis of the Failure Surface under Cyclic Load-
ingbySEM..............................105
6 Summary and Conclusion 110
Bibliography 113
Appendix 123
A COMP-Gc code for analytical calculation of fracture toughness
in multidirectional laminates 123
B General structure of the user element routine UEL 138
ivAbbreviations
a Crack length
A Extensional stiffness matrix of the laminate (Jone’s notation [82])ij
A Area of the cohesive zoneCZ
b Specimen width
B Matrix of derivative of shape functions
B Coupling stiffness matrix of the laminate (Jone’s notation [82])ij
C Compliance
C Loading-line complianceL
c Loading lever length
CFRP Carbon Fibre Reinforced Plastic
CTE/NSF Crack Tip Element/ Non Singular Field Approach
D Flexural stiffness matrix of the laminate (Jone’s notation [82])ij
DCB Double cantilever beam
d Cyclic interface damage parametercyclic
d Damage parameter in fiber directionf
d Damage parameter perpendicular to fiber directionm
d Quasi-Static interface damage parameterQS
d Damage parameter in shear directions
E Elastic modulus in longitudinal direction11
E Elastic modulus perpendicular longitudinal direction22
E Elastic modulus in thickness direction33
vE Elastic modulus in upper sublaminateu
E Elastic modulus in lower sublaminatel
E Flexural elastic modulus11,f
ENF End notch flexure
G Strain energy release rate
G Strain energy release rate in mode II
G Critical strain energy release rate in mode IIc
G Strain energy release rate in mode IIII
G Critical strain energy release rate in mode IIIIc
G Critical total strain energy release ratec
G In-plane shear modulus in 1-2 direction12
G Out of plane shear modulus in 1-3 direction13
h Specimen thickness
h Thickness of the upper sublaminateu
h Thickness of the lower sublaminatel
K Initial stiffness of the interface element
L Specimen half span length
L Length of the cohesive zoneCZ
N Matrix of shape functionsI
P Applied Load
S Compressive in-plane shear strengthc
S Longitudinal in-plane shear strengthL
u Displacement tensor
VCCT Virtual Crack Closure Technique
X Tensile strength in fiber directiont
X Compressive strength in fiber directionc
Y Tensile strength transverse to fiber directiont
Y Compressive strength transverse to fiber directionc
viα Thermal coefficient of expansion
δ Loading point displacement
δ Normal component of interfacial mixed mode displacementn
δ Total interfacial mixed mode displacementm
δ 1st shear component of interfacial mixed mode displacements
δ 2nd shear component of interfacial mixed mode displacementt
fδ Total mixed mode interfacial displacement at final separation
m
0δ Normal interfacial mixed mode displacement at delamination onset
n
0δ Total mixed mode interfacial displacement at delamination onset
m
0δ 1st shear interfacial mixed mode displacement at delamination onset
s
0δ 2nd shear interfacial mixed modet at d onset
t
Strain tensor
η Mixed mode parameter defining the failure locus
σ Normal stress acting in fiber direction11
σ Normal stress acting transverse to fiber direction22
τ In-plane shear stress12
τ Normal component of interfacial mixed mode tractionsn
τ 1st shear component of interfacial mixed mode tractionss
τ 2nd shear component of interfacial mixed mode tractionst
0τ Normal component of interfacial mixed mode strength
n
0τ 1st shear component of interfacial mixed mode strength
s
0τ 2nd shear component of interfacial mixed mode strength
t
vii