ABSTRACT Dr. Kara J. Peters.)

ABSTRACT

WEBB, SEAN CHRISTIAN. Damage Monitoring in Composite Structures through High

Speed, Full-spectral Interrogation of Fiber Bragg Grating Sensors. (Under the direction of

Dr. Kara J. Peters.)

This research validates a newly developed high speed, full-spectral interrogator for

dynamic measurements of embedded fiber Bragg grating sensors and demonstrates new

damage monitoring capabilities for composite structures based on this unique sensing

capability. The new instrumentation enables rapid measurements of strain and vibration for

structural health monitoring of composite structures and is capable of scanning speeds up to

300 kHz. Several tests were conducted to validate the new measurement system. Fiber Bragg

grating sensors were embedded in composite laminates which were then exposed to low-

velocity impacts. The system captured the impact in real time and revealed new information

on the material being tested. Matrix cracking and delamination of the plies were observed

through the new high speed rate capabilities of the measurement system. Birefringence of the

optical fiber due to transverse compressive loading resulted in peak splitting in the FBG

sensor response.

To further test the new dynamic measurement capabilities, a vibration platform was

developed for lab testing to simulate a realistic in-flight aircraft environment. For

characterization of the platform, testing was simplified by mounting FBG sensors on a thin

aluminum plate near a notch tip. As non-uniform strain increased with tension, the forced-

vibration response of the thin plate revealed changes in the sensor frequency response.

Numerical finite-element simulations were conducted to validate the measurements. During

static loading, simulations of the FBG sensor response were conducted by extracting axial

strain from the elemental solution of the model to use as input into a modified transfer

matrix. The simulations indicated increasing distortion in the full-spectral FBG response as

the stress concentration impinged greater magnitudes of non-uniform strain at the location of

the sensor.

The final step in this research embedded FBG sensors in composite lap joints to

monitor cyclic fatigue damage during a realistic in-flight aircraft environment. Dynamic full-

spectral measurements were conducted at 100 kHz to study the dynamic precursors to joint

failure. The full-spectral information was used to avoid dynamic measurement errors

encountered when interrogating a complex multi-peak spectrum using traditional peak

following or edge filtering techniques. As damage accumulated, frequency analysis of the

corrected peak wavelength indicated progressive nonlinear dynamic behavior marked by

intermittent frequencies and amplitudes not associated with the external harmonic excitation.

The broadband, nonlinear frequency response revealed a transition to a chaotic state of

vibration attributed to accumulated damage. Numerical simulations were used to simulate the

fatigue damage by introducing plastic deformation and geometric nonlinearities to the lap

joint. The dynamic behavior was assessed by performing forced-vibration transient analyses.

Comparable transitions in the dynamic behavior of the lap joint captured by the FBG sensor

were found during the simulations and can be attributed to fatigue damage at the adhesive

layer.

Damage Monitoring in Composite Structures through High Speed, Full-spectral Interrogation

of Fiber Bragg Grating Sensors

by

Sean Christian Webb

A dissertation submitted to the Graduate Faculty of

North Carolina State University

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

Mechanical Engineering

Raleigh, North Carolina

2013

APPROVED BY:

_____________________________ ______________________________

Dr. John F. Muth Dr. Mohammed A. Zikry

_____________________________ ______________________________

Dr. Kara J. Peters Dr. Robert T. Nagel

Chair of Advisory Committee

ii

DEDICATION

I would like to dedicate this dissertation to several individuals to whom this would

not have been possible without. To my best friend and beautiful wife Danielle, who had

patience and love, and inspired me with encouragement throughout my graduate career.

Without her, none of this would be possible. To my late grandfather, Dr. Don Hoyle

Lovelace, who used every opportunity he could to brag on all of his grandkids. He obtained

his Doctorate of Education from East Tennessee State University, loved his wood shop,

model airplanes, and most importantly his family and faith. I dedicate this dissertation in

honor of him. To my momma Kaye Webb, who believed in me and encouraged me every

step of the way with her love, faith, and desire to want nothing but the very best for me and

my brother and sisters. To my dad, Eric Webb, who inspired me to do my best in everything I

did and to aim for the skies. To my grandmother, Shirley Lovelace who presented me at a

young age with the most influential gift I would ever receive, a Bible that told me of the

promise of love and forgiveness through the gospel of Jesus Christ. To my grandparents,

Johnny and Judy Webb, whose faith, love, and laughter always filled me with joy. To David,

Susan, and Emma Wyatt and Geraldine Sanders who have blessed me with their love and

support. I dedicate all my successes in life to the one who provided them, my personal Lord

and Savior Jesus Christ. Through His finished work and promise of salvation I received my

purpose in life.

iii

BIOGRAPHY

Sean Christian Webb was born on March 22, 1987 to Kaye and Eric Webb and grew

up in the mountains of Spruce Pine, North Carolina. He grew up listening to the sounds of his

heritage through talented folk singers and flat pickers like Doc Watson, native of Deep Gap,

NC. Today, Sean enjoys playing acoustic guitar, hiking, camping, and flying small aircraft.

While pursuing his Bachelor’s of Science in Aerospace Engineering he received his private

pilot’s license in the Summer of 2007 at the Rutherfordton County Airport (FQD). Sean

obtained his B.S. in Aerospace Engineering in May of 2009 from North Carolina State

University. In August 2009, he went on to join Dr. Kara Peters as a graduate research

assistant in the Mechanical and Aerospace Engineering Department at North Carolina State

University. Under her direction in the Smart Composites Laboratory, a strong research focus

was placed on damage monitoring of composite aircraft components using high speed, full-

spectral interrogation of embedded fiber Bragg grating sensors. In May 2011, he completed

his Master’s of Science in Aerospace Engineering and continued to pursue a Doctor of

Philosophy in Mechanical Engineering.

iv

ACKNOWLEDGMENTS

I would like to extend my sincerest appreciation to Dr. Kara Peters for her

unwavering guidance, insight, and encouragement throughout my graduate career. I truly

believe I was blessed with one of the most enthusiastic, dedicated, and intellectually gifted

advisors a young researcher could have. Thank you Dr. Peters for your support and direction

throughout the years, my achievements could not have been possible without your influence.

I also would like to thank my committee members Dr. Mohammed Zikry, Dr. John

Muth, and Dr. Bob Nagel for their advice and support throughout my graduate studies. Also,

I would like to thank Spencer Chadderdon, Tyrie Vella, Nikola Stan, Dr. Steve Schultz, and

Dr. Richard Selfridge of Brigham Young University for their collaboration and technical

expertise with the interrogation unit. Additionally, members of the Smart Composites

Laboratory at North Carolina State University; Peter Shin, Young Song, Sachin Pawar, Drew

Hackney, Nehemiah Mabry, Egbe Eni, Gary Martin, Kevin McCants-Brown, and Chun Park

for their friendship and encouragement throughout this research project. Lastly, I would like

to thank my good friend Jesse Fulton who was always there to lend me a hand and encourage

me along the way.

The financial support provided by the National Science Foundation through grant #

(CMMI 0900369] is gratefully acknowledged. Finally, I would like to thank the faculty and

staff of the Department of Mechanical and Aerospace Engineering at North Carolina State

University.

v

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vii

LIST OF FIGURES ........................................................................................................... viii

CHAPTER 1 INTRODUCTION ...........................................................................................1

1.1 OVERVIEW ................................................................................................................1

1.2 FIBER BRAGG GRATING SENSORS .......................................................................5

1.3 SCOPE OF RESEARCH..............................................................................................7

CHAPTER 2 FBG SENSOR HIGH SPEED FULL-SPECTRAL INTERROGATION ........ 15

2.1 MOTIVATION .......................................................................................................... 15

2.2 INSTRUMENT OPERATION ................................................................................... 18

2.3 DATA REPRESENTATION ..................................................................................... 19

CHAPTER 3 LOW-VELOCITY IMPACT TESTS ............................................................. 25

3.1 EXPERIMENTAL METHODS ................................................................................. 26

3.2 DISCUSSION ............................................................................................................ 27

3.3 CONCLUSIONS........................................................................................................ 34

CHAPTER 4 VIBRATION OF A DOUBLE-NOTCHED THIN ALUMINUM PLATE ...... 47


4.2 VIBRATION OF UNIFORMLY STRAINED FBG SENSOR.................................... 51

4.3 RELATIVE SENSITIVITY AND BRAGG WAVELENGTH DEPENDENCE ......... 52

4.4 VIBRATION OF NON-UNIFORMLY STRAINED FBG SENSOR .......................... 54

4.5 FULL-SPECTRAL FREQUENCY RESPONSE ........................................................ 56

4.6 STRAIN GAGE TESTING FOR BUCKLING OF ALUMINUM SPECIMEN .......... 57

4.7 NUMERICAL SIMULATIONS ................................................................................. 59

vi

4.8 FILTERING OF FULL-SPECTRAL DATA .............................................................. 61

4.9 CONCLUSIONS........................................................................................................ 63

CHAPTER 5 CHARACTERIZATION OF FATIGUE DAMAGE IN COMPOSITE LAP

JOINTS—EXPERIMENTS ........................................................................... 84

5.1 INTRODUCTION ..................................................................................................... 85


5.3 FATIGUE RESPONSE OF LAP JOINT .................................................................... 93

5.4 PULSED PHASED THERMOGRAPHY ................................................................... 96

5.5 RESIDUAL FBG RESPONSE TO FATIGUE AND PRETENSION LOAD .............. 97

5.6 PEAK WAVELENGTH FREQUENCY RESPONSE .............................................. 102

5.7 DYNAMIC FULL-SPECTRAL MEASUREMENTS ............................................... 103

5.8 CONCLUSIONS...................................................................................................... 104

CHAPTER 6 CHARACTERIZATION OF FATIGUE DAMAGE IN COMPOSITE LAP

JOINTS—SIMULATIONS ......................................................................... 130

6.1 INTRODUCTION ................................................................................................... 131

6.2 NUMERICAL SIMULATION METHODS ............................................................. 132

6.3 NUMERICAL SIMULATION OF EXPERIMENTAL PULL TESTS...................... 137

6.4 SIMULATION OF FREE-VIBRATION FREQUENCY RESPONSE OF PRISTINE

LAP-JOINT .............................................................................................................. 139

6.5 SIMULATION OF FORCED-VIBRATION LAP JOINT ........................................ 140

6.6 CONCLUSIONS...................................................................................................... 143

CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK .. 166

REFERENCES.................................................................................................................. 170

vii

LIST OF TABLES

Table 5.1 Definition of measurement states for Specimen 1 after different fatigue cycles and

loading conditions........................................................................................... 128

Table 5.2 Definition of measurement states for Specimen 2 after different fatigue cycles and

loading conditions........................................................................................... 129

Table 6.1 Material properties of woven twill carbon fiber prepreg used for fabrication of lap

joint adherends ............................................................................................... 163

Table 6.2 Calculated natural frequency values for first five modes of lap joint. All frequency

values are in Hz .............................................................................................. 164

Table 6.3 Specifications for numerical simulations and experimental measurements ......... 165

viii

LIST OF FIGURES

Figure 1.1 Schematic of FBG sensor reflected spectrum under various strain states .............13

Figure 1.2 Dynamic FBG full-spectral measurements at 100 Hz shown for impact strikes 24

and 30 of a woven graphite-epoxy laminate from Propst et al. (2010) ...............14

Figure 2.1 Schematic of source of wavelength hopping. Left hand side shows simulated FBG

spectra with increasing load. Primary peak is labeled A, secondary peaks are

labeled B and C. Scenarios # 1 and # 2 show strain measurements extracted from

peak wavelength interrogator. ...........................................................................21

Figure 2.2 Block diagram of FBG full-spectral interrogator and generation of the time-

varying wavelength spectrum: (a) The measured time-varying optical power is

combined with (b) the wavelength-time mapping to construct (c) individual

wavelength spectrum. .......................................................................................22

Figure 2.3 Photograph of FBG full-spectral interrogator .....................................................23

Figure 2.4 (a) Single full-spectral scan from the MEMS tunable optical filter. (b) False-color

spectral mapping of multiple high-speed scans of FBG reflection spectra. (c) 2D

transformation for presentation. Color scales represent intensity. Red represents

the highest intensity while blue is the lowest. ....................................................24

Figure 3.1 Cross section schematic of specimen layup components showing overlapping

peel-ply, protective putty, FBG sensor, and outer Mylar layers (Propst et al.,

2010). ...............................................................................................................36

Figure 3.2 Photograph of bottom 12 layers of carbon fiber prepreg lamina. The FBG sensor

for this specimen was placed at the midplane. ...................................................37

Figure 3.3 Photograph of vacuumed layup before placing into the hot press for curing. .......38

Figure 3.4 Specimen dimensions and location of FBG sensor relative to impact location. ....39

Figure 3.5 Photograph of instrumented drop tower impactor. ...............................................40

Figure 3.6 Process of FBG spectral data visualization: (a) Schematic of impact event

beginning with impactor freefall, to contact between impactor and laminate,

through rebound of impactor. Dashed line is laminate neutral axis. (b) Example

ix

wavelength scans collected during a single impact event (at 534 Hz). (c)

Conversion of same wavelength scans into spectral map where color represents

intensity. Data in this example have not been filtered. .......................................41

Figure 3.7 Measured, full-spectral response of embedded FBG sensor (a) in Specimen 1

during strikes 6, 20, 72, 86, and 110 (from top to bottom; (b) in Specimen 2

during strikes 2, 21, 80, 126, and 148 (from top to bottom). The intensity values

for all graphs in each column are normalized to the same maximum. ................42

Figure 3.8 Measured, full-spectral response of embedded FBG sensor (a) in Specimen 3

during strikes 3, 9, 12, 19, and 21 (from top to bottom; (b) in Specimen 4 during

strikes 2, 9, 14, 19, and 28 (from top to bottom). The intensity values for all

graphs in each column are normalized to the same maximum. ..........................43

Figure 3.9 Wavelength sweeps measured before and after impact for strike 110 of Specimen

1. Inset shows 2x2 twill geometry of woven carbon fiber. .................................44

Figure 3.10 Measured FBG reflected spectrum: (a) strike #80 from Figure 3.4(b) interrogated

at 100 kHz; (b) spectral sweep from previous specimen interrogated at 534 Hz

(Propst et al., 2010) (wavelength shift is referenced to the Bragg wavelength).

The maximum intensity color scale is not the same for both figures. .................45

Figure 3.11 Theoretical prediction of peak wavelength interrogator response from full-

spectral data obtained from specimen of Figure 3.4(a), strike #26. Measured peak

tracking data is plotted from Park et al. (2010) and was collected at 295 kHz.

Normalized strain is scaled to maximum strain value measured and is linearly

proportional to peak wavelength value. .............................................................46

Figure 4.1 Photograph of vibration platform and tensile loader. ..........................................65

Figure 4.2 (a) Dimensions of DEN aluminum specimen A (R=2.5 mm) and specimen B

(R=0.5 mm). (b) CAD model of manual tensile machine used to induce non-

uniform strain on test specimens. ......................................................................66

Figure 4.3 (a) PZT-forced acceleration response of vibration platform and (b) corresponding

frequency response spectrum. ...........................................................................67

x

Figure 4.4 (a) Single full-spectral sweep of FBG reflection during uniform loading, 130 με

axial strain. (b) Corresponding dynamic measurements during static and

vibratory loading. (c) Single full-spectral sweep of FBG reflection during

uniform loading, 300 με axial strain. (d) Corresponding dynamic measurements

during static and vibratory loading. ...................................................................68

Figure 4.5 Single scan of FBG reflection spectrum exposed to uniform vibratory load from

specimen A (top left). Experimentally measured and predicted relative sensitivity

(top right). Fast Fourier transforms of wavelength intensity vs. time for chosen

wavelengths A-D across the reflected band. ......................................................69

Figure 4.6 Single full-spectral sweep of FBG reflection during static loading (left).

Corresponding dynamic measurements during static and vibratory loading (right)

for mean static tensile strain of (a) 900 με (b) 2,300 με (c) 5,600 με (d) 6,200 με

and (e) 8,100 με ...............................................................................................71

Figure 4.7 False-color mappings of full-spectral measurements during static and vibration

loading for various intensities of non-uniform strain (left). False-color mapping

of fast Fourier frequency response across reflected band for each load step

(right). All false-color mappings are normalized to the maximum of the data set.

.........................................................................................................................73

Figure 4.8 (a) Single static sweep of distorted spectra plotted as solid black line. Four sweeps

1-4 cover a full period at 150 Hz, each as a dashed grey line. (b) Foil strain gage

measurement during DAQ and PZT activation. .................................................75

Figure 4.9 (a) Finite-element mesh using PLANE 82 elements and plane stress conditions.

(b) Geometry and boundary conditions implemented during quarter-symmetry

finite-element analysis. .....................................................................................76

Figure 4.10 Contour plot of elastic tensile strain in vertical direction (axial direction of FBG)

for a single load step using ANSYS finite-element software. Red represents a

maximum value and blue represents the minimum. Legend indicates

dimensionless axial strain units. ........................................................................78

xi

Figure 4.11 Experimentally measured reflection spectra from the FBG of specimen B (solid

black line) are shown at a static load of (a) 48.0, (b) 86.4, (c) 88.0, (d) 111.0, (e)

112.0, and (f) 120.0 MPa. Numerically predicted FBG response are shown as

dashed line. Experimental spectra are normalized to the maximum reflectivity of

the numerical model for comparison. ................................................................79

Figure 4.12 (a) Dynamic full-spectral measurement of FBG reflection spectrum during

resonance of specimen B at 150 Hz, equivalent to the PZT excitation frequency.

(b) Static (3 ms) and vibratory (30 ms) FBG response after small increase in

load. (c) Using finite-element modal analysis, the natural frequency variation of

specimen B as load is increased in increments of 1.0 kPa. .................................81

Figure 4.13 2nd

-order Butterworth stop-band digital filter response. .....................................82

Figure 4.14 (a) Unfiltered dynamic full-spectral measurement of FBG reflection spectrum

exposed to uniform vibration. (b) Filtered measurement from (a) using 2nd

-order

Butterworth stop-band digital filter. (c) Single sweeps of FBG exposed to non-

uniform loading during static condition (solid black line), 150 Hz vibration

(dotted), and digitally filtered (dashed). ............................................................83

Figure 5.1 Composite adherends for lap joint fabrication, prior to cutting. ......................... 106

Figure 5.2 (a) Dimensions of composite lap joint made in accordance to standard ASTM

D3165. (b) Micrograph of embedded FBG sensor. .......................................... 107

Figure 5.3 Photograph of vibration platform and lap joint mounted in the tensile loader .... 108

Figure 5.4 Experimentally measured load-displacement curves during tensile loading of lap

joint specimens.. ............................................................................................. 109

Figure 5.5 (a) Fully-reversed cyclic controller input. (b) Measured crosshead displacement

curve. Data was not recorded between 400 and 600 cycles.. ........................... 110

Figure 5.6 Hysteresis diagram for two representative cycles of lap joint specimen fatigue life.

Cyclic direction is indicated by arrows.. .......................................................... 111

Figure 5.7 Pulsed-phase thermography phase angle images for single specimen after different

fatigue loading cycles. Number of applied fatigue cycles is indicated on each

xii

figure. Figures (c) and (e) were obtained after static tension was applied to

specimen......................................................................................................... 112

Figure 5.8 (a) Measured full-spectral FBG response immediately after 600 cycles of fatigue

(left) and during pretensioning and release (right). Same measurements after

cycles (b) 1000 and (c) 1600. .......................................................................... 114

Figure 5.9 (a) Raw full-spectral data from Specimen 1 after 1000 cycles of fatigue loading.

Color scale corresponds to reflected intensity with red as maximum intensity. (b)

Peak wavelength data shown with two consecutive 8 ms Hamming windows with

50% overlap. (c) Windowed data used for FFT computation of first discrete time

increment. (d) STFT computed for entire data set.. ......................................... 116

Figure 5.10 STFT (left) and FFT (right) computed for extracted peak wavelength information

after each fatigue loading block shown for Specimen 1. .................................. 117





Figure 5.13 Phase plane representations of FBG measurements from Specimen 1: after 200

cycles using (a) peak intensity values and (b) corrected peak wavelengths; and

after 600 cycles using (c) peak intensity values and (d) corrected peak

wavelengths. ................................................................................................... 123

Figure 5.14 Full-spectral measurements shown for fatigue damage cases (A-J). For each case,

6 milliseconds of the static spectra are shown followed by 50 millisecond

acquisition during vibration, and finally 6 milliseconds of the harmonic-specific

stopband digitally filtered spectra.. ................................................................. 124

Figure 5.15 FFT computations shown across the full-spectrum of wavelengths in the FBG

sensor response for each fatigue loading case of Specimen 1 (A-J).. ............... 126

Figure 6.1 Finite element model geometry and mesh. SOLID 45 8-noded brick elements were

used to model both the adhesive and composite adherends. The adhesive layer is

refined to further increase accuracy.. ............................................................... 145

xiii

Figure 6.2 Hysol EA9394 paste adhesive stress-strain curve extrapolated from Sandia

National Laboratory report (Guess et al., 1995). .............................................. 146

Figure 6.3 Boundary conditions and applied loading during (a) transient tensile loading (b)

transient forced-vibration and (c) free-vibration modal analyses.. ................... 147

Figure 6.4 (a) Fracture surface after failure of adhesively bonded lap joint specimen and (b)

failure modes.. ................................................................................................ 148

Figure 6.5 Progression of damage at the adhesive layer of lap joint measured experimentally

using pulsed-phase thermography and then used as input into finite-element

model. The initial simulation (A) is defect-free (pristine model). .................... 149

Figure 6.6 Example of three-dimensional geometry of defect used in finite-element model..

....................................................................................................................... 150

Figure 6.7 Experimental measurements and numerical simulation of load-displacement curve

during tensile loading of composite lap joints.. ............................................... 151

Figure 6.8 (a) Axial strain distribution (in x direction) along FBG sensor at the adhesive layer

extracted from 3D finite-element model at applied axial load of 6.4 kN. (b)

Normalized axial strain contours (in x direction) near joint overlap region,

normalized by the far-field axial strain of 338 με.. .......................................... 152

Figure 6.9 (a) Shear strain distribution along FBG sensor at the adhesive layer extracted from

3D finite-element model at applied axial load of 6.4 kN. (b) Shear strain contours

near joint overlap region, normalized by the far-field shear strain of -3219 με.

....................................................................................................................... 154

Figure 6.10 Mesh configurations for convergence modal analysis performed on finite-

element model. Total number of elements for each model is shown.. .............. 156

Figure 6.11 Calculated natural frequencies and corresponding mode shapes from modal

analysis of lap joint specimen with fixed-fixed boundary conditions.. ............. 157

Figure 6.12 Measured forced-vibration loading and corresponding sinusoid-sum curve fit

shown for (a) one period and (b) 10 periods of 150 Hz dominant frequency

component ..................................................................................................... 158

xiv

Figure 6.13 (a) FFT of measured forced-vibration and (b) of sinusoid-sum approximation

used for simulation. ........................................................................................ 159

Figure 6.14 STFT of measured and simulated FBG peak wavelength data after selected

accumulated fatigue cycles and loading conditions. ........................................ 160

Figure 6.15 FFT of axial strain time history extracted from numerical simulations of (a)

plastic deformation of the adhesive for peak axial strain of 5387 με and (b) an

interfacial defect size of 30.5% of total bond area. .......................................... 162

1

CHAPTER 1

INTRODUCTION

1.1 OVERVIEW

Inspection techniques in recent years have evolved to fit the unique nature of

advanced composite structures. In addition, structural health monitoring (SHM) has evolved

as a method to replace costly routine or time-based maintenance with preventative condition

based monitoring of the structure. Numerous nondestructive evaluation (NDE) techniques

have been applied to monitor the structural integrity of composites including acoustic

emission, infrared thermography, ultrasonic C-scanning, and x-ray imaging (Magalhaes et

al., 2005; Meola et al., 2004; Biggiero et al., 1983; Li et al., 2010). Fiber Bragg grating

(FBG) sensors have been applied as strain, temperature and cure monitoring sensors for a

variety of applications related to composite materials (Kuang et al., 2003). The FBG sensor

presents several advantages, including its resistance to electromagnetic interference, low

weight, and small size. Surface mounted FBG sensors can be applied to retrofit existing

structures and capture strain or temperature profiles at multiple locations on the structure.

One of the truly unique characteristics of FBG sensors is that they can be embedded in

laminated composites for internal monitoring of localized strain fields during curing, service

or repair of the composite. During fabrication, embedded FBG sensors can be located in the

vicinity of future, subsurface damage sites and if embedded properly, do not initiate or

2

accelerate the propagation of critical damage modes (Sirkis et al., 1994a; 1994b; Garrett et

al., 2009).

In a review of embedded FBG sensors for composites monitoring (Ferdinand et al.,

2002), aeronautics equipment manufacturer Ratier-Figeac in collaboration with CEA-LIST

successfully used embedded FBG sensors for resin flow mapping in an Airbus A400M

composite propeller blade to improve the injection process by detecting dry zones or voids

that may form. Garrett et al. (2009) used quasi-static full-spectral measurements of

embedded FBG sensors in woven twill carbon fiber laminates exposed to impact to monitor

subsurface residual stresses. Also, embedded FBG sensors have been used to monitor

debonding in honeycomb sandwich composites (Minakuchi et al., 2007). The authors found

that the formation of resin fillets after curing would impose a complex strain gradient across

the sensor even before applied loading. Once the sandwich composites were subject to

impact the honeycomb cells would debond from the adhesive layer releasing the non-uniform

strain loading imposed by the resin fillets on the sensor. The return to a uniform FBG

response was concluded to be associated with debonding in the honeycomb sandwich

composites. Furthermore, embedded FBG sensors have been used to study fatigue damage

of composite structures (Maurin et al., 2002). The authors embedded FBG sensors in

composite train bogies to study the long-term effects of fatigue, light exposure, and extreme

temperature changes. During a three week period the composite specimen was subject to

accelerated aging tests in a climatic chamber where the bogie was exposed to over 10 million

cycles of fatigue. Static measurements of the FBG sensors were performed every 24 hours

and found accumulating residual stresses as fatigue progressed.

3

All of these previous studies take advantage of the FBG sensors versatility to gain

accurate subsurface strain information by being embedded between lamina during

manufacturing. The quasi-static measurements reveal local changes in the host material that

occur on times scales that range from 1 – 1000 seconds. However, FBG sensors have an

excellent dynamic response and can also be used to capture damage events that occur on

much smaller time scales. Edge filtering of the FBG reflection spectrum or interrogation

using a conventional peak follower can be used to detect high frequency strain information

and is usually limited by the acquisition system and not the actual sensor capabilities.

For this reason, FBG sensors have been applied to measure dynamic strain related to

vibration modes and impact responses (Park et al., 2012; Ling et al., 2004; Park et al., 2010).

Park et al. (2012) used surface mounted FBG sensors mounted on the leading edge of a

composite wing to detect bird strikes at 200 km/h resulting in impact energies over 700 J.

Peak tracking of the FBG sensor reflection spectrum indicated oscillations up to +/- 1000

microstrain that occur on time scales less than 200 microseconds. Benterou et al. (2011) used

embedded chirped-FBG sensors in a 4 inch column explosive to track detonation waves that

propagate at speeds greater than 7 km/s. The unique broad reflection band of chirped gratings

allows location of the sensor to be directly correlated with reflected wavelength. The

detonation wave was tracked by monitoring the actual demolition of the sensor which results

in loss of reflective power at that wavelength or location. Okabe et al. (2007) used surface

mounted FBG sensors on a thin composite plate to capture lamb waves produced by a piezo-

ceramic stack actuator. Peak tracking the FBG sensor suggested that damaged areas in the

composite plate between the actuator and sensor resulted in a delay in the arrival time of the

4

lamb waves. Researchers have also applied FBG sensors to investigate the feasibility of

active vibration control and the development of a hybrid vibration monitoring system for

surface mounted applications (Ambrosino et al., 2007; Mizutani et al., 2011; Arai et al.,

2002). Additionally, FBG sensors have been used as acoustic sensors to measure ultrasonic

mechanical vibration of piezoelectric transducers, proving their high sensitivity and detection

capabilities across a wide frequency range (Takahashi et al., 2000). In each of these dynamic

measurement cases, peak wavelength interrogation or edge filtering was applied to follow the

dynamic wavelength shifts of the FBG. These techniques require that the shape of the FBG

reflected spectra remains constant for accurate measurement results.

However, embedded sensors experience complex, multi-component stress states,

particularly near damaged regions. In addition, FBG sensors do not integrate local

distributions along the gauge length, but rather can reveal detailed strain or temperature

profiles at the sub-millimeter scale through induced distortion in the reflected or transmitted

FBG spectrum (Peters et al., 2001). In consequence the spectral response of the FBG sensor

in reflection is distorted from a single resonance peak to a complex spectrum. While this

complex spectrum provides detailed sensing information on stress states within the structure,

this information cannot be obtained without full-spectral scanning of the FBG sensor

spectrum. For many applications related to damage monitoring, it is therefore important to

capture the full-spectral response of the FBG.

5

1.2 FIBER BRAGG GRATING SENSORS

The FBG sensor is a permanent periodical perturbation in the index of refraction of an

optical fiber core. This index modulation can be expressed mathematically as

eff eff eff

2( ) 1 cosn z n n z

(1)

where z is the coordinate along the axis of the fiber, is the fringe visibility of the

modulation, the grating period, effn the effective index of refraction of the fiber for the

fundamental mode and effn the “dc” average index change (Erdogan et al., 1997). (z) is

the grating chirp function which describes any variation in the grating period along the

grating length. The FBG sensor acts as a “wavelength-dependent filter,” meaning that when a

broad spectrum of wavelength is passed through the FBG, a narrow bandwidth of

wavelengths is reflected, while all others are transmitted. When / 0d z dz the reflected

spectrum has the form of a narrow Gaussian peak, as shown in Figure 1.1. The wavelength at

maximum reflectivity is referred to as the Bragg wavelength, B, and is determined by the

condition,

eff2B n (2)

As axial strain, a, is applied to an unconstrained FBG, the Bragg wavelength shifts to lower

wavelengths (compression) or higher wavelengths (tension) (see Figure 1.1). The applied

strain is linearly encoded in the FBG Bragg wavelength shift,

2

eff12 12 111

2

Ba

B

np p p

(3)

6

where p11 and p12 are photo-elastic constants and the Poisson’s ratio of silica.

When a non-uniform axial strain field is applied to the FBG (i.e. / 0d z dz ), the

reflected spectrum can show significant distortion as shown in Figure 1.1. The form of the

spectral distortion varies depending upon the specific axial strain distribution. A second type

of spectral distortion commonly seen in embedded FBG sensors is due to transverse loading

on the optical fiber (i.e. perpendicular to the optical fiber axis). For non-hydrostatic loading

cases, the diametrical loading creates birefringence in the optical fiber, leading to two axes of

propagation in the fiber (Wagreich et al., 1996). The lightwave propagating through the fiber

is split into two modes, each experiencing a slightly different Bragg wavelength as they pass

through the FBG. When recombined, the reflected spectrum demonstrates a distinctive two

peak form such as shown in Figure 1.1. This transverse strain component is particularly

strong for FBGs embedded in composite laminates with high residual stresses, woven

microstructures or during impact events (Propst et al., 2010; Kuang et al., 2001; Zhang et al.,

2003).

The final potential contribution to the distortion of the reflected spectrum shown in

Figure 1.1 is due to a periodic perturbation to the grating amplitude by an envelope with

period e, significantly larger than the original period, . This second modulation,

commonly known as superstructuring, leads to periodically spaced resonance peaks in the

reflected spectrum with spacing, (Eggleton et al., 1994)

2

eff2

B

en

(4)

7

What distinguishes these peaks are their large number, wide wavelength spacing over several

nanometers and periodic spacing. In Chapter 3, it will be seen that the physical architecture

of the woven laminate can create a modulation in the transverse compressive stress

component acting along the length of the FBG. In this case, the superstructuring in the FBG

is through the stress-optic effect.

1.3 SCOPE OF RESEARCH

The primary goal of this research is to validate a newly developed high speed, full-

spectral interrogator for dynamic measurements of embedded fiber Bragg grating sensors and

to demonstrate new damage monitoring capabilities for composite structures based on this

unique sensing capability. The high speed full-spectral interrogator was designed by the

Electrical Engineering Department of Brigham Young University, in collaboration with the

Mechanical and Aerospace Department at North Carolina State University, and is based on a

MEMs Fabry-Pérot tunable optical filter used for scanning the sensor at extremely rapid

rates.

Previous research by Propst et al. (2010) applied an earlier design of the FBG full-

spectral interrogator presented in this research, capable of scanning speeds up to 534 Hz. The

spatial-temporal regions which the various modes of damage occur were identified for woven

graphite-epoxy laminates exposed to low-velocity impact. Propst et al. (2010) found that

damage types include short duration events such as fiber breakage and matrix cracking, as

well as longer duration matrix relaxation and delamination. Also, the quasi-static post-

8

impact residual stress states were assessed once the material reached equilibrium in the

seconds and minutes following the impact event. Propst et al. (2010) concluded these

damage types and their order of progression all contribute to the overall health of the

composite. As such, monitoring of the structure should include measurements over the full

range of damage-related lengths and durations in order to fully characterize the composite

health. However, the limited interrogation speeds resulted in low fidelity of information

during the impact event. As shown in Figure 1.2, Propst et al. (2010) captured two impact

strikes with an embedded FBG sensor interrogated in reflection at 100 Hz. Due to the

limited interrogation speed for this application, very little is known beyond the observance

that the impact occurs, results in either tensile or compressive stress of the sensor, and may

cause peak splitting.

Since the work of Propst et al. (2010), new developments in the design of the high

speed full-spectral interrogator enabled high speed / high resolution strain monitoring of

subsurface damage in composites at acquisition speeds up to 300 kHz (Vella et al., 2010), as

discussed in Chapter 2 of this dissertation. In this dissertation, the new capabilities of the

instrumentation are validated through experimental testing and used to gain high speed

dynamic strain information at the embedded sensor location never before achieved. For a

complete assessment of the dynamic measurements it is first required to understand that

proper acquisition speed of the instrumentation is entirely dependent on the application and

often depends on both loading type and the mechanics of the material being monitored.

Oversampling is computationally expensive while under sampling could result in sacrificing

dynamic spectral features that contain detailed information on the damage state of the host

9

composite material (i.e., peak splitting). Therefore, the requirement for such a high speed

full-spectral interrogator would be that the instrumentation be versatile enough to provide

sufficient scanning speeds and full-spectral resolution for various dynamic loadings and

damage modes. In order to achieve this goal, the research plan was divided into the following

objectives:

1. Validate the newly developed instrumentation by capturing the dynamic full-spectral

response of embedded FBG sensors in composite laminates in a lab setting. We chose

to expose the composite laminates to various low-velocity impact energies and use

the high speed interrogator to capture the impact event.

2. Design, assemble, and characterize a realistic in-flight aircraft environment that

would provide known harmonic vibrations to transmit across the composite structure

and embedded FBG sensors during operation.

3. Conduct data analyses to develop routines for handling the introduced environmental

noise. Two methods are considered:

o Digitally filtering out the environmental noise to retrieve the static full-

spectral strain state of the FBG sensor.

o Actively monitoring the environment-induced harmonic resonances in the

FBG response as damage progresses and correlating deviations from the

baseline frequency response (undamaged state) as a damage indicator.

4. Combine all the information gained from previous experiments to monitor the

structural health of a relevant aerospace composite structure exposed to a realistic

10

damage mode and noisy environment. Because of their relevance to the aerospace

industry we chose to characterize fatigue damage in composite lap joints.

o The joints are first subject to fatigue and then excited using a harmonic

vibration spectrum closely associated with a fully-operating aircraft during

flight.

o Frequency analyses of both the full-spectral and peak wavelength information

are conducted to monitor changes in the structural dynamic behavior that

could be attributed to local damage that accumulates across the joint overlap

adhesive layer near the FBG sensor location.

The achievement of each of these goals will be presented in detail in this dissertation.

This dissertation is organized as follows: Chapter 1 presents an introduction to this research,

which includes the motivation, background of the use of FBG sensors in composite

structures, and an overview of the project objectives. In Chapter 2, complete details on the

design and operation of the high speed full-spectral FBG sensor interrogator are presented.

The need for high speed full-spectral interrogation over traditional peak follower and edge

filtering techniques are discussed. Chapter 3 describes the experimental low-velocity impact

testing of composite laminates used to validate the operation and data interpretation of the

full-spectral interrogator. Dynamic, full-spectral interrogation is performed during impact at

100 and 300 kHz. Advances in spectral-strain resolution from previous identical tests

performed at 534 Hz are examined. Multiple impact energies are used to monitor any spectral

changes in the sensor response and account for adjustments needed to be made to the

11

interrogator if any to capture damage events that occur at various temporal scales.

Birefringence of the optical fiber caused by transverse compressive loading resulted in peak

splitting during impact. A comparative study on identical tests performed using a traditional

peak follower reveals dynamic measurement errors known as wavelength hopping that could

occur if the full-spectral information is not known.

In Chapter 4, characterization of a vibration platform used to simulate a realistic in-

flight aircraft environment is presented. The full reflection spectrum of surface mounted FBG

sensors near the edge of a double-notched thin aluminum specimen is interrogated at 100

kHz during harmonic excitation. During non-uniform axial strain induced from the sharp

notch the dynamic FBG sensor full-spectral response is assessed. A conventional stop-band

digital filter is used to eliminate harmonic noise to retrieve the static FBG sensor strain state.

Chapter 5 presents a final experiment used to combine all previous efforts to characterize

fatigue damage in composite lap joints. The full-spectral FBG sensor response is first used to

avoid dynamic measurement errors by extracting the corrected peak wavelength information

to conduct frequency analyses from the standpoint of a traditional peak follower. The

frequency content of this signal is analyzed by computation of the fast Fourier transform

(FFT) and short-time Fourier transform (STFT). Transitions from an undamaged state

represented by a steady-state frequency response to aperiodic dynamic behavior of the peak

wavelength are attributed to accumulated fatigue damage across the joint overlap. Phase

plane representations are used to confirm the need for full-spectral interrogation and the

errors that result if wavelength hopping occurs.

12

In Chapter 6, simulations of the composite lap joint are used to numerically verify the

experimental results found in Chapter 5. Using a commercially available finite-element

software package, nonlinearities in the form of plastic deformation and geometric defects are

introduced at the adhesive layer of the joint to simulate the accumulated fatigue damage

endured during the experiments in Chapter 5. Similar frequency analyses are performed on

extracted axial strain time histories and compared to the experimental peak wavelength

results. Finally, Chapter 7 presents conclusions drawn from this research and

recommendations for future work.

13

Figure 1.1 Schematic of FBG sensor reflected spectrum under various strain states.

14

Figure 1.2 Dynamic FBG full-spectral measurements at 100 Hz shown for impact strikes 24 and 30 of

a woven graphite-epoxy laminate from Propst et al. (2010).

15

CHAPTER 2

FBG SENSOR HIGH SPEED FULL-SPECTRAL

INTERROGATION

This chapter describes the operation and signal decomposition of the high speed full

spectral interrogator to be used for dynamic FBG sensor measurements acquired up to 300

kHz.

2.1 MOTIVATION

The dynamic interrogation of FBG sensors in uniform strain or temperature fields is

typically performed through wavelength filters or peak wavelength follower controllers

(Todd et al., 2007). The accurate output of these interrogators relies on the reflected spectrum

of the FBG remaining of the same form and simply shifting in wavelength. In contrast to

other strain or temperature sensors, the response of the FBG is sensitive to non-uniformities

along the sensor axis. The presence of non-uniformities in the applied strain or temperature

field distorts the initial, single peak structure of the FBG reflected spectrum into multiple

peaks or other forms. The presence of spectral distortion can create errors in the interrogator

response. In extreme cases, the spectral distortion can lead to “wavelength hopping” in which

16

a peak wavelength interrogator switches between peaks in the distorted spectrum, making the

strain or temperature measurement appear to abruptly increase or decrease.

Kuang et al. (2001a; 2001b) first observed this effect when they embedded FBG

strain sensors in laminates (both unidirectional and angle-ply) and fiber-metal laminates

(both unidirectional and cross-ply) subjected to tensile loading. The authors also measured

the reflected spectrum of each FBG sensor at selected times using an optical spectrum

analyzer. Wavelength hopping was observed in sensors embedded in both the angle-ply and

cross-ply laminates. In contrast, the response of the FBGs embedded in the unidirectional

laminates demonstrated excellent linearity throughout the tests. The presence of wavelength

hopping correlated with changes in the shape of the FBG reflected spectra, which were not

observed for the unidirectional laminates. These results emphasize the effect of the local

micro-structure on the initial residual stress state applied to the FBG sensor and therefore on

the linearity of the FBG response during loading.

Güemes et al. (2001) and Kosaka et al. (2004) later confirmed these results for FBG

sensors embedded in unidirectional and plain woven, laminated tensile coupons and braided

composites. In each of these studies, the response of a peak follower interrogator was

collected and wavelength hopping correlated to spectral distortion in the FBG response. In

particular, Kosaka et al. (2004) demonstrated that spectral distortion was present at both

loads near the failure strain of the host material and after several cycles of fatigue loading. In

other words, the observed spectral distortion can also be due to damage in the host material

even if significant initial residual stresses were not present. Spectral distortion is not limited

to embedded sensors and has also been observed from surface mounted sensors due to

17

nonlinearities in the local strain field or adhesive bonding to the structure (Suárez et al.,

2003).

Figure 2.1 shows a schematic of the source of wavelength hopping in peak

wavelength measurements due to FBG spectral distortion. FBG reflection spectra were

simulated for the case where two separate sections of the grating are exposed to different

axial strain magnitudes (e.g. for the case where a portion of the FBG sensor is not adhered

properly to the structure). The first spectrum (before loading) is a single peak (labeled A),

however as the loading increases, multiple peaks appear in the spectra. The secondary peaks

(labeled B and C) appear beginning with the second spectrum. In the third spectrum, two of

the peaks (A and C) are very close in amplitude. At this point the peak wavelength

interrogator would follow the closest peak to the previous measured value which was the

wavelength of peak A in the previous time step. The selected peak depends upon the

movement of the spectra during the particular time step. If the peak C is chosen, the strain

measurement would appear to jump to the value of that peak (as shown in scenario #1), but

would jump back to peak A once the two peaks recombined at the next time step. On the

other hand if the peak wavelength follower remained with peak A, it could jump to peak B in

the fourth spectrum and follow peak B until the end of the test (as shown in scenario #2).

Solutions to prevent this wavelength hopping include increasing the data acquisition

speed such that the peak wavelength follower can correctly stay with the original peak

(which is not always possible for dynamic measurements) or capturing the full-spectral

output of the FBG reflection spectrum. When full-spectral interrogation is applied to the FBG

sensor, the unique information encoded in this distortion has been successfully applied to the

18

measurement of stress concentrations (Peters et al., 2001; Colpo et al., 2007), crack bridging

forces (Studer et al., 2003; Sorensen et al., 2008), curing of a resin matrix (Güemes et al.,

2002) and the presence of delamination (Garrett et al., 2009; Ling et al., 2005b; Yashiro et

al., 2005; Palaniappan et al., 2006; Propst et al., 2010). Due to the limitations in acquisition

speed for FBG interrogators, this full-spectral interrogation has been limited to quasi-static

loading cases until recently.

However, in Chapter 3 we capture the full-spectral response of a dynamically loaded

FBG sensor at 100 and 300 kHz and compare it to measurements of a peak wavelength

interrogator at 500 kHz. We investigate the role of wavelength hopping on the output of the

peak wavelength interrogator.

2.2 INSTRUMENT OPERATION

The full-spectral response in reflection of all FBG sensors in this research was acquired with

a dynamic, full-spectral interrogator recently developed by the authors. Complete details of

the interrogator and post-processing of the data can be found in Vella et al. (2010). Figure 2.2

shows a block-diagram of the interrogation system. A wide bandwidth lightwave signal is

generated by the amplified spontaneous emission (ASE) source. This input is then amplified

by an erbium doped fiber amplifier (EDFA) to increase the power of the signal entering the

FBG and therefore entering the MEMs filter. As the ASE light output power is close to the

saturation power for the EDFA, a variable attenuator was inserted between the two

instruments to adjust the power to just below the saturation value. The output of the EDFA

19

passes to the FBG sensor. The reflected output of the FBG sensor then passes through the

MEMS tunable Fabry Perot filter pre-packaged with a photodiode. The measured voltage

output of the photodiode is linearly proportional to the output lightwave intensity of the

Fabry Perot filter. The function generator drives the tunable filter with a sinusoidal voltage.

The amplitude of the sinusoidal voltage determines the amplitude of the wavelength sweep.

The mean value of the wavelength sweep is adjusted with a DC voltage offset added to the

function generator signal. By driving the filter with a sinusoidal voltage it settles into a

steady-state condition, thus eliminating overshoot problems, while real-time data storage and

post-processing overcomes the need for real-time processing.

The photodiode and function generator output was captured as a function of time and

then post-processed into a time-varying reflection spectrum. The analog-to-digital conversion

(ADC) card has an acquisition rate of 100 MSamples s-1

, meaning full spectral sweeps could

be acquired up to 300 kHz. In order to calibrate the wavelength to time conversion, the ASE

source and FBG sensor were replaced with a tunable laser, scanned at known wavelengths, as

described in Vella et al. (2010). This calibration had to be performed for each wavelength

range and acquisition speed applied in the experiments. Figure 2.3 shows the laboratory

implementation of the full-spectral interrogator.

2.3 DATA REPRESENTATION

A second-order Chebyshev stop-band filter was applied to each data set prior to

processing the time-varying data to eliminate periodic noise that appeared in the measured

20

optical power. To visualize the large amount of data, the individual wavelength scans were

combined to form a spectral map in which the color represents the intensity of the reflection

spectrum at a particular wavelength and time. An example of this spectral mapping process is

shown in Figure 2.4. All FBG sensors used during testing were based on the 1550 nm

telecom band. There exists an inverse relationship between spectral resolution and

wavelength scanning range of the filter. Optimal wavelength scanning windows were

determined on the material loading and expected strain response of the FBG sensors.

Wavelength scanning windows varied between 4 nm – 7 nm during the experimental studies

presented.

21

Figure 2.1 Schematic of source of wavelength hopping. Left hand side shows simulated FBG spectra

with increasing load. Primary peak is labeled A, secondary peaks are labeled B and C. Scenarios # 1

and # 2 show strain measurements extracted from peak wavelength interrogator.

22

Figure 2.2 Block diagram of FBG full-spectral interrogator and generation of the time-varying

wavelength spectrum: (a) The measured time-varying optical power is combined with (b) the

wavelength-time mapping to construct (c) individual wavelength spectrum.

23

Figure 2.3 Photograph of FBG full-spectral interrogator.

24

Figure 2.4 (a) Single full-spectral scan from the MEMS tunable optical filter. (b) False-color spectral

mapping of multiple high-speed scans of FBG reflection spectra. (c) 2D transformation for presentation. Color scales represent intensity. Red represents the highest intensity while blue is the

lowest.

25

CHAPTER 3

LOW-VELOCITY IMPACT TESTS

Now that the technology needed to acquire high-speed measurements is fully

developed, the next step is to validate the instrumentation in a lab setting. We demonstrate

the measurement of wavelength hopping in dynamic fiber Bragg grating sensor

measurements and its effect on the interpretation of the dynamic behavior of a composite

laminate. Strain measurements are performed with FBG sensors embedded in laminates,

subjected to low-velocity impacts, with data acquired using a commercial peak wavelength

following controller and a high-speed full-spectral interrogator recently developed by the

authors. As the peak wavelength data is collected at approximately the same acquisition rate

than the actual dynamic response of the laminate, the wavelength hopping does not appear as

a sudden jump in the interrogator output, but rather in different apparent dynamic responses

for repeated events. The peak follower response is theoretically predicted from the full-

spectral interrogator measurements. We demonstrate that dynamic wavelength hopping does

occur, that it changes the apparent dynamic behavior of the composite and that it can be

directly predicted from the dynamic spectral distortion. We also demonstrate that full-

spectral data acquisition at speeds lower than those required to fully resolve the dynamic

event creates apparent measurement errors due to wavelength hopping as well. For future

studies, the use of the high-speed full spectral interrogator would eliminate the ambiguities in

26

dynamic response of peak wavelength interrogators, when present. These results can be

found in a paper published by the authors (Webb et al., 2011).

3.1 EXPERIMENTAL METHODS

Laminated composite specimens were prepared from 24 layers each of 2 x 2 twill

weave carbon fiber–epoxy pre-preg (Advanced Composites LTM22/CF0300). A cross

section of the specimen layup can be found in Propst et al. (2010) and is shown in Figure 3.1.

We chose the woven material architecture to highlight nonuniformities in the strain applied

to the embedded FBG sensor. The resulting specimen thickness was 4 mm and the

dimensions of the specimens were 115 mm x 115 mm. Photographs of the specimen layup

before being placed in the hot press for curing are shown in Figures 3.2 and 3.3. A

polyimide coated optical fiber containing a single FBG sensor was embedded either at the

mid-plane or between layers three and four below the mid-plane as listed in Table 1. The

FBG sensor was offset 16 mm from the point of impact for each specimen (see Figure 3.4).

The FBG location was chosen based on previous experience, such that the FBG would be

sensitive to the presence of damage and would demonstrate a significant amount of spectral

distortion before the end of the laminate lifetime (Garrett et al., 2009; Propst et al., 2010).

Each of the composite laminates was fabricated in a hot-press under applied temperature and

pressure following the procedure of Propst et al. (2010). All samples were cured following a

stepped temperature profile of 15 minutes at 50 °C, 15 minutes at 65 °C, and 180 minutes at

27

80 °C, followed by 30 minutes without heating. A constant pressure of 458 kPa was

maintained throughout the temperature cycle.

Multiple low-velocity impacts were applied to each composite specimen using a

drop-tower impactor until perforation of the specimen. The impactor consists of a 19 mm

diameter hemispherical steel impacting probe on a 5.5 kg aluminum cross-head as shown in

Figure 3.5. Specimens were mounted between two 76 mm diameter steel clamping rings with

a layer of 1.5 mm neoprene film on each side to distribute clamping pressure evenly over the

clamped area. The specimens were impacted at an input velocity of 2.1 m/s or 2.3 m/s

corresponding to impact energies of 12.1 J and 14.5 J respectively (see Table 1). The cross-

head was manually arrested during the rebound following impact to prevent secondary

strikes. Failure was defined as complete perforation of the sample with no rebound of the

cross-head.

The full-spectral response of the FBG sensors in this study was interrogated at 100-

300 kHz, over a wavelength range of 1543.5 to 1552 nm. An example of the spectral

mapping process during impact is shown in Figure 3.6.

3.2 DISCUSSION

In this section, we present representative data obtained from several specimens during

individual impacts. Figure 3.7 shows spectral sweeps that were obtained during five different

strikes in the lifetime of a specimen with a FBG sensor embedded at the laminate midplane,

interrogated at 100 kHz. The particular strikes presented were chosen to represent different

28

stages in the laminate lifetime. This specimen was impacted at a velocity of 2.1 m/s (12.1 J)

and survived 114 strikes before final failure.

From the beginning of the laminate lifetime, we observe peak-splitting in the spectral

response during the impact event. Peaks are defined in each image as localized maximum

intensities. For example in the first image of Figure 3.7(a), three peaks can be observed

during the impact event. Although of different magnitudes, each of the peaks has the same

time response. The peak with maximum amplitude is in fact the one with the least

wavelength shift. Of the two peaks measured in strike 6, the axial strain component

dominates the one with the smaller wavelength shift in compression (lower wavelengths).

The compressive strain peak with the larger wavelength shift observed in strike 6 is due to

the presence of transverse compression on the FBG during impact and is released after the

impact event. The axial strain was also released after the impact event. There was no

measureable difference in the FBG reflected spectrum prior to and after the impact event for

these early strikes, thus no residual strain was present in the laminate at the FBG sensor

location.

In strike 72 (Figure 3.7(a)), the sensor axial response was slightly in tension (higher

wavelengths), as the neutral axis moved upward through the laminate due to damage

propagating from the lower surface (Propst et al., 2010). At strike 72, the neutral axis was

approximately at the same level as the FBG sensor location. To further confirm the source of

the two peaks, we observe that the wavelength shift dominated by the axial strain component

increased from the initial compressive value and eventually became tensile (see strike 86),

whereas the wavelength shift due to the transverse compressive component remained the

29

same. In contrast, the intensities of the two peaks were similar in strike 72. This is also due to

the increased residual transverse compression stresses present on the optical fiber as the

damage increases. Prior to the impact event during strike 110, the FBG reflected spectrum

was highly distorted with several peaks. As this image was obtained near the end of the

laminate lifetime, the residual stresses normal to the laminae interfaces have grown

significantly.

Figure 3.7(b) shows spectra sweeps from a second specimen also impacted at 2.1 m/s,

for which the FBG sensor (interrogated at 100 kHz) was embedded below the laminate

midplane. This specimen survived 150 strikes. For this specimen, the spectral sweeps were

initially in tension from the first strike, as the FBG sensor was located well below the neutral

axis of the specimen. The effect of transverse compression on the optical fiber was thus to

split the axial peak. In strike 148, the duration of the impact event has clearly increased since

the earlier strikes and strong relaxation is seen in the peak wavelength signal.

With the current high-speed full-spectral interrogator, maximum wavelength

resolution can be obtained up to 100 kHz. The scanning speed can be increased up to 300

kHz, however the wavelength resolution decreases with increasing scanning speeds beyond

100 kHz. At these higher scanning rates, there is therefore a tradeoff between temporal and

wavelength resolution. To demonstrate the effects of scanning rate, two specimens were

impacted at an increased impact velocity of 2.3 m/s (14.5 J). Figure 3.8 plots spectral sweeps

obtained during five different strikes in the lifetime of these specimens which survived 21

and 28 strikes to failure respectively. For the data of Figure 3.8(a), the FBG was interrogated

at 300 kHz, while for the data of Figure 3.8(b), the FBG was interrogated at 100 kHz. For

30

both specimens the FBG sensor was embedded below the midplane of the composite

laminate.

The measured spectra from both of these specimens show similar behaviors to that of

the previous two specimens. We observe peak splitting, a lengthening response time with

increased damage and relaxation towards the end of the laminate lifetime. Significant

oscillation of the FBG response can also be seen in the final strike of Figure 3.8(b),

potentially due to post-impact vibration of the optical fiber once delamination has reached

the FBG location. While the signal noise level of the data of Figure 3.8(a) is larger than that

of Figure 3.8(b), no additional spectral features can be identified from the measurements at

300 kHz as compared to 100 kHz. The scanning rate of 100 kHz is thus sufficient for the low

velocity impact energies tested. Future studies of embedded FBG sensors for the

measurement of dynamic events at rates above those tested in this work would potentially

benefit from the higher scanning rate capabilities.

As seen in the data of Figures 3.7 and 3.8, significant spectral distortion in the FBG

sensors was observed throughout the lifetime of the composite laminates, particularly during

the dynamic impact events. The sources of this spectral distortion include both the non-

uniform strain distributions and transverse loading discussed in Chapter 1. Furthermore, after

a critical amount of damage accumulation, the woven geometry of the laminate

microstructure placed a periodic, post-impact stress perturbation on the FBG sensor,

significant enough to create superstructuring of the FBG. The clear presence of

superstructuring can be observed in the data of strike 110 in Figure 3.7(a), as at least six

distinct peaks were observed in the spectrum before the impact event. After the impact event,

31

several peaks were still observed in the spectrum, although the bandwidth and intensity

increased and decreased respectively, a further indication of increasing compression normal

to the optical fiber axis. Figure 3.9 shows measured wavelength sweeps from this data before

and after strike 110. In order to confirm that these multiple peaks are in fact due to

superstructuring, we calculated the theoretical peak spacing due to the 2 mm weave spacing

of the two-dimensional twill material. For this sensor B = 1546 nm, yielding = 0.41 nm

from Eq. (4). This wavelength spacing is superimposed on the curves of Figure 3.9 and

approximates the measured peak spacing. Superstructuring of the FBG was also observed for

the specimen of Figure 3.7(b) before and after strike 148, through the large number of

resonance peaks in the reflected spectrum.

We now consider the effects of this spectral distortion on the output of FBG

interrogators. The FBG reflection spectrum measured during strike #80 from Figure 3.7(b)

and measured during a similar strike from a specimen previously interrogated at 534 Hz are

shown in Figure 3.10. These two sensors were thus interrogated with the same interrogator,

but at different data acquisition rates. Signal oscillations that were observed when the sensor

was interrogated at 534 Hz were not observed at the 100 kHz interrogation rate. These

oscillations occurred at random strike numbers and were previously thought to be due to

noise or vibrations of the laminate. It is now clear that they were due to the dynamic peak-

splitting seen in Figure 3.10(a) and the inability of the slower scanning rate to resolve peaks

of smaller amplitudes. Figure 3.10(b) shows a clear example of wavelength hopping in which

32

apparent oscillations in the sensor output were due to the measurement of different peaks in

the FBG reflected spectrum at different time steps.

We also use the full-spectral data collected from the specimen of Figure 3.7(a) to

compare to actual peak wavelength tracking data collected previously on a similar specimen.

Peak tracking data, plotted in Figure 3.11, was measured from a FBG embedded in a

specimen identical to that of Figure 3.7(a) and subjected to the same loading conditions (Park

et al., 2010). This sensor was embedded one layer closer to the midplane than that in the

specimen of Figure 3.7(a). The actual peak wavelength data was collected with a Micron

Optics Si920 interrogator and measured by tuning a wavelength filter to a known starting

peak wavelength and using feedback to follow that local maximum during the dynamic

measurement. Measured peak wavelength response histories are plotted at various stages in

the laminate lifetime: strikes 16-18, 39-41 and 138-140 (the specimen survived 140 strikes).

The shape of the peak wavelength response varied considerably over the laminate lifetime,

but always had one of the general three forms plotted in Figure 3.11.

To compare the measured peak wavelength tracking results with the current data, we

calculated the theoretical response of a peak-tracking interrogator based on the full-spectral

data from strike #26, also plotted in Figure 3.11. The presence of multiple peaks is visible

throughout the impact event. For this example, all peaks were relatively close in amplitude.

The full-spectral data is plotted in the middle section of Figure 3.11 with theoretical peak

wavelength tracking results superimposed as black lines. The FBG reflected spectrum prior

to strike #26 contained two distinct peaks, therefore the peak tracking was calculated starting

from each of these peaks. Additionally, one of the peaks split into two separate peaks of

33

almost identical magnitude, approximately 3 ms into the impact event, so both of these peaks

were also tracked. As the amplitudes of the multiple peaks are very similar, small

perturbations to the signal would easily cause the peak-tracking interrogator to switch

between these curves for different strikes.

The three peak wavelength response histories qualitatively follow those obtained

from the previous experiment. This is a strong indication that the different strain histories

measured using the peak wavelength tracking data are due to wavelength hopping. The

direction of strain is opposite for the two examples due to the FBG locations just above and

below the original neutral axis of the laminate. The different strain time histories plotted

from the peak wavelength data in Figure 3.11 were previously thought to indicate changes in

the laminate response over the lifetime (Park et al., 2010). However, these strain histories are

more strongly indicators of the relative peak amplitudes in the FBG reflection spectrum.

These peak amplitudes depend strongly on the transverse compressive stress and non-

uniformity along the FBG. Therefore the measured strain histories are indicators of changes

in the residual strain state and indirect indicators of changes to the laminate dynamic

response. The relation of these changes to the strain state may not be known or even

repeatable between identical specimens, as we cannot tell a-priori from the peak wavelength

data which peak is being tracked. Therefore while peak tracking systems can perform well

for surface mounted FBGs, full-spectral scanning is essential for embedded FBGs in cases

where damage may be present in the host material.

34

3.3 CONCLUSIONS

In this study, we demonstrated the effects that wavelength hopping can have on

dynamic measurements with FBG sensors. This demonstration was performed with FBG

sensors embedded in composite laminates subjected multiple, low-velocity impacts. In the

first example full-spectral data acquisition was performed at a rate lower than that required to

fully resolve the dynamic impact event. The presence of wavelength hopping created

apparent oscillations in the strain response. By acquiring the full-spectral data at a faster rate

(100 – 300 kHz) these apparent oscillations were no longer present in the measurements. In

the second example, measurements collected using a peak wavelength interrogator (at a

sufficiently fast rate to resolve the dynamic event) were shown to bifurcate due to the

presence of multiple peaks in the reflection spectrum. In both of these cases, applying full-

spectral interrogation of the FBG spectrum at a sufficient data acquisition rate eliminated the

uncertainties in the measurement due to the wavelength hopping.

The form of the spectral distortion (and therefore the resulting errors in strain or

structural response measurements) are dependent upon the local microstructure surrounding

the FBG, the placement of the FBG relative to this microstructure, the changes in this

microstructure due to damage and the nature of the loading applied to the structure. It is

therefore not possible to predict the spectral distortion for a given application, or to calibrate

a “gauge factor” for peak wavelength measurements to eliminate errors to this spectral

distortion. The measurement of the full-spectral response of the FBG sensor eliminates

uncertainties due to wavelength hopping or bandwidth changes. These measurements could

35

then be used to correct strain measurements or identify changes to the local material such as

due to damage.

36

Figure 3.1 Cross section schematic of specimen layup components showing overlapping peel-ply, protective putty, FBG sensor, and outer Mylar layers (Propst et al., 2010).

37

Figure 3.2 Photograph of bottom 12 layers of carbon fiber prepreg lamina. The FBG sensor for this

specimen was placed at the midplane.

38

Figure 3.3 Photograph of vacuumed layup before placing into the hot press for curing.

39

Figure 3.4 Specimen dimensions and location of FBG sensor relative to impact location.

40

Figure 3.5 Photograph of instrumented drop tower impactor.

41

Figure 3.6 Process of FBG spectral data visualization: (a) Schematic of impact event beginning with impactor freefall, to contact between impactor and laminate, through rebound of impactor. Dashed

line is laminate neutral axis. (b) Example wavelength scans collected during a single impact event at

534 Hz (Propst et al., 2010). (c) Conversion of same wavelength scans into spectral map where color represents intensity. Data in this example have not been filtered.

42

Figure 3.7 Measured, full-spectral response of embedded FBG sensor (a) in Specimen 1 during strikes

6, 20, 72, 86, and 110 (from top to bottom; (b) in Specimen 2 during strikes 2, 21, 80, 126, and 148 (from top to bottom). The intensity values for all graphs in each column are normalized to the same

maximum.

43

Figure 3.8 Measured, full-spectral response of embedded FBG sensor (a) in Specimen 3 during strikes

3, 9, 12, 19, and 21 (from top to bottom; (b) in Specimen 4 during strikes 2, 9, 14, 19, and 28 (from top to bottom). The intensity values for all graphs in each column are normalized to the same

maximum.

44

Figure 3.9 Wavelength sweeps measured before and after impact for strike 110 of Specimen 1. Inset

shows 2x2 twill geometry of woven carbon fiber.

45

(a) (b)

Figure 3.10 Measured FBG reflected spectrum: (a) strike #80 from Figure 3.4(b) interrogated at 100

kHz; (b) spectral sweep from previous specimen interrogated at 534 Hz (Propst et al., 2010) (wavelength shift is referenced to the Bragg wavelength). The maximum intensity color scale is not

the same for both figures.

46

Figure 3.11 Theoretical prediction of peak wavelength interrogator response from full-spectral data obtained from specimen of Figure 3.4(a), strike #26. Measured peak tracking data is plotted from

Park et al. (2010) and was collected at 295 kHz. Normalized strain is scaled to maximum strain value

measured and is linearly proportional to peak wavelength value.

47

CHAPTER 4

VIBRATION OF A DOUBLE-NOTCHED THIN

ALUMINUM PLATE

In this chapter we will apply the high-speed, full-spectral interrogator to measure for

the first time the response of FBG sensors in a complex strain field subject to vibration. We

consider two cases: with and without an initial spectral distortion due to non-uniform strain

along the length of the FBG. Previous work has measured only the dynamic response at a

single wavelength which is valid when no spectral distortion is present. We will interrogate

the full-spectral response of the FBG sensors at 100 kHz. The sensors are surface mounted

near the notch tip of an aluminum double edge notch specimen near a stress concentration

and therefore exposed to a non-uniform strain distribution. Simultaneously, the specimen will

be subjected to a vibration spectrum with multiple harmonic components.

There are three major outcomes from these experiments. First we will demonstrate

that the full-spectral response of a FBG sensor can be measured during vibration. The

measurements of the FBG response with an initial spectral distortion clearly show the

transient response and are verified through simulation. Secondly, we will measure the effects

of spectral distortion on the full-spectral vibration response of the FBG. To our knowledge,

such a measurement has not been previously achieved. Finally, we demonstrate that the use

48

of the high-speed, full-spectral interrogator permits the separation of the spectral distortion

and the harmonic vibration from the FBG response signal through classical filtering and can

therefore be applied to measure non-uniform strain fields in noisy environments. The full-

spectral data provides easier interpretation of the sensor response and the information it

contains on the strain state of the host material.


For this work we required two simultaneous loading capabilities for the FBG sensor:

a controlled, non-uniform static load along the FBG gauge length and a steady-state

vibration. A vibration platform was therefore designed and fabricated on which a uniaxial

tensile loader was mounted. The vibration platform was designed to provide a vibration

spectrum typical to aircraft flight environments, based on a similar concept from Ceniceros et

al. (2001). The single-axis vibration platform was constructed of a stainless steel 61 cm x 61

cm x 6.1 cm optical breadboard with a honeycomb core (ThorLabs PBH11105), mounted on

a single-axis pillow-block assembly, as shown in Figure 4.1. The breadboard was actuated by

a piezo-electric (PZT) stack actuator (PI P-840.40) mounted below the vibration platform.

The stroke range and push force of the actuator at full power and oscillation was 60 microns

+/-20% and 1000 N, respectively. The motion of the board was constrained to small

displacements using two adjustable turnbuckle-spring biases on each side of the platform. A

low-voltage PZT amplifier provided a 50 V DC offset voltage to the PZT stack. The PZT

stack was driven by a function generator at an excitation frequency of 150 Hz and peak-to-

49

peak amplitude of 6 V. An accelerometer with a sensitivity 100 mV/g (PCB Piezotronics

C33) was mounted directly to the breadboard and used to characterize the vibration platform

frequency components.

We designed a tensile tester that could be mounted directly on the vibration loading

platform to apply a static, non-uniform strain along the FBG gauge length. The FBG sensor

was mounted near the notch tip of an aluminum (2024) double-edge-notch (DEN) tensile

specimen. Increasing the tension applied to the specimen increased the magnitude of the non-

uniformity in the applied strain field.

Two separate DEN tensile specimens were fabricated. The dimensions of specimens

A and B, as shown in Figure 4.2(a), were 274 mm x 97 mm. The thickness of each specimen

was 0.81 mm. The notch radius of specimen A was 2.5 mm, fabricated using a CNC milling

machine. Specimen B had a notch radius of 0.5 mm to achieve a higher magnitude of non-

uniform strain on the FBG sensor than that of specimen A. A polyimide coated optical fiber

containing a single, 10 mm long FBG sensor was mounted using cyanoacrylate glue 1.6 +

0.25 mm from the notched-edge (see Figure 4.2(a)). The unloaded Bragg wavelength for the

FBG sensors mounted on specimens A and B were 1558.0 and 1552.0 nm, respectively. The

intensity spectra for the FBGs in specimens A and B were collected at a spectral acquisition

rate of 100 kHz (with a wavelength resolution of 84 pm) and wavelength ranges of 1557.0 to

1561.5 nm and 1551.5 to 1562.5 nm respectively.

During each experiment, a DEN tensile specimen was mounted in the manual tensile

tester shown in Figure 4.2(b). This tensile tester was then rigidly mounted on the vibration

platform as shown in Figure 4.1. A fine threaded machine bolt was inserted into the manual

50

tensile test assembly to generate small increments of elongation of the DEN thin aluminum

specimen. To apply tension, the bolt was torqued by one half turns, equivalent to 0.51 mm

axial translation of the nut. The specimen loading and data collection was performed in the

following order: (1) The reflection spectrum of the FBG was first measured without applied

strain or added vibration; (2) the PZT actuator was activated, inducing a steady-state

vibration spectrum with a fundamental frequency of 150 Hz on the optical platform and in

turn, the DEN thin aluminum specimen. The FBG reflection spectrum was measured during

this state for approximately 300 ms; (3) the PZT actuator was turned off and the tensile load

was increased one increment. The FBG reflection spectrum was then measured; (4) the PZT

actuator was activated and the FBG reflection spectrum was measured for approximately 300

milliseconds. Steps 3 and 4 were repeated until the specimen failed or the signal to noise was

too low.

Before conducting the tensile tests on the DEN thin aluminum specimens, we

characterized the forced response of the vibration platform induced by the PZT excitation.

The periodic motion can be seen in the raw voltage data of the accelerometer output, plotted

for a period of 10 ms in Figure 4.3(a). While the excitation was at a single fixed frequency,

the response of the vibration platform is defined by a summation of multiple modes and

higher harmonics. We therefore plot the fast Fourier transform (FFT) of the accelerometer

output in Figure 4.3(b) (calculated over a longer window than that shown in Figure 4.3(a)). A

sampling rate of 100 kSa/s was used, well above that to avoid frequency aliasing. It is clearly

seen the excitation frequency transmits to the vibration platform, at f0 = 149.8 Hz. The next

five harmonics also appear in the data at approximately 300, 450, 600, 750 and 900 Hz,

51

although the fifth harmonic at 750 Hz is not much above the noise level. Some additional

frequency components appear around 400, 500 and 950 Hz which may be due to cross-talk

between the other frequency components or resonance frequencies of the board. This

behavior is ideal for emulating a realistic vibration environment in which FBG sensors are

typically exposed.

4.2 VIBRATION OF UNIFORMLY STRAINED FBG SENSOR

During the tensile loading test, the FBG sensor was first interrogated in reflection at

100 kHz without any applied strain or induced vibration to the specimen or platform. As

expected, the response was a harmonic wavelength shift in the narrow bandwidth reflected

spectrum. The DEN tensile specimen was then loaded in tension. Figure 4.4(a) shows a

single sweep of the FBG reflection spectrum of the FBG sensor of specimen A when the

average strain along the FBG was 130 . The high speed full-spectral interrogation is

presented as a false-colored mapping during non-vibratory, static loading for 3 ms (Figure

4.4(b)). At this low tensile level, a single resonance peak spectrum was reflected by the FBG

with peak reflectivity at 1558.13 nm. The PZT was then excited at 150 Hz, and the dynamic

FBG response was measured for 30 ms and is also shown in Figure 4.4(b). All false-color

mapping plots in this article were normalized to the maximum intensity of the data sets for

each specimen. The spectral modulation in the FBG response is evident from visual

inspection. The visible modulation has a period of 6.7 ms, clearly due to the fundamental 150

Hz excitation frequency. The harmonic strain amplitude was 40 strain, calculated from the

52

shift of the peak centroid. Figures 4.4(c) and (d) show an increase in tension on the specimen

creating an additional uniform shift of the Bragg peak by 0.2 nm, equivalent to 170 , a

total average strain of 300 . The full-spectral static measurement and dynamic

measurement are again shown for this load step for a period of 3 ms and 30 ms, respectively

in Figure 4.4(d). Although still uniformly loaded, spectral broadening is present in the FBG

spectrum. The full width at quarter maximum (FWQM) of the reflected peak increased to

0.49 nm. From these measurements, we observe that the full-spectral interrogator reproduces

the harmonic vibration of the FBG as expected. The measurement of the FBG full-spectral

response during harmonic vibration is consistent with what we expect from peak wavelength

vibration measurements, for example those performed previously by Mizutani et al. (2011).

4.3 RELATIVE SENSITIVITY AND BRAGG WAVELENGTH DEPENDENCE

From the plot of Figure 4.4 it is unclear if the higher frequency components were

transmitted to the tensile loader, the aluminum specimen and finally to the sensor. To better

highlight the frequency components that were transferred to the FBG sensor, the full spectral

sweeps obtained during the vibration loading are analyzed in more detail in Figure 4.5. The

single spectral sweep from Figure 4.4(a) is repeated in Figure 4.5. Four reflected wavelength

values (indicated by points A, B, C, and D) of the FBG spectrum were analyzed. Points A

and C were chosen to be at the maximum strain sensitivity of the FBG at wavelength values

above (A) and below (C) the Bragg wavelength. Wavelength B was chosen to be the local

53

maximum of the reflection spectrum, in this case the Bragg wavelength. Wavelength D was

chosen to be sufficiently far from the Bragg wavelength near the edge of the reflected band.

For each discrete wavelength of the full-spectral scan, there is a unique modulation in

the reflected intensity as a function of time. The fast Fourier Transform (FFT) of the intensity

as a function of time at each of the four wavelengths A-D was calculated and is shown in

Figure 4.5. The amplitude of the reflectivity modulation is different for the different

wavelength values, as the local slope of the reflectivity vs. wavelength is different at the four

wavelengths. Across the reflected band, the local maximum intensity value in the frequency

response for each wavelength was normalized to the maximum amplitude of the entire data

set measured in decibels. Following the approach of Takahashi et al. (2000), the relative

sensitivity of the FBG is plotted against the analytical sensitivity prediction (the measured

gradient across the reflected band) in Figure 4.5 (top right). For uniform strain, the largest

vibration mode transmitted to the FBG sensor was consistently at the excitation frequency,

150 Hz. The experimentally measured sensitivity compares well with the analytical model,

although there are some differences near the lower wavelength A.

On the edge of the reflected band at wavelength A, the FBG clearly detects the

fundamental 150 Hz excitation frequency in addition to the 2nd

, 3rd

, and 4th harmonics. At

1558.13 nm, the Bragg wavelength is indicated by point B where the modal transfer

diminishes quite considerably, with only the 2nd

harmonic shown barely above the noise

floor. At this wavelength, the shallow slope at the Bragg peak results in fading of the

dynamic signal. At 1558.25, wavelength C indicates the highest magnitudes of frequencies

that transfer to the sensor. Therefore, this entire data set is normalized to the maximum (0

54

dB) of the wavelength frequency response at wavelength C. These experimental

measurements confirm that higher sensitivity of amplitude is associated with the edge of the

reflected band, where the reflectivity versus wavelength gradient is the strongest, not at the

Bragg wavelength. The fundamental 150 Hz excitation frequency and the 2nd

and 3rd

harmonics at 300 Hz and 450 Hz, respectively, are observed in the frequency domain of

wavelength D at 1558.48 nm. It was also observed that wavelengths that are outside the edge

of the narrow reflected band did not contain these amplified frequency components of the

vibration platform.

4.4 VIBRATION OF NON-UNIFORMLY STRAINED FBG SENSOR

Even at the maximum load applied to specimen A, the reflected spectrum of the FBG

sensor only demonstrated broadening. A second specimen, specimen B, with a smaller notch

radius was then tested under the same conditions. The smaller notch radius increases both the

average strain and the non-uniformity of the strain field along the length of the FBG for a

given applied tensile load. Recalibration of the tunable filter scanning window had to be

performed a couple of times between load levels to follow the FBG reflection spectrum

which was shifted to significantly higher wavelengths. Representative full-spectral reflection

measurements collected from the FBG sensor on specimen B during static and dynamic

measurements are shown in Figure 4.6.

Figure 4.6(a) shows a shift from the unloaded Bragg wavelength of 1552.0 nm to

1553.1 nm, a measurement of 900 uniform tensile strain. Once the vibration load was

55

added to the specimen, small amplitude oscillations were barely visible in the spectral

response plotted in Figure 4.6(a). The harmonic oscillations were still present, as will be seen

later in the FFT analysis of the data; however less dynamic strain amplitude was transferred

to the FBG sensor due to the higher tension at the notch location as compared to the previous

specimen. As the tensile loading was increased, the FBG was clearly exposed to non-uniform

strain resulting in a dual peak spectrum, as seen in Figure 4.6(b). Also, peak broadening

initiated as a result of the increasing strain field variations in the vicinity of the notched edge.

Figure 4.6(c) plots the reflected FBG spectra at an average strain along the grating length of

approximately 5,600 . This average strain was calculated based on the wavelength shift of

the reflected spectrum centroid. Three distinct peaks are observed with a FWQM of 2.1 nm.

This spectral distortion is consistent throughout the measurements from specimen B. Figure

4.6(d) plots the FBG spectra at an increased load, resulting in further distortion of the FBG

reflection spectrum. The measurement observed in Figure 4.6(e) was obtained at the highest

exposure to non-uniform strain achieved. Spectral broadening, peak splitting, and power

attenuation of the reflected band are observed throughout the spectra of Figure 4.6. The

maximum average static strain along the FBG length, measured in the testing of specimen B,

was 8,100 (0.81%).

For each of the loading cases in Figure 4.6, the spectral distortion did not visibly

change once the vibration was applied. This result implies that the original spectral distortion

can potentially be separated from the harmonic vibration by post-processing of the data. This

will be discussed in Section 4.8. In contrast to the results from Specimen A, there was a static

56

shift of the upper edge of the reflected band to lower wavelengths for cases (b) through (e).

The cause of this shift will be investigated in Section 4.6. The increased loading further

increases the non-uniform strain on the FBG by intensifying the stress concentration at the

notch. The higher frequency modes propagate at a much lower amplitude and therefore do

not further distort the spectra as expected. Further loading of the specimen and sensor

resulted in crack propagation from the notch tip and failure of the specimen.

4.5 FULL-SPECTRAL FREQUENCY RESPONSE

In Figure 4.7(a), the uniformly strained FBG sensor response from specimen A is

shown for both static and dynamic loadings (left). Also, the FFT computed for each

wavelength sweep is shown as a false-color map (right). Each FFT is normalized to the

maximum frequency amplitude of all the data from that specimen. Figure 4.7(a) shows the

strong transmittance of the excitation frequency, 150 Hz, and the dropout of the dynamic

strain at the Bragg wavelength (1558.4 nm) seen in Figure 4.5. The only difference between

Figure 4.7(a) and Figure 4.5 is the small increase in uniform tensile loading. Therefore, the

amplitude at 150 Hz in Figure 4.7(a) represents a local minimum at the Bragg peak and local

maxima on the edges of the narrow band.

The remaining plots shown in Figure 4.7 are from the FBG of specimen B.

Throughout the entire experiment this specimen experiences both uniform and non-uniform

strain but does not show significant amplitudes in the excitation frequency 150 Hz. Instead a

distributed frequency spectrum of higher harmonics with lower amplitudes was observed.

57

Figure 4.7(b) shows the FBG response of specimen B during the early transition to non-

uniform strain and the corresponding FFT mapping. Signatures of highly non-uniform strain

are present along with the effects of frequency response on band location. As expected, the

transmission of modes to the FBG sensor is still only observed within the narrow band and

abruptly diminishes outside the edges of the signal. Therefore any harmonic vibration

observed in the signal is due to the PZT excitation and are not artifacts of driving the tunable

optical filter or other instrumentation. From these measurements it is observed that for a

given dynamic load, the amplitude of the frequency components varies between the vibration

modes, but are only present at the harmonic frequencies, rather than randomly across the

reflected band.

4.6 STRAIN GAGE TESTING FOR BUCKLING OF ALUMINUM SPECIMEN

As seen in Figure 4.6(b)-(e), a static shift of the FBG reflection spectrum to shorter

wavelengths was observed when the vibration loading was initiated. To investigate if this

was an artifact of the instrumentation), a true change in the FBG response, or a physical

change in the strain state, strain data was also collected using a conventional electrical

resistance strain gage. A second specimen identical to specimen B was fabricated with a FBG

sensor in the same location and a strain gauge mounted adjacent to the FBG sensor. The

electrical resistance strain gauge measures the average strain along the sensor gauge length

and is therefore not influenced by the strain non-uniformity (Peters et al., 2001). The full-

spectral mappings of the FBG sensor in this specimen are identical to those presented in

58

Figure 4.7. A single scan from the static full-spectral measurement is plotted as a solid black

line in Figure 4.8(a). Four equally-spaced scans covering a single period of the 150 Hz

vibration measurement are also plotted in Figure 4.8(a) to show a full cycle of spectral

measurements once the PZT was activated. As the four spectral sweeps are almost

indistinguishable in Figure 4.8(a), it is clear that the FBG was exposed to a relatively large

static strain shift after which the strain oscillated at the excitation frequency with a much

lower amplitude.

To test whether this observed static strain was real, the FBG data was compared with

simultaneous measurements from the electrical resistance strain gauge. Figure 4.8(b) plots

the strain measurements obtained from the strain gauge, acquired with a System 6000

StrainSmart Data Acquisition system (Vishay). The activation of the DAQ system can be

seen in Figure 4.8(b) at the beginning of the measurement by a spike in output voltage. The

strain gauge response was then measured for 10 seconds before the PZT was activated at 150

Hz. At 10.2 seconds the measurement indicated an abrupt shift in tensile strain after which

the strain gage settled into a new equilibrium position. This observation verifies that

activating the vibration loading actually induced the thin rigid plate to move into a different

equilibrium condition, presumably by localized buckling in the vicinity of the notch tip. The

DC wavelength shift observed in Figures 4.6(b)-(e) was therefore due to an actual change in

strain state near the notch tip and not an artifact of the FBG sensor response or

instrumentation.

59

4.7 NUMERICAL SIMULATIONS

Numerical modeling of the DEN specimen was performed using ANSYS, a

commercially available finite-element analysis software. The aim was to model the static

response of the FBG to better understand the non-uniform strain field induced by the notch

tip as a function of load and validate the experimental measurements. The thin aluminum

(DEN) specimen was modeled using one-quarter symmetry boundary conditions and two-

dimensional, plane stress elements. Shown in Figure 4.9(a), the finite element mesh was

generated using solid PLANE 82 elements with mesh refinement near the notch tip to

account for the stress concentration. The uniform tensile loading and symmetric boundary

conditions applied to the model are shown in Figure 4.9(b). The static analysis was

performed iteratively, increasing the applied tensile load and extracting the axial elastic strain

profile along the FBG gauge length at each load step. A contour plot of elastic strain in the

FBG axial direction is shown for a single load step in Figure 4.10. Due to the notch tip,

strong non-uniform color contours along the length of the FBG are observed. Extracted strain

profiles from the finite-element analysis were then input into the modified transfer matrix

method of Prabhugoud et al. (2004), which accounts for the effects of strain gradients, to

predict the FBG reflection spectrum based on the non-uniform strain profile. Prabhugoud et

al. (2004) and Ling et al. (2005a) have shown that this method accurately predicts the FBG

output reflected spectrum when the strain distribution along the FBG gauge length is known.

The numerically predicted FBG response to the non-uniform static loading is plotted

against an experimentally captured reflection spectra of specimen B for the same tensile load

in Figure 4.11. The experimentally measured spectra were normalized to the maximum

60

reflectivity of the numerical prediction to eliminate effects of power attenuation in the

experiments. The numerical model does not reproduce the experimentally collected reflection

spectra exactly, however, the extent of distortion and key appearance of spectral broadening

and peak splitting are well represented. These results demonstrate that the spectral distortion

was created by the non-uniform strain field near the notch tip. Differences in the two sets of

spectra are most likely due to the positioning of the FBG sensor and the machined geometry

of the notch tip.

The same finite element model was also applied to verify the vibration resonance

condition measured by the FBG sensor at a particular tensile load. A single FBG with Bragg

wavelength of 1550.0 nm was mounted on a specimen identical to specimen B and loaded in

the same manner as for the previous specimens. At a low tensile load level, a resonance

condition was observed from the FBG response, shown in Figure 4.12(a). The excitation

frequency at 150 Hz has clearly transmitted to the FBG, inducing a harmonic strain

amplitude of 560 , calculated from the peak wavelength shift. The mean axial strain of the

FBG was 860 at this load value. Figure 4.12(b) shows the FBG response after as slight

increase in tension on the specimen. The Bragg peak has shifted to 1551.6 nm and the

spectral oscillations have clearly damped out due to the increased stiffness of the specimen.

To verify that this resonance condition was at the predicted load level, a modal analysis was

performed using the ANSYS model. The geometry and boundary conditions remained the

same; however the elements were replaced with SHELL 95 elements to allow calculation of

out-of-plane displacement caused by vibration. The modal analysis was performed for load

61

steps from 0 to 10.0 kPa and the first natural frequency of the specimen was recorded. The

natural frequency as a function of load is plotted in Figure 4.12(c). From the numerical

results, the natural frequency of the unloaded DEN specimen B was 105.7 Hz. It also seen

that at an applied tensile stress of 3.47 kPa the natural frequency matches the PZT excitation

frequency, 150 Hz. From the ANSYS model, the mean axial strain along the FBG gauge

length was 810 at an applied tensile force of 3.47 kPa, less than a 6% difference from the

measured value. The unusually large spectral oscillations shown in Figure 4.12(a) are

therefore due to the fundamental resonance condition of the DEN thin aluminum specimen.

4.8 FILTERING OF FULL-SPECTRAL DATA

The final goal of this study was to determine if the vibration induced harmonic strain

could be successfully removed from the FBG spectral response data, to permit the extraction

of spectral distortion in noisy environments. Previous studies have confirmed the use of fiber

Bragg gratings for vibration sensing. However, most studies have investigated the FBG either

unloaded or uniformly loaded in strain prior to the introduction of vibration. The results of

this section discuss the interpretation of the FBG sensor exposed to both uniform and non-

uniform strain during vibration and the practical use of a classical, second–order stop-band

Butterworth digital filter for each of these cases.

Based on the frequencies identified Figure 4.3(b), a digital filter was designed with

the frequency response shown in Figure 4.13. This multi-band digital filter design requires

that the environmental vibrations in which the FBG is mounted or embedded be

62

characterized with known frequency components. The digital filter is comprised of a

summation of stop-band filters of equal order and attenuation at each known harmonic of the

induced vibration loading. The cutoff frequencies for each stop-band were defined at the -

3dB location. The second-order Butterworth digital filter was chosen for its infinitely flat

response in the pass-band and little to no ripple in the stop-band. Windowing the bandstop

filtered signal with a Hanning window reduces spectral leakage into the stopband, however,

in this study changes in filter performance were minimal and did not need further addressing.

For practical applications, further filter design may be necessary to address issues such as

phase distortion, mistuning and non-stationary vibration environments.

The full-spectral measurement of the uniformly loaded FBG sensor from specimen A,

exposed to 150 Hz vibration, is shown in Figure 4.14(a). Each wavelength sweep in Figure

4.14(a) was then filtered and plotted in Figure 4.14(b). The natural frequencies of the

vibration platform are clearly strongly diminished, resulting in the original static

measurement of the FBG reflection spectrum. A single scan of the FBG reflected spectrum

from specimen B with significant spectral distortion is plotted before vibration loading in

Figure 4.14(c) as a solid black line and with vibration loading as a dashed black line. This

data was digitally filtered, similar to the uniform strain case and plotted as a grey dotted line

in Figure 4.14(c). As it is difficult to distinguish the filtered spectrum and the spectrum

measured during vibration, it is evident that filtering the wavelength intensity for the non-

uniform spectrum recreated the reflected spectrum after the static shift due to the change in

equilibrium of the DEN specimen. The digital filter also smoothed out the noise in the

individual spectral sweeps. Therefore the use of full-spectral measurements could be used to

63

separate the statically distorted reflection spectrum in these experiments. Furthermore, these

results indicate that other classical digital filtering methods could most likely be applied to

isolate spectral distortion in the response of FBG sensors mounted on or in structures

subjected to more complex vibration environments.

Finally, we comment on how the spectral information could be used in practice. Once

the spectral distortion is isolated from the imposed vibration, the spectrum could be inverted

to reveal the strain distribution along the gauge length of the FBG. This inversion is typically

performed through an evolutionary algorithm, in which the input strain distribution is varied

and the predicted reflected spectrum is compared to the measured one (Gill et al., 2004). For

these experiments, the input strain distribution was known (through the finite element

simulations), therefore this optimization was not performed. Therefore, in contrast to other

strain gauges, for which the only average strain along the gauge length is reported, the sensor

output is the local strain distribution in the region of the strain gauge. This strain distribution

could then be used, for example, to identify stress concentrations due to local damage or the

presence of cracking (typically indicated by the high strain gradients).

4.9 CONCLUSIONS

We measure the full-spectral response of a FBG sensor during harmonic vibration

with and without an initial spectral distortion due to a non-uniform, static strain field. The

results demonstrate that the measurements of the FBG response without initial spectral

distortion are identical to those previously measured with peak wavelength interrogators.

64

The measurement of the FBG full-spectral response with initial spectral distortion also

contained the excitation vibration harmonics, however did not include further distortion of

the reflected spectrum as a result of the vibration. Numerical simulations of the FBG

response well predicted the spectral distortion due to the non-uniform strain field and the

resonance condition of the DEN specimen used in the experiments. Finally, we demonstrated

that the use of the high-speed, full-spectral interrogator permits the separation of the spectral

distortion and the harmonic vibration from the FBG response signal through filtering and can

therefore be applied to measure non-uniform strain fields in noisy environments. These new

findings offer innovative contributions to the area of strain measurements and damage

detection for structures in dynamic environments.

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Figure 4.1 Photograph of vibration platform and tensile loader.

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Figure 4.2 (a) Dimensions of DEN aluminum specimen A (R=2.5 mm) and specimen B (R=0.5 mm).

(b) CAD model of manual tensile machine used to induce non-uniform strain on test specimens.

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Figure 4.3 (a) PZT-forced acceleration response of vibration platform and (b) corresponding

frequency response spectrum.

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Figure 4.4 (a) Single full-spectral sweep of FBG reflection during uniform loading, 130 axial strain. (b) Corresponding dynamic measurements during static and vibratory loading. (c) Single full-

spectral sweep of FBG reflection during uniform loading, 300 axial strain. (d) Corresponding dynamic measurements during static and vibratory loading.

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Figure 4.5 Single scan of FBG reflection spectrum exposed to uniform vibratory load from specimen

A (top left). Experimentally measured and predicted relative sensitivity (top right). Fast Fourier transforms of wavelength intensity vs. time for chosen wavelengths A-D across the reflected band.

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Figure 4.6 Single full-spectral sweep of FBG reflection during static loading (left). Corresponding

dynamic measurements during static and vibratory loading (right) for mean static tensile strain of (a)

900 (b) 2,300 (c) 5,600 (d) 6,200 and (e) 8,100

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Figure 4.7 False-color mappings of full-spectral measurements during static and vibration loading for

various intensities of non-uniform strain (left). False-color mapping of fast Fourier frequency

response across reflected band for each load step (right). All false-color mappings are normalized to

the maximum of the data set.

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Figure 4.8 (a) Single static sweep of distorted spectra plotted as solid black line. Four sweeps 1-4 cover a full period at 150 Hz, each as a dashed grey line. (b) Foil strain gage measurement during

DAQ and PZT activation.

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Figure 4.9 (a) Finite-element mesh using PLANE 82 elements and plane stress conditions. (b)

Geometry and boundary conditions implemented during quarter-symmetry finite-element analysis.

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Figure 4.10 Contour plot of elastic tensile strain in vertical direction (axial direction of FBG) for a single load step using ANSYS finite-element software. Red represents a maximum value and blue

represents the minimum. Legend indicates dimensionless axial strain units.

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Figure 4.11 Experimentally measured reflection spectra from the FBG of specimen B (solid black

line) are shown at a static load of (a) 48.0, (b) 86.4, (c) 88.0, (d) 111.0, (e) 112.0, and (f) 120.0 MPa. Numerically predicted FBG response are shown as dashed line. Experimental spectra are normalized

to the maximum reflectivity of the numerical model for comparison.

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Figure 4.12 (a) Dynamic full-spectral measurement of FBG reflection spectrum during resonance of

specimen B at 150 Hz, equivalent to the PZT excitation frequency. (b) Static (3 ms) and vibratory (30 ms) FBG response after small increase in load. (c) Using finite-element modal analysis, the natural

frequency variation of specimen B as load is increased in increments of 1.0 kPa.

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Figure 4.13 2nd

-order Butterworth stop-band digital filter response.

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Figure 4.14 (a) Unfiltered dynamic full-spectral measurement of FBG reflection spectrum exposed to

uniform vibration. (b) Filtered measurement from (a) using 2nd

-order Butterworth stop-band digital

filter. (c) Single sweeps of FBG exposed to non-uniform loading during static condition (solid black line), 150 Hz vibration (dotted), and digitally filtered (dashed).

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CHAPTER 5

CHARACTERIZATION OF FATIGUE DAMAGE

IN COMPOSITE LAP JOINTS—EXPERIMENTS

In this chapter we measure the in-situ response of a fiber Bragg grating (FBG) sensor

embedded in the adhesive layer of a single composite lap joint, subjected to harmonic

excitation after fatigue loading. After a fully-reversed cyclic fatigue loading is applied to the

composite lap joint, the full spectral response of the sensor is interrogated at 100 kHz during

two loading conditions: with and without an added harmonic excitation. The full-spectral

information avoided dynamic measurement errors often experienced using conventional peak

wavelength and edge filtering techniques. The short-time Fourier transform (STFT) is

computed for the extracted peak wavelength information to reveal time-dependent

frequencies and amplitudes of the dynamic FBG sensor response. The dynamic response of

the FBG sensor indicated a transition to strong nonlinear behavior, followed by chaotic

vibration as fatigue-induced damage progressed. The ability to measure the dynamic

response of the lap joint through sensors embedded in the adhesive layer can provide in-situ

monitoring of the lap joint condition. These results can be found in a paper recently

submitted by the authors (Webb et al., 2013b).

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5.1 INTRODUCTION

Adhesively bonded composite lap joints pose an interesting challenge to inspection

and monitoring because they cannot be disassembled in the same manner as bolted metallic

joints during routine maintenance and inspection. Numerous nondestructive evaluation

(NDE) techniques have been applied to monitor the structural integrity of adhesively bonded

joints including acoustic emission, infrared thermography, ultrasonic C-scanning, and x-ray

imaging (Magalhaes et al., 2005; Meola et al., 2004; Biggiero et al., 1983; Li et al., 2010).

Coupling of this inspection data with data collected in-flight or in between inspections can

potentially provide an accurate and detailed description of the joint condition. Due to the

localized nature of lap joints, applying sensors on the structure near the lap joint, or

embedded in the adhesive layer in the lap joint, is a viable option for collecting rapid data on

the joint integrity. Numerous authors have applied active sensors/actuator pairs on either side

of lap joints to both propagate waves through and collect data on the response of the joint to

high-frequency excitation (Shin et al., 2012; Fasel et al., 2010a, 2010b; Na et al., 2012). For

example, sweeping the input frequency to derive frequency response functions can provide

quantifiable measures of the joint condition (Shin et al., 2012).

More direct measurements of the joint condition can also be made by integrating

sensors directly into the adhesive layer, as long as the sensors do not degrade the

performance of the joint. In particular, fiber Bragg gratings have been applied extensively

due to the possibility to embed a dense array of sensors and their unique sensitivity to

nonuniform strain fields such as those induced by damage in the adhesive layer (Jones et al.,

2002; Herszberg et al., 2005; McKenzie et al., 2000; Silva-Munoz et al., 2009; Ning et al.,

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2012; Bernasconi et al., 2011). Jones et al. (2002) and Bernasconi et al. (2011) observed the

effects of local strain gradients due to cracking in the adhesive layer, resulting in spectral

distortion of the FBG reflected spectrum. The presence of such strain gradients was verified

through finite element analyses and ultrasonic and thermo-elastic measurements. These

results were later expanded by Murayama et al. (2012) who included the large displacements

and elastic-plastic behavior of the joint adhesive in the finite element models to further refine

the strain field calculations along the length of the FBG sensor array, again confirmed with

experimental measurements.

A second approach has been to pre-chirp the fiber Bragg grating, inducing a wide

spectral response bandwidth before it is loaded, and then use the correspondence between the

spectral bandwidth and the physical bonded length of the sensor to actually locate damage

(Okabe et al., 2004; Palaniappan et al., 2007; Palaniappan et al., 2005; Takeda et al., 2003).

Palaniappan et al. (2008) successfully monitored disbond initiation and growth due to cyclic

fatigue in adhesively bonded composite lap joints within a chirped FBG embedded in a single

composite laminate adherent. The experimental measurements were modeled using finite

elements and were found to agree well with the numerical simulations, leading the authors to

conclude that the embedded chirped FBG was capable of predicting the disbond front with a

precision of 2 mm.

However, one commonality between these FBG sensor applications is that the

measurements were made under a static applied tensile load. In other words, these

measurements could not be made in-flight and do not take advantage of the high sensitivity

of the joint structural dynamics to the presence of damage. Xiacong et al. (2012) conducted

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numerical and experimental vibration-based tests to measure the dynamic response of single

lap joints. Experimental measurements agreed well with finite element analyses to predict the

natural frequencies, mode shapes, and frequency response functions however conclusions

were limited to correlating an increase in adhesive bond line thickness to increasing

structural damping. A large body of previous work has also demonstrated the complex

behavior of composite structures in dynamic environments where the response to harmonic

excitation can often be nonlinear (Ribeiro et al., 2006; Balachandran et al., 1990; Carpinteri

et al., 2005) and involve complex strain fields (Challita et al., 2012; Vaziri et al., 2002; Sato

et al., 2009).

The major barrier to applying the embedded FBG sensor measurements under

dynamic loading has been that the presence of spectral distortion, which gives the sensors

their unique sensitivity, also presents a challenge when collecting the needed spectral data at

sufficiently high data acquisition rates. In this chapter, we apply a recently developed

dynamic full-spectrum FBG sensor interrogator to the measurement of the spectral response

of the FBG sensor embedded in a lap joint, during dynamic loading. We demonstrate that the

use of the full spectrum interrogator eliminates response errors due to the spectral distortion

and permits the dynamic analysis of the sensor response. The lap joint is excited with a

multicomponent harmonic excitation in the frequency range typically experienced in flight.

We demonstrate that the dynamic response of the lap joint as it progresses from linear to

nonlinear to potentially chaotic behavior, with increasing fatigue damage, can be determined

strictly from the FBG sensor response. In a Chapter 6, the lap joint dynamical behavior with

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fatigue-induced damage is simulated and the correlation of the behavior, experimentally

measured through the FBG sensors, to the presence of the damage states verified.


This section describes the fabrication of bonded composite lap joint specimens with

FBG sensors embedded in the adhesive bond and fatigue loading of these specimens. In-

between fatigue cycle blocks, a multiple frequency harmonic excitation was applied to the

specimens, to simulate an in-flight environment, during which time the full-spectral response

of the FBG sensors was measured using the unique, high-speed full-spectral interrogator

shown earlier in Figures 2.2 and 2.3 in Chapter 2. The harmonic excitation and FBG

interrogation are also described in this section.

All lap joint specimens consisted of four adherends each fabricated using eight layers

of 2x2 twill woven carbon fiber prepreg (Advanced Composites LTM22/CF0300). Each

lamina was sized 25.4 cm x 27.94 cm, oriented with the 0˚ direction of the prepreg material.

Prior to the lamina layup, a layer of Mylar vacuum bag, two layers of breather sheets, and a

single layer of peel ply was placed on a 30.48 cm x 30.48 cm aluminum plate. Each lamina

was sequentially stacked on top of each other, aligned with the 0˚ orientation, and covered by

peel ply, breather sheet, and Mylar, as the top layer. The edge of the vacuum bag was sealed

using plumber’s putty and a vacuum drawn out. An additional aluminum plate was used to

cover the top Mylar sheet and to evenly distribute the pressure during the curing process.

The bulk specimen was placed in a hot press, preheated to 50 ºC and pressurized at a

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constant pressure of 8.27 MPa. The applied temperature profile consisted of 15 minutes at

50 ºC, 15 minutes at 65 ºC, and 180 minutes at 80 ºC, followed by 30 minutes with the

heating elements off, allowing the specimen to cool. After the four hour curing cycle, the

specimen was removed from the hot press and allowed to continue cooling to room

temperature. The eight-layer CFRP laminate was then cut to 2.54 cm x 10.16 cm pieces using

the Felker TM-75 tile saw shown in Figure 5.1.

The laminate surfaces were prepared for joining by sanding and cleaning each

adherend with Al2O3 60 grit sandpaper and isopropyl alcohol. The four adherends were

joined using Hysol EA-9394 structural aerospace paste adhesive. A drywall scraper was used

to evenly distribute the adhesive to ensure a uniform bondline thickness. A polyimide coated

optical fiber containing a single, 10 mm long FBG sensor was embedded within the adhesive

layer of each lap joint during this process. After the FBG was embedded, the lap joints were

placed in the hot press at 66 ºC for one hour, and then removed for 24 hours and allowed to

cool to room temperature. A total of 40 specimens were fabricated for testing, although some

did not include embedded sensors and were used for preliminary testing of the fatigue life of

the lap joint. The final dimensions of the composite lap joint are shown in Figure 5.2(a) and

follow the ASTM D3165 standard for single lap joint testing. A micrograph of an embedded

FBG sensor is shown in Figure 5.2(b) and indicates an adhesive bond line thickness of

approximately 100 micrometers. It can be seen that there is a large contact area between the

top and bottom adherends and the embedded sensor, which implies that there will be good

shear load transfer to the sensor during tensile loading of the lap joint.

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The goal of these experiments was to measure and analyze the response of the

embedded FBG sensor to vibration induced loading at different levels of fatigue damage in

the lap joint. To induce realistic fatigue damage in the lap joints, we applied low-cycle

fatigue loading to accumulate damage at the adhesive layer of the composite lap joint. Using

an Instron servohydraulic fatigue testing machine, a load-controlled, fully-reversed cyclic

loading was applied to the composite lap joint with a frequency of 3 Hz and blocks of 200

cycles. After each 200 cycle loading block, the lap joint was removed from the fatigue

testing machine to perform a measurement of the FBG full-spectral response during static

and harmonic loadings, as described in the next section. Pulse phase thermography images of

the lap joint were also collected immediately after the lap joint was removed from the fatigue

testing machine, to independently measure the damage condition in the joint. The lap joint

was then remounted in the fatigue testing machine for further cyclic loading. The cyclic

loading and FBG sensor measurements were repeated until the lap joint failed or the signal to

noise ratio of the FBG sensor was too low. To ensure that the lap joints did not prematurely

fail, the peak-to-peak amplitude of the cyclic loading was determined based on an initial

tension to failure test of three lap joint specimens. The displacement-controlled tests were

conducted at a rate of 0.5 mm/minute until the lap joint failed by brittle fracture at the

adhesive layer. The resulting peak amplitude for the cyclic testing was chosen to be 445 N,

approximately 13% of the maximum load supported by the specimens.

A vibration platform was designed and fabricated on which a uniaxial tension loader

was mounted. The tension loader was designed to be mounted directly on the vibration

loading platform to apply a pretension load on the composite lap joint after fatigue loading

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(Webb et al., 2013a; Ceniceros et al., 2001). To enact a pretension load on the lap joint, a fine

threaded machine bolt was inserted into the assembly and torqued by two full turns,

equivalent to 2 mm axial translation of the nut. The single-axis vibration platform was

constructed of a stainless steel 61 cm x 61 cm x 6.1 cm optical breadboard with a honeycomb

core (ThorLabs PBH11105), mounted on a single-axis pillow-block assembly, as shown in

Figure 5.3. The breadboard was actuated by a piezo-electric (PZT) stack actuator (PI P-

840.40) mounted below the vibration platform. The stroke range and push force of the

actuator at full power and oscillation was 60 microns +/-20% and 1000 N, respectively. The

motion of the board was constrained to small displacements using two adjustable turnbuckle-

spring biases on each side of the platform. A low-voltage PZT amplifier provided a 50 V DC

offset voltage to the PZT stack. The PZT stack was driven by a function generator at an

excitation frequency of 150 Hz and peak-to-peak amplitude of 6 V.

The forced-response of the vibration platform, induced by the PZT-excitation, was

previously characterized using an accelerometer with a sensitivity 100 mV/g (PCB

Piezotronics C33), mounted directly to the breadboard (Webb et al., 2013a). The periodic

motion can be seen in the raw voltage data of the accelerometer output plotted for a period of

10 milliseconds originally shown in Figure 4.3 in Chapter 4. While the excitation was at a

single fixed frequency, the response of the vibration platform is defined by a summation of

multiple modes and higher harmonics, as seen in the fast Fourier transform (FFT) of the

accelerometer output in Figure 4.3(b) (calculated over a longer window than that shown in

Figure 4.3(a)). A sampling rate of 100 kSa/s was used for the accelerometer, well above that

to avoid frequency aliasing. It is clearly seen the excitation frequency transmits to the

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vibration platform, at f0 = 149.8 Hz. The next five harmonics also appear in the data at

approximately 300 Hz, 450 Hz, 600 Hz, 750 Hz, and 900 Hz, although the fifth harmonic at

750 Hz is not much above the noise level. Some additional frequency components appear

around 400, 500 and 950 Hz which may be due to cross-talk between the other frequency

components or resonance frequencies of the board. This behavior is ideal for emulating a

realistic vibration environment in which FBG sensors are typically exposed.

In between each fatigue loading block of 200 cycles the lap joint was loaded in the

following 6 steps, during each of which the FBG sensor response was measured for

approximately 300 milliseconds:

1) The lap joint was mounted in the loading frame without pretension or added

vibration;

2) The PZT actuator was activated at a fundamental frequency of 150 Hz ;

3) The PZT actuator was turned off and the lap joint was pretensioned;

4) The PZT actuator was activated while the lap joint was pretensioned;

5) The lap joint was unloaded and the PZT actuator was turned off;

6) The PZT actuator was activated;

The pretension magnitude was 50% of the lap joint axial loading capacity and was the same

for all experiments. In this manner, the FBG response was measured with and without

vibration immediately after the fatigue loading, with potentially added damage due to the

pretension load, and in the residual stress state after the pretension was removed.

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The intensity spectra for each FBG sensor was collected at a spectral acquisition rate

of 100 kHz (with a wavelength resolution of 84 pm) and wavelength range of 1559.5 to

1566.2 nm. A second-order Chebyshev stop-band filter was applied to each data set prior to

processing the time-varying data to eliminate periodic noise that appeared in the measured

optical power. For these experiments, only the peak wavelength shift of the FBG sensor was

required, from which the dynamic response of the lap joint will be determined. However, the

presence of multiple strain components and non-uniformities in strain fields creates peak-

splitting in the FBG spectral response which can lead to erroneous dynamic response

measurements (Webb et al., 2011). Therefore, we measured the full-spectral dynamic

response of the FBG sensors and then calculated the peak-wavelength shift from this full-

spectral response. The peak wavelength of the dynamic measurements was extracted by

following the primary peak in the static full-spectral measurement conducted before the

transient measurement, independent of its intensity relative to the other peaks. This method

was chosen because it closely resembles the algorithm used for a conventional peak follower.

5.3 FATIGUE RESPONSE OF THE SINGLE LAP JOINT SPECIMENS

To estimate the appropriate maximum load to be applied during fatigue loading,

several uniaxial tests until failure were conducted on representative lap joint specimens. The

load-displacement results from the three specimens are shown in Figure 5.4. The curves

indicate the same initial joint stiffness, but diverge from each other rapidly. The load at first

failure and maximum load for each specimen varied considerably, presumably due to the

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manual manufacturing process. Specimen 1 represented the best specimen fabrication, since

differences in adhesive bond thickness or regions with improper adhesion reduce the

maximum shear load that a lap joint can support. This measured response of Specimen 1 will

be verified numerically in Chapter 6. The differences in specimen stiffness also indicate

expected differences in fatigue life between specimens. The maximum shear load capacity of

the lap joint was calculated to be 3.4 kN by averaging the maximum shear load reached in

each of the three tests. The corresponding average maximum shear stress of the three

specimens was found to be 10.54 MPa. The peak-to-peak amplitude was therefore set for all

future fatigue loading to 0.445 kN, 13% of the maximum shear load capacity. This amplitude

represents low-cycle fatigue which is characterized by the plastic deformation of the

adhesive, due to the relatively high magnitude of stress. By contrast, high-cycle fatigue is

normally conducted with much lower stress amplitudes that introduce predominantly elastic

deformation. The goal of this work is to replicate the complex strain state when accumulated

damage is governed by fatigue-induced plasticity at the adhesive layer.

The measured envelope and mean value per cycle of the load-controlled constant

amplitude input is shown in Figure 5.5(a). Because we conducted full-spectral measurements

of the embedded FBG sensor during excitation in increments of 200 cycles of fatigue of the

lap joint the envelopes are discontinuous. We observe a slight decrease in peak-to-peak

amplitude (see Figure 5.5(a)) and a change in the mean crosshead displacement curve (see

Figure 5.5(b)) with increasing fatigue cycle, due to residual stain at the end of each cycle.

This change in load and displacement envelopes was not considered a problem since the goal

was to enact a realistic damage mode upon the lap joint and not perform material

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performance testing. The load vs. displacement response for one of the lap joint specimens is

plotted for two representative load cycles in Figure 5.6, one early and one late in the fatigue

testing. By comparing the hysteresis plots, it is observed that the stiffness of the lap joint

decreased with increasing cyclic loading, as expected.

Pulsed phased thermography imaging was also used as an independent measurement

of the fatigue-induced damage in-between fatigue cycle blocks. Details of the pulsed phase

thermography imaging process can be found in Shin et al. (2013). Pulsed phase images of a

representative lap joint specimen are shown at different stages of fatigue life in Figure 5.7.

This same specimen will later be used for comparing the FBG sensor results in Sections 5.4-

5.5. Regions of high phase contrast are indicators of delamination or poor bonding within the

specimen. The region of high phase contrast on the left-hand side of the specimen appearing

before fatigue loading was applied and was due to insufficient resin distribution during cure,

visible from the side of the specimen. This defect was located in the grips when the specimen

was loaded in cyclic loading, and therefore did not affect the performance of the joint. A

second fabrication defect approximately 15 mm in diameter at the top edge of the joint to the

left of the overlap shear area is also visible in Figure 5.7(a). After 200 cycles of fatigue the

lap joint accumulated damage around this preexisting defect, as shown in Figure 5.7(b). The

defect grew to approximately 33 mm in diameter and spanned across the length of the

overlap shear area. In the later images (Figures 5.7(c-d)), the damage region in the overlap

shear area remained approximately the same. Figures 5.7(c) and (e) were obtained

immediately after residual tension was applied to the specimens on the vibration-loading

platform. This residual tension temporarily increased the phase contrast in the overlap shear

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area. The pulsed-phase images then indicate a momentary relaxation in the phase contrast of

the defect regions after the fatigue loading. Visual inspection of these pulsed phase images

and those of other the specimens, confirmed that fatigue damage typically started from pre-

existing defects, increased with fatigue cycles and created a highly non-uniform strain state

in the shear overlap region. This non-uniform strain state will create distortion in the later

FBG sensor spectral measurements and emphasizes the need for full-spectral interrogation of

these FBG sensors during the dynamic loading cases.

5.4 RESIDUAL FBG RESPONSE TO FATIGUE AND PRETENSION LOAD

We now consider the static and dynamic response of the FBG sensors embedded in

the adhesive bond. As described in Section 5.2, full-spectral data from the FBG sensors was

collected immediately after each fatigue loading cycle block, during pre-tensioning of the

joint and during excitation of the specimen. The static full-spectral FBG response is shown

for a single specimen, Specimen 1, after chosen fatigue loading blocks in Figure 5.8. This

specimen survived 2201 cycles of fatigue. The FBG response is plotted for three different

loading conditions: immediately after cyclic fatigue, during the static pretension loading, and

after this pretension was released. It is evident that both cyclic fatigue and axial pretension

loading caused changes in the local stress state of the FBG resulting in wide variations in the

full-spectral response.

In Figure 5.8(a), after 600 cycles the spectral response was no longer uniform and

indicates two dominant peaks. Once the lap joint was tensioned, the full-spectral FBG

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response represents a broadened, multi-peak spectrum often associated with complex strain

fields, consistent with the observations of previous authors (Jones et al., 2002; Bernasconi et

al., 2011; Murayama et al., 2012). The spectrum indicates two considerably smaller peaks

separated by approximately 2.1 nm. The release of this tensioned state indicates a return to a

narrow, but still multi-peak spectrum. After 600 cycles of fatigue, differences in the spectral

response of the post-fatigue and post-tensioned (residual) state indicate that damage was

accumulated at the adhesive layer due to the low-cycle fatigue and was further accumulated

due to the tension loading. After 1000 cycles of fatigue, the static full-spectral FBG response

began to transition to a nearly uniform shape immediately after fatigue, as shown in Figure

5.8(b). Once tensioned, the spectrum diminished in peak intensity and broadened to form two

peaks in much closer proximity than previously observed in Figures 5.8(a). After 1600 cycles

of fatigue, the FBG response had completely returned to a uniform reflection after fatigue

and tensioning as shown in Figure 5.8(c). This return to a uniform state indicates the sensor

was relieved from the complex strain field and was therefore likely debonded from the

composite adherends.

5.5 FREQUENCY RESPONSE OF EXTRACTED PEAK WAVELENGTH

Nonlinear dynamic responses in composite structures have been attributed to several

different sources including the external excitation frequency (Ribeiro et al., 2006), amplitude

of excitation (Singha et al., 2009; Baghani et al., 2011; Wu et al., 2006), and random material

properties (Chandrashekhar et al., 2010). A linear dynamic system is characterized by

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constant natural frequencies and vibrates at frequencies of an externally applied harmonic

excitation. In contrast, a nonlinear system under harmonic excitation vibrates at frequencies

other than those externally applied (Pai et al., 2007). For example, Ribeiro et al. (2006)

numerically demonstrated that if a static compressive force is applied to a composite plate,

slightly varying the frequency of harmonic excitation results in a nonlinear response

characterized by the appearance of subharmonics and chaotic motion. For a system that does

not demonstrate nonlinearities in an initial state, Pai et al. (2007) concluded that even under

small vibrations the dynamic response of a structure can be nonlinear as the result of

sustained damage. As the vibration amplitude and frequency inputs remained the same for all

tests in this work, we can therefore relate the changes in system dynamic behavior to the

presence of fatigue induced damage.

Once the peak wavelength information was extracted from the full-spectral

measurements, we conducted spectral frequency analyses on the measured signals. The fast

Fourier transform (FFT) was first computed to get an averaged-sense of the frequency

components that exist within the dynamic signal. Afterwards we calculated the short-time

Fourier transform (STFT) by discretizing the time signal into small, equal-length windows to

compute the FFT. The STFT yields insight as to whether there are transient behaviors in the

sensor dynamic response. Figure 5.9(a) depicts the raw full-spectral data recorded during

excitation of the lap joint. The peak wavelength was set to be the peak of maximum intensity

in the static full-spectral measurement before excitation and then followed in the dynamic

full-spectral data, as shown in Figure 5.9(b). For all STFT computations an 8 ms Hamming

window with 50% overlap was used (shown in Figure 5.9(b)), yielding the optimal balance in

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both the time and frequency domains. The windowed data from the initial 8 ms time

increment is shown in Figure 5.9(c). Finally, the STFT computation for the entire peak

wavelength data set is shown in Figure 5.9(d).

The loading state of the lap joint during each measurement has been provided in

Tables 1 and 2, respectively, with the corresponding FFT and STFT obtained at these loading

states plotted in Figures 5.10 and 5.11. Specimen 1 was first exposed to 200 fatigue cycles.

As shown in Figure 5.10, case A, the peak wavelength signal indicates very poor

transmission of the excitation frequency of 150 Hz. As found in Webb et al. (2013a) this is to

be expected due to the low sensitivity to vibration at the Bragg peak, we would expect much

higher transmission of the excitation frequency, and the corresponding harmonics, if the

analysis was applied at the edge of the spectral band. However, as the spectral band later

distorted, we used the peak wavelength for analysis. The lap joint was then subjected to a

static pretension load, released, and exposed to excitation. During the entire acquisition time,

the peak wavelength vibration characteristics are obscured by the dominant 0 Hz mean

frequency as shown in Figure 5.10, case B. After pretension was reapplied (see Figure 5.10,

case C) a low, but observable, 850 Hz component in the transient signal appeared in the

STFT at approximately 130 ms. This and other frequency peaks at approximate harmonics of

the excitation signal appear in cases D and E.

A transition from linear to non-linear behaviors can be identified by several features

in the STFTs for later FBG sensor measurements as the fatigue cycles were increased and

damage of the lap joint progressed. These are shown in Figure 5.11, cases F through J. The

first feature is the transient behavior of the resonant frequencies. After 800 cycles of fatigue,

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the FFT indicates strong resonances at 150 Hz, 450 Hz, and 850 Hz as shown in Figure 5.11,

case F. However, the time-dependent nature of these harmonic responses is better represented

in the corresponding STFT. The 850 Hz component is strongest at approximately 90 ms into

the acquisition time, whereas the 150 and 450 Hz components are intermittent throughout the

time signal. This behavior continues to be more evident in the later cases G through J.

Secondly, sub-harmonic components appear in the response of strongly nonlinear structures

(Carpinteri et al., 2005). These are harmonic components below the primary excitation

frequency of 150 Hz. These sub-harmonic components are particularly visible in Figure 5.11,

cases G and H near 75 Hz. Finally, we observe the transition from a quasi-periodic response

with finite frequency components related to the excitation harmonics to aperiodic motion

with broadband frequency components again indicative of a nonlinear system (Touze et al.,

2011). For example, the resonant frequency near 900 Hz visible in case F, decreases in

frequency reaching a frequency closer to 750 Hz in case J. We also observe that the

bandwidth of this resonance condition between 750 and 900 Hz increases through cases G

through J.

Similar loading was applied to a separate specimen, Specimen 2, to verify the

previous results and to correlate changes in the FBG sensor response with the pulsed-phase

thermography measurements of Figure 5.7 (from the same specimen). Specimen 2 survived

600 cycles before failing after being loaded in a pretensioned state. The FFT and STFT

calculated from the FBG data for Specimen 2, obtained at the loading cases listed in Table 2,

are shown in Figure 5.12. Again, early in the lap joint lifetime (cases B-D) the harmonics of

the excitation frequency are present in the FFT but with low visibility, indicating a relatively

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linear response. In Figure 5.12, case E, the dynamic response to the harmonic excitation is

plotted after 400 cycles under the applied tensile load. As for the previous specimen, the

tension loading increases the visibility of the multiple frequency components, as compared to

case D. In case E we observe multiple frequency components in the FFT and STFT as well as

the beginning of sub-harmonic components below 150 Hz. Finally, the dynamic response is

fully nonlinear in case F, after 600 fatigue cycles, demonstrated by the wide bandwidth of

frequency components and their transient behavior, indicating a transition towards chaotic

vibration. Specimen 2 failed in the next block of applied fatigue cycles after the

measurements shown in case F.

The formation of a broad bandwidth of frequencies that are transient in nature in both

specimens strongly suggests accumulated damage at the adhesive layer of the composite lap

joints. To verify this argument, we observe the embedded FBG sensor in Specimen 2 was

embedded near an irregular shaped defect at the adhesive layer, present after fabrication that

gradually progressed across the overlap shear area with increasing fatigue cycles, seen in the

pulse-phase thermography measurements in Figure 5.7. This increasing damage area

resulted in the non-uniform strain distributions, creating the static spectral distortion shown

in Figure 5.8. At this point we can conclude that the nonlinear dynamic behavior of the FBG

sensor was also due to the presence of the complex strain field and the nonlinear dynamic

behavior of the lap joint itself, and can therefore be used as an indicator of progressive joint

damage for structural health monitoring applications. A numerical verification of the role of

the damage on the nonlinear response of the lap joint and therefore the FBG sensor is

provided in the Chapter 6.

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5.6 PHASE PLANE REPRESENTATIONS

In this section, we calculate the phase plane representation of the FBG peak

wavelength measurements to further demonstrate the importance of the proper extraction of

the peak wavelength from full-spectral data. The phase plane diagram obtained from the FBG

data is plotted for two measurements from Specimen 1 in Figure 5.13. The phase plane

diagrams were calculated by mapping the shift in peak wavelength versus the relative

wavelength shift velocity. The spacing between data points on the horizontal axis is 0.02 nm

and is the discrete resolution of the analog-to-digital converter used. Similarly, the spacing

on the vertical axis is 2 x 10-7

nm/s, which corresponds to the digital filter resolution divided

by the 100 kHz data acquisition rate.

In Figures 5.13 (a) and (c), the peak wavelength data was extracted by choosing the

wavelength at maximum intensity. In these cases, the phase state is localized at four different

locations within the phase plane, with wavelength shifts up to 1.0 nm, typical of a system

with a quasi-periodic response. The spacing between these four regions has significantly

decreased between Figures 5.13 (a) and (c). In contrast, the peak wavelength data in Figures

5.13 (b) and (d), were extracted for the same two loading cases by following the primary

peak, as described earlier. For these cases, the phase state is localized within a single, narrow

region of the phase plane, typical of a system with a linear response. The difference in the

phase plane representations for the same loading cases is due to the multiple-peak FBG

reflected spectrum with near-equal intensities. Slight variations in strain or the presence of

noise often create wavelength hopping in the experimental FBG data which led to the

erroneous phase plane representations in Figure 5.13 (a) and (c). A 1 nm peak wavelength

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shift, as seen in these cases, would correspond to an extremely large strain developing in the

adhesive and therefore falsely indicate imminent failure of the joint. In fact, the regions in

Figures (b) and (d) are subsets of the phase plane diagrams in Figures (a) and (c).

5.7 DYNAMIC FULL-SPECTRAL INTERROGATION

As a final note, we present measurements of the dynamic full-spectral FBG response

after incremental stages of fatigue damage endured by the lap joint. The dynamic full-

spectral measurements are shown in Figure 5.14. The peak wavelength used for frequency

analyses shown in previous sections are a subset of the raw full-spectral data shown. The

total accumulated fatigue loading applied before each measurement was conducted is shown

for Specimen 1 in Table 5.1. The intensity spectra for the FBG sensor was collected at a

spectral acquisition rate of 100 kHz (with a wavelength resolution of 84 pm) and wavelength

range of 1559.5 to 1566.2 nm. All color mappings are normalized to the peak of maximum

intensity for the entire data set shown. For each data set shown, 6 ms of the static full-

spectral response is shown, followed by 50 ms during vibration, and finally 6 ms after the

full-spectral information is digitally filtered by a conventional 2nd

-order Butterworth

stopband filter. The stopbands were designed to be narrow and placed at the driving

frequency of 150 Hz and each of the higher harmonics in the excitation signal. The filter

frequency response can be found in Chapter 4. As to be expected of a transient signal, the

static harmonic-specific filter does not remove all dynamic contributions of the signal as

shown in the last 6 ms of each data set in Figure 5.14. Also, the fast Fourier transform (FFT)

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is computed across the full-spectrum of the FBG response and is shown as a color mapping

in Figure 5.15. All color mappings are normalized to the maximum of the data set shown

corresponding to the 0 Hz mean frequency (0 dB).

We acknowledge that transient behavior in the peak wavelength signal found earlier

by the STFT exists across the full-spectrum with varying sensitivity. The sensitivity is the

least at each of the multiple peaks that exist in the highly distorted FBG spectrum. Future

work will look into analyzing the rich information contained in the full-spectral distortion.

5.8 CONCLUSIONS

The change in dynamic response of a lap joint with progressive fatigue-induced

damage was directly measured through a fiber Bragg grating (FBG) sensor embedded in the

adhesive layer of the lap joint. The full-spectral information avoided dynamic measurement

errors often experienced using conventional peak wavelength and edge filtering techniques.

The dynamic response of the FBG sensor indicated a transition to strong nonlinear behavior

as fatigue-induced damage progressed. STFTs computed from the extracted peak wavelength

information revealed time-dependent frequencies and amplitudes of the dynamic FBG sensor

response. The eventual aperiodicity of the transient signal suggested a transition into a quasi-

periodic state followed by chaos, represented by a broad bandwidth of frequencies

unassociated with the externally applied excitation. Pulse-phase thermography images

verified the progression of accumulated damage across the lap joint as a function of cyclic

fatigue and indicated non-uniformity in the shape of the defect impinging on the embedded

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FBG sensor. Finally, calculating the phase plane representations of the dynamic peak

wavelength signals highlighted the importance of properly extracting the peak wavelength

information from full-spectral FBG sensor dynamic measurements. The full-spectral,

dynamic measurements reveal the need for future work to assess the rich information

contained in the spectral distortion during dynamic environments. The ability to measure the

dynamic response of the lap joint through sensors embedded in the adhesive layer can

provide in-situ monitoring of the lap joint condition.

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Figure 5.1 Composite adherends for lap joint fabrication, prior to cutting.

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Figure 5.2 (a) Dimensions of composite lap joint made in accordance to standard ASTM D3165. (b) Micrograph of embedded FBG sensor.

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Figure 5.3 Photograph of vibration platform and lap joint mounted in the tensile loader.

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Figure 5.4 Experimentally measured load-displacement curves during tensile loading of lap joint specimens.

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Figure 5.5 (a) Fully-reversed cyclic controller input. (b) Measured crosshead displacement curve.

Data was not recorded between 400 and 600 cycles.

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Figure 5.6 Hysteresis diagram for two representative cycles of lap joint specimen fatigue life. Cyclic

direction is indicated by arrows.

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Figure 5.7 Pulsed-phase thermography phase angle images for single specimen after different fatigue

loading cycles. Number of applied fatigue cycles is indicated on each figure. Figures (c) and (e) were obtained after static tension was applied to specimen.

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Figure 5.8 (a) Measured full-spectral FBG response immediately after 600 cycles of fatigue (left) and

during pretensioning and release (right). Same measurements after cycles (b) 1000 and (c) 1600.

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Figure 5.9 (a) Raw full-spectral data from Specimen 1 after 1000 cycles of fatigue loading. Color

scale corresponds to reflected intensity with red as maximum intensity. (b) Peak wavelength data shown with two consecutive 8 ms Hamming windows with 50% overlap. (c) Windowed data used for

FFT computation of first discrete time increment. (d) STFT computed for entire data set.

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Figure 5.10 STFT (left) and FFT (right) computed for extracted peak wavelength information after

each fatigue loading block shown for Specimen 1.

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121



123

Figure 5.13 Phase plane representations of FBG measurements from Specimen 1: after 200 cycles

using (a) peak intensity values and (b) corrected peak wavelengths; and after 600 cycles using (c) peak intensity values and (d) corrected peak wavelengths.

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Figure 5.14 Full-spectral measurements shown for fatigue damage cases (A-J). For each case, 6 milliseconds of the static spectra are shown followed by 50 millisecond acquisition during vibration,

and finally 6 milliseconds of the harmonic-specific stopband digitally filtered spectra.

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Figure 5.15 FFT computations shown across the full-spectrum of wavelengths in the FBG sensor

response for each fatigue loading case of Specimen 1 (A-J).

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Table 5.1 Definition of measurement states for Specimen 1 after different fatigue cycles and loading

conditions.

Measurement Fatigue Lifetime

A 200 cycles

B 200 cycles after tension

C 200 cycles during tension

D 400 cycles during tension

E 600 cycles after tension

F 800 cycles

G 800 cycles after tension

H 1000 cycles

I 1000 cycles after tension

J 1600 cycles after tension

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Table 5.2 Definition of measurement states for Specimen 2 after different fatigue cycles and loading

conditions.

Measurement Fatigue Lifetime

A 0 cycles

B 200 cycles

C 200 cycles after tension

D 400 cycles

E 400 cycles after tension

F 600 cycles

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CHAPTER 6

CHARACTERIZATION OF FATIGUE DAMAGE

IN COMPOSITE LAP JOINTS—SIMULATIONS

In this chapter we simulate the response of fiber Bragg grating sensors embedded in

the adhesive layer of a composite lap joint, as the joint is subjected to harmonic excitation.

To simulate accumulated fatigue damage at the adhesive layer, two forms of numerical

nonlinearity are introduced into the model: (1) progressive plastic deformation of the

adhesive and (2) increasing the boundary of an interfacial defect at the adhesive layer across

the overlap shear area. The simulation results are compared with previous measurements of

the dynamic, full-spectral response of such FBG sensors for condition monitoring of the lap

joint. Short-time Fourier transforms (STFT) of the locally extracted axial strain time

histories reveal a transition to nonlinear structural behavior of the composite lap joint by

means of intermittent frequencies that were observed in the experimental measurements and

are not associated with the external excitation. The simulation results verify that the changes

in measured dynamic FBG responses are due to the progression of damage in the lap joint.

These results can be found in a paper recently submitted by the authors (Webb et al., 2013c).

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6.1 INTRODUCTION

In Chapter 5, the fatigue damage of a composite lap joint was monitored using full-

spectral interrogation of fiber Bragg grating sensors embedded at the adhesive layer. During

full-spectral interrogation of the FBG sensor at 100 kHz, the lap joint was excited with a

multicomponent harmonic excitation in the frequency range typically experienced in flight.

As damage progressed, spectral frequency analyses of collected FBG sensor data

demonstrated a transition from a linear vibration structural response to a transient response

including intermittent vibration frequencies not associated with the external excitation.

These experiments demonstrated that the dynamic response of the lap joint as it progresses

from linear to nonlinear, to potentially chaotic behavior, due to the presence of increasing

fatigue damage, and that this behavior can be determined strictly from the FBG sensor

response. The goal of this chapter is to simulate the dynamic behavior of the lap joint, and

the resulting FBG sensor response, and verify that changes in the FBG behavior are in fact

due to the presence of fatigue induced damage.

A review of analytical and numerical modeling of adhesively bonded composite lap

joints can be found in Banea et al. (2009). Most previous works have focused on predicting

the strength or failure of the bonded joints subjected to different loading conditions. The

challenge in these models is to accurately represent the behavior of the adhesive and its

interface to the adherends. For example, a fracture mechanics approach by calculating the

local energy release rate at the tip of a predisposed crack in the adhesive as is often applied to

predict the growth of failure (Hutchinson et al., 1992). Alternatively, other researchers have

applied a local damage modeling or the cohesive-zone approach, including the effects of

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adhesive-adherend interfacial behavior, to simulate the damage progression (Needleman et

al., 1987; Ungsuwarungsri et al., 1987; Tvergaard et al., 1992). However, for this work we

apply a continuum mechanics approach, assuming a perfect bond between the adhesive-

adherend interface (Harris et al., 1984; Adams et al., 1986; Crocombe et al., 1990) since the

failure criteria are not included. We implement a finite-element model to simulate the

forced-vibration response of the composite lap joint to confirm that the presence of

nonlinearities are due to the introduction of fatigue induced damage. From the results of

Chapter 5, damage is accumulated at the adhesive layer of the lap joint by means of

incremental low-cycle fatigue loading. The large stresses experienced during loading

suggests that local plastic deformation occurs as a result of softening of the adhesive layer.

Additionally, matrix cracking and interfacial fracture is observed near and around the FBG

sensor in post-mortem images of the fracture surface. Therefore, we introduce two separate

forms of numerical nonlinearity into our model: a nonlinear material response in the adhesive

and an interfacial defect across the joint overlap experimentally measured using pulsed-phase

thermography. From these models the short-time Fourier transform (STFT) is calculated

from extracted axial strain time histories and signatures of damage from this response as

nonlinearities are introduced are compared to the previous experimental results.

6.2 NUMERICAL SIMULATION METHODS

This section describes the numerical modeling process used for simulation of the

composite lap joint. We used a commercial numerical finite-element solver (ANSYS 12.1) to

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model the lap joint with the goal of attributing variations in the structure’s dynamic

properties near the FBG sensor to progressions of damage as fatigue increases. To accurately

assess the information gained from the simulations, several preliminary analyses were

conducted including transient modeling of experimental pull tests and a convergence modal

analysis to determine the optimal mesh refinement. Once these simulations were conducted a

thorough assessment of the forced-vibration response of the lap joint was performed.

The dimensions of the composite lap joint are shown in Chapter 5, and follow the

ASTM D3165 standard for single lap joint testing. The model geometry and refined mesh are

shown in Figure 6.1. The three-dimensional (3D) model mesh was generated using 8-noded

SOLID45 brick elements to simulate both the multi-linear elastic paste adhesive and the

linear elastic carbon fiber-epoxy adherends. A structured mesh was used when possible,

however, irregular shaped boundaries created while simulating the interfacial defect required

free element meshing and optimal refinement at the adhesive layer. The adhesive bond line

thickness of approximately 100 micrometers (as measured from microscopy images of the

specimens) required further refinement at the adhesive layer, as seen in Figure 6.1, which

increased computational costs but ensured model convergence.

All lap joint specimens consisted of four adherends each fabricated using eight layers

of 2x2 twill woven carbon fiber prepreg (Advanced Composites LTM22/CF0300). The four

adherends were joined using Hysol EA-9394 structural aerospace paste adhesive. The

orthotropic material properties of the 2x2 woven twill carbon fiber prepreg are listed in Table

6.1. The multi-linear elastic stress-strain curve of the paste adhesive used for the simulations

was extracted from a Sandia National Laboratory report (Guess et al., 1995) and is shown in

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Figure 6.2. It is observed the paste adhesive is highly elastic up to 3% strain and then begins

to yield and experiences plastic deformation thereafter. The small strain linear elastic

Young’s modulus of the Hysol EA-9394 paste adhesive is reported as 4.136 GPa with

Poisson’s ratio of 0.37.

Once the 3D model was meshed and confined by fixed-free boundary conditions, a

transient analysis was performed to simulate lap shear tests (pull tests) of the composite lap

joint. To accurately simulate the experiments a displacement-based boundary condition at a

rate of 0.5 mm / minute was placed on an area 25.4 mm x 12.7 mm on both adherend faces

on one end of the lap joint to match the clamped area used in the tensioning machine. Rigid

body motion was then prevented by applying fixed boundary conditions at the opposing end

across the clamped area. The resultant load on the specimen endfaces and the relative

displacement between the endfaces was calculated at each displacement step for comparison

with the measured load-displacement curves. The boundary and loading conditions applied

for each simulation are shown in Figure 6.3.

The free-vibration response of the composite lap joint was then simulated by

conducting a modal analysis so that the natural frequencies and mode shapes of the defect-

free model were known. This analysis also served to calculate an appropriate mesh

refinement by requiring that the first natural frequency converge to within a tolerance of 2%.

The free-vibration analysis was performed applying fixed-fixed boundary conditions without

pre-tensioning the lap joint to enable the load-free resonances to be known.

Finally, a transient analysis was conducted to simulate the forced-vibration response

measurements. A sinusoid-sum approximation was used to simulate the experimentally

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acquired forced-vibration loading of the vibration platform, measured using an

accelerometer. This signal consisted of the driving frequency of 150 Hz at the normalized

maximum at 0 dB in addition to harmonics at 300 Hz (-20 dB), and 600 and 900 Hz (-30 dB).

The forcing function was applied transversely at the center of the overlap area of the lap

joint, as shown in Figure 6.3(b). The approximation served not only as a good estimate for

the experimental measurements but to also filter noise and features in the signal not

associated with the actual dynamics of the excitation. For this analysis, numerical

nonlinearities were introduced that simulate accumulated fatigue damage: (1) a nonlinear

material response in the adhesive and (2) an interfacial defect at the adhesive layer. The

simulation of damage in the joint is described in more detail in the following section. All

simulations were performed during fixed-fixed boundary conditions as would be the case

during the experiments. No pretension load was applied so that observed changes between

each simulation could be solely attributed to the method used to introduce nonlinearity. The

midpoint of the joint overlap is at the exact location of the FBG sensor midpoint used during

the experiments in Chapter 5, therefore the strain in the x-direction at this point was extracted

from the simulation at each time step to represent the axial strain measured by the FBG

sensor.

Once the dynamic axial strain information was extracted from the elemental solution

at the FBG sensor midpoint we conducted spectral frequency analyses on the simulated time

histories. The fast Fourier transform (FFT) was first computed to get an averaged-sense of

the frequency components that exist within the dynamic signal. Afterwards we calculated the

short-time Fourier transform (STFT) by discretizing the time signal into small, equal-length

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windows to compute the FFT. For all STFT computations a 13 millisecond Hamming

window with 50% overlap was used, because of the optimal balance it gave in both the time

and frequency domains.

As observed in Chapter 5, the damage accumulated at the adhesive layer of the lap

joint was consistent with that due to incremental, low-cycle fatigue loading. The large

stresses experienced during such loading and the viscoelastic behavior of the adhesive led to

plastic deformation and softening of the adhesive layer, as well as matrix cracking and

interfacial fracture near and around the FBG sensor. As a result, complex residual strain

states existed around the FBG sensor. The complexity of these residual strain fields increased

with increased fatigue cycles. We needed to accurately represent this accumulated fatigue-

induced damage in the numerical simulations for a verification of the experimental results.

We applied two forms of numerical nonlinearity in the simulations, one representing the

softening of the adhesive and one representing interfacial fracture, and compared their effects

on the vibration response of the lap joint. In reality the failure mode contains both of these

effects, however, we simulated them separately to isolate their effect on the response of the

lap joint and the response of the embedded FBG sensor.

Plastic deformation of the adhesive layer was first implemented in the model by

artificially introducing residual strain into the adhesive after each loading block, so as to

increase the nonlinearity in the relevant portion of the adhesive stress-strain curve in Figure

6.2. Numerically, the shift in the stress-strain curve was implemented by artificially

increasing the amplitude of the applied force to reach peak axial strains during the transient

simulations of 3791, 5387, 6702, and 13,240 με.

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Secondly, a geometric defect was implemented in the adhesive layer by removing

elements in the meshed model. The defect size was progressively increased for five

consecutive simulations. The defect geometry modeled was measured in increments of 200

fatigue cycles for a representative specimen using pulsed-phase thermography. The fracture

surface of this test specimen after failure is shown as the shaded regions in Figure 6.4. More

details on the measurement technique and method used to extract the defect boundary can be

found in Shin et al. (2013). Figure 6.5 shows the defect input for the five simulations

conducted. Figure 6.5(A) indicates the defect-free lap joint and was simulated to retrieve a

baseline model. Figures 6.5(B-E) indicate an interfacial defect that advances across the joint

overlap area. Figure 6.6 shows the 3D geometry of the defect represented in Figure 6.5(B)

before meshing. For all simulations, the defect was assumed to propagate uniformly through

the thickness of the lap joint adhesive bond. For this simulation, the adhesive material

response was modeled as linear elastic with the small strain modulus and Poisson ratio

values, and the peak-to-peak amplitude of vibration was kept constant to eliminate effects

due to softening of the adhesive modeled in the previous case.

6.3 Numerical Simulation of Experimental Pull Tests

To estimate the maximum load to be applied during fatigue loading, uniaxial tests

until failure of lap joint specimens were conducted using a servohydraulic tensioning

machine at a crosshead displacement rate of 0.5 mm / minute. The measured load-

displacement results from the three specimens are shown in Figure 6.7. There was a large

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variability in the load-displacement response between the specimens, both in the initial

stiffness and in the maximum load. During the experimental pull tests the lap joints failed

from either of two failure modes: cohesive failure caused by brittle fracture of the adhesive

layer (Specimen i) or by interfacial failure, likely caused by poor surface preparation or

application of the adhesive (Specimens ii and iii).

A transient analysis of the finite element model shown in Figure 6.3(a) was conducted

at the same displacement rate, for a total simulation time of 48 seconds and time step of 0.2

seconds. This corresponds to a total simulated crosshead displacement of 0.4 mm at the free

end of the composite lap joint. The failure modes were not incorporated into the finite

element model, as the goal was to verify the initial load-displacement response. The linear

load-displacement response from the finite element model is also shown in Figure 6.7. The

slope of the predicted load-displacement curve model closely follows that of the linear region

of Specimen i, as expected. This simulation validates the quasi-static response of the finite

element model and confirms that the response of Specimens ii and iii were dominated by the

variable manufacturing quality.

The axial strain distribution (in the x direction) was also extracted from the finite-

element model at the location of the FBG sensor, as shown in Figure 6.8. Figure 6.8 plots the

strain distribution at a crosshead displacement of 0.4 mm. The expected non-uniformity in

the axial strain distribution across the lap joint overlap area agreed well with previous

research (Ning et al., 2012; Murayama et al., 2012). Similarly, the in-plane shear strain

distribution along the FBG location was extracted at the same loading condition and is shown

in Figure 6.9. The magnitude of shear stresses is much greater at the edges of the lap joint

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overlap area, also in agreement with published findings (Sayman et al., 2012; Krishna et al.,

2009; Li et al., 1999; da Silva Lucas et al., 2009; Ficarra et al., 2001).

6.4 Simulation of Free-Vibration Frequency Response of Pristine Lap-Joint

A mesh convergence analysis was performed on the finite element model based on

the free vibration modal analysis with fixed-fixed boundary conditions as shown in Figure

6.3(c). These boundary conditions are the same when the lap joint was later subjected to

forced vibration loading. The mesh convergence criteria was set to be that the first natural

frequency converged to within 2% of that computed for a mesh with half as many elements.

The results of the convergence analyses are shown in Figure 6.10 and Table 6.2, from which

the mesh with 452,840 elements was used for the later forced-vibration simulations. The first

5 natural frequencies and mode shapes were also extracted from the solution, as shown in

Figure 6.11. The first natural frequency converged to 383 Hz and resulted in a bending mode

shape in the direction of the applied vibratory load as expected. This was the only natural

frequency that is contained in the harmonic excitation loading spectrum bandwidth of 900 Hz

to be applied later. The third mode shape resulted in a bending motion in the xz plane with a

frequency of 1394 Hz. While modes 1, 2, and 4 are all bending modes about the z axis, the

fifth mode shape was the first twisting motion about the longitudinal axis with a frequency of

2366 Hz.

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6.5 Simulation of Forced-Vibration Lap Joint

The measured forced-vibration response from the vibration platform is plotted with

the fitting function used for the simulations in Figure 6.12. The simulated forcing function

was applied transversely at the center of the overlap area of the lap joint, as shown in Figure

6.3(b). The sinusoid-sum curve also well represents a smoothed version of the applied

loading, removing the higher frequency component that was beyond the frequency bandwidth

of the actuator. The corresponding FFT for each signal was also computed and are plotted in

Figure 6.13. The sinusoid-sum approximation corresponds well with the experimentally

measured resonant frequencies. The one exception is the fifth harmonic at 750 Hz which

appears at a smaller magnitude in the measured signal than in the simulated excitation signal.

The forced-vibration analysis was computed for a total simulation time of 150 ms with a time

step of 3.5 x 10-4

s.

The primary objective of this study was to identify common features in the dynamic

behavior of two numerical models used to replicate the fatigue damage of the lap joint

measured by the FBG sensor embedded in the adhesive layer in Chapter 5. For each

simulation, the STFT was computed for the axial strain time history extracted from the

midpoint of the joint overlap. The evolution of this computation as the simulated damage is

increased is shown for the two numerical methods in Figure 6.14. The plastic deformation

simulations are shown in order of increasing levels of peak axial strain in the adhesive layer.

The interfacial defect simulations are shown in order of increasing defect size. The

specifications for each simulation method are shown in Table 6.3. For the experimental

measurements, the peak wavelength was extracted from the full-spectral FBG response and

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used to compute the STFT. The accumulated fatigue cycles for the experimental

measurements are also shown in Table 6.3. These simulations are not intended to be used for

quantitative comparison with the experimental results, but rather to qualitatively reveal

similar observances or patterns in the STFT.

The baseline models (A) to simulate the undamaged lap joint were appropriately

defined by (1) purely elastic deformation (2) and a pristine adhesive layer. We expect the

simulated responses of both the elastic and defect-free models to be linear, with frequency

components mirroring that of the applied excitation. As the simulated damage increases, we

expect the frequency response to transition to demonstrate features identified with nonlinear

dynamic behavior previously observed experimentally in Chapter 5. The baseline model of

the plastic deformation simulations replicated the exact forced-vibration amplitude measured

experimentally and resulted in an expectedly low peak axial strain of 0.29 με. From Figure

6.14, it can be observed that the response reached a steady-state condition. The much lower

amplitudes of the 300 Hz, 450 Hz, 750 Hz, and 900 Hz harmonics did not appear due to the

strong contrast with the 150 Hz and 600 Hz components. However, the defect simulation did

indicate transient features before damage is introduced but was limited to a low bandwidth of

frequencies. As expected, the experiments indicated little to no transient behavior early on in

the lap joint lifetime.

As simulated extent of damage was increased, both numerical methods shifted from a

quasi steady-state response to a transient one. Initially, the experimental measurements were

less sensitive to this shift, however, agreed well with the overall trend toward nonlinear

dynamic behavior as fatigue cycles were increased. Because the material response was no

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longer at a steady-state equilibrium condition, the STFT gave valuable information on the

transient behavior of the signals. As the simulated damage progressed, both numerical

methods indicated consistent 60 ms low-frequency transients that ranged from 0 – 300 Hz.

Simulations (C) and (D) of the interfacial defect model indicate the influence of the defect at

the location of the sensor where the axial strain time histories are extracted. As can be seen

in Figure 6.5, the defect begins to cross the midpoint of the adhesive layer enacting

geometric non-uniformities across the sensor location. However, because changes in the

defect boundary are only slight between simulations shown between (C) – (E) the STFT

measurement appears to be not as sensitive as compared to the plastic deformation

simulations.

Finally, as the simulation includes further damage of the lap joint we observe a strong

resemblance to nonlinear structural behavior. This behavior is characterized by the

broadening frequency bandwidth in the transient response of the material not associated with

the simulated excitation frequencies. This is clearly seen in the experimental FBG

measurements in the latter stages of fatigue damage and is confirmed by the numerical

simulations.

Finally, additional indicators of damage can be seen from features observed by

calculating the FFT of the peak wavelength dynamic simulations. Figure 6.15 plots two

examples of the FFT, one obtained from the plastic deformation simulation and one from the

geometrical defect simulation. The narrow, well-defined frequency components found in the

baseline models are no longer visible but have transformed into a noisy, ill-constructed

spectrum of frequencies. The noticeably lower amplitude and slightly shifted frequency of

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the 150 Hz component to 180 Hz can be observed. It is difficult to discern whether the 150

Hz component truly shifted to remain at 180 Hz or rather if this component appears because

the FFT is averaging a highly transient response. Nevertheless, a 90 Hz sub-harmonic now

appears in the spectrum. Carpinteri et al. (2005) demonstrated that transitioning towards

deterministic chaos in vibrating damaged structures is often associated with sub-harmonic

components appearing in the response of strongly nonlinear structures leading to a period

doubling route to chaos.

6.6 CONCLUSIONS

These numerical analyses show that the complex strain fields due to fatigue-induced

damage endured by the FBG sensor can be accurately simulated by similar phenomena that

occur during large amplitude excitation and simulation of an interfacial defect that progresses

across the joint overlap. The large amplitude excitation enabled simulation of accumulating

damage at the adhesive layer by forcing the adhesive to endure plastic deformation.

Introducing a simulated defect that increases in size also captured geometric nonlinearities

that exist when actual damage is present at the adhesive layer and during excitation of the lap

joint. Both effects contribute significantly to the FBG sensor host material and correspond

well with the previous experimental results found in Chapter 5.

From the experiments previously conducted, a transition from linear to nonlinear

chaotic behavior is observed by analyzing the peak wavelength information from an

embedded FBG sensor as fatigue-induced damage is increased. These simulations verify the

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previous experiments contain rich information on the structural health of the composite lap

joint. From the results, the progression of damage at the adhesive layer can be qualitatively

identified by observing the evolving nature of transient features in the dynamic material

response using the short-time Fourier transform (STFT). The results from Chapters 5 and 6

suggest that embedded FBG sensors can be used to retrieve complex, dynamic strain

information to assess the local damage state of adhesive bonds in composite lap joints.

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Figure 6.1 Finite element model geometry and mesh. SOLID 45 8-noded brick elements were used to

model both the adhesive and composite adherends. The adhesive layer is refined to further increase

accuracy.

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Figure 6.2 Hysol EA9394 paste adhesive stress-strain curve extrapolated from Sandia National

Laboratory report (Guess et al., 1995).

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Figure 6.3 Boundary conditions and applied loading during (a) transient tensile loading (b) transient

forced-vibration and (c) free-vibration modal analyses.

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Figure 6.4 (a) Fracture surface after failure of adhesively bonded lap joint specimen and (b) failure

modes.

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Figure 6.5 Progression of damage at the adhesive layer of lap joint measured experimentally using

pulsed-phase thermography and then used as input into finite-element model. The initial simulation (A) is defect-free (pristine model).

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Figure 6.6 Example of three-dimensional geometry of defect used in finite-element model.

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Figure 6.7 Experimental measurements and numerical simulation of load-displacement curve during

tensile loading of composite lap joints.

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Figure 6.8 (a) Axial strain distribution (in x direction) along FBG sensor at the adhesive layer

extracted from 3D finite-element model at applied axial load of 6.4 kN. (b) Normalized axial strain contours (in x direction) near joint overlap region, normalized by the far-field axial strain of 338 με.

154

Figure 6.9 (a) Shear strain distribution along FBG sensor at the adhesive layer extracted from 3D

finite-element model at applied axial load of 6.4 kN. (b) Shear strain contours near joint overlap

region, normalized by the far-field shear strain of -3219 με.

156

Figure 6.10 Mesh configurations for convergence modal analysis performed on finite-element model.

Total number of elements for each model is shown.

157

Figure 6.11 Calculated natural frequencies and corresponding mode shapes from modal analysis of

lap joint specimen with fixed-fixed boundary conditions.

158

Figure 6.12 Measured forced-vibration loading and corresponding sinusoid-sum curve fit shown for

(a) one period and (b) 10 periods of 150 Hz dominant frequency component.

159

Figure 6.13 (a) FFT of measured forced-vibration and (b) of sinusoid-sum approximation used for

simulation.

160

Figure 6.14 STFT of measured and simulated FBG peak wavelength data after selected accumulated

fatigue cycles and loading conditions.

162

Figure 6.15 FFT of axial strain time history extracted from numerical simulations of (a) plastic

deformation of the adhesive for peak axial strain of 5387 με and (b) an interfacial defect size of

30.5% of total bond area.

163

Table 6.1 Material properties of woven twill carbon fiber prepreg used for fabrication of lap joint

adherends.

Property Value Units

Young’s Modulus (E) - -

X 24 GPa

Y 10 GPa

Z 10 GPa

Poisson’s Ratio (ν) - -

Xy 0.30 -

Yz 0.50 -

Xz 0.02 -

Shear Modulus (G) - -

Xy 4 GPa

Yz 3 GPa

Xz 4 GPa

Density - -

Ρ 1530 kg/m^3

164

Table 6.2 Calculated natural frequency values for first five modes of lap joint. All frequency values

are in Hz.

Mode number

Number of elements 1 2 3 4 5

7364 625 1929 2523 3498 3668

57521 446 1343 2037 2407 2417

230494 389 1185 1535 2108 2379

452840 383 1163 1394 2055 2366

165

Table 6.3 Specifications for numerical simulations and experimental measurements.

Simulation

or

measurement

Plastic deformation

peak axial

strain (με)

Geometric defect

percent of total

bond area (%)

Measurement

fatigue

lifetime (cycles)

A 0.29 0 0

B 3791 20.2 200

C 5387 30.5 200 after tension

D 6702 38.2 400

E 13240 42.4 400 after tension

F - - 600

166

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

FOR FUTURE WORK

This study validated and tested a newly developed high speed, full-spectral

interrogator for dynamic measurements of embedded fiber Bragg grating sensors to enable

damage monitoring in composite structures. We demonstrated the effects that wavelength

hopping can have on dynamic measurements with FBG sensors. This demonstration was

performed with FBG sensors embedded in composite laminates subjected multiple, low-

velocity impacts. Initially, full-spectral data acquisition was performed at a rate lower than

that required to fully resolve the dynamic impact event. The presence of wavelength hopping

created apparent oscillations in the strain response. By acquiring the full-spectral data at a

faster rate (100 – 300 kHz) these apparent oscillations were no longer present in the

measurements. Also, measurements collected using a peak wavelength interrogator (at a

sufficiently fast rate to resolve the dynamic event) were shown to bifurcate due to the

presence of multiple peaks in the reflection spectrum. In both of these cases, applying full-

spectral interrogation of the FBG spectrum at a sufficient data acquisition rate eliminated the

uncertainties in the measurement due to the wavelength hopping.

The form of the spectral distortion (and therefore the resulting errors in strain or

structural response measurements) are dependent upon the local microstructure surrounding

167

the FBG, the placement of the FBG relative to this microstructure, the changes in this

microstructure due to damage and the nature of the loading applied to the structure. It is

therefore not possible to predict the spectral distortion for a given application, or to calibrate

a “gauge factor” for peak wavelength measurements to eliminate errors to this spectral

distortion. The measurement of the full-spectral response of the FBG sensor eliminates

uncertainties due to wavelength hopping or bandwidth changes. These measurements could

then be used to correct strain measurements or identify changes to the local material such as

due to damage.

In later experiments, we measured the full-spectral response of a FBG sensor during

harmonic vibration with and without an initial spectral distortion due to a non-uniform, static

strain field. The results demonstrated that the measurements of the FBG response without

initial spectral distortion are identical to those previously measured with peak wavelength

interrogators. The measurement of the FBG full-spectral response with initial spectral

distortion also contained the excitation vibration harmonics, however did not include further

distortion of the reflected spectrum as a result of the vibration. Numerical simulations of the

FBG response well predicted the spectral distortion due to the non-uniform strain field and

the resonance condition of the DEN specimen used in the experiments. Finally, we

demonstrated that the use of the high-speed, full-spectral interrogator permits the separation

of the spectral distortion and the harmonic vibration from the FBG response signal through

filtering and can therefore be applied to measure non-uniform strain fields in noisy

environments. These new findings offer innovative contributions to the area of strain

measurements and damage detection for structures in dynamic environments.

168

Measurements of a fiber Bragg grating (FBG) sensor embedded at the adhesive layer

of a single composite lap joint subjected to harmonic excitation after fatigue loading were

also acquired. The full-spectral information avoided dynamic measurement errors often

experienced using conventional peak wavelength and edge filtering techniques. The dynamic

response of the FBG sensor indicated a transition to strong nonlinear behavior as fatigue-

induced damage progressed. STFTs computed from the extracted peak wavelength

information revealed time-dependent frequencies and amplitudes of the dynamic FBG sensor

response. The eventual aperiodicity of the transient signal suggested a transition into a quasi-

periodic state followed by chaos represented by a broad bandwidth of frequencies

unassociated with the externally applied excitation. Pulse-phase thermography images

verified the progression of accumulated damage across the lap joint as a function of cyclic

fatigue and indicated non-uniformity in the shape of the defect impinging on the embedded

FBG sensor. Finally, calculating the phase plane representations of the dynamic peak

wavelength signals highlighted the importance of properly extracting the peak wavelength

information from full-spectral FBG sensor dynamic measurements. From our knowledge,

this chapter demonstrates for the first time the complex transient behavior of an embedded

FBG sensor at the adhesive layer of a composite lap joint using high speed full-spectral

interrogation.

Lastly, numerical analyses showed that the complex strain fields due to fatigue-

induced damage endured by the FBG sensor can be accurately simulated by similar

phenomena that occur during large amplitude excitation and simulation of an interfacial

defect that progresses across the joint overlap. The large amplitude excitation enabled

169

simulation of accumulating damage at the adhesive layer by forcing the adhesive to endure

plastic deformation. Introducing a simulated defect that increases in size also captured

geometric nonlinearities that exist when actual damage is present at the adhesive layer and

during excitation of the lap joint. Both effects contribute significantly to the FBG sensor host

material and correspond well with the previous experimental results. The simulations

verified the experimental measurements contain rich information on the structural health of

the composite lap joint. The progression of damage at the adhesive layer can be qualitatively

identified by observing the evolving nature of transient features in the dynamic material

response using the short-time Fourier transform (STFT). These results suggest that embedded

FBG sensors can be used to retrieve complex, dynamic strain information to assess the local

damage state of adhesive bonds in composite lap joints.

This work has demonstrated the promising capabilities of the new high speed full-

spectral interrogator. This work used the full-spectral FBG response to avoid dynamic

measurements such as wavelength hopping that may occur with traditional interrogation

techniques while the sensor is exposed to complex strain fields. The majority of the analyses

were performed from the “corrected peak wavelength” approach. Essentially, extracting the

correct peak wavelength and then pursuing data analyses and interpretation of the material

health from the traditional view. However, the distortion in the FBG response contains rich

information on the strain state of the host material and offers considerable insight far past

frequency analysis of the peak wavelength. Therefore, there is a strong need for future work

to look more closely at interpreting the dynamic full-spectral distortion during realistic

damage and excitation of composites (i.e., fatigue damage).

170

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ABSTRACT Dr. Kara J. Peters.)

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