development and experimental verification of a …
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DEVELOPMENT AND EXPERIMENTAL VERIFICATION OF A
STRUCTURAL HEALTH MONITORING SYSTEM FOR COMPOSITE BEAMS
WITH EMBEDDED FIBRE BRAGG GRATING SENSORS
A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY
BY
BORAY DEĞERLİYURT
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
AEROSPACE ENGINEERING
SEPTEMBER 2017
Approval of the thesis:
DEVELOPMENT AND EXPERIMENTAL VERIFICATION OF A
STRUCTURAL HEALTH MONITORING SYSTEM FOR COMPOSITE
BEAMS WITH EMBEDDED FIBRE BRAGG GRATING SENSORS
submitted by BORAY DEĞERLİYURT in partial fulfilment of the requirements for
the degree of Master of Science in Aerospace Engineering Department, Middle
East Technical University by,
Prof. Dr. Gülbin Dural Ünver Dean, Graduate School of Natural and Applied Sciences
Prof. Dr. Ozan Tekinalp Head of Department, Aerospace Engineering
Assoc. Prof. Dr. Melin Şahin Supervisor, Aerospace Engineering Dept., METU
Examining Committee Members:
Prof. Dr. Yavuz Yaman _______________________ Aerospace Engineering Dept., METU
Assoc. Prof. Dr. Melin Şahin _______________________ Aerospace Engineering Dept., METU
Prof. Dr. Serkan Özgen _______________________
Aerospace Engineering Dept., METU
Assist. Prof. Dr.Gökhan O. Özgen _______________________ Mechanical Engineering Dept., METU
Assoc. Prof. Dr. Erdem Acar _______________________ Mechanical Engineering Dept., TOBB
University of Economics and Technology Date: 07.09.2017
iv
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced all
material and results that are not original to this work.
Name, Surname: Boray Değerliyurt
Signature:
v
ABSTRACT
DEVELOPMENT AND EXPERIMENTAL VERIFICATION OF A
STRUCTURAL HEALTH MONITORING SYSTEM FOR COMPOSITE
BEAMS WITH EMBEDDED FIBRE BRAGG GRATING SENSORS
Değerliyurt, Boray
M. Sc., Department of Aerospace Engineering
Supervisor : Assoc. Prof. Dr. Melin Şahin
September 2017, 104 pages
Structural Health Monitoring (SHM) is a discipline of development and application of
monitoring and detecting adverse changes and damage in a structure in operation. This
study explains development of a SHM system of composite beams with embedded
Fibre Bragg Grating (FBG) sensors and its verification through experiments.
There are considerations that require attention during manufacturing of composite
specimens with embedded sensors. During manufacturing, protective teflon tubes are
added to the ingress and egress regions to prevent fibre-optic wire breaking due to
stress concentrations. Moreover, as interrogator connectors at the tip of fibre optic
wires cannot stand high autoclave temperatures, they are cut and joined back to fibre
optic wires again after manufacturing through fusion splicer device.
There are three types of experiments performed for the verification; tension, vibration
and fatigue torsion. The verification is done through comparing embedded FBG
sensors data to that of corresponding surface mounted ones. To establish strain relation
between embedded and surface mounted FBG sensors, strain distributions over the
vi
cross-section of the beam are calculated by finite element analyses (FEA) for each
experiment. When embedded sensors satisfy the obtained strain distributions in each
experiment, the developed SHM system with embedded FBG sensors will be proved
to work properly.
Furthermore, data of the surface mounted FBG sensor and the strain gauge are also
compared in tension experiments. They both satisfy strain distributions calculated
from FEA. Noise signals of both sensors are extracted and compared in both time and
frequency domains.
As a result of the experiments, strain data of the embedded FBG sensors satisfy
necessary strain conditions calculated from FEA for each experiment. In free vibration
experiment, embedded sensors successfully capture the resonance frequencies
corresponding to the first two out-of-plane bending modes of the composite specimen,
values of which are the same as the ones captured by the surface mounted FBG’s.
Moreover, FBG sensors are observed to have better performance than strain gauges in
terms of noise content.
Results of three types of experiments verify that the SHM system with embedded FBG
sensors works properly. Therefore, it is shown that embedded sensor technology can
successfully be applied on composite specimens.
Keywords: Fibre Bragg Grating, Embedded Sensor, Composites, Manufacturing,
Experimental Study, Structural Health Monitoring.
vii
ÖZ
GÖMÜLÜ FİBER BRAGG IZGARA ALGILAYICILAR İLE DONATILMIŞ
KOMPOZİT KİRİŞLER İÇİN BİR YAPISAL SAĞLIK İZLEME
SİSTEMİNİN GELİŞTİRİLMESİ VE DENEYSEL DOĞRULAMASI
Değerliyurt, Boray
Yüksek Lisans, Havacılık ve Uzay Mühendisliği Bölümü
Tez Yöneticisi : Doç. Dr. Melin Şahin
Eylül 2017, 104 sayfa
Yapısal Sağlık İzleme, faal bir yapı üzerindeki olumsuz değişimleri ve hasarları izleme
ve tespit etme yöntemlerinin uygulamasını ve geliştirilmesini kapsayan bir disiplindir.
Bu çalışma kompozit kirişlerin gömülü Fiber Bragg Izgara (FBG) algılayıcılarla bir
Yapısal Sağlık İzleme sisteminin geliştirilmesini ve çeşitli deneyler ile doğrulanmasını
anlatmaktadır.
Gömülü algılayıcılı kompozit üretiminde dikkat edilmesi gereken bazı hususlar
bulunmaktadır. Bu bağlamda, fiber optik telin kompozit yapı giriş ve çıkış
bölgelerindeki gerilme yığılmalarından kopmaması için üretimlerde giriş ve çıkış
bölgelerine koruyucu teflon tüpler eklenmiştir. Ayrıca fiber optik telin ucundaki
sorgulayıcı bağlantıları, yüksek otoklav sıcaklıklarına dayanıksız olduğundan,
sorgulayıcı bağlantıları kesilmiş, üretimden sonra ise füzyon ek cihazıyla tekrar fiber
optik tellere bağlanmıştır.
Bu çalışmada üç adet doğrulama deneyi yapılmıştır; bunlar çekme, titreşim ve yorulma
burulma deneyleridir. Deneysel doğrulama, gömülü algılayıcıların yüzeye monte
viii
algılayıcılarla karşılaştırılmasıyla yapılmıştır. Gömülü ve yüzeye monteli FBG
arasındaki ilişkinin belirlenmesi için sonlu elemanlar analizleri ile her bir deney için
kesit boyunca gerinim dağılımı hesaplanmıştır. Eğer gömülü algılayıcılar gerekli
gerinim dağılımını sağlarsa, geliştirilen yapısal sağlık izleme sisteminin düzgün bir
şekilde çalışmış olduğu gösterilmiş olacaktır.
Ayrıca, yüzeye monteli FBG algılayıcı ve gerinim ölçer verileri karşılaştırılmıştır. İki
algılayıcı da sonlu elemanlar analizlerinden elde edilen gerinim dağılımını
sağlamaktadır. Gürültü sinyalleri iki algılayıcı için elde edilmiş ve birbirleriyle hem
zaman hem de frekans düzleminde karşılaştırılmıştır.
Deneylerin sonucunda, gömülü algılayıcıların sonlu elemanlar analizlerinden elde
edilen gerekli gerinim koşullarını sağladığı görülmektedir. Serbest titreşim
deneylerinde, kompozit numunelere gömülü algılayıcılar ilk iki düzlem dışı eğilme
moduna karşılık gelen rezonans frekans değerlerini yüzeye monte algılayıcılarla aynı
değerde ölçmüştür. Ayrıca FBG algılayıcıların gürültü bazında gerinim ölçerlerden
daha iyi performans gösterdiği de gözlemlenmiştir.
Üç farklı deney sonucunda gömülü algılayıcı içeren yapısal sağlık izleme sisteminin
düzgün bir şekilde çalıştığı gösterilmiş ve sonuçta FBG algılayıcı teknolojisinin
kompozitler üzerinde başarıyla uygulanabildiği de görülmüştür.
Anahtar kelimeler: Fiber Bragg Izgara, Gömülü Algılayıcı, Kompozit, İmalat,
Deneysel Çalışma, Yapısal Sağlık İzleme.
ix
To my family
x
ACKNOWLEDGEMENTS
I would like to express my special gratitude to Assoc. Prof. Dr. Melin Şahin for all of
their guidance, support, patience and encouragement throughout the preparation of the
thesis and sharing his experience on Fibre Bragg Grating experiments. I also wish to
state my sincere gratitude to Prof. Dr. Yavuz Yaman for providing valuable advice
about preparation of the thesis and sharing his experience about theoretical studies.
I would also like to thank Turkish Aerospace Industries (TAI) Rotary Wing
Technology Center for its financial support and providing the necessary software and
hardware for the analyses and experiments throughout the study. I would like to thank
Cansu Karataş for her cooperative effort.
I thank to, my mother Nimet, my father Mehmet for all their support throughout my
life. I also thank to my close friends for their sympathetic attitudes.
xi
TABLE OF CONTENTS
ABSTRACT ................................................................................................................. v
ÖZ .............................................................................................................................. vii
ACKNOWLEDGEMENTS ......................................................................................... x
LIST OF TABLES ..................................................................................................... xv
LIST OF FIGURES .................................................................................................. xvi
LIST OF SYMBOLS ................................................................................................ xxi
CHAPTERS
1. INTRODUCTION ............................................................................................. 1
1.1 Motivation of the Thesis ........................................................................... 1
1.2 Objective of the Thesis .............................................................................. 2
1.3 Assumptions and Limitations of the Thesis .............................................. 2
1.4 Scope and Outline of the Thesis ................................................................ 3
2. LITERATURE SURVEY ................................................................................. 5
2.1 Introduction ............................................................................................... 5
2.2 Structural Health Monitoring (SHM) ........................................................ 5
2.2.1 Classification of SHM.......................................................................6
2.2.2 Classification of Structures Undergone SHM...................................8
2.2.3 Sensors Used for SHM Applications...............................................11
2.3 Overview of FBG Sensors and Its SHM Applications ............................ 13
2.3.1 Pros and Cons of FBG Sensors.......................................................13
2.3.2 Working Principle of FBG Sensors.................................................14
xii
2.3.3 SHM Applications of FBG Sensors...............................................16
2.3.4 Applications of Embedding FBG Sensors in between Composite
Plies............................................................................................................17
2.4 Conclusions ............................................................................................. 19
3. BASELINE FINITE ELEMENT MODELLING AND ANALYSES OF THE
COMPOSITE BEAMS FOR SHM APPLICATIONS .......................................... 21
3.1 Introduction ............................................................................................. 21
3.2 FEM and FEA for Tension Applications ................................................ 22
3.2.1 Finite Element Model for Tension Applications.............................22
3.2.2 Boundary Condition Model for Tension Applications....................23
3.2.3 Finite Element Analyses for Tension Applications.........................24
3.3 FEM and FEA for Vibration Application.................................................28
3.3.1 Finite Element Model for Vibration Applications...........................28
3.3.2 Boundary Condition Model for Vibration Applications..................29
3.3.3 Finite Element Analyses for Vibration Applications.......................29
3.4 FEM and FEA for Torsion Applications ............................................... ..33
3.4.1 Finite Element Model for Torsion Applications..............................33
3.4.2 Boundary Condition Model for Torsion Applications.....................34
3.4.3 Finite Element Analyses for Torsion Applications.........................35
3.5 Conclusions ............................................................................................. 41
4. DEVELOPMENT OF THE SHM SYSTEM OF COMPOSITES WITH
EMBEDDED FBG SENSORS .............................................................................. 43
4.1 Introduction ............................................................................................. 43
4.2 Description of the Composite Beams ...................................................... 43
4.3 Manufacturing of Composite Specimens with Embedded FBG Sensors 45
xiii
4.4 Data Acquisition System ........................................................................ .48
4.4.1 Interrogator System of FBG Sensors...............................................50
4.4.2 Optical Interface Cables..................................................................51
4.4.3 FBG Wires......................................................................................52
4.4.4 Female-Female FC/APC Fibre Optic Adaptor................................52
4.5 Description of the Experiments for Verification of the Developed SHM
system with Embedded FBG’s ......................................................................... 53
4.5.1 Description of Tension Experiments...............................................53
4.5.2 Description of Vibration Experiments............................................55
4.5.3 Description of Fatigue Torsion Experiments..................................56
4.6 Conclusions ............................................................................................. 57
5. RESULTS AND DISCUSSIONS ................................................................... 59
5.1 Introduction ............................................................................................. 59
5.2 Results and Discussions of Tension Experiment Case Study ................. 59
5.2.1 Comparison and Discussion of Strain Data of FBG and SG from
Tension Experiment Case Study ..............................................................61
5.2.2 Comparison and Discussion of Strain Data of Embedded and Surface
Mounted FBG from Tension Experiment Case Study................................65
5.3 Results and Discussions of Vibration Experiment Case Study ............... 68
5.4 Results and Discussions of Fatigue Torsion Experiment Case Study ..... 72
5.5 Conclusions ............................................................................................. 78
6. CONCLUSIONS AND FUTURE WORK...................................................... 81
6.1 General Conclusions ............................................................................... 81
6.2 Recommendations for the Future Work .................................................. 82
REFERENCES ........................................................................................................... 85
xiv
APPENDICES
A. DERIVATION OF SHEAR STRAIN DISTRIBUTION OF INFINITE
COMPOSITE CROSS-SECTION UNDER TORSION ....................................... 95
B. SUPPLEMENTARY PLOTS OF TENSION TESTS .................................... 99
B.1 Force vs Displacement Plots ................................................................... 99
B.2 Strain vs Strain Plots ............................................................................. 100
B.3 Force vs Strain Plots .............................................................................. 101
C. SUPPLEMENTARY PLOTS OF FATIGUE TORSION TESTS ................ 103
xv
LIST OF TABLES
Table 2.1 Classification of Structures [45] ................................................................ 9
Table 3.1 Mean and Amplitude Values of Surface Shear Strain under Fatigue
Load............................................................................................................................ 41
Table 4.1 Thickness-wise Positions and Orientations of Sensors .......................... .44
Table 5.1 Slopes of the FBG-SG Strain Curves shown in Figure 5.1 ..................... 62
Table 5.2 Slopes of the Force Strain Curves shown in Figure 5.2 .......................... 63
Table 5.3 Slopes of the Embedded – Surface Mounted Strain Curves shown in Figure
5.6................................................................................................................................66
Table 5.4 Slopes of the Force Strain Curves shown in Figure 5.7 .......................... 68
Table 5.5 Natural / Resonance Frequency and Modal Strain Ratio Results ........... 71
Table 5.6 Shear Strain Ratio Values of the curves in Figure 5.13 .......................... 75
Table 5.7 Shear Strain Values at z=h ...................................................................... 76
Table 5.8 Shear Strain Values at z=0.584h ............................................................. 78
Table 5.9 Errors of Data of Embedded FBG Sensors with respect to Surface Mounted
ones.............................................................................................................................79
xvi
LIST OF FIGURES
Figure 2.1 Flowchart of Structural Health Monitoring [16] ....................................... 7
Figure 2.2 Classification of Structures before and after in-situ SHM and Damage
Detection.....................................................................................................................10
Figure 2.3 Working Principle of Fibre Bragg Grating [1] ........................................ 15
Figure 2.4 Teflon Tubing at Ingress/Egress Region [59] ......................................... 18
Figure 3.1 (a) Geometry, Stacking Sequence and (b) Finite Element Model of 1/8
Composite Beam for Tension Test ............................................................................. 22
Figure 3.2 Applied Boundary Conditions on Composite Beam Model for Tension
Test..............................................................................................................................23
Figure 3.3 Mesh Convergence Plot of Grip Displacement by Changing Planar
Element Edge Lengths ............................................................................................... 25
Figure 3.4 Mesh Convergence Plots of Axial Strain at the Surface by Changing Planar
Element Edge Lengths ............................................................................................... 25
Figure 3.5 Mesh Convergence Plots of Grip Displacement by Changing Element
Thicknesses ................................................................................................................ 26
Figure 3.6 Mesh Convergence Plots of Axial Strain at the Surface by Changing
Element Thicknesses .................................................................................................. 26
Figure 3.7 Axial Strain Distribution with respect to Normalized Position along z-Axis
for Full Displacement of 0.5 mm ............................................................................... 27
Figure 3.8 Force vs. Strain Graph for Maximum Grip Displacement of 0.5 mm ..... 28
Figure 3.9 Full Composite Beam Geometry and Stacking Sequence for Vibration
Tests................................... ........................................................................................ 28
xvii
Figure 3.10 Applied Boundary Conditions on Composite Beam Model for Vibration
Tests............................................................................................................................29
Figure 3.11 Mesh Convergence Plot of 1st Out-of-Plane Natural Frequency by
Changing Planar Element Edge Lengths.................................................................... 30
Figure 3.12 Mesh Convergence Plots of 2nd Out-of-Plane Natural Frequency by
Changing Planar Element Edge Lengths.................................................................... 30
Figure 3.13 Mesh Convergence Plots of 1st Out-of-PlaneNatural Frequency by
Changing Element Thicknesses ................................................................................. 31
Figure 3.14 Mesh Convergence Plots of 2nd Out-of-PlaneNatural Frequency by
Changing Element Thicknesses ................................................................................. 31
Figure 3.15 (a) 1st Out-of-Plane Bending (f=51.9 Hz), (b) 1st Torsion (f=278.4 Hz), (c)
2nd Out-of-Plane Bending (f=415.6 Hz) Mode Shapes .............................................. 32
Figure 3.16 Modal Axial Strain Distribution along z-Axis for First Two Out-of-Plane
Bending Modes .......................................................................................................... 33
Figure 3.17 Full Composite Beam Geometry and Stacking Sequence for Torsion
Tests............................................................................................................................33
Figure 3.18 Assigned Rigid Body Constraints for Torsion Model ........................... 34
Figure 3.19 Applied Boundary Conditions on Reference Points of Torsion Model . 35
Figure 3.20 Mesh Convergence Plots of Angle of Twist by Changing Planar Element
Edge Lengths .............................................................................................................. 36
Figure 3.21 Mesh Convergence Plots of Shear Strain at the Surface by Changing
Planar Element Edge Lengths .................................................................................... 37
Figure 3.22 Mesh Convergence Plots of Angle of Twist by Changing Element
Thicknesses ................................................................................................................ 38
Figure 3.23 Mesh Convergence Plots of Shear Strain at the Surface by Changing
Element Thicknesses .................................................................................................. 38
Figure 3.24 Shear Strain Distribution along z-axis for φ=40⁰ .................................. 39
xviii
Figure 3.25 Shear Strain – Angle of Twist Plot under Torsion ................................. 40
Figure 3.26 One Cycle of Surface Shear Strain Driven by Pulsating Angle of Twist
with Maximum Value of 40 degrees with frequency of 3 Hz ................................... 40
Figure 4.1 Geometry of Composite Beams for (a) Tension, Vibration and (b)
Torsion Tests .............................................................................................................. 44
Figure 4.2 Cut Prepreg Plies and Cutting Machine in Epsilon Kompozit Inc. ....... 46
Figure 4.3 FBG Wire to be Embedded on Laid Plies [67] ..................................... 47
Figure 4.4 Fusion Splicer Device ........................................................................... 47
Figure 4.5 Flowchart of Manufacturing of the Composite Beams with Embedded
FBG’s..........................................................................................................................48
Figure 4.6 Manufactured Composite Beam with Embedded and Surface Mounted
FBG.............................................................................................................................48
Figure 4.7 Wavelength Capturing through SmartSoft [68] .................................... 49
Figure 4.8 Wavelength and Strain Data through SmartSoft [68] ........................... 50
Figure 4.9 FBG Interrogator ................................................................................... 51
Figure 4.10 Optical Interface Cable ......................................................................... 51
Figure 4.11 FBG Wire with Pigtail Connector......................................................... 52
Figure 4.12 Fibre Optic Adaptor .............................................................................. 53
Figure 4.13 Tension Test Setup ................................................................................ 54
Figure 4.14 Optical Fibre Covered by Teflon Tube Exiting below Grip Region .... 54
Figure 4.15 Vibration Test Setup ............................................................................. 55
Figure 4.16 Specimen under Fatigue Torsion Load ................................................. 56
Figure 5.1 Axial Strain of Surface Mounted FBG with respect to that of Strain
Gauge..........................................................................................................................61
Figure 5.2 Axial Force versus Strains for SG and FBG Comparison ..................... 62
xix
Figure 5.3 Initial and Moving Averaged Strain Signals by FBG and SG in Closer
View............................................................................................................................63
Figure 5.4 Noise Strain Signals Extracted by Moving Average Method .................. 64
Figure 5.5 Frequency Distributions of Noise Signals of FBG and Strain Gauge ..... 65
Figure 5.6 Axial Strain of Embedded FBG with respect to Surface Mounted FBG . 66
Figure 5.7 Force – Strain Plot of 2nd and 3rd Beam Specimens for each FBG
Sensor..........................................................................................................................67
Figure 5.8 Strain Response due to Impact............................................................... 69
Figure 5.9 Amplitude of Strain FRF of Surface FBG for each Test ....................... 70
Figure 5.10 Amplitude of Strain FRF of Embedded FBG for each Test .................. 70
Figure 5.11 Composite Strain FRF of Embedded and Surface Mounted FBG
Sensors........................................................................................................................ 70
Figure 5.12 Shear Strain at z=0.584h vs Shear Strain at z=h .................................... 73
Figure 5.13 Shear Strain Ratio γxy(0.584h) / γxy(h) versus Number of Cycles ......... 74
Figure 5.14 Mean Value of Shear Strain at z=h with respect to Number of Cycles . 75
Figure 5.15 Amplitude of Shear Strain at z=h with respect to Number of Cycles ... 76
Figure 5.16 Mean Value of Shear Strain at z=0.584h with respect to Number of
Cycles..........................................................................................................................77
Figure 5.17 Amplitude of Shear Strain at z=0.584h with respect to Number of
Cycles..........................................................................................................................77
Figure B.1 Axial Force – Displacement Plots of 1st Beam Specimen...................... 99
Figure B.2 Axial Force – Displacement Plots of 2nd Beam Specimen ..................... 99
Figure B.3 Axial Force – Displacement Plots of 3rd Beam Specimen ................... 100
Figure B.4 Embedded FBG Data with respect to Surface Mounted FBG Data of 2nd
Beam Specimen ........................................................................................................ 100
xx
Figure B.5 Embedded FBG Data with respect to Surface Mounted FBG Data of 3rd
Beam Specimen ........................................................................................................ 101
Figure B.6 Axial Force versus Strain Plot of 2nd Beam Specimen......................... 101
Figure B.7 Axial Force versus Strain Plot of 3rd Beam Specimen .......................... 102
Figure C.1 Torque Response with Respect to Number of Cycles ........................... 103
Figure C.2 Surface Mounted FBG at z=h Response with Respect to Number of
Cycles........................................................................................................................103
Figure C.3 Response of Embedded FBG at z=0.584h with Respect to Number of
Cycles........................................................................................................................104
Figure C.4 Response of Embedded FBG at z=0 with Respect to Number of
Cycles…....................................................................................................................104
xxi
LIST OF SYMBOLS
𝐴 Area
𝑏 Half Width of the Beam
𝐸 Young’s Modulus
𝑓 Frequency
𝐹 Axial Force
𝐺 Shear Modulus for Isotropic/Transversely Isotropic Materials
𝐺𝑥𝑦 x-y Shear Modulus
𝐺𝑥𝑧 x-z Shear Modulus
ℎ Half Thickness of the Beam
𝑖 Index of Ply Number
𝐾𝑇 Bragg Wavelength Shift – Temperature Sensitivity
𝐾𝜀 Bragg Wavelength Shift – Strain Sensitivity
𝐿 Length of Non-Clamped Portion of the Beam
𝐿𝑥 Average Element Length along x-axis
𝐿𝑦 Average Finite Element Length along y-axis
𝐿𝑧 Average Finite Element Length along z-axis
xxii
𝑚𝜀 Slope of Strain-Strain Line
𝑚𝐹 Slope of Force-Strain Line
𝑛𝜀 Constant term of Strain-Strain Line
𝑛𝐹 Constant term of Force-Strain Line
𝑁 Total Number of Plies at one Symmetry Side
𝑡 Time
𝑢 x Component of Displacement
𝑣 y Component of Displacement
𝑤 z Component of Displacement
𝑥 x coordinate
𝑋 X Coordinate
𝑦 y coordinate
𝑧 z coordinate
𝛾𝑥𝑦 x-y Component of Shear Strain
𝛾𝑥𝑧 x-z Component of Shear Strain
Δ𝑇 Temperature Difference
Δ𝜆 Bragg Wavelength Shift
𝜀𝑥 Axial Strain Along x Direction
𝜀𝑥∗ Normalized Modal Axial Strain Along x Direction
xxiii
𝜃 Angle of Transformation
𝜏𝑥𝑦 x-y Component of Shear Stress
𝜏𝑥𝑧 x-z Component of Shear Stress
𝜙 Angle of Twist
𝜙0 Peak to Peak Value of Angle of Twist
1
CHAPTER 1
INTRODUCTION
1.1 Motivation of the Thesis
Structural Health Monitoring (SHM) is an application of continuous monitoring of
changes in a structure. With appropriate features, SHM is simply identifying what
happened to the structure concerned, how it works, or how healthy it is by including
changes in the structure.
Composite materials are frequently used in aerospace structures because of their
weight advantages. Since composite materials exist at the critical parts of aerospace
structures, they should be monitored. To achieve SHM of composites, at least one
monitoring sensor is needed.
Fibre Bragg Grating (FBG) sensors are appropriate for composite monitoring since
FBG’s can be embedded in composite structures, which makes them preferred
especially in aerospace studies. Through embedding, internal monitoring is also
possible.
Several advantages were also mentioned in the literature. FBG sensors can be very
small and have light-weight. They are stable and insensitive to harsh environments.
Multiplexing ability of FBG’s provides simple measurements along a single line.
Distributed FBG sensors can use thousands of discrete FBG points in the same line
and all data can be taken from single cable connected to single channel of an
interrogator.
Although multiplexed FBG’s are beyond the scope of this study, development and
verification of a SHM system of composite beams with single embedded FBG’s is
established in this thesis.
2
1.2 Objective of the Thesis
This study has two main objectives, which are development and verification of SHM
system with embedded FBG sensors.
The development of a SHM system includes manufacturing of the composite beams
with embedded FBG sensors where FBG embedding methods are also developed but
several precautions should be taken while embedding FBG sensors. Development of
the system also includes setting up data acquisition system of FBG sensors.
The second objective is the experimental verification of the SHM system developed.
Three tests namely; tension, vibration and fatigue torsion, were conducted. Baseline
finite element models (FEM) are created. Through finite element analyses (FEA),
strain distributions along thickness-wise direction are developed at the cross-section
concerned for different types of loading/boundary conditions, which are in tension,
vibration and fatigue torsion. Natural frequencies from modal model is also extracted.
According to expected strain distributions obtained from FEA, accuracy of strain
values of the embedded FBG sensors are checked with respect to the surface mounted
ones. Therefore, this objective is simply to conduct experiments of composite beams
with surface mounted and embedded sensors and to check whether all sensors provide
data with expectable accuracy. If all sensors regarding their spatial locations and
orientations do provide correct data, the SHM system is shown to be working correctly
and be appropriate for SHM applications.
1.3 Assumptions and Limitations of the Thesis
The list below gives all assumptions and limitations in the thesis:
- All sensors are assumed to be aligned perfectly.
- Composite beams are observed to have some plastic deformation and shown
non-linear behaviour during tension experiment. These effects are neglected in
all calculations.
3
- Sampling frequency of FBG interrogator system is limited to 2500 Hz and this
value was set during vibration tests. For all other quasi static tests, sampling
rate of 50 Hz was assigned.
- Vibration tests were output-only tests and therefore obtaining of strain mode
shape analyses are beyond the scope. The study is also limited to resonance
frequency value observation and comparison to embedded-surface mounted
FBG data.
- Tension and fatigue torsion tests are assumed to be quasi-static.
- In FEM, composite materials are taken as orthotropic.
- It is assumed that embedded FBG sensors do not affect the response of the host
material and thus FEM does not include the modelling of embedded FBG
sensors.
- Finite element analyses of fatigue torsion test only contains torsion, angle of
twist and strain data at the static torsion load without material degradation.
Advanced simulation of fatigue behaviour and progressive failure analyses are
beyond the scope of this study.
1.4 Scope and Outline of the Thesis
Chapter 2 shows all literature review of this thesis. It includes SHM
methodology and use of sensors for SHM applications. As FBG sensors are of the
primary concern, they are introduced with their working principle, advantages and
disadvantages. Moreover, embedded FBG manufacturing methods are also presented.
Chapter 3 explains baseline FEM and FEA for tension, vibration and fatigue
torsion applications. Boundary condition for the FEM is also included for all three
cases. Three FEA provide information about strain distribution over the cross-section
of the beam specimens.
Chapter 4 introduces all components of the SHM system. It includes
manufacturing procedure of composite beams with embedded FBG sensors.
Information gathered in the literature research was also applied to manufacturing.
4
Moreover, components of data acquisition system of FBG’s are shown and the features
of it including the software is also explained in details. Consequently, the tests
conducted to verify the SHM system, which also comprises the test setup are
presented.
Chapter 5 explains all results including the post-processing and the comparison
of the test data obtained from sensors and FEA. It is also concluded in this chapter that
the developed system works properly and is appropriate for SHM applications.
In Chapter 6, ultimate conclusion of this study is made. What is accomplished
is also explained in this chapter. Moreover, further developments are also
recommended as future work.
5
CHAPTER 2
LITERATURE SURVEY
2.1 Introduction
High labour force is needed to extend the service life of air platforms through heavy
maintenance and inspection with high costs; on the other hand, Structural Health
Monitoring (SHM) is a cost-saving method to reduce those maintenance efforts [1].
All SHM applications and its classification are presented here. Structure undergone
SHM should have at least one sensor and FBG’s are appropriate sensors to be
embedded into composites. That is why FBG sensors are selected for this study and a
brief overview of FBG sensors including its SHM application, working principle and
embedding methods are also presented in this chapter.
2.2 Structural Health Monitoring (SHM)
Structural Health Monitoring (SHM) is an application of detecting and interpreting of
adverse changes [2]. Guan and Karbhari [3] defines that the Vibration Based Structural
Health Monitoring (VBSHM) is a study of monitoring changes in the vibrational
characteristics of a structure such as; mass, stiffness, damping that affects the global
vibrational response of the structure. Pavlopoulou [4] used the concept In-situ
Monitoring and Online Monitoring referring SHM during operational (i.e. in service)
conditions.
SHM has been applied to various structures. The most frequent online SHM
applications encountered are the bridges [3, 5-15]. Moreover, large numbers of simple
beam and plate experiments have been performed to develop new SHM techniques [2,
4, 5, 12, 16-40]. Other SHM studies are applied to ships, pressure vessels, buildings,
6
pipelines, ships, air foils/wings, wind turbine bases, wind turbine blades, helicopters
and helicopter rotor blades.
2.2.1 Classification of SHM
SHM may be non-destructive or destructive. Non-Destructive Testing and Evaluation
(NDT&E), also called as Non-Destructive Testing (NDT) or Non-Destructive
Evaluation (NDE), is a testing procedure to monitor without modifying structure and
without creating any damage. Therefore, non-contact sensors are needed as contact
sensors generally modify structural parameters because of their mass and assembly
modifying the geometry and create damage such as drilled hole. NDT&E includes
testing methods of visual inspection, ultrasonic testing, acoustic emission, eddy current
testing, liquid penetrate testing, magnetic particle inspection, magnetic flux leakage,
eddy current testing, alternating current field measurement, radiography,
thermography and some vibration analyses [41, 42].
Complete SHM has various processes shown in Figure 2.1 according to Ooijevar [16].
Structure may undergo an excitation which can be environmental or pre-determined.
Damage can be created by either environment (i.e. in-service) or manually. Response
is measured through sensors such as accelerometers, strain gauges etc. Sensor selection
is also crucial for SHM. As SHM needs sensors, passive structures become sensory
structures for SHM unless non-contact sensors for NDT&E are established. After
response data is obtained through sensors, desired features are extracted through
various methods such as modal analysis, frequency response function (FRF) methods
etc. or those desired features can directly be used. The extracted features are either
used as an indicator for presence of damage (Level 1) or to identify damage states
(higher levels).
7
Figure 2.1 Flowchart of Structural Health Monitoring [16]
As seen from Figure 2.1, Ooijevar [16] defines four damage detection levels. Level 1
is determining existence/presence of damage, Level 2 is determining location of
damage, Level 3 is determining extent/severity of damage and Level 4 is predicting
remaining life. According to Dervilis [43], one more level is included between Level
2 and Level 3. That level is determining type of damage such as crack, delamination,
notch etc. Therefore, damage levels can be summarized as follows:
Level 1: Existence of damage,
Level 2: Location of damage (requires Level 1),
Level 3: Type of damage (requires Level 1 and 2),
Level 4: Severity/Extent of damage (requires Level 1 and 2),
Level 5: Remaining service life (requires Level 1, 2 and 4).
Level 1 only points that there is some adverse change in the structure and it is integral
part of SHM. Higher levels require more advanced level of damage detection
disciplines. As damage detection needs a processor connected to sensors on the
structure, it upgrades sensory structure to smart structure for damage detection. After
damage detection is completed, remaining life of the structure and failure probabilities
can also be estimated (Level 5), through statistical and fatigue analysis. If probability
is low, structure is continuously monitored without any repair. If probability is high, it
is repaired or replaced by the new one. Any SHM processes do not have to include all
the aforementioned levels, but must include Level 1. As levels with success are
8
covered from 1 to 5, the quality of SHM increases. Level 3 can be omitted and can be
considered as extra but it increases the qualities of Level 4 and Level 5.
However, after applying some of those levels, errors must occur because of
calculations (such as differentiation, round off errors, FEM/FEA errors, assumptions
made, noise and calibration effects, etc.) Errors are classified as [16, 44],
False Positive: Indication of damage when none is present
False Negative: No indication of damage when damage is present
2.2.2 Classification of Structures Undergone SHM
Structures undergone SHM should also be grouped and the types of the structures
should be highlighted. Structures are classified as passive, sensory, active, adaptive
and smart (i.e. intelligent) structures [45]. Passive structures are structures without
sensor, controller, actuator and processor. If passive structure is equipped with sensors,
it becomes sensory structure, unless non-contact sensors are used. If sensory structure
is also equipped with actuators that change the response of the structure and it becomes
active one. If active structure is equipped with controller such as mechanisms, remote
control and even human intervention that drives actuator properly, it becomes adaptive
structure. However, with technological advances, a controller should be equipped with
a processor driving actuator instantly and processing sensor input. An adaptive
structure with processor is called as a smart structure. Table 2.1 shows summary of
structure classification.
9
Table 2.1 Classification of Structures [45]
Sensor Actuator Controller Processor
Intelligent Material X X X X
Adaptive Material X X X
Active Material X X
Sensory Material X
Passive Material
Figure 2.1 shows that SHM requires sensors. Moreover, damage detection procedure
requires a processor that develops a relation between inputs through sensors and
damage states. Therefore, structures monitored may change their type referring to
Table 2.1. Considering the main aim of the thesis research, having an in-situ SHM,
passive structure should initially be built or manufactured. Depending on the sensor
assembly, it either becomes sensory structure or remains as passive structure. If sensors
are used so-called as “scanners”, meaning that sensors do not have any contact and/or
any connection with the structure itself, structure remains passive, as sensors are not
the integral part of the structure monitored. On the other hand, contact sensors
assembled to the structure may or may not change the type of the structure. If sensors
are permanently attached or embedded, the structure becomes sensory as permanent
connection of sensors can be considered as being integral part of the structure. If
sensors are temporarily used at some periods with assembling and disassembling for
each monitoring period, structure remains as a passive one as sensors are not the
integral part of the structure.
In summary, structures with permanent assembly of sensors become at least sensory
structures (or more advanced one); whereas, with temporary and non-contact sensors,
it remains as passive. The structures with permanent contact sensors can be considered
as smart structure, if sensory structure is additionally undergone damage detection,
which requires processor to compile appropriate damage detection algorithms. On the
10
other hand, sensory structures without damage detection remain as sensory. As seen
from Table 2.1, the structure not equipped with controller and actuator cannot be
completely smart. Another definition of smart structure is a structure that can alter its
structural behaviour to improve safety and/or can monitor its integrity [29]. Since in
the case of damage detection, structure is only able to monitor its own integrity and it
has no actuator and controller; it is classified as “smart in terms of damage detection”.
On the other hand, structures with temporal and non-contact sensors are not considered
as smart, as a processor is not connected to structure, but are occupied by sensors only.
Figure 2.1 schematically explains modification for in-situ SHM and damage detection.
Figure 2.2 Classification of Structures before and after in-situ SHM and Damage Detection
Classification of NDT&E, on the other hand, is somehow more complicated. Non-
contact sensors always provide NDT&E as sensors are not touching to structure and
therefore not threatening the structural integrity. On the other hand, usage of contact
11
sensors may make SHM as non-destructive or not depending upon the sensor assembly
methods. If assembly creates structural change (so-called damage) on the structure
such as drilling holes, causing delamination etc., monitoring is not non-destructive.
Contact sensor assemblies that are not modify structure, such as bonding with
appropriate adhesives, magnets etc. can provide NDT&E.
As the structures with embedded sensors are always with those sensors over their entire
life starting from its manufacturing, they are directly considered as inherently sensory,
the monitoring technique can also be considered as NDT&E as no additional assembly
of any other sensors is required for further testing.
2.2.3 Sensors Used for SHM Applications
Accelerometers are the most frequently used sensors for SHM applications because of
their costs and availability. For example, ten accelerometers at each different positions
and directions exist to capture responses of towers of Vestas 80 and NEG-Micon 250
wind turbines for structural health monitoring [46]. You [5] used MICA 2 wireless
accelerometers for SHM and damage detection of pedestrian bridge and simply
supported beam, emphasizing flexible use of Wireless Sensor Networks (WSN).
Zwing et al. [47] used triaxial accelerometers for SHM of a blade with cross-section
of an air foil. Luczak et al. compared measurement quality of accelerometer, LDV and
micro flown probes under dynamic excitation in the study of blade experiments. They
concluded that all the sensors provided correct results and any of the sensors can be
selected from the group depending on the conditions; however, they also stressed that
the accelerometers could modify structure and cause shifts in natural frequencies [48].
Piezoelectric materials are also widely used for SHM purposes because of their
lightweight, compactness and simplicity. Piezoelectric materials (PZT) are deformed
because of force, stress, pressure, temperature etc. and it generates electricity to be
measured. On the other hand, when an electricity is supplied to piezoelectric material,
it deforms and creates force. Hence, piezoelectric materials are also used as actuators.
Bassett [49] used piezoelectric accelerometers for SHM application of a wind turbine
12
located in Canada. Piezoelectric sensors are used especially with wave propagation
techniques. Lehmann et al. [38] used PZT as both sensor and actuator for damage
detection of a composite plate through guided wave technique. In several studies [4,
17, 30-32, 34, 43], several piezoelectric transducers are used to measure lamb/guided
wave responses for SHM, in some of those [17,31,34,43], Piezoelectric Wafer Active
Sensors (PWAS) providing output of electro-mechanical impedance are used for
electro mechanical impedance method for SHM purposes. On the other hand, Grisso
[28] developed hardware with piezoelectric sensors providing output of electro-
mechanical impedance.
Laser Doppler Vibrometer (LDV), which is also called as Scanning Laser Doppler
Vibrometer (SLDV) and Scanning Laser Vibrometer (SLV), provides non-contact
measurement and therefore, structure mass is not modified by the sensor assembly
[25]. Dai et al. [12] defined that LDV is a non-contact sensor based upon the Doppler
effect of a laser beam reflected back from subject and made measurements on a high-
rise building model, a concrete wall, a bridge and a beam. In several researches [16,
19, 22, 24, 35], a successful damage localization was conducted through extracting
features from measurement of LDV. Vinod [19] also used lamb wave methods on
various structures scanned successfully by a LDV sensor.
Various other sensors were used for SHM purposes as well. Mahmood [50] studied
identification of mechanical properties of concrete using touching sensors of rebound
hammer and ultrasonic velocity tester. Although contact occurs, it is not bonded to
structure but touches structure through human intervention temporarily while testing,
and the study may, therefore, be considered as non-contact, as structure is passive. In
Pavlopoulou’s study [4], C-scan and sampling phased array sensors detected pre-
introduced damage of composite patch through non-contact scanning. In the study of
Farahani [10], array of geophones - seismic velocity transducers – are present for SHM
of bridges.
Strains are also considered as damage sensitive parameters and therefore strain gauges
are suitable sensors for SHM and damage detection. As strain is a damage sensitive
13
parameter, Biru [7] obtained strain data of bridge through conventional strain gauges
to monitor its health.
There are large numbers of SHM studies with Fibre Bragg Grating as the technology
is advancing. As the focus of this research study is FBG sensors, all applications are
given in the next section in detail.
2.3 Overview of FBG Sensors and Its SHM Applications
Fibre Bragg Grating (FBG) sensors are type of optic sensors, more versatile compared
to other optic sensors and are available in the market [51]. FBG sensors have been
used for the last decades and have accuracy similar to strain gauges [37]. Embedded
FBG sensors have also been used for SHM and damage detection of composites since
FBG’s invention (1987) [40] and been applied for SHM purposes recently [52]. FBG
sensors are the most used among fibre optic sensors in damage detection applications
[34]. FBG sensors are the most promising tool for load monitoring and damage
detection [1] and are useful for detecting impact damage and delamination [34] as well.
FBG sensors are also used in acoustic/ultrasonic damage detection applications
replacing PZT sensors [1].
2.3.1 Pros and Cons of FBG Sensors
Several advantages of these sensors are mentioned in the literature as;
- FBG sensors have low cost [1].
- FBG sensors can be very small and have light-weight; moreover, pattern on
optical wire, where measurements are made, can be as small as possible [1, 34,
40, 52, 53-59]. Therefore, FBG sensors do not modify the host structure and
the mass of them is almost negligible [60].
- FBG sensors are stable and insensitive to harsh environment such as corrosion,
water and signal attenuation, background noise, electrical and magnetic
14
interference, power surges unlike electrical strain gauges and they are also
chemically stable [16, 34, 40, 52, 54-61].
- Simple and less wiring is needed for several measurement points, as several
FBG’s can transfer different wavelength data along a single line [58, 60].
- Especially in long-term tests, FBG’s are not prone to drift unlike electrical
strain gauges [34, 55, 60]. FBG sensors do not require recalibration and can be
used throughout their life [54, 59].
- Distributed sensors based on FBG’s are able to perform dynamic
measurements unlike other types of distributed fibre optic sensors [51].
- Transmission losses are low and long-distance monitoring is possible [56, 57].
- Embedding FBG’s into composites is possible to monitor their life inside the
structure without altering their mechanical properties [34, 40, 51, 52, 54, 57-
59, 62].
Despite FBG sensor’s lots of advantages, it also has also some disadvantages
mentioned in the literature as follows:
- FBG’s have much higher temperature dependency than strain gauges have
[60].
- Unlike strain gauges, FBG’s have different gage factor values for tension and
compression [60], and in the study of Kleckers [60], for instance, gauge factors
of FBG is provided as 0.805 for tension and 0.788 for compression.
- FBG sensors are very fragile and require extra attention during installation [58,
59].
- Measurement range of distributed FBG’s are short, up to 70 m for static and 7
m for dynamic, whereas, other distributed sensors can statically measure up to
tens of km’s [51].
2.3.2 Working Principle of FBG Sensors
FBG sensors work based on spectroscopy, method of capturing of wavelength changes
of reflected light source [53]. FBG’s work by simply measuring optical wavelengths.
15
Incoming broadband UV light is sent through optical wire; optical cores/mirrors
(called “Gratings”) reflect narrow band about some wavelength (called “Bragg
wavelength”). Bragg Wavelength is proportional to grating spacing and effective
refractive index [1, 51, 58, 63]. Working principle of single FBG can be seen in Figure
2.3.
Figure 2.3 Working Principle of Fibre Bragg Grating [1]
Bragg wavelength shift is proportional to strain and temperature [60, 63]. For constant
temperature, wavelength shift can directly be converted to strain value using linear
relation. Typical FBG has Bragg wavelength of 1550 nm, sensitivity of 1.2 pm/µε and
can be shifted ±40nm for strain/temperature measurements [59, 63]. Most of the FBG
sensors are available with temperature compensation [51] as FBG sensors are so
sensitive to temperature changes.
Multiplexing ability of FBG’s offers a great potential [16, 34]. As FBG’s have
narrowband wavelength response and wide operating range, they can be highly
multiplexed [40, 59]. It is possible to multiplex tens or hundreds of FBG’s in a single
fibre line [1]. FBG sensors are adaptable to high frequency and low strain values at
wavelength division multiplexing, making sensors simpler in comparison with
conventional strain gauges [56]. Using different gratings at different places on single
16
line, each measurement region has different Bragg Wavelength and shifts can
separately be captured at single channel [63].
Distributed FBG sensors can use thousands of discrete FBG points on the same line
and all data can be taken from single cable connected to single channel of interrogator
[18, 51]. Distributed FBG use Optical Frequency Domain Reflectometry (OFDR)
technique with swept-wavelength interferometry [51] and OFDR’s provide high
spatial resolution and fast scanning rate [59]. However, interrogation is more complex
than that of single FBG and FBG arrays. As distributed FBG sensors are beyond the
scope of this thesis work, interrogation method is not given.
2.3.3 SHM Applications of FBG Sensors
It is shown in this section that various SHM applications can be done through FBG
sensors. Several SHM applications with FBG sensors also exist in the literature and
each study is discussed one by one.
Doornink et al. [15] summarized in-situ monitoring applications of several bridges,
one highway bridge in Iowa-US and several large-span bridges in China.
Kahandawa et al. [40] successfully conducted a SHM experiment of composite plate
with embedded FBG using their improving developed data acquisition system with
Artificial Neural Network (ANN) for strain extraction.
Doyle and Staveley [55] applied in-situ SHM of a marine with several embedded
single and multiplexed FBG arrays, and captured strain behaviour during sea trials.
Pedrazzani et al. [57] conducted fatigue-bending test of 9 m long wind turbine blade
with embedded and surface mounted OFDR (distributed) sensors. The blade had pre-
induced defects. In the fatigue test, sensors were able to capture all growing defects.
Moreover, surface mounted sensor was broken earlier and embedded sensors endured
longer under fatigue loading.
Güemes and Fernandez-Lopez [37], applied identification of loosen bolts located at
single lap joints of aluminium plates through distributed fibre-optic sensors. They
17
measured strain values at the regions around present and loosen bolts, and observed
that strain values were different around loosen bolts compared to intact ones. They
concluded that loosen bolts could be detected through monitoring strain deviations
from its intact case.
An et al. [56] applied damage detection application of truss structures through FBG
sensors through an algorithm based on curvature (strain) mode shapes, and they
successfully detected damage through their algorithm using strain data measured by
FBG sensors.
2.3.4 Applications of Embedding FBG Sensors in between Composite Plies
This study also deals with SHM of composites. SHM of composites requires
monitoring of internal plies due to their anisotropic nature and having complicated
damage modes and thus SHM of composites with surface mounted sensor network is
not sufficient and embedded surface technology is needed. Although surface assembly
is easier, it is not suitable as optical fibres are very fragile. It is also possible to detect
damage inside the composite materials through strain monitoring. [40, 58]
FBG sensors are suitable to be embedded between layers of technical textiles and
composites without affecting strength of the structure [34, 40, 51, 52, 54, 59, 62]. As
these sensors can be used with composites with minimum instrumentation, FBG’s are
very capable of in-situ monitoring [1, 34, 52]. Fibre optic sensors can also be
embedded into structure to get better measurement results with protection from
temperature, moisture and humidity [18, 55].
On the other hand, during manufacturing process, residual strain is accumulated in
fibre optic sensors, and thus for unloaded case accumulated strain may present [18, 40,
57]. Kahandawa et al. [40] observed residual strain drop of their embedded FBG sensor
after curing, even the curing temperature is only 30⁰C. Therefore, the residual strain
should also be considered for unloaded reference. Using that property, through
18
embedded FBG’s, in-situ monitoring of temperature and residual strain is possible [55,
59].
During residual strain accumulation of embedded FBG’s, wavelength spectrum is
highly distorted and peak wavelength splitting and broadening may occur because of
transverse strains [58, 59, 64]. For polyimide or acrylate recoated FBG’s, distortion of
spectrum is less such that single peak can be detected [58, 64].
Embedded FBG sensors are vulnerable at ingress-egress regions, and they may be
broken at that regions [52, 64]. As pressure gradient is very large, severe bending of
optical fibre occurs at ingress-egress regions [58]. In some studies, precautions, such
as teflon tube placement around the fibre optic cable at ingress and egress regions of
structure, were taken to prevent damage of the cables from the stress concentrations
occurring [55, 57-59, 62]. Figure 2.4 shows one application of protective teflon tubing.
Another solution to prevent stress concentrations at ingress-egress regions is to use
surface/edge mounted connectors [52, 58, 59, 64]. However, these connectors may
degrade strength of the host structure and they may deform during manufacturing that
cause alignment problems [58]. Some technology on wireless transmission of
embedded FBG’s are still advancing including miniaturized read-out units to be
embedded [64].
Figure 2.4 Teflon Tubing at Ingress/Egress Region [59]
19
2.4 Conclusions
The aim of the research study is to conduct SHM through embedded FBG sensors.
Therefore, SHM background and classification of it are explained in details. As sensors
are needed for SHM applications, various sensor applications are also researched.
There are extremely wide variety of selection of sensors and FBG sensors are observed
to be capable of internal monitoring. Their working principle, various applications,
advantages and disadvantages are also discussed. On the other hand, manufacturing of
embedded FBG sensors has some key points and these points are utilized during
manufacturing of the developed SHM system in this particular study.
20
21
CHAPTER 3
BASELINE FINITE ELEMENT MODELLING AND ANALYSES OF THE
COMPOSITE BEAMS FOR SHM APPLICATIONS
3.1 Introduction
In this chapter, three finite element models of the composite beams are created. Two
of them are composite beam with tabbing that represents beams for tension and
vibration tests. Because of the symmetry, tension model is 1/8 of the complete beam
model. On the other hand, vibration model is complete beam model because of
unsymmetrical loading. The last model is a composite beam without tabbing for
torsion tests.
These three models are discussed in separate sections. Mesh convergence analyses are
made for three models until relative errors are reached below the threshold value of
0.5%. After convergence, required results are extracted from FEA and presented in
this chapter.
One of the aims of this chapter is also to calculate strain distributions, which are
baseline for strain measured by sensors for comparison. Strain distributions at the
centre of each beam, where sensors are possibly located, are calculated. Sensor
positions at each manufactured beam are also shown in Figure 4.1 and Table 4.1 in
Section 4.2 in details.
22
3.2 FEM and FEA for Tension Applications
3.2.1 Finite Element Model for Tension Applications
Solid finite element model is created through ABAQUS software. Because of
symmetry, 1/8 beam model is created. All elements have orthotropic material property.
Most of the elements are solid brick elements but for simpler mesh, solid wedge
elements are also used at tapered tab region. Longitudinal beam axis is x axis, width
axis is y axis and thickness axis is z axis. 1/8 of the composite beam geometry, stacking
sequence and finite element model with tab region mesh can be seen from Figure 3.1.
(a)
(b)
Figure 3.1 (a) Geometry, Stacking Sequence and (b) Finite Element Model of 1/8 Composite Beam
for Tension Test
Each node of solid elements has 3 translational degrees of freedom. For analyses, four
sets of solid elements are used. Element types are as follows:
23
- Elements with linear interpolation (8 noded brick and 6 noded wedge) and
reduced integration: C3D8R and C3D6R
- Elements with quadratic interpolation (20 noded brick and 15 noded wedge)
and reduced integration: C3D20R and C3D15R
- Elements with linear interpolation (8 noded brick and 6 noded wedge) and full
integration: C3D8 and C3D6
- Elements with quadratic interpolation (20 noded brick and 15 noded wedge)
and full integration: C3D20 and C3D15
After mesh convergence analyses, appropriate element set is selected.
3.2.2 Boundary Condition Model for Tension Applications
Since the model and loading are symmetric, symmetry boundary conditions should be
applied for the simplicity. Symmetry BC’s are listed below:
- At the symmetry cross-section, y-z surface (x=0), u=0.
- At the side, x-z surface (y=0), v=0.
- At the bottom, x-y surface (z=0), w=0.
Loads are applied according to book of Tabbing Guide [65]. Uniform grip pressure
and surface traction along x direction are applied on the tab surface. Figure 3.2 shows
boundary conditions on the composite beam.
Figure 3.2 Applied Boundary Conditions on Composite Beam Model for Tension Test
24
3.2.3 Finite Element Analyses for Tension Applications
According to classical lamination theory, composites with symmetric stacking
sequence have uncoupled bending and axial responses. By separating axial
components, and neglecting Poisson’s ratio, axial strain can be obtained as given by
Equation (3.1).
𝐹 = 𝑏𝜀𝑥 ∑ 𝐸𝑖(𝑧𝑖+1 − 𝑧𝑖)
𝑁
𝑖=1
(3.1)
where subscripts of the parameters inside the summation represent ply index.
It is clear that Equation (3.2) gives area of i’th ply. Substituting area from Equation
(3.2) into Equation (3.1) gives, strain relation given by Equation (3.3).
𝑏(𝑧𝑖+1 − 𝑧𝑖) = 𝐴𝑖 (3.2)
𝜀𝑥 =𝐹
𝐸𝐴 (3.3)
where
𝐸𝐴 = ∑ 𝐸𝑖𝐴𝑖
𝑁
𝑖=1
(3.4)
Mesh Convergence Analyses:
For mesh convergence analyses, planar element edge lengths 𝐿𝑥 and 𝐿𝑦 values are
adjusted and then, element thickness 𝐿𝑧 values are adjusted separately until sufficient
convergence is obtained. Required element lengths and thicknesses are selected until
relative error below threshold value of 0.5% is achieved.
For constant surface traction of 5 MPa and grip pressure of 77.5 MPa, mesh
convergence study is performed. Strain data at the surface are extracted at the
symmetry centre of the beam at (x,y,z)=(0,0,h).
25
Mesh convergence behaviour with respect to planar edge values (Lx and Ly) are given
in Figure 3.3 and 3.4 for half tab displacement and axial strain at the surface
respectively. As the model represents half of the full displacement, half displacement
values are plotted. Average element thickness Lz is 0.583 mm.
8 noded-reduced integration elements are not sufficient and require finer mesh. 20
noded elements converge rapidly. Between the last increment, x-y element lengths of
5 mm and 10 mm, convergence behaviour of 20 noded elements with full integration
is the best with relative errors of 0.06% for displacement and 0.01% for strain.
Figure 3.3 Mesh Convergence Plot of Grip Displacement by Changing Planar Element Edge Lengths
Figure 3.4 Mesh Convergence Plots of Axial Strain at the Surface by Changing Planar Element Edge
Lengths
0.295
0.3
0.305
0.31
0.315
0.32
0.325
5101520
u/2
[m
m]
Lx=Ly [mm]C3D8R C3D8 C3D20R C3D20
3140
3145
3150
3155
3160
3165
3170
5101520
ε x[µ
ε]
Lx=Ly [mm]C3D8R C3D8 C3D20R C3D20
26
Similarly mesh convergence behaviour with respect to element thickness (Lz) are given
in Figure 3.5 and 3.6 for half tab displacement and axial strain respectively. Similarly,
20 noded element with full integration has the best behaviour. It has relative error
values of -0.02% for displacement and 0.0003% for strain.
As a result, 20 noded elements with full integration (C3D20) are used during the
analyses. Average element edge lengths of Lx=Ly=10 mm and Lz=0.583 mm are taken,
since error values are below 0.5% at the last increment.
Figure 3.5 Mesh Convergence Plots of Grip Displacement by Changing Element Thicknesses
Figure 3.6 Mesh Convergence Plots of Axial Strain at the Surface by Changing Element Thicknesses
0.297
0.298
0.299
0.3
0.301
0.302
0.303
0.304
0.305
0.350.450.550.650.750.85
u/2
[m
m]
Lz [mm]
C3D8R C3D8 C3D20R C3D20
3148
3150
3152
3154
3156
3158
3160
3162
3164
3166
3168
3170
0.350.450.550.650.750.85
ε x[µ
ε]
Lz [mm]
C3D8R C3D8 C3D20R C3D20
27
Results:
Strain distribution on z-axis at the centre of the beam is calculated. Under constant
displacement value of 0.5 mm, different pressure values of 0 and 155 MPa, with and
without geometric non-linearity (NLGEOM), strain distributions are plotted in Figure
3.7. Strain values of initial state, when grip pressure is applied without any other axial
load, is taken as zero reference for strain and displacement. For all cases, strain
distribution is always constant with respect to z-coordinate and four analyses provide
very close strain values. Therefore, during tension applications, all sensors should give
the same value regardless of their positions along z-axis. With this information, strain
values can be compared directly during the coming tension tests.
Figure 3.7 Axial Strain Distribution with respect to Normalized Position along z-Axis for Full
Displacement of 0.5 mm
Force values are plotted with respect strain for different pressure values. Analyses with
linear (NLGEOM-OFF) and non-linear geometry (NLGEOM-ON) are shown in
Figure 3.8. Maximum full axial displacement is kept constant and equal to 0.5 mm, as
tension tests are displacement controlled. On the model, displacement of 0.25 mm
should be obtained, because the model represents half portion that creates axial
displacement. It is concluded from Figure 3.8 that non-linear geometry and pressure
0
0.2
0.4
0.6
0.8
1
2850 2852 2854 2856 2858 2860 2862 2864
z /
h
εx [µε]
NLGEOM OFF - P=0 MPa NLGEOM ON - P=0 MPa
NLGEOM OFF - P=155 MPa NLGEOM ON - P=155 MPa
28
effects are negligible as plots in Figure 3.8 are close agreement for different pressure
values with and without geometric non-linearity.
Figure 3.8 Force vs. Strain Graph for Maximum Grip Displacement of 0.5mm
3.3 FEM and FEA for Vibration Applications
3.3.1 Finite Element Model for Vibration Applications
Solid finite element model is also created through ABAQUS software. Since boundary
conditions are not symmetric, full beam model with tabbing is created. Finite element
and node specifications are the same as those for axial test given at Section 3.2.1.
Figure 3.9 gives full beam model geometry and stacking sequence.
Figure 3.9 Full Composite Beam Geometry and Stacking Sequence for Vibration Tests
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 500 1000 1500 2000 2500 3000
F [
N]
εx [µε]
NLGEOM OFF - P=0 MPa NLGEOM ON - P=0 MPaNLGEOM OFF - P=155 MPa NLGEOM ON - P=155 MPaEq. 3.3
29
3.3.2 Boundary Condition Model for Vibration Applications
Figure 3.10 shows boundary conditions on the composite beam for vibration
applications. At one end, both tab surfaces are clamped (i.e. 6 degrees of freedom are
fixed).
Figure 3.10 Applied Boundary Conditions on Composite Beam Model for Vibration Tests
3.3.3 Finite Element Analyses for Vibration Applications
Mesh Convergence Analyses:
For mesh convergence analyses, planar element edge lengths 𝐿𝑥 and 𝐿𝑦 values are
adjusted and then, element thickness 𝐿𝑧 value is adjusted seperately until sufficient
convergence is obtained. 8 noded-full integration elements have very poor
convergence behaviour with relative error values about 20%, and not shown in
convergence plots.
Mesh convergence behaviour with respect to planar edge values (Lx and Ly) are given
in Figure 3.11 and 3.12 for the first and second out-of-plane bending natural
frequencies, respectively. Average element thickness Lz is 0.583 mm.
There is also one torsional mode in between. Convergence behaviour is not shown, as
vibration applications only include bending excitation (i.e. node of torsional mode is
excited) and strain results at the possible sensor locations are exactly zero.
30
20 noded elements converge rapidly. Between the last increment, x-y element lengths
of 5 mm and 10 mm, convergence behaviour of 20 noded elements with reduced
integration is the best with relative errors of -0.03% for the first and -0.05% for the
second out-of-plane bending natural frequencies.
Figure 3.11 Mesh Convergence Plot of 1st Out-of-Plane Natural Frequency by Changing Planar
Element Edge Lengths
Figure 3.12 Mesh Convergence Plots of 2nd Out-of-Plane Natural Frequency by Changing Planar
Element Edge Lengths
Similarly mesh convergence behaviour with respect to element thickness (Lz) are given
in Figure 3.13 and 3.14 for the first and second out-of-plane natural frequencies
51.1
51.2
51.3
51.4
51.5
51.6
51.7
51.8
51.9
52
52.1
5101520
f [H
z]
Lx=Ly [mm]
C3D8R C3D20R C3D20
410
411
412
413
414
415
416
417
418
419
5101520
f [H
z]
Lx=Ly [mm]C3D8R C3D20R C3D20
31
respectively. Similarly, 20 noded element with reduced integration has the best
behaviour. It has relative error values of -0.04% for first and -0.05% for second out-
of-plane bending natural frequencies.
As a result, 20 noded elements with reduced integration (C3D20R) are used during
analyses. Lx=Ly=10 mm and Lz=0.583 mm are taken, as relative errors are below 0.5%
threshold.
Figure 3.13 Mesh Convergence Plots of 1st Out-of-Plane Natural Frequency by Changing Element
Thicknesses
Figure 3.14 Mesh Convergence Plots of 2nd Out-of-Plane Natural Frequency by Changing Element
Thicknesses
49
49.5
50
50.5
51
51.5
52
52.5
0.350.450.550.650.750.85
f [H
z]
Lz [mm]
C3D8R C3D20R C3D20
390
395
400
405
410
415
420
0.350.450.550.650.750.85
f [H
z]
Lz [mm]
C3D8R C3D20R C3D20
32
Results:
The first three mode shapes of the beam are given in Figure 3.15. The first and the
third mode shapes are out-of-plane bending mode shapes of natural frequencies of 51.9
Hz and 415.6 Hz respectively, the second mode shape, on the other hand, is torsional
mode shape of natural frequency of 278.4 Hz. Modal strain distribution on the first
three modes on z-axis are also calculated. As seen from Figure 3.16, modal strain
distribution is linear with respect to position along z-axis for bending modes. Modal
strains are normalized such that, at the upper surface (z=h) modal strain value is 1.
Modal strain values of torsional mode on z-axis are zero. Therefore, peak value at
natural frequency of the torsional mode in frequency domain of the strain data is not
expected.
(a)
(b)
(c)
Figure 3.15 (a) 1st Out-of-Plane Bending (f=51.9 Hz), (b) 1st Torsion (f=278.4 Hz), (c) 2nd Out-of-
Plane Bending (f=415.6 Hz) Mode Shapes
33
Figure 3.16 Modal Axial Strain Distribution along z-Axis for First Two Out-of-Plane Bending Modes
3.4 FEM and FEA for Torsion Applications
3.4.1 Finite Element Model for Torsion Applications
Solid finite element model is created through ABAQUS. Symmetry conditions cannot
be used, as symmetry planes are deformed under torsional load. Therefore, full model
is created. Geometry and stacking sequence of the torsion model can be seen from
Figure 3.17. The composite beam is not tabbed. Element specifications are the same
as those of tension and vibration models.
Figure 3.17 Full Composite Beam Geometry and Stacking Sequence for Torsion Tests
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-1 -0.5 0 0.5 1
z / h
εx*
1st Bending Mode 2nd Bending Mode
34
3.4.2 Boundary Condition Model for Torsion Applications
Before applying boundary conditions, grip regions are set to be rigid body. As seen
from Figure 3.18, left surfaces and right surfaces are separately assigned to move rigid
and controlled by two separate reference points.
Figure 3.18 Assigned Rigid Body Constraints for Torsion Model
First reference point (RP1) controlling left grip surfaces is fixed in all directions. On
the other hand, second reference point (RP2) controlling right grip surfaces is fixed in
four directions except translation and rotation about x axis (U1 and UR1). Depending
on application, either concentrated torque about x axis (CM1) or rotation about x axis
(UR1) is assigned to desired value. Axial translation (U1) is free. Assigned boundary
conditions on reference points can be seen from Figure 3.19.
35
Figure 3.19 Applied Boundary Conditions on Reference Points of Torsion Model
3.4.3 Finite Element Analyses for Torsion Applications
Sensor locations are at the centre in width direction and away from smaller edges.
According to elasticity theory with equilibrium and strain-displacement relations for
static torsion, shear strain distributions away from smaller edges can be derived.
Expression of shear strain away from smaller edges is derived in Appendix A and the
result is given in Equation (3.5).
𝛾𝑥𝑦 = −2𝑧𝑑𝜙
𝑑𝑥 (3.5)
Strain values from Equation (3.5) is not completely analytic. Value of 𝑑𝜙 𝑑𝑥⁄ is
extracted from corresponding FEA. That derivative is calculated by using
displacement values since solid elements do not support rotational results. Angle of
twist is calculated from kinematic relation given by Equation (3.6).
𝜙(𝑥) = − arctan𝑣(𝑥, 0, ℎ)
ℎ (3.6)
y displacement values (v) can directly be extracted from FEA. 𝑑𝜙 𝑑𝑥⁄ is calculated
using finite derivative from quadratic interpolation as seen from Equation (3.7).
36
Δ𝜙
Δ𝑥|
𝑥=0=
4 [𝜙 (𝐿𝑥
2) − 𝜙 (−
𝐿𝑥
2)] − [𝜙(𝐿𝑥) − 𝜙(−𝐿𝑥)]
2𝐿𝑥 (3.7)
Mesh Convergence Analysis:
For mesh convergence analyses similarly 𝐿𝑥 and 𝐿𝑦 values are adjusted and then, 𝐿𝑧
value is adjusted seperately until sufficient convergence is obtained. For constant
torque of 35000 N.mm, angle of twist and shear strain data on z-axis are extracted.
Mesh convergence behaviour with respect to planar edge length changes are given in
Figure 3.20 and 3.21. 8 noded elements are not sufficient and require finer mesh. 20
noded elements with full integration have the best convergence behaviour with errors
of 0.4% for angle of twist and 0.2% for shear strain.
Figure 3.20 Mesh Convergence Plots of Angle of Twist by Changing Planar Element Edge Lengths
0.0
7.5
15.0
22.5
30.0
37.5
45.0
2.557.51012.51517.520
φ[⁰]
Lx,Ly [mm]
C3D8 C3D8R C3D20 C3D20R
37
Figure 3.21 Mesh Convergence Plots of Shear Strain at the Surface by Changing Planar Element
Edge Lengths
Element thickness convergence curves of angle of twist and shear strain are plotted in
Figure 3.22 and 3.23. As 8 noded elements with reduced integration is extremely poor
for planar mesh convergence, they are not plotted.
20 noded elements converge rapidly as element thicknesses change. For angle of twist,
C3D20 elements have the best convergence behaviour. However, for shear strain plot
20 noded elements with reduced integration seems to be better. In general, C3D20
elements are considered to have the best performance because of the behaviour at
planar edge length plots. Error values are around 0.2% for both angle of twist and shear
strain for the last increment.
Average element lengths of Lx=Ly=5 mm and Lz=0.568 mm are used in the results as
relative errors are below threshold value of 0.5%.
0
5000
10000
15000
20000
25000
30000
2.557.51012.51517.520
γxy
[µε]
Lx,Ly [mm]
C3D8 C3D8R C3D20 C3D20R
38
Figure 3.22 Mesh Convergence Plots of Angle of Twist by Changing Element Thicknesses
Figure 3.23 Mesh Convergence Plots of Shear Strain at the Surface by Changing Element
Thicknesses
Results:
Static torsion analyses are conducted and the obtained results are explained here. As
seen from Figure 3.24, shear strain distribution is linear with respect to position along
36.8
37.0
37.2
37.4
37.6
37.8
38.0
38.2
38.4
38.6
38.8
0.350.450.550.650.75
φ[⁰]
Lz [mm]
C3D8 C3D20 C3D20R
24500
24800
25100
25400
0.350.450.550.650.75
γxy
[µε]
Lz [mm]
C3D8 C3D20 C3D20R
39
z-axis. It holds for analyses with both linear and non-linear geometry. Moreover
Equation (3.5) also holds for both linear and non-linear geometry.
It is observed from the analyses without non-linear geometry (NLGEOM) effects that
axial strain along the beam axis is exactly zero over the cross-section at the centre of
the beam. Conversely, when non-linear geometry effect is not neglected, and it is also
observed from the analyses that axial strain along the beam axis is not zero and it
changes non-linearly with respect to angle of twist.
Figure 3.24 Shear Strain Distribution along z-axis for φ=40⁰
Torsion applications also include fatigue torsion under pulsating sinusoidal load of
angle of twist oscillating between 0 and 40 degrees with frequency of 3 Hz. Fatigue
torsion application is considered to be quasi-static and static shear strain distribution
in Figure 3.24 is assumed to be valid for fatigue torsion applications as well.
For fatigue torsion applications, variation of surface shear strain with respect to angle
of twist is plotted Figure 3.25, which is needed for shear strain variation in time
domain. As angle of twist variation is known in time domain, strain values can be
mapped into time domain from angle of twist variation. Strain values at corresponding
angle of twist in Figure 3.25 is mapped into time domain for one period as shown in
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-30000 -15000 0 15000 30000
z / h
γxy [µε]
NLGEOM - OFF Eq 3.5 - dphi/dx from NLGEOM OFF
NLGEOM - ON Eq 3.5 - dphi/dx from NLGEOM ON
40
Figure 3.26. Since the frequency is 3 Hz, Figure 3.26 is shown between 0 and 1/3
seconds, which is the interval of one period.
Figure 3.25 Shear Strain – Angle of Twist Plot under Torsion
Figure 3.26 One Cycle of Surface Shear Strain Driven by Pulsating Angle of Twist with Maximum
Value of 40 degrees with frequency of 3 Hz
Mean and amplitudes of time signal of the surface shear strain shown in Figure 3.26
are calculated and also shown in Table 3.1. Furthermore, mean and amplitude values
of shear strain values at any position along z-axis can be found by using the linear
distribution shown in Figure 3.24. For instance, mean and amplitude of shear strain at
0
5000
10000
15000
20000
25000
30000
0 5 10 15 20 25 30 35 40
γ xy
[µε]
φ[⁰]
NLGEOM-OFF
NLGEOM-ON
0
5000
10000
15000
20000
25000
30000
0.0000 0.0833 0.1667 0.2500 0.3333
γ xy
[µε]
Time [s]
NLGEOM - OFF NLGEOM - ON
41
z=0.584h can directly be found by scaling down the surface strain by its position along
z-axis (i.e. by multiplying strains in Table 3.1 by 0.584).
Table 3.1 Mean and Amplitude Values of Surface Shear Strain under Fatigue Load
Mean Value of γxy Amplitude of γxy
NLGEOM - OFF 13129 µε 13129 µε
NLGEOM - ON 12442 µε 12110 µε
3.5 Conclusions
For three different types of loading applications, different finite element analyses are
performed in this chapter. Mesh convergence analyses are completed and 20 noded
solid elements are observed to show the best behaviour requiring more computational
time. Nevertheless, convergence is achieved at relatively coarse meshes. For instance,
computation times do not exceed 30 minutes (in a 6-core 3.2 GHz workstation with 32
GB RAM) even for the torsion analyses with non-linear geometry effects.
To test embedded sensors, strain distributions are also needed. With these
distributions, test results obtained from embedded FBG’s can be easily compared with
that from surface mounted sensors. Moreover, axial force to strain distributions from
FEA of tension applications and natural frequencies from FEA of vibration
applications are also obtained. For fatigue applications, mean values and amplitudes
of strain values are calculated in the time domain. All results are baseline for the tests
and are used to be compared with the upcoming test results.
42
43
CHAPTER 4
DEVELOPMENT OF THE SHM SYSTEM OF COMPOSITES WITH
EMBEDDED FBG SENSORS
4.1 Introduction
This chapter explains how to develop the SHM system with embedded FBG’s, which
is composed of manufacturing methods, data acquisition system and description of the
experiments conducted for SHM applications. Initially, specimen geometries and their
sensor positions for tension, vibration and fatigue torsion experiments, and then, the
manufacturing of those specimens are described.
Four composite beams were manufactured for three different types of experiments.
There are several surface mounted and embedded sensors, FBG and strain gauge (SG),
at different positions of each beam. After manufacturing, the beams are connected to
the data acquisition system, setup and specifications of which are explained in this
chapter. Furthermore, those three types of experiments, through which the developed
system is verified, are also discussed.
4.2 Description of the Composite Beams
Four composite beams were manufactured with surface mounted and embedded
sensors. Geometry of the beams and their coordinate system can be seen from Figure
4.1. All sensors are located at the centre of the specimen by considering x and y
positions, and hence they are located at different positions along z-axis. Planar sensor
locations can also be seen from Figure 4.1 and positions along z-axis of all sensors are
summarized in Table 4.1.
44
(a)
(b)
Figure 4.1 Geometry of Composite Beams for (a) Tension and Vibration and (b) Torsion Tests
Table 4.1 Thickness-wise Positions and Orientations of Sensors
Specimen Sensor Orientation Position along z-Axis Experiment
1st Beam FBG 0⁰ z=h (Surface Mounted)
Tension SG 0⁰ z=-h (Surface Mounted)
2nd Beam FBG 0⁰ z=h (Surface Mounted)
Tension FBG 0⁰ z=0 (Embedded)
3rd Beam FBG 0⁰ z=h (Surface Mounted) Tension &
Vibration FBG 0⁰ z=0.584h (Embedded)
4th Beam
FBG 45⁰ z=h (Surface Mounted)
Fatigue Torsion FBG 45⁰ z=0.584h (Embedded)
FBG 45⁰ z=0 (Embedded)
According to tabbing guide of composites [65], tension specimens should have tabbed
regions, and therefore, tension specimens were manufactured with tabbing. On the
45
other hand, the beam for torsion test has no tabbing, as there is no tabbing standard for
composite beams for torsion tests.
Sensor locations and functions of each composite beam are discussed one by one as
follows:
- 1st Beam specimen is manufactured without any embedded sensor. After
manufacturing, one FBG and one SG are mounted to opposite surfaces of the
beam. This specimen is used for comparison of FBG and SG in tension tests.
- 2nd Beam specimen is manufactured with one embedded FBG at the centre of
the beam thickness-wise. After manufacturing, one FBG is mounted to the
surface of the beam. This beam was undergone tension tests to compare strain
values of embedded FBG at the centre to surface mounted one.
- 3rd Beam specimen is manufactured with one FBG sensor at z=0.584h offset
from the centre plane. Similarly, one FBG is mounted to the surface of the
beam for comparison. This beam was undergone tension tests and also
vibration tests.
- 4th Beam specimen has two embedded FBG’s one at z=0 (centre) and one at
z=0.584h. Moreover, one FBG is also mounted to the surface. This beam was
undergone fatigue torsion test. Before fatigue torsion test, it was also
undergone static torsion tests. In this study, fatigue torsion test and its analyses
are described. Detailed description and analyses of static torsion tests are
available in Karataş’s [66] study.
4.3 Manufacturing of Composite Specimens with Embedded FBG Sensors
Composite beams were manufactured by using glass-fibre prepregs. Removing the
beams with embedded sensors by cutting them from one plate is a very difficult task.
So, the prepreg materials were cut in planned dimension and laid accordingly.
However, in width direction, the layers were cut longer than planned such that the free
edges of the beam were to be smoothened with cutting operation using band saw. The
manufactured cut plies can be seen from Figure 4.2.
46
Figure 4.2 Cut Prepreg Plies and Cutting Machine in Epsilon Kompozit Inc.
Several prepregs were laid until ply of embedded FBG reached. Then, these plies were
taken into vacuum bagging. After vacuum bagging, FBG sensors were laid and
adjusted, and calculated points of the ingress/egress edges were marked.
To protect the FBG wires from the stress concentrations at ingress-egress regions,
teflon tubes were used, and they were adjusted such that they pass through marked
positions. With this method, FBG’s were adjusted in a simple way. Figure 4.3, from
part of the previous study [67] shows laid FBG with teflon tubes on plies.
Remaining plies were laid on embedded sensor and they were taken into one last
vacuum bagging. FBG wires were evacuated from vacuum bagging with tight sealing
to prevent resin leakage. After the last vacuum bagging, composite beams were taken
into autoclave for curing.
47
Figure 4.3 FBG Wire to be Embedded on Laid Plies [67]
Pigtail connectors of FBG sensors were cut out before manufacturing, as pigtail
connectors were expected to melt at high curing temperatures. After manufacturing,
pigtail connectors were re-joined to FBG wires through fusion splicer device, which
can be seen from Figure 4.4.
Figure 4.5 shows flowchart that summarizes manufacturing specimens with embedded
FBG’s.
Figure 4.4 Fusion Splicer Device
48
Figure 4.5 Flowchart of Manufacturing of the Composite Beams with Embedded FBG’s
At the end of the curing in autoclave, other FBG sensors and strain gage were mounted
on the corresponding surfaces of the beams. One of the composite beam specimens
with embedded and surface mounted FBG sensors can be seen from Figure 4.6.
Figure 4.6 Manufactured Composite Beam with Embedded and Surface Mounted FBG
4.4 Data Acquisition System
Optical fibres with single FBG used in this study have central (unloaded) Bragg
wavelength of 1550 nm. Bragg wavelength peak is automatically captured by
interrogator system in real time, and is transformed to strain value using Equation
(4.1). Captured Bragg wavelength through SmartSoft interface [68] can be seen from
Figure 4.7.
49
Δ𝜆 = 𝐾𝜀𝜀 + 𝐾𝑇Δ𝑇 (4.1)
For all FBG in this study, values of 𝐾𝜀 and 𝐾𝑇 are 1.2 pm/µε and 11 pm/⁰C,
respectively. For static and modal tests in laboratory studies, temperature hardly
changes. For fatigue tests with long duration, ambient temperature may change. Even
for 10 ⁰C temperature change, strain values are observed to shift up or down with
magnitude of 92 µε as this value is considered as negligible. Therefore, the second
term in Equation (4.1) is neglected in this study.
On the other hand, it is possible to offset strain value for zero referencing. It is needed
especially for residual strain cancellation just after manufacturing of the beams. With
zero-referencing, wavelength-strain data of FBG’s can be seen from Figure 4.8.
Figure 4.7 Wavelength Capturing through SmartSoft [68]
50
Figure 4.8 Wavelength and Strain Data through SmartSoft [68]
4.4.1 Interrogator System of FBG Sensors
FBG interrogator is the main data acquisition unit. It has wavelength range of 1528-
1568 nm, which corresponds to 33300 µε strain range. FBG interrogator provides
opportunity to measure strain data with high sampling frequency, which makes it
possible to conduct vibration tests with high frequency range. Interrogator unit can
provide sampling frequency up to 2.5 kHz with full wavelength and strain range. By
narrowing down wavelength and strain range, it is possible to get data with sampling
rate larger than 2.5 kHz.
Figure 4.9 shows interrogator system used in this study. It has four channels for optical
fibre wires supporting up to 16 FBG’s per one optical fibre. It has also power
connection, Ethernet connection and USB socket.
USB logging capability provides system can store data without any other processor. It
is designed for logging data during real flights without any other computer.
51
Figure 4.9 FBG Interrogator
4.4.2 Optical Interface Cables
Between each channel of interrogator and each FBG wire, four optical interface cables
are needed. One end of it is connected to interrogator channel and the other end is
connected to FBG wire with FC/APC connection. Figure 4.10 shows an optical
interface cable.
Figure 4.10 Optical Interface Cable
52
4.4.3 FBG Wires
FBG wires are the main measurement unit. As explained in Section 2.3.2, broadband
light is sent and reflected back from FBG’s and digitized by interrogator. It may have
single FBG at one point or several FBG’s at multiple points. In this study, all
applications include sensors with single FBG.
FBG wires have FC/APC pigtail connectors at one end, and the other end of it is free.
Figure 4.11 shows a FBG wire with a pigtail connector.
FBG wires are polyimide recoated, which can withstand high temperatures. During
autoclave, high curing temperatures occur and polyimide recoated wires remain
protected.
Figure 4.11 FBG Wire with Pigtail Connector
4.4.4 Female-Female FC/APC Fibre Optic Adaptor
Connectors of interface cables and pigtail connectors of FBG wires have both male
FC/APC connectors. One intermediate adaptor, seen from Figure 4.12, is needed to
connect them. Male connectors of interface cables and FBG pigtails can fit into female
connectors of the adaptor as this adaptor connects interface cables to FBG wires.
53
Figure 4.12 Fibre Optic Adaptor
4.5 Description of the Experiments for Verification of the Developed SHM
system with Embedded FBG’s
4.5.1 Description of Tension Experiments
Setup for tension experiments can be seen from Figure 4.13. MTS tension test machine
is the main test unit, which has 330 kN static and 250 kN dynamic force capacity. The
beams were supported by wedge grips by pressure. Embedded sensor wires with
protective teflon tubes exited at the gap below the beam between the grips as seen from
Figure 4.14, and these wires exiting from the beams were connected to FBG data
acquisition unit.
1st beam specimen has also one strain gauge bonded on its surface. Therefore, both
strain gauge data acquisition system as well as that of FBG were used. Data acquisition
systems were connected to data acquisition PC, from which all data were monitored
during the tests.
54
Figure 4.13 Tension Test Setup
Figure 4.14 Optical Fibre Covered by Teflon Tube Exiting below Grip Region
55
Sampling frequency of MTS interrogator system was set to be 20 Hz, and sampling
frequencies of strain gauge and FBG interrogator were set to be 50 Hz. All the tests
were conducted with displacement rate of 1 mm/min. As maximum axial displacement
was 0.5 mm, each test took 30 seconds.
4.5.2 Description of Vibration Experiments
Setup of the vibration experiments can be seen from Figure 4.15. Tab surfaces of the
beam at one end were fixed by slotted clamps with bolts, nuts and washers, and these
clamps were fixed by fixture grips. Embedded and surface mounted FBG’s were
connected to interrogator system through interface cables and FC/APC adaptors.
The beam was excited by impact hammer at its free end for 16 times and strain values
of both sensors were recorded by the data acquisition PC at a sampling frequency of
2.5 kHz in order to extract the resonance frequencies from the obtained strain signals
(see Section 5.3).
Figure 4.15 Vibration Test Setup
56
4.5.3 Description of Fatigue Torsion Experiments
MTS tension-torsion test machine is the main load unit and it has ±45 angle of twist,
100 kN axial force and 1100 N.m torque capacity. The composite beam was supported
and rotated by the wedge grips via applied pressure. The beam specimen for fatigue
torsion test and MTS tension-torsion machine can be seen from Figure 4.16.
Axial displacement of the grips supporting one end of the beam was kept free such that
zero axial force was read in order for the beam to be loaded by pure torsion.
The beam has two single embedded FBG sensors which are evacuated from the side
of the beam at grip region with teflon tubes. Moreover, the beam has also one surface
mounted FBG. All sensors were oriented 45 degrees from the main beam axis for shear
strain measurement.
Figure 4.16 Specimen under Fatigue Torsion Load
57
Sampling frequencies of MTS and FBG interrogator system were set to be 50 Hz.
Pulsating angle of twist loading varies sinusoidally with frequency of 3 Hz oscillating
between 0 and 40 degrees. Time function of angle of twist is given in Equation (4.2).
𝜙(𝑡) =𝜙0
2(1 + sin 2𝜋𝑓𝑡) (4.2)
where 𝜙0 = 2 𝜋 9⁄ and 𝑓 = 3𝐻𝑧.
The experiment lasted about one hour, which corresponds to approximately 10000
cycles. Surface mounted FBG was broken earlier (at 720th cycle), on the other hand,
embedded sensors were observed to be healthy throughout the test.
4.6 Conclusions
Components of the SHM system are discussed one by one in this chapter in details.
Description of the composite beams and manufacturing of those are also explained.
The most important manufacturing points are protective teflon tubes covering FBG
wires at ingress/egress regions and cutting and re-joined pigtail connectors through
fusion splicer device. After manufacturing of the specimens, interrogator system was
connected to power supply and PC, and embedded and surface mounted FBG sensors
were connected to interrogator systems through intermediate connectors. After
completing the data acquisition system assembly, sensors provided Bragg
Wavelengths that could be captured by interrogator systems. Therefore, manufacturing
of the specimens was successful and the system was ready for SHM experiments,
which are also discussed in this chapter.
58
59
CHAPTER 5
RESULTS AND DISCUSSIONS
5.1 Introduction
This section is mainly composed of three sections; tension, vibration and fatigue
torsion case studies, and all results of these three case studies are presented in this
chapter. Experimental results with available baseline finite element analyses are also
given for comparison. Strain signals of embedded sensors are mainly compared to
surface mounted ones according to strain distributions obtained through FEA for each
case study.
Moreover, as tension experimental results are very straightforward to analyse,
additional analyses are also performed. Strain data of surface mounted FBG and SG
and its noise contents are also compared in tension experiment case study. Stiffness
values (i.e. EA) of each beam assigned to corresponding FEM are compared to
experimental data for all sensors regarding force-strain graphs. That comparison shows
how mechanical parameters are assigned to FEM representing material properties of
composite beam specimens.
5.2 Results and Discussions of Tension Experiment Case Study
All force, displacement and strain data were logged in time domain separately during
each tension test. Time values of each data were adjusted and force-displacement,
force-strain strain-displacement and strain-strain curves were plotted for different
sensors.
60
To compare strain data of the sensors, post-processing of the experimental data is
performed, which is summarized as follows:
- Axial strain and force values are plotted with respect to displacement for each
test and each sensor separately. By doing this, strain and force data become as
a function of displacement instead of time, which makes it possible to average
force and strain values at corresponding displacement values.
- Force and strain values are averaged for each sensor and each specimen.
- Required plots are created and presented.
- Strains of two arbitrary sensors on the beam specimen are compared through
fitted lines by least squares regression in the form of strain-strain and force-
strain curves as shown by Equations (5.1) and (5.2), respectively.
𝜀𝑥,2 = 𝑚𝜀𝜀𝑥,1 + 𝑛𝜀 (5.1)
𝐹 = 𝑚𝐹𝜀𝑥 + 𝑛𝐹 (5.2)
Offset values (𝑛𝜀 , 𝑛𝐹) are disregarded in discussions, as those values exist because of
zero-offsetting errors, which are not sensor dependent. On the other hand, slope values
( 𝑚𝜀 , 𝑚𝐹 ) should closely be discussed, as 𝑚𝜀 values completely represent
characteristics of the sensor responses and 𝑚𝐹 represents stiffness behaviour. From
the results of FEA for tension applications, expected slope values are given in
Equations (5.3) and (5.4) for correct zero offsetting (i.e. 𝑛𝜀 = 𝑛𝐹 = 0).
𝑚𝜀 = 1 (5.3)
𝑚𝐹 = 𝐸𝐴 (5.4)
Equation (5.3) implies strain data of any two sensors on each beam should be equal.
On the other hand, Equation (5.4) is expected because of Equation (3.3) satisfied by
FEA.
As force-displacement curves are not relevant to embedded and surface mounted FBG
sensor comparison, they are given in Appendix B.1 as supplementary graphs.
61
5.2.1 Comparison and Discussion of Strain Data of FBG and SG from Tension
Experiment Case Study
1st beam specimen having one surface mounted FBG sensor and one strain gauge is
used for FBG and SG comparison under tension load. Moreover, noise comparison is
also performed in time domain through the method of moving average.
According to strain distribution shown by Figure 3.7, axial strains of SG and FBG
sensors are expected to be equal at each point, which are checked by slope of fitted
lines by least squares regression.
Figure 5.1 shows SG and FBG strains with respect to each other for the tension
experiment with equal strain line obtained from FEA. Linear line is also fitted to
experimental data and slope of it is shown with that of FEA in Table 5.1.
Error value of the slope of experimental FBG vs SG curve is 1.6%. Nevertheless, very
close agreement is observed between experimental data and equal strain line from
FEA, as two curves are nearly coincident as seen from Figure 5.1.
Figure 5.1Axial Strain of Surface Mounted FBG with respect to that of Strain Gauge
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
FB
G -
ε x[µ
ε]
SG - εx [µε]
FEA Experiment
62
Table 5.1 Slopes of the FBG-SG Strain Curves shown in Figure 5.1
Slopes of FBG-SG Curves - 𝑚𝜀
Expected Value from FEA 1.000
Experimental Data through Fitted Line 1.016
Force – Strain curves are also plotted for FEA comparison to experimental data as
shown by Figure 5.2. Linear lines are also fitted to experimental data similarly and
values of these can be seen in Table 5.2.
Error values of the force-strain slopes between FBG and SG curves are again 1.6%.
Nevertheless, they are nearly coincident. However, force-strain curve calculated by
FEA are not coincident with experimental curves. There are error values about -12%
between slopes of force-strain curve by FEA and both sensors. These errors may due
to the stiffness errors because of misestimations of Young’s Moduli, which require
updating the values of Young Moduli in FEM.
Figure 5.2 Axial Force versus Strains for SG and FBG Comparison
0
5000
10000
15000
20000
0 500 1000 1500 2000 2500 3000
F [
N]
εx [µε]
FBG SG FEA
63
Table 5.2 Slopes of the Force Strain Curves shown in Figure 5.2
𝑚𝐹 [N/µε]
FEA (𝐸𝐴) 6.421
Strains from FBG 7.287
Strains from SG 7.405
Noise comparison of SG and FBG sensors under tension is also performed in this
section. First of all, noise cancellation is made through moving average method.
Moving average is a smoothing method averaging of a time point with its adjacent
time points in some time radius and may have some weighting methods as well. In this
study, however, weighting is not used and average values are taken directly with some
time radius. The radius value is determined by trial and error and the best behaviour is
observed for time radius r=0.2 s. Application of method of moving average are given
in Figure 5.3 at arbitrary interval in closer view showing that the oscillatory behaviour
of the strain signals are removed especially as it can be seen from the response of SG.
Figure 5.3 Initial and Moving Averaged Strain Signals by FBG and SG in Closer View
820
840
860
880
900
920
940
9 9.2 9.4 9.6 9.8 10
ε x[µ
ε]
t [s]
Surface FBG
Moving Average FBG
Strain Gauge
Moving Average S. Gauge
64
Smoothened strain signals with moving average are assumed as noise free. Therefore,
the difference of initial strain data with noise and strain data with moving average
without noise for each sensor gives pure noise content of the each signal. Figure 5.4
shows extracted noise signal by moving average method in time domain. As seen from
Figure 5.4 that the data of strain gauge is much noisier than that of FBG sensor. Noise
amounts are calculated with standard deviations, which are 0.87 µε for FBG and 5.31
µε for strain gauge. Therefore, it can be concluded that FBG sensors provide strains
with less noise content than that of SG’s.
As seen from Figure 5.3, the initial signal of strain gauge oscillates about the signal
with moving average with some frequency. Whereas, it is very hard to observe
oscillations of FBG signals as noise contents are comparably lower. To observe
frequency contents of the noise, Fast Fourier Transform (FFT) of the noise signals in
Figure 5.4 are taken and amplitudes of FFT of noise signals are shown in Figure 5.5.
The frequency axis is shown up to nyquist frequency of 25 Hz.
Figure 5.4 Noise Strain Signals Extracted by Moving Average Method
-15
-10
-5
0
5
10
15
0 5 10 15 20 25 30
ε x[µ
ε]
t [s]
S. Gauge Noise FBG Noise
65
Figure 5.5 Frequency Distributions of Noise Signals of FBG and Strain Gauge
Noise content of FBG is not exactly concentrated on some frequency but it has some
small noise content distributed around 1 to 4 Hz. On the other hand, strain gauge has
both noise content concentrated at 5 Hz and its harmonics with very large values
compared to FBG sensors. This may create serious problems when vibration
experiments are conducted. Peaks of the noise of strain gauge might be identified as
resonance of the structure and might result in false inspections; or it might give
distorted frequency plots of a structure having resonances around harmonics of 5 Hz.
In summary, FBG sensors have lower noise content and is not concentrated on any
frequency, which makes it possible to get strain data with high quality and high signal
to noise ratio.
5.2.2 Comparison and Discussion of Strain Data of Embedded and Surface
Mounted FBG from Tension Experiment Case Study
Axial strain under tension should be equal for all sensors regardless of their positions
along z-axis as shown by FEA. 2nd and 3rd beam specimens have one embedded sensor
and one surface mounted sensor. Surface mounted sensors are taken as reference and
the data of embedded sensors are expected to be equal to the data of the surface
mounted ones. Embedded-Surface Mounted FBG strain graphs of 2nd and 3rd beam
5.00Hz,6.79µε.s
9.99Hz, 1.28µε.s
14.99Hz, 0.30µε.s
19.99Hz0.60µε.s
0
1
2
3
4
5
6
7
8
0 5 10 15 20 25
|FFT
of
No
ise
| [µ
ε.s]
Frequency [Hz]
Abs. V. of FFT of SG Noise
Abs. V. of FFT of FBG Noise
66
specimens averaged from multiple tests are given in Figure 5.6. Moreover, strain-strain
plots of each test without averaging can also be found in Appendix B.2. Linear lines
also fitted to the strain-strain curves from the experiment. The slopes are listed in Table
5.3. As seen from Table 5.3, those error values of the slopes are as low as -1.2% and
-0.15% for 2nd and 3rd beam specimens respectively and this means that the embedded
strain values are nearly equal to those of surface mounted ones. In other words, the
embedded FBG sensors work properly and provide correct and reliable results.
Figure 5.6 Axial Strain of Embedded FBG with respect to Surface Mounted FBG
Table 5.3 Slopes of the Embedded – Surface Mounted Strain Curves shown in Figure 5.6
Slopes of Embedded vs. Surface Strain
FEA 1.000
2nd Beam Specimen 0.988
3rd Beam Specimen 0.999
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
Em
bed
ded
FB
G -
ε x[µ
ε]
Surface FBG - εx [µε]
FEA Experiment - 2nd Beam Experiment - 3rd Beam
67
Force-strain plots of each test without averaging can also be seen from Appendix B.3.
In this section, average force-strain plots of each specimen with strain values from
embedded and surface mounted FBG’s are shown in Figure 5.7. Multiple test values
are averaged for 2nd and 3rd beam specimens. The slopes are listed in Table 5.4. Curves
of the surface and embedded FBG curves are nearly coincident for each beam
specimen. On the other hand, FEA underestimates the slope values because of smaller
Young’s Moduli assigned to FEM. The errors are around -15% and -6% for the 2nd and
the 3rd specimen respectively. Those errors indicate that Young Moduli values should
be updated for each specimen.
Figure 5.7 Force – Strain Plot of 2nd and 3rd Beam Specimens for each FBG Sensor
0
5000
10000
15000
20000
0 500 1000 1500 2000 2500 3000
F [
N]
εx [µε]
2nd Beam - Embedded FBG 2nd Beam - Surface FBG3rd Beam - Embedded FBG 3rd Beam - Surface FBGFEA
68
Table 5.4 Slopes of the Force Strain Curves shown in Figure 5.7
Slopes of Force-Strain Curves [N/µε]
FEA 6.421
2nd Beam Specimen Surface FBG 7.541
Embedded FBG 7.633
3rd Beam Specimen Surface FBG 6.797
Embedded FBG 6.824
5.3 Results and Discussions of Vibration Experiment Case Study
Fast Fourier Transform (FFT) of strain responses due to each impact composed of
2048 data points are taken through MATLAB to extract excited resonance frequencies
of the beam. Several post-processing methods are applied for embedded and surface
mounted FBG comparison. Post-Processing of the strain data is summarized as
follows:
- 16 strain signals of surface mounted and embedded FBG sensors were logged
for 16 impacts. Therefore, 32 strain signals were recorded in time domain in
total.
- FFT of each strain signal is taken to obtain strain frequency response function
(FRF) and amplitudes of those are plotted with respect to frequency between 0
Hz and 1250 Hz which is half of the sampling frequency (i.e. Nyquist
Frequency).
- 16 amplitudes of the strain FRF plots are averaged in the frequency domain to
obtain so-called composite strain FRF which provides better visualisation for
the resonance frequencies.
- The resonance frequencies and their corresponding modes are also identified
by using FEA results (i.e. via normal mode dynamic analyses) for vibration
applications (Section 3.3.3).
69
- Modal strain values, which are peak amplitude values at the resonance
frequencies, are extracted from the composite strain FRF.
- Modal strain values of each sensor at each resonance frequency are compared
according to modal strain distribution found by the FEA (Figure 3.16).
Initially, an example of the time response of strains of embedded and surface mounted
sensors can be seen from Figure 5.8. The strain responses are observed to be damped
free vibration responses.
Figure 5.8 Strain Response due to Impact
FFT of all 32 strain signals are taken and strain FRF’s of the 16 individual responses
due to each impact can be seen from Figure 5.9 and 5.10 for surface mounted and
embedded FBG respectively. Each individual strain FRF of the response in Figure 5.9
and 5.10 is shown by different colour. All 16 amplitudes of FRF are then averaged in
frequency domain for each FBG sensor and that composite FRF can be seen from
Figure 5.11. From Figure 5.11, the first two resonance peaks are very clear for the both
sensors and corresponding resonance frequencies captured by both sensors are exactly
the equal. The frequency values are listed in Table 5.5 with FEA calculations.
Similarly, embedded to surface mounted modal strain ratio values are also listed in
Table 5.5.
-80
-60
-40
-20
0
20
40
60
80
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6ε x[µ
ε]
t [s]
Surface FBG - z=h Embedded FBG - z=0.584h
70
Figure 5.9 Amplitude of Strain FRF of Surface FBG for each Test
Figure 5.10 Amplitude of Strain FRF of Embedded FBG for each Test
Figure 5.11 Composite Strain FRF of Embedded and Surface Mounted FBG Sensors
0.0001
0.001
0.01
0.1
1
10
0 250 500 750 1000 1250
|FF
T(ε
x,s
urf
ace)
| [µ
ε.s]
f [Hz]
0.0001
0.001
0.01
0.1
1
10
0 250 500 750 1000 1250
|FF
T(ε
x,e
mb
edd
ed)|
[µ
ε.s]
f [Hz]
0.01
0.1
1
10
0 250 500 750 1000 1250
|FF
T(ε
x)|
[µ
ε.s]
f [Hz]Embedded FBG Surface FBG Natural Freq. By FEA
71
Table 5.5 Natural / Resonance Frequency and Modal Strain Ratio Results
f [Hz] εx∗(0.584h) εx
∗(h)⁄
1st Mode(*) 2nd Mode(**) 1st Mode(*) 2nd Mode(**)
FEA 51.9 415.6 0.584 0.584
Experiment 50.7 418.1 0.570 0.577
% Difference (***) 2.4% -0.6% 2.4% 1.2%
(*) The first out-of-plane bending mode (**) The second out-of-plane bending mode (***) Percent difference of FEA results from the experimental ones
As seen from Table 5.5, the first two resonance frequencies from the experiments are
those of the first and the second out-of-plane bending modes as they are very close to
theoretical natural frequency values calculated by the FEA. On the other hand, as
found from the FEA, there is another natural frequency at 278.4 Hz in between, which
is natural frequency of the first torsional mode. However, in experimental strain FRF
plot in Figure 5.11, there is no peak value around the natural frequency of the torsional
mode, as sensor positions are at the nodes of the torsional mode (i.e. where axial modal
strains are zero).
Modal strain distribution is linear with respect to position along z-axis which implies
that the ratio of embedded to surface modal strain values are constant and equal to ratio
of positions of each sensor along z-axis (i.e. 0.584h/h). With that information, modal
strain ratio is calculated from FEA and compared to the experimental data. Error values
of 2.4%, 1.2% are observed for the first and the second out-of-plane bending modes
respectively. Those values are acceptable in experimental studies, as the resonance
frequencies at each peak of composite strain FRF plots in Figure 5.11 are nearly
coincident with natural frequencies calculated by FEA. Those errors may be because
of misestimation of stiffness values of the FEM, or they may be because of geometrical
imperfections due to manufacturing (i.e. positions of the sensors cannot be known
exactly), missing peak amplitude values because of the digital sampling or small
orientational errors of FBG sensors.
72
5.4 Results and Discussions of Fatigue Torsion Experiment Case Study
In torsion experiments, shear strain of a structure should be monitored. However, FBG
sensors cannot measure shear strain values directly. In this application, strain values
of the FBG’s are manipulated such that shear strains can directly be obtained.
Transformation relation gives axial strain value of FBG sensors at any position along
z-axis. General transformation equation in any axial direction X is given in Equation
(5.5).
𝜀𝑋(𝑧) = 𝜀𝑥(𝑧) cos2 𝜃 + 𝜀𝑦(𝑧) sin2 𝜃 + 𝛾𝑥𝑦(𝑧) sin 𝜃 cos 𝜃 (5.5)
where X-axis is an axis on x-y plane rotated 𝜃 from positive x-axis (twist axis) that
represents direction of FBG sensors, for which 𝜃 = 45°. On the other hand, axial and
transverse strains are assumed constant along z axis. 𝛾𝑥𝑦is assumed zero at z=0 (i.e.
centre plane) as can be seen from Equation (3.5). FBG strain values at z=0 and any z
are given in Equation (5.6) and (5.7) respectively.
𝜀𝑋(0) =𝜀𝑥 + 𝜀𝑦
2 (5.6)
𝜀𝑋(𝑧) =𝜀𝑥 + 𝜀𝑦
2+
𝛾𝑥𝑦(𝑧)
2 (5.7)
Subtracting Equation (5.6) from Equation (5.7) and multiplying by two gives directly
the shear strain at any z value. Therefore, shear strain values at two different sensor
locations (at z=0.584h or z=h) can directly be obtained by combining corresponding
FBG data with that of embedded FBG at the centre (z=0), which is expressed in
Equation (5.8).
𝛾𝑥𝑦(𝑧) = 2[𝜀𝑋(𝑧) − 𝜀𝑋(0)] (5.8)
Several post-processing methods are applied on strain responses for FBG comparison.
Post processing of the experimental data can be summarized as follows:
- Strain data of FBG’s are converted to shear strain data according to Equation
(5.8)
73
- Mean values and amplitudes of the strain signals are calculated for 60 seconds
(i.e. 180 cycles) intervals.
- Required curves are plotted with cycle resolution of 180 cycles, and presented
in this section.
Figure 5.12 shows shear strain curves at z=0.584h and z=h, where one embedded and
surface mounted FBG are located respectively. It includes average strain curve of the
static torsion tests from study of Karataş [66] with maximum angle of twist of 20
degrees. Linear curve is also fitted to static torsion data. Slope of the static strain curve
is 0.555, while from FEA, the required slope is calculated as 0.584. These results give
error value of -5.0%. Moreover, mean and amplitude values from the fatigue torsion
tests are nearly coincident with strain-strain curve calculated from the FEA results.
On the other hand, it is not possible to fit a line to mean and amplitude values of fatigue
torsion strains. Instead, further analyses with different plots and tables are presented
to identify the behaviour of fatigue torsion responses in details.
Figure 5.12 Shear Strain at z=0.584h vs Shear Strain at z=h
Because of the linear strain distribution expected from FEA in Section 3.4.3, shear
strain ratio γxy(z=0.584h)/γxy(z=h) (i.e. embedded to surface shear strain ratio) should
0
1500
3000
4500
6000
7500
0 2500 5000 7500 10000 12500
γ xy(0
.584h)
[µε]
γxy(h) [µε]
Static Torsion [66] Fatigue Torsion Mean Value
FEA Fatigue Torsion Amplitude
74
be constant and equal to 0.584. Figure 5.13 shows shear strain ratios from the
experiment and FEA. The mean value and the amplitude of the shear strain from the
experiment satisfies the required strain ratio from FEA as all curves are very close for
all the cycle values.
Table 5.6 shows corresponding minimum and maximum shear strain ratio values.
From these values, the maximum error values of -1.1% for mean value and 2.7% for
the amplitude are calculated. These errors may be because of sampling losses or the
adjustment errors of the sensors, but are acceptable for the fatigue torsion test results
as can be seen from Figure 5.13 that the shear strain curves are almost coincident.
However, Figure 5.13 is limited to the maximum cycles of 720 as surface FBG was
broken at that cycle. 720 cycles are not satisfactory for the comparison purposes as the
experiment lasted about 10000 cycles. At the remaining cycles, only the shear strain
at z=0.584h could be monitored. Therefore, after 720th cycle, the strain data of
embedded sensors can only be compared to FEA results.
Figure 5.13 Shear Strain Ratio γxy(0.584h) / γxy(h) versus Number of Cycles
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
150 250 350 450 550 650 750
γ xy(0
.58
4h
) /
γ xy(h
)
Number of Cycles
Mean Value Amplitude FEA
75
Table 5.6 Shear Strain Ratio Values of the curves in Figure 5.13
Shear Strain Ratio - γxy(0.584h) /γxy(h)
Minimum Maximum
FEA 0.584 0.584
Mean Value 0.577 0.581
Amplitude 0.587 0.599
On the other hand, the mean and the amplitudes of shear strain values at the surface as
limited to 720 cycles as shown by Figure 5.14 and 5.15. Both the mean value and the
amplitude of strain response are very close to FEA with non-linear geometrical effects
for large deformations. The maximum and the minimum values are presented in Table
5.7 with FEA with non-linear geometrical effects (i.e. NLGEOM – ON). The error
values of -0.87% and -1.8% are calculated for the mean value and the amplitude of the
strain response respectively which are also acceptable as shear strain responses of the
experiment in Figure 5.14 and 5.15 are nearly coincident to those of FEA results with
non-linear geometry.
Figure 5.14 Mean Value of Shear Strain at z=h with respect to Number of Cycles
0
2000
4000
6000
8000
10000
12000
14000
150 250 350 450 550 650 750
γ xy
[µε]
Number of Cycles
Experiment NLGEOM -OFF NLGEOM -ON
76
Figure 5.15 Amplitude of Shear Strain at z=h with respect to Number of Cycles
Table 5.7 Shear Strain Values at z=h
Shear Strain Values at z=h [µε]
Minimum Maximum
Mean Value FEA 12442 12442
Experiment 12334 12349
Amplitude FEA 12110 12110
Experiment 11897 11928
The mean and the amplitude of shear strain values are shown in Figure 5.16 and 5.17
respectively at z=0.584h where one of the embedded FBG’s is placed. The maximum
and the minimum values are presented in with FEA with non-linear geometrical effects
for large deformations in Table 5.8. At the beginning of the test, the mean value of the
shear strain from the experiment is very close to that obtained from the FEA with non-
linear geometrical effects. However, at the large number of cycles, the strain values
from the experiment drops and the maximum error value of -4.2% is calculated which
0
2000
4000
6000
8000
10000
12000
14000
150 250 350 450 550 650 750
γ xy
[µε]
Number of Cycles
Experiment NLGEOM -OFF NLGEOM -ON
77
corresponds to minimum mean shear strain value shown in Table 5.8. This drop may
be because of plastic deformation of the beam that may change deformation shape that
affects mean strain values. On the other hand, the amplitude values from the
experiment are coincident to FEA result with non-linear geometrical effects.
Maximum error value of the amplitude of the shear strain is -1.4%. The error values
can be considered as acceptable for this particular test as the shear strain responses in
Figure 5.16 and 5.17 are coincident to FEA results especially at the beginning of the
experiment (i.e. lower cycle values).
Figure 5.16 Mean Value of Shear Strain at z=0.584h with respect to Number of Cycles
Figure 5.17 Amplitude of Shear Strain at z=0.584h with respect to Number of Cycles
0
1000
2000
3000
4000
5000
6000
7000
8000
0 2000 4000 6000 8000 10000
γ xy
[µε]
Number of Cycles
Experiment NLGEOM -OFF NLGEOM -ON
0
1000
2000
3000
4000
5000
6000
7000
8000
0 2000 4000 6000 8000 10000
γ xy
[µε]
Number of Cycles
Experiment NLGEOM -OFF NLGEOM -ON
78
Table 5.8 Shear Strain Values at z=0.584h
Shear Strain Values at z=0.584h [µε]
Minimum Maximum
Mean Value FEA 7263 7263
Experiment 6961 7183
Amplitude FEA 7069 7069
Experiment 6972 7138
Strain responses directly measured by FBG sensors and torque plots are also given in
Appendix C as supplementary information. The individual sensor responses are not
steady unlike the combined shear strain responses using Equation (5.8) having shown
in this section (Figure 5.14-5.17).
5.5 Conclusions
In this section, the results of three experimental case studies are discussed. The
embedded sensors are compared to surface mounted ones according to the calculated
results obtained from the FEA. Table 5.9 summarizes all maximum error values of
strain data obtained from the embedded FBG sensors based on the surface mounted
sensors according to strain distributions calculated by the FEA.
79
Table 5.9 Errors of Data of Embedded FBG Sensors with respect to Surface Mounted ones
Data of Embedded FBG Maximum Error
Tension Experiment Case
Study Axial Strain -1.2%
Vibration Experiment Case
Study
Natural/Resonance Frequency 0.0%
Modal Strain -2.4%
Fatigue Torsion Experiment
Case Study (*)
Mean Value of Shear Strain -4.2%
Amplitude of Shear Strain -1.4%
(*) As surface mounted FBG was broken at 720th cycle, error values with respect to FEA of fatigue
torsion applications is used instead of surface mounted FBG.
All the results of errors of embedded FBG sensors show that the embedded FBG
sensors provide expected signals with low amount of errors below 5%. They proved
that the system with embedded FBG sensors works properly and are appropriate for
SHM applications as verified by three different experimental case studies.
80
81
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1 General Conclusions
In this study, a Structural Health Monitoring System with embedded FBG sensors are
developed. FBG sensors are embedded between composite plies. The manufacturing
of those specimens requires some key points as the interrogator connectors at the tip
of FBG wires melt at high autoclave temperatures. As a precaution, these connectors
were cut before manufacturing, and after curing at autoclave, these connectors are
joined to FBG wires through fusion splicer device. The second important point is the
protection of the FBG wires at ingress/egress regions, at which high stress
concentrations occur and thus FBG wires may be broken. To prevent it, protective
teflon tubes are added to these regions covering FBG wires providing a degree of
flexibility while moving and assembling specimens.
On the other hand, components of data acquisition system are also introduced. It
requires some connection elements between interrogator system and FBG sensors.
Interrogator specifications with its software including sampling rate and strain
intervals are also explained.
The performance of the manufactured system is verified through three different tests,
which are namely; static tension, vibration and fatigue torsion tests. Before the tests,
the baseline finite element models are created. The finite element analyses provide
expected strain behaviour of the SHM system which includes strain distributions with
respect to position along z-axis (i.e. thickness-wise direction). With these information,
the test values are then checked and additionally, the force-strain relations for the
82
tension experiments and the resonance frequency values for the vibration experiments
are also extracted.
In tension experiments, each embedded FBG, surface mounted FBG’s and strain gauge
satisfy the expected constant axial strain distribution that is also calculated from the
FEA. It means that the SHM system works properly under tension load. Moreover, the
amount of noise content in the strain gauge and FBG sensor data is then compared,
and it is observed that the FBG sensor contains much less noise signal than that of the
strain gauge. The force-strain analyses are also performed and some errors occur
because of the misestimation of the mechanical parameters, indicating that the
mechanical parameters should be updated for each beam specimen.
In the vibration case, the resonance frequencies extracted from embedded FBG are
exactly equal to those of the surface mounted ones. Moreover, the modal strain values
of the embedded FBG sensors satisfy the required values when compared to the surface
mounted ones.
On the other hand, during the torsional fatigue experiments, the surface mounted FBG
is broken earlier, and for larger number of cycles, the shear strain measured by
embedded sensors can only be compared to FEA. The mean values and the amplitudes
of the shear strain responses of the embedded FBG sensor locations satisfy the shear
strain results found from the FEA.
In summary, the SHM for the developed system is verified by three types of
experimental case studies. The embedded FBG sensors provide necessary strain data
with respect to reference surface FBG according to strain distributions calculated by
the FEA. Therefore, it can be concluded that the developed system with embedded
FBG sensors works properly and be also considered as an applicable technology to
beam-like aerospace structures.
6.2 Recommendations for the Future Work
In this thesis, a SHM system of composite beams with embedded FBG sensors is
developed and verified through tension, vibration and fatigue torsion experiments.
83
Further applications can be performed in the future work, and various applications can
be recommended for the future work as follows:
- Various other tests such as modal, bending, bending fatigue, combined tests,
may be performed for further performance analyses.
- A system with embedded FBG with multiplexing can be developed for spatial
strain information.
- A system for plate and shell like composite structures as well as beam like
composite structures can be developed.
- A system with embedded FBG sensors may be developed for full-scale
components.
- Manufacturing methods of embedded FBG sensors may be extended for in-situ
(i.e. real operational) SHM applications.
- A system for rotary structures (like wind turbine and helicopter rotor blades)
can be developed with FBG wiring applications.
- Specimens with pre-induced damage with embedded sensors may be
manufactured and damage detection studies through embedded FBG’s may be
performed and levels of SHM can be increased via theses damage detection
applications.
84
85
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94
95
APPENDIX A
DERIVATION OF SHEAR STRAIN DISTRIBUTION OF INFINITE
COMPOSITE CROSS-SECTION UNDER TORSION
In-plane displacement field under torsion is defined by Equation (A.1) and (A.2):
𝑣 = −𝑧𝜙(𝑥) (A.1)
𝑤 = 𝑦𝜙(𝑥) (A.2)
Axial displacement of i’th ply should be defined piecewise given in Equation (A.3), as
each ply group has different material property.
𝑢𝑖 = 𝑢𝑖(𝑦, 𝑧), 𝑓𝑜𝑟 𝑧𝑖−1 ≤ 𝑧 < 𝑧𝑖 (A.3)
Strain relations of i’th ply are given in terms of displacement fields in Equation (A.4)
and (A.5)
𝛾𝑥𝑦,𝑖 =𝜕𝑢𝑖
𝜕𝑦− 𝑧
𝑑𝜙
𝑑𝑥 (A.4)
𝛾𝑥𝑧,𝑖 =𝜕𝑢𝑖
𝜕𝑧+ 𝑦
𝑑𝜙
𝑑𝑥 (A.5)
Eliminating ui from Equation (A.4) and (A.5) gives Equation (A.6).
𝜕𝛾𝑥𝑦,𝑖
𝜕𝑧−
𝜕𝛾𝑥𝑧,𝑖
𝜕𝑦= −2
𝑑𝜙
𝑑𝑥 (A.6)
Strain-stress relations are given for transversely isotropic material in Equations (A.7)-
(A.9).
96
𝐺𝑥𝑦,𝑖 = 𝐺𝑥𝑧,𝑖 = 𝐺𝑖 (A.7)
𝜏𝑥𝑦,𝑖 = 𝐺𝑖𝛾𝑥𝑦,𝑖 (A.8)
𝜏𝑥𝑧,𝑖 = 𝐺𝑖𝛾𝑥𝑧,𝑖 (A.9)
Equilibrium equation and substituted strain expressions are shown by Equation (A.10)
and (A.11) respectively.
𝜕𝜏𝑥𝑦,𝑖
𝜕𝑦+
𝜕𝜏𝑥𝑧,𝑖
𝜕𝑧= 0 (A.10)
𝜕𝛾𝑥𝑦,𝑖
𝜕𝑦+
𝜕𝛾𝑥𝑧,𝑖
𝜕𝑧= 0 (A.11)
Boundary conditions are given for only upper half of the cross-section. Because ply
sequence is symmetric. Half of the cross-section, where 𝑧 ≥ 0, is only considered with
N laminates, as shear centre is at the centre of cross-section of symmetric composite.
Three sets of boundary conditions are explained. Shear strain values normal to
boundaries must be zero. Corresponding boundary conditions are given in Equation
(A.12) and (A.13)
𝜏𝑥𝑦,𝑖(±𝑏, 𝑧) = 0 (A.12)
𝜏𝑥𝑧,𝑁(𝑦, ℎ) = 0 (A.13)
As shear centre is located at (y,z)=(0,0), shear strain components towards shear centre
should be zero. Otherwise, additional strains and stresses creating deflection other than
torsion existed. Equation (A.14) and (A.15) give required boundary conditions.
𝜏𝑥𝑦,1(𝑦, 0) = 0 (A.14)
𝜏𝑥𝑦,𝑖(0, 𝑧) = 0 (A.15)
97
Continuity conditions between adjacent ply groups with different materials give two
additional boundary condition between each ply group. Axial displacement must be
continuous along y direction at some z value defining interlaminar plane. As axial
displacement is continuous along y, its derivative is also continuous. Considering
Equation (A.4), first term is continuous. Second term is independent of ply number
and inherently continuous. Therefore 𝛾𝑥𝑦 must be continuous. Moreover, normal shear
stress component must also be continuous. Equation (A.16) and (A.17) give required
boundary conditions.
𝛾𝑥𝑦,𝑖(𝑦, 𝑧𝑖) = 𝛾𝑥𝑦,𝑖+1(𝑦, 𝑧𝑖) (A.16)
𝜏𝑥𝑧,𝑖(𝑦, 𝑧𝑖) = 𝜏𝑥𝑧,𝑖+1(𝑦, 𝑧𝑖) (A.17)
When width of the cross-section is much larger than thickness ( 𝑏 ≫ ℎ ), several
simplifications occur. Away from smaller edges ( |𝑦| ≪ 𝑏 ), cross-section can be
approximated to have infinite width. With that condition, cross-section geometry away
from edges are not function of y anymore. All strain and stress components can be
assumed not to be as a function of y. Under that condition, disregarding boundary
conditions at y=±b, all remaining equations simplify. Equation sets of 𝜏𝑥𝑦,𝑖, 𝛾𝑥𝑦,𝑖
and𝜏𝑥𝑧,𝑖, 𝛾𝑥𝑧,𝑖 become decoupled.
Simplified Equations (A.10), (A.13) and (A.17) become Equations (A.18)-(A.20).
𝜕𝜏𝑥𝑧,𝑖
𝜕𝑧= 0 (A.18)
𝜏𝑥𝑧,𝑁(ℎ) = 0 (A.19)
𝜏𝑥𝑧,𝑖(𝑧𝑖) = 𝜏𝑥𝑧,𝑖+1(𝑧𝑖) (A.20)
From Equations (A.18)-(A.20), 𝜏𝑥𝑧 is constant, continuous and at maximum z value,
it is zero. With these information for all thickness values,
𝜏𝑥𝑧(𝑧) = 0 (A.21)
98
𝛾𝑥𝑧(𝑧) = 0 (A.22)
That means, 𝛾𝑥𝑧 is negligible away from smaller edges (|𝑦| ≪ 𝑏).
Similarly simplified Equations (A.6), (A.14) and (A.16) give Equations (A.23)-(A.25).
𝜕𝛾𝑥𝑦,𝑖
𝜕𝑧= −2
𝑑𝜙
𝑑𝑥 (A.23)
𝜏𝑥𝑦,𝑖(0) = 0 (A.24)
𝛾𝑥𝑦,𝑖(𝑧𝑖) = 𝛾𝑥𝑦,𝑖+1(𝑧𝑖) (A.25)
By substituting 𝜏𝑥𝑦,𝑖 from Equation (A.8) into (A.24), 𝛾𝑥𝑦,𝑖 is continuous linear
function with slope of −2𝑑𝜙
𝑑𝑥with zero value at z=0 as seen from Equation (A.23)-
(A.25). Then 𝛾𝑥𝑦 for all z can be solved and is given in Equation (A.26)
𝛾𝑥𝑦 = −2𝑧𝑑𝜙
𝑑𝑥 (A.26)
This result is identical to shear strain distribution of thin isotropic beams [69]. For
laminates, it is concluded that, the same strain assumption can be made.
99
APPENDIX B
SUPPLEMENTARY PLOTS OF TENSION TESTS
B.1 Force vs Displacement Plots
Figure B.1 Axial Force – Displacement Plots of 1st Beam Specimen
Figure B.2 Axial Force – Displacement Plots of 2nd Beam Specimen
0
5000
10000
15000
20000
25000
0 0.1 0.2 0.3 0.4 0.5
F [
N]
u [mm]Test 1 FEA
0
5000
10000
15000
20000
25000
0 0.1 0.2 0.3 0.4 0.5
F [
N]
u [mm]
Test 1 Test 2 Test 3 Test 4 FEA
100
Figure B.3 Axial Force – Displacement Plots of 3rd Beam Specimen
B.2 Strain vs Strain Plots
Figure B.4 Embedded FBG Data with respect to Surface Mounted FBG Data of 2nd Beam Specimen
0
5000
10000
15000
20000
0 0.1 0.2 0.3 0.4 0.5
F [
N]
u [mm]
Test 1 Test 2 FEA
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
ε x,
Em
bed
ded
FB
G[µ
ε]
εx, Surface FBG [µε]
Test1 Test2 Test3 Test4
101
Figure B.5 Embedded FBG Data with respect to Surface Mounted FBG Data of 3rd Beam Specimen
B.3 Force vs Strain Plots
Figure B.6 Axial Force versus Strain Plot of 2nd Beam Specimen
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
ε x,
Em
bed
ded
FB
G [
µε]
εx, Surface FBG [µε]
Test1 Test2
0
5000
10000
15000
20000
25000
0 500 1000 1500 2000 2500 3000
F [
N]
εx [µε]
Test 1 - Surface FBG Test 1 - Embedded FBG
Test 2 - Surface FBG Test 2 - Embedded FBG
Test 3 - Surface FBG Test 3 - Embedded FBG
Test 4 - Surface FBG Test 4 - Embedded FBG
102
Figure B.7 Axial Force versus Strain Plot of 3rd Beam Specimen
0
5000
10000
15000
20000
0 500 1000 1500 2000 2500 3000
F [
N]
εx [µε]
Test 1 - Surface FBG Test 1 - Embedded FBG
Test 2 - Surface FBG Test 2 - Embedded FBG
103
APPENDIX C
SUPPLEMENTARY PLOTS OF FATIGUE TORSION TESTS
Figure C.1 Torque Response with Respect to Number of Cycles
Figure C.2 Surface Mounted FBG at z=h Response with Respect to Number of Cycles
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 2000 4000 6000 8000 10000
Torq
ue
[N.m
m]
Number of Cycles
Mean Value Amplitude
0
1000
2000
3000
4000
5000
6000
7000
150 250 350 450 550 650 750
ε X[µ
ε]
Number of Cycles
Mean Value Amplitude
104
Figure C.3 Response of Embedded FBG at z=0.584h with Respect to Number of Cycles
Figure C.4 Response of Embedded FBG at z=0 with Respect to Number of Cycles
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 2000 4000 6000 8000 10000
εX[µ
ε]
Number of Cycles
Mean Value Amplitude
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 2000 4000 6000 8000 10000εX[µ
ε]
Number of Cycles
Mean Value Amplitude