Assessment of Triboluminescent Materials for Intrinsic Health Monitoring of Composite Damage Tarik J

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2013 Assessment of Triboluminescent Materials for Intrinsic Health Monitoring of Composite Damage Tarik J. Dickens

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COLLEGE OF ENGINEERING

ASSESSMENT OF TRIBOLUMINESCENT

MATERIALS FOR INTRINSIC HEALTH MONITORING OF COMPOSITE DAMAGE

TARIK J. DICKENS

A Dissertation submitted to the Department of Industrial and Manufacturing Engineering in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Spring Semester, 2013 Tarik J. Dickens defended this dissertation on April 4, 2013.

The members of the supervisory committee were:

Okenwa Okoli Professor Directing Dissertation

Naresh Dalal University Representative

Ted Liu Committee Member

Richard Liang Committee Member

The Graduate School has veriﬁed and approved the above-named committee members, and certiﬁes that the dissertation has been approved in accordance with the university requirements.

ii “There is a God shaped vacuum in the heart of every man which cannot be ﬁlled by any created thing, but only by God, the Creator, made known through Jesus ” - Blaise Pascal

“You are never given a dream without also being given the power to make it true. You may have to work for it, however” - Richard Bach

“Give me six hours to chop down a tree and I will spend the ﬁrst four sharpening the axe” - Abraham Lincoln

iii ACKNOWLEDGMENTS

Life is truly a gift, and the ability to lend ones faculties to the sciences is a rewarding experience. The old saying says, “It takes a village to raise a child”. Likewise, it takes a smorgasbord of individuals to raise a scientist and engineer. To my loving wife, Elizabeth Dickens M.D., thank you for your constant encouragement and beautiful editing. Humbly, I would like to thank my Mother and Father, and extended family and friends, for their continued support and undying love for their son in his academic pursuits. To my inner circle, “who needs enemies, when you have friends like these”.

I would also like to thank the members of my committee. To Dr. Okoli, special thanks and gratitude for giving me the oppurtunity to pursue my dreams. To all the many discussions, rebukes, guidance and display of patience. I would like to thank Dr. Naresh Dalal of the Chemistry Department, Dr. Richard Liang the Director of HPMI and Dr. Ted Liu of the Industrial & Manufacturing Engineering Department for serving on the committee. I would also like to thank Dr. Ben Wang, whom also helped guided this research eﬀort in its early stages.

This work would not have been possible without the help of several individuals. I would also like to extend my gratitude to Mrs. Stephanie Salters, Prof. John Taylor, Dr. Park , James Horne and Gerald (Jerry) Horne for their tremendous help over the years. In addition, I would also like to thank the eﬀorts of Dr. David Olawale, Garret Sullivan, Dr. Jasim Uddin, Jesse Smithyman, Phong Tran and the many others for their participation in the Patronas SHM group (Jin Yan, Stephen Tsalickis, Jolie Breaux and Chelsea Armbrister). To my greatly extended family and colleagues that have made learning very enjoyable. Special thanks to the department of Industrial Manufacturing Engineering and the High Performance Materials Institute.

iv TABLE OF CONTENTS

ListofTables...... viii

ListofFigures ...... ix

Abstract...... xv

1 Introduction 1 1.1 Motivation ...... 2 1.2 ResearchProblemStatement ...... 3 1.3 ResearchObjectives ...... 7 1.4 Dissertation Organization ...... 10

2 Literature Review 11 2.1 Composite Materials ...... 11 2.1.1 Modern to Advanced Composites ...... 11 2.1.2 Fiber-reinforcement ...... 12 2.1.3 Polymer Matrices ...... 13 2.1.4 Multi-scale Composites ...... 14 2.1.5 Composite Processing and Fabrication ...... 15 2.2 Composites & Failure ...... 16 2.3 Mechanics of Composite Materials ...... 19 2.3.1 Composite Summary ...... 28 2.4 Structural Health Monitoring ...... 28 2.4.1 Biological Mimicry ...... 28 2.4.2 Damage & Health Monitoring ...... 30 2.4.3 Non-destructive Evaluation - Modern & Emerging ...... 32 2.4.4 SHM Summary ...... 39 2.5 Sensory Mechanism: A Principle Component ...... 40

v 2.5.1 Sensory Signal Emission ...... 40 2.5.2 Triboluminescence ...... 40 2.5.3 Modeling Luminescence: Triboluminecscent Intensity and Spectral Analysis...... 52 2.5.4 Summary - Sensory Mechanism ...... 61 2.6 Literature Summary ...... 62

3 Overview Methodology & Experimentation 65 3.1 PhaseI&IIExperimentalMethods ...... 66 3.1.1 Materials ...... 66 3.1.2 Fabrication ...... 67 3.1.3 Mechanical Testing Procedure ...... 69 3.1.4 Sample Characterization ...... 73

4 Triboluminescent Enhanced Composites 77 4.1 ExperimentalOverview ...... 77 4.2 The Triboluminescent Response of Concentrated Prismatic Composite Beams 79 4.2.1 Introduction ...... 79 4.2.2 Fabrication & Testing of Concentrated Beams ...... 80 4.2.3 Results & Discussion of the Tribolumuiscent Evaluation ...... 81 4.2.4 Summary ...... 92 4.3 An Experimental Triboluminescent Response to Pre-notched Beams . . . . 93 4.3.1 Introduction ...... 93 4.3.2 Method ...... 94 4.3.3 ExperimentalResults ...... 95 4.3.4 Experimental Discussion ...... 98 4.3.5 Summary ...... 107 4.4 Relating Energy Criterion of Triboluminescence by the Experimental J-integral Method ...... 108 4.4.1 Introduction ...... 108 4.4.2 Experimental Method ...... 108 4.4.3 Fabrication Procedure ...... 110 4.4.4 Results and Discussions ...... 111 4.4.5 Summary ...... 127

vi 4.5 Phantom Analysis: Analyzing the Triboluminescent Signal and Mechanical Proﬁle...... 129 4.5.1 Introduction ...... 129 4.5.2 Design of Experiments: Revisited ...... 129 4.5.3 Methods and Results of the Phantom Analysis ...... 133 4.6 ExperimentalDiscussionOverview ...... 137 4.6.1 Explanation of the Triboluminescent Composite ...... 137

5 Modeling Excitation of Triboluminescent Composites 140 5.1 ModelingPremise...... 142 5.2 Modeling Background ...... 146 5.2.1 Function of Strain Energy ...... 147 5.2.2 A Bi-exponential Model for Light Intensity ...... 149 5.2.3 A Modiﬁcation to Chandra’s De-trapping Model to include Load- displacement Phenomena ...... 151 5.3 Finitie Element Method Implementation: A 2D COMSOL Representation . 157 5.3.1 FEM Construction of the COMSOL Model ...... 157 5.3.2 Viewing Stress-strain Distributions of Crack-tip Features in COMSOL 165 5.4 Modeling Light Intensity per Bending of Composite Beams ...... 167 5.4.1 Implementation of Governing Excitation Model ...... 167 5.4.2 Variation of Triboluminescent Intensity as Feature of Volume Fraction 170

6 Conclusion & Recommendations 179 6.1 Summary of Results ...... 179 6.2 Contributions ...... 184 6.3 Recommendation for Future Work ...... 187

A Monte-Carlo Simulations 192

Bibliography ...... 197

Biographical Sketch ...... 211

vii LIST OF TABLES

2.1 Defects associated with composite systems [36]...... 17

2.2 Emerging NDE for composites and emerging NDE for composites [36]. . . . . 33

2.3 Luminescence types/Excitation source...... 43

2.4 Theories and hypotheses organized by crystal class...... 46

2.5 Theories and hypotheses organized by mechanism...... 47

2.6 Promising triboluminescent materials...... 48

4.1 Average parasitic inﬂuence from TL ﬁller content...... 89

4.2 Tabulation of speciﬁc properties...... 90

4.3 Factors&levels...... 95

4.4 Summary statistics of the DoE study...... 96

4.5 Overall statistics of the DoE study...... 97

4.6 Overall ANOVA chart for Luminescent intensity...... 99

4.7 ANOVA for Luminescent intensity...... 99

5.1 Compilation of Monte-Carlo simulation results...... 172

5.2 A direct omparison of Monte-Carlo simulation results versus the experimental results from Section 4.2...... 173

viii LIST OF FIGURES

1.1 High payoﬀ for aerospace applications and the composite usage has an ever- increasingtrend...... 4

1.2 Failed vertical tail kit of the Airbus A300 aircraft [17]...... 5

1.3 High-level roadmap of the proposed research...... 8

2.1 Woven structures of ﬁber reinforcements [19]...... 12

2.2 Physical and chemical process in thermoset polymer curing cycle...... 14

2.3 Macroscopic depiction of failure modes in composites after impact [37]. . . . 18

2.4 Fracture features of reinforced composite laminates. (a) interlaminar, (b) intralaminar, and (c) translaminar fracture [19]...... 19

2.5 Plate undergoing tensile stress on crack [41]...... 20

2.6 Ideal and real crack scenarios [41]...... 21

2.7 Generalityofmultiplefailuremodes...... 22

2.8 Concentration of stress lines at crack-tip of a notched specimen [43]...... 24

2.9 The displacement mode calculation for work energy of a loaded sample [43]. . 24

2.10 Example eshelby contours of the J-integral formulation [43]...... 26

2.11 (a) Strain energies at diﬀerent displacements, (b) resultant energy curves at corresponding displacement [44]...... 27

2.12 Schematic description of SNS derived from human biology [66]...... 36

2.13 Proposed piezoelectric active wafer system with arrayed sensing [67]...... 37

ix 2.14 Schematic description of the SMART Layer design [13]...... 37

2.15 Quantum theory for explanation of (a) Bohrs model of energy level transitions (b)excitationtoemission...... 42

2.16 Quantum conﬁnement on digressing length scale...... 43

2.17 Modiﬁed chart of luminescent derivatives from ML/TL [93]...... 44

2.18 a) TL intensity of various inorganic thin ﬁlms under the same friction conditions, b) Eﬀect of Mn additive amount on TL intensity [80]...... 51

2.19 Schematic of energy-transfer that result in ZnS:Mn2+ PL emissions [89]. . . 52

2.20 Schematic energy level diagram of mechanoluminescence of coloured alkali halide crystals [88, 133]...... 58

2.21 A modiﬁed schematic of the piezoelectric theory illustrating TL phenomena upon cleavage [91]. Excitation occurs via suﬃcient electrical potential in a gas discharge (d) which accumulates upon new fracture surfaces...... 59

3.1 Experimental and modeling approach...... 65

3.2 Three step mold and sample fabrication process for casted particulate composites...... 67

3.3 Schematic of the three-point bend sample geometry and single-ended notch highlighting the eﬀective length of casted particulate composites. The eﬀective lengths utilized in the entire study were 0.5, 1.5, 2.5, 3.5 and 4.5...... 68

3.4 An illustration of the three-point bend schema for ﬂexural loading of concentrated composite short beams...... 69

3.5 The mechanical testing (a) three-point bend ﬁxture and machine setup, and (b) optical insulation and enclosure...... 70

3.6 Three-point bend photo-sensor alignment ﬁxture...... 71

3.7 Setup and instrumentation diagram for PMT and PV cell sensors...... 74

x 4.1 An illustration of the three-point bend schema for ﬂexural loading in view of crack propagation and plausible mechanism for particulate excitation of TL doped resin matrices. Plausible TL mechanism stem from (1) elastic, (2) plastic and (3) fracture-like distrubances as originally described by Walton [85]. 78

4.2 Representative cross plot of the transient TL response to stress of ﬂexural samples of a 50 %wt. concentration (intensity is in arb. unit) [146]...... 81

4.3 Characteristic time decay of TL ZnS:Mn emission and spectral proﬁle regisitered by the Hamamatsu PMT [18]...... 84

4.4 Inﬂuence of ZnS:Mn concentration on the intensity of TL emissions and ﬂexural strength (breaking stress) [146]...... 85

4.5 (a - c) Visual analyses of the black and white frame by frame images reveal the propagating fracture and subsequent TL emission of a 55 10 mm2 specimen × outlined by white horizontal lines [146]...... 88

4.6 Double plot of intensity and speciﬁc bending stiﬀness versus concentration loading for a loading rate of 40 mm min−1 [146]...... 91 ·

4.7 Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the TL response as measured by thephotomultiplierdetector...... 101

4.8 Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Load response...... 102

4.9 Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Displacement response. . . . 103

4.10 Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Strain energy response for 5 %vol...... 105

4.11 Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Strain energy response for 10 %vol...... 106

4.12 The experimentl formulation of the J-integral (a) load-displacement, (b) en- ergycurvesand(c)J-integralcurve...... 109

xi 4.13 Comparison of the signal emission (blue line) and load-displacement (green dashed line) plots of the two-phase (unreinforced) TL concentrated composite ﬂexural beams with respect to time. The representative trend for brittle fracture of concentrated polymers only displays one Triboluminescent peak at macro-rupture and crack-propagation...... 112

4.14 Comparison of the transient signal emissions (blue line) and the load-displacement (green dashed line) curve for three-phase (reinforced) TL concentrated composite beam under ﬂexural load indicating multiple emissions along the failure cycle...... 113

4.15 Micrographs of (a) ZnS:Mn phosphor, (b) specimen fracture and (c) ZnS:Mn sheared components at 50 % concentration [146]...... 116

4.16 Micrographs of the through-thickness eﬀective length of (a) pristine resin, and (b) concentrated resin beam cross-section...... 117

4.17 Micrographs of (a) concentrated resin showing evidence of direction of fracture in view of crack notch, and (b) an excerpt of an encased ZnS:Mn sheared particle.117

4.18 Micrographs of an encapsulated ZnS:Mn particulate with signs of deformation and in view of micro-crack phenomenon...... 118

4.19 The J-integral graph for TL/VER composites pre-notched specimens indicating the critical displacements for the composite system is 0.13 mm...... 119

4.20 The J-curve for reinforced (GF) concentrated beams at 5 percent ﬁber volume fraction with a critical fracture requirement greater than 6.927J/m2...... 123

4.21 Micrographs of (a) concentrated composite showing evidence of micro-fracture and direction of fracture in view of crack-tip, and (b) an excerpt of a minute micro-damage site...... 126

4.22 The energy signatures of the experimental design study with calculation of strain energy and the residual energy of loaded two-phase composites. . . . . 130

4.23 The relationship of the force derivative and intensity with varying eﬀective length as represented in the Design of Experimental study for the production oftriboluminescentintensity...... 131

4.24 The relationship of the feature derivate with inﬂuence of strain-energy in the production of triboluminescent intensity...... 132

xii 4.25 Observed dependence of the TL intensity-ZnS:Mn on the applied force ﬁrst derivative of loading in two-phase composite showing aligned bifurcations. . . 134

4.26 Observed dependence of the TL intensity-ZnS:Mn on the applied force ﬁrst derivative of loading in three-phase composite showing aligned bifurcations. . 135

4.27 Illustration of the movement in time of a concentrated beam and its in-situ TL response, where the process occurs from loading at time, ta, initial loading, tb, and the general fracture processor at time tc, td and te...... 138

5.1 Deformation and geometrical strecthing of an internal solid material . . . . . 141

5.2 An example three-dimensional load-displacement curve...... 143

5.3 Three-dimensional phantom plot of TL intensity-load-time curve illustrating the signiﬁcance of the inﬂection point indicating triboluminescent emissions in two-phase composites...... 144

5.4 Flowchart of the algorithm for simulating the load proﬁle under three-point bending for TL simulation...... 145

5.5 Case of (a) constant force and (b) linear force...... 147

5.6 Linear elastic strain energy of a volumetric material...... 148

5.7 An Illustration of the simulated force derivation (dp/dt), and its relation to to the distortion and bending of the concentrated solid composite short beam. . 150

5.8 A simulated TL signal modeled by the Bi-exponential model...... 151

5.9 Deformation luminescence explained on the order of the energy level excitation as a de-trapping model for ZnS:Mn ...... 153

5.10 Computational numerical methods selection...... 157

5.11 Finite element model construction of three-point bend experiement in COMSOL.159

5.12 Finite element model approximation for deﬂection of a composite beam with von-Misesstress...... 165

xiii 5.13 Geometrical view of the FE model of the graphical stress-strain concentration as portrayed by the strain-energy density of the simulated concentrated particulate composite ﬂexural beams with eﬀective length of (a)0.5, (b) 2.5 and (c)4.5 mm at critical load. The region of interest are the concentrations around the crack-tip and the stress-states under the applied load...... 166

5.14 The simulated 3D phantom plot representation of simulated TL signal modeled by an Bi-exponential model at the forcing of flexural loading of a 2D flexural beam resolved by finite element operation...... 168

5.15 Monte-carlo simulation of the MATLAB Live-Link for COMSOL. This is a partial simulation equal to 40/1000 sample runs for a concentration of 50%. . 171

5.16 Comparison of the experimental chart and the simulated chart of the intensity (black) and specific stiffness (blue) with respect to filler concentration. . . . . 173

5.17 Comparison of the experimental chart and the simulated chart of the intensity (black), experimental intensity (blue) and DoE estimation (red) with respect to ﬁller concentration. The conﬁdence bands (%95 C.I.) have been provided for the DoE and Monte-Carlo simulation...... 175

A.1 Monte-carlo simulation for 0% fraction. The simulation size is equal to 20/1000 sampleruns...... 192

A.2 Monte-carlo simulationfor 5% fraction. The simulation size is equal to 20/1000 sampleruns...... 193

A.3 Monte-carlo simulation for 10% fraction. The simulation size is equal to 20/1000 sample runs...... 194

A.4 Monte-carlo simulation for 25% fraction. The simulation size is equal to 20/1000 sample runs...... 195

A.5 Monte-carlo simulation for 50% fraction. The simulation size is equal to 20/1000 sample runs...... 196

xiv ABSTRACT

Advanced composites offer robust mechanical properties and are widely used for structural applications in the aerospace, marine, defense and transportation industries. However, the inhomogenous nature of composite materials leaves them susceptible to problematic failure; thus the development of a means for detecting failure is imperative. Damage occurs when a load is applied and a distortion of the solid material results in deformation. This process also results in straining of the material. Strain, however, is a physical result of work being performed on a solid material making energy the commonality among all failure mechanisms. This study investigated the feasibility of using Triboluminescent zinc-sulphide manganese (ZnS:Mn) phosphors concentrated in vinyl ester resin for damage monitoring of polymer composites under flexural loading. These particulates react to straining or fracturing by emitting light of varied luminous intensity and detecting the crack initiation presently leading to catastrophic failure(s). Un- reinforced vinyl ester resins and fiber-reinforced composite beams incorporated 5 - 50 % wt. concentrations of TL fillers, and were subjected to three-point bend tests. The intent of flexural testing was to observe the transient response of triboluminescence (TL) in both two- and three-phase composite systems throughout the failure cycle of notched beams, while changing the geometric constraints. Results indicate TL crystals emit light at various intensities corresponding to crystal concentration, the notch-length and imminent matrix fracture. The fracturing or deformation energy was estimated by the method of J-integral with varied notch-lengths, where a lower threshold for excitation was found to be approximately 2 J/m2, far below its critical fracture energy ( 3 & 7 J/m2). Consequently, ≤ ∼ concentrated samples showed nearly 50 % reductions of mechanical moduli due to high loading levels, which subsequently affected the Triboluminescent response. As a result, an optimal 6 % vol. of TL particulates was chosen for further study and exhibited significant signal-to-noise response. Scanning electron microscopy (SEM) revealed particulate inclusions with shearing bands and semblance of particle to resin adhesion, as well as, cases of micro-cracking in reinforced samples. Despite significant parasitic affect to mechanical properties, the luminescent properties of TL occur at rupture for unreinforced composites. The cases of TL concentrated reinforced composites show detection of localized matrix phenomenon which are related to the material response and incurring internal strain-energy prior to any catastrophic failure. This indicates that TL in composite systems has the potential to detect micro-failures (micro- cracks) related to the weak matrix component. The triboluminescent signal was simulated as a rate-dependent model considering the load profile of the composite beam is known.

xv CHAPTER 1

INTRODUCTION

Advanced composites are increasingly being used for structural applications in the aerospace, marine, defense and automotive industries due to their high speciﬁc strength and stiﬀness

(to-weight ratios), as well as lightness (low-density) and durability [1, 2]. However, since

ﬁber-reinforced composites (FRCs)/ﬁber-reinforced polymers (FRPs) often lack the detailed material property data associated with metals, the development of means for detecting failure is imperative [2]. In particular, the use of composites in safety critical structures leads to uneasiness since the mechanical response in damage-worthy or in-service applications is not well understood in the composite engineering community.

As design and functionality requirements of engineering structures such as spacecraft, aircraft, naval vessels, buildings, dams, bridges and ground-based vehicles become more complex, structural health monitoring (SHM) and damage assessment is becoming more rigorous. Assessing structural health is pertinent to demonstrating the uniqueness, utility and smartness of composite materials in the advent of a new material class of third generation composites. The incorporation of Triboluminsecent materials present many advantages to modern technologies, and inundate advanced structures with intrinsic self-sensing capabilities.

1 1.1 Motivation

The highlight of composite usage is its energy-absorbance mechanism. In composite materials, internal material failure generally initiates long before any change in its macroscopic appearance or behavior is observed [3]. FRP composites are generally heterogeneous on the macroscopic scale. In addition, the individual lamina that constitute a laminated continuous fiber reinforced composite are therefore directionally anisotropic. Thus, unlike metallic materials, composites have no single, similar self-propagating crack or noticeable ductile failure. Metals show visible damage caused by impact mainly on the surface of structures, while onset of damage remains hidden inside composite structures especially when subjected to low velocity impact such as bird collisions or tool droppings [1, 4]. If damage is difficult to detect it may cause integrity issues that can seriously decrease the material strength and alter their effectiveness in structural application [5, 6].

The following forms of internal material failure may be observed separately or jointly in the damage zone, and may result in component failure: matrix micro-cracking, fiber breakage, fiber separation (debonding), and delamination. Matrix cracking and delamination are the most common damage mechanisms of low velocity impact, and are dependent on each other [7]. Initial damage is usually through matrix micro-cracking, followed by delamination. Naturally, we attribute strength in composites with the accolades of the solid fiber reinforcement. However, the role of the polymer matirx is uniquely consistent with the onset of failure. Thus, the intrinsic polymer matrix behavior is a first component critical feature for monitoring structural integrity. With the first principle failure initiation, matrix cracking, the load transfer mechanism in the composite becomes broken which results in loss of stiffness and consequential catastrophic failure [3]. For instance, when an aircraft collides with a bird, it can cause potentially catastrophic damage [3]. Low velocity impacts in particular present a challenge to the utilization of composites, since at these velocities;

2 impact damage may not be readily visible. Therefore, devising means of intelligently sensing the onset of failure at no-cost and analagous time is imperative.

1.2 Research Problem Statement

Structural health monitoring (SHM) is the convergence of mega-macro-micro systems to provide real-time assessment for structures involving composite material systems. Re- search is racing towards various schemes and counterparts to achieve sensing reliability for host structures [8–11]. Such systems have to be resurrected cautiously and in a holistic fashion. Much emphasis has been placed on bio-mimicry as a design technique for concise exploration and experimental solution. The resultant nature of composite materials is ﬂawed intrinsically, and those ﬂaws produce antiquated damage mechanisms that ultimately aid in good composite mechanical properties. Structural composite health monitoring (SCHM)/Intrinsic monitoring (iSHM) of composite systems is a necessity, with the primary objective of locating damage by quick detection to readily perform maintenance or in-service diagnostic checks.

Health monitoring is the acquisition, validation and analysis of technical data to facilitate life-cycle management decisions [12]. As design and functionality requirements of engineering structures such as spacecraft, aircraft, naval vessels, buildings, dams, bridges and ground-based vehicles become more complex; the rigors of SHM and damage assessment will increase simultaneously.

For example, composite usage in commercial aviation has steadily increased over the past 30 plus years [13]. This trend can be seen in Figure 1.1. The aerospace industry has one of the highest payoﬀs for SHM since damage can lead to catastrophic and expensive failures, and the aircraft involved have regular associate costly inspections. Even more so, increased composite integration is on the rise. Currently 27% of an average aircraft’s life

3 Figure 1.1: High payoﬀ for aerospace applications and the composite usage has an ever-increasing trend.

cycle cost is spent on inspection and repair [13]; a ﬁgure that excludes the opportunity cost associated with the time the aircraft is terminally grounded. An airline can have on average penalty costs of $100k per day for unscheduled aircraft [12]. In addition, common cause problems such as bird strikes have become an increasing daily problem. In recent times, the risk of bird strikes has risen 40% in 2009 compared to data from 2000 to 2008 [13].

Structural problems can also occur in infancy stages of fabrication and handling and even during in-use maintenance and servicing [6]. These low-velocity impacts produce barely visible impact damage (BVID), which is dangerous if left untreated because it presents defects which are high probable sites for onset and growth of damage. Most of the advances in SHM have concentrated mainly on active vibration control and on potential aerospace and civil applications [13].

In the case of Boeings new 787 line realeased in 2012, incorporates 50 % advanced ﬁber-

4 reinforced composite materials and have been in design for 20 years [14–16]. Compnonents incoporating carbon/epoxy systems include the fuslegae, tailkit and wing structures. De- spite the advantages over aluminum as a structural material, complexity in design criteria and industry wide standardization for composite inspection is lacking. The next generation of aircraft will employ 90% by weight of composite materials, as it can reduce complex assemblies like fasteners [14]. Although composites saw there introduction into aerospace over 40 years ago, the expanse into commercial aircraft occured with Airbus. Incidentally, the ﬁrst to market approach has not been without some early disadvantages.

Figure 1.2: Failed vertical tail kit of the Airbus A300 aircraft [17].

Noted as one of the ﬁrst in-service failure incidents of areospace composites, the New

York flight of American Airlines A300 accident occured in 2001 (Figure 1.2). Later cited as pilot error, the high excessive loading caused during flight maneuvering resulted in de- tachment of the vertical tail from the fuselage [17]. This signifies that pilots could greatly benefit from greater diagnostics during service, as a means to judge integrity versus flya- bility. Furthermore, recent headlines from the exploits of Airbus and Boeing, two of the largest aircraft manufacturers, have listed composite technology as a material gamble. Early in February of 2012, both manufacturers released modern versions of their stylized aircaraft.

Both manufactures saw material related pre-service damage as a part of the manufacturing issues relating to tolerances of composite components.

5 The application of localized damage detection and assessment of composite structures, especially impact damage, is still in its infancy. Research has also shown that no single technique in the modern materials era on its own can provide reliable results. Integrating several nondestructive evaluation (NDE) techniques could provide a solution for real-time health monitoring, but maybe computationally and time sensitive. Such studies, utilizing acoustic emission (AE) and laser shearography have reported considerable success, but the length-scale of damage is too close to becoming catastrophic incidences. Notably, damage detection has to be reliable while at the same time cost eﬀective.

The answer may lie with the development of damage sensing systems by the use of mechano-tribo-luminescent crystals embedded in the composite matrix. This will employ a biomimetic approach, because the crystals react to straining or fracture by emitting light of varied luminous intensity. Thus, a ﬁber-reinforced laminate concentrated with triboluminescent (TL)/mechanoluminescent (ML) crystals acting as health sensors to its host material, will give an indication of failure site initiation well ahead of catastrophic failure. This in-situ health monitoring system is comprised of embedded TL/ML crystals and optoelectronics for signal termination and processing. The stresses that occur during operation of a composite structure often lead to damage when events produce concentrated states. Assessing the ability of TL and its materials, may provide key mechanical information concerning stresses within the length-scale of composite structures. Key features of integration within composites is a critical need to the growing knowledge of triboluminescent based composite damage systems. This work is a continuation of novel M.S. work which outlined a means of dispersing TL ﬁller materials and a quantitative metric for dispersion in scaled composites.

Upon the forefront is a system level issue of sensor placement. Thus, the present work concerns the enacting and interaction of TL inclusion in composite matrices. Integrated material understanding is a precedence to system optimization for eﬃcient optoelectronic

6 collection guides for signal processing, which is the reason for this research work.

1.3 Research Objectives

Essentially, a SHM system (SHMs) consists of two major components; the sensory mechanism comprised of signal initialization and data transmission. The over arching case for new non-destructive technologies were made in the previous section. This work highlights the sensory initialization faction in the systems of advanced composite materials which has been understated in the prior literature concerning use of Triboluminescent properties.

The integration and available luminescent properties with interaction in composites have not been discussed in detail. More importantly, the individaul constiuents have not been scrutinized for their role with integrated TL. In addition, eﬀorts to realize the necessary transport medium from which energy collection is proﬀered and overall development of a novel SHMS consisting of the interaction between two key physical phenomena are explored in this study. The following chapters are devoted to reviewing modern monitoring practices and discuss mechanism behind TL as components for a structural damage sensor, albeit global or local sensing.

The formulation of a ‘TRiP SHM’ system is predicated on construction of a system of fundamentals or triune sensory mechanism . Elements of a holistic sensory system are:

1. Signal emission

2. Signal reception

3. Signal transmission

This chapter discusses the methodology, case experiments and organization of characterization methods in this research scope. The development of the comprised systems has

7 been denoted the ‘TRiP SHM’ system, concerning the TL and photo-active phenomena.

During the course of this research, focus has been placed on examining the practical mechanism for TL and mechanical properties of vinyl ester resin doped with triboluminescent materials. A novel approach to discovering photon detection capabilities via optoelectronic technology has been reserved for future endeavors, but is essential to the formation of the sensory mechanism proposed.

Figure 1.3: High-level roadmap of the proposed research.

A roadmap of the basic research areas for development of the sensory mechanism are found in Figure 1.3. Characterization and optimization of this particular system in regards to feasible solutions will entail a scrutinization of the three parameters. In actuality, the parameters can have dual functionality, but must follow the enumerated precedent act to function as a damage sensor. The organization of this research approach focuses on the signal emission through TL as outlined by Phase I (Figure 1.3). The exploration into the signal reception and transmission are addressed in Phases II and III. Combining initiated ﬂexural

8 emissions and PV detection will indicate levels of performance for a SHM system predicated on TL and photo-electric/active phenomena. Based on the photoelectric principle, signal transmission in the novel system will depend on the availability and eﬃciencies of creating excited photons into mobile electrons within the optoelectronic detection device. Detection has been estimated by preliminary research as accessible through PV technology [18].

This research contributes to addressing the deﬁciencies surrounding the amalgamation of triboluminescent ﬁllers in the composite technology. This ultimately results in the implementation and design of intrinsic photo-detection in two and three-phase composites.

This will further validate a scalable triboluminescent based system as TL materials remain a ubiquitous element in the composite matrix. The primary research objectives are:

(1) achieve fundamental understanding of the role and mechanism of TL materials in a structural member, (2) fabricate structural beams to excite TL at a known location during experimentation, (3) characterize the fracture mechanics under review of the triboluminescent pattern and spectral information, and (4) simulate the load response of simple three point bending, in conjunction, simulate the light intensity produced upon TL based on the loading of the ﬂexural specimen.

Design of Experiments (DoE) has been chosen as an experimental means for observing the system results and inﬂuential factors. Another objective of this work, is to estimate the lower threshold for TL excitation. Therefore, an experimental procedure for estimating fracture mechanics hve been employed for two-phase and three-phase composites. This will allow for estimation of the lower most level of system sensitivity indicated by TL. In addition, the modeling of the TL excitation coupled with an energy-based measurement is a paramount goal.

The benchmark for TL technology is to provide detection, severity, and location of matrix dominated failures. The matrix mode is the ﬁrst and most prominent site for the

9 occurrence of initial failure. Because as such, the primary work focuses on the interaction of TL in the composite matrix component. The hope is to observe if TL can accurately portray the load history of a structural member, although, this study is limited to an external examination.

1.4 Dissertation Organization

Science is what we can observe, test, study and demonstrate. This assessment is the onset of exploratory research combining multiple disciplines to achieve far reaching goals.

Concerning the two major subject and research areas, progress will be limited and thus part of the underlying goals is to state the research path forward following the conclusion of this research. This research is outlined in a methodical nature concerning apparent sensory mechanism for a structural monitoring system predicated on triboluminescent technology.

Particularly, sections have been divided to include discussions on composite material systems, signal generation, and signal transmission with emphasis on the speciﬁc material selection. Chapter 2 outlines the pertinent background research to the developed approach.

Chapter 3 - 4 describes the testing methodology, experimental procedures enacted and the respective discussion of the observable results of this experimentation. The roadmap and outline presented in Chapter 3 will be limited to Phase I & II research goals. Chapter 5 outline the model derivation and simulations. Lastly, the conclusion is objectiﬁed in Chapter

6 with future recommendations for continued study and development of the TRiP SHM scheme. An Appendix is also supplied.

10 CHAPTER 2

LITERATURE REVIEW

2.1 Composite Materials

2.1.1 Modern to Advanced Composites

Composite materials differ from traditional materials that have been used since the manufacturing boom of the late nineteenth century. By definition, a composite is comprised of two or more distinct materials usually of fibrous and resin materials. In practice, composites exist in a combination of many basic material systems and are classified by those specific material systems considering matrix or reinforcement type. Polymer-matrix (PMC), metal- matrix composites (MMC), ceramic matrix composites (CMC) or carbon-carbon composites

(CCC) comprise the matrix classiﬁcation [19]. There are distinct advantages of the individual constituents, for example, the extreme tensile nature of the ﬁbers and load transfer capabilities of the resin matrices. Together these two or more dissimilar constituents can provide unique material properties, with consideration of weight-to-performance, not seen in conventional materials.

These structural properties associated with composite materials can be tailored upon selection of oriented ﬁbers and type of matrix. The polymer resin matrices acts as the load transferring mechanism, and also provides for mechanical and environmental stability. Load transfer is made possible through the binding of polymer molecules to the sizing of ﬁber

11 reinforcement or other constituent. No matter the application, the interfacial properties of constituent composites are critical to high-performance. Performance is most likely based on mechanical properties, such as, strength, stiﬀness and interfacial adhesion. Notably, yield stress and modulus comprise basic measurements for advanced composite materials.

2.1.2 Fiber-reinforcement

Fiber reinforcements can exist in principal as individual fiber filaments, chopped monofil- aments or woven structures. Fiber woven structure exists as mats, textile fabrics and multi- directional woven structures. Fiber woven structures are the most widely used form of fiber reinforcement. Fabrics can be constructed in textile mills to form weaves and patterns consisting of yarns and tows that aide in manufacturability and processing (i.e. plain, basket, twill, satin, cross-ply, unidirectional weave) of composite laminates. Examples of common textile patterns are shown in Figure 2.1.

Figure 2.1: Woven structures of ﬁber reinforcements [19].

The primary function of fiber filaments and tows are to act as load bearing structures. Structural significance is determined by chemical composition and structure. Some modern fiber types are glass fibers, carbon fibers, graphite fibers, boron fibers, aramid

fibers and polyethylene fibers. The primary building blocks of these sets of fibers include

12 quartz/textbackslash silica, graphitic layers and other sophisticated polymers. These ﬁber types listed range from economical alternatives to high performance materials considering mechanical, thermal and electrical properties.

2.1.3 Polymer Matrices

The term polymer describes a long repeating chain or sections of monomers. Monomers are low molecular weight simple molecules that have the ability to link together through covalent bonding and undergo a process of vitriﬁcation or curing. The word poly-mer, in greek means many mers/particles. The science of polymers were introduced by Herman [20], and later expanded by Flory [21] and Gennes [22, 23].

Polymers can be synthetically developed by polymerization of simple molecules. There are two classes of polymers; thermoplastics and thermosets. Thermoplastics are soluble solution processible and reversible materials. They are known to soften and ﬂow upon heating, and solidify on cooling. Examples of thermoplastic polymers include polyethylene, Nylon

66, polystyrene and poly(ethylene terephthalate). Fabrication usually implores some soften- ing and melting to allow forming and molding. The synthetic resins are hardened through a heating process known as vitriﬁcation/curing. Curing of thermosets are irreversible chemical reactions usually rendered by a catalyst or form of energy input. A thermosetting resin undergoes an irreversible chemical reaction during cross-linking and eventual curing, some- times simultaneously processed with elevated temperatures. Thermoset polymers follow a three stage chemical cycle.

The A-stage which describes the raw state of small molecules with functional groups before saturated covalent bonding. This stage is the point of low viscosity. The accompanying

B-stage is the point when the resin has become highly branched known as gellation. At this state nearly half the monomers of the resin are polymerized. The molecules are spread out

13 Figure 2.2: Physical and chemical process in thermoset polymer curing cycle. and the material is very moldable because of moderate viscosity. C-stage is the final stage in which the resin has become completely cured and crosslinking is near optimal. A depiction of this process is described in Figure 2.2. The most actively used thermoset resin systems are polyesters, epoxies and vinyl ester resins (in chronological order). Resin systems such as phenolics and olefins have been synthesized in the last quarter century. Due to the specific chemistry polymers are highly temperature sensitive and often fail under abnormally high or low temperatures due to their chemistry.

2.1.4 Multi-scale Composites

Traditionally, composite ﬁllers have been utilized for cheap volume exchange and matrix toughening agents [23]. Fillers can be comprised of micro or nano constituents. Work on modeling techniques to predict material properties have been addressed for particulate composite systems [24–33].

In the last decade with large discovery in nano-materials, nanotechnology has found usage in composite materials. Namely, the carbon nanotube has been studied vigorously for its manufacturability and additive properties [34]. In some cases, Nanotubes are grown

14 radially on reinforcement to enhance the interfacial properties of the inter-phase region in composites.

2.1.5 Composite Processing and Fabrication

Fabrication of composite depends on the type of matrix system and its physical form, as well as form and combination of the reinforcement. Thermoplastics rely on the shaping and molding from conventional plastics and metal forming. Thermosets, however, require further processing steps in where the material forming is separate from the shaping [6].

Open and closed molding techniques are two types of manufacturing that are typically employed when making advanced composites, in what is known as liquid composite molding (LCM). Open molding is a relatively simple manufacturing method. However, during the open mold process, hazardous pollutants may be admitted into the air. Therefore, closed-molding techniques have become main stream. Close-molding techniques include resin transfer molding (RTM) and vacuum assisted resin transfer molding (VARTM). Clas- sic and Open mold methods for thermosets include bag molding processes, and hand lay-up and spray-up techniques. Other highly automated processes include ﬁlament winding, ﬁber placement, pultrusion and sheet molding for composite fabrication.

Among closed molding techniques, VARTM processes have several advantages over its counterparts. First, the vacuum bag allows an exact fit over the fiber preform which drastically reduces resin rich areas associated with open mold techniques. Secondly, the process is carried out in a closed mold making it a “green process”. Lastly, the process requires minimal vacuum or injection pressure (- 14.7 psi). The low injection pressure allows for the use of low cost tooling during processing. The filling process of the liquid resin is governed by several factors, such as injection gate/vent design, temperature and material properties.

Infusion techniques have existed for nearly 60 years[6]. The following are the essential

15 components to the LCM fabrication process. (1) a mold or tooling to contain the materials of construction, (2) the layup of reinforcement to form a ﬁber preform and (3) the matrix component, which in liquid or semi-liquid form is driven by pressure or vacuum for saturating the ﬁber preform to eventually form a cured composite.

High tolerance parts can be fabricated with autoclave processing. Autoclave process involves a unique pressure and temperature proﬁle in a closed chamber. This style of manufacturing usually involves prepreg materials. For large parts, this requires very large oval chambers. Currently, Out-of-autoclave or non-autoclave processing has seen increasing interest compared to tradition autoclave processing. The advantages are low fabrication cost due to low energy, low setup and preparation time and no need for nitrogen gas for pressure and temperature proﬁle. Progress towards out-of-autoclave processing began in the 1980s and progressed towards quality processibility for prototype limited life parts in the 1990s [35].

2.2 Composites & Failure

When a load is applied to a material, a deformation known as strain is produced.

However, strain itself is a physical result of work being performed by an impartation of energy. Therefore energy is the commonality among all damage and failure mechanisms.

Composites are an amalgamation of two or more distinct materials whose compilation oﬀer unique material properties. Discussing composite materials for structural health-monitoring or condition monitoring ideally requires reviewing the occurrences of onset structural defects on global and localized scales. Despite the advantages achieved by composite usage (i.e. light-weight, corrosion resistive, stronger), composite structures are brittle in nature and less durable during service. In particular, the issue of multi-velocity impact damage in laminated composites can be cataclysmic under certain loading conditions. This type of common

16 Table 2.1: Defects associated with composite systems [36].

DEFECTS IN COMPOSITES Structural Manufacturing Environmental Delamination Porosity Thermal damage De-bonding Contamination Corrosion Damaged fiber Improper cure Fatigue damage Cracks (micro) Resin rich/poor Loss of properties (modulus) Voids Interface integrity Missing adhesive Mis-oriented fibers/ply Wavy fibers Thickness variance Dimensional problems impact throughout a structures life-cycle (assembly and structure usage) can produce a number of failure modes within in a composite system. Specific types of defects that occur throughout a composite components lifetime are listed in Table 2.1.

In most cases, the majority of structural defect types are resultant of fatigue damage or creation of defects through multi-velocity impacts. In practice, defects can occur during manufacturing, fabrication and in service. Composite failure can occur in the following subsets (the instance of penetration only occurs in the case of impact failure):

Matrix mode - cracking occurs parallel to the ﬁbers due to tension, compression or • shear

Delamination mode - produced by interlaminar stresses •

Fiber mode - in-tension ﬁber breakage or pull-out and in-compression ﬁber buckling •

Penetration mode - mass completely perforates the impact surface •

The types of failures aﬀecting mechanical behavior of composites are (1) buckling, (2)

ﬁber-pullout, (3) ﬁber breakage, (4) matrix cracking (shear, bending), (5) delamination,

17 and (6) perforation. In continuous reinforced composites, fracture types are classiﬁed as interlaminar, intralaminar and translaminar fracture features. Types of failure are depicted pictorially in Figure 2.3 and represent the general cases of major failure modes. Examples of fracture features in laminate composites are depicted in Figure 2.4.

Figure 2.3: Macroscopic depiction of failure modes in composites after impact [37].

Delamination is an instance of layer by layer separation usually caused by inter-laminar stresses in the matrix (Figure 2.4 (a)). Matrix cracking occurs when sufficient distortional energy weakens the bonds allowing bending or shear transformation. The reinforcement materials can fail within a composite by means of fiber pull-out due to poor interfacial adherence in-tension or complete fiber breakage when transverse failure occurs. Buckling is the occurrence of wrinkling and warping under a compressive strength. Furthermore, damage in composites often begins on the non-impacted surface commonly in the form of internal delaminations. This barely visible impact damage (BVID) can severely decrease the structural integrity and mechanical capacity of a composite component, due to abiding residual strengths. Most composites are brittle in nature and can only absorb energy in elastic deformation and through damage mechanisms, and not by plastic deformation [38].

Impact damage can be relegated to local contact damage or global structural damage.

18 Figure 2.4: Fracture features of reinforced composite laminates. (a) interlaminar, (b) intralaminar, and (c) translaminar fracture [19].

Local damages may occur visibly as seen in perforation and permanent indentation, or have aspects of global damage (propagating failure) with invisible structural flaws. Particularly, local damage is the consequence of fiber and matrix crushing in the contact zone usually leading to perforation. However, global damage is an elusive complex three-dimensional pattern of matrix and fiber defects with possible invisible delaminations at larger scales [39].

It is helpful to view failure in composite materials in two general viewpoints: gradual/fatigue and catastrophic/impact failure which can both result in micro or macro-ﬂaws.

2.3 Mechanics of Composite Materials

Fracture Mechanics. When the local strength or ductility of a material is exceeded, a crack (two free surfaces) is formed. During continued loading, the crack propagates through a section until complete rupture occurs. Linear elastic fracture mechanics (LEFM) applies the theory of linear elasticity to the phenomenon of fracture propagation of cracks.

The resistance to fracture is defined as the fracture toughness, which can be quantified and measured. The Griffith theory and revised compliance method utilize the earliest works of energy balance to express fracture mechanics in computational form [40].

19 Linear Elastic Fracture Mechanics. In view of crack propagation it is of equal interest to ascertain at what value of an external force a crack will start to migrate particular on a microscopic scale. This requires calculation of the stresses at the crack tip. Fracture propagation, which can be introduced as ﬂaw like defects or inclusions, can develop into cracks in a material. Thus cracks become points of high stress. For example, consider an elliptical hole in a material plate undergoing uniform tensile stress, S (Figure 2.5).

Figure 2.5: Plate undergoing tensile stress on crack [41].

The elliptical hole, however minute, has an eﬀect on the stress distribution around the hole parallel to the nominal stress S. Given an x-y coordinate system, the parallel stress,

σy, rises sharply away from the center of the crack. Theoretically, a stress concentration, kt, exists over the boundaries of the ellipse. The stress concentration factor is a ratio of the maximum stress located remotely to the nominal stress. If the half height d, approaches zero, this provides a narrow slit-crack where σy and kt become infinite quantities. There- fore, in order to maintain an infinite stress state and concentration of stress, the crack tip must be narrow and sharp. The tip of the crack is where a finite value of the theoretical

20 stress is manifested. The material will thus yield and deform at this point. This region of deformation is called the plastic zone. The resultant is a crack-tip opening displacement

(CTOD), δ, where the tip undergoes a ﬁnite separation to a non-zero radius (Figure 2.6).

Figure 2.6: Ideal and real crack scenarios [41].

This is the likely case for ductile materials. For brittle materials, like that of polymers, elongated voids bridge the succumbing crack faces (crazing region) as shown in Figure 2.6(c).

This would entail little plastic deformation and result in failing by fracture. Under the deﬁnition of the stress intensity factor, K, it is assumed that the materials involved behave in linear elastic fashion as presented by Hookes Law. The stress intensity factor, K, is a material property, and is best described as a measure of resistance to crack propagation. It also gives an indication of the stress state. Mechanically, a crack is said to be aﬀected by a materials geometry, crack size, and gross stress [41]. Crack propagation through the solid, either as a result of fatigue, or by brittle or ductile fracture, is by far the most common cause of failure [42].

The critical value at which a material can withstand fracture or crack propagation is called the fracture toughness, KC . Uniquely, the fracture toughness has the ability to characterize the magnitude of stresses in the vicinity of the crack as a measure of crack

21 severity. In general, the stress intensity factor, K, is expressed by:

K = FS√πa (2.1)

Where factor, F , is dependent on geometry and crack size, S is the applied stress, and a is the crack half-length.

Mechanically diﬀerent modes of crack initiation exist in three displacement modes: (I) opening mode, (II) sliding mode and (III) tearing mode. Commonly, cracks appear perpendicular to loading. The opening mode is caused by perpendicular loading to the crack plane. This creates a division where the newly created surfaces move apart. It has been said this mode accounts for 95% of all fracture events within a solid material [41]. Mode I is a tension dominated event. Mode II or the sliding is produced by parallel forces to the crack plane and perpendicular to the crack line. This results in a sliding back of the leading edge of one face from the other. Finally, mode III is caused by sliding forces parallel to the crack surfaces and crack line. The latter two distinct modes are not common occurrences.

These modes are demonstrated in Figure 2.7.

Figure 2.7: Generality of multiple failure modes.

The stress intensity factor, K, can be denoted with a subscript for either modes of fracture (i.e. KI , KII ). For mode I fracture, the plane strain fracture toughness, deﬁned as the critical stress intensity factor under plain strain conditions is a quantiﬁable measurement of the resistance to fracture of a material. The fracture toughness in relation to applied

22 stress is given by equation:

KIc = YS√πa (2.2)

Where KIc is the mode I fracture toughness, Y is a factor comprised of geometry and loading of specimen, and a is the crack length. Furthermore, the term for Y is a dimensionless correction factor related to a and b. For bending of single edge beams, mode

I fracture can be represented by:

K = 1.12Sg√πa (2.3)

Here, Sg is derived from the moment of the bending stress which is equivalent to 6Mnb2t.

M is the moment of the beam, b is the width, Y is 1.12 and t is the beam thickness.

Griffith Theory - Compliance Method. The Griffith criterion is an attempt to fulfill a requisite for crack propagation. The requisite states that for the propagation of a crack, the stress at the tip must exceed the theoretical strength of the material. The Griffith theory is the stress concentration approach based on the energy balance within a material solid. No solid material is perfectly aligned and without any defects. The failure of a solid occurs within the presence of high local stresses and strains in the vicinity of defects. This creates a stress field, which can be depicted as lines that will become distorted or skewed together upon loading. If a crack is propagating the lines of force act as elastic strings and group together near the crack tip (Figure 2.8). This grouping of stress lines means more force a particular area hence stress concentration.

For instance, lets consider the potential (elastic) energy stored in a material plate with crack under Mode I. Again, assuming linear-elasticity the potential energy, U, can be viewed as 1 U = Pδ (2.4) 2

23 Figure 2.8: Concentration of stress lines at crack-tip of a notched specimen [43].

Where, P , is the applied load(N) and, δ, is the displacement at the point of loading.

Toughness or similarly related stiﬀness can be determined by the area under the load- displacement curve (Figure 2.9). The potential energy U, is represented by the triangular shaded area seen in Figure 2.9. In addition, the load versus stress curve reveals experimental modulus.

Figure 2.9: The displacement mode calculation for work energy of a loaded sample [43].

As described in the above Figure 2.9(b), for a crack to grow to a small quantity da, the stiﬀness of the material must decrease. This decrease as a result of crack initiation

24 is denoted dU and is the amount of energy required to grow a crack by da. The rate of exchange of potential energy with increasing crack area is deﬁned by Equation 2.5 and denoted as the strain-energy release rate, G.

dU 1 dU G = − = − (2.5) tda − t da

Succinctly, this is the energy required for crack advance per unit length of crack per unit thickness. The crack area is represented by t da. Concerning Griﬃths thermodynamic energy balance, two things happen when a crack propagates. First, elastic strain energy is released in the volumetric material. Secondly, two new surfaces or crack surfaces are created which represent a surface energy term. Thus, an existing crack will propagate if the elastic strain-energy released by doing so is greater than the surface energy created by the new crack surfaces.

The stress intensity, K, and the Griﬃth’s energy factor, G, are related as follows

K2 G = (2.6) E

K2(1 v)2 G = − (2.7) E

Where E is the material elastic modulus and ν is the Poissons ratio. Equation (6) accounts for thin specimens in the plane stress case. For thick specimen, a plane strain is accounted for by equation (7).

J-Integral Approach. The strain energy release rate can also be determined by integration of the J-integral. The J-integral provides a value of energy required to advance a crack in an elastic-plastic material. The J-integral can be experimentally determined by calculating the potential energy available for crack extension [44]. A method for practically determining the J-integral is given by Begley and Landes [45]. It is derived from the

25 interpretation of Eshelby from Cherepanov and Rice [46]. The potential energy diﬀerence between two identical loaded bodies having a neighboring crack sizes is represented as contours around a crack (Figure 2.10).

Figure 2.10: Example eshelby contours of the J-integral formulation [43].

If the bodies have a closed contour, (i.e. ABCDEFA), when external forces and internal stressess arise, the theory of energy conservation can be applied to the integral J.

∂U J = (2.8) − ∂a

Where U is the potential energy and a is the initial crack length. For instances of linear elasticity and slight yielding, J is equal to the driving crack force, G. The J-integral is a two-dimensional line integral along a counterclockwise contour gamma surrounding the crack tip. Based on Eshelbys interpretation [47], the potential energy per unit thickness is deﬁned on a surface integral as

∂u J = (Wn T i )ds (2.9) x − i ∂x ZΓ

Where W is the strain energy density or strain per unit volume

1 W = (σ ǫ + σ ǫ + σ 2ǫ y) (2.10) 2 x x y y x x

26 And T is the traction (tensor) vector pointing to the extents of the contour, deﬁned as

T =[σxnx + σxnx + σyny] (2.11)

The ds term is an element of length along Γ, and u is the displacement in the x direction.

The units of the J-integral are in units of energy per unit of length, area or volume (i.e.

J/m2 or N/m). In the case for plane stress for linear elastic materials, the J-integral has the following relation to the stress intensity factor found in equation (6).

K2 J = G = (2.12) E

Figure 2.11: (a) Strain energies at diﬀerent displacements, (b) resultant energy curves at corresponding displacement [44].

Experimentally, the J-integral can be determined by establishing several notched samples at pre-described crack lengths. The load-displacement curves are obtained for an initial crack length C1, A1 and resultant strain energy at the displacement δ1 (Figure 2.11). Once tabulated for several displacement intervals, the values for the strain energies are plotted against crack lengths. This results in the energy curves displayed in Figure 2.11(b). If ones takes the slope of each energy curve, also known as the J-curve, a critical displacement can be found to coincide with the greatest slope estimate. The largest estimated slope is the

27 critical J-integral value at which the material will have reached its highest allowable stress intensity.

2.3.1 Composite Summary

Towards increasing composite usage in industry, SHM must have a reciprocal develop- mental relationship. For the progression of advanced materials, structures must accompany means to facilitate decisive structural prognosis and multi-functionality. Because of the anisotropic nature of composite materials, damage can initiate in a multi-faceted manner.

With two or more distinct materials comprised into one structural entity, BVID is often associated with structurally dynamic and fatigue damage. Attention towards the matrix constituent is even more alarming, considering the polymer matrices are the weaker of the traditional two components of a composite material. The fracture mechanics greatly depend upon the material property characteristics, where usually material modulus is an important parameter.

2.4 Structural Health Monitoring

2.4.1 Biological Mimicry

Nature holds within itself unique innate solutions for real world technological problems.

A majority of problems encountered in science and engineering over the centuries most likely have a pre-existing solution or equivalent counterpart in nature [48, 49]. Imitation of biological systems will aide in achieving SHM capabilities. By sampling the constructs of nature, borrowing ideas and patterns of function novel techniques can be realized. For example, the human nervous system comprises various components and inner workings that are elctro-chemical in nature; primarily the brain (CPU), central vertebrae (temporary

CPU), and the vast array of nerves. By this unique form of mimicry we have a structure from whence to map out the intricacies of an advanced material nervous system, although

28 not organic, known as structural health monitoring. Most biological systems behave in this manner.

Theses biological systems account for varying events such as pressure, damage, humidity, strain, fatigue, and moisture [50]. Likewise, all of these elements are essentially parameters engineers have deemed signiﬁcant to diagnosing material systems.

The Human Body. The human body is the source of an intricate system of electrochemical communications network known as the nervous system. Its function is to detect and interpret internal/external stimuli. The brain and spinal cord comprise the central nervous system (CNS), which is extended by the connecting nerves and receptors that comprise the peripheral nervous system (PNS) [51]. The combination of these macro-systems in the human body underlined and overlaid with millions of receptors responsible for detecting the

ﬁve senses (touch, taste, smell, sight and hearing), gives the inherent ability to account for conditions aﬀecting pressure, humidity, noise, fatigue, and temperature.

Nerves are the primary channels to convey stimulatory signals. At the end of each nerve are neurons or sensory cells. These cells receive information from the environment, then output signals through elongated channels extending from the neuron called, dendrites and axons. Axons are the means for communicating with other nerves in what is referred to as a synapse or linkage between neurons. These connections are vital for transmitting electrical signals that release chemicals known as neurotransmitters. Impulses from the nerve structure are transmitted by continuous conduction along the length of the axon.

Overall, it is the stimulus that is converted into an electronic signal and transmitted to a sensory neuron [52]. Sensory neurons connect the signals to sensory receptors and then guided to the CNS. The control component of the CNS is the housing and deliberation of information sent as electrical signals [51]. Primarily its connection to the whole of the body is through the spinal cord, which is the continuation of the brain stem, cerebrum, and

29 cerebellum connection. The CNS processes signals, transmitting messages back and forth to the effecting organ than motor neurons. These receptors and neurons consist of the PNS which is vital to biological health monitoring. Depending on the function (the five senses), the human body has a specific set of organs to collect and disseminate signals given an innate organic health monitoring system.

2.4.2 Damage & Health Monitoring

Structural health monitoring (SHM) is an evolving ﬁeld of technology aimed at inter- preting data from sensing devices to provide critical information concerning the adverse eﬀects of internal or external damage of base components in order to enhance reliability and reduce costs of assessing structural integrity. Current SHM involves the monitoring of structural integrity over elapsed periods of time where catastrophic and residual stresses can arise. Health monitoring also relies on historical data to make inferences or critical judgments concerning life cycle assessment (LCA) and economical sensor placement. These decisions are made in near real-time and rely heavily on statistical analysis and complex algorithms for detection of out of control post damage events, as well as time consuming detection instrumentation. A structural review of this type is known as Non-destructive

Inspections (NDI), Non-destructive Evaluations (NDE) or Non-destructive Testing (NDT).

In general, the development of a structural health monitoring system covers four major areas: integrated sensor networks, signal generation, signal processing, and signal interpretation [53]. Other critical components of a complete SHM system include sensor archi- tecture, communications, computation, power consumption/contribution, and intervention.

The main objectives of SHM for third generation advanced composites that will include multifunctional aspects, are to obtain subsets of the following directives to present extreme safety measures for critical structures. The representative order dictated here is usually associated with a progressing feature of technology [53, 54].

30 1. Damage existence (Detection)

2. Location of damage (Localization)

3. Type of damage (Assessment)

4. Extent of damage (Assessment)

5. Diagnosis/Prognosis (Prediction)

6. Self-healing /energy harvesting (Regeneration)

The above list is a grading scale for detection technology encompassing modern and future condition based or structural health monitoring of critical components. The distinction between diagnostics and prognostics arises between detection and damage quantification in service versus upon known damage assessment in order to ascertain remaining useful service- life [55]. Damage assessment of various systems is unique to the particular structure under observation (i.e. damage to the rudder of an airplane). Thus, damage can be defined as changes that are inflicted on a system that affect its continual performance. Damage occurrences in composite systems are quite different from the modern materials that have been utilized for decades. Generally, all materials decrease in performance (i.e. mass, strength, stiffness, etc.) as flaws are introduced, making outfitted structures less reliable over time.

For the branding of composites, issues of non-linear structural mechanics makes for an even more complex material failure system. For all systems, it is known that minute ﬂaws are usually the culprit for gradual failure propagation. This can result in catastrophic failure.

Identifying damage, location and the severity at those minute defects is the overall issue and the precursor for detecting and predicting macroscopic fatigue or catastrophic events.

Furthermore, systems of SHM can be classiﬁed into two categories; passive or active sensing. For a passive sensing system, only sensors (i.e. transducers, piezoelectric patches,

31 strain gauge, etc.) are installed in the structures. Sensor measurements are constantly taken in real time and compared with a set of pre-damage referenced or base data. A passive system will estimate the condition of the structure based on a comparison of past and present information. Hence, the technique of data comparison for interpretation of structural conditions is crucial for the reliability of the system and most eﬀorts are exhausted in this area computationally. The system would require either a data bank with a history of pre-stored data to store large data sets for featured comparisons [56]. For an active sensing system, known external excitation mechanisms are intentionally inputted into the structures through built-in calibrated devices such as transducers or actuators. Since the inputs are known comparable quantities, they can be strongly related to a physical change in the structural condition such as onset of damage. Active sensing systems are more technologically compatible with distributed and on-line monitoring systems than passive systems, but are not developed enough for continual, large scale monitoring.

2.4.3 Non-destructive Evaluation - Modern & Emerging

Current techniques for structural damage monitoring of in-use structures are known as non-destructive evaluations or non-destructive inspections. The forename non-destructive, implies inspection of structures by evasive means that do not require the physical testing by caustic assessment. Table 2.2 is a set of classical and advancing inspection technologies.

With modern technologies and several advancements, NDE methodology has been the standard practice for industry for some time now (Table 2.2). Emerging technologies have been derived from the database of modern NDE practices (Table 2.2). Its segway from metal inspection into composites has been slow to address specific material differences, but seeks to provide reliable detection techniques for deducing micro-sized flaws. Only ultrasonic methods provide the adequate resolution needed to assess mechanical condition and structural integrity [36]. However, practical implementation of ultrasonic testing requires point

32 Table 2.2: Emerging NDE for composites and emerging NDE for composites [36].

Modern Practices: Advanced Technologies: Ultrasonic scanning X-ray Tomography Acoustic emission Laser Ultrasonic Tap Test Holography Resonance Laser-optical X-ray Vibro-thermography Visual Acousto-ultrasonic Optical D-sight Thermal Interface integrity Eddy current Structure problems (geometry)

to point measurements, although, computerized C-scans have made it possible to increase throughput. Structural complexity, however, presents tremendous operational diﬃculties.

C-scans are sound in ﬁnding impact damage and ﬁber fatigue, and the elusive delamination defects but lack prognosis of mechanical state (giving no indication of lifecycle state). This is the popular tool of choice for aerospace industries.

X-ray imaging was originally designed for inspecting metals for detection of voids and cracks. Particularly, real-time imaging has enabled X-ray technology to image the geometrical features to detect discontinuities [53]. Acoustic emission (AE) testing uses stress waves that travel from source to a sensor, detecting various failure processes associated with composite failure such as deformation, crack growth, degradation and fiber-matrix damage. The power of the AE method is in distinguishing between different microstructural flaws. The consistent visual practices involve regular walk-abouts in order to manually test structural components as a way to detect surface discontinuities or in instances manual tap testing to decipher material difference by sound. Another type of visual aid is dye penetration. Here, a liquid dye substance is applied to the structure and allowed to seep through any present surface cracks. If any cracks exist they should be visually detectable by UV irradiation.

In this case, the dye becomes a nuisance and rather messy process for inspection. Visual

33 inspections are one of the most common types of NDT but do not oﬀer the detection level of a sub-surface inspection method.

These specific inspection procedures became mandatory after the fuselage of an Aloha airline flight ripped open in 1988 [57]. In fact, inspection practices encompass a pre-flight

”walk around” to assess any visual damage, which usually occurs over the course of every

ﬂight. Every 6000 – 12,000 ﬂights, critical components must be disassembled and inspected by more sophisticated inspection methods which require tremendous downtime [58]. This human intervention is not the best practice for composite usage and assurance for continued reliability. Non-destructive inspections involve searching, repairing, and post searches to ensure compliance of the composite structure.

The major challenges to using NDE as a SHM technology, is related to size and geometry, and arrangement of a component. For the large industrial structures damage sensing techniques involve laborious visual inspection, c-scans, and other non-destructive means. In the present trend of NDT application on aircraft 70-80% of NDT is performed on the airframe, structure, landing gears and the rest carried out on engine and related components [53].

NDT is the most economical way of performing inspection and this is the preferred way of discovering cracks or any other irregularities in the airframe structure [53]. But in scheduled maintenance it is diﬃcult to ﬁnd the defects rapidly, as the maintenance of aircraft must be accomplished within scheduled time and then released in time for commercial operation [53].

The time to detection is an issue for NDT, because unless a ﬂaw is visibly noticeable, detection can be masked by sub-surface defects. Nearly, 70 % of cracks occur because of fatigue and these cracks likely existed sub-surface before any visual damage could be seen [59, 60].

A major challenge to using modern practices is its non-value added aspects and potential to overlook defects. For instance, 80% of airframe maintenance inspections are visual in nature [61]. Scanning of structures by combinatorial means is also becoming an industry

34 leader. For large components such as a wing structure, would require positioning and tran- sit times of the aircraft. Scanning large parts requires strenuous eﬀort and is perplexed by advanced geometries.

Nemat Nassers group has worked on disseminating information by embeddable sensors

Fast Fourier Transforms (FFT) [62]. Loweke et al. [62, 63] worked on developing smart composite materials that monitor their own health using embedded micro-processors and sensors to form network communication nodes in the layers of a composite. They rely on the two-dimensional FFT to determine the global components of a strain or temperature distributions. Large volumes of information are generated, so two methods for implement- ing the distributed 2D FFT were developed based on row-column algorithms for eﬃcient assessment of monitoring health of composite materials. To further this investigation, work was done to embed and produce sensors of this type in composite structures. Under Scaaf et al., the Nasser group has explored the applications of smart composites as an issue of the mechanical coupling of the sensor to the host material to assess its integration in structure in which they have found considerable eﬀects [64, 65]. They concluded 2D FFT can be a useful tool in revealing the relative magnitudes in a material but the integration methods results in 85 % reduction of the material fatigue strength.

Schulz and company [11], investigated intelligent composites through means of piezoelectric patches and scanners. Primarily by acoustic emission gathering and vibratory sensors such as the scanning laser vibrometer (SLV) which has the ability to measure vibration responses across a structure at several spatial points. Using two differing methods (boundary effect deflection) and operational deflection pattern recognition (ODPR), they were able to distinguish damage by observing the natural frequencies of structure and extract its damaged state. Recently, Schulz et al. [66], emphasized the problem of detecting damage in complex geometries and structural joints, because damage often initiates at joints and

35 Figure 2.12: Schematic description of SNS derived from human biology [66].

locations where section properties change. This can be addressed through a biomimetically inspired approach known as passive structural neural system (SNS). SNS is a highly distributed continuous sensing system that provides high sensitivity to damage by connected nodes. The SNS operates continually by monitoring Lamb wave propagation representing acoustic emissions (AE) under simpliﬁed instrumentation (Figure 2.12).

The uniqueness of the SNS approach, is the n number input channels from the sensors and only two channels of output to reduce complexity. Figure 2.12 illustrates the SNS in the body of an aircraft structure. The sensors would be attached to the inner surface for continuous health monitoring. These sensors are connected to form the SNS that is in turn connected to the computer for data acquisition, storage, and analysis. The type of lamb waves measured by the SNS depends on the type and location of the sensor. In this research by Kirikera and Schulz, piezoelectric strain sensors (PZT) are used in a bi-directional format and can sense in-plane and out-of plane wave propagation enhancing detection [66]. The SNS

36 reduces the required number of data acquisition channels necessary to monitor a structure, which will also allow for diﬀerent combinations of sensor incorporation (i.e. TL sensor).

Figure 2.13: Proposed piezoelectric active wafer system with arrayed sensing [67].

Giurgiutiu, has been expanding a piezoelectric active wafer (PWAS) system for both individual probing and hotzone phased array [68]. PWAS are considered to be a less expensive, non-intrusive surface or embeddable technology. As Figure 2.13 describes, the arrays located in hotzones are connected to repositories are dissemination points. This could be wireless.

Figure 2.14: Schematic description of the SMART Layer design [13].

37 The Stanford Multi Actuator Receiver Transduction Layer (SMART Layer) derived from the Haywood team, is a commercial impact monitor system utilizing the unique sensing abilities of piezo-electric sensors arrayed and connected to printed circuit cells [13]. The

SMART Layer is embeddable technology that utilizes sensors and transporting arrays to create a distributive sensing layer that can easily be implanted in pre-preg production (RTM processes). Figure 2.14 displays a depiction of the embedded sensor. These peizoceramic sensors in a circuit array form have been suggested for production monitoring alongside life cycle monitoring [13].

Commercially, there have been few adopted embedded technologies for SHM. The necessity for measurable structural reliability is essential. Sandia National Lab in partnership with Boeing recently incorporated an in situ crack-detection sensor into its NDI standard practices manual for Boeing airframes [69]. This is a step in addressing and meeting the needs for reduced human assistance. The sensors are manufactured by Structural Monitor- ing Systems, Inc. (SMS), based in Australia and are said to be inexpensive, reliable, durable, and easy applicable to host structures. These continuous sensors have been reported to be able to detect hidden cracks, erosion, and impact damage, among other defects in aging aircraft structures. This technology is also based on piezoelectric patches and thin ﬁlm circuit boards.

In regards to nanotechnology and SHM systems, some research has demonstrated simple, eﬀective and real-time diagnostic, and repair techniques featuring electrically conductive carbon nanotube additives that are easily transferrable into the host structure. These nano-materials are the wave of new materials that oﬀer a plethora of unique properties

(mechanical, electrical, thermal) as the graphene era continues onward. One such system has shown that by monitoring volume and through-thickness resistance, one can determine the extent and propagation of fatigue-induced damage such as crack and delamination

38 growth in the vicinity of stress concentrations with carbon nanotube composites. The conductive nanotube network also provides opportunities to repair damage by enabling fast heating of the crack interfaces; the authors show up to 70% recovery of the strength of the undamaged composite [70]. These advances could result in enhanced safety, reliability, and service life for polymer composites that are used in engineering applications [27]. Other results like these have been demonstrated in the work of Pham et al., where thermo-plastic matrices were made conductive by nanotube incorporation [71]. Conjugated polymers and carbon nanotubes possess interesting optoelectronic and physicochemical properties that are attractive for their use as transducer-active materials in various sensing devices [72].

In addition, carbon nanotechnology will allow for multifunctional sensing capability for pressure, temperature, and strain, etc., although challenges may exist with synthesizing continuous CNTs for sensors.

2.4.4 SHM Summary

The race towards health monitoring of structural components is a race towards biologically inspired solutions. Bio-inspired themes have innate solutions towards active health monitoring to assess location and damage within composite laminates in real time. Non- traditional materials are allowing for reduced complexity compared to standard techniques, and nanotechnology will eventually lead in this exploration because of its high strength to weight ratios, and self-healing beneﬁts. A consensus among researchers believes embeddable devices (i.e. FBGs, MEMS, TL, CNTs, PZT) with emphasis on node reduction, as well as reducing the data structure will greatly facilitate intrinsic health diagnosis. Furthermore, micro-level detection will allow for increased health sensing functionality, and provide detection prior to catalytic failure. Most research is based on pseudo-strain gauges (i.e. PZT), in order to directly relate event information in correlation with selected health monitoring capture technology having the ability to decipher location and a level of damage charac-

39 terization. The central themes expressed by these various systems are only local means of detection at best, and are predicated on post processing to determine structural health.

The race towards adequate SHM will involve embeddable technology that can assess in real-time with distributive sensing on a global as well as local scheme. Understanding The initialization of damage signals and transmission of signals is a primary concern for building a SHMs where sensory mechanism forms the base technology.

2.5 Sensory Mechanism: A Principle Component

2.5.1 Sensory Signal Emission

Using principles of intelligent design, a sensory mechanism is a multistep process including some stimuli-signal, signal-conversion, conversion-reception, and then a reception- transmission. Natures way of sensing involves the sensory receptor, an organic ampliﬁer and dense neural network to convey and interpret the presence of a stimuli. Here in this review section, we highlight the use and mechanism of luminescence and their materials to be used as simultaneously as a receptor and general stimuli. As the initial precedence for a sensory mechanism, the signal emission is discussed in this review as a stimulatory signal initiated by the action of triboluminescence. TL is under review for its applicability in detecting matrix failures in composites through embeddable materials as illustrated in impacts of glowing composites by Sage et al. [73,74]. Light is an interesting form of energy that can be utilized to siganl failure in materials.

2.5.2 Triboluminescence

Triboluminescence is light upon mechanical rubbing or fracture. This is synonymous with Deformation (DL) and Fracto-luminescence (FL) [75, 76]. TL is under review for its applicability in detecting matrix failures in composites through embeddable materials of micron and nanoparticle size. Also notable is light emanation from photon bombardment

40 namely Photoluminescence (PL), and Mechanoluminescence (ML) which is comparable to elastic deformation upon mechanical stress [77]. However, the mechanisms of TL an be linked to other distinct phenomena of luminescence such as: cathodoluminescence, electroluminescence, ﬂuorescence and phosphorescence [28, 78–80]. This can make determination of the underlying mechanism complicated and an unsettled agreement on excitation strate- gies. The eﬃciencies of TL light have strong correlation to synthesis and size of materials, most reports explore the excitation mechanism, chemical synthesis of materials, and the duration of the emissions [81–84].The extent of these matters can be noted in reviews by

Walton [85], Sweeting et al. [86], Sage et al. [87] and Olawale and Dickens [88]. Here, brief emphasis will be placed on the opposing arguments. Instead, the discussion will center around known mechanisms and approaches to model the luminescent production.

Kinetics of General Luminescence. Luminescence takes multifarious forms, and its various types surrounding the subject of TL will be discussed in this review. Material synthesis and structure determines the exact form of luminescence. Compounds may exhibit luminescence, but only at small eﬃciencies making it virtually impossible to detect [86].

There efficiencies can greatly be enhanced with addition of impurities or dopants to the lattice of a host structure. In particular, the interactions are governed by physical laws with the main theories derived from piezoelectric effects and quantum theory to explain sufficient TL and PL.

Luminescence of any form is derived from energy accretion on a molecular scheme. Light itself is a form of energy made up of photons and the emission of light from a source of energy is called luminescence. According to Bohr’s model, electrons accompany diﬀering energy levels around the nucleus of an atom remain active upon excitation. This can be used to explain the excitation and emission of typical ﬂuorescence that accompanies PL observations.

41 Figure 2.15: Quantum theory for explanation of (a) Bohrs model of energy level transitions (b) excitation to emission.

Bohrs model explains the nature of particles and their subsequent atoms, where each atom is made up of protons, electrons, and neutrons. In this model the nucleus is the ground state and it requires certain energies to rise from a ground state to higher energy levels (Figure 2.15). Upon impact or excitation, particles absorb the necessary energy needed to ascend energy levels from low to high. The ground state is the closest to the core

(valence band), and it is the electrons that can have mobility to ascend to higher energy states (conduction band).

The ascension of these electrons through the energy levels produce‘s the charge required for illumination as shown in the schematic in Figure 2.15. Emission of light happens when particles lose (give oﬀ energy in the form of photons) energy by descending through lower energy levels. As illustrated in Figure 2.15(b), electrons are excited (1) to a state where they exceed higher energy levels and (3) emit light when falling through preceding energy levels. Types of luminescence can be distinguished by examining the excitation source as described in Table 2.3, although this review is focused on TL observations.

Concerning quantum confinement [82], which has gained considerable confidence for explaining enhanced mechanisms for TL an PL efficiencies alike, molecules and electrons exist in discrete localized states (orbitals). As illustrated in Figure 2.15, emission or what

42 Table 2.3: Luminescence types/Excitation source.

Luminescent type Excitation source Cathodoluminescence Electrons Photoluminescence (PL) (UV) Photons Chemiluminescence Chemical reaction energy Electroluminescence (EL) Electric ﬁeld Triboluminescence (TL) Mechanical energy Mechanoluminescence (ML) Mechanical energy is really a semi-conduction process has to allow electrons to be excited from the valence band (VB) to the states of the conduction band (CB). Depending on the excitation source

(Table 2.3) determines the allowed movement of electrons to higher states of energy. In the case of TL, this is a limited reoccurrence of holes originating in the VB. With regards to

PL, the electron holes are continually created as long as photon bombardment (wavelength dependent) is consistent.

Figure 2.16: Quantum conﬁnement on digressing length scale.

Quantum confinement in localized states becomes apparent due to the nature of particle or crystal size (illustrated in Figure 2.16). The belief is related to the proximity of crystals on a molecular scale, and its effect on the bandgap of host materials. Confinement refers to the proximity of molecules that cause the charge carrier transfer rate to be higher in nanoparticles than in bulk states due to tunneling [89]. If the particle size is reduced during synthesis below the exciton Bohr radius, tunneling will occur and crystalloid materials that

43 are closer in alignment and have a higher interaction that will then promote accelerated charge transfer [25].

Theory of Triboluminescence. The piezoelectric eﬀect is the dominant theory concerning the majority of materials with asymmetric (non-centrosymmetric) crystal structures. The theory for piezoelectricity was ﬁrst proposed by Longchambon [90]. Recently,

Chakravarty et al. [91] expounded upon the existing mechanism by proposing an amended piezoelectric theory, with rival theories being explained for TL materials that are not piezoelectric in nature [81, 92]. If any contradictions do exist, they exist in explaining TL in symmetric crystal structures. Half of all compounds exhibit some form of TL/ML [86].

Due to the variation in crystal structure, it is likely that other mechanisms for TL besides the piezoelectric eﬀect, exist. However, it can be conﬁrmed that a mechanism for charging

(not necessarily charge separation) must occur to produce a luminescent event.

Figure 2.17: Modiﬁed chart of luminescent derivatives from ML/TL [93].

The diagram in Figure 2.17 shows the organization of luminescent phenomena in relation

44 to TL. ML and TL in most respects are analogous, and they are delineated into fracture and deformation luminescence. FL is a piezo-dominated mechanism, which relies on charge separation upon newly created surfaces, and DL relates to charged dislocation of defects.

DL is further segregated into luminescence by elastic and plastic deformation.

The piezoelectric eﬀect is the production of charge separation upon the onset of a newly created fracture surface. It occurs only in non-conductive materials and has an asymmetric crystal structure [94]. In crystollagraphic structures, asymmetry and non-centrosymmetric refers to those without an inversion center. The piezoelectric eﬀect was discovered by the

Curie brothers in 1880 [95]. They found that when a mechanical stress was applied on crystals such as, Si02, Rochelle salt, and cane sugar, an electrical charge was produced.

The charge produced a voltage signiﬁcantly proportional to the stress. Thus, piezoelectric crystals generate an electric potential (ﬁeld) from applied stress. This is also the case for most abundant TL materials [91]. A direct correlation between TL intensity and the charge produced during fracture of Rochelle salt crystals suggested the possibility of a piezoelectric origin for TL [96]. This investigation on the piezoelectric behavior of orthorhombic crystals

(a stretching of the cubic lattice) indicated TL is a structure sensitive event. This suggests TL only appears in non-centrosymmetric crystals. Further work consisting of organic orthorhombic cases alluded to events of TL only during crystal fracture. Various studies indicate, TL originates from excited molecules of a nitrogen discharge, which suggests that the overall mechanism of excitation may involve creation of charged surfaces during fracture followed by excitation of nitrogen molecules by electrons being accelerated between the surfaces [97, 98]. This hypothesis is further adopted because the large quantity of nitrogen in the ambient atmosphere. Table 2.4 is a classiﬁcation of TL theories pertaining to crystal structure. A material such as ZnS would be considered a piezoelectric mechanism by its non-symmetric structure.

45 Table 2.4: Theories and hypotheses organized by crystal class.

Centro-symmetric Non-symmetric Defect theory Piezoelectric theory I Electriﬁcation Piezoelectric theory II

From the aforementioned text, piezoelectricity (non-centrosymmetric) of crystals is needed for TL. In contradiction, studies of centrosymmetric TL compounds do not support a piezoelectric instance [98–100]. Sweeting et al. [101], stated that non-centrosymmetric

(piezo) crystal structure is necessary for tribophotoluminescence in pure covalent compounds and that impurities in centrosymmetric materials are important to TL creation in all likelihood [101, 102]. The disorders or dislocations within centrosymmetric crystals might provide the local dissymmetry to support charge separation. Essentially, the defects in the lattice serve as weak members and react to emit light. Defects might present an instance of charge dislocation, but there has not been enough evidence to support this conclusion suﬃciently. The major question is whether disorders within lattice structures cause charge separation or dislocations cause electron accretion that will result in the luminescent phenomena. Crystal structure appears to be a determining factor in TL production. Chen et al. [103], suggest TL is predicated on suﬃcient charge separation for TL, regardless of crystal structure. Further understanding might be reached by further classifying TL into fractured induced and non-fractured induced criterion. Table 2.5 lists the subcategories of

TL theories and hypotheses towards mechanism of charge accretion.

Fracture-to-TL can be explained by piezoelectricity for non-centrosymmetric crystal structures. In contrast, the case for symmetrical systems cannot be explained by a piezoelectric instance. Symmetric crystals in the presence of dislocations in crystal lattices produced by impurities provide the deformation needed to produce TL. DL is the result of excitation of luminescent centers (defects) by moving charged dislocations [105]. Dislocation is an

46 Table 2.5: Theories and hypotheses organized by mechanism.

Luminescent Theory Mechanism Literature Piezoelectric I existing FL-gas discharge [91, 97] [101, 102] Piezoelectric II amended FL-gas discharge [91] Defect & disorder DL-charge dislocations [33, 100–102] Electriﬁcation Frictional reaction, internal cleavage [92, 97, 100,104] Thermal High pressure eﬀfect [92, 100, 104] Chemical Chemical reaction by mechanical energy [92]

irregularity or crystallographic defect within the host lattice. The nature of the charged dislocations is the base for recombination of e-h pairs resulting in luminescent output.

From their experimentation with a tetrahedral manganese complex, Zink and Hardy explain the mechanism for TL excitation as an instance of a population of electrical excited states at high pressure [100, 104]. Electriﬁcation is caused by the rubbing together of two dissimilar materials initiating charge recombination or electrical impact. However, frictional electriﬁcation is hardly a proven instance since TL can be excited by grinding with a wide variety of materials. TL can also be observed in other crystals without grinding, such as thermal shock by submersing the crystals in liquid nitrogen.

Hardy et al., also explains that at high pressure, the thermal population of a electronic state different from the ground state could occur [100, 104]. If the ground state and an excited state respond differently to the medium, the application of pressure can cause a shift in the relative energies and the inter-nuclear coordinates. It has been demonstrated that states which are higher in energy than the ground state at atmospheric pressure can become thermally populated at high pressures. Thermal population of the excited states under pressure is likely in the manganese system based on the high-pressure spectroscopic results. However, this mechanism may not be unique in describing TL in centrosymmetric crystals because crystal defects could provide a small number of sites where the centricity is destroyed and electrification could then have an important effect.

47 Several of the proposed mechanisms operating simultaneously may play a role in TL/ML emissions. The proposed mechanisms are attempts to explain the phenomena, but do not offer enough definitive proof to claim one mechanism as the explanation for TL production for the entirety of crystalloid materials. However, piezoelectric materials and their non- centricity do allude to a method of fracture induced TL. The theories for luminescence of various symmetric crystals are perplexed by their explanation and lack of physical evidence to date. Triboluminescence is an intrinsic property of the crystals and is discussed in terms of the piezoelectrification produced during the movement of cracks in the crystals [106].

Promising Triboluminescencent Materials. TL intensity is the major factor in selection of suitable TL materials. Emphasis is placed on the amount of light emitted upon excitation and the visibility by the naked eye as a means test. The human eye is sensitive to greenish-yellow light at a wavelength near 555-580 nm [86]. Triboluminescent research to date has explored the use of thin ﬁlms as well as bulk materials, but much recent emphasis has been placed on nano-synthesized particles as suitable optical materials. A chart of speciﬁc TL materials are in Table 2.6. This discussion highlights the main TL/ML materials used in this work, ZnS:Mn, with honorable mention to the europium complex (EuD4TEA) and strontium (SAO) complexes as other highly Triboluminescent materials.

Table 2.6: Promising triboluminescent materials.

Peak emission Crystal material wavelength Lifetime MP Literature (nm) (µ s) (◦C) ZnS:Mn 520-590 65-508 230 [73, 74, 89, 91, 107] EuD4TEA 613 486-538 250 [108, 109] SrAl2O4:Eu 520 n/a n/a [73, 74, 107, 110–112] Organic+Tb 550 446 290 [73, 74, 107] Ester 525 n/a 195 [73, 74, 107] Sucrose 337 n/a n/a [86] MAC 435 n/a n/a [113]

48 The TL is a distinct phenomena that lends itself to other notable diﬀerences that might be advantageous of damage sensing. However the compatibilty of the foreign material is of crucial importance, since the material will need to be integrated within a structure. A prerequisite outlined for integration in composite materials is a melting point greater than the composite cure temperature ( 120 ◦C) [73]. Other distinct caveats to the spectral ≥ information form luminescent signals are range of wavelength (peak emission) and ﬂuo- rescent decay time. The wide range of peak emissions can be seen in Table 2.6. These spectral tendencies might lend itself to a damage alarming system based on a variegated and multicolored scheme [107].

Zinc Sulphide Manganese (ZnS:Mn). Zinc Sulphide (ZnS) is a widely popular and studied material, moreso, due to its electroluminescence, and application in scintal- lation and ﬁeld emission devices [89, 114]. Zinc Sulphide: Manganese (ZnS:Mn) is a wide bandgap (Eg 3.7 eV) II-VI compound semiconductor material. In their bulk states they are mainly manufactured as phosphor crystals, with most dated research focusing on synthesis of nanoparticulates [115]. Experimentation with Zn S:Mn phosphors produces piezoelectric discharges of yellow ﬂuorescence [89, 114–117]. In light of mechanical weight, the crystal density is approximately 4.1 (g/ml). The modulus of ZnS has been estimated to be within the range of 79-115 GPa [118]. The nanoindentation hardness and elastic modulus values have been measured for bulk ZnS with a hardness value of 1.9 GPa and an elastic modulus value of 75 GPa [116]. The modulus of ZnS has been estimated to be within the range of 79-

115 GPa depending on the crystal orientation, although it was experimentally determined to be 70 GPa [118]. It has been reported that the elastic, plastic and fracto-luminescence occurs at stresses of 1, 30, and 100 MPa, respectively [117]. The TL intensity of ZnS is visible to the naked eye, and is considered by researchers to be the best alternative for TL applications when considering luminosity [119,120]. Chudacek [119], found that the TL yield of

49 ZnS is proportional to the time change of the exciting pressure. When ZnS is crushed, very frequent intense light impulses are obtained which last for longer than 10−4 sec (100 µs) and remain predictable if exciting pressure does not exceed 700 kg cm−2 [119,121]. TL was further explored by Hollerman et al, whose study showed a relationship between impact force and light intensity giving further vindication towards signify levels of severity [76].

The light intensity of Zn S can be greatly increased when doped with an activator such as manganese [122]. Luminescent properties of ZnS can be controlled using various dopants such as Ni, Fe, Mn, and other materials like Cu [122, 123]. Diﬀerent activators (i.e. Cu,

Eu) can be used to change the emission wavelength of the doped phosphors. They not only give luminescence in various regions but can add to the excellent properties of the host ZnS. Presently, transition metal ions and rare-earth ions have been given attention as dopant materials ( i.e. Ni2+- Mn2+, Pb2+-Cu2+, Cu2+-Cu2+, Mn2+-Eu2+) [124]. The

PL spectra for different Mn concentrations showed that during changing the concentration of Mn ions, there is a maximum emission in optimum doping ( 5.5% of Mn) [125]. It has also been found that 5 % Mn incorporation presents sufficient TL five times higher than that of undoped ZnS, with crystallinity greatly enhancing the TL intensity [39]. When consideration is given to nanometered synthesis of ZnS and dopants a considerable increase in luminescent properties are noticed, due to a quantum size effect/confinement known to nanomaterials. A large variety of methods are employed for synthesizing 1-D nanostructures via thermal diffusion, laser ablation, electrochemical fabrication, epitaxy, high temperature reactions, micro-emulsion, and solvo-thermal methods to name a few [123–127].

In literature, various mechanisms have been proposed to explain the luminescence of

ZnS:Mn2+ [83, 84]. Study of the PL mechanism of bulk Zn:Mn2+ shows that the Mn ion accelerates hole recombination of the ions electronic state due to quantum conﬁne- ment [82, 128]. In one mechanism, it has been proposed that the Mn2+ ﬁrst traps a hole

50 Figure 2.18: a) TL intensity of various inorganic thin ﬁlms under the same friction conditions, b) Eﬀect of Mn additive amount on TL intensity [80].

and then subsequent recombination with an electron results in Mn2+ in the excited state.

Alternatively, an exciton may be bound to Mn2+ and recombination of the bound exciton promotes the Mn2+ in the excited state. Both mechanisms may be present in bulk and nano

ZnS:Mn forms [89]. The emission from Mn2+ can be excited either directly by recombination of a bound exciton at Mn2+ or via hole trapping in Mn2+. Subsequent recombination with an electron in shallow traps result in Mn2+ in an excited state, (Mn2+)*, which gives rise to the well-known orange/yellow PL emission. This yellow emission of ZnS:Mn is typically as-

2+ sociated with the Mn transitional states (4T1 - 6A1) and its relative peak approximately

585 nm (2.12 eV) [83, 89]. The scheme of this emission is summarized in the following equations:

Mn2+ + h+ Mn3+ (2.13) vb →

Mn3+ + e− (Mn2+)∗ (2.14) →

51 (Mn2+)∗ Mn2+ + hv (2.15) → Mn

Figure 2.19: Schematic of energy-transfer that result in ZnS:Mn2+ PL emissions [89].

The transition processes denoted by (1), (2), and (3) are illustrated in the following

Figure 2.19 and show the energy transfer (recombination) process that result in transitions

4T1 - 6A1 excited states. It is evident that tightening of the transitional bands inﬂuences the spectrum of light emitted, which is apparent by the incorporation of Mn.

2.5.3 Modeling Luminescence: Triboluminecscent Intensity and Spectral Analysis

Many materials that have exhibited TL/ML have been researched and experimented to resolve analytical and numerical solutions to the light intensity conundrum. Several re- searches in the late 1970s and early 1980s reported eﬀorts in luminescent intensity models

[40, 41, 50, 57-59]. TL kinetics and mechanisms are trapped between the following mechanics of PL and ML. Not all TL materials are PL, but the majority exhibits certain PL qualities. In an attempt to quantify TL mechanics, the pressure dependence of ML leads to luminescence by mechanical stimuli. In this subsection we review some topical arguments to the treatment of modeling the luminescent intensity.

52 Phosphor Thermometry. The equation related to ﬂuorescence decay time and for all substantial purpose PL intensity varies as a function of temperature and is of phosphor thermometry class. Based on photometry and thermometry, light intensity can be written as:

− t I = I0e τ (2.16)

where,

I = Fluorescent light intensity (arbitrary units)

Io= Initial ﬂuorescent light intensity

t = time after excitation

τ = prompt ﬂuorescent decay time

Equation 2.16 governs instances of both TL and PL events. Essentially, this is the time needed to reduce the light intensity to e−1 (36.8%) of its initial mark. Fluorescence

(or afterglow) is itself a decrease in emission over time by the emission centers (molecule responsible for unique property) [76]. TL phenomena itself is a time-dependent process, where light intensity I is proportional to the rate of new surface creation. Surface energy increases while propagation of recent fractured surfaces accumulates releasing energy in the form of light. This can be shown by a derivation of this model. As shown in Figure 2.15, let the excitation phase be a population (N) of particles given enough mechanical energy to ascend energy levels. The number of excited particles (n) over time is proportional to the population (N) present given by Equation 2.17. Essentially, variable k becomes a constant based on the relaxation time (τ). The derivation is as follows:

dn N (2.17) dt ∝−

53 dN = kN (2.18) dt −

dN = kN (2.19) dt − Z Z

− t N = N0e τ (2.20)

Finally, light intensity is presented as the accumulation of photons/excited population released as shown in Equation 2.17, where I and Io are substituted in as the ﬁnal and original intensity of the population Equation 2.20 [65]. Likewise, in a wave form light intensity can be addressed as being proportional to the amplitude squared [66]. A wave form can be observed by measuring its wavelength.

Energy Balance Formulation. TL by piezoelectric theory ﬁrst reported by Longcham- bon [90, 129], showed experiments where TL materials were crushed in liquid and in air.

The discharge of gases in the midst of newly created surfaces of crystals was a major TL breakthrough. This has been reevaluated over the decades by Belyaev [130], Chandra [81],

Sweeting [86], and Chakravarty [91]. There is evidence to support gas forming upon the discharge from cleavage of crystals is nitrogen based. This is described succinctly in a report as having two possible mechanisms [91]. Based on the piezo-theory, a requirement for a cracked crystal bears the piezoelectric charge in the unstressed region of the cracked walls, while the modiﬁed theory carries the existence of an initial charge that propagates along with the crack. The second method is the most dominate theory. Either way, TL intensity is related to intensity of discharge which is dependent on the rate of creation and annihilation of new surfaces (mobile cracks) that are formed from induced pressure.

A modiﬁcation to the phosphor thermetric model in Equation 2.16, gave rise to a more

54 pronounced kinetic model. The kinetics of TL in crystals can be explained in terms of strain-rate and expressed by the following equation:

t I = I r2t2e− τ C (2.21) 0 − 1

where C1 is a constant factor, Io is the initial intensity, t is duration of time, and τ is the mechanical relaxation time. This is derived from a known TL material (sucrose crystals) in experiments by Chandra et al. [81], and can be used to explain the behavior of the general

TL phenomena.

Recalling Griﬃth theory (energy balance) of crack growth and initiation, when a crack is at the point of stress it propagates releasing elastic energy where subsequent balance of surface energy (γ) is needed [40]. The crystals associated with TL are subject to these principals of crack initiation. Individual TL crystal intensity, I, is proportional to the rate of nucleation of potential surface area and can be written as Equation 2.22.

I = ∝(F˙ W˙ ) (2.22) − γ − B

α is a constant

γ - surface energy

F - rate of free energy

WB - rate of work of the boundary forces

Its relation to the standard kinetic elastic energy E can be followed by

1 E = Yε2 (2.23) 2

55 Y is the Youngs modulus of crystal elasticity. If the crystal is deformed by a strain rate r, then the strain rate in a crystal at time t can be given by

ε = rt (2.24)

TL intensity will be a maximum at the time twice the relaxation time τ of a crystal.

2αY τr2 I(r) = o C (2.25) max γe2 −

Thus, strain-rate is a deﬁning variable in TL phenomena (the argument of strain-rate is interconnected with mobile crack formation). In other words, the rate or time frame at which strain is incurred will dictate the light intensity observed because of newly formed surfaces (cracks). Hence, the high correlation between TL intensity and crystal deformation.

However, note that crack growth would occur within fractions of a second. Chandra and

Zink, were later able to theoretically expand upon their approach arriving at an intensity model to account for velocity and stress of an impact [81].

dn ηbV u3ν3 βu2ν2 I = = e−αt(1 e−αt)2exp( (1 e−αt)2) (2.26) dt α2h3 − − α2h2 −

where η is the normalization constant predicated on TL behavior, b is a proportionality constant, V, is the crystal volume, u, is an instrumental compression factor, ν, is the impact velocity, h is the thickness of the crystal, t is time after TL emission, α is in relation to crystal viscosity, and β comprises of the attrition coeﬃcient related to crack mobility. For relatively high velocity impacts Equation 2.26 can be written as

ηbV u3ν3 βu2ν2 I = exp( (1 e−αt)2) (2.27) α2h3 − α2h2 −

56 This is due to the minute time span of the TL event, where αt in Equation 2.27 is relatively small [97]. Equation 2.27 is also analogous to I = dn/dt, given that TL intensity is based upon the rate of excitation centers, so total intensity would be a sum of those singular intensities. Furthermore, the time dependence of TL seems to be related in terms of the creation of mobile cracks. This would suggest TL only occurs for crystal fracture and therefore may reside from a charged surface mechanism upon newly formed cracks.

Plastico-triboluminescence. Plastico-TL is luminescence produced during plastic deformation of solids where fracture is not required. It can be excited by the mechanical or electrostatic interaction of dislocations with defect centers; electriﬁcation of crystal surfaces by the movement of charged dislocations; or thermal excitation in the stressed regions of solids such as colored alkali halides, II-VI compounds, alkaline-earth oxides, and metals [131]. Chandra et al. [132], reported on the luminescence arising from the plastic deformation of colored alkali halides using pressure steps. They found that in the elastic region where the strain increases linearly with the stress, TL intensity also increased linearly with stress. In the plastic region where the strain increased drastically with stress according to the power law, the TL intensity also increased drastically with stress and followed the power law. The steps involved in the TL of x- or γ-irradiated alkali halide crystals can be as follows and is illustrated by Figure 2.19.

The aforementioned Figure 2.20, illustrates that (i) Plastic deformation cause movement of dislocations from defects. (ii) The moving dislocations capture electrons from the inter- acting F-centers lying in the expansion region of dislocations. (iii) The captured electrons from F-centers move with the dislocations and they also drift along the axes of dislocations.

(iv) The recombination of dislocation-captured electrons with the holes lying in the dislocation donor band gives rise to the light-emission characteristic of the halide ions in hole centers [133].

57 Figure 2.20: Schematic energy level diagram of mechanoluminescence of coloured alkali halide crystals [88, 133].

Fracto-triboluminescence. Fracto-TL is luminescence produced due to the creation of new surfaces during the fracture of solids. During fracto-TL, there is creation of charged surfaces at fracture (Figure 2.21) due to processes such as piezoelectriﬁcation, defective- phase piezoelectriﬁcation, movements of charged dislocations, and charged defect barodif- fusion [131]. There is neutralization of these surface charges by the charge carriers or ions produced from the dielectric breakdown of the intervening gases and solids. This results in the production of luminescence that resembles a gas discharge (e.g. sucrose, tartaric acid,

Rochelle salt) or luminescence of a solid (e.g. coumarin, resorcinol and phenanthrene) or one that combines the characteristics of both the intervening gases and solids (e.g. uranyl nitrate hexahydrate, impure saccharin and chlorotriphenyl-methane) [86, 131].

Chandra [131], gives a detailed description of the theory of fracto-TL. If the crystal with thickness H is cleaved along a plane parallel to its width w, with velocity of crack propagation being ν, provided α t 1, then the TL intensity may be given as: 3 ≤

I = 2(η1α1 + η2α2)γwvt (2.28)

58 Figure 2.21: A modiﬁed schematic of the piezoelectric theory illustrating TL phenomena upon cleavage [91]. Excitation occurs via suﬃcient electrical potential in a gas discharge (d) which accumulates upon new fracture surfaces.

where γ is the charge density of the newly created surfaces, α1 and α2 are the rate constants for the relaxation of charges on the newly created surfaces, α3 = α1 + α2, and

η1 is the luminescence eﬃciency associated with the movement of carriers produced by the dielectric breakdown of the crystals while η2 is the eﬃciency associated with the movement of electrons and ions produced by the dielectric breakdown of intervening gases.

Chakravarty et al. [91], explains fracture-luminescence in terms of peizoelectriﬁcation as a surface event. When the virgin surfaces of a crystal are breached, positive and negative charges propagate along crystalline fractures. These charges shoot across the fracture region colliding in fractions of a second. Excitation of illumination occurs via suﬃcient electrical potential in a gas discharge (d) as shown schematically in Figure 2.21. A schematic of the piezoelectric theory illustrating TL phenomena upon cleavage [91]. The mechanical tensile stress being applied to the material generates substantial voltages in the area of breakage.

In essence, it is the piezoelectric event that results from present crystalline impurities. As more and more cracks start to propagate, the voltage across the surface increases until a discharge of electromagnetic energy is released photonically. The intensity of the discharge

59 is dependent upon impact velocity and the rate of creation of newly fractured surfaces [91].

Composite Damage Sensing with Triboluminescence. Although, there has been generation of literature concenring TL and a proposed use, not much experimental work has been done on near application with structural materials. Eﬀorts in TL damage sensing with composite experimentation were ﬁrst perpetuated by Sage and Bourhill of the Defense

Evaluation Research Agency (DERA) located in the U.K., from which this group has generated numerous works on the practicality of Triboluminescent sensing. [74,113,134]. Their results were greatly magnified once suitable materials were realized. To date they have experimented with menthyl-9-anthracenecarboxylate (MAC) and a terbium complex [113], through impacting at low-velocites. This group was also the first to propose and demonstrate effective reception and transmission by use of optical fibers [135]. Optical fibers were used as a transport medium considering optical fibers are able to intercept emissions and internally refract rays along the fiber core. This is thought to be due to side-coupling, where the fiber deforms suffuciently to allow light leakage since attenuation is natural occuring when bended in communication applications. This however presented unique problems to the myriad of composite materials, as the integrity of the optical fiber must be kept in- sulated during operation. In addition, if the compsite system is not transparent or near translucent the TL can be diminished.

Using embedded TL particles as failure indicators, the DERA group [74], reported transmission of light emissions from embedded TL crystals can be aided by the procurement of polymeric optical fibers. In addition to utilizing solid silica fibers, hollow optical fibers were doped with a photon absorbing laser dye (Rhodamine 6G), making light detection possible.

This is known as a, ﬂuorescent ‘down conversion’, which is aimed at eﬃcienctly shifting the wavelength of the triboluminescent emissions. In essence, doping the hollow optical

ﬁbers (silica capillaries) themselves with PL materials will reduce the loss of light created

60 by host absorption. PL materials will absorb the surrounding ambient light produced by the TL crystals, thus hindering all other noise influences. The system set up by the DERA team is comprised of bulky liquidus sensors which will undoubtedly lead to bulky detec- tors as optical fibers only supply a medium for transport and could pose a hazard. Hadzic et al., explains that precautions must be exercised with use of optical fibers embedded in composites [136]. If the density of fibers is too high, it can affect the desired physical performance of the laminate itself. The results of Hadzics experimentation indicated medium optical fiber embedment will not degrade the mechanical properties of the host composite although, many researchers have highlighted the negative effects of embedding bulky materials [136–138]. Nevertheless, the DERA group [113], successfully demonstrated structural damage monitoring in both glass-fiber and (optically black) carbon-fiber composites through use of polymeric positioned optical fibers. Upon impact, the onset of structural damage is indicated by light emission; the severity of damage is indicated by the overall light intensity of two embedded photoluminescent fibers. The laser dyes have proved light detection is possible in the common place CFRCs which acts as an opaque medium.

2.5.4 Summary - Sensory Mechanism

The luminescent phenomena known as TL, can be used as the initial signal in a sensory mechanism to indicate a forceful event has indeed occurred to a structural member.

Research has indicated ZnS with Mn activator as a luminescent sensor capable of emitting copious amounts of light even when encased in composite matrices. The piezoelectric eﬀect on an atomistic scale is the mechanism behind TL, which is prominent in crystal structures that lack symmetry. The intensity of light depends on the strained creation of fracture surfaces and velocity of fracture events. Sage and Bourhill [113], have attempted to harness the intensity of TL emissions with dye doped silica capillaries to eﬃciently absorb and transmit

TL light to counteract blackbody reinforcement material. This is a unique approach to

61 standard optical ﬁber embedment; but optical ﬁbers are bulky and a liquid medium is not a desirable component for most applications. These optoelectronic devices have high resolution and sensitivity, but are bulky and require large power management. A less parasitic approach is needed. Engineering and material research will need to address interception and transmission of emissions by suitable means in order for luminescent sensors to remain viable.

The Piezoelectric theory is the most agreed upon source for the TL response. The crystallographies of most TL materials are a conundrum of unexploited events because of the luminescence of a vast amount of crystals. TL materials have the propensity to lack a center of symmetry in their crystal structure [101]. This suggests the validity of a piezoelectric

(charge separation) event, which is partially accountable for TL emission [121, 139]. An electric ﬁeld is produced during fracture and cleavage of crystals resulting in opposite charges being formed on the walls of the surfaces [121]. The privation of a mutual excitation model is only compounded by the plethora of distinct crystal structures. These structures exhibit a range of centrosymmetric or asymmetric crystal conﬁgurations that are with or without an inversion center. Because of the distinct material types and failure to excitation, TL can be viewed by deformation type in its range of ML.

2.6 Literature Summary

With the advent of structural composites and a database of failure analysis, third generation composites are uniquely positioned to have multifunctional capabilities far beyond structural performance. In combinatorial fashion, science and technology together can incorporate smart materials for life cycle assessment. If SHM is to occur on a composite member, detecting the subsets of impact failure holds no additive value for structural re- liance and consumer safety. True power of detection technology will be in its ability to

62 sense fatigue or slow patterns in the local and global arena. This is a needed technological innovation, as composite materials enter the supply chain of aerospace, marine, civil and military applications. Most notably, both military and commercial aircraft have seen a rise in composite usage to roughly 50 -80 % by weight. This includes critical structural components including fuselage, wings, and tail-kits. These aircraft components experience multiple operational and fatigue stresses during the life and operation.

With better understanding of TL excitation mechanism, implementation of damage sensing through varied luminescent phenomena depends greatly on the maneuverability techniques employed. A suitable method for sensor realization is in situ damage detection.

By this method, a matrix of TL materials embedded in composite materials are placed in such an orientation that the impact of the projectile or operational stresses over time will trip pain sensors at the occurring damage location. However, retrieving the emission from

TL is the key objective in ascertaining location of damage in composites. Thus a SHMS of this type will be an eﬃcient means of capturing TL phenomena by nano-technological means.

To harness TL emissions for damage detection, will encompass creation of a new paradigm in relation to a sensory mechanism. Work utilizing triboluminescent materials have resided heavily on researching new triboluminescent materials and on exploring impact responses from thin-ﬁlms and little work on integration and testing with composites. The linearity of triboluminescent materials have been observed and demonstrated in work by Chandra et al. [140], Zink et al. [100], Xu et al. [80, 110, 120, 141] and Hollerman et al. [76, 142]. The interaction with composite materials is not a working topic, although, Sage and Bourhill have stated compatibility with composite material components [73, 74]. Uniquely, experimental eﬀorts in mutual excitation and damage mechanism of concentrated composites are not active areas of research.

63 This review covers the essential mechanisms attributed to phenomena surrounding TL and Photocatalysis. The relation to SHM is seen in the sensory mechanism that is inherent to SHMS predicated on signal emission and viable signal transmission. Triboluminescence provides a platform in which to sense structural damage at minute levels and provide unique information concerning event severity. Photocatalysis within titanium dioxide semiconduc- tors allow for interception of light, and in the presence of a construct (i.e. CNTs), will provide means for transporting information for SHM determination. Photocatalysis provides the link with respect to the photovoltaic eﬀect found in solar cell technology.

64 CHAPTER 3

OVERVIEW METHODOLOGY & EXPERIMENTATION

This chapter discusses the methodology, case experiments and organization of characterization methods in this research. This is in relation to the formulation of a ‘TRiP SHM’ system. The ‘TRiP SHM’ system is predicated on construction of fundamental components for a triune sensory mechanism. Elements of a holistic sensory system include signal emission, reception and transmission.

Figure 3.1: Experimental and modeling approach.

The lower level roadmap of the experimental methods approach is illustrated in Fig- ure 3.1. The schema is a three part testing and modeling approach for a basic formulation

65 for a SHM system utilizing TL and the photo-electric phenomena. Phase I consists of a

DoE approach for assessing the parameters during ﬂexural testing. Phase II involves mi- cromechanical and FEM approximations of system modulus, and integration of luminescent intensity. Phase III will be featured in the future work, but is not an objective of the present work. The combination of the three phases, however, comprise the creation of the sensory mechanism which is at the heart of the proposed sensing technology.

3.1 Phase I & II Experimental Methods

3.1.1 Materials

Highly triboluminescent ZnS:Mn phosphors were utilized in this study. The ZnS:Mn

(GL25/N-U1) phosphors were purchased from Phosphor Technology Ltd. (United King- dom). The size distribution as reported by the MSDS are roughly between 2-20 µm diameter between acquired batches of ZnS:Mn phosphors. Particle size distribution analyzed by

Beckam Coulter Counter (100 um aperture) produces a majority of 18.5 µm sized phosphors in the 95th percentile. The density is reported to be 4.10 g/ml, exhibiting optical emissions approximately near 585 nm in the orange spectrum. The decay of illumination is classiﬁed as medium short decay proﬁle. The composite material matrix employed in this study is the thermosetting ARMORSTAR IVEXC410 vinyl ester blended infusion resin from Cook

Composites & Polymer (CCP). Norox MEKP-925H (methyl ethyl ketone peroxide) was used as a catalyst and curing agent as instructed by CCP at levels not exceeding 2.4%.

The ﬂexural strength is reported to be 110 MPa, with a ﬂexural modulus approximately

4,069 MPa. Concerning the secondary experimentation, chopped glass ﬁber whiskers were purchased from Fibre Glast Development Corp. with lengths of 6.4 mm. Per manufacturer, a custom sizing agent of silane was applied. The diameter of the chopped ﬁbers was approximately 13 microns.

66 3.1.2 Fabrication

Mold Design & Fabrication. The samples fabricated in this work were two and three-phase composite short beams. In one case, ﬁber reinforcement was added to fabricate three-phase composite systems. This case study is discussed in Chapter 4. Flexural testing involved static loading of short semi-uniform and thick beam samples. Therefore, female molds were manufactured using transparent siloxane rubber (Dow Corning).

Figure 3.2: Three step mold and sample fabrication process for casted particulate composites.

The female molds were fabricated from 3D printed male molds as illustrated in Figure 3.2.

In all, five differing molds were constructed, each having a unique effective length. The

“eﬀective length” is considered the length above the pre-notch in the female mold (Figure

3.3). The eﬀective lengths used in the major study were 0.5, 2.5 and 4.5 mm. Once the female molds were procured, they were cleaned and coated with poly vinyl alcohol (PVA) as a release agent. After cleaning and preparation, particulate composite samples were casted.

67 Sample Fabrication. After mold preparation, fabrication of single edge notched beam samples were then casted and made of unreinforced ARMORSTAR IVEX vinyl ester resin concentrated with ZnS:Mn ﬁllers. The specimens were cast with nominal dimensions

55 10 5 mm and poured under room temperature conditions and left to cure overnight. × × During mixing and pouring of resin and catalyst, the mixture was allowed to age 40 min- utes before addition of particulates. MEKP was used as a catalyst based on a 2 percent by polymer weight ratio as suggested by the manufacturer.

Figure 3.3: Schematic of the three-point bend sample geometry and single-ended notch highlighting the eﬀective length of casted particulate composites. The eﬀec- tive lengths utilized in the entire study were 0.5, 1.5, 2.5, 3.5 and 4.5.

An illustration of the short beam sample is given in Figure 3.3. The effective length of the sample is clearly defined as the available material length along the vertical fracture line. The effective length and notch lengths are identified in the magnified illustration as eL and nL, respectively. In this study, the notch or pre-notch length is the difference of the standard sample thickness (5 mm).

68 3.1.3 Mechanical Testing Procedure

Mechanical tests were carried out on particulate composite samples, where the primary task was to observe the loading and TL response. The tests consisted of flexural loading onto composite single-edge notched beams (SENB). Three-point bend (3PB) tests were carried out on the specimens using the MTS Insight electromechanical testing system in accordance with the ASTM D790 standards [143]. A three-point bend fixture containing 4 mm diameter rollers was used in this study. The flexural tests provided a repeatable method for conducting observations of the mechanical and optical behaviors of stress conditions at crack initiation and propagation through polymer concenntrated matrices. Bend tests were conducted with a span length (L) and cross-head speed as discussed in the experimental design (Table 4.3).

Figure 3.4: An illustration of the three-point bend schema for ﬂexural loading of concentrated composite short beams.

69 Figure 3.4 is a schematic of the test setup. The mid-plane is the center vertical and horizontal plane of a sample beam. This is labeled as the neutral axis and the vertical fracture line in Figure 3.4. Based on the load and sample geometry, the bending moment and shear diagram indicate the type of failure experienced during this test.

Testing Setup. The physical setup is shown in Figure 3.5(a), where a standard three- point bend ﬁxture (Shimadzu Corp.) has been adapted to the MTS insight system. The additional ﬁxturing is ammended by the base blocking mount and the hexnut locking bar.

This results in a compliance change with 4 additional points of freedom. This compliance change has been addressed to provide reliable displacement measurements.

(a) (b)

Figure 3.5: The mechanical testing (a) three-point bend ﬁxture and machine setup, and (b) optical insulation and enclosure.

Figure 3.5(b) displays the optical enclosure constructed to restrict the ambient lighted enviroment for TL emission measurement. To support the photon sensors for incident measurement, an alignment ﬁxture was fabricated to adhere to the housing of the base

70 three-point bend ﬁxture (Figure 3.6). The sensor harness houses two photonic sensors in a perpendicular orientation concerning the side faces of the composite samples. Operations for conducting TL testing require a dark enviroment, and thus ambient light is diminished by the above means. In addition, an opaque garmet is wrapped around the enclosure to provide additional insulation support.

Figure 3.6: Three-point bend photo-sensor alignment ﬁxture.

Data Reduction. The mechancial tests were carried out in accordance with the

ASTM D790 standard for calculation of ﬂexural properties [143]. This required inputing the particular method in the standard framework of the MTS Insight electromechanical machine and TestWorks software. The ﬂexural strength (σf ) adopted in the software platform is calculated by: 3P L σ = max (3.1) f 2bd2

where, Pmax is the applied load, L is the span length, b is the specimen width, and d is the depth of the beam. Flexural strength is the theoretical value of stress on the surface at

71 failure of specimen.

The ﬂexural strain (ǫf ) was obtained by:

6Dd ǫ = (3.2) f L2 where, D is the maximum deﬂection of the center of the beam. The ﬂexural modulus was determined from the elastic limits of the stress-strain curve. Assuming shear deformation is negligible, the modulus is obtained from the equation:

L3m E = (3.3) f 4bd3 where, m is the slope of the initial portion of the load-displacement curve. With the single concentrated load on the beam the corresponding end deﬂection,delta, can be determined from derivation of the strain energy of the beam. Strain energy, U, of a beam is equal to the work of the applied load [43, 144]. Since deﬂection or displacement (δ) corresponds to the acting load (see equation 3.4), strain energy and work can be written as:

P U = W = δ (3.4) 2

P is the acting load or force. Therefore, a beam loaded by a force P will yield a displacement or deﬂection equal to: 2 δ = U (3.5) P

The speciﬁc bending stiﬀness, K, of a composite beam is calculated by:

E K = (3.6) ρ2

The speciﬁc property calculation will serve as a quality check for the short beam samples.

The speciﬁc bending stiﬀness will indicate if specimens have similar structural composition.

72 Calculations for failure stress and strain will be computed throughout this work. However, an estimation of material modulus was not conducted due to the non-uniform geometery presented by the single-edge notch. An estimation of material modulus is not suﬃcient under these conditions. The calculations will serve only for the means of sample comparison and data reduction.

3.1.4 Sample Characterization

Optical Analysis. Optoelectronic measurements are the detection of the electromagnetic spectrum in the visible range. As the ﬂexural load was applied, a Hamamatsu H10722 series (formerly H5784) photo-multiplier tube (PMT) and low-cost photovoltaic (PV) cell were utilized to monitor the excitation emissions (a voltage based photon counter) during loading progression of the concentrated TL/VER specimens. The device was situated in front of the side facing mid-plane, direclty adjacent to the loaded notch form by the alignment ﬁxture as noted in Figure 3.6. The output tube is a voltage based programmation and thus serves only as an electrical measurement of intensity. A power supply of 5 V is required to operate the PMT. No polychromatic spectral information was obtained, however, the spectrum for the ZnS:Mn substances are noted in literature [83, 142].

The device setup and instrumentation is depicted in Figure 3.7. Data acquisition is acquired through the NI USB-6210 DAQ (National Instruments) device with connection to a mobile

PC. This is a 16 pin acqusition housing card with connectivity through USB 2.0. The

Hamamatsu photodetector is a special class of PMTs graded for low-light detection and sensitivity. It is a metal package insulating PMT where an internal ampliﬁer converts a current reading into a voltage output for easy signal processing. The peak sensitivity is roughly 400 nm, with an output capacity between 1–10 V. Note: The gain of the PMT module is set to 0.55 V on the Agilent A3630 power supply for all experiments. Primarily,

73 Figure 3.7: Setup and instrumentation diagram for PMT and PV cell sensors.

the unﬁltered signal is processed during integration of mechanical and optical analysis. A current, therefore, charge accretion formula can be applied to approximate the number of photons/sec detected. The amount of photons/sec that strike the photocathode member can be calculated for monochromatic light by the following formula [145]:

V = P K G V/A (3.7) × s × × in which,

P = light power (photon/s at a given wavelength)

74 Ks = cathode radiant sensitivity at a given wavelength

G = gain of PMT

V/A = 1V/µA, voltage conversion ratio

V = readout voltage value

In addition, in subsequent experiments a CCD camera was used to monitor optical illuminations along the fault-line at time of initial and final loading for minor samples. This approach was utilized to inspect and review triboluminescence along the entire field of view of the specimen. Those findings were originally discussed in Dickens et al. [146].

Mechanical Analysis. The mechanical analysis describes mechanical calculations related to the testing procedure and discussess analysis by computational means. The

ﬂexural test and sensor data were taken simultaneously during the testing of each specimen, however, the acquisition was initiated separately. The load-displacement curves of each specimen test were manipulated using MATLAB scripts to calculate the strain energy based on work energy principles [40,144]. The strain energy signature was superimposed over the optical data and analyzed as such. Furthermore, the superimposed experimental data were reduced to rate estimations near the time of fracture (1 ms deviations) and the TL events. In addition, an experimental and computational estimation was utilized to resolve the strain- energy release rate. This method was proﬀered by Bagley and Landes [45], and implemented through use of COMSOL multiphysics software.

Microscopy. Characterization of ﬂexural samples were conducted using Scanning

Electron Microscopy (SEM) observations to perform fractography analysis. The JEOL

JSL-7401 SEM has a 1.2 nm resolution at an accelerating voltage of 15 kV and a working

75 distance of 10 mm. An additional feature and function of the JEOL-SEM is the Energy

Dispersive Scanninning (EDS) operations, also known as ‘Elemental analysis’. SEM was used as a visual tool to examine the surfaces of the test samples. Specimens were coated with a gold sputtering device in 5 nm layers to allow for SEM operation and visualization.

Test specimens were only examined on the fractured surface after testing. Elemental analysis were performed on select specimens as to acertain the deformation types of individual crystal domains.

76 CHAPTER 4

TRIBOLUMINESCENT ENHANCED COMPOSITES

4.1 Experimental Overview

Structural health monitoring and non-destructive evaluations are a means for determining the integrity of advanced material structures and assessing if vessels can continually operate under designed conditions. On a basic level, structural or damage monitoring systems consist of interception and transmission of generated signals from structural sensors. The characterization and tabulation of this paired construct between interception and transmission comprise the sensory mechanism needed to perform diagnosis and prognosis for determination of structural integrity [53,54]. For a triboluminescent based SHM system, detection (signal conversion and transmission) is the limiting factor for estimating viability as a damage sensor. This is primarily due to the ubiquitous nature of singleton microscopic sensory receptors via encapsulated ZnS:Mn particulates and the nature of their spatial lo- cale within the resin matrix [146]. Considering the susceptibility of matrix related failure much emphasis has been placed on the study of the matrix interaction. Considering the microscopic level of deformation, this unique facet will enable reduction of false-alarms associated with detecting microscopic, and therefore microscopic damage. Triboluminescent excitation is a transfer of mechanical energy into photonic emissions. In this work, the

77 primary means for excitation is via quasi-static ﬂexural loading.

Figure 4.1: An illustration of the three-point bend schema for ﬂexural loading in view of crack propagation and plausible mechanism for particulate excitation of TL doped resin matrices. Plausible TL mechanism stem from (1) elastic, (2) plastic and (3) fracture-like distrubances as originally described by Walton [85].

Figure 4.1 is a schematic of the ﬂexural test setup. The cut-out describes the plausible excitation mechanism of concentrated two-phase composite triboluminescent emissions upon composite deformation via ﬂexural loading, and thus resulting in matrix cracking. As stated by Walton [85], three basic occurrences for particulate triboluminescent inclusions are said to exist from physical deformable interactions: (1) elastic disturbance, (2) a plastic-like disturbance and (3) a fracture-like disturbance (enumerations are labeled in Figure 4.1).

Failure initiates on the tensile side , i.e. the base of the ﬂexural beam, when the material’s compressive strength is equal to or greater than its tensile strength [147]. Forms of these three deformation states were observed in microscopy along the exposed fracture plane

(included in section 4.4.4). Further discussion on the mechanism and time evolution of TL is located in Section 4.6.1.

The aim of this research is to better understand how mechanical energy upon deforma-

78 tion (or failure initiation) in composite structures is converted into optical energy through the triboluminescing of encapsulated ZnS:Mn phosphors. Secondly, the conversion of optical energy by a PV detector will be addressed for its sensory capability and future system integration. Chapter 4, discusses the experiments and results of (1) Method of visual analysis, (2) Statistical method of Design of Experiments, (3) Method of J-integral evaluation and (4) Two & Three-phase composites.

4.2 The Triboluminescent Response of Concentrated Prismatic Composite Beams

4.2.1 Introduction

This work is aimed at understanding the relationship between applied stress and TL emissions in concentrated polymer matrices. The fabricated specimens are prismatic beams with uniform geometry. Flexural bending tests were conducted to ascertain the mechanical and optical behaviors of stress conditions at crack initiation and propagation. Optoelec- tronic instruments were used to provide a wide ﬁeld view of the at-large experiment, as well as, a quantitative measurement of the excited strain-to-emission phenomena. As described in Chapter 3, optical analysis was carried out using a low-light photomultiplier tube (PMT) in conjunction with a micro-visual web-cam. Acquisition was carried out through integration of instruments with the MATLAB data acquisition toolbox for instrument control.

The enhanced composites are concentrated with a well known triboluminescent material.

The inclusion of diﬀering types of ﬁllers in composites has been studied widely [146, 148].

Speciﬁcally, ﬁllers have been utilized for structural support. However, triboluminescent materials and namely, ZnS:Mn phosphors are traditionally soft inclusions. Therefore, the inclusion of TL materials will not aid in the structural response [146]. However, their inclusion in the matrices allows for unique sensitivity and view of stress-strain conditions

79 when record by video [110, 111, 149, 150]. Initial observations of TL emissions were made upon initial ﬂexural loading of the test samples at the compressive and tension loading locations. This is only observed on the top surface, which is not in view of the optoelectronic instruments. For the case of initial compression and contact, luminescence was attributed to the contact stress of surface crystals. In particular, this addresses the detection of in- service problems associated with tool droppings which would be indication of immediate surface damage and prelude to potential sub-damage. Literature suggests that ZnS:Mn is a low modulus material, making it desirable for inclusion, and will exude tribo-emissions at pressures greater than 1 MPa (speciﬁcally 0.7 MPa in the case of ultrasonic excitation)

[118, 121, 151]. The fabrication, testing and results of the ﬂexural experimentation are discussed in the following sections.

4.2.2 Fabrication & Testing of Concentrated Beams

Specimens were cast in accordance with the methods described in Chapter 3. Test samples were made of ARMORSTAR IVEX vinyl ester resin concentrated with ZnS:Mn

(Phosphor Technology Ltd.) at 5, 10, 25 and 50 % wt. particulates. A Sample size of 30 specimens were tested for each ﬁller volume fraction point. A pre-fabrication notch was not incorporated in these samples, but a razor was used to lightly score the specimen across the perpendicular midspan of the beam. This was done to ensure stress concentration and crack initiation along the mid-plane, and without drastically altering the rectangular geometry of the short prismatic beam samples.

Quasi-static load tests were conducted with a span length of 50 mm with a cross- head speed range of 20-40 mm min−1. As the ﬂexural load was applied, the Hamamatsu · H5784 photo-multiplier tube (PMT) was utilized to monitor the illumination during loading progression of the front facing mid-plane. A simple webcam was used to monitor optical illuminations along the fault-line at time of initial and ﬁnal loading.

80 4.2.3 Results & Discussion of the Tribolumuiscent Evaluation

The Triboluminescent Signal. Figure 4.2 illustrates a typical plot of the acquired temporal stress and light spectral data. In this study, the spectral data is in reference to the transient light intensity and is not to be confused with the wide spectrum graph associated with wavelength. The raw data in Figure 4.2, is a voltage response as measured by the voltage-PMT device. The response is from a 50 % wt. particulate sample.

Figure 4.2: Representative cross plot of the transient TL response to stress of ﬂexural samples of a 50 %wt. concentration (intensity is in arb. unit) [146].

From Figure 4.2, light emission is notable after cessation of load (blue line) indicated by the peak rise in intensity value at time, 9.46 s (black line). Corresponding failure and signal peak similarities were also observed in literature [121,141,152]. The magnitude of the light intensity signal is extremely sharp and instantly rises to a maximum . This rise denotes the

81 quick nature of specimen fracture which is observed in the cross-plot by the residual drop in stress (Figure 4.2). In this particular case, the stress vs. time plot shows that failure occured after 9.46˜ s, which corresponds with the luminescent excitation in this particular sample. Crack propagation occurs within milli-seconds, denoted by the sharply decreasing load signal to a 100 % load drop-off. From this, it may be inferred that a measurment of light emission only occurred upon specimen fracture, or in the time evolution of the peak and decreasing load. In the elastic regime that leads to brittle material failure, there is no measurable intermediate time-length in which embedded ZnS:Mn is excited sufficiently by the flexural load to register an emission. To induce emissions it is known that a certain internal strain must be produced. The strain energy density in the case of elastic brittle failure is quite small and confined to the axial length surrounding the crack tip. Once crack initiation and propagation occur in the brittle failure cycle, the crack front will have extended through the entire fault length of the specimen, leading from the crack to the point of applied load. This is characteristic of elastic brittle behaviour and is understood that the loading profile is elastic in nature up to material separation [153]. The fracture and crack propagation occurs in the near luminescent time-scale of the emitted light. All samples concentrated at 5, 10, 25 and 50 wt. % revealed the exact excitation trend at the structural material yield point. This is a feature observed in various research works, where the deformable excitation event occurs at the same instance as the luminescent emission.

In most cases, the ‘structure’ acted upon, is a thin-ﬁlm substrate or bulk material where presseure has been applied by friction (i.e. scratching or crushing) [33, 79, 83, 85, 141], compression [110, 111], or by inter-mediate velocity impact [58, 74, 80, 113, 142, 154]. This is in aggreement with the ﬁndings of Chandra et al. [121], and may be attributed in this occurrence to the encapsulated particulates and the interfacial state within the host polymer matrices. Further discussion on this subject matter is addressed in Section 4.6.1. This is only discernable when observing the transient response and not relying solely on the spectral

82 emission. Because of the clear nature of luminescence at point of rupture, this investigation suggest it is a case of fracto-luminescence. However, the fracto-luminescence is related to the macro-scopic rupture. It is a plausible hypothesis, that elastico- and plastico-luminescence does indeed occur on the micro-scale during deformation. Walton, explained that there could be elastic and plastic conditions given the nature of exciting TL is rather complex phenomena [85]. The ability to free trapped electrons could occur from creation of new surfaces, electric potentials across surfaces or movement of dislocations throughout the process. It has been stated, that TL response consists of 5 % elastic-, 80 % plastic- and 15

% fracto-luminescence [85]. The reproducible elastico ML is a unique property of ZnS:Mn due to its excitation by piezoelectriﬁcation of dislocalized structure [121]. However, the current setup and instrumentation does not allow for spectral determination at the micron scale level.

The decay signal of triboluminescent materials, and more speciﬁcally ZnS:Mn, is fairly unique property that is only viewable by transient analysis. The ZnS:Mn particulate is a luminophore or phosphor material. According to Strange [122], the term phosphor is

ﬁrmly established to indicate a ﬂuorescent material. Thus the material once excited will have a unique phosphorescent decay related to the impurities in the host lattice. The tail of the signal is known to follow an exponential decay curve [18, 58, 142]. This is a sole distinguishing mark for detecting the TL signature.

Figure 4.3 illustrates the time decay of ZnS:Mn. An initial rise occurs within microseconds (resulting in a maximum response), and is followed by a dampened and much slower fall in the signal over several milliseconds. Several TL materials can be identiﬁed by their spectral glow curves (PL), and are established in literature [85, 155].

Triboluminescence is mutually based on: (1) the number or amount of TL material, and

(2) a resultant of the force magnitude. Based on assumptions from phosphor thermometry,

83 Figure 4.3: Characteristic time decay of TL ZnS:Mn emission and spectral proﬁle regisitered by the Hamamatsu PMT [18].

the intensity of TL is proportional to the crystal population, I dn/dt, present in the bulk ≈ material. The population of potentially excited ZnS crystals is represented by, n, over a differential time t. The intensity should therefore rise instantaneously at a time t corresponding to the excitation event signifying a large portion of crystals, n, were excited in an instance.

This alludes to the potential for TL sensitivity according to the ﬁller concentration. Fur- thermore, the excitation of piezoelectric TL crystals is based on the premise that thresholds exist within each TL material to produce luminescence, and an inﬂux of mechanical energy towards illumination will create an upward trend until a maximum discharge potential is reached [91]. This is also related to the trapping process associated with electroluminescent and piezoelectric ZnS:Mn, and may follow similar expressions of the rate equations derived by Kim et al. [156]. The loading rate dependence of ML in SAO phosphors is similar to the mechanism of ZnS:Mn. Both SAO and ZnS:Mn recieve their TL from the presence of ionic impurities, the inorganic activators present as impurities in the host material which

84 aid in recombination. The defects or impurities of Mn2+ and Eu2+ are related to ZnS and

SAO, respectively. Kim et al. represented the paramount equation as a function of Eu+ population and excitation with instantaneous loading rate [156]. If the defect densities can be determined then the magnitude would be a by-product of the densities and load rate.

This higlights the coincident nature of crystal population and applied force.

Figure 4.4: Inﬂuence of ZnS:Mn concentration on the intensity of TL emissions and ﬂexural strength (breaking stress) [146].

Figure 4.4, describes the relationship of the ZnS:Mn concentration with the average emitted light intensity at maximum ﬂexural stress. The double plot displays TL intensity as a function of concentration for loading rates 20 and 40 mm min−1. The reported intensity measurement is also an average maximum response from a single signal. It may be observed that as the concentration of TL ﬁller material (ZnS:Mn) increases, the resulting emitted

85 light intensity increases linearly in agreement with literature [81, 104, 121, 154]. However, there was some deterence from the linear relation observed in this experimentation. The distinction between crosshead speeds is not discernable considering the 20 and 40 mm · min−1 loading rates.

From Figure 4.4, it is shown that an increasing intensity trend is observed despite the loading rate, although, discrepancies arise for intermediate concentration levels between 5 and 25 %wt. The noted decline in the average intensity, amidst a rising light intensity trend, at a concentration of 25 %wt. might indicate concentration quenching phenomena observed by Liu et al. [157]. Considering the solid state photoluminescenct (PL) yield of

TL materials reported by Duignan et al. [79], minimal spectral diﬀerence exists between the PL and TL spectra of ZnS:Mn indicating their mechanisms are highly correlated. This is also noted for the photoluminescence and electroluminescence (EL) of ZnS:Mn [155,158].

The varying spectral intensity for intermediate values suggests these abrupt changes in intensity are in eﬀect due to the nature of Mn+ introduced during doping of ZnS. This abrupt behavior is a momentary atomistic concentration related relaxation, whereby, the transfer of energy from the host ZnS lattice to Mn+ are impeded by non-radiative recombination centers [157]. A diagram of this process was presented in Figure 2.18 and described in

Equations 2.13 - 2.15. Non-radiative recombination centers caused by Mn+ doping, hinder the energy transfer from the host lattice to Mn sites in a phenomenon known as ‘concentration quenching’. Concentration quenching is associated with the interstitial sites of dopant impurities, signifying the asymmetry of Mn doped ZnS phosphors as a piezoelectric material and the overall mechanism for TL based on the generation from defect centers [101, 121].

This points to the piezoelectriﬁcation mechanism for TL as deduced from the PL and EL.

Figure 4.4 also indicates that opposing concentration quenching levels exist. Diﬀering concentration levels appear for the two ﬂexural loading rates. The concentration quenching

86 degree outlined by the 40 mm min−1 rate appears at a concentration of 25 %wt. In the · same manner, a quenching point is denoted at 25 %wt. for loading at 20 mm min−1. In · addition, a quenching point was also established at 10 %wt. by the lesser loading rate.

However, the magnitude of the diﬀerence between loading rates is thought to be negligible for the variation in this experiment. Concentration quenching is a more desirable conclusion to the abberations observed during both loading cycles at intermediate values, because the integrity of the ZnS:Mn crystals should remain un-altered during the curing of the matrix.

The crystallinity of the filler material is assumed to be pure considering the known synthesis route assumed by the manufacturer requires firing above 500 ◦C. Several reviewed synthesis methods require annealing above 500 ◦C, where crystallinity is said to increase as annealing temperature increases for ZnS:Mn synthesis [158]. The exothermic reactions during fabrication and resin curing do not exceed roughly 100 ◦C [27]. Therefore, the intermediate concentration levels invoke a suppression of the recombination process involved in Tribo- luminescent production. However, more effort needs to involve analysis of the dispersed states and localization of stress at the active sites.

Visual Content Analysis. The illuminated macroscopic fracture zone was captured by a micro-camera (Micro Innovations) in conjunction with the photomultiplier detector measurements. Analyzing the moving frames permited the detection and determination of temporal events not based on a single image. As such, each specimen was observed for its mechanical excitation. In addition, it was found that emissions coincided with fracture propagation for all test with TL-concentrated samples.

Figure 4.5 shows a representative pattern of the fracture events of TL-concentrated resin matrices under ﬂexural load as recorded. The outline of the sample position and roller supports were drawn for clarity. The process as observed is outlined between Figure 4.5 (a) upon contact, (b) mid-span, and (c) fracture emission events. The corresponding cut-outs

87 Figure 4.5: (a - c) Visual analyses of the black and white frame by frame images reveal the propagating fracture and subsequent TL emission of a 55 10 mm2 × specimen outlined by white horizontal lines [146].

are close-ups of the excitation events. Frame by frame analysis (15 frames/s) reveal that the fracture event occurred within milliseconds. The transient response of tribo-emissions occurred approximately within 333 ms (resolution 1 ms), which is the time-span from ∼ the frame in Figure 4.5(a) to the frame in Figure 4.5(c). The emission events occur at initial loading (Figure 4.5(a)), in what appears to be appreciating internal strain at the mid-span(Figure 4.5(b)), and at the timely complete fracture of the concentrated specimen(Figure 4.5(c)). From this measurement perspective the detected signal is thought to be a macro-accumulation. The expedient rise in the intensity plot (Figure 4.2), is thought to be the accumulation of the initial and ﬁnal emission signal. However, it is plausible to suspect that the incidence of Figure 4.5(a-b) and intermediaries, is too low to be detected and only the ﬁnal event is recorded.

This is in agreement with the 0.2 ms emission spectra observed during individual excitation of ZnS:Mn materials by other researchers [154]. Earlier, in Figure 4.2, TL emissions were observed only at the instance of fracture and not at initial loading of the specimen.

Albeit, it was observed by the naked eye that there is initial TL due to contact of impactor on the top surface of the beam. Intermittent TL would have been a desirable outcome

88 towards internal elastic deformation, as outlined by Walton [85], in the elastic-like physical disturbance of TL. The video micrographs indicate that emissions occurred at the instance of crack initiation, but well into the failure cycle at the critical load point. The forego- ing suggests that the observed light emission in Figure 4.5(a), indicates the initiation of stress concentration above the pre-crack microseconds before rupture.The light emission in

Figure 4.5(b) is not as intense as the initial emission, indicative of a lower energy release perhaps due to some relaxation in the stress state (with limited crack-propagation) at the mid-plane of the beam. In the final frame (Figure 4.5(c)), light emission of an increased intensity may be observed. This is indicative of a final component failure and end of crack propagation accompanied by specimen fracture. Furthermore, the change in the relative positions of light emissions in frames a-c (Figure 4.5) may be indicative of the crack propagation features. The flexural conditions of this experiment reveals the dynamic evolution of TL in a structure under advancing crack phenomena which is a new highlight of the knowledge base.

Mechanical Analysis. The ﬂexural test results coupled with the photometric results from specimens with varying doping concentrations are presented in Table 4.1.

Table 4.1: Average parasitic inﬂuence from TL ﬁller content.

Concentration (wt.) 0 % 5 % 10 % 25 % 50 % Intensity (arb. un.) 0.002 0.014 0.030 0.016 0.057 Strength (MPa) 95.4 51.3 49.5 36.0 55.4 ( 15.8) ( 17.6) ( 7.6) ( 7.9) ( 6.0) ± ± ± ± ± Modulus (MPa) 3113.2 3136.9 2493.8 3422.8 3383.6 ( 469.9) ( 755.46) ( 225.9) ( 190.84) ( 849.64) ± ± ± ± ±

The three-point bend test results (Table 4.1) indicate on average the ﬂexural properties of the samples decrease with increasing ZnS:Mn concentration, lowering the ﬂexural strength of the compounded samples from a pristine strength of 95.4 MPa to a reduced 36.0 MPa for

89 ﬁller fraction over 25 %wt. Nonetheless, an increase in average ﬂexural strength is recorded at 50 %wt. concentration. This may suggest an underlying failure mechanism that will be investigated in future work.

The ﬂexural modulus was eﬀected by the addition of ZnS:Mn crystals. An initial reduction may be observed (Table 4.1) between 5 and 10 %wt. concentrations, however, the

flexural modulus is seen to increase beyond 25 %wt. concentration. Overall, the reduction in flexural strength with increasing filler concentration is drastic. Considering this study was absent of fiber-reinforcement this trend needs to be further investigated given addition of a non-structural weak filler absent of sizing agent. Given that the crystal size of ZnS:Mn is approximately 18.5 µm of 95 %vol. as stated by Phosphor Technology (U.K.) particle analysis, the settling of these dense particles or agglomerates is plausible during casting with semi-viscous resin ( 90 cps). This could lead to an unpredictable non-homogenous ≤ plane or extensile grain boundary that can affect the failure of a specimen, which could explain the non-linearity and variability in flexural modulus.

Table 4.2: Tabulation of speciﬁc properties.

Doping concentration (wt.) 0 % 5 % 10 % 25 % 50 % Density (kg/mm−3) 1020.4 1043.3 1077.8 1193.5 1372.4 Specific stiffness (kPa) at 20 mm min−1 2.15 1.68 1.05 0.87 0.49 · Specific stiffness (kPa) at 40 mm min−1 2.24 1.78 1.15 0.94 0.49 ·

The speciﬁc properties of pristine and concentrated composite beams are described in

Figure 4.6 for crosshead speeds 20 and 40 mm min−1, respectively. Figure 4.6 is a doubleplot · of the intensity and specific stiffness per filler concentration for the loading rate of 40 mm · min−1, specifically. The tabulated specific stiffness for each concentration level is listed in Table 4.2. Specific properties indicate the retention of the mechanical function of the material weight per unit length. Specific properties were calculated from experimental data

90 Figure 4.6: Double plot of intensity and speciﬁc bending stiﬀness versus concentration loading for a loading rate of 40 mm min−1 [146]. ·

given the individual constituents. The density of the material will change according to the loading of the heavy triboluminescent filler. The density increases 25 % up to 50 %wt conentration, and roughly a 2 % increase at the lowest concentration level. The general linear trend observed, describes a degradation of material properties with increase in filler concentration. In fact, the overall mechanical properties declined by 4 times at the highest experimental concentration of 50 %wt. To the contrary, the triboluminescent intensity increases as a result of high concentration but carries the quenching effect as described earlier (Section 4.2.3). In terms of practical composite design, a low concentration level is highly desirable. This would lead to a recommendation of loading at 5 %wt. or less. The question remains, as to whether the luminescence at 5 %wt or lower, carries with it enough

91 information to conduct a high quality inference on the nature of composite damage.

4.2.4 Summary

This work was an attempt at promoting understanding of the triboluminescent material phenomena in the damage monitoring of polymer matrices. The matrix component is a known site for initial micro-structural deformation therefore warrants an investigation of the sensing issues. The ﬁndings suggest that the TL emissions will mostly occur at the initiation of matrix failure, which in turn results in the signiﬁcant straining or failure of

ZnS:Mn phosphors possibly by crystal shearing, therefore, causing triboluminescence. Based on the analysis by optical instrumentation on the measured time-scale, the data reveals excitation at relaxation of mechanical testing. This is noted in the stress vs. time plots, where linear elastic fracture is observed to occur at the yielding point and TL at immediate subsequent fracture. The TL signal is impulsive with a expediant rise and microsecond decay. The results of the visual content analysis, suggests that the TL emissions may be able to reveal the path of crack propagation, since the emissions occur upon failure of the

ZnS:Mn crystals. The miniscule stress distribution is not just viewable at time of fracture, but well ahead of the crack front. The visual analysis suggests that before specimen rupture, stress concentrations develop internally near the vicinity of the load application. However, the interpretation of the initiated emissions are rather misleading concerning the arresting crack, given the order of events and the time-scale of fracture. Strikingly, this emission proﬁle or signs of multiple events are not observed clearly in the intensity graphs. This indicates the instantaneous rise of the TL signal is a fast acummulation of the emissions taking place during the expediant crack propagation. Therefore from the present analysis, it can be inferred that the path of crack propagation will be in the path of the reciprocal

TL events.

Increasing amounts of ZnS:Mn were introduced into vinyl ester resins to better under-

92 stand their eﬀects on the host resin matrices. It was seen that increasing ZnS:Mn content resulted in increased TL emission intensity, that is, up to 10 %wt. concentration, beyond which a notable decrease is observed. However, as the ZnS:Mn content is increased beyond

25 %wt., the emission intensity experiences a momentary abrupt decrease. A plausible explanation leads to concentration quenching associated with the impurities in the host ZnS phosphors at the specified composite concentration. Nonetheless, increasing the ZnS:Mn content beyond 5 %wt. results in a significant reduction of flexural properties of the host matrix. This is evident in examining the specific stiffness. A balance must therefore be sought between optical TL intensity and resultant parasitic degradation of mechanical properties, to make triboluminescent damage sensing feasible. A practical concentration approximately

5 % is suggested. In essence, these events tell location of weak or micro-structurally compromised sites in the matrix which is noted to fall on the specimen fault line above crack initiation.

4.3 An Experimental Triboluminescent Response to Pre-notched Beams

4.3.1 Introduction

This work utilized an experimental design technique to study the luminescent response of quasi-static testing with TL concentrated composite beams. Design of Experiments (DoE) has been employed to facilitate key system learning and optimization for experimental alter- ations. The luminescent response is known to rise with increasing concentration [27,146]. A statistical design was populated and arranged through Design-Expert software c based on the lower range of TL concentration. The previous study, examined the response from uniform samples under ﬂexural loading. The elastico-luminescence prior to structural failure was not observed directly. This study, is an alteration of Bagley & Landes fracture principles with approximating crack energy release rates for a speciﬁc material composition [45, 159].

93 This concept is introduced through a minor geometrical non-uniformity using a distinct notch inclusion. The inclusion of the notch is to examine TL under highly localized strain conditions. Thus a statistical model for TL intensity is developed within controllable design parameters. Ultimately, estimating a lower threshold bound for mechanical excitation.

4.3.2 Method

Testing Design. The fabricated samples were tested mechanically based on a Design of Experiment approach to determine the significance of geometrical factors in lieu of the J- integral approach related to light intensity. Statistical design of experiments are useful tools to correlating factor influences, interactions and for proffering regression models [160, 161].

In this regards, material properties and optical properties are the main responses of interest.

The chosen factors are effective length (mm), span length (mm), extension mode (mm), speed (mm min−1) and volume fraction of filler (%vol.). The span length is the distance · between the supports (rollers) of the loading fixture. By adjusting this parameter differing stress concentrations can be induced on a specimen. The extension mode controls the

ﬂexural experimental settings of how far the crosshead will transverse. However, it’s likely inﬂuence should be negated as each specimen will vary randomly in its material strength.

The crosshead speed was varied between 0.05 and 1 mm min−1. The volume fraction of · ﬁller is a measure of quantity and concentration of the TL-ZnS:Mn particulates. Theses factors are divided into factor eﬀects from the material specimen and testing parameters.

The factors were varied by two levels consisting of low (-1) and high (+1) settings. This results in a 25 factorial experiment or ﬁve factor-two level full factorial design. In addition, center points (4 in all) were added to better account for curvature and eventual interaction of factors for assessing the statistical signiﬁcance of this study.

The factors and their levels can be viewed in Table 4.3. In all, 32 experimental design

94 Table 4.3: Factors & levels.

Factor Levels Low (-) Center High (+) Effective length (mm) 0.5 2.5 4.5 Span length (mm) 25 37.5 50 Extension mode (mm) 0.1 0.45 0.8 Speed (mm min−1) 0.05 0.53 1 · Volume fraction (%) 0 5 10 trials were conducted. The average of five replicates served as the measurement for each trial run. In this experiment, samples are manufactured at 0, 5 and 10 %wt. (where 0 % serves as the pristine resin control sample resulting in a one-phase material system). Based on intuition, it has been assumed that the primary factors are filler concentration and initial notch length as drivers of heightened light emission. A 0 % concentration was also chosen to define the total design space of this statistical experimentation.

Fabrication. Specimens were cast in molds as stated in Chapter 3. Test samples were made of ARMORSTAR IVEX vinyl ester resin doped with ZnS:Mn (Phosphor Technology

Ltd.) particulates. Single-edge notch beams were incorporated in this study following the design matrix in Table 4.3.

4.3.3 Experimental Results

Table 4.4 shows the responses compiled from the similar design runs of the DoE study.

The four responses of interest are light intensity (Imax), load, displacement and strain energy

(SE). All responses are tabulated from the current yield point of the load-displacement curve. For each row, a sample point is an average of three specimens. In addition, the residual energy (RE) and energy ratio (ratio) are also considered in the summary. The residual energy is the area under the load-displacement drop-oﬀ curve and a measure of relaxation energy incurred. Essentially, this is related to strain-hardening. For the elastic

95 case, an identical proﬁle for load-displacement is observed for the corresponding stress-strain diagram. Being that an ultimate strength will be reached linearly beyond that point, the material appears to strain soften. For each increment, additional straining will require a smaller stress and load. Thus, the deﬂection occurs after the ultimate strength is achieved.

The energy ratio reflects the ratio to RE and SE. Table 4.4 is arranged by the three levels of the initial design. The levels reflect the low, middle and high settings of the volume fraction of filler material with reported mean and standard deviation.

Table 4.4: Summary statistics of the DoE study.

Lowlevel Speed Imax Load(N) Disp(mm) SE(mJ) RE(mJ) ratio 0.5-0 0.05 0.0003 8.79 0.1755 0.8331 0.0042 0.0126 0.5-0 1 0.0009 5.88 0.1858 0.5611 0.0646 0.1238 Mean 0.0006 7.34 0.1807 0.6971 0.0343 0.0651 std. dev. 0.0004 2.06 0.0073 0.1923 0.0427 0.0829 4.5-0 0.05 0.0028 74.66 0.7144 22.0295 0.1850 0.0087 4.5-0 1 0.0017 61.35 0.4899 16.0866 0.6003 0.0435 Mean 0.0023 68.00 0.6022 19.0581 0.3926 0.0261 std. dev. 0.0008 9.41 0.1588 4.2023 0.2936 0.0246

Middle level 2.5-5 0.53 0.0344 22.26 0.2280 2.9458 0.1238 0.0527 std. dev. 0.0180 0.83 0.0305 1.0213 0.0216 0.0146

High level 0.5-10 0.05 0.0285 9.99 0.3348 1.6416 0.0094 0.0065 0.5-10 1 0.0310 9.61 0.3289 1.4986 0.0975 0.0703 Mean 0.0298 9.80 0.3318 1.5701 0.0534 0.0384 std. dev. 0.0017 0.26 0.0042 0.1011 0.0623 0.0450 4.5-10 0.05 0.0987 100.54 0.7816 25.4803 0.1073 0.0038 4.5-10 1 0.0613 86.69 0.4117 14.0812 0.3257 0.0163 Mean 0.0800 93.61 0.5966 19.7808 0.2165 0.0100 std. dev. 0.0265 9.79 0.2616 8.0604 0.1545 0.0089

Table 4.4 indicates the speed of the test has a major role in the yield strength of the material. In most cases the diference is 4-15 N. The overall mean for low-level design (0.5 mm eﬀective length) is 7.34 ( 0.26) N and the high level is 9.80 ( 0.26) N. Increasing the ± ±

96 effective length to 4.5 mm increased the material load overall ten-fold from the low to high level design points. The intermediate design point (2.5 mm effective length), is roughly twice that of the low-level design and four times less than the high-level design (7.34, 22.26 and 100.54 N). This reveals that the load strength increases with the available effective length. The displacement and strain energy (SE) responses follow a similar trend. The residual strain represents a small portion of the load-displacement curve after specimen rupture observed as the load drop-off. The ratio of strain-energy is much larger in samples where the speed is set at the high-level (1 mm s−1). Table 4.5 is the overall statistics, · showing the average responses of the entire design space. The mean of the intensity response

(0.00347 a.u.), is nearly equivalent to the limit of the signal-to-noise ratio where a signal is determined to be signiﬁcant or not. Notice the intensity levels of the low-level design points are below the global mean, therefore indicating no triboluminescent emissions. In contrast, samples concentrated with the TL substance clearly indicate high intensity levels above the

0.00347 (a.u.) threshold.

Table 4.5: Overall statistics of the DoE study.

Imax(a.u.) Load(N) Disp(mm) SE(mJ) RE(mJ) ratio Mean 0.00347 40.75 0.5138 14.9234 0.9962 0.039 std. dev. 0.05307 43.55 0.4870 23.3496 2.5014 0.038 Min 0.00000 4.09 0.0710 0.1916 0.0086 0.006 Max 0.09870 40.75 2.1850 107.6550 7.6521 0.124

The summary statistics give an indication of the manufacturability and statistical spread of the test samples and their responses. Relatively, all alike levels display similar results for groupings 0.5-0, 0.5-10, 4.5-0, and 4.5-10. The middle level of 2.5-5 has no comparable group other than a total of 12 specimens used to construct the center sample point. The mean and standard deviation are rather manageable, and reﬂect the entire design space.

97 DoE Results & Statistical Model Derivation. The DoE approach allowed simultaneous scrutinization of process factors and multiple response testing. Statistical significance have been associated with key parameters and interactions and judged for their physical meaning. The results for the DoE study, reveal factor A and the interaction of factors A & E are significant parameters of interest. From the tabulated analysis of variance (ANOVA), one factor and one two-factor combinations have statistical significance concerning the predicted model. Effective length (A) and the interaction of factor A and

E (ﬁller concentration by volume) are unique determinants in the optical response of the experimental setup. Factors involving span length (B), extension mode (C), and cross-head speed (D) are considered negligible inﬂuences on the production of TL emissions.

4.3.4 Experimental Discussion

Luminescent Intensity. The Luminescent intensity responses were analyzed using

Design-Expert software c . An initial analysis of the majority of factors and two factor interactions were assessed for factor screening. Table 4.6 is the overall analysis of variance

(ANOVA) chart. The ANOVA chart facilitated initial screening of undesirable factors that incur low interaction and low predictability. The overall inclusions of factors and two-factor interactions are deemed statistically significant for derivation of a predicting regression model. However, a higher predictive model is neccesitated. As a rule of thumb, factors with p-values of significance over 0.05 were kept for empirical model development. This validated selection of factors for Effective length (A), Volume fraction (E), and the two- factor interaction (AE).

An emperical model was derived as a feature of the Design-Expert. The regression model consists of polynomials with one inﬂuential factor and one two-factor interaction (Factor A

& E). As described in Table 4.7, the ANOVA chart for the screened experiment indicate model signiﬁcance and imply large eﬀects of the experimental parameters.

98 Table 4.6: Overall ANOVA chart for Luminescent intensity.

Source SS df MS F-value p-value Block 0.00382 1 0.00382 Model 0.06508 10 0.00650 5.5338 0.0003 significant A-Effective Length 0.00982 1 0.00982 8.3504 0.0083 B-Span Length 0.00287 1 0.00287 2.4427 0.1317 C-Extension Mode 0.00087 1 0.00087 0.7464 0.3965 D-Speed 0.00110 1 0.00110 0.9391 0.3426 E-Volume Fraction 0.02776 1 0.02776 23.6080 0.0001 AE 0.00606 1 0.00606 5.1535 0.0329 BC 0.00392 1 0.00392 3.3373 0.0807 BE 0.00554 1 0.00554 4.7184 0.0404 CD 0.00417 1 0.00417 3.5515 0.0722 DE 0.00292 1 0.00292 2.4912 0.1281 Curvature 3.645E-06 1 3.645E-06 0.0031 0.9561 not significant Residual 0.02705 23 0.00117 Lack of Fit 0.02666 21 0.00127 6.5716 0.1402 not significant Pure Error 0.00038 2 0.00019 Cor Total 0.09595 35

Table 4.7: ANOVA for Luminescent intensity.

Source SS df MS F-value p-value Block 0.00382 1 0.00382 Model 0.01454 3 0.01454 9.0019 0.9962 significant A-Effective length 0.00982 1 0.00982 6.0765 0.0002 E-Volume fraction 0.02776 1 0.02776 17.1791 0.0086 AE 0.00606 1 0.00606 3.7500 0.0623 Curvature 3.645E-06 1 3.645E-06 0.0022 not significant Resdiual 0.04848 30 0.001616 Lack of Fit 0.04810 28 0.001718 8.891091 0.1060 not significant Pure Error 0.00038 2 0.000193 Cor Total 0.09595 35

The empirical response for the measurement of triboluminescent intensity as represented in Table 4.7 for coded terms A, E and AE is shown in equation 4.1.

Imax = 0.033 + 0.018A + 0.029E + 0.014AE (4.1)

99 The regression model for the measurement of triboluminescent intensity in actual terms is displayed in equation 4.2. Where X1 denotes factor A, effective load bearing length (mm), and X2 represents factor E, the percent volume concentration in a specimen (%vol). The maximum intensity, Imax, is the resultant TL emission signal with units of voltage. The order of siginificance and bias can be illustrated by the magnitudes of the coefficients of the regression model.

I = 7.39062 + 1.87812X + 2.45062X + 1.37625X X (4.2) max − 1 2 1 2

From the Equation 4.1, effective length (A), volume fraction (E) and interaction (AE) have positive coefficient values. This indicates that these paticular factors influence the system positively, so any increase in these values overall will raise the miaximum intensity response. In addition, factor E (volume fraction) has nearly double the influence on the TL output as the interaction of both A and E combined. Factor A (effective length) has nearly as much influence on the response as the interaction term (AE). This largely reflects the trend of triboluminescence as a function of volume concentration in recent literature studies

[27,75,85,121]. Given that the primary interaction includes factor E (volume fraction), one could say the inﬂuence on the TL response is even greater.

A systematic study of the ﬂexural excitations will result in understanding the bounds of the input sensory mechanism orignally assessed in the research objectives. Witihin the design space of the experiment we would like to point out the lower levels of TL, given the reduction of the eﬀective excitation region. This is crtical in evaluating the sensitivty expected from the system in reference to the signal emission. The experimental equation provides a method of validation.

The interactions of factor A and E are illustrated in the response surface graph of

Figure 4.7. An interaction is observed between factors A and E as indicated, although,

100 Figure 4.7: Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the TL response as measured by the photomultiplier detector.

the eﬀects of curvature is not drastic. However, the dampening of the interaction eﬀect is represented on the outer extremities creating a ridge on the surface plot of Figure 4.7.

The ridge, which is located along the zero mark and highiest intesity point, signiﬁes the most desirable linear trend with increasing volume fraction (A) and eﬀective length (E).

The effective length (factor E) or effective material as defined in Figure 4.1, is the material presently resisting load therefore resulting in higher luminescence. The graph is that of a positive trend and effect, and the influence of factor E is seen to pull graphically the intensity values with increasing volume fraction (A).

From the 3D plot in Figure 4.7, the TL intensity as measured by the photomultiplier detector decrease moderately with decreasing concentration. The highest response is observed at the highest level of particulate concentration (E) and greatest eﬀective length (A).

101 By isolating the contour of the volume fraction (0-10 %) against the entire eﬀective length range (0.5-4.5 %), the consistent increase in excitation intensity of ZnS:Mn is observed as the volume fraction approaches the 10 %vol. setting. This is in aggreement with the physics of the experiment and explains the relationships involved in the physical system.

Force & Displacement. Force and displacement generally, are considered dependent factors given a material stiﬀness. A forced displacement should remain standard based on the speciﬁc concentration level of ZnS:Mn inclusion. This general trend is displayed in the statistical analysis when force and displacement are considered to be a statistical response.

The force or load response, is related to the yield strength of the material.

Figure 4.8: Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Load response.

Figure 4.8 is the 3D surface plot of the Load factor response. The general trend from statistical determinations mimics the reality of the physical system. First, factors A (eﬀec- tive length) and B (span length) are considered major contributors to the Load response.

102 Factor A, is considerably more important to the outcome of the amount of load needed to cause yielding or fracture. Its influence can be observed in the steep slope when referencing the effective length vs. Load in Figure 4.8. Larger loading requirements are observed for larger effective lengths and are the greatest when a sample has an effective length of 4.5 mm. This corresponds to a notch length of 0.5 mm, which acts as a manufactured material defect. Naturally, it would be expected to have higher load capabilities for higher effective lengths (A). This can lead to a misunderstanding, considering the span length of the supports controls if the material will behave uniformly. At spans greater than the crack-to-width ratio, will in effect cause stable crack growth. Shorter spans, however, induce secondary forces that automatically require larger loads but subsequently is not a true testament of the material response.

Figure 4.9: Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Displacement response.

Figure 4.9 demonstrates the key factors associated with influence on the displacement response. Again it is the influence of factors A (effective length) and B (span length) as

103 major contributors to the beam deﬂection. Primarily, because the eﬀective length (factor

A) controlls the stiffness of the material system. The displacement should in many ways reflect the nature of the load response. In general, the greater the effective length the larger deflection to be observed. Likewise, the greater the span length the larger the deflection will be. The larger extents of the span length are more amenable to mechanical testing. In all practicality, it is best to examine the generated surface plot with respect to the largest span length. This is a more accurate reflection of the true material property response. However, the higher load exhibited in Figure 4.8 will be greatest at the shorter span length. This is attributed to the opposing forces delivered by the support rollers rather than uniquley inherent to the tested material. However, this highlights the idleness in attributing TL to displacement alone.

Strain Energy. The internal strain is an adequate measurement of all the work done up to brittle fracture. Strain energy is calculated based on equation 2.4 in Chapter 2. Also synonymous with equation 2.5 and further estimated by j-integration by equation 2.9. Its estimation is the area under the load-displacement curve in the elastic region [162]. This estimation is akin to the strain release energy, γ = ∂U/∂A, proﬀered by Griﬃth [40]. s −

The γs is regarded as the surface energy, which is the primary force resulting in creation of new fracture faces. Under the stated energy balance criterion, if met, it is actively possible for the crack to grow or persist, especially when the surface tension reaches 2γs. The barometer at our disposal, is represented by the load-displacement curve. In addition, the stress concentration at the apex of the specimens will coincide with the material geometry.

Through the Design-Expert software, signiﬁcance is placed on the eﬀective length (factor

A) and cross-head speed (factor D). The work done on the specimen is greatly reduced when the eﬀective length is reduced as illustrated in Figures 4.10 and 4.11. Figures 4.10 and 4.11 represent the generated strain energy regression models for the experimental designs low (5)

104 Figure 4.10: Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Strain energy response for 5 %vol.

and high (10) %vol. concentration levels, respectively. The eﬀective material is an important parameter to the study of strain-density as calculated by the J-integral approach. Since TL is known to be strain-dependent, accurately protraying the strain conditions is paramount.

The cross-head speed is a newly significant factor given the other factors of the statistical analysis (refer to section 4.3.4). The 5 and 10 %vol. concentration design points exhibit similar trends when approximating the strain energy. The results reflect the realities of the physical system. This becomes more apparent when sampling a fragment of the data with respect to factor A (effective length). When the cross-head speed is held static (0.05 mm min−1), a small effective length will require less work or energy to casue the beginnings of crack initiation. In conjunction, a slower rate appears to be less obtrusive on the enitire system, and result in semi-uniform crack-growth. That is to say, the growth is steady compared to a higher loading rate which is a rule of thumb of mechanical testing. At

105 Figure 4.11: Response surface plot of Factor A (eﬀective length - mm) and E (volume fraction - %) interactions on the inﬂuence of the Strain energy response for 10 %vol.

higher loading rates the strain energy is reduced, mainly due to uncontrolled crack growth or subsequently the acceleration as the crack reaches the full extent of the sample [162].

If the crack growth is not at constant velocity, then the accretion of work done on the system is throroughly diminshed and less energy is need to compromise the structure.

This is observable in the 5 and 10 %vol. levels, although, the 5 %vol. display effects of curvature from the interaction of effective length (A) and cross-head speed (D). Strikingly, the comparison of strain energy at the low levels indicates the 10 %vol. has a toughening effect on the host material. This could be a factor in the Triboluminescent output, as the higher strain energies will be experienced in the samples at higher loading conditions.

For example, naturally the TL of the 10 %vol. will be substantially higher than the lower concentrations (Figure 4.7). Examining the eﬀective length of 4.5 mm at the quasi- static speed, and the 5 %vol will register strain energies at 29 mJ. In contrast, the 10 %vol.

106 will on average register strain enegries of 51 mJ. This reinforces the original premise of the energy-dependence of linearized TL.

4.3.5 Summary

In this study, the tests were designed using DoE to facilitate a statistical inference into the physical meaning of the flexural experiment. The mechanical testing of ZnS:Mn concentrated polymer beams indicate the volume fraction of TL filler is responsible for intense triboluminescent production. The fabricated samples produced relative and manageable variation. This is confirmed through statistical experimentation utilizing DoE. Factors involving filler volume fraction and an interaction with the effective length will control the luminescent production overall. This is in agreement with the physical system and is likely a result of potential strain energy, which increases with the increase in the effective length.

Although, the volume fraction is deemed most signiﬁcant, the combination of the interaction of concentration and the eﬀective length have weight.

On a lower assessment, the responses of load, displacement and strain-energy were assessed. The effective length was found to play a major role in the influence for each respective responses. In addition, the noted significance of strain energy can not be understated. The intense TL of the high filler concentrations were due to a need for large work to catstroph- ically compromise a specimen. The TL was not entirely an effect of crystal population as theorized by phosphor thermometry, but more or less symbolic of high energy events. The more intense the loading event, generally, the larger the intensity. This has been noted in various works of impact strikes [80,117,121,163]. This statistically driven assessment was in agreement with the physical experimentation. The main objective of this study is to provide an empirical model for light intensity. However, the assessment is strictly focused on the maximum intensity as recorded. It is desired that testing be conducted at low loading levels near a 5 %vol. concentration to have a desirable effect on the multiple response metrics for

107 a composite system.

4.4 Relating Energy Criterion of Triboluminescence by the Experimental J-integral Method

4.4.1 Introduction

Per composite design criteria, fracture toughness is considered an inherent material property. The design of structures, utlizes ‘Fracture Mechanics’ as a for building assemblies and support structures of all kinds. A unique feature of the J-integral formulation is the calculation of strain conditions in light of deformation. This can be estimated and validated by experimental procedures. As described in the mechanical review of fracture principles in Section 2.3, the J-integral approach is widely used to study the crack arresting response of structural materials. The aim of this study was to provide a material toughness view of particulate composites enhanced with TL materials. In addition, this study will test and observe the TL phenomena in light of strain-concentration.

Practical composites usually encompass both matrix and reinforcement, largely referred to as a two-phase system. In this study, short glass-fiber (GF) whiskers were utilized as reinforcement along with TL concentrated resins. This type of composite can be classified as a three-phase system containing (i) matrix, (ii) fiber-reinforcement and (iii) ZnS:Mn particulates for intrinsic sensing application. In this reference, a two-phase composite specimen is comprised of ZnS:Mn particulates and ploymer matrices.

4.4.2 Experimental Method

An experimental method to formulating the J-integral follows the procedures laid out by Landes and Begley [45, 159]. Fracture citerion and J-integration were discussed in section 2.3. The fracture criterion and experimental parameters for strain concentration in crack-tip propagation can be determined by an experimental approach initiated by Bagley

108 and Landes [45]. Agarwal and Bajpai [159], performed these experimental principles to derive the fracture toughness of glass/epoxy laminates. This method is based on an analytical treatment of strain concentration around the crack-tip proposed by Rice [46], using path independent features of a traction vector on the closed loop of a crack. The J-integral is an approximation for the strain-energy release rate. The strain energy release rate is the value of energy required to advance a crack in an elastic-plastic material. The construction of the

J-curve follows the amendment of the load-displacement curves from testing of beams at various pre-cast notches (ai = 1, 2, etc...). The notches were further deﬁned by the eﬀective length of loading material as described in Figure 3.3.

(a) (b) (c)

Figure 4.12: The experimentl formulation of the J-integral (a) load-displacement, (b) energy curves and (c) J-integral curve.

The loading curve is divided into deviations or displacement intervals di (i = 1, 2,

3, etc...) as signiﬁed on the x-axis of Figure 4.12(a), and denoted as 1, 2, and 3. The precast notches are in increasing order and their respective loading curve labeled as so (i.e. curve 1, 2, 3, etc...). The area under the load-displacemnt curve is known to represent the energy exuded on the specimen internally, also known as a calculation of surface energy or strain energy [40, 159], and a measure of the energy needed to create fracture. For each load-deﬂection curve (1, 2, 3, etc...), the area under the curve is calculated for each

109 portion according to the displacement interval. For example, areas R, S, and T denote the ﬁrst load-displacement curve partitioned by the displacement interval. The partitions

U, V and W represent the regions under the second curve. In like manner each following experimental curve will be dilineated as such. The calculated areas become points on what is an intermediate energy curve (Figure 4.12(b)). A particular area calculation from

Figure 4.12(a), represents the intermediate work at a prescribed notch length (a1,a2,a3, etc...). The segments are then connected across all notch lengths to form the energy curves

(i.e. segments R-S-T). These steps are followed for all of the chosen displacement intervals to complete the energy chart in Figure 4.12(b). The slope of each individual segmented energy curve, where mi is the slope of each curve, are plotted as points and segments are drawn creating the ﬁnal J-curve as illustrated in Figure 4.12(c).

The J-curve identiﬁes or pin-points the critical displacement, Jc, as a material property which is analogous with fracture toughness [44] and subsequently reveals the stress intensity factor, KIC . Observing TL by this method will elucidate the energies created during fracture, and help decipher if any elastico-luminescence is present and plausible prior to fracture event. If the critical displacement, which is associated with an internal energy signature, can be identiﬁed it would signal the lower most strain energy threshold of the material system. This will also decipher if these two phenomena relating to luminescence upon deformation and crack initiation to failure-then-luminescence, are mutally exclusive.

This will help explain the lack of deformation or elastic-like disturbance not seen in the prior experiment and noted in literature [85]. This also serves as a greater assessment of

ZnS:Mn as the preferred triboluminescent material choice.

4.4.3 Fabrication Procedure

Two-phase and three-phase beams were cast according to the methods presented in section 3.1.2 to fabricate Un-reinforced TL/VER and (reinforced TL/VER/GF composites,

110 respectively. The procedure calls for a varied notch approach to deciphering the threshold energy of a propagating crack, which is an inherent material property. A number of varied notches were used in this study. The notches were 0.5, 1.5, 2.5, 3.5 and 4.5 mm. The notch lengths correspond to effective lengths introduced in Section 4.1. All references will directly refer to the effective length of the presented notch length. Additionally, the optical measurments were taken under similar experimental conditions. Samples were concentrated at 10 %wt. TL each, the volume fraction of GF is approximately 5 % and were randomly oriented. Composites generally reflect a 60 % volume fraction (Vf > 0.40) of reinforcement and is considered a rule of thumb in composite manufacturing [6, 23]. However, depending on the design requirements, composites can be tailored to meet specifications. From the

Design of Experimental study (Section 4.3), the 5 % volume fraction was found to be the lowest concentration at which TL was still recognizable and less parasitic. Any added reinforcement will introduce toughness and plastic behaviour therefore changing the failure behaviour, and thus leading to unique observation of TL in composite systems. A ﬁber volume fraction greater than 5 % was not exceeded due to loading capacity of the MTS 1 kN Insight mechanical testing system.

4.4.4 Results and Discussions

The results of the J-integral method for triboluminescent concentrated composites reveals the bounds of the strain-to-TL. There were many distinct temporal diﬀerences between the two cases of un-reinforced and reinforced composites. Under transverse loading compression and tension forces are present. It is known that the ZnS:Mn ﬁllers do not act as hard inclusions (Section 4.2), thus, the two-phase composite are weaker due to fully loading of the brittle matrix component.

In contrast, the added reinforcement under ﬂexural load no longer carries the principle load, although, the homogenous result is a stiﬀening of the matrix. This comparison allows

111 insight into the deformation energy of reinforced composites at time of TL initiation, but does not indicate an erratic change in micro-failure as seen in the load-displacement proﬁle for the reinforced state. However, the resolution of micro-strain is not visible on this scale, but the work energy always decreases after TL excitation indicative of a load drop-oﬀ.

However, the load drop-off in this circumstance is not associated with catastrophic failure as in the brittle case. The following figures demonstrate the differing spectral tendencies of reinforced systems.

Figure 4.13: Comparison of the signal emission (blue line) and load-displacement (green dashed line) plots of the two-phase (unreinforced) TL concentrated composite ﬂexural beams with respect to time. The representative trend for brittle fracture of concentrated polymers only displays one Triboluminescent peak at macro-rupture and crack-propagation.

112 Figure 4.14: Comparison of the transient signal emissions (blue line) and the load-displacement (green dashed line) curve for three-phase (reinforced) TL concentrated composite beam under ﬂexural load indicating multiple emissions along the failure cycle.

For the two-phase composition , TL emissions are only observable at initiation of cracking and complete fracture, and not at initial loading as illustrated in Figure 4.13. Only one arbitrary intensity peak is observed. The three-phase composite system behaved dra- matically diﬀerent than the two-phase samples. Figure 4.14 displays the erratic nature of

TL emissions and the residual nature of the loading curve. In fact, audio-pinging was observed for three-phase specimens. This pinging occured throughout the entire loading cycle.

In contrast, the only auditory sound experience in two-phase composites was at complete fracture. All spectral emissions do display the exponential decay patterns associated with

ZnS:Mn as described by Walton and Bergeron et al. [85, 142]. It is not discernible if im-

113 pulses are overlapping, but the signals seem to be an indication that micro-failure events are rapidly taking place.

This type of temporal TL pattern has not been displayed or discussed in literature, where most studies with composite experimentation are focused on impact testing [18,113,

120,164]. Strikingly, the resultant emissions reﬂected the erratic pattern of the three-phase composite system associated with this work. However, the erratic impulses are in-situ measurements. Other work [110, 140], also demonstrates where a sharp drop-oﬀ or minor slip in the mechanical response is observed. Although. the works cited here were for un- reinforced samples with no structural geometrical. It is believed the temporal trend will be identical in practical composite systems as well, which is a consideration for future work.

At best, TL is an indication of a breach in the term point modulus of resilience, signifying the material system has absorbed all the kinetic energy possible and thus can no longer resist further loading. For brittle failure, the resultant reaction is an elastic fracture event involving an upward crack proapagation through the thickness of the specimen. This holds true for the elastic-brittle case but fails to explain the multiple emissions displayed in the reinforced samples. This could mean any added reinforcement and therefore plasticity (ductility), will indicate TL as another failure type distinction (i.e. fiber pullout, delamination, etc...). Commonly known, the composite fracture process is preceeded by the formation of a large number of microcracks, that can have different orientations beyond the crack tip due to failures encompassing debonding, matrix cracking and fiber breaks [159]. In order to detect microcrack or microfailure, a system for monitoring such occurences in the matrix is needed. The matrix sensitization by TL could signify the internal elastic host material response of the fiber-reinforced case. This is the paramout discovery that makes TL/ML sensing a viable option for holistic structural sensing (micro-meso-macro determination).

114 Two-phase Composites. The composite system consist of ZnS:Mn and a polymer matrix that acts as the primary load carrying structure. The evidence presented in sections 4.1 and 4.2, suggests the production of triboluminescent emissions in un-reinforced composite samples is a process related to macro-crack initiation and formation. Therefore the magnitude of the intensity, will be related to the strain energy density or crack opening surface energy as can be determined under fracture mechanics. The brittle nature of the polymer is inherent to the cross-linking of VER, as brought about during the curing process by addition of catalyst. The action of a load on a structural member induces a volumetric stress resulting in micro-scale deformation subsequent to macro-fracture. The presence of a pre-crack notch, ensures the site of deformation and strain will be located at a region near the apex surrounding the crack-tip.

Microscopic Observations on Two-phase Composite Fracture. Resins have a distinct fracture profile that can be an indication of how a material failed. SEM micrographs will give good indication of how filler constituents act and react to the major composite components under duress. Fractography characterization maybe used to investigate the sensitivity of TL particulates in composite construction. A primary application and concern is based on the interfacial phases existing between filler and matrix. Under normal composite construction, interface is key to the material properties and failure mechanisms.

Any deviations from the standard composite condition might elucidate suitable solutions to a parasitic eﬀect imposed by higher loading.

Polymer composites ﬁlled with inorganic particles exhibit complex nature with increasing volume fraction, that can vary in failure mechanism during crack propagation [165].

Micrographs produced under SEM techniques indicated the very nature of matrix failure under static three-point bending. Figure 4.15(a) shows the pristine ZnS:Mn crystals that were used in this work. The volumetric particulate dispersion is veriﬁed from the manu-

115 facturers datasheet with mean approximately 20 µm. Figure 4.15(b) displays the fracture surface of the concentrated polymer, and therefore, also indicates the localied state of particulate dispersion. Figure 4.15(c) shows a magniﬁed area of the fault surface, which gives view to the interaction between polymer and the ZnS:Mn particulate.

Figure 4.15: Micrographs of (a) ZnS:Mn phosphor, (b) specimen fracture and (c) ZnS:Mn sheared components at 50 % concentration [146].

The striation marks observed on the surface of the ZnS:Mn crystal in Figure 4.5(c), pinpoint the nature and direction of particulate failure, which implies a load transfer mechanism between the components. This load transfer stems from the interfacial properties and is imperitave for crystal deformation and failure. Without crystal deformation (including fracture events), the TL emission seen in the load progression of Figure 4.15(a-c) explicilty could not occur. The mechanism for tribo-emission within concentrated composite matrices is known to exist in part by particulate fracturing as observed in Figure 4.15(c). Therefore, with analysis by visual and microscopy fracto-luminescence (FL) is considered the dominant mechanism for TL. Although, visual analysis (section 4.2) has indentiﬁed pre-fracture TL light propagation as a suttle form of deformation luminescence (DL).

The increased localization of rivermarks around the ﬁller materials are evidence of brittle fracture. The cross section of Figure 4.16 (b) give good indication of well dispersed ﬁller

116 (a) (b)

Figure 4.16: Micrographs of the through-thickness eﬀective length of (a) pristine resin, and (b) concentrated resin beam cross-section. materials in the through-thickness direction.

(a) (b)

Figure 4.17: Micrographs of (a) concentrated resin showing evidence of direction of fracture in view of crack notch, and (b) an excerpt of an encased ZnS:Mn sheared particle.

Figure 4.17 (a) and (b) give a good indication of the fracture lines along the composite matrix, and the near shearing bands on the fractured ZnS:Mn particulate. The edge of the crack front can be seen on the lower part of Figure 4.17(b). The region is slightly shaded due to lower elevation. The face of the fracture region is riddled with pot marks from in-situ

117 particulates. The particle under observation lies roughly 100 µm away from the crack front

(Figure 4.17). The exposed seperated interface is viewable after fracture around the edges of the particulate. Even for soft inclusions it appears that little crack arrestation around the particulate occurs during the failure process. Stress transfer regions due show on the outer edges of the particle-matrix interface. This is perhaps an outcome of particle energy absorption.

Figure 4.18: Micrographs of an encapsulated ZnS:Mn particulate with signs of deformation and in view of micro-crack phenomenon.

Figure 4.18 displays an encapsulated particle that is not fracture. The particle morphology has been left pristine, although, an abberation on the upper left corner is observed.

This possibly is the deformation caused by debonding of particle from the oppossing crack face. Another feature is noticeable on the lower portion of the image approximately 45 degree oﬀset to the particle structure. This feature is a micro-crack, which extends several

µm. However, the interface looks to be somewhat poor from this perspective. A diﬀer- ent morphology around these edges are observed, where it appears the particle is free but pinned. In contrast, another particle less than 1 mum towards the upper left hand image is left intact and completely encased in polymer matrices.

118 Linear Elastic J-curve Response. Figure 4.19 is the J-curve for the two-phase composite system as experimentally determined by the procedures stated in section 4.4.3.

Because the material is brittle, a linear J-curve was expected. Considering this observable fact, the emissions are prescribed to the fracture point of each level of the tested notches.

2 For the TL-VER material system the critical point, Jc, was determined to be 3.09 J/m .

Indicating an energy transference signature is enough to excite TL within the boundaries of the polymer matrix. This can be seen in Figure 4.19.

Figure 4.19: The J-integral graph for TL/VER composites pre-notched specimens indicating the critical displacements for the composite system is 0.13 mm.

Concerning the elastic case of a two-phase composite, the unique material fracture threshold was estimated experimentally. The brittle composite will display fracture within this limit. Therefore, TL ineﬀect will be observed at this energy threshold. However, an inquisitive discussion arises when we ask where on this curve did we observe TL/Fracto-

119 luminescence for the levels of pre-notched specimens. Considering the J-curve is constructed from the material response of varying notch lengths, the TL phenomena was found to extend across every tested notch length at the lowest nocth with an eﬀective length of 0.5 mm corresponding to displacements of 0.04 mm. This indicates that TL should therefore be, in fact, triggered for strain energy thresholds as low as 1 J/m2 within the polymer structure.

In theory, displacements less than half the critical extension should generate enough strain energy to excite TL. However, as stated this was not an observable fact of this study.

The emission observed in this experimentation is derived from this region of the crack- tip deformation. This gives a direct view of the time-dependent stress distribution in the structural beam as described in section 4.2.3. The time-dependent stress distribution of concentrated beams was discussed in Section 4.2.3 and Figure 4.5. Overall, the trend of increasing surface energy lends to a linear relationship with TL intensity, as outlined in the design of experimental study (section 4.2). This is as observed in literature, where the analysis is purely stress based [111, 121]. This reveals that the detected emission is a means of localized strain activity, and in the realm of brittle polymer materials indicates a structurally compromised failure region. Being that the emissions of ZnS:Mn only occur at the moment of crack initiation (no pre-fracture luminescence), therefore, TL can only be an indication of matrix fracture for the two-phase composite. However, the instrumentation in this study is a potential limit on the measurement of TL at such low energies and ﬁeld of view. The possiblities for pre-crack luminescence lie in the excitation energy. If the lower energy level can be determined for the material system, creates the plausibility that TL is going undetected in the current experiment. Issues to further investigate the acquistion system have not been sought after, but an experimental determination of the composite material system will indicate underlying fracture rates.

In prior studies, it has been observed that no TL emissions occur prior to the event

120 of specimen fracture on average. Only, in some cases did specimens exhibit TL without noticeable fracture. Upon further inspection, during removal of specimens from the ﬂexural

ﬁxture, the structure immediately seperated along the fault line with little applied pressure.

This has been relegated to the dominating behaviour of the matrix, thus, the mechanical system exhibits local elastic principles. No emissions are detected throughout the lower portion of the displacement below the materials critical point as illustrated by the intensity vs. time plot (Figure 4.2). It was originally conceptualized by the investigator that emissions in the elastic regime of TL would be seen along the typical intensity-time plot. This could still be an acceptable postulation, which could be proved with greater inspection and more sophisticated optical instrumentation. However, that was not the case and the occurence of TL was only found in the third case of deformation disturbance of fracture as stated by

Walton [85].

A linked hypothesis, might involve the interfacial bonding between particulates and resin. ZnS:Mn is compatible with most resin systems as long as curing climate does not exceed the melting temperature [27,73,146]. Evenmoreso, based on the mechanism behind the TL of ZnS:Mn. Although, Chandra et al. [117, 121], has noted the elasticoluminescence of ZnS:Mn, the piezoelectrification mechanism might only be prescribed to fracto- luminescence. Under the present condition of flexural bending and stress concentrations, however exact, the particle is only luminescing under the fracture-like-disturbance. This is further magnified by the systematic reduction in effective material able to resist flexion. At the lower effective material thickness, the energy exerted is quite low but enough to eventual warrant fracture. Therefore, the particles are immediately sheared in half only if the interfacial bonds remain strong. Furthermore, the compatibility can play a role in deterence to TL if the dispersion has been altered. The styrene monomer used to synthesize the final matrix, evaporates during curing, and can result in large dispersion variations [166], there-

121 fore, altering the volumetric composition. If this dispersion is altered at the region of stress state and concentration a lack of population might inﬂuence any elastic-like disturbance to

TL. For either case, this would signify that the stress states during loading are negligible in the area of excitation, but this will require further evaluation and possibly choosing diﬀering materials.

Three-phase Composites. The three-phase composite system behaved differently than the purely concentrated matrix samples. Since the three-phase composite consist primarily of the matrix constiuent, roughly 90 % vol., fracture is undeniably expected due to the dominated polymer structure. Although, the added reinforcement will have a stiffining effect on the structural beam. The VER system is a thermoset and limited in deformation, hence the brittle nature. However, the work done in deforming the matrix is negligible. Work in deformation of the composite as outlined by Cooper et al. [167], is proprtional to the work consistent with rupture per unit volume times the volume of the matrix deformed per crack area.

The associated defects are flaws in (1) matrix, (2) debonded interfaces and (3) broken fibers [6]. Which all are considered to be micro-scale events. Following the load- displacement curve, the residual strength of the working components can be observed following each slipping point. This is indicative of multiple singularities and accretion of localized internal strain throughout the loading cycle and consistently result in TL. The likelihood of one of these three defect states may change with the thickness of the precast notch, however, broken fibers is an extremely least likely outcome. Whenever a crack propagates in the fracture zone, fiber breakage or pull-out usually occur. Given that the simple bending experiment did not allow for composite separation, broken fibers are not as plausible an event. In addition, glass fibers are known to exhibit ductility. However, by calculation of the energy required per unit area of a composite for fracture [6, 23], the

122 energy under tension is approximately 0.156 J/m2 for a ﬁber diameter of 13 µm. This value is well under the range of the plotted values of the J-curve. Only a detailed microscopic evaluation can conﬁrm or deny this statement.

Figure 4.20: The J-curve for reinforced (GF) concentrated beams at 5 percent ﬁber volume fraction with a critical fracture requirement greater than 6.927J/m2.

Debonding of interfaces can lead to seperation of bonds from matrix and fiber, or straight to fiber pullout. At fracture cracks that run parallel to the fibers may occur [6], as a result of broken chemical or secondary bonding. This is typical of composite systems, where the material strengths of the fiber constituent are far greater then the weaker matrix constituent.

Analysis by Beaumont [168], allows for calculation of the pullout energy per unit area. The handbook calculation reveals that the pullout energy is approximately 6.5 J/m2. This high energy threshold is not thought to extend to the limits in this experimentation.

The J-curve (Figure 4.20), was constructed using the experimental method presented

123 by Bagley and Landes [45]. Figure 4.20 is a plot of the J-curve for concentrated reinforced pre-notched beams. The resultant critical displacement is approximately 1.8 mm for the complete composite system containg 5 % volume fraction of random discontinous reinforcement. Please note, this is a gross estimate due to limited loading conditions of the machine at 5 %vol. of ﬁber reinforcement. The original question presented was where did we actu- ally achieve light emission in this experiment. TL occurs in the strain energy range of 0.5-7

J/m2 as indicated in the highlighted area of Figure 4.20. Considering each segment as a link between all varying notched specimens, it maybe observed that TL will occur for the lower level effective length of 0.5 mm (4.5 notch length). This would place the existence of TL at a displacment below the critical displacement. The first residual point was estimated to occur at a displacement of 0.7 mm on the load curve for the 4.5 notched specimen. This region is highlighted in Figure 4.20. This is in the range of beam displacements of 0.7-1.8 mm. Con- trary to the TL of the elastic case, the in-elastic TL appears to occur prior to catastrophic failure and wide deformation as reported. This implies a different luminescing process for macro-excitation or internal excitation mechanism related to failure. Walton’s fracture like disturbance does not apply here [85]. The Tribolumnescent emissions must be relegated to either the physical deformable interactions of an elastic or plastic-like disturbance.

In all instances, the samples containing reinforcement did not result in complete specimen fracture and continued to resist load over time. Multiple irregular emissions were observed as seen in Figure 4.14. It was clearly observed that emissions occur with the sharp digression points in the load-displacement curve. Although further investigation is needed, this is believed to be partially due to matrix interaction from fiber slippage and pullout. This is consistent with known composite failure mechanisms, where matrix/fiber interface become a major failure mode operation, although, there might not be sufficient energy transfer to triboluminesce. It is assumed that failure in fiber composites emanate

124 from internal defects within the structure, whether they are inherent or caused during failure progression. However, the role of the matrix in composite failure can not be overstated.

Shi et al. [169], measured the acoustic emissions under load application of a composite. The results revealed that micro-cracking took place prior to main failure. The energy required for matrix fracture is relatively low. Because the TL-ZnS:Mn filler is embedded in the matrix makes it susecptible to the stresses congealed around the particle from the present matrix encasement. This might further describe why in the two-phase brittle case TL is not visible or detected during loading. However for the three-phase compsite, this seems to imply matrix cracking is taking place under the loading conditions, and subsequent strain energy, as outlined in the J-curve. In testing of unidirectional composites, load-drops simil- iar to this experimentation were observed [170]. In Iosepescu shear test, damage described as longitudinal matrix cracks were a common occurence in 0o speciimens. Two different directional lay-ups were produced with 90o and 0o. The 90o specimens showed brittle failure and a load-drop-off ending in ultimate failure. Contrastingly, 0o specimens exhibited minor load drop-offs throughout the failure cycle until ultimate rupture. The behaviour of the 0o shear sample is consistent with the results of the random orientation of fiber whisker in this work, and has been attributed to small load drop from notch root cracking. Therefore, it is likely that the matrix related defects are the cause of triboluminescent emissions in the loading flexural, and the damage is most likely to occur near the artificial beginning stage crack.

Microscopic Observations on Three-phase Composite Fracture. Crack failure for three-phase composites are denoted a diﬀerent failure mode than two-phase composites.

Figure 4.21(a)(a) displays the fracture features found on the notch-tip, and therefore, indicates the localied path of propagation. Three micro-crack features are indentiﬁed for the three-phase composite, where ﬁbers are oriented randomly. Random micro-fractures are

125 (a)

(b)

Figure 4.21: Micrographs of (a) concentrated composite showing evidence of micro- fracture and direction of fracture in view of crack-tip, and (b) an excerpt of a minute micro-damage site.

observed at loads signiﬁcantly below the ultimate strength of the composite. One feature runs 45o from the fault-line, and is the largest visible crack roughly 50 µm. The second, originates from the center notch and is oriented -80o from the fault-line. Figure 4.15(b)

126 shows a magniﬁed area of one particular microcrack (a thrid feature), left of the simulated crack-tip and less than 2 µm separation. The “trident-like’ miniature cracks extending from the notch-tip are characteristic of random oriented ﬁbers. This brings to the light, the issue of exact TL upon composite beam deformation. If the majority of micro-cracks were created and initiated at the same time, then the measured TL could be a mixture of all the micro-crack events. It could also be the case that the luminescent observation follow each micro-crack feature as propagation is likely deterred by reinforcement. However, this presents evidence that TL can be related to formation of micro-developments within the failure of a randomly reinforced composite with simulated crack feature (SENB).

4.4.5 Summary

The J-integral reveals the strain energy release rate proffered by Griffith [40]. This work concerning the mechanical reinforcement, serves as ab initio investigation for future testing with TL concentrated reinforced composite systems. Particularly, the particulate composite and its behavior can influence the strain-to-stress characteristics of the known optical properties of the enhanced system. Analysis has been conducted on the micro- scale and reveals the nature of triboluminescent materials in brittle matrix fracture. The strain energy release rate, is a property related to the modulus of the material system as a feature of the materials resistance to yielding and fracture. In view of catastrophic failure, a threshold energy is needed to rupture a composite structural beam. The experimental method for J-integration has led to discovery of a critical energy threshold for un-reinforced composite beams. As expected, the un-reinforced beams resulted in a linear elastic critical

2 energy threshold nearing, Jc = 3 J/m . The results indicate un-reinforced specimens tend to rupture at displacements approximately 0.13 mm. This is the approximate displacement for observing TL in concentrated VER matrices. Although, the lower energy threshold is as low as 2 J/m2. However. no elastic-like distrubances resulted in full TL with larger

127 eﬀective length samples.

Concerning the reinforced case, the J-integral is curvilinear which is a reﬂection of the anisotropy of composites [159]. An indicate detection of TL signals as low as approximately

2 J/m2 at the lowest notch setting. The critical threshold is extended to approximately

7 J/m2 with displacements up to 1.8 mm for fiber volume fractions of 5 % at the testing limits of this research study. This experimental method further establishes the relationship between stress-strain conditions and the excitation of TL/ML output. This study also indicates the lower threshold of TL excitation. Coincidentally, the higher the pre-notch length, and thus lower the effective load bearing area, results in a lower failure load needed to compromise the structural specimen. In contrast, the lower the pre-notch crack, and therefore greater the effective loading bearing area, the higher the stress invoked, thereby inducing strain energy needed to begin initial deformation. The light emission also followed this trend, with the brightest emission occuring with the largest effective length specimen at approximately 6.927 J/m2.

The behavior of un-reinforced composites is strikingly diﬀerent from reinforced TL concentrated specimens. Un-reinforced beams demonstrate classic linear elastic fracture mechanics with a resultant single TL emission existing at catastrophic failure and macro-crack propagation. In contrast, practical reinforced beams exhibited multiple emissions during the loading cycle. Considering the non-linearity of the practical composite construct, these emissions are coupled with the failure events of matrix micro-cracking and subsequent frequent material relaxation. Fiber pull-out is associated with the degradation of the matrix during loading, as well. This is symptomatic of a breech in the ﬁber/matrix interface.

In addition, the TL signals themselves have random intensity spikes where the magnitude seems to also follow a random format in the residual loading curve. However, it is likely that the micro-matrix related defects are the cause of Triboluminescent emissions in the

128 flexural loading of randomly oriented fibers. Therefore, the efforts to model the existing multi-physical phenomena have been limited to the brittle elastic case for this work. A proffer for continued work will be featured in section 6.3.

4.5 Phantom Analysis: Analyzing the Triboluminescent Signal and Mechanical Proﬁle

4.5.1 Introduction

Macro-luminescent emissions of concentrated two-phase composites show unique results in the fracturing of the structural host under static loading. This phenomenon is even hyper-extenuated when tested as a three-phase system. Because of the unique but separate acquisition of mechanical testing data and the light intensity response, a new approach to analyzing these features has been devised. Phantom analysis is the superposition of the mechanical and the optical acquired data during a test run. By definition, the term phantom is an illustration, part of which gives a transparent effect so as to permit representation of details otherwise hidden from view. This is an attempt to rectify the inner working material aspects and the abstract TL phenomena upon deformation. Particularly, the influence of strain-energy and the rate depedence are factors that need to be explored in more detail.

The results are collated and quantiﬁed herein for the previous experimentation with two- and three-phase composites.

4.5.2 Design of Experiments: Revisited

In section 4.3, an experimental study using a Design of Experiment approach was conducted for varying effective lengths. It was found that the effective length had a large influence in the materials strain energy response or energy needed to rupture the sample.

The role of strain energy in terms of fracture mechanics is well described in literature. How- ever, the role strain energy in relation to TL is also critical because of the incorporation in

129 a host material (i.e. resin matrices).

Figure 4.22: The energy signatures of the experimental design study with calculation of strain energy and the residual energy of loaded two-phase composites.

The energy signatures in Figure 4.22 show the complete trend of the role of strain energy in the production of TL. The parameters, strain and residual energy are indicated in the graph as SE and RE, respectively. The strain energy is the total area under the load-displacement curve. The residual energy is comprised of the area under the drop-oﬀ of the load-displacement curve. According to the design levels of the Design of Experiment

(DoE), the low and high levels are ploted as energy versus the light intensity. The intensity of light appears to increase linearly with the increase in strain energy. Subsequently, the

130 residual energy, which is an estimate of the load drop-oﬀ, maintains an equivalent energy release across all design levels. The intensity, however, increases with the design levels and is reﬂective of the volume concentration of TL material.

Figure 4.23: The relationship of the force derivative and intensity with varying eﬀective length as represented in the Design of Experimental study for the production of triboluminescent intensity.

Revisting the assessment of the Design of Experiment (DoE) study for the two-phase composite, the eﬀect of the force derivate can be seen in relation to the driving factor concerning the material response. Figure 4.23 shows the realtionship of increasing intensity as the magnitude of the force derivative (dP/dt) becomes more substantial, signaling an expediant fracture event. The plot is discretized into the ﬁve design partitions presented in

Table 4.4. The design are dilineated as 0.5 and 4.5 eﬀective lengths at low and high levels of concetrated composites (0 and 10 %vol.). The central design points are also displayed

131 (effective length 2.5 mm at 5 %vol.). Notice the concentrated composite samples are labeled in red (effective length 0.5 mm at 10 %vol., effective length 2.5 mm at 5 %vol., effective length 4.5 mm at 10 %vol.). The greatest effective length of 4.5 mm, shows the largest a range of intensity levels with the magnitude of the force derivative.

Figure 4.24: The relationship of the feature derivate with inﬂuence of strain-energy in the production of triboluminescent intensity.

Reviewing the three concentration levels also displays the concentration eﬀect on light intensity. The concetration levels at 0 %vol. are not triboluminescent and are not signiﬁcant values (denoted by the black and green labels). Figure 4.24 is a plot of the feature vector versus intensity. The feature vector is the product of the force derivative and the point-by- point strain-energy calculation. A similar trend akin to the force vector is observed, and reminiscent to the trend in Figure 4.22 featuring the breaking strain-energy.

132 For the pristine composite there are no triboluminescent emissions, but the energy needed to rupture the samples are evident in the increasing force derivative versus eﬀective length of material. These results are present in Figure 4.22 and 4.23, where the intensity is relatively zero. This fact, also signiﬁes the combination of rate dependence and the need for an internal energy to result in fracture. The higher the magnitude of the force derivative

(Figure 4.23) at an appreciating strain-energy point (Figure 4.24), will ulimatley drive the triboluminescent response and may provide a key link to understanding the TL intensity.

4.5.3 Methods and Results of the Phantom Analysis

To best evaluate the true nature of deformation in a triboluminescent composite beam, the data was manipulated to extract the nominal measurement on a standard time-scale. It was found that in the linear elastic experiments on brittle resin the maximum signal could be correlated with the calculated strain energy. Strain energy is a measure of work, and the accompanying pre-notch allowed the adjustment of the fracture energy. The emission rate is determined by the rate of deformation or strain. This was accomplished through disection of the load proﬁle and intensity data surrounding the deformable event or instance of emission.

The area under the load-displacemnt curve is known to represent the energy exuded on the specimen internally, also known as a calculation of surmounting surface energy [40, 159].

Considering the optical signal would indicate the rate of voltage per second (raw signal) or with respect to the load-displacement curve results in a unit of energy per second, also known as Work (J/s). This allows insight into the deformation energy at time of TL initiation, but does not indicate an erratic change in micro-strain. However, it is not visible on this scale, but the work energy always decreases after excitation emission. This parallels the ﬁndings of most work [27, 83, 127, 140], where a sharp drop-oﬀ or minor slip in the mechanical response is observed. The temporal trend will be identical in practical composite systems as well.

133 Since it was concluded in Section 4.3 and 4.4, that the inﬂuence of strain energy leading to and resulting in fracture, makes it a desirable measurement to employ in derivations related to TL. In the case of two-phase composites, the fracture and TL portray excitation emissions as rate dependent events during mechanical loading and specimen rupture. The excitation is a proponent of an expediant change in the loading curve whether linear or non-linear.

Figure 4.25: Observed dependence of the TL intensity-ZnS:Mn on the applied force ﬁrst derivative of loading in two-phase composite showing aligned bifurcations.

Figure 4.25 is a plot of the light intensity, load-displacement curve, the force derivative and the amended strain-energy inﬂuence (from bottom to top). Analyzing the derivative

134 graphs of Figure 4.25(c-d), no change in the slope is observed before specimen failure.

From this purview, it is observed that a single emission arises with the load drop-oﬀ and instantaneous change in the force derivative. This is indicative of the load drop-oﬀ and subsequent material energy release while loading in three-point mode. Figure 4.25 represents the typical plot for the behaviour of the brittle polymer matrices inudated with Zns:Mn particulates.

Figure 4.26: Observed dependence of the TL intensity-ZnS:Mn on the applied force ﬁrst derivative of loading in three-phase composite showing aligned bifurcations.

The case of three-phase composite loading and triboluminescent emissions demonstrates the erratic nature of TL excitation. Figure 4.26 demonstrates further, in regards to Sec-

135 tion 4.4.4, that emissions occur with the loading patterns of the sample. Through view of this analysis it is clearly observed that emissions accompany bifurcations or gradients in the derivative of the loading profile. The loading profile in Figure 4.26(b) parallels the excitation events observed in Figure 4.26(a). The bifurcations are evident in Figure 4.26(c), when observing the first derivative of the load with respect to time.

The bifurcations are a result of the load drop-oﬀ experienced by the sample. The derivative at the drop-oﬀ points are negative, and therefore, the plot of Figure 4.26(c) and (d) are negative indicating the load is quickly decreasing at discrete segments in time

(Figure 4.26(b)). As stated in Section 4.4.4, these points of inflection are evidence of microstructural failure which appear as energy release points on the original load profile. Under this analysis, the time of peak stresses and strains can be identified with change in load and signified by the TL event. These peak conditions correlate well when plotted on the time-scale with the triboluminescent emissions. It appears the TL emissions only derive for inflection points relating to a change in sign of the force derivative.

Considering that the strain-energy rate is increasing as load is allowed to increase, a partitioned measurement of strain energy may be multiplied by the first derivative of the load profile to reveal the true strain conditions. The augmented SE profile can be seen in

Figure 4.26(d). The problem here lies in the erratic nature of TL emissions upon an energy signature and loading condition. It appears, a derivative analysis on the loading proﬁle can aid in ascertaining the time and loading condition of TL emission, but the magnitude of the load and strain conditions do not neccessarily correspond with the magnitude of TL.

Just like the excitation mechanism conundrum for TL, the host material stress conditions make deciphering TL rather complex. There are notably 13 excitation emissions reported in

Figure 4.26(a). Both plots of the ﬁrst derivative (Figure 4.26(c)) and strain energy modiﬁed

(Figure 4.26(d)), have 13 or more bifurcations of note.

136 A plausible argument could be made that the luminescence may be spreadout further away from the crack-tip. If this were evident, then diﬀering stress conditions will occur as one goes away from the high concetrated crack. Therefore, given an eﬀective material length pertubations could occur by: (1) a single propagating crack or (2) multi-directional micro-cracks (distinct events surrounding the high concentration point). The second case becomes more probable for composites with reinforcement. Needless to say, it appears there are other notable factors at work in the phiysics of emissions and their intensities. However, the relation to bifurcations highlighted in the derivative of the applied force and magnitude of the strain energy show considerable correlation.

4.6 Experimental Discussion Overview

4.6.1 Explanation of the Triboluminescent Composite

Explaining the TL of concentrated matrices that make up a two-phase composite, can be resolved in the time diﬀerential of an excitation event. The excitation with a time domain was explained experimentally in section 4.2.3. Subsequent visual content analysis revealed that the micro-frames captured the intense TL signal during the ﬂexural loading of the beam, indicating fracto-luminescence on the macro-scale event. In general, it may be said

TL is rate dependent. The rate at which TL is induced, is dependent on the transfer of energy from a macro-stimuli, to an atomistic scale given the excitation energy needed to begin recombination at the energy levels. Therefore, spontaneous emissions are not likely to occur, making sensing by triboluminescent materials advantageous over conventional sensing methodologies.

Figure 4.27 is a schematic of the step-by-step ﬂexural loading process with the emission and excitation event occuring at the last frame. TL is a time indepedent event but is dependent on the deformation state of the beam, where the force derivative changes signs.

137 Figure 4.27: Illustration of the movement in time of a concentrated beam and its in-situ TL response, where the process occurs from loading at time, ta, initial loading, tb, and the general fracture processor at time tc, td and te.

This process occurs from a time ta to te, and each time denotes a segment in time. The time of initial loading is known as ta. The time of specimen fracture is known as te. The frames denoted “pre-failure” states, and Frames 1-3 encompass the entire loading-to-fracture profile (Figure 4.27). The pre-failure states, as denoted by time t t , occur upon initial a ⇒ b loading and material contact. The first frame encompasses the loading profile of the primary exciation model. The e, stands for excitation. Further developed, frames 1 - 3 partition the steps of the TL excitation event, and are denoted as occuring at time segments t t , c ⇒ e which coincides with the rupture of the sample. Therefore the load drop-off represents time te associated with the largest point of deflection and egress point for the brittle case.

The load drop-off signals a fast crack propagation (t t ), with significant velocity. The d ⇒ e difference between Frame 2 and that of 3, exist in the excitation forces accruing within the specimen around the notched beam or inherent material crack. At time, td, the strain energy (SE) has reached a material maxim to open a crack, resulting in rupture at time, te.

As originally explained in Figure 4.1, it is Plausible that the TL mechanism stems

138 from both elastic, plastic and fracture-like distrubances. It is assumed that TL will occur at the breach of any crack foundation, which indicates any pre-voided areas will become potential sites of excitation events in fabricated composites. Chudacek [171], oﬀered a

Griﬃth approach to fracto-size TL. His sentiments were further suggested by Chakravarty et al. [91], and the mechanism of new surface creation for the proliferation of TL. The brittle case, has a known fracture mechanism and thus new surface creation along the fault plan of the notch.

The fast propagating crack in the varying particulate beams result in emissions correlated to the size of the pre-crack and/or single-edge notch. The more energy needed internally to support crack formation, and thus catastrophic failure, reusults in a higher intensity emission. The linear results are interpreted by two diﬀering positions: (1) The inherit linearity of TL from the perspective of driving force and, (2) the depreciation of structural length and thus decreasing the driving force. Both are considered to be a factor in this experimentation. However, both views derive from the rate of compression of forcing linearirty as earmarked in literature [85,121,141,142,172], and the translational deformation rate accompanied during the loading process in this study.

Being that the soft ZnS:Mn particle is most likely not able to resist crack growth and likely has an adequate interfacial properties, the particle itself succumbs to the growing crack with the matrix material. On the contrary, particles were seen to be left intact but with deformation marks indicating plastic-like disturbances are abundant. Even more abundant was the elastic type particulates that were found submerged in the polymer resin. Because of the nature of brittle fracture and fractoluminescence, an elastic disturbance is less likely in the conﬁnes of this experimentation. Evidence of this can be seen in the micrographs of Section 4.4. At this point, the material modulus is signiﬁcantly reduced meaning the emission of TL is an indication of damage.

139 CHAPTER 5

MODELING EXCITATION OF TRIBOLUMINESCENT COMPOSITES

If in-stu health monitoring is to progress through the proposed energy-based approach involving TL materials, then modelling techniques will facilitate the design multi-scale composites for future engineering structures. To date, there is a lack of research work on modeling the dynamics of luminescence beyond a thin-ﬁlm approach and a commensurable understanding regarding practical composites. Although sporadic, several research works have been conducted on prediction of ML/TL emissions, therefore outlining the maximum and total emissions related to several labaratory experiments [58, 85, 91, 141].

However, these were bulk TL materials without the integration in composites. In fact, all TL oberservation have been classiﬁed as an impulse response, which has a unique rise and decay feature [18, 85, 88, 113, 141, 154]. Over the last decade, there have only been two research groups working on the performance of TL-integrated polymer composites and its damage sensing capabiliites [113, 173]. These studies were carried out on the impact properties [18, 113], and associate composite analysis [164, 173]. However, no attempt to devise a system of composite prediction and TL performance has existed outside the HPMI research group [27, 173, 174]. The goal is to achieve this objective, through energy-based relations, as it is an initial feature of all damage creation.

140 Based on fracture mechanics of materials, the deformation of TL composites will result in emissions that accompany the leading edge fracture propagation. The region above the crack-tip under duress has a material strain and stress concentration surrounding the evolving crack front which is preceded by a distortional energy.

Figure 5.1: Deformation and geometrical strecthing of an internal solid material

Since deformation or displacement is essentially a geometrical stretching or rotation of a

finite solid as illustrated in Figure 5.1, TL can indicate possible deformation of matrix and damage interaction of fibrous components of the composite system. However, the proffered approach in this section concerns only the two-phase composite case. Modeling TL with the inclusion of fibers (three-phase composites) will be an advanced topic to be considered in future work.

The application of TL during ﬂexural loading assumes piezoelectric homogeneity, considering ZnS:Mn is a piezoelectric material and is ubiquitously dispersed in the resin matrix.

The dispersion of ZnS:Mn phosphors by direct mixing make it a ubiquitous application of Triboluminescent emissions and derives points for potential local sensing. Any elastic

ML/TL of ZnS:Mn is due to the presence of Mn ions [117, 121]. The crystal structure of

ZnS:Mn is non-centrosymmetric, and has a high piezoelectric constant near these defect sites

141 resulting in luminous elastic-plastico-fracto-luminescence. Considering fracture mechanics, general theory of mechanics of materials and piezoelectric-stimulated electron detrapping model by Chandra [117], a modiﬁed-model for maximum TL intensity has been derived for states of stress.

The goal of this work is to provide a novel method for the simulation of two-phase composites as it pertains to ab nitio Triboluminescing crystals, as well as studying and understanding the incorporation effect of TL fillers in a polymer matrix beam. TL materials, integrated in composites is a time-invariant system whose dynamics are coupled with the rate of change of the loading parameters (i.e. energy based, load, displacement). The novel method involves the structuring of governing equations to resolve the complex nature of luminescence through mechanical deformation. This exploration will be validated by mimicking the aforemention physical flexural experiments (Section 5.4).

5.1 Modeling Premise

For the brittle fracture of polymer beams, it was found that TL occured upon specimen fracture and cessation of load. This serves as a primary case for modelling the behaviour of TL respective of external deformation. There are two principal data collection schemes concerning the physical experimentation, a combinatorial approach for analysis involved a two-step data reduction. This analysis of the 3D view of excitation will provide a unique discrimination of the deformation to TL. The elastic brittle curve can be modeled with (1) simple beam theory and (2) the impulse response can be modeled as an exponential decay problem.

First, the mechanical testing data was analyzed and a three-dimensional plot of the load, displacement and time were captured from the load proﬁle (Figure 5.2). The plots below contain data from the bending of a brittle polymer beam sample. Displacement, load

142 Figure 5.2: An example three-dimensional load-displacement curve.

and time are associated with the brittle fracture of the beam via the steep load drop-oﬀ.

A plot of the load-displacement would show a linear elastic line, as well as displacement or load with respect to time. A second phenomenon is introduced in each plot, which represents the intensity response from a piezoelectric material that impulses at the beam fracture point (Figure 5.2). The purpose of this eﬀort is to model this system with a point load. The impulse is only associated with respect to time, and is automatically resolved for a displacement or given load proﬁle.

Figure 5.2 is the plot of the displacement response under gradual loading. Dispalcement and time can be isolated to show the linearity of the material response, which is characteristic of brittle fracture. Likewise, the load and time curve can be isolated to reveal the load proﬁle. Also, the respective variables can be isloated interchangeably to anaylze the relative responses. Secondly, the data was consolidated in what is known as a ‘phantom’ plot, which

143 depicts the intensity, load and/or displacement and time signatures. The phantom plots generated from the experimental and simulated cases are a continuation from the analysis in Section 4.5.

Figure 5.3: Three-dimensional phantom plot of TL intensity-load-time curve illustrating the signiﬁcance of the inﬂection point indicating triboluminescent emissions in two-phase composites.

This profile is superimposed on the TL intensity graph, which depicts a mechanical and optical view of the data collected throughout the experiment (Figure 5.3). In Figure 5.3, the red arrows located at each axis show the direction of increasing values. If one follows the path of the load profile, it is clearly seen that light emanates at the egress point. This point has been labeled, the ‘pivot’ or ‘inflection’ point. The inflection point is highlighted in red and marked in Figure 5.3. The rate of load drop-off indicates an accelerated decline occuring in tenths of a second. The Triboluminescing of ZnS:Mn is thought to be transpiring approximately less than the alloted time for a drop-off in load. This is an assumption that

144 Figure 5.4: Flowchart of the algorithm for simulating the load proﬁle under three- point bending for TL simulation.

will hold true throughout the remainder of this discussion. The significance of the pivot point, indicates that a microscopic deformation has occured, hence TL emission. Since TL occurs within the integrated materials that are micron sized fillers, a considerable amount of pressure on the structural beam results in crystal deformation. However, failure in real-time is a global catastrophic deformation event that results in fracturing of the filled polymeric beam. The following subsections outline the model formulation for beam theory and TL production.

To predict the luminescent properties and compare the predicted properties with the experimental results, theoretical simulations for near-composites has been carried out in this research. Figure 5.4 charts the modeling approach for simulating the load proﬁle to resolve the TL signal. Considering selection of a two-phase composite, the ﬂexural modulus is sampled from an experimental distribution assuming the composite is of homogenous com-

145 position. The mechanics of simple bending are then tabulated according to finite element analysis (FEA) and solved in the partial differential equation (PDE) program. Once the load profile is generated the intensity is resolved using a step function formulation, given that light intensity follows an exponential curve.

5.2 Modeling Background

Modeling the TL of light emitting materials was discussed in Section 2.5.3 and have been investigated by Longchambon [90], Walton [85], Zink [106] and notably Chandra et al. [117,121]. Oddly enough, the above mentioned reviews were conducted on bulk powders and thin-films in impact experiments. The advantages to testing as a bulk material, is the use of a finite volume, and the choice of luminesent material makes it easy to investigate experimentally. However, the impacting of samples often are not readily repeatable and give no indication of the true nature or influence in a composite structural member. Hence, the need for a structural test to assess its full potential in characterizing compostie material damage. A modified model has been arranged to predict the light intenisty phenomenon from repeatable flexural testing of TL - concentrated composite beams.

ZnS:Mn is a widely studied ML material. Its material form and nature in composite host allow for the following assumptions when tested in a ﬂexural member:

1. Composite and particulate homogeneity. Therefore, the stress limits of the particulate

are akin to the host material.

2. Implied pristine interface between particulate and host matrices (good interfacial

bonding).

3. Unique and uniform particulate dispersion (negilibe settling).

146 4. Luminesccence as observed in side-sensing by the photo-detector, occurs above the

formation of a prescribed crack-tip and is rate-dependent.

5. The production of luminescence is dependent upon crystal de-trapping [121].

The following sections discuss the background of the modeling approach including the function of strain energy, a bi-exponential model for light intensity, and a modiﬁed model by Chandra [117, 121], to predict the maximum intensity given a strain state.

5.2.1 Function of Strain Energy

For solid materials, strain energy is a representation of the work done on an inﬁnitesimal solid object. Work is physically deﬁned by a force, F , and a distance where the force in the direction of the deformation does physical or virtual work. For the general case

W = Fxdx (5.1)

Figure 5.5: Case of (a) constant force and (b) linear force.

Figure 5.5 (a) and (b) depict representations of constant and linear force, respectively.

For constant force calculations, the work is the product of the force and corresponding displacement. For linear force where the force is proportional to the displacement, δ, the work done is 1 W = F x (5.2) 2 0 0

147 For a volumetric material (Figure 5.6), when a force, Fx, with corresponding stress, σx =

Fx/a2, elastic displacement, δ, and strain, ε, the work relation can be expressed as

1 W = F δ (5.3) 2 x

Figure 5.6: Linear elastic strain energy of a volumetric material.

The strain energy, U, can be expressed as:

1 1 W = δ a2ε a = δ ε a3 (5.4) 2 x x 2 x x where εx = δ/a or the elongation of the material. The strain energy per unit volume is equal to the area under the stress-strain curve. For a volumetric material, the strain energy density, u, can be written as 1 3 U δxεxa W = = 2 (5.5) V a3 where, V , is the volume of the material. The elementary strain energy density on an element is then 1 w = σ ε (5.6) 2 x x

The σ is the normal stress. Strain energy density has units in SI metric of J/m3. Note that

1 J/m3 and 1 Pa are both equal to 1 N/m2. Since the data in this experiment is load- based, stress and strain measurements are not desribale. The work energy in equation 5.5

148 will be used as the strain energy but is determined from the information contained in the load-proﬁle. The units for strain energy are mJ. A magnitude force, P , is equal to the strain-energy rate, dW/dt, and the displacement rate, du/dt. The diﬀerentiation of the strain-energy with solution for the force derivative is

d d dW du P = (2 ( )−1) (5.7) dt dt dt dt

The work involved in the displacement of the beam is represented in the force curve respective of time. The differential, dP/dt, is the force derivative describing the rate of loading in simple three-point bending. The displacement term, du/dt, represents the transient transverse deflection of the beam which is the primary displacement point located at the notch-tip and reflected in the loading curve. The strain-energy term, dW/dt, is the appreciating surface energy with respect to time. As previously mentioned in the disccusion of

Section 4.6.1, the specimen will rupture when the surface is double the material allowance,

2γs as stated in Griﬃth’s theory [40].

Figure 5.7 is an illustration of the force derivative as result of a two-phase composite.

The load-displacement curve was linear-elastic up until the point of fracture (approximately

0.2 s), where the dP/dt graph indicates the abrupt change in load. The magnitude of the birﬁrcation or single peak is the term-point derivative. This can be thought of as a force

(N) per second, indicating a rapid drop in the loading curve. The load derivative can be estimated if the strain-energy rate and displacement are known for a given time interval.

5.2.2 A Bi-exponential Model for Light Intensity

The triboluminescenct emission as a feature of concentrated composites behaves strikingly diﬀerent than previous experiments with non-structural samples. Although, a single spike in emission is observed in most research work, the emissions occuring in concentrated

149 Figure 5.7: An Illustration of the simulated force derivation (dp/dt), and its relation to to the distortion and bending of the concentrated solid composite short beam.

composite beam experiments behave on a different scale. Considering two & three-phase composites the emissions occur at fracture but also at points of inflection in the load- dispalcement profile. The latter reflects the case of three-phase composites where material stiffness is enhanced through fiber reinforcement, but the loading profile indicates multiple inflection points associated with developing micro-damage (Section 4.4.4). It is the focus of this work to explain through model derivation the luminosity of the brittle fracture case, and thus only one inflection point.

The triboluminescent signal is an expeditious propagation of photons from the excited bulk ZnS:Mn crystal. As discussed in section 4.2.1, the emission of ZnS:Mn is unique to the material and exhibits a distinct decay signature. The triboluminescence of ZnS:Mn can be approximated using a Bi-exponential model that reﬂects the peak magnitude and exponential proﬁle of decaying luminescence. Equation 5.8, represents the bi-exponential

150 model as a diﬀerential equation,

∂I 0, if t

Figure 5.8: A simulated TL signal modeled by the Bi-exponential model.

Figure 5.8 describes the simulated response of Triboluminescing ZnS:Mn encapsulated in a polymer matrix beam. The experimental data is plotted in red, and the simulated response is blue.

5.2.3 A Modiﬁcation to Chandra’s De-trapping Model to include Load-displacement Phenomena

A physical model was developed for the maximum intensity of ZnS:Mn by Chandra et al. [121]. This work presents a modiﬁed form of the de-trapping model. The modiﬁcation

151 in relation to the physical experimentation is an acceptible approach given the mechcani- cal loading parameters in the experiment (i.e. load, displacement). Side-luminescence or surface sensing, as emissions propagate out toward the photo-detector, is an unbounded measurement of the distortion occurring at the point where stress concentration can inﬂu- ence the surrounding innate particles and therefore result in luminescence. Homogeneity is implied macroscopically, but luminescence will be regional according to the stress accretion in the host material (i.e. polymer matrices). The energy expended on the luminescing crystals are rate-dependent.

The mechanism for elastic ML excitation in ZnS:Mn particles is understood to occur during deformation causing a piezoelectric field as a result of the non-centrosymmetric crystal structure [86, 139]. Non-radiative release of energy accompanies the elevation and fall of electrons to the VB occurring after electron excitation. During this process, electrons reaching the CB may recombine with the holes considered trapped in the defect centers presented by Mn2+ ions. In the presence of the piezoelectric field, a decrease in trap- depth occurs allowing detrapping/generation of electrons from filled-electron traps that are propelled to the CB. This in turn makes it more efficient for light emission during electron- hole recombination that is transferred and excites Mn2+ ions.

Therefore, luminescent output will be a function of detrappable sites and the mechanical energy needed to release electrons (Figure 5.9). The electron detrapping model presented by Chandra et al. [117,121], is based on the piezoelectric charge mechanism of ZnS:Mn that involves excitation, secondary events and de-excitation. The piezoelectric charge, Q, near

Mn2+ ions is compressed at a rate, P˙ , or strain rate, and can be written as:

Q = d0P = d0Pt˙ = d0Y εt˙ (5.9)

2 d0 is the piezoelectric constant associated with Mn , P is the applied pressure, and Y is the

Youngs modulus of the crystal material. Based on the derivation of the compressed charge

152 Figure 5.9: Deformation luminescence explained on the order of the energy level excitation as a de-trapping model for ZnS:Mn rate of Mn ions, an estimation of the luminous intensity of ZnS:Mn can be expressed as

I = ησΩN N n ZτµB2d2Y (t t )˙ε (5.10) 1 t h 0 m − th where,

η = the eﬃciency of Mn2+ ions to emit light during e-h recombination

σ = capture cross section

Ω = crystal volume

2+ N1 = concentration of Mn ions

Nt = concentration of ﬁlled electrons

nh = concentration of hole centers

Z = the inverse of the electric charge

153 τ = lifetime of the electrons

µ = electron mobility in the crystal

B = the correlating factor between the piezoelectric ﬁeld F and the piezoelectric charge

In this derivation, light creation depends on the production of excited electrons and emit light during energy transformation as discussed above. In order to reduce the total number of detrappable traps, nto, to nto/e by the detrapping of filled electron traps in ZnS:Mn crystals, a characteristic piezoelectric field must be produced. The piezoelectric field is denoted Fc. Its relation can be written as

dn nt = = Znt (5.11) −dF Fc

−1 where nt is the number of ﬁlled electron traps at any time t and for Z = Fc . Given nto is the total number of ﬁlled electron traps, the total number of detrapped electrons can be stated by through integration using Equation 5.11.

n =(n n )= n [1 exp(Z(F F )] (5.12) d t0 − t t − − th

here F = Fth representing a threshold ﬁeld and nt is taken to be equivalent to nto considering an activation volume (ΩN ). For the elastic case, Z(F F h) is considered low and the 1 − t prior Equation 5.12 can be written as

n = n [1 1+(Z(F F )] = n Z(F F ) (5.13) d t0 − − th t0 − th

By diﬀerentiating equation (24) with respect to time t, reveals the rate of the detrapping of electrons dn dF d = n Z (5.14) dt t0 dt

154 Equation 5.14 is thus equal to the rate of generation of electrons to the conduction band, denoted by g dF g = n Z (5.15) t0 dt

Based on the lifetime of electrons in the conduction band, τ, and the rate of ﬂow of electrons in the conduction band of the crystal, the rate of electron-hole recombination needed to excite Mn2+ centers can be expressed as

dF R = σn r = σn n ZτµF (5.16) h h t0 dt

If the eﬃciency of the Mn2+ ions operates at eﬃciency, η, then light emitted during absorption of non-radiative energy can be expressed as

I = ηR (5.17)

OR dF I = ησn n Zτµ(F F ) (5.18) h t0 − th dt

dF I = ησΩN N n Zτµ(F F ) (5.19) 1 t h − th dt

The piezoelectric ﬁeld F and the piezoelectric charge, Q, are related by F = BQ. Bisknown as the piezoelectric correlation factor. In like manner, Fth, are related by Fth = BQth.

Equation 5.18 represented by the stated relation then becomes

dQ I = ησΩN N n ZτµB2(Q Q ) (5.20) 1 t h − th dt

Since Q = d0P , equation 5.20 can is written to represent intensity in terms of pressure, P

dP I = ησΩN N n ZτµB2d2(P P ) (5.21) 1 t h 0 − th dt

155 As described in equation 5.21, equation 5.21 can be written in terms of strain rate as well. Primarily, the constant values for d and ﬁeld F are 3.3 10−11 CN −1 and 3.7 0 × × 104V cm−1, respectively [117, 121]. Remembering, F = BQ, the correlation factor, B, concerning the piezoelectric ﬁeld, F , allows for representation of the force derivative, dP/dt.

This expression is simpliﬁed to represent the rate of force of the homogenized material. For simpliﬁcation, this equation can be expressed as:

d I = χ P (5.22) dt

The initial intensity in terms of strain-energy inﬂuence as represented by the force derivative, dP/dt, can be written as:

d dW du I = χ (2 ( )−1) (5.23) 0 dt dt dt

The χ term includes all of the physical parameters related to ZnS:Mn given in the initial list. Thus, the amplitude, A, in equation 5.8 is a representation of ,I0, the original intensity. The magnitude of the TL intensity is driven by the incurring internal energy and is a maximum intensity value. This is directly related to the physics of the crystal

+ material. The efficiency of the Mn ions and the filled electron concentration term, Nl, are related to the volume fraction of ZnS:Mn. The decay of the luminescence is easily resolved as an exponential function and thus gives the overall profile for the transient TL emission.

The strain-energy rate during deﬂection of the beam can be substituted in for the force derivative, therefore, estimating the magnitude of luminescence for a given volume fraction.

156 5.3 Finitie Element Method Implementation: A 2D COMSOL Representation

5.3.1 FEM Construction of the COMSOL Model

The estimation of the force derivative and strain-energy generation neccessitated modeling of the load-displacement curve. As it is a key feature in the progression of two-and three-phase Triboluminescent emissions. A predictive mechanical model was desired to mimic the load-displacement proﬁle of two-phase composites, for their brittle fracture upon loading. As a means to validate experimental results from the DoE design space, a FEM approach was utilized.

Figure 5.10: Computational numerical methods selection.

A numerical methods approach was uitlized for its computational standard and implementation. Figure 5.10 describes a table of mechanical modeling approaches to resolving the three-point bend test. Originally, it was proposed to use a combinatorial system of equations for resolving a 1 - Dimensional solution for deﬂection. This would require derivation of the partial diﬀerential Euler-Lagrange equation, which is computationally expensive at the moment. It also requires use of MATLAB programming as the language does not contain a structural solver for this type problem. A 3-Dimensional simulation was also

157 computationally expensive for this particular study. Therefore, a half-model was used in the implementation through COMSOL multiphysics platform. The hope, is that this can latter be utilized for equation-based modeling within the commercial platform. This can be used in-conjunction with MATLAB to run a comprehensive simulation trial.

The aim of the current work was to provide an estimation of the load history and a view of the stress concentrations along the fault-line of sampled beams. In this model a study of the force-deﬂection of three-point bend mechanical testing is simulated. The model uses a linear-elastic material model together with contact conditions to simulate stress-strain conditions during loading. A common parameter in fracture mechanics, is the stress-intensity factor KI , which provides a means to predict if a speciﬁc crack will cause the specimen to fracture. When this calculated value becomes equal to the critical fracture toughness of the material KIC (a material property), then fast catastrophic fracture occurs.

Currently, the COMSOL package is absent of failure models and the brittle fracture was estimated as a rate production from sampling the experimental load-curves in Section 4.2.

The predicted load proﬁles was found to undershoot the displacement values of the range of experimental data (0.07 - 2.20 mm). The specimen material is comprised of a particulate composite and thus presents anisotropic conditions. Although, it was assumed the two-phase composite consisted of a homogenous component. Throughout this investigation, only the

Flexural modulus was considered and was varied as a function of ﬁller concentration. Since the modulus is known to degrade with loading, care must be taken during interpretation of the results. It has also been noted that future studies should include micro-mechanical estimations of the overall particulate modulus to capture the anisotropic conditions. This can include theory by Halpin-Tsai [175]. Presently, the modulus is calulated from a normal distribution of the ﬂexural modulus from the experimental observations in Table 4.1 and are inputs for the Monte-Carlo approach outlined in Section 5.4.2.

158 The following outline the FEM approach to resolving the simple ﬂexural bending of a composite beam.

1. Describe geometry (2D sketch of short beam and notch geometry)

2. Construct subdomains (contact interfaces)

3. Prescribe point loads (points of contact for simple three-point loading)

4. Create desired mesh

5. Solve global system of equations

Figure 5.11: Finite element model construction of three-point bend experiement in COMSOL.

The model was constructed to reflect the experimental case of flexural loading with one crosshead, two supports, and the flexural beam (Figure 5.11). The short-beam is

159 compressed between a support rollers and an impacting roller. The specimen with width of 10 mm, height of 5 mm, and length of 55 mm has a single-edge notch. The single edge notch beams have length a = 0.5, 2.5 and 4.5 mm on the left vertical edge. The base of the notch is 2.1 mm, throughout. For simplicity and ease of computation, only half of the physical experiment is modeled thus invoking symmetry. FEM simulations were performed by COMSOL software in conjunction with MATLAB. The crosshead and sample are modeled as contact pairs, while the supports were created with stationary boundaries.

The applied physics include Solid Mechanics and Contact Coupling. The model describes a cross section of the SENB assuming plane strain conditions. The contacting surfaces are rigid, however, the rollers and beam are dissimilar materials with diﬀering modulus (i.e. vinyl ester beams, steel rollers).

The roller supports and impactor are 3.9 mm in diameter. In the domains of the short beam, additional domains are constructed to create paths for integration contours for the calculation of KI . An external load is applied as a point load, through the movement of the roller impactor such that the specimen experiences a parametric load from approximately 0

- 100 N (determined by the experimental distribution). It is of special interest to investigate the eﬀect of Triboluminescence during duress of the single-edge notched beam. Figure 5.11 shows the undeformed geometry of the SENB.

Euler-Bernoulli Model Background Implementation. The bending of specimens can be described by Euler-Bernoulli theory. The Euler-Bernoulli equation describes the relationship between the beams displacement and the applied load. The classic representation is given below:

d2 du2 (EI )= q (5.24) dx2 dx2

160 This is a 1-Dimensional analysis of beam deﬂection. The curve u(x) describes the deﬂection of the beam in the z-direction at some position point in x.

Where in the classical respects variables represent,

u = the deﬂection/displacement

E = the elastic modulus

I = the second moment of inertia

du/dx = the slope of the beam

M = EI du/dx is the bending moment

q = the distrubuted load as a function of x, u or other variables

A direct modiﬁcation of this theory to include dynamic systems is known as the Euler-

Lagrange equation. The derivation lies in the minimization of the Lagrangian function

L 1 ∂ 1 ∂u2 S = µ( )2 EI( )2 + q(x)u(x,t) dx (5.25) 2 ∂t − 2 ∂x2 Z0 The formulation involves a K.E. term where µ is the corresponding mass per unit length.

The 2nd term represents the P.E. due to internal forces along the beam, and the 3rd term represents the P.E. due to the external load.

The derivation of the Euler-Lagrange equation is as follows:

1 ∂ 1 ∂u2 L = µ( )2 EI( )2 + q(x)u(x,t) (5.26) 2 ∂t − 2 ∂x2

µ EI L = u˙ 2 u2 + qu (5.27) 2 − 2 xx

161 L L(x,t,u, u,u˙ ) (5.28) ≡ xx

the corresponding Euler-Lagrangian equation is then,

∂L ∂ ∂L ∂2 ∂L ( )+ 2 ( ) = 0 (5.29) ∂u − ∂t ∂u˙ ∂x ∂uxx

now substitute the following terms back into equation 5.6

∂L ∂L ∂L = q;( )= µu˙;( )= EIuxx (5.30) ∂u ∂u˙ ∂uxx −

plugging in to the original equation reveals:

q µu¨ (EIu ) = 0 (5.31) − − xx xx

Therefore, the time-dynamic equation implemented in the FEM code, are written as

∂2 ∂2u ∂2u (EI )= µ + q (5.32) ∂x2 ∂x2 − ∂t2

The COMSOL FEM is instituted as a constitutive model which deﬁnes the relationship between stress and strain. This requires application of uniform properties where a small deformable volume element involves a shape change. This then forms a suitable criterion to describe the average stress and deformation in a region of the material. General requirements for deriving constitutive equations state that laws of thermodynamics must uphold and the basis of the coordinate system must be sustained. Considering isotropic linear

162 elastic material properties, stress-strain relations can be viewed as

ε 1 v v 0 0 0 1 11 − − ε v 1 v 0 0 0 1 22 − −  ε  1  v v 1 0 0 0   1  33 = − − + α∆T (5.33)  2ε  E  0 0 0 2(1 v) 0 0   0   23   −     2ε   0 0 0 0 2(1 v) 0   0   13   −     2ε   0 0 0 0 0 2(1 v)   0   12         −    The inverse relationship can be described by

1 v v v 0 0 0 σ11 − 1 σ22 v 1 v v 0 0 0 1    −    σ33 E v v 1 v 0 0 0 Eα∆T 1 = − (1−2v) (5.34)  σ23  xy  0 0 0 0 0  − (1 2v)  0     2       (1−2v)  −   σ13  0 0 0 0 2 0  0    (1−2v)     σ12   0 0 0 0 0   0     2          Here, E and ν are Youngs modulus and Poissons ratio (x=1+ν, y=1 2ν), α is the coeﬃcient − of thermal expansion, ∆T is an increase in temperature of the solid. For plane stress deformation, where σ33 = σ23 = σ13 = 0, the stress-strain relations can be simpliﬁed as

ε 1 v 0 1 11 1 − ε = v 1 0 + α∆T 1 (5.35)  22  E  −    2ε 0 0 2(1 v) 0 33 −       And the inverse

σ 1 v 0 ε 1 11 E − 11 Eα∆T σ = v 1 0 ε 1 (5.36)  22  (1 + v2)  −   22  − (1 + v)   σ 0 0 (1 v)/2 2ε 1 33 − 12        

For ﬁnite element approximations where displacements are related to stress and strains, the strain energy can be computed for plane stress assuming no thermal loading as

163 Given that strain energy density is related to stress-strain by U = 1/2σε, the matrix formulation can be describe by

1 1 u = εT σ = εT [D]ε (5.37) 2 2 where[D] serves as the global term for stiﬀness

1 v 0 E v 1 0 [D] = 2 (5.38) (1 + v )  (1−v)  0 0 2   This study will encompass a linear-static analysis, which is often called static analysis because loads independent of time. In linear static analysis, the stiﬀness matrix, [D], is calculated once for the original undeformed shape. Therefore, to solve a linear-static-analysis problem, one only needs to solve a set of linear algebraic equations. The displacements produced upon application of stress are represented as vectors with three components.

The three normal and three shear components of stress are represented as tensors equation (Equation 5.36). A stress measure known as ”von-Mises”, is used to generate stress plots. The von-Mises stress is a scalar quantity made up of the magnitudes of all six stress components. The equation for von Mises stress is

1 2 2 2 1/2 σVM = [(σ1 σ2) +(σ2 0) + (0 σ1) ] (5.39) √2 − − −

for plane stress (2-D) or σ33 = 0, yielding is expected when σy >σVM and thus

1 σ2 = [(σ σ )2 + σ2 + σ2] (5.40) VM 2 1 − 2 2 1

σ2 = σ2 σ σ + σ2 (5.41) VM 1 − 1 2 2

164 5.3.2 Viewing Stress-strain Distributions of Crack-tip Features in COMSOL

In Figure 5.12, the von-Mises stress and strain energy density can be viewed for VER/TL composite beams. The localization of stress and strain is visibly indicated below where minimal stress is generated from the two supports, the cross-head, and the region of initial failure (deformation) along the base plane. The von-Mises stress is a yield criterion for elastic and plastic materials. Thus light intensity will be maximum at the breaking stress or fracture yielding of the specimen. The stress-ﬁelds and geometrical strain-energy can be seen for various eﬀective lengths in Figure 5.12 - 13.

Figure 5.12: Finite element model approximation for deﬂection of a composite beam with von-Mises stress.

The COMSOL model only relinquishes a proﬁle of the stress-strain distribution ahead of short beam failure (Figure 5.12). This is a stationary study where time is not an included

165 factor and failure is not simulated. The multiple ﬁgures below, explain the analysis of the visual images of Figure 5.13, where emissions were observed to occur at both the top and crack concentrated and initiated regions. Experimentally, failure occured near loads of 5 -

100 N, given the eﬀective length of the sample.

(a) (b) (c)

Figure 5.13: Geometrical view of the FE model of the graphical stress-strain concentration as portrayed by the strain-energy density of the simulated concentrated particulate composite ﬂexural beams with eﬀective length of (a)0.5, (b) 2.5 and (c)4.5 mm at critical load. The region of interest are the concentrations around the crack-tip and the stress-states under the applied load.

Figure 5.13(a) - (c) displays the strain-energy density as computed by the simple bending model in COMSOL. The concentration of distrortional energy is easily observed for effective lengths of 0.5, 2.5 and 4.5 mm. Figure 5.13(a) - (c) correspond with the aforemention effective lengths, respectively. Note, the color scheme is not comparable across effective material length and magnitude of strain-energy, and only serves as a quality comparison.

However, the spatial intensity describes the eﬀected areas. Stress-strain concentrations are observed at the contact of the initial loading site directly under the applied load. In addition, concentrations of stress-strain conditions can be seen around the notch tip with higher concentrations in red and diminishing conditions radially outward. For the case of 2.5 and

4.5 eﬀective material length, a visual concentration appears around the notch. In contrast,

166 for the lower most eﬀective length of 0.5 mm, a noticeable notch is not observed and the stress-states appear primarily due to roller contact. These visual methods reﬂect the nature of the strain-energy accumulated leading up to and during fracture of the composite. This serves as additional proof for the triboluminescent emissions seen in the visual content analysis in Section 4.2.3, where the signal luminesced away from the notch µs before the region around the crack-tip became illuminated. However, the magnitude implied directly under the applied load from the FE study is not reciprocated in the experimental observation of

Section 4.2.3. This pre-crack illumination is most likely a case of deformation luminescence

(i.e. elastico-plastico disturbance), however, brief.

5.4 Modeling Light Intensity per Bending of Composite Beams

5.4.1 Implementation of Governing Excitation Model

The experimental results of Section 4.5, helped lay the foundation for the modiﬁed- modeling approach. This was a major objective of this research work. As pointed out, a physical parameter based model was deemed most applicable as it provides for inputting of the strain-rate dependent feature associated with TL. More importantly, it provides the link between experimental ﬁller volume fraction and the crystallic concentration and other parameters related to the ZnS:Mn crystal. To predict the luminescent properties and compare the predicted properties with the experimental results, theoretical simulation for two-phase composites has been carried out in this research.

There are two governing phenomena occuring in the experimental testing of TL concentrated composite beams. The phenomena of TL and the bending of beams, are coupled through independent variables of time and deformation energy. A diﬀerential equation can be used to describe the instantaneous triboluminescenct emissions, which are implemented

167 as a step functional for the bi-exponential feature. Euler-bernoulli equations can be described for time in the Euler-Lagrange differential equation. Resolving these two equations that describe the unique phenomena will offer prediction of in-situ sensing and elucidate the physical ramifications of inherent luminescent composites. The magnitude, A, is driven by the strain energy computed from the differentiation of the loading profile (Figure 4.23).

The load profile of a near-composite beam gives indication of strain concentration at points of inflection, and therebye generates TL. This rate phenomena was observed in Figure 4.26, and is greater emphasized for the three-phase composite system where multiple inflection points have occurred.

Figure 5.14: The simulated 3D phantom plot representation of simulated TL signal modeled by an Bi-exponential model at the forcing of flexural loading of a 2D flexural beam resolved by finite element operation.

168 In this study, COMSOL Multiphysics is used to predict the mechanical loads and displacements of the ﬂexural beams. The load-displacement curve is extracted in an interative process through LiveLink to MATLAB and the triboluminescent intensity is computed.

Figure 5.14 displays the simulated light intensity derived from the load profile generated in a finite element model. COMSOL is executed with the LiveLink for MATLAB. This way the MATLAB-based progressive damage algorithm is useful to simulate the load-drop of the two-phase brittle composite case. In the flexural bending simulation, the load is applied from the top roller as seen in Figure 5.12. Because of the close contact with the beam, a vertical load cause deflection upon the opposing forces of the supports. This is a direct

2D representation of the physical experiment. The load parameter is updated through a parametric opertaion, where the parameter is derived from a ﬁtted distrubution of experimental loads. This paramter is passed to the MATLAB script which runs the COMSOL simulation from the MATLAB enviroment. The outputs of the displacement are recorded for each processing step and then collated. The progressive damage is modeled as a rate drop-oﬀ from analzying the experimental results of Section 4.2.

Figure 5.14 shows clearly the results of the simulation. The FEM resolves the displacement of the beam according to the stiffness of the material. The values, however, undershoot the experimental values of deflection described in this research study. However, the behaviour of the triboluminescent intensity remains quite clear and defined. The excitation point along the phantom plot (Figure 5.14), indicate the excitation event will apear after an intial inflection in the load-time curve corresponding with the magnitude of dP/dt.

This is in high agreement with the experimental results. The driving force of the intensity was shown in Section 4.5, to be related to the force derivative and strain-energy phenomena. Therefore, these paramters were substituted in the modifed-Chandra’s strain-intensity model and the result are thereof.

169 It has been shown how the MATLAB LiveLink for COMSOL has been used to implement a progressive algorithm for simulating the bending of three-point bending. It has also been shown that by extracting the load-displacement and its derivative proﬁle, the light intensity of Triboluminescing ZnS:Mn can be shown to exist as a step-function. As a drawback, comparing the luminescent intensity is not a sound appraoch to validating experiments with luminescent materials. However, the trends and behaviours can be noted as such. Another drawback to the present approach is the lack of a deeper materials inference on whether the composite has micro-damage modes present. A clear concise structural determination is needed. Being that this is the brittle matrix case, the appearnace of emissions does indicate a loss in material stiﬀness. However, it is the goal of the group to move towards a mechanical inference.

5.4.2 Variation of Triboluminescent Intensity as Feature of Volume Fraction

Validation of Modiﬁed-Triboluminescent Intensity Model & the FE extraction. Validation has been attempted by revisting the observations of Section 4.2, which dealt with the loading of prismatic beams. Under the current scenario light emission is said to be prodeuced by (1) elastic, (2) plastic and (3) fracture distrubances. The combination of the three disturbance types lead to excitation at macro-fracture on the side-face above the crack-opening of a beam. The concentrated sample beams which vary from 0-50 % contribution have a linear eﬀect on the Triboluminescing upon rupture.

Coincidentally, the luminescence will also be effected by the stiffness of the concentrated beam. It has been noted in Section 4.2, that the stiffness does succomb to a parasitic effect at a high loading level. In Section 4.3, it was demonstrated that reducing the effective material area decreases the stiffness and amount of fracture energy generated in comprim- ising the sample beam. The combination of generated fracture energy and the particulate

170 concentration level, may introduce variation in the measurement of TL. This disscussion will involve the primary study from Section 4.2 and plausible arguments towards what may be inﬂuenceing the Triboluminescent output.

Considering the modiﬁed-Chandra model (Equation 5.23), the triboluminescent output was calculated in units of counts per second (or photons/s). To aide in simplifying the analysis a conversion formula (Equation 3.7) was used to render the intensity values in units of the experimental results (i.e. V). The conversiion was discussed in Section 3.1.4.

Figure 5.15: Monte-carlo simulation of the MATLAB Live-Link for COMSOL. This is a partial simulation equal to 40/1000 sample runs for a concentration of 50%.

171 Monte-carlo simulations were run for estimating the limits of the MATLAB-COMSOL model where a load history is generated and the luminescent intensity is therefore simulated.

The inputs to the model are filler weight fraction and the number of simulation runs are preset. The weight fractions experimented in this simulation were 0, 5, 10, 25 and 50 % wt. A sample mean and variance for failure load and material modulus were taken from the data presented in Table 4.1. The load at yielding and the flexural modulus differed from concentration to concentraation during the principle experiment. The hopes were that the

Monte-Carlo simulation would capture the variance of the original experiment. Figure 5.15 is an example monte carlo simulation for computing the simulated intensity as function of the strain-energy related term used to calculate the Force-derivative. The above ﬁgure is an example of the 50 %wt. fraction. The mean and standard deviations for the following terms are reported. On average a mean failure load of 79.96 N ( 42.26) was observed at ± the 50 %wt. fraction, which corresponds to a luminescent intensity of 1.373 x 1011 (cps). A voltage conversion of 0.140 (V). The mean Force-derivative is 9.46 x 109 (N/s) indicating a sharp drop in the load-displacement curve. The modulus is 3381.36 MPa ( 893.69) which ± is simialr to the value reported in Table 4.1.

Table 5.1: Compilation of Monte-Carlo simulation results.

Concentration (%wt.) Mean (V) -95% CI +95% CI 0 0.0000 0 0 5 0.0124 0.0106 0.0141 10 0.0247 0.0202 0.0292 25 0.0615 0.0532 0.0698 50 0.1400 0.12 0.16

The corresponding intensities across the entire Monte-Carlo simulation were in a range of 109 to 1010 photons per second, which contrast the smaller range ( 108) of the reported experimental values. The entire set of simulations can be found in the Appendix. Table 5.1

172 is a compilation of the Monte-Carlo simulation with the reported mean and conﬁdence intervals. A direct comparison of the experimental results and simulated intensites can been seen in Table 5.2.

Table 5.2: A direct omparison of Monte-Carlo simulation results versus the experimental results from Section 4.2. Concentration (%wt.) Simulated Intensity (V) Experimental Intensity (V) %err 0 0.0000 0.0024 n/a 5 0.0124 0.02737 54 10 0.0247 0.01796 38 25 0.0615 0.01265 386 50 0.1400 0.05843 140

Figure 5.16: Comparison of the experimental chart and the simulated chart of the intensity (black) and specific stiffness (blue) with respect to filler concentration.

173 Figure 5.16 displays the double plot of the experimentally determined light intensity and the simulated results. In addition, the experimental specific stiffness was reported, and provide circumspection of the parasitic degradation upon filler concentration. The specific stiffnes is plotted on the second y-axis with respect to the concentration of ZnS:Mn.

The chart indicates that the intensity of TL increase with ﬁller concentration up to 50

%vol. Concerning specific stiffness, which is a measure of stiffness per density of material, the trend is to a small degree curvilinear with fast approaching degradation. However, a sudden decrease in the overall light intensity appears at 10 % concentration point.

Figure 5.16 shows the comparison between the simulated intensity as a feature of the force derivative based TL-strain intensity model, and the experimental results reported originally in Section 4.2.3 (Figure 4.6). It may be seen from Figure 5.16, a moderate correlation exists between the simulated and experimental Triboluminescent intensity. Consequently, the concentration-quenching phenomena discussed in Section 4.2.3 was not observed for the increasing ﬁller volume fraction. On the other hand, the strict linearity of the TL is observed in the output of the simulated values. The percent error are reported. The negative percentages mean the simulation was under-valued for the intermediate concentrations.

Under estimations were found for concentrations from 0 to 10 % concentration. However, the extremit’s were found to have amenable correlation. Currently, the model is limited in scope and can not capture the quenching conundrum.

Revisiting the secondary experimentation with the Design of Experiments (Section 4.3), a graph of the intensity is also plotted. The combined plot can be seen in Figure 5.17. In relation to the DoE study, a point prediction was made for the multiple regression model generated from the statistical analysis (Equation 4.2). A measurement of light intensity was computed from the parameters, eﬀective material length and ﬁller concentration, as

174 provided by the statistical model in the point prediction toolbox.

Figure 5.17: Comparison of the experimental chart and the simulated chart of the intensity (black), experimental intensity (blue) and DoE estimation (red) with respect to ﬁller concentration. The conﬁdence bands (%95 C.I.) have been provided for the DoE and Monte-Carlo simulation.

The DoE representation is outlined by the red line and markers in Figure 5.17. Conﬁ- dence intervals were also presented, indicated by the red brackets. Upon additional review of the prediction of Triboluminescent emissions, it is found that the statistical inference grossly over estimates the intensity values of the experimental. Only the concentration values of 0 and 5 % fractions were found to be within in the scope of the DoE. The concentration is limited to an estimation from 0, 17 and 30 %wt. concentration (0, 5 and 10

%vol., respectively). Concerning the simulated intensity, the experimental results lie within

175 the conﬁdence bands up to the highest loading level. However, the 95% C.I. bands appear to enlarge with increasing concentration. On average, the simulated intensity is linear and does not represent the bulk concentration quenching phenomena observed in the experimental results of Section 4.2 and Figure 5.17. This highlights the diﬃculty in estimating the optical response beyond concentrations of 5 %wt.. This also illustrates the uncertainty in prediction when a high loading concentration is used in practice. This further alludes to an underlying mechanism for luminescent supression on the average.

Linear trends involving the light intensity and specific stiffness measurements were ex- emplified. Although, inconsistencies were observed for the medium loading levels, light intensity is still known to increase with increasing concentration of TL filler. Monte-carlo simulation establish upper and lower values as a wide range view of the experimental parameters of the physical flexural bending system.

Discussion on the Variation as Feature of Volume Fraction. Further work has been suggested to establish the limits of predicting TL, and for the material properties constraints and concentration levels. It was suggested that a source of error in the analysis ans simulation, maybe due partly to (1) dispersion issues and relation to concentration quenching, (2) varying stress-strain distribution, (3) micro-mechanics and (4) distinctive failure modes of multi-phase composites. The piezoelectric constant, d0, may be another source of error, and could have interaction with the aforementioned situations. This would mean the piezoelectric coeﬃcient is not constant and changes with the applied stress.

Foremost, particulate dispersion is a known issue in processing of composites. The high density of ZnS:Mn makes continued suspension in liquid resin matrices difficult. Furhter complicating the process, is the time-dependent curing cycle and initial low-viscosity. ZnS:Mn is a phosphor material, and suffers from wettability which makes for easy aggregation on initial processing. These concerns may affect dispersion and ultimately impede light emission.

176 As stated in the review Section 2.5.3 and discussion in Section 4.2.3, phosphor thermometry comprises the basic illumination principles and will undoubtedly show effects of crystal concentration. These effects could be negative or positive, but anything other than uniformity is not desirable. With addition in resin matrices, acting as a non-structural filler, any agglomeration will decrease strong interfacial boundaries and alter the stress conditions, particularly, if dry voided areas are present. This could have a profound interaction with the concentration phenomena discussed in Section 4.2.3, that shows a retardation of the luminescent response which is said to be a plausible explanation for the experimental results [157]. This would effect the bulk crystal properties and their reaction in the host material.

Secondly, the stress-strain states surrounding the crack-tip are of notable concern. This was uniquely described when the correlation in the force derivative did not show a coincident magnitude eﬀect. The magnitude of the force derivative did not indicate a linear intensity response. This leads to further speculation that varying luminescence will occur before and around an active crack feature. SEM images of Figure 4.21, showed the multiple micro- crack features of the three=phase composite. If specimens form microcracks in simultaneous fashion, then the TL events recorded could be a measurement of all events combined or from a partial response.

Furthermore, the micromechanics may indeed play an important role in what appears to be initially prescribed to a micro-scale event. This is was postulated by the visual content analysis and the FEM solution with view of strain distrubutions. The area of luminescence observed under visual analysis points to miniscule distortion as the stress moves from the top of the default line, and downwards to the crack site. The material distortion will be a maximum along the fault-line as illustrated in Figure 4.1. This is validated by the locations of stress in the regions around the crack-tip and under the applied load (Figure 5.13).

177 Lastly, these notions are further expounded upon when we consider both two-phase and three-phase composites. Two-phase composites undoubtedly showcase brittle failure

(Figure 4.2). Conversely, the three-phase composite samples never reached their maximum yield, but still exhibited illuminations. The complimentary notions give rise to a fourth argument for discrepancies in observed emissions, and greater diference in composite type.

The nature of damage in either composite phase is not identical in micro-mechanical failure or transient mechanical response. The supplementary reinforcement brings with it multiple failure modes in contrast to the exclusivity of dominant brittle resin failure. It was indicated in Section 4.4.4, that the energies generated were large enough to have predominantly matrix-related failure. With the random oriented fibers carrying the bulk of the load, a causation of matrix failures would result in minor decrease in the load carrying ability of the structural beam, considering the matrix component assists in distributing the load. This would be a fascinating finding if micro-matirx cracks could be either detected ar quantified.

This is subject to further examination, and is part of an ongoing investigation. The intial SEM micrographs in Section 4.4.4, displayed the variation in micron scale damage as a feature of the particulate disturbances. Particulates were found the be sheared in half, deformed but partially undisturbed and debonded. This alludes to multiple damage modes applied to the luminescing particles as was originally assumed in Section 4.1.

178 CHAPTER 6

CONCLUSION & RECOMMENDATIONS

6.1 Summary of Results

The need for developing non-destructive structural health monitoring techniquies for composites is imperative. Current research works focus on metal-based solutions from modern technology for detecting damage in advanced composite structures. The use of composites over the twenty-first century is without bounds. Further complicating the problem of health monitoring for arriving advanced composite systems, is the capital intensive inspection equipment and maintenance schedules. This research study addressed the plausibility of detecting and characterizing damage in composite structures as a precursor to a novel SHM practice. A methodical approach was considered for tackling the stated research problem utilizing a luminescent phenomena called TL (Chapter 3- 5). TL is an optical flux response to mechanical stimuli, or in this case, a concentration of strain around the sample crack-tip induced by a mechanical load. Concentrated particulate composite short beams were manufactured containing differing structural single-edge notches and particulate volume fractions. Fiber-reinforced particulate composites were also fabricated as a secondary experiment. The test procedures invoked precise mechanical stress in particulate composite beams, in order to excite repeatable emissions, utilizing standard mechanical loading practices. Composites with and without fiber reinforement were fabricated, and revealed

179 that TL indicates damage for brittle matrices (two-phase) and for micro-matrix damage with random discontinuous ﬁber orientation (three-phase). The emission feature can be predicted for concetrated composite beams, if the loading proﬁle is known.

In summary:

1. A ﬁrst experiment revealed the illumination proﬁle for the near-composite beams. It

has been shown that repeated TL can exist for the fracturing of concentrated beams

(two- and three-phase composites), where a simulated defect is present as a notch or

crack.

2. Concerning two-phase composites for initial understanding of the feeble brittle resin

matrices, analysis of the spectral and loading curves reveal the emissions accompany

instantaneous crack propagation and catastrophic behaviour. In addition, visual con-

tent analysis revealed the path of crack propagation will be in the path of the recip-

rocal TL events. However, the stress-strain conditions occur within in micro-seconds

and will require further analysis to fully proﬁle the expedient mechanism involed in

pre-crack luminescence ahead of crack opening. Literature indicates ZnS:Mn as an

elastico-TL material which should show signs of precrack luminescence at larger in-

tervals leading up to rupture. This is believed to be due to low material strength and

expediant beam fracture, and the presence of adequate interface where ZnS:Mn only

reacts as a member of the host (ZnS:Mn takes on the property of the host material due

to its soft inclusion). However, this research work indicates the observed luminescence

is primariliy related to macroscopic fracture of the brittle matrix.

3. The second experiment involving a Design of Experiments approach, derived a system-

atic equation to describe the maximum TL output under ﬂexural loading conditions.

The geometrical paramters were scaled to produce beams with diﬀering potential en-

180 ergy levels to clarify a lower threshold for triboluminescent excitation in the dominated

polymer composite. The polymer matrix limited the TL response of ZnS:Mn to the

stress-strain conditions of the host matrix. This was considered to be a macro-scopic

case of TL. In addition, the major factor inﬂuencing the respective triboluminescent

output was found to be the eﬀective material length. The eﬀective material length is

synonomous with the amount of internal energy required to open a crack and produce

further fracturing.

4. A ﬁnal experiment, by incorporating the experimental J-integral method for determi-

nation of fracture mechanics has elucidated the complex fracture energy relationship

of notched specimens. The material system was found to have a critical fracture en-

ergy of approximately 3.09 J/m. The TL emission were found to produce a linear

relationship with accompanying strain conditions in two-phase composites. For the

three-phase composite, the critical displacement was ascertained to be larger than 7

J/m and a low energy threshold was found to be near a 2 J/m according to the lowest

notch setting. TL was observed in three-phase composites at the low notch settings

and at energies less than 2 J/m.

5. Through further analysis, the loading proﬁle correlated the time extension of excita-

tion emissions corresponding to the drop in load during the failure cycle. This trend

extends to both two-phase and three-phase composites. In addition, the diﬀerential

of the load proﬁle reveals the dependence of TL on the loading rate as described by

negative values of the force derivative and their alignment to the excitation events.

Also, strain energy as a modiﬁer to the diﬀerential helps to explain the magnitude

of TL emissions with correlated load. Upon revisiting the DoE experimental data,

the relationships between strain energy and the rate dependence are further qualiﬁed.

However, the magnitude of the force derivatives and strain-energies are still a conun-

181 drum and are believed to be related to further heterogenous stress band arround the

crack-tip. This research work further alludes to the piezoelectric mechanism for for

TL-ZnS:Mn excitation as the rate dependency remains prominent.

6. The triboluminescent emission can be simulated as a bi-exponential decay model. The

calculations are carried out by a step-function to re-create the un-excited and exciation

curve. The exciation follows the force derivative and threrefore the time of excitation

or the constriants of the step-function. The ﬂexure of particulate composites are

simulated in a ﬁnite element code utilizing COMSOL multiphysics software. The load-

proﬁle is recorded and inputted in MATLAB program to decipher the force derivative,

a well as, the strain energy at point of two-phase compiste fracture. In addition, using

a previous model by Chandra et al. [121] and modiﬁed in this study, the maximum

intensity is substituted as the initial intensity in the bi-exponential model. The results

produced a simulated replication of the phantom plots which give a 3D view of TL

upon loding of a concentrated composite beam. When concentration is the main

study, the variation in the FEA showed mixed results. The scale of intensity is within

the range of the experimental values, however, the modiﬁed-intensity model did not

reﬂect the dampened experimental response found in the intermediate concentration

values. This is a limitation of the current model.

As a consequence, experimental results conﬁrm initiation of TL in all cases of concentrated specimens where dispersion is periodic. The volume fraction ranges from 5 and 10 percent particulate inclusion. This indicates existence of TL at lower loading fractions, which is near the neccessary industrial practice of a 2 percent defect allowance. The chosen

TL material, ZnS:Mn, has been stated to act as a non-reinforcing particulate in standard composites [27]. The principal mechanism of fracture mechanics in composites, illustrates

TL on a length-scale amenable to early crack propagation and other failure types related

182 to the ﬁber/matrix interface. This indicates the triboluminescent ability to signal or detect low energy events, that correspond with the basic internal workings for deformation in constituted materials as described by Griﬃth [40]. In the case of reinforcement, this means internal or direct sub-surface failures are inidicated by TL emissions as indicated in

Section 4.4.

Utilizing visual analysis and ﬁnite element analysis of particulate beams, it has been shown that the TL emission during ﬂexural loading, do parallel internal stress-strain events.

These stress-strain events are prominent at locations around the pre-crack tip and initial load contact region. Their intensities, which is a feature of the stress-strain magnitude, roughly quantify the amount of deformation taking place and the site of highest occurrence.

By implementation of the experimental J-integral, it was shown that an energy threshold to induce TL can be as low as 2 J/m when dispersed in VER and the case of reinforcement.

The difference in the two revolve around the excitation mechanism. It is evident the two- phase composite is excited through a elastic and fracture-like distrubance. Although, it can be said for certain that only one ase may appear in a macro-fracture event. However, the reinforced case shows evidence of local matrix/fiber damage evident in the pinging during experimentation, and through initial calculations of internal energies. Incorporating a new analysis technique, known as ’phantom analysis’, the temporal signals were unified.

The phantom analysis show the succinct influence of strain energy as a driving force for emissions of photons. This is observed in the J-integral experimental methods test and by observing the derivative of the loading profile. In the first case, the TL emission seems to have a linear realtionship with the amount of strain energy produced during the fracture event. On the other hand, the bifurcations observed in the load profile correlate TL with the rate change of loading conditions and further influence of strain energy. The behavior of un-reinforced composites is strikingly different from reinforced TL concentrated specimens.

183 Un-reinforced beams demonstrate classic linear elastic fracture mechanics with a resultant single TL emission existing at catastrophic failure. In contrast, practical reinforced beams exhibited multiple emissions during the loading cycle.However, it is likely that the micro- matrix related defects are the cause of triboluminescent emissions in the flexural loading of randomly oriented fibers. Therefore, the efforts to model the existing multi-physical phenomena have been limited to the brittle elastic case for this work. The ductility of adding reinforcement mechanically is a homogenous like component concerning material failure, although, the triboluminescent signature suggests failure is an increasingly heterogeneous process. The heterogeneous failure process observed results in hidden stress concentrations from fiber-matrix type failure modes and not stringently adhered to the failure by micro- cracks in the matrix support as originally assumed.

6.2 Contributions

Industries utilizing advanced composite materials need real-time and reliable structural health monitoring. The majority of research concerning condition or health monitoring involves non-value added inspection processes with bulky sensors, making detection extremely costly. TL offers innate sensory mechanism through its ubiquitous application and material sensitivity. From literature, we know in part why and how, TL exists as a physical phenomenon [85, 86, 91, 139]. Research focused on finding new TL materials [85, 86, 127], their underlying physical mechanisms and ab initio SHM applications through doped optical fiber systems [73,74,113,142,172]. However, the mechanical and optical behavior in a composite system is not fundamentally discussed or explored. The fundamental question concerning integration in polymer composite materials relies on where TL will occur.

The work herein describes the use of a highly known triboluminescent material for detection of miniscule crack and defect creation in composite specimens. An experimental method

184 was devised and a numerical model was derived for modeling the physical phenomena associated with triboluminescent concentrated composites. This is a profound study into the interaction of TL materials in conjunction with composite behavior. I have assessed the mechanical and distortional energies related to the fracture mechanism and associated them to a physical model for key process parameters. In addition, I have led research into a novel way to convert TL damage emissions for transmission by fabricating a 3D optoelectronic device which could serve as an integrated transmission network. The bulk of this research work and discussion is reserved for further developments. Subsequently, this device will meet a required need for sensors in todays structural and condition monitoring; where ﬂexibility and integration of sensors is a major requirement for future third generation composites. In this work, we viewed the intrinsic TL sensing response from a composite view by observing

TL phenomenon for near and complete composites.

Overall, my contribution is at the system level where a novel SHM system has been proffered based on a energy-based paradigm for creation of a novel senory mechanism. My contribution to the knowledge is to answer the question of where, in relation to stress-strain during structural loading. Furthermore, this involves the unique approach of detecting failure in composite systems using TL and light detection by optoelectronics. Specifically, my approach concerns the development of finite element procedures for predicting stress- strain relations and the response of light intensity in a volumetric material. This is realized by combining physical modeling of the triboluminescent response of ZnS:Mn proffered by

Chandra et al. [172], in association with stress-strain relations of modern material mechanics. We sought to scrutinize each component of such a system to provide a linkage of future research works. A systematic laboratory test was determined, where triboluminescence is readily obtained. The addition of phantom analysis will be the building block for future programmable assessments of failure and the TL signal.

185 In short, the key ﬁndings are:

From the perspective of this manuscript, it was found that the loading history of • ﬂexurally tested concetrated samples yielded enough information to model the eﬀects

of applied load and Triboluminescent intensity.

It was conﬁrmed that a rate-dependence of TL excitation with integration in polymer • matrix composites exist as a feature of the strain-energy. The force-derivative as a

rate interpretation indicates the time of the excitation event. The magnitude of the

event is still under review, but is believed to be related to the rate of release and

internal strain energies. This lends credence to the overall objective of correlating an

energy-based approach towards SHM.

In the structural sense, TL is an indication of reduction in stiﬀness of material. This • process can be an indication of local material diﬀerence or global indications. It was

found that in the case of two-phase composite, TL, is a terminal determination of the

stiﬀness. Meanwhile, the three-phase is only an indication of failure but on a local

and micron-scale. TL can detect micro-cracks in ﬁber-reinforced systems. This is

primarily related to the particulate inclusion in the weaker resin matrices component.

Strain energy is a driving factor in the production of instantaneous TL impulses (i.e. • experimentain with the eﬀective material length). In addition, the lower threshold

of TL excitation was obtained by method of J-integral analysis. The experimental

method of the J-integral demonstrated that TL occurs on a lower energy order and

can be an indication of micro-stress.

It was demonstrated that practical composites will need to contain less than 6 % vol. • to have negligible eﬀect on material properties, whilst, still maintaining a susecptible

light intensity signal. Alarger loading concentration will have an adverse eﬀect on the

186 material properties.

6.3 Recommendation for Future Work

This is the undertakening of a greater body of work toward a holistic structural health monitoring systems comprised of novel smart sensor technologies. Structural monitoring is an antiquated eﬀort to endow non-biological structures with self-sensing capabilities. Cru- cial to the development and viability of SHMS are indeed related to their sensing methods.

This requires inclusion of bulky sensors and related items that can have adverse eﬀects on material properties. TL has a plethora of unique and innate mechanism for basing an active and passive damage monitoring scheme. A general roadmap was given in Figure 1.3 outlining the road to SHM, and Figure 3.1 with a focus on the research aspects. Necessary work in termination is another key fundamental area of research for a TL based system that must be addressed. Signal processing is paramount for harnessing the true power of a

TL-based system. With light collection proven to be plausible by photovaltaics, an estimation of patch-type versus integrated sensor can commence. The acute descrepency involves the efficiency of an operating cell and the ability of cold TL emissions to be detected and transmitted. Transmission over long distances is a significant key to the enxtension of this proposed idea and research. Finally, implementation in standard composite systems is a neccessity for true system verification. Further research will need to be completed on the random effects of TL incorporated in fiber-reinforced composite systems. Primarily, what other fillers could be incorporated to oppose the parasitic influence of non-structural fillers.

Priorities for future experimentation are addressed below for (1) Composite mechanics, (2)

Composite processing and (3) Sensory integration:

(1) Composite Mechanics

1. The reproducible elastico ML is said to be a unique property of ZnS:Mn due to its

187 piezoelectriﬁcation excitation mechanism [121]. The current setup and instrumenta-

tion is inadequate to make a determination for spectral analysis at the micro scale

level. Therefore, greater acquisition will be employed to collect a minor-view spectrum

of TL in concentrated composites. This is a step towards simulating a representative

volume element (RVE) to predict intensity and observe stress conditions at the micron

scale which is related to the overall go-no/go determination of SHM. This study should

also include interfacial stress transfer, as well as, realtime visualization under SEM.

A one particulate study is desired. The determination of the lowest sensing element

(micron-scale), and therefore, greater resolution makes sensing by TL an advantageous

process versus laborous NDE practices

2. The bifurcations of the applied force derivative explain the nature of TL and it’s

rate dependency. With further experimental and FE analysis, the triboluminescent

intensities were found to behave in parallel with the particular strain energies experi-

enced by the loading of a structural specimen. Unique to this study is the observance

of detection of damage/failure, spatial location and intensity quantiﬁcation from the

ephemeral TL emission.

3. A mainstay to composite mechanical test is fatigue testing. The general manual to

fatigue test are found in ASTM STP 91-A and ASTM D671. As we know, composites

in practical applications are not static loads but dynamic in nature. Fatigue testing is

a method for determining the dynamic behaviour of materials over time and altering

loads. The main exercise will be to determine where TL appears in the alternating

load cycle, accompanied with the number of cycles up to damage in composite samples.

This experiment will totally deﬁne how TL can be utilized as health monitroing devices

in advanced composites. There are other composite material testing procedures like

shear and creep that need to be explored in greater detail. This is a major prioirty

188 and task.

4. Progressive failure models and implementation in numerical or ﬁnite element analysis

is essential to understanding the composite mechanics of TL. Treatment concerning

ﬁber orientation in random, longitudal and discontinuous composites need to be ex-

plored in more detail. Particularly, composites tend to behave non-linearly which

makes prediction more cumbersome. This research work relied on the bifurcations

exuded by the load-displacement curve to signal TL. Considering, the reinfroced case

showed an abundance of inﬂection points, extraction and generation of the load curve

could provide the neccessary information needed to make structural inferences. The

elementary beam model, could provide a beginning to predicting the load state if the

Euler-Bernoulli equations can be coupled with a diﬀerential of the light intensity.

5. This item could be placed in the composite mechanics or sensory mechanism cate-

gory. The modeling of the Triboluminescent response is analogous to resolving the

loading proﬁle of a structural member. A more reﬁned model is sought to interpret

the emissions signal to physical generation of energies that act on the solid body there-

fore producing deformation. The question then becomes, if these energies signatures

related to individual failure phenomena including matrix and acts of debonding.

(2) Composite Processing

1. The manufacturing of practical composites that include ubiquitous sensor elements is

a tremendous challenge. The TL particulates present there own challenges and are

further complicated by an additional sensor element. In prior studies [27, 146], test

were conducted on practical composites for impact studies. Termination of transmis-

sion components were noted as a potential barrier.Eﬀorts to combine utility or form

is the likely best approach to achieving practicality. The suggestion of this research

189 study is to incorporate the TL sensorS and a realized transmission component as once

complete device for composite integration.

(3) Sensory integration

1. From Conversion to Transmission: Initial testing has shown that light can propagate

through doped resins alone, as well as doped ﬁber reinforced plastics (FRP) laminates

with material transparency being a major hindrance [146]. Because of the opaqueness

of most composite systems, a novel extraction method is needed for ballistic transport

capabilities. Currently, work has been undertaken to estimat the in-situ capabilities of

a transmission scheme involving PV technology. The technology extends to a ﬂexible

CNY based cell based dye-sentisized solar cells that could potentially be woven into

engineering textiles. Lastly, electrical testing and equivalent circuit modeling of an

optoelectronic device comprise Phase III. Such a model will decipher the viability of

utilizing PV technology as a transmission medium for cold-TL emissions. Speciﬁcally,

addressing the issues of conversion and photon eﬃciencies needed to conduct pho-

tocurrent in a common optoelectronic device. Natural plastic optical ﬁbers have been

investigated by the HPMI group, and have found to transmit light by side coupling,

however, this means is ineﬃcient. This will serve as a benchmark for future endeavors

into optoelectronic means of transmission.

2. The goal of having a complete sensory mechanism for TL intrinsic capabilities is in

sight. Continued eﬀorts on the subjects of intelligent design in converting and trans-

mitting signals are important gaps of need. Transmitting signals equated to that of

TL is a novel experience. This operation needs to entail a guide or pathway for dam-

age signals to be terminated in a viable manner for data collection. There are many

optoelectronic avenues for transmission of light, that being ﬁber optics, PV technol-

ogy and bulk sensors. However, ﬂexible and embeddable means for transmission are

190 functional criteria. In recent work, conversion has been deemed possible through re-

ception by photo-voltaic route [18]. The advances of PV technology towards creation

of ﬂexible optoelectronics have been explored and are under continued development

in this research group [176]. Uniquely, a method for low-light collection was proﬀered

by synthesis and assembly of a novel collection device to absorb and conduct photonic

energy from triboluminescent emissions. A characteristic circuit model will be applied

to predict the current generation from TL production and act as the feature vector

for the sensory mechanism.

3. Sensory mechanism: To bring about a novel monitoring scheme, the data and a com-

puterized system for scrutinizing information must take place. The signal emissions,

reception and transmission form the basic building blocks for a potent approach to

pin-pointing micro-macro-damage. The form factor of such a system and devices are

essential for the practical application of non-destructive monitoring. Eﬀorts to reduce

the computational cost of analyzing real-time and histroical data are a major concern.

This research group will need to make eﬀorts to eﬃciently provide pattern recognition,

as well as, ensuring false alarms are non-existent. A scheme for detectin micro-ﬂaws

has been proﬀered and will need additional development to realize the full potential

of a distributive sensing system.

191 APPENDIX A

MONTE-CARLO SIMULATIONS

Figure A.1: Monte-carlo simulation for 0% fraction. The simulation size is equal to 20/1000 sample runs.

192 Figure A.2: Monte-carlo simulationfor 5% fraction. The simulation size is equal to 20/1000 sample runs.

193 Figure A.3: Monte-carlo simulation for 10% fraction. The simulation size is equal to 20/1000 sample runs.

194 Figure A.4: Monte-carlo simulation for 25% fraction. The simulation size is equal to 20/1000 sample runs.

195 Figure A.5: Monte-carlo simulation for 50% fraction. The simulation size is equal to 20/1000 sample runs.

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210 BIOGRAPHICAL SKETCH

The author was born and raised in sunny Florida. He is the youngest addition to the union of Frank and Mary Dickens. Before coming to Tallahassee in 1992, the author’s Father served twenty years in the Navy and his Mother worked for the state for twenty years. During his residency in Tallahassee he attended the area’s public schools. Before entering Florida State University’s baccalaureate program, he was a student attending Tallahassee Community College where he received his Associate in Arts degree. He recieved a B.S.I.E. and M.S.I.E from Florida A& M University - Florida State University College of Engineer- ing, respectiviely, 2005 and 2007. He has won awards from the Society of Manufacturing Engineers, grants from the National Science Foundation and was recently awarded a grant in Entrepreneurial Excellence as part of the Jim Moran Institute’s InNOLEvation challenge. His life’s goals are to be an eﬃcient educator, promote the entrepreneurial spirit, and continue the duties of the knowledge worker.

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