Impact Response of Strengthened Glass with Ultrahigh Residual Compressive Stresses

IMPACT RESPONSE OF STRENGTHENED GLASS WITH ULTRAHIGH RESIDUAL COMPRESSIVE STRESSES

PHILLIP A. JANNOTTI

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2015

To my hero

ACKNOWLEDGMENTS

Thanks to my family and friends for their support during my graduate studies, without which my time as a graduate student would not be have been as enjoyable. A special thanks to my girlfriend, Jen, who put up with me during my time here at Florida. Through good times and bad, it is with all of your support that I have reached this point in my life.

Thanks to my graduate committee, Dr. Ghatu Subhash, Dr. Peter Ifju, Dr. Nagaraj

Arakere, and Dr. John Mecholsky, for their time and attention reviewing my work. Their insight and suggestions have been invaluable to my research. I would like to especially express gratitude to my advisor, Dr. Ghatu Subhash. I sincerely appreciate everything you have done for me, for reading and re-reading every manuscript revision, and for watching and re-watching every presentation. I truly appreciate the countless hours you have invested in me.

This research was made with Government support under and awarded by DOD, AirForce

Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG)

Fellowship, 32 CFR 168a, and by Saxon Glass Technologies.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 7

LIST OF FIGURES ...... 8

ABSTRACT ...... 11

CHAPTER

1 INTRODUCTION ...... 13

Strengthened Glasses ...... 13 Applications ...... 14 Characterization ...... 14 Aims ...... 15

2 TRANSPARENT MATERIALS ...... 19

History ...... 19 Glass ...... 20 Glass Strengthening ...... 20

3 RESIDUAL STRESS DISTRIBUTION ...... 26

Background ...... 26 Materials ...... 27 Experimental Method ...... 28 Results and Discussion ...... 30 Conclusions...... 35

4 STATIC AND DYNAMIC INDENTATION RESPONSE ...... 41

Background ...... 41 Materials ...... 42 Experimental Method ...... 43 Results and Discussion ...... 46 Surface Indentation Hardness ...... 46 Indentation Damage Evolution ...... 49 Subsurface Indentation Hardness Variation ...... 52 Subsurface Indentation Damage ...... 57 Conclusions...... 58

5 IMPACT-INDUCED DAMAGE PROPAGATION MORPHOLOGY ...... 69

Background ...... 69 Materials ...... 70 Residual Stress Distribution ...... 71 Bulk Properties ...... 71 Results...... 73 Discussion ...... 81 Conclusions...... 85

6 IMPACT-INDUCED DEFORMATION AND ENERGY DISSIPATION MECHANISMS ...... 95

Background ...... 95 Materials ...... 95 Experimental Method ...... 96 Results and Discussion ...... 97 Impact Damage Evolution ...... 97 Low velocity impact ...... 98 Moderate velocity impact ...... 99 Summary of the impact damage ...... 102 Energy Balance ...... 107 Kinetic energy of bar dilation ...... 107 Kinetic energy of ejecta ...... 110 Frictional energy ...... 112 Energy due to fragmentation ...... 113 Elastic wave energy ...... 115 Other ...... 116 Summary of the energy balance ...... 117 Conclusions...... 117

7 SUMMARY ...... 128

Residual Stress ...... 128 Properties ...... 128 Impact Response ...... 129 Future Work ...... 130 High Compression, Low Case-Depth Strengthened Glasses ...... 130 Raman Spectroscopy ...... 131

APPENDIX: ELASTIC WAVE VELOCITIES ...... 136

LIST OF REFERENCES ...... 137

BIOGRAPHICAL SKETCH ...... 145

LIST OF TABLES

Table page

5-1 Bulk material properties of the as-received and strengthened glass bars...... 86

6-1 Selected material properties for the as-received glass, the strengthened glass, and the steel ball...... 119

LIST OF FIGURES

Figure page

2-1 Representative residual stress profiles for strengthened glass cross-sections as viewed through the side of a semi-infinite glass plate ...... 24

2-2 Schematic of the ion exchange process ...... 24

2-3 Process of stress development due to ion exchange for a semi-infinite plate in the x- and z- direction as viewed through the cross-section ...... 25

3-1 Images of the glass specimens ...... 36

3-2 Imaging the photoelastic fringe patterns using white light in a circular polariscope...... 36

3-3 Micrograph of the isochromatic fringe patterns as viewed through the unstrengthened face of the thick (9.9 mm) specimen ...... 37

3-4 Residual stress profile determined by photoelasticity using a thick (9.9 mm) specimen and a circular polariscope in dark-field arrangement...... 37

3-5 Photoelastic fringe patterns of thin (0.71 mm) glass specimen as viewed through circular polariscope using white light ...... 38

3-6 Complete residual stress profile in strengthened glass specimen determined by photoelasticity ...... 39

3-7 Photoelastic micrographs of the edge of the thin (0.71 mm) glass sample utilizing index matching oil...... 40

4-1 The strengthened glass specimen with exposed unstrengthened glass surface ...... 60

4-2 Schematic of the dynamic indentation hardness tester (DIHT) ...... 60

4-3 Static and dynamic Vickers hardness data for various load ranges on the strengthened and as-received glass surfaces ...... 61

4-4 Micrographs of indentation-induced damage at comparable low loads on strengthened and as-received glass surfaces ...... 62

4-5 Micrographs of indentation-induced shear faulting at comparable low loads on strengthened and as-received glass surfaces ...... 63

4-6 Micrographs of indentation-induced damage at comparably high load levels ...... 64

4-7 Micrographs of indentation-induced shear faulting on strengthened glass surfaces at comparably high loads ...... 65

4-8 Isochromatic fringe patterns near the edge of unstrengthened surface with hardness and residual stress data superimposed ...... 66

4-9 Influence of residual stress on hardness change ...... 67

4-10 Micrographs of the indentations at various depths on the unstrengthened glass surface ...... 68

5-1 Schematic of the setup used for the ball impact experiments ...... 88

5-2 Images of the glass bars when viewed in a circular polariscope under white light ...... 88

5-3 Residual stress profiles determined by photoelasticity ...... 89

5-4 Impact damage due to ball impact at 261 m/s on an as-received glass bar...... 90

5-5 Impact damage due to ball impact at 345 m/s on a strengthened glass bar ...... 91

5-6 High-speed shadow light images of the damage propagation in a strengthened glass bar due to ball impact at 334 m/s ...... 92

5-7 High-speed imaging of impact damage ...... 93

5-8 Plot of the damage front velocity profiles for both as-received and strengthened glass bars as a function of the damage front position ...... 94

6-1 Schematic of the test setup used for ball impact experiments...... 120

6-2 High-speed images of the damage induced by low velocity impacts ...... 121

6-3 High-speed images showing damage evolution due to moderate velocity impacts ...... 122

6-4 Trends in deformation mechanisms as a function of impact velocity ...... 123

6-5 Plot of the average self-sustained damage front velocity for strengthened glass bars of varying cross-sectional dimensions ...... 124

6-6 High-speed images of the periodic relief induced in the strengthened glass bars due to wave splitting ...... 124

6-7 High-speed images revealing the representative dilation behavior observed ...... 125

6-8 High-speed images illustrating the fine particles ejected from the impact site ...... 125

6-9 Images of steel ball after impact ...... 126

6-10 Fragment characteristics for the as-recevied and strengthened glasses ...... 127

6-11 Summary of the contributions of various elastic and inelastic deformation mechanisms to the overall energy balance ...... 127

7-1 Raman spectra for as-received and strengthened glass ...... 134

7-2 Raman map data for static indentations ...... 135

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

IMPACT RESPONSE OF STRENGTHENED GLASS WITH ULTRAHIGH RESIDUAL COMPRESSIVE STRESSES

Phillip A. Jannotti

May 2015

Chair: Ghatu Subhash Major: Mechanical Engineering

Chemically strengthened glasses have been widely used for protecting cell phone, TV, and laptop displays as well as for protecting homes and buildings against high-velocity winds and debris. In the current study, a state-of-the-art chemically strengthened glass was examined, and found to contain residual compressive stresses up to 1 GPa, case-depths approaching 1 mm, and residual tension on the order of tens of MPa. Due to difficulties in obtaining the residual stress profile for such glasses, a robust birefringence technique was proposed to measure the residual stresses by utilizing multiple specimens of different thicknesses to match the appropriate spatial resolution to the given stress magnitude and stress gradient severity.

Currently, only limited information is available discussing the influence of strain rate on the mechanical response of glasses, especially strengthened glasses. Quasistatic and dynamic indentations were conducted on as-received and strengthened glass surfaces in order to assess the influence of residual surface compression and strain rate on the indentation response. The variation in indentation-induced fracture characteristics was also analyzed to assess the utility of such glasses for applications where optical transparency and fracture-resistance are desired. It was found that residual compressive stress and increased strain rate led to increased hardness

values and mitigated cracking. Additionally, residual compression promoted increased shear deformation, while increased strain rate led to reduced shearing and increased densification.

Subsurface hardness profiles on the glass cross-section revealed that residual compression slightly increased hardness, while residual tension dramatically decreased hardness. It was also found that the hardness values were improved over the as-received value to a depth beyond the compressive layer.

To assess the real-world impact response of strengthened glasses, ball impact tests coupled with high-speed imaging were performed to characterize the impact-induced damage morphology and energy dissipation modes. It was found that strengthened glass exhibited increased damage front velocities, self-sustained damage growth (correlated with tensile strain energy), suppression of spall fracture, increased frictional contact, increased ejecta velocities, reduced depth of non-uniform dilation, and an additional mode of uniform dilation (correlated with compressive strain energy).

CHAPTER 1 INTRODUCTION

In many civilian and military applications, protection against impact requires materials with both high-strength and optical transparency. Towards this end, materials such as glasses, ceramics, and polymers have gained considerable attention [1, 2]; however, glasses remain amongst the most popular material choices. In fact, traditional glasses can be modified to increase fracture strength and improve damage-resistance, and are termed strengthened glasses.

Strengthened Glasses

Traditional glasses can be processed by surface modification techniques, whereby residual compressive stresses are introduced into the surface layers of the glass. The residual compressive stresses induced within the glass surfaces renders the glass less sensitive to surface flaws and have been shown to increase the mechanical strength [3-6]. As glasses and other brittle materials fail in tension [7], the compressive stresses can impede crack propagation and even prevent their initial appearance [8]. In the current study, surface compressive stresses were generated by a chemical treatment called ion exchange. The glass is placed into a salt bath where large salt ions exchange with smaller ions in the glass surface. Upon cooling, the large size disparity generates residual compression in the exchanged layers along with interior balancing tension (discussed in more detail in Chapter 2).

Consider that the residual compressive stresses function to counteract local tensile stresses to increase the fracture strength proportional to the degree of strengthening (i.e., greater surface compression leads to greater fracture strength). The severity (size/depth) of the flaw which is effectively protected by the compressive layer is governed by the depth of the compressive zone. Recent developments in chemical strengthening (i.e., ion exchange) have resulted in the ability to introduce residual surface compressive stresses as high as 1 GPa with 13

case-depths stretching to almost 1 mm [3, 4, 9], making chemically strengthened glasses excellent candidates for a range of advanced applications.

Applications

Applications of strengthened glasses include hurricane- and earthquake-resistant architectural windows, impact-resistant covers on solar panels, display screen covers for cell phones, laptops and TVs [3, 4], and vehicle windshields (cars, high-speed trains, aircraft) [1].

They are even employed for cartridges used in epinephrine injectors (EpiPen®). Whether protecting sensitive electronics or vehicle/building occupants from high-velocity particles, debris, or other flying projectiles, it is of vital importance to thoroughly characterize and understand the material behavior.

Characterization

In order to understand the influence of processing on the mechanical response, a material must first be characterized. For strengthened glass, the most important consideration is the residual stress distribution. In order to directly compare the materials to the mechanical response, non-destructive optical methods are choice methods for analyzing the residual stresses. Due to the very high levels of residual compressive stress and the steep compressive stress gradient in chemically strengthened glasses, analyzing the stress profile is difficult. Thus, simple, yet robust techniques must be devised to analyze complex stress profiles in advanced ion-exchanged glasses.

For materials intended for dynamic applications where impacts can occur due to particles, debris, or the glass articles being dropped onto hard surfaces, it is crucial to fully understand the influence of processing (residual stress state) on the resultant mechanical response at a range of loads and loading rates. Because material behavior at high strain rates can differ drastically from

its quasi-static response, experimental observation and characterization of the deformation processes specific to the high-rate regime must be identified and understood.

Indentation measurements are frequently used as microscale mechanical characterization tools due to their simplicity and flexibility in testing materials by merely adjusting the applied load and loading rate. In determining mechanical properties and associated deformation behavior, strengthened glasses cannot simply be characterized using standard testing procedures.

Owing to the fact that the strengthened glasses possess gradients in residual elastic stresses and chemical structure, one must take into account a potential gradient in mechanical response from the strengthened surface into the interior of the glass. Thus, an understanding of the subsurface mechanical response is key.

Beyond microscale indentation, impact experiments have been identified as a viable means of assessing the real-world (macroscale) impact response. Compared to indentation experiments which probe the local material response, impact testing can provide the ability to observe macroscale damage mechanisms that occur during impact events. Such tests can help identify evident failure modes and key mechanisms of energy dissipation.

Aims

This dissertation details studies to develop a fundamental understanding of the influence of ultrahigh residual stresses due to ion exchange on the dynamic impact response of strengthened glass. The study has been divided into four aims:

1. Evaluate the residual stress distribution in chemically strengthened glass.

2. Assess the influence of chemical strengthening on the mechanical response by utilizing static and dynamic indentations.

3. Investigate the effects of high residual stress levels on the dynamic fracture propagation characteristics.

4. Determine the chemical strengthening effects on the operative deformation mechanisms and the energy dissipation modes due to impact.

Chapter 2 gives a brief history of transparent materials, namely glass. The basics of glass strengthening are also covered, with a comparison between the more common thermal strengthening and the more advanced chemical strengthening. Lastly, a detailed description of the ion exchange method, the chemical strengthening treatment used to process the strengthened glasses in this study, is presented.

Chapter 3 describes a photoelastic method for evaluating complex residual stress distributions with ultrahigh levels of residual stress and severe stress gradients. Photoelasticity is a well-established technique which allows the stress state to be viewed as visible colored fringes, thereby offering the opportunity to directly measure the residual stress profile. Here, the challenge was to measure the ultrahigh compressive stresses and the extremely steep stress gradient within a narrow region of less than 20-30 microns. Note that greater stress levels result in more fringes and more severe stress gradients result in more closely-spaced fringes. Because the number of fringes is proportional to specimen thickness, specimens of different thicknesses were used for evaluating different stress levels and stress gradients. Thus, by superposing the residual stress profiles, a composite profile was obtained where the high stress regions and moderate-to-low stress regions were evaluated separately.

Chapter 4 presents an experimental evaluation of the indentation response of as-received

(stress-free) and chemically strengthened glass evaluated under quasi-static (15 s duration) and dynamic (100 µs duration) loading rates for a range of loads. This gave insight into the effects of the ultrahigh surface compressive stresses and strain rate on the measured hardness values. As strengthened glass is essentially a graded material (with gradation in residual stress state with depth), the hardness profile as a function of depth from the strengthened surface was of interest. 16

Static indentation was performed on faces which were mechanically polished to remove the strengthened material and expose the subsurface. This allowed for the subsurface indentation response to be determined as a function of depth, i.e., residual stress. It allowed for the treatment process to be rapidly assessed in order to determine the resulting gradient in mechanical property variation with depth. The morphology and severity of indentation damage on the as-received and strengthened glasses (surface and subsurface) for varying loads and loading rates was also determined.

Chapter 5 describes a method for examining the impact-induced damage propagation for as-received and chemically strengthened glass bars. Ball impact experiments were performed (up to 345 m/s) with the intent of better understanding how chemical strengthening influences the morphology of the fracture propagation. Using high-speed imaging (up to 500,000 frames per second) the damage propagation was assessed as a function of impact velocity for the as-received and strengthened glasses. Additionally, using the time history of damage propagation, the damage velocity was also determined. The results provide insight into the nature of damage initiation and propagation under the influence of both impact-induced and processing-induced stresses.

Chapter 6 details the experimental characterization of impact-induced deformation mechanisms and corresponding energy dissipation modes. Using high-speed imaging, the operative damage modes were identified and characterized for a range of ball impact velocities up to 345 m/s. The results were used to tabulate energy dissipation due to elastic wave propagation, frictional contact, fracture surface creation, and the kinetic energy of particles/fragments.

Chapter 7 summarizes the major findings of the current study. Future research directions are also outlined. This includes examining the mechanical response of strengthened glasses with varied magnitudes of maximum residual compression and shallow case-depth. Lastly, the use of

Raman spectroscopy is proposed in order to develop an improved understanding of indentation- induced deformation behavior, namely the densification of the glass structure.

CHAPTER 2 TRANSPARENT MATERIALS

History

The history of transparent materials cannot be told without first beginning with glass.

Most people probably think of glass as a man-made material, but nature actually created the first glasses. Naturally-formed glasses can trace their origins back to the beginning of time, predating recorded history. Glasses found in nature are formed when rocks are raised to high temperatures due volcanic activity, meteorite impacts, or lightning strikes, and are then rapidly cooled [10,

11]. The first uses of glass can be dated back to the stone-age, where volcanic glass (obsidian) was used to form tools and weapons [12]. It wasn’t until around 3000 BCE that man-made

(rather low-quality) glasses are believed to have arisen [13, 14]. In the many years since, mankind has found innumerable uses for glass from the beautiful to the functional, becoming an integral part of everyday life. Owing to its boundless uses (past, present, and future), we continue to adapt glass to our various needs, experimenting with better ways to produce and process it.

And, because few other man-made materials exhibit such broad applicability at a reasonable cost, glass has remained a viable solution for current and future challenges. Due to the ubiquity of glass in modern society we rarely think about our continued need for glass and other transparent glass-like materials.

Today, one of the principle functions of transparent materials and the focus of this study is the use of transparent materials, specifically glass, for protective applications (protecting people, electronics, etc.). One early example of the use of protective glasses in American History was in World War II for airplane cockpits to protect pilots [15]. Currently, high-strength glasses can be used for wind- and debris-resistant architectural windows, cell phone screens, EpiPen® cartridges, vehicle windows, etc. [2, 3]. The most pervasive, and obvious, constraint of these 19

materials is optical transparency. Because this class of materials requires not only good mechanical performance, but also excellent transparency, material choices are more limited compared to traditional (opaque) structural materials.

Glass

Glass is a non-crystalline, or amorphous, material with no long range structural order.

Most glasses are primarily composed of silica (silicon dioxide, SiO2) which is the most common constituent of sand, and lesser amounts of other compounds or phases [11]. There are many types of glasses used including soda-lime glass (plate glass), borosilicate, aluminosilicate glass, lead glass, and fused silica glass [2]; however, the focus of this study is aluminosilicate glasses, specifically lithium aluminosilicate glass. [11] Aluminosilicate glasses contain some amount of aluminum oxide in its composition. It is similar to borosilicate glasses, but is more chemically- resistant and can withstand greater temperatures. In order to improve the properties and mechanical response of these glasses, a variety of glass strengthening procedures have been developed.

Glass Strengthening

Several types of strengthening techniques exist whose aims stem from the following general concepts:

 Reduction of flaw population and flaw severity (firepolishing or chemical etching)  Resistance to stress corrosion/environmental effects at the crack tip (coatings)  Surface compression (thermal and chemical tempering)

The strengthening mode of interest in the current study is residual surface compression.

This can be accomplished by either thermal or chemical means. One of the most popular strengthening methods is called thermal tempering. For this process, the glass temperature is raised above the glass transition temperature Tg [11] and then rapidly cooled. This develops a

temperature gradient across the glass cross-section, with the surface cooling faster than the glass interior. As the glass cools to room temperature, the center region acquires tensile stresses, while the outer surface regions acquire compressive stresses. The level of surface compression that is achieved can be increased by increasing the cooling rate, the thermal expansion coefficient of the glass, and the difference in thermal expansion coefficient of the glass and the cooling medium.

Unfortunately, the residual stress profile due to thermal tempering is parabolic and developing high levels of surface compression comes at the cost of increased interior tension (i.e., increased risk of tension-driven failure) (Figure 2-1A). Another disadvantage of thermally tempered glass is the difficulty in strengthening (to a meaningful degree) small glass specimens less than 3 mm in thickness. Additionally, there is a measurable loss in specimen geometry because the glass is raised to temperatures above the glass transition temperature and rapidly cooled. Despite having comparable depths of strengthening, the magnitude of compressive stresses generated is relatively small (on the order of several hundred MPa) [3].

As an alternative to thermal tempering, a popular chemical treatment process for glasses is ion exchange. Here, the glass is placed into a molten salt bath, where ions within the surface layer of the glass are replaced with salt ions [11] (Figure 2-2). Typically, smaller alkali ions in the glass are substituted for larger, denser alkali ions from the surrounding molten salt bath. As the glass is cooled, the salt ions are squeezed and become wedged into spots once filled by smaller glass ions. This results in the development of residual compressive stresses in the exchanged surface regions and balancing tension persisting through the interior region.

Typically, the compressive stresses are 400-1000 MPa and the stress gradient is steep, while the interior tension level is much less compared to thermally tempered glasses (tens of MPa) and nearly constant (Figure 2-1B). Unlike thermal tempering, chemical strengthening offers the

ability to induce huge compressive stresses while minimizing interior tension. It also allows for very thin glass articles to be processed with high levels of residual compression, e.g., Gorilla

Glass® for cell phone screens. Lastly, ion-exchanged glasses exhibit little geometric distortion during processing due to lower processing temperatures (well below Tg). Figure 2-3 shows the process of stress development in ion-exchanged glasses in more detail. Consider the case of a semi-infinite glass slab (in the x-y plane). Initially, the glass is untouched and stress-free (Figure

2-3A). Then the glass is placed into molten salt bath at elevated temperatures. Here, the diffusion of invading salt ions principally occurs in the z-direction (thickness). Once the outer glass layers are stuffed by large invading ions, the glass will swell due to the size disparity between the parent glass alkali ions (e.g., lithium) and the alkali salt ions (e.g., sodium and potassium). If free expansion were allowed to take place without constraint the resulting dimensional changes would appear, as shown in Figure 2-3B. In reality, the ion exchange process is carried out at temperatures well below the glass transition temperature (0.5Tg) [11]. Thus, the glass body cannot expand feely and unconstrained. In this case, the glass will dilate freely in the z-direction, but tries to swell non-uniformly in the x- and y-directions. This is clearly seen in the non- uniform dilation in the y-z plane during free expansion (Figure 2-3B). To satisfy compatibility criteria, which requires the interdependence of various strain components [16], the uneven expansion is suppressed. Therefore, the glass dilates uniformly in the x- and y-directions, as seen in Figure 2-3C. Elastic residual stresses are then generated as a result of enforcing compatibility criteria (elastic suppression of incompatible deformation) [4].

The amount of surface compressive stress generated within the specimen can vary depending on the ion exchange time, processing temperature, and salt bath used (potassium and sodium nitrates [17]). However, the main consideration is the composition of the starting, parent

glass. There is a requirement of the glass to contain sufficient alkalis in their composition to exchange. However, increasing the alkali content can often result in a reduction of the temperature at which viscoelastic relation occurs. Therefore, glasses best suited for ion exchange are those with increased alumina or mixed alkali content. The presence of a greater amount of alumina and alkali content promotes greater alkali diffusion coefficients. Also, when two alkalis are present in the glass the inter-diffusion coefficient increases. For example, a lithium-sodium glass is more easily strengthened (greater inter-diffusion coefficient) compared to a sodium- containing glass. Using ion exchange, almost any shape and size of glass can be strengthened.

Unlike thermal tempering, the processing temperature for this chemical process is well below the glass transition temperature, so the possibility for geometric distortion is minimized. More importantly, the resulting compressive stresses are significantly greater (approaching 1 GPa).

The process also allows much smaller glass parts to be strengthened, providing a significant reduction in weight for the given application. However, the process may take several hours or even days to achieve the desired result. Because the stated advantages over thermal tempering come at a cost, its application may be limited to advanced civilian or military uses.

Figure 2-1. Representative residual stress profiles for strengthened glass cross-sections as viewed through the side of a semi-infinite glass plate. A) Thermally strengthened glass and B) chemically strengthened glass. Note the differences in stress magnitudes and stress gradient severity.

Figure 2-2. Schematic of the ion exchange process. The glass A) before and B) after processing. The wedging of the large salt ions into the smaller spots once filled by glass ions leads to the development of residual compressive stresses in the exchanged regions as the glass cools.

Figure 2-3. Process of stress development due to ion exchange for a semi-infinite plate in the x- and z- direction as viewed through the cross-section. The schematic shows the glass A) before and after ion exchange, B) if free expansion were allowed, and C) when compatibility criterai is enforced (Repoduced from Varhsneya (1994) [11])

CHAPTER 3 RESIDUAL STRESS DISTRIBUTION

Background

A convenient and popular method to determine residual compressive stresses in glasses is photoelasticity. It is a fully mature technique for full-field stress analysis of structural components, dating back almost 150 years to the first observations of birefringence made by

Brewster in the 1850s. In particular, this method has been extensively used to analyze residual stresses in transparent materials such as glasses [17-20]. The induced stress-state, either internal or external, can cause a phase difference in the incident polarized light passing through the stressed material. This difference is directly related to the level of stress in the material. There are two typical arrangements that can be used to acquire birefringence data: a plane polariscope or circular polariscope [21]. In the plane polariscope arrangement both isoclinics and isochromatics are obtained as opposed to only the isochromatics in a circular polariscope.

Isoclinics are loci of points at which the principal strain orientation is the same and isochromatics are loci of points at which the maximum shear stress in the viewing plane are constant. In this study only the isochromatic fringe orders will be analyzed in order to obtain the steep residual stress profile beneath the strengthened surface and to determine the magnitude of maximum residual compressive surface stress. It is also important to note that the density of fringes is directly proportional to the stress gradient [22].

ASTM standard C1422 – 10 [23] details the method by which residual stress measurements in chemically strengthened glasses should be made to determine the case-depth of compressive layer and the stress profile. This standard has inherent difficulties which can lead to problems in data accuracy, equipment costs and ease of implementation. Most notably, the procedure for the measurement of the residual stress using birefringence compensators can be 26

confusing and often subjective to accurately implement for glasses with high magnitude of surface compression and steep stress gradients just below the strengthened surface. For example, the use of a suitable compensator, such as a Berek compensator, leads to some level of subjective judgment as to whether the (dark) zero order fringe has been moved to the proper location (i.e. the sample edge).

In Chapter 3, a simpler, more robust technique is utilized to determine not only the high residual compressive stress level but also the steep gradient in the stress profile within tens of microns depth beneath the surface of an ion exchanged glass specimen. Thus, the objective of the current study is to examine and analyze the spatial variation of residual stress profile in the chemically strengthened glass using a photoelastic fringe counting method.

Materials

Rectangular bars of as-received (untreated) and chemically strengthened lithium aluminosilicate glasses were obtained from Saxon Glass Technologies. The residual stress in the strengthened glass has a composite profile as a result of a two-step ion-exchange process: an exchange of potassium (K+) ions for sodium (Na+) ions which produces a relatively short (tens of microns) but high magnitude compressive stress profile followed by a shallower compression profile due to the exchange of Na+ ions for lithium (Li+) ions to a depth of approximately 1 mm beneath the surface. Initially, “thick” glass bars of dimensions 23 mm x 9.9 mm x 7.6 mm were used with the intent of determining the complete residual stress profile (Figure 3-1A). Select surfaces from this strengthened glass were ground and polished off in order to remove the strengthened layer of glass material up to a depth of approximately 1 mm on two opposite sides of the rectangular bar. These polished surfaces were referred to as “unstrengthened” surfaces so as to differentiate them from the as-received glass surfaces. The intent is to utilize these two

surfaces to probe the residual stress profile beneath the strengthened surface by passing polarized light through these unstrengthened surfaces. When light is passed through the unstrengthened surfaces in the circular polariscope arrangement, the resulting fringe pattern will reflect the stress gradient from the top and bottom strengthened surfaces to the interior of the specimens [18]. Due to the relatively large thickness of this specimen, it is difficult to fully discern the photoelastic fringes closest to the edge of the specimen (within a few tens of microns depth), where a steep stress gradient is expected. Therefore, “thin” glass specimens of dimensions 24 mm x 8.4 mm x

0.71 mm (Figure 3-1B) were prepared to improve spatial resolution of the fringes under an optical microscope at high magnification and to determine the maximum magnitude of compressive stress on the glass surface.

Experimental Method

A circular polariscope in dark-field arrangement fitted with a digital camera was employed to image the photoelastic (isochromatic) fringe patterns resulting from the residual stresses introduced into the strengthened glass. The rectangular glass bars were first imaged under white light to obtain colored fringes so as to determine the zero order fringe (black), which denotes the transition from compressive stress to tensile stress. The location of this zero order fringe also represents the depth of the compressive stress zone beneath the strengthened surface.

By observing the evolution of the colored fringes on either side of the zero order fringe, the fringe order at any location and hence the stress value at that location can be determined. In the regions of high fringe order (e.g. near the specimen edges), crisp fringes cannot be obtained in white light for accurate fringe counting as the fringes become highly diffused. Therefore, it becomes essential to view the fringes under monochromatic light where crisp fringes can be obtained for precise fringe order measurement [22]. In this study, a green optical bandpass filter

(centered on 550 nm) was used to increase the fringe contrast. The fringes appear as distinct black lines on a uniform green background. Thus, white light is used to determine the zero order fringe (using colored fringes) and green filtered light is used for high fringe order measurement, especially in regions where the stress gradient is steep (i.e. close to the edge). For improved resolution, the polariscope was also coupled to an optical microscope (Olympus model BX51) with light polarizing capabilities.

An important constraint for using thick specimens is the likelihood of perspective foreshortening. Due to the angle at which the specimen is being viewed through a camera lens or microscope objective, perspective foreshortening occurs which yields an image exhibiting invalid fringe pattern and spacing. This optical anomaly is mitigated by aligning the center of the camera lens or microscope objective along the edge being analyzed, thereby avoiding the overlapping of fringes from different planes and providing crisp fringes for accurate fringe counting. The occurrence of foreshortening is related to the thickness through which polarized light must pass through the sample. Foreshortening is minimized by using a thin sample, which provides a more accurate estimate of stress close to the edge.

Once the isochromatic fringe orders have been ascertained, the principal stress difference along any fringe can be determined by [21],

σ1 – σ2 = N λ / c h (3-1) where N is the fringe order, h is specimen thickness in the viewing direction, λ is the wavelength of the light and c is the stress-optic coefficient (3.15 Brewsters, 1/Pa, for the strengthened glass)

[3]. For fringes measured at the edge of the unstrengthened surface, the maximum surface compressive stress can be determined directly by recognizing that the stresses perpendicular to this edge becomes zero (σ2 =0). Equation 3-1 then readily yields σ1.

Results and Discussion

Under white light, the isochromatic fringe patterns viewed through the unstrengthened surface revealed high fringe orders along the specimen edges, as shown in Figure 3-2A. A schematic illustrating the viewing direction is given in Figure 3-2B. A higher magnification image of these fringes is shown in Figure 3-2C. From this image, the zero order fringe can be identified as a dark black fringe amidst colored fringes [24], indicating a case-depth of approximately 0.8 mm. Additionally, knowing that along the glass periphery the stress state is compressive and in the interior it is tensile, the stress gradient directions were readily established. However, the fringes viewed through the unstrengthened surface under white light became too diffused as the edge of the strengthened surface was approached (due to high stress gradient) and therefore, the fringes could no longer be accurately counted (Figure 3-2C).

Significant improvements in fringe contrast were gained through the utilization of a green optical bandpass filter (550 nm) and an optical microscope (10X objective) as illustrated in Figure 3-3. It is seen that there are 15 fringes in the compressive zone and ~2 fringes in the tensile zone. Note that the fringe density increased towards the edge, reflecting a steep stress gradient in the stress value as the sample edge (i.e., strengthened surface) was approached. Using Equation 3-1, the maximum compressive stress was determined to be 265 MPa on the surface and the maximum tensile stress was 44 MPa in the interior of the specimen. The maximum compressive stress value was significantly less than the reported surface compressive stress which ranged between

650 MPa and 1 GPa in the strengthened glass [3]. This discrepancy equated to an estimated 22 to

42 unresolved (or missing) photoelastic fringes close to the edge.

Using Equation 3-1, the fringe order data was converted into principal stress differences.

Figure 3-4 shows the residual stress profile as a function of position (depth) from the

strengthened surface. This plot is directly proportional to the maximum shearing stress distribution integrated through the specimen thickness in the viewing direction. For equilibrium, the area above and below the curve should be equal. In this case, the tensile zone is 15% greater compared to the compressive zone. This difference was attributed to an inability to resolve additional fringes close to the edge in a thick specimen. Thus, although the long range compressive stress and the tensile stress profiles can be easily determined using a thick specimen, the limitation of the current optical set up is an inability to accurately resolve the fringe count and the associated stress value closest to the edge of the specimen.

From Equation 3-1, note that the number of fringes N is directly proportional to the thickness h. Therefore, a significant reduction in sample thickness results in a proportional reduction in viewable fringes and hence a higher accuracy in determining the fringe orders close to the edge. A thinner specimen of 0.71 mm (7.2% of the original sample thickness), shown in

Figure 3-1, was obtained by polishing the thick sample for further analysis. The thinner sample resulted in a proportional decrease in the number of expected compressive stress fringes.

Conversely, one fringe in the thin sample is approximately equivalent to ~14 fringes in the original (9.9 mm) sample.

The thin glass sample was first analyzed in white light using a circular polariscope coupled with an optical microscope in order to determine the total compressive stress fringe count close to the edge. It can be established from Figure 3-5 that the two interior fringes (black) are zero order fringes, while the very fine fringes closest to the edge represent 4 whole compressive fringe orders when viewed using a 20X microscope objective. It was noted that 4 compressive fringe orders exist within a narrow region 25 microns from the strengthened surface. By comparison, 4 fringes in the thin specimen equate to a residual compression 4 times

the magnitude of what was measured in the thick specimen. Using Equation 3-1 for the thin specimen, the compressive stress near the surface is now estimated to be 984 MPa. According to the ASTM standard which allows for linear extrapolation, the maximum value could be expected to be around 1075 MPa. Given the immense stress level and narrow region within which these stresses exist, this indicates a steep stress gradient in this narrow 25 micron region.

Figure 3-6 illustrates the compressive stress profile obtained by combining the results from the two specimens. Note that the majority of the steep stress gradient exists in a narrow 25 micron region, where the compressive stress decreases from close to 1 GPa to around 300 MPa and beyond this depth the earlier profile obtained from thick specimen can be used to construct the residual stress profile. Considering the equilibrium condition, the force balance (difference in the areas under stress vs depth profile) between the compressive and tensile exhibits a less than

2% discrepancy which further validates the measured stress value using the above approach.

To further verify the fringe order observed in the above configuration, a similar analysis was performed on a sample placed in an index-matching immersion oil to enhance the fringe contrast (Figure 3-7). The immersion oil is a transparent oil with specific optical characteristics and when used in conjunction with optical microscopy, it improves the spatial resolution of the optical microscope by a factor of 1/n, where n is the refractive index of the fluid (n = 1.5) [25].

This is due to the reduced refraction of light entering the microscope lens as well as the increased numerical aperture of the objective lens that occurs when viewing the sample immersed in index- matching fluid. Although the specimen edges experienced minor blurring, the photoelastic fringes became crisper and allowed for more accurate fringe counting. Both approaches conclusively illustrated the presence of 4 whole fringe orders.

Although there appears to be a partial fringe order beyond the fourth compressive stress fringe (Figure 3-5B and Figure 3-7B), the optical limitations of the setup do not allow for accurate identification of a possible fractional fringe order. As well, the greatest power objective that could be employed was the 20X primarily due to limited working distance of typical microscope lenses compared to the distance required to focus on the fringe patterns. It should also be noted that the maximum fringe order observed was not constant along the edge of the sample. This was due in part to the polishing process used to prepare the thin glass specimen where small fragments (a few microns in size) were chipped away from the perimeter of the sample and the fringe order was slightly lower in these areas. Because the stress distribution is so highly localized to the extreme exterior of the glass specimen, material loss at the outer most edges during sample preparation resulted in reduced maximum fringe order in these regions.

Thus, the maximum surface compressive stress value determined using the above method is consistent with the values determined by measuring retardation with a compensator as well as modulus of rupture (MOR) values of 1 GPa using a ring-on-ring setup, given by Varshneya and

Spinelli [3]. However, one may be interested in quantifying the uncertainty in the current method. Examining each of the terms in Equation 3-1 for sources of error, it is noted that the error in partial fringe counting is approximated to be around 0.16. However, for whole fringes the counted fringe value does not yield appreciable error. The error associated with the optical bandpass filter for green light at 550 nm (Melles Griot model F40-550.0) is related to the tolerance of the bandwidth of allowable wavelengths (± 36 nm). The stress-optic coefficient, which is an experimentally determined value, is a material constant and is not dependent on the method used. This value was taken from literature [3]. Finally, the error associated with the

measurement of specimen thickness is ± 0.002 mm. Using the root-sum squared method given in

Equation 3-2, the uncertainty of various aspects of this analysis were found as shown below,

2 0.5 Uσ = [ ∑(θi • ui ) ] (3-2) where θi = ∂σ/∂Xi, Xi is the given variable and ui is the error associated with the measurement of that variable. The largest uncertainty corresponded to the measurement of the maximum surface compressive stress. Accordingly, the near-surface compressive stress calculation (984 MPa) was found to have an uncertainty of ± 6.6% (65 MPa). Recall that the maximum compressive stress measurement is based on linear extrapolation of the stress profile. If a conservative estimate of uncertainty in fringe count (ui = 0.5) is considered for the maximum surface compressive stress which lies beyond the last measurable whole fringe near the specimen edge, then the uncertainty increased to ± 14.2% (153 MPa). All other values measured exhibited less than 5% uncertainty.

The utility of the high levels of surface compressive stress and large case-depth in the strengthened glass can be seen for numerous applications where high strength and fracture resistant surfaces are required. These applications include windshields for aircraft which must endure being struck by foreign objects (e.g., birds), and solar energy harvesting panels in extreme desert environments where the panels have to withstand high-velocity impacts by small sand particles or under hail storms. It has been found that large compressive stresses introduced into the glass surface can effectively suppress radial crack formation [26-29] during Vickers indentation. The high surface compressive stress levels are expected to improve the surface hardness in the compressive zone compared to the as-received (untreated) glass samples. In fact, ion-exchange methods have been shown to also result in elevated values of elastic modulus, apparent fracture toughness, Weibull modulus and modulus of rupture (MOR) [3, 30].

Conclusions

The residual stress profile due to the chemical exchange process was determined on a thick and a thin strengthened glass specimen using a simple photoelasticity approach. While the thick specimen provided the residual compressive and tensile stress profile at larger depths, the thin specimen provided a more accurate description of the compressive stress profile with in a small depth close to the edge. In the thick specimen, a total of 15 compressive stress fringes corresponding to a maximum surface compressive stress level of 265 MPa, and around 2 tensile fringes corresponding to a maximum tensile stress level of 44 MPa were observed. However, the optics used for the thick sample could not resolve the high density of fringes resulting from high stress gradients close to the edge. Utilizing high magnification optics on the thin specimen the number of fringes were proportionally reduced to 4 fringe orders, which corresponded to a maximum surface compressive stress of 1075 MPa close to the strengthened surface. It was determined that a large stress gradient exists close to the edge of the sample and the stress level dropped rapidly to ~300 MPa within a short depth of 25 microns in the strengthened glass.

Lastly, residual stress measurements in chemically strengthened glasses can often prove to be difficult and confusing to conduct using ASTM standard C1422-10 [23]. Consequently, the technique of direct fringe measurement used in the current study to analyze the strengthened glass demonstrated a more effective and straightforward method than the birefringence compensation technique noted in ASTM standard C1422-10 [23].

Figure 3-1. Images of the glass specimens. The A) thick (9.9 mm) and B) thin (0.71 mm) specimen. The strengthened and unstrengthened glass surfaces are indicated accordingly.

Figure 3-2. Imaging the photoelastic fringe patterns using white light in a circular polariscope. A) Dark field photoelastic fringe patterns for the thick (9.9 mm) specimen B) as viewed through the unstrengthened surface of the strengthened glass, and C) an enlarged image of the bottom edge of the unstrengthened face which illustrates the large number of fringes and increasing fringe density toward the edge. Note that the camera was positioned and focused on the bottom edge of the sample to eliminate perspective foreshortening.

Figure 3-3. Micrograph of the isochromatic fringe patterns as viewed through the unstrengthened face of the thick (9.9 mm) specimen. The image was taken using a 10X objective and a circular polariscope (dark-field arrangement) with a green optical bandpass filter centered on 550 nm. A total of 15 whole fringes in the compressive region and 2 whole fringes in the tensile region are observed.

Figure 3-4. Residual stress profile determined by photoelasticity using a thick (9.9 mm) specimen and a circular polariscope in dark-field arrangement.

Figure 3-5. Photoelastic fringe patterns of thin (0.71 mm) glass specimen as viewed through circular polariscope using white light. A) Full-field image of thin specimen, B) a photoelastic micrograph of the edge of the thin glass sample as viewed using a 20X objective, and C) an enlarged view of the last 30 microns of the sample revealing additional fringes near the sample edge. The viewable fringe orders are indicated.

Figure 3-6. Complete residual stress profile in strengthened glass specimen determined by photoelasticity. The near-edge profile was determined using the thin (0.71 mm) sample and the bulk profile was determined using the thick (9.9 mm) sample.

Figure 3-7. Photoelastic micrographs of the edge of the thin (0.71 mm) glass sample utilizing index matching oil. A) As viewed using a 20X objective and B) an enlarged view of the 4 compressive stress fringes.

CHAPTER 4 STATIC AND DYNAMIC INDENTATION RESPONSE

Background

To quantify the strengthening that results from the ion exchange process it is necessary to determine the mechanical properties of the strengthened material. A common material property that is easy to determine and has been shown to relate to impact performance is indentation hardness. Indentation hardness has been related to the early part of projectile interaction with impacted material and consequently to blunting and erosion of the projectile [31-35]. Despite numerous attempts to relate impact performance to mechanical properties, hardness is one of the only commonly agreed upon properties with strong correlation [34, 36-38]. Furthermore, because of the ease of implementation and cost-effectiveness of static indentation measurements, hardness has become a popular metric for material characterization [39]. However, this method does not capture the rate sensitive behavior of brittle materials due to the long loading duration

(15 seconds) which results in quasi-static deformation. On the other hand, the use of dynamic hardness experiments [39, 40] can provide such information by generating high-rate indentations which in turn can be used to gain insight into the effects of strain rate on hardness and indentation-induced damage.

Literature exists of indentation studies examining the influence of residual stress on hardness [41, 42], but these studies do not address the rate sensitivity of hardness due to residual stresses. As well, various investigations have been performed to examine the static and dynamic

Vickers hardness of ceramics and brittle materials [39, 40, 43-46], but little is known of the rate- sensitive indentation behavior of strengthened glasses, such as Ion-Armor™. Furthermore, a number of studies have explored the residual stress profile with depth resulting from the strengthening process [4, 9, 18, 47], but, to our knowledge little is known with regard to the 41

subsurface hardness profile as a function of depth for a strengthened glass with ultrahigh residual compressive stresses. Such studies allow for the determination of the extent of the surface strengthening process and the influence of resulting residual stress on the measured hardness values.

In Chapter 4, indentation experiments were utilized to both qualitatively and quantitatively assess the effects of ultrahigh residual compressive stresses (due to ion exchange) on the static and dynamic indentation response of a new class of chemically strengthened glass, called Ion-Armor™. This glass has been shown to attain a high level of surface compressive stress close to 1 GPa [9] and large case-depths up to 1 mm [3]. The variation in hardness with load, strain rate and depth (from the strengthened surface), as well as its indentation-induced fracture characteristics are examined to assess the utility of such glasses for applications where high transparency and strength are desired. Photoelasticity was employed to determine the subsurface residual stress profile with depth.

Materials

Rectangular bars of as-received and chemically strengthened lithium aluminosilicate glass with dimensions 23 mm x 9.9 mm x 7.6 mm (Figure 4-1A) were obtained from Saxon

Glass Technologies. The strengthened bars were chemically strengthened in mixed molten salt baths of potassium (K+) and sodium (Na+) ions using a procedure discussed by Varshneya and

Spinelli [3]. Recently, Jannotti et al. [9] conducted systematic photoelasticity studies which determined that the surface compressive stress developed reached ~1 GPa, while interior balancing tensile stress were 37 MPa. Select surfaces (Figure 4-1A) of these strengthened bars were ground and polished off in order to entirely remove the strengthened layer of glass material up to a depth of approximately 1 mm. These surfaces were referred to as “unstrengthened”

surfaces so as to differentiate them from the as-received glass. These unstrengthened surfaces will be used to probe the mechanical response of the material beneath the strengthened faces from the outer exchanged (compressive layers) into the interior (tensile zone) of the glass bars.

Experimental Method

Static and dynamic indentations were conducted to ascertain the influences of load, residual surface compressive stress and strain rate on the measured hardness values and indentation-induced damage evolution. Load ranges for hardness measurement were limited to avoid excessive cracking and material removal. Static hardness values were averaged based on at least 10 individual indents at a given load to provide a representative hardness value. The dynamic hardness values were not averaged because the load level for each indentation was different due to varying indenter velocities. For both static and dynamic Vickers indentation, the indent diagonal lengths and load (measured from the load cell) were used to determine the hardness. Nanoindentation hardness values were determined based on the Oliver-Pharr method.

The static Vickers indentation experiments were performed using a standard hardness tester (Wilson® Instruments Tukon™ model 2100B) with a Vickers diamond indenter tip.

Ultralow load indents (1 mN) were made using a nanoindenter (Hysitron triboindenter) with a

Berkovich tip to determine the maximum increase in hardness due to the thin layer of ultrahigh compressive stress (~1 GPa) existing nearest the strengthened surface. The static indentation loading durations were approximately 15 seconds. Dynamic indentations were then performed using a custom-made dynamic indentation hardness tester (DIHT) as illustrated in Figure 4-2.

The utility and operating principles of dynamic indentation hardness measurements are well- described on metals and ceramics in literature [39, 40]. The DIHT consists of a long rod (or incident bar) with an indenter inserted at one end and a flange-sleeve-rigid mass assembly, also

known as a momentum trap, at the other end [48]. The specimen whose hardness is to be determined is placed on top of a high frequency (~200 kHz) load cell (Kistler model #9213).

This load transducer is anchored to a rigid base. The indenter tip is brought into contact with the specimen before the dynamic indentation. A striker bar is launched from a gas gun towards the flanged-end of the incident bar. The impact of the striker generates both a compressive stress wave followed by a tensile stress wave (due to the momentum trap) in the incident bar. The momentum trap ensures that only a single compressive pulse reaches the indenter tip and the rest of the waves are rendered tensile while travelling towards the indenter tip. Therefore, the indenter tip moves forward into the specimen only once, causing the desired indentation, and then retracts back in several incremental steps. Thus, a single indentation is achieved on the specimen within a short loading duration. The loading duration of indentation is proportional to the length of the striker bar, while the depth (or load) of indentation depends on the velocity of the striker bar. Typical loading durations using a 6 inch striker bar are on the order of 60 µs. A common question in such dynamic measurements is the strain rate of deformation. As is well known, the deformation within an indentation zone is highly non-uniform with the highest strains close to the indenter tip and gradually decreasing strains away from the tip. Therefore, an average strain rate is defined as the ratio of the indenter velocity to the average length of the indentation diagonals [39, 40]. Typically, average strain rates are around 1000/s.

Then, to investigate the hardness profile as a function of depth on both the strengthened and unstrengthened glass surfaces, static indentations were made from one edge to the other edge on both the strengthened and unstrengthened surfaces at a load of 1.96 N (0.2 kg). Recall that the chemical strengthening of glass causes residual compressive stresses up to certain depth from a strengthened surface and that the unstrengthened surface has been polished to remove the

strengthened layer. Furthermore, the residual stress state and magnitude change with depth from the edge of the strengthened surface. By measuring the hardness on the lateral surface (indicated as “unstrengthened” in Fig. 4-1) from one edge to the other, the influence of residual stresses on the hardness (increased or decreased compared to the as-received glass value) will provide indication of the extent and influence of the compressive stresses present from the strengthened surfaces down to a certain depth. Such a procedure is commonly employed in materials which have been case hardened [22, 23].

All Vickers indentations were examined using an optical microscope (Olympus model

BX51) with Nomarski interference contrast capabilities. The indents were observed using both bright-field microscopy as well as differential interference contrast microscopy (DIC). All measurements of indentation diagonals were made immediately after each row of indents was completed. Measurement accuracy was ± ~3%. Also, note that all comparisons between measured hardness values on the strengthened and raw glass surfaces under static and dynamic loading were made at the same indentation load of 19.6 N (2 kg). Finally, a circular polariscope with white light and green filtered light (550 nm) was employed to image the photoelastic fringes patterns evolved due to the residual stresses in the strengthened glass. Under white light, the coloured fringes facilitated the detection of compressive and tensile stress regions as well as the zero order fringe (dark band) which represents the stress free zone. The zero order fringe also indicates the transition from compression to tension [19]. For low fringe orders, analysis under white light was appropriate; however, higher order fringes become diffused toward the edge of the specimen and the exact fringe order could not be accurately discerned. Therefore, a green optical bandpass filter (monochromatic light) was used while imaging the higher order fringes to improve image contrast. Nevertheless, the common problem in photoelastic measurements is a

limitation in spatial resolution, especially in regions of severe stress gradients (high fringe density). This is easily resolved by minimizing the specimen thickness (in the viewing direction), which drastically improves the resolution.

Results and Discussion

Surface Indentation Hardness

The static and dynamic hardness values of the strengthened and the as-received glass surfaces are plotted in Figure 4-3. Static hardness values are denoted by empty points while dynamic hardness values are denoted by solid points. Likewise static hardness trends are denoted by dotted lines and dynamic trends are given by the solid lines. It is important to note that unlike the static hardness data, each dynamic data point represents one hardness value at one specific load level (based on striker bar velocity). It is evident from Figure 4-3 that all of the hardness measurements (static and dynamic) exhibited a load-dependence, known as the indentation size effect [49, 50]. For brittle materials, the indentation size effect (ISE) is well documented [39, 51-

54]. The ISE is observed as a decrease in hardness with increasing indentation load. Beyond a certain load a constant hardness value is reached, but this specific load is material dependent.

Although it was observed that the measured hardness began to level off once a certain indentation load was reached, incipient cracking at greater loads did not always allow for the determination of the exact load at which the hardness values became constant. This is a common concern while testing brittle materials due to their increased propensity for cracking.

After analyzing the hardness measurements as a function of load under static and dynamic indentation, the beneficial effects of the ion exchange process on the indentation hardness could be inferred. From Figure 4-3 it was observed that the hardness of the strengthened surface was greater than that of the as-received glass. Under static loading, the

hardness was 5.80 ± 0.27 GPa for the strengthened glass and 5.32 ± 0.05 GPa for the as-received glass. Under dynamic loading, the hardness was 7.15 GPa for the strengthened glass and 6.44

GPa for the as-received glass. Because each data point represents an individual indent (rather than an average) and there is no repetitive sampling at specific loads, no measurement error is reported for average dynamic hardness. The strengthened surface showed an increase in both static and dynamic Vickers hardness of 9.0% and 11.0%, respectively, compared to the as- received surface at a load of 19.6 N (2 kg). These findings are consistent with previous studies where compressive stresses were shown to result in elevated hardness values [30, 41, 42]. The errors reported above take into account only the error incurred due to scatter in material response. The optical measurement uncertainties introduced by the image resolution are less than

1% and are negligible.

The observed increases in static and dynamic hardness can be readily attributed to the high levels of residual compressive stress present on the strengthened glass surfaces. Recall that during the ion exchange process the surface of the ion exchanged glass is heavily flooded with larger Na+ and K+ ions. Due to the wedging of these larger ions into the glass matrix, large residual compressive stresses (determined to be close to 1 GPa [9]) were generated along the in- plane direction. Such high levels of in-plane residual compression strongly resist the penetration of the indenter, giving rise to notably greater hardness values compared to that of the as-received glass. Essentially, the residual compressive stresses provides an opposing force to the applied force reducing the net applied force which contributes to the indentation. Thus, this leads to increased apparent hardness. Additionally, the compression yields increased hardness due to the nature in which is influences the indentation deformation behavior of the glass. Recognize that inelastic deformation of the glass surface during indentation is accommodated largely by shear

sliding along shear fault lines punched into the glass surface. The residual compression can provide a closure force on the fault lines making relative slippage more difficult, thereby resisting downward penetration of the indenter by inhibiting shear sliding. In fact, studies by

Chen et al. (2006) [55] and Haag et al. (2014) [56] have shown that in-plane compressive stress can reduce the plastic zone size beneath the indent and provide increased resistance to plastic deformation leading to increased hardness. The influence of compression on the indentation deformation characteristics will be discussed in more detail in the next section, Indentation

Damage Evolution.

Other influencing factors induced by ion exchange can include modification of material properties such as elastic modulus and density. Studies by Kese et al. [41] showed that compressive stresses can present a notable effect not only on the hardness, but also on the elastic modulus. As the elastic modulus was observed to exhibit proportionality to indentation hardness

[13], an increase in elastic modulus due to high levels of residual compression would then be expected to predict elevated values of hardness. Lastly, one cannot forget that the strengthened case layer is a stuffed-derivative of the parent glass which has a greater density. Li et al. (2014)

[57] have drawn a link between the denser ion exchanged glass and increased hardness.

Similar improvements in hardness values were observed due to increased strain rate

(Figure 4-3). The dynamic hardness of the strengthened glass was 23.3% greater than its static hardness. In addition, the hardness of the as-received glass showed a 21.1% increase in hardness under dynamic loading compared to its static hardness. The enhancement of hardness observed under dynamic loading rates is a beneficial trait for a material that is intended to be used for resisting high-velocity impacts (i.e. solar panel covers in extreme desert environments or transparent armor applications). As well, it further highlights the importance of material testing

under high loading rates for materials intended for dynamic applications. These results are in line with established high strain rate literature on ceramics in which mechanical properties, such as

Vickers hardness, were found to increase with loading rate [46, 58]. Also note that the dynamic indentation hardness could be accurately determined at significantly greater load levels because of the reduced damage surrounding the dynamic Vickers imprint.

Indentation Damage Evolution

By analyzing the optical micrographs of static and dynamic indentations, it was possible to assess the influences exhibited by residual stress and loading rate on the damage evolved under comparable indentation load levels. Figure 4-4 illustrates a comparison of the indentation- induced damage patterns due to static indentations on strengthened and as-received glass surfaces at the same load levels. The measured hardness and load level is also indicated on each micrograph. Under static loads, little or no damage/cracking is seen on the strengthened surface until a load of 9.8 N (1 kg) is reached, as evidenced by Figure 4-4A. Only shear fault lines were observed to run parallel to the edges of indentation impressions. On the other hand, the as- received glass exhibited minor cracking at 2.9 N (0.3 kg) (not shown for brevity), as well as shear faulting, radial cracking and lateral cracking at 9.8 N (1 kg), as shown in Figure 4-4B. The results indicated that the presence of compressive surface stresses acted to suppress the appearance of radial cracking which was so prominent in the as-received lithium aluminosilicate glass. The micrographs also illustrate a visible transition in the deformation behavior. The indent imprint in the strengthened glass showed increased shear faulting, due to increased shear deformation. As has been noted above, the high levels of residual compression act to confine the plastic zone beneath the indentation. This leads to increased localization and accumulation of strain and shear flow on individual shear lines. This is especially pronounced at the surface

which leads to enhanced shear faulting and material ‘flow’ towards the glass surface (i.e., pile- up). Haag et al. (2014) [56] demonstrated that residual compression in bulk metallic glasses led to an increased number of shear steps on the surface with larger step heights (i.e, more discrete shear lines). The inelastic deformation in the as-received glass can be described as being more homogenous with less surface-concentrated shear flow. This leads to less pile-up and shear bands which cannot be visibly resolved on the surface.

Despite the sole influence of the residual compressive stress on the indentation response, it is important to examine the additional influences of strain rate on the observed indentation- induced damage progression. The micrographs presented in Figure 4-4C and Figure 4-4D illustrated the damage evolved due to dynamic indentations. At a low load of 13.3 N (1.36 kg), the strengthened surface revealed minimal crack development. Only shear faults were formed along the periphery of the imprint. The influence of strain rate on the indentation-induced damage can be attributed to a transition in the inelastic deformation modes between shearing and densification. For high rate indentation, the contact times are dramatically reduced: 100 microseconds compared to 15 seconds. As the indentation process occurs more rapidly, less time is available to nucleate and grow cracks. As well, this means less time to accommodate shear deformation. Instead, the glass is forced to densify by hydrostatic compression as the glass cannot be displaced out of the path of the indenter in time. This is evidenced in the micrographs as a reduction in shear faults under dynamic loading (Figure 4-5). As the shear component of indentation deformation leads to increased residual stresses and increased residual stress-driven cracking compared to the hydrostatic component, reduced shearing at high strain rates reduces the indentation-induced residual stresses which can drive cracking. As well, recall that the presence of shear lines (indicative of increased severity of shear deformation) leads to more

points of crack nucleation as flaws are presumed to emanate from the intersection of the shear lines. Clearly, reduced cracking in strengthened glasses can be further enhanced at increased strain rates.

Although it is typical to observe the evolution of radial crack systems emanating from the corners of Vickers indentation impressions (Figure 4-4B and Figure 4-4D) in brittle materials such as glass [59], the high level of residual compressive stress present on the strengthened surface suppressed radial crack formation up to 147 N (15 kg) under static indentation and for all load ranges examined under dynamic indentation. In fact, no radial cracks were observed under dynamic up to almost 200 N (not shown for brevity). Additionally, the reduction in shear faulting due to increased strain rate is more easily observed at high loads (Figure 4-7). As it has been proposed by Hagan [60] and Lawn et al. [61] that shear faults are sources of median, radian and lateral cracking, it is clear that the ultrahigh surface compressive stresses acted to inhibit surface crack initiation (most notably radial cracking) despite the significant amount of shear faulting observed at high loads above 100 N. Beyond 98.1 N (10 kg), static indentations exhibited notable cracking (namely lateral cracks). These lateral cracks initiated prior to surface evidence of radial crack formation, similar to what has been observed in literature [62], suggesting that in the presence of ultrahigh levels of residual compression radial cracking occurs secondary to lateral cracking. Because lateral cracks grow parallel to the in-plane compressive stresses they are less inhibited by the stresses. Once formed the ion-exchange-induced compression can keep the cracks growing approximately parallel to the surface as observed by [63]. At a load level of 147

N (15 kg), radial crack formation was observed. As radial cracking becomes operative, the radial cracks intersect with already growing lateral cracks to form large regions of material removal, or spallation. In this way, lateral cracking and spall can become more severe in strengthened glasses

as the residual compression can force the cracks to travel longer distances before merging with surface. As radial cracks are commonly viewed as strength-limiting flaws, the critical indentation load threshold at which radial cracking is observed can be viewed as an important parameter for materials design. This type of information is useful in quantifying the beneficial fracture resistance offered by ion exchanged glass. Here, the compressive stresses of ~1 GPa yielded increased resistance to radial cracking of ~1400% based on the load at which consistent radial cracking was observed.

Subsurface Indentation Hardness Variation

The ion exchange process results in high residual compressive stresses on the surface and a severe stress gradient with depth below the strengthened surfaces. The stress state is then tensile in the interior region (Figure 4-1) so as to satisfy overall equilibrium conditions. For this reason, it is of particular interest to explore the spatial variation of mechanical properties as a function of depth on both the strengthened and the unstrengthened surfaces. Recall that the glass specimens being investigated in this study are only partially surface strengthened, because select surfaces (referred to as the unstrengthened surfaces in Figure 4-1) have been polished to remove the strengthened layer so as to expose the subsurface material. Static microindentation was therefore used to characterize the residual stress profile based on the influence of residual stresses on hardness variation. Vickers hardness measurements were conducted across the entire length of the strengthened and unstrengthened surfaces.

Hardness measurements on the strengthened surface showed that the hardness remained approximately constant (6.12 ± 0.06 GPa) from one edge to the other and, thus, are not shown for brevity. This indicated that the strengthening process resulted in consistent improvement to the properties across the entire strengthened surface. This is expected as the residual stress on the

surface should be uniform in magnitude and vary only with depth below the strengthened surface. On the contrary, the subsurface hardness profile on the unstrengthened surface showed appreciable gradation in hardness values from the edge into the interior region. The subsurface hardness profile (Figure 4-8) was plotted as the change in hardness compared to the as-received hardness value, referred to as the hardness increment. Clearly, near the edges the hardness is significantly increased over the as-received glass hardness value, while the interior region exhibits a slightly lower hardness value compared to the as-received glass value.

To further quantify the relationship between the residual stress state and the indentation hardness, photoelasticity was employed. When polarized light passes through a birefringent material (such as glass), the light is split into two different wave fronts, each oriented parallel to a principal stress direction and travelling at a different velocity [22, 24]. Using a circular polariscope, the resulting fringe patterns were correlated to residual stress levels and related to the hardness. As detailed in Jannotti et al. [9], the overall residual stress profile in the bulk specimen can be determined using a thick specimen and a typical polariscope, but a thin specimen and high magnification optics are required to determine the ultrahigh compressive stress levels near the edges (within tens of microns). The entire residual stress profile is shown in

Figure 4-8. The compressive stress level on the strengthened surface is close to 1 GPa, decreasing rapidly to less than 300 MPa within 25 microns. The stress profile in the examined specimen gradually tended to zero in the bulk specimen at a depth of 0.9 mm from the surface where the zero order fringe is indicated. Beyond this depth the residual stress state becomes tensile in the glass interior and approximately constant at 37 MPa.

By superposing both the trends in the residual stress state and the hardness, the influence of residual elastic stresses on the indentation response can be determined (Figure 4-8). As noted,

the highest hardness value occurs at the edges where the highest residual compressive stresses exist. Moving inwards the hardness decreases as the stress state becomes increasingly more tensile. This hardness profile is consistent with the reported typical residual stress profiles in strengthened glass [17, 47, 64]. Notice that a steep drop in hardness occurs just below the surface due to the severe residual stress gradient beneath the strengthened surface. The hardness trend becomes more gradual where the stresses and stress gradient became more moderate. Once the stress state became constant, so too did the hardness trend. Beyond ~1.2 mm, the measured hardness dropped below the as-received hardness and became constant at ~1.5 mm. This suggested that compressive stresses increased the hardness values, while tensile stresses had the potential to decrease the hardness values. However, an unexpected trend was observed from

Figure 4-8. It is clear that the residual compressive stress zone induced by chemical treatment extends only to a depth of 0.9 mm (from photoelasticity); however, the depth to which the hardness is improved over the as-received glass hardness is ~ 1.2 mm. These results suggest that improvements in apparent hardness due to the ion exchange process may extend beyond the depth of the compressive stress layer.

Just beyond the zero stress fringe, prior to the tensile stress becoming constant, there existed an anomalous tensile maximum (at 1.5 mm depth) which stretched to slightly more than

2 mm (~2.2 mm) before leveling off. At around the same time the hardness was observed to stabilize (Figure 4-8). The presence of this anomalous tensile maximum in ion-exchanged glass is well-documented in the literature [17, 65-68], but there is no unified conclusion with regards to the reason for its existence. Recently, it was speculated by Varshneya [4] that the wedging of larger Na+ and K+ ions into the Li-glass causes a significant plastic stretch of the underlying substrate structure which extends beyond the case-depth. It was reasoned that this plastic

relaxation led to the development of a tensile maximum just beyond the compressive layer.

Hence, it is proposed that the effect of these foreign alkali ions on mechanical response may also extend beyond the case-depth. Note that the wedging of the large salt ions is accommodated by both elastic and plastic strain, with the elastic strains leading to residual elastic stresses.

Therefore, a combined influence of elastic and plastic strain gives rise to the observed hardness trend.

In addition to using microindentation to characterize the residual stress profile, the hardness increments can be analyzed as a direct function of residual stress magnitude (Fig. 4-9).

In essence, the residual stress profile and hardness trend from Fig. 4-8 were combined. By plotting the hardness increment determined on the unstrengthened surface (at a 2 N indentation load) at varying depths , i.e., stress magnitudes, the change in hardness due to compressive stresses reaching -215 MPa and tensile stresses up to 37-44 MPa were revealed. Notice that the influence of the maximum compressive stresses (up to -1 GPa) were not captured by this technique. The finite size of indents placed on the unstrengthened face (30 μm at 2 N load) does not allow for hardness to be probed nearest the edge where the greatest stresses exist. Hardness values can only be determined to within 90 μm of the strengthened edge; however, the compressive stress increases rapidly from -250 MPa at 25 μm depth to -1075 MPa at the strengthened edge. As it is common for ion-exchanged glasses to contain their maximum stresses in narrow regions tens of microns from the strengthened surface, it was of interest to develop a method which can evaluate hardness changes due to the large compressive stresses and severe stress gradients just below the strengthened surface.

Rather than assessing hardness changes on the unstrengthened surface, indentation was performed on the strengthened surface. Notice that when indentation is performed on the

strengthened surface, varying stress levels in the regions beneath are probed (Fig. 4-9B). It is proposed that such a method can be used to predict the hardness behavior in the subsurface regions due to the evolving residual stresses. First, the plastic zone developed beneath the indent was approximated as a hemisphere with a radius equivalent to that of the indent impression

(described by Yoffe). Then, the stress magnitude in the deformed volume was averaged by means of integrating the residual stresses at various depths over the plastic zone and normalizing the computed value by the total plastic zone volume. The average stress value was viewed as the effective stress which acts upon the indenter during indentation, resulting in the developed impression. Thus, by performing indentations on the strengthened surface at a range of loads (1 mN to 30 N), the plastic zone sizes and, hence, the effective stress levels were varied. This allows for the determination of hardness increments at (effective) compressive stress levels of

-350 to -1015 MPa.

It can observed from Figure 4-9 that huge compressive stresses (~1 GPa) yield a comparable increase in the apparent hardness values, while modest tensile stresses (tens of MPa) result in significant reductions in the hardness values. For the maximum (effective) compressive stress of -1015 MPa, the maximum observed increase in hardness was 0.84 GPa. Comparatively, for the maximum tensile stresses of 37-44 MPa, the hardness was reduced by ~0.12 GPa. This reveals mild sensitivity of hardness to compressive stresses and significant sensitivity to tensile stresses. The trend lines in Fig. 4-9 indicated the ratio of hardness change (in GPa) per MPa of residual stress to be 3x10-3 GPa/MPa for tensile stresses and 1x10-3 GPa/MPa for compressive stresses. This denoted a three-fold increase in the sensitivity of hardness to tensile stresses compared to compressive stresses. Varying sensitivity of hardness to compression and tension is rationalized for several reasons. First, it has been demonstrated in Fig. 4-5 and Fig, 4-7 that

residual compressive stresses lead to enhanced shear deformation (evidenced by increased shear faulting). This shear faulting is proposed to lead to a softening effect, which reduces the hardness enhancement due to compressive stresses. Thus, compressive stresses yield a reduced hardness increase. Furthermore, during indentation the material itself provides intense lateral constraint for the indentation deformation. Added residual compression does not dramatically enhance lateral constraint, which leads to little change in the indentation response. On the other hand, the residual tension dramatically diminishes lateral constraint and makes the material more easily penetrated, leading to a more pronounced influence on the indentation response. This can be confirmed quantitatively by describing the yield behavior of the glass with von Mises yield criterion. The indentation problem is simplified to a case of uniaxial compression (due to indentation) along with laterally applied compression or tension due to residual stresses. The following equation can then be derived,

1 3 휎푌 = 휎 − √휎2 − 휎2 (4-1) 푁 2 퐿 푌 4 퐿

푌 where 휎푁 is the critical indentation normal stress, 휎퐿 is the laterally applied stress, and 휎푌 is the

푌 yield strength of the glass. When 휎퐿 is positive (tensile lateral stress), 휎푁 required for yielding is

푌 much smaller. When 휎퐿 is negative (compressive lateral stress), 휎푁 required for yielding is only slightly increased. This provides a quantitative basis for the aforementioned rationale. Thus, the hardness behavior is much more sensitive to residual tensile stresses.

Subsurface Indentation Damage

In order to evaluate the influence of varying stress state on damage evolution, the cracking patterns due to Vickers indentations were analyzed on the unstrengthened surface at various depths from the strengthened surface within the tensile and compressive zones (Figure 4-

10). As expected from the indentation impressions on the strengthened surface, the beneficial compressive stresses present up to a depth of 0.9 mm, the damage patterns within the compressive zone illustrated reduced indentation-induced cracking compared to the as-received glass surfaces. However, for indentations performed within the central tensile region, the indentation-induced cracking was more significant, but still in the absence of radial cracking.

The findings presented here agree well with previous studies [8, 29], as the crack growth and severity were shown to be initially reduced near the material surface due to the high compressive stresses, and as the depth increased toward the central region of the specimen, crack growth was less inhibited.

Conclusions

Static and dynamic Vickers indentation experiments on the strengthened and as-received glass surfaces revealed notable ISE and rate-sensitivity in hardness. The hardness of the strengthened glass was greater than the as-received glass under static and dynamic loading as a result of the ion exchange treatment (9.0 and 11%, respectively). The dynamic hardness values of both the strengthened and the as-received glass surfaces showed an increase over the static hardness values due to increased strain rate (23.3% and 21.1%, respectively. Additionally, the strengthened surface exhibited a suppression of radial cracking for static loads up to 147 N (15 kg) and for all dynamic loads examined. For the as-received glass, lateral and radial cracking was observed to initiate at very low loads and become increasingly more severe with increasing load levels. However, the strengthened and as-received glass surfaces both showed a significant increase in crack resistance at high loading rates. It was also observed that high levels of residual compression promoted shear deformation, while increased strain rate reduced shear faulting and enhanced densification. Indentation studies on the unstrengthened and strengthened surfaces

demonstrated a useful technique for characterizing the residual stress profile based on the change in hardness values. Lastly, residual tension was shown to profoundly influence the hardness values compared to residual compression which only slight affected hardness.

Figure 4-1. The strengthened glass specimen with exposed unstrengthened glass surface. A) Image of the rectangular glass bar with strengthened and unstrengthened (‘polished’) surfaces indicated. B) Isochromatic fringe patterns observed through the unstrengthened surface with a circular polariscope in dark-field arrangement

Figure 4-2. Schematic of the dynamic indentation hardness tester (DIHT).

Figure 4-3. Static and dynamic Vickers hardness data for various load ranges on the strengthened and as-received glass surfaces. This data reveals ISE and significant increases in material hardness under dynamic loading for both surfaces.

Figure 4-4. Micrographs of indentation-induced damage at comparable low loads on strengthened and as-received glass surfaces. Static indentation damage on A) strengthened glass and B) as-received glass. Dynamic indentation damage on C) strengthened glass and D) as-received glass. Included on each micrograph are the load and the average Vickers hardness value at that load. Note the significant decrease in damage on the strengthened glass and under dynamic loading.

Figure 4-5. Micrographs of indentation-induced shear faulting at comparable low loads on strengthened and as-received glass surfaces. Static indentation-induced shear faulting on A) strengthened glass and B) as-received glass. Dynamic indentation- induced shear faulting on C) strengthened glass and D) as-received glass. Included on each micrograph is the indentation load. Note the reduce severity of shear faults on as-received surfaces and under dynamic loading .

Figure 4-6. Micrographs of indentation-induced damage at comparably high load levels. A- B) Static indents and C-D) dynamic indents. Included on each micrograph is the indentation load as well as the hardness value at that load, if measured. Note the significant reduction in indent size and damage for dynamic indentation compared to static indentation even when the dynamic load is greater than the static load.

Figure 4-7. Micrographs of indentation-induced shear faulting on strengthened glass surfaces at comparably high loads. A-B) Static indents and C-D) dynamic indents. Included on each micrograph is the indentation load. Note the reduce severity of shear faults under dynamic loading.

Figure 4-8. Isochromatic fringe patterns near the edge of unstrengthened surface with hardness and residual stress data superimposed. Variation in static hardness with depth from edge-to-core on the the unstrengthened surface showed greater hardness values close to the edge and lower values in the central region.

Fig. 4-9. Influence of residual stress on hardness change. A) Image depicting strengthened and unstrengthened faces showing variation in stress, i.e., fringes, below the strengthend surface. B) Schematic of the stress variation beneath the indent and the effective residual stress within the plastic zone. C) Hardness change as a function of residual stress magnitude. Empty diamonds in C denote hardness changes measured on the unstrengthened face (blue – compressive stresses, orange – tensile stresses), while black X’s are hardness changes measured on the strengthened surface.

Figure 4-10. Representative micrograph of indentations made at various depths on the unstrengthened glass surface. A) Rows of indentations made across the unstrengthened surface. Select images of damage evolved in the B) compressive region and C) tensile zone. The indentation load and hardness are indicated in the micrographs.

CHAPTER 5 IMPACT-INDUCED DAMAGE PROPAGATION MORPHOLOGY

Background

In order to assess the suitability of strengthened glasses for dynamic applications, an in- depth understanding of the high rate material response under a range of loads and strain rates is essential. To this end, the experimental examination of dynamic fracture modes, damage front velocities and associated deformation mechanisms is crucial for material development and computational models. Studies on the impact and penetration response of transparent materials have been conducted by numerous researchers [69-82]. However, there are limited studies on the high velocity impact behavior of strengthened glasses [63, 80, 83]. In a study by Strassburger et al. [83], it was concluded that strengthened glass front layers in laminated glass plates did not yield substantial improvements over as-received glass front layers. Later, the use of strengthened glass as an intermediate layer illustrated reduced damage severity in subsequent layers [84]. A novel feature of the dynamic fracture of strengthened glasses is the notion of internally-fueled, self-sustained fracture fronts. Currently, limited studies have provided an in-situ observation of self-sustained failure in thermally tempered glasses in the form of glass blocks [63, 85] or tear drop-shaped glass (called Prince Rupert’s drops)[86-88]. These thermally tempered glasses contain parabolic stress profiles marked by moderate surface compression (several hundred megapascals) with interior balancing tension of approximately half the value of the surface compression. The current study will extend these direct observations to chemically strengthened glasses which have steep compressive stress profiles with ultrahigh surface compression (~1 GPa on the surface) and near-constant, low interior balancing tension (tens of megapascals).

The focus of this investigation is the impact response of a chemically strengthened glass, trade-named Ion-Armor™. Recently, Jannotti et al. [9] reported a systematic photoelastic 69

analysis on strengthened glass bars where it was determined that the maximum level of compressive stress near the surface was found to be close to 1 GPa with a case-depth of ~0.8 mm. The residual stress distribution and loading rate were found to have a strong influence on the hardness and indentation fracture characteristics [26]. It was therefore expected that these high levels of residual compressive stress (and associated stored elastic energy) would present a profound influence on the impact behavior of the strengthened glass. The results of an investigation to understand the influence of residual stresses on the damage propagation characteristics due to ball impact on a chemically strengthened glass with ultrahigh residual surface compressive stress are reported.

Materials

Lithium aluminosilicate glass bars of approximate dimensions 100 mm by 7.6 mm by 8.6,

10 or 12 mm were chemically strengthened using a patented ion exchange process by Saxon

Glass Technologies, Alfred, NY. The bars were immersed in a mixed molten salt bath (NaNO3-

+ KNO3) at 475 ºC for up to ~24 hours [3], whereby the smaller lithium (Li ) glass ions were exchanged with larger sodium (Na+) and potassium (K+) salt ions to a depth of ~0.8-1 mm and

20-30 microns from the glass surface, respectively. Due to the size disparity between the native

Li+ ions and invading Na+ and K+ ions and the enforcement of compatibility criteria, large residual compressive stresses are generated in the exterior layers of the glass with balancing tensile stresses in the glass interior [9]. This residual stress results in the generation of stored elastic energy in the strengthened glass.

Experimental Method

Residual Stress Distribution

The residual stress state in each bar was examined using a circular polariscope in dark- field arrangement. Full-field assessment of the residual stress state was made with a digital camera (Olympus model E-450 digital SLR, Center Valley, PA, USA), while an optical microscope (Olympus model BX51, Center Valley, PA, USA) was used to examine narrow regions just below the strengthened surface where greater stress levels and severe stress gradients were present [9]. In the presence of residual stresses, when polarized light was passed through the glass, colored fringes resulted which provided an indication of the magnitude of the stress and severity of the stress gradient due to the strengthening process [22]. The observed fringes represented the stress state at each point averaged through the thickness in the viewing direction.

For this reason, select strengthened bars were polished on two parallel surfaces to remove the strengthened case-layer. This allowed for a more accurate depiction of the residual stress profile in the subsurface layers when viewed through the polished faces. Unlike slicing, progressive polishing slowly removed the strengthened case-layer without leading to catastrophic fracture of the strengthened glass bar. Residual stresses were computed using the fringe-counting method where the number of fringes is directly related to the residual stress level. More details of the photoelastic method used for stress determination are provided elsewhere in Chapter 3.

Bulk Properties

The bulk material properties of the as-received and strengthened glass bars were determined to quantify the effects of the ion exchange process. The density was determined using Archimedes principle. The longitudinal and shear wave velocities were measured using an ultrasonic pulser-receiver system (Olympus model 5072PR, Waltham, MA, USA) paired with a

high-speed digital oscilloscope (LDS Nicolet Sigma 90 Transient Oscilloscope, Middleton, WI,

USA; 100 MHz). The density and elastic wave velocities (i.e., longitudinal and shear), were utilized to estimate material properties such as Poisson’s ratio, elastic modulus, and shear modulus as per ASTM Standard E494-10 [89]. Additionally, the Rayleigh (surface) wave velocity was calculated as a function of the shear wave velocity and the Poisson’s ratio [90] as provided in Appendix: Elastic Wave Velocities. This allowed the measured damage front velocities to be compared with the Rayleigh wave velocity of the respective glasses.

Ball Impact Experiments

Ball impact experiments were conducted on the as-received and strengthened glass bars at a range of velocities from 52 to 345 m/s. Unlike the strengthened glass samples used for residual stress measurements, the bars used for impact testing were not polished on parallel (front and back) faces. Instead, these test samples retained the compressive layer due to strengthening on all faces, forming a continuous layer of near-surface compression. For impact testing, each bar (as- received or strengthened) was held in line with the barrel of a gas gun (Figure 5-1). The alignment was verified using an in-barrel laser guide. A steel ball of 4.8 mm diameter was held in a PVC foam sabot and launched towards the glass bar. The sabot was stopped by a rigid aluminum block while the steel ball continued to travel towards the glass bar. The impact occurred on a small rectangular face perpendicular to the axis of the bar (normal-incidence impact). The damage induced and its propagation characteristics were recorded using a high- speed camera (Vision Research® Phantom v710®, Wayne, NJ, USA) at 281,000 to 500,000 frames per second (fps), with an interframe time of 3.56 to 2.00 microseconds, respectively. The camera was then positioned on a long sample surface perpendicular to the impact direction (Figure 5-1 Figure 5-1). White light and shadow light imaging methods were utilized to capture the fracture propagation characteristics. White light illumination allowed for an examination of the makeup of the fragmented damage (in-situ), but the use of shadow light dramatically enhanced the contrast between the damaged and intact glass. The ball impact velocity was calculated by tracking the time-displacement history of the ball prior to impact on the glass bars.

Because the exact time of impact was not readily known due to the discrete nature of the imaging method, the instant of impact (t = 0) was approximated from successive images prior to the initial observation of damage. The damage front propagation velocity at various times was then 72

calculated based on the position of the damage front from two successive frames and assigned to the average position between the frames.

Results

Residual Stress Distribution

Figure 5-2 reveals the fringe patterns observed under white light in a circular polariscope for as-received and strengthened glass bars. No fringes were present in the as-received glass

(Figure 5-2A). However, due to chemical strengthening a large number of closely-spaced fringes were present along the edges of the strengthened glass associated with a high level of residual compressive stress and steep stress gradient (Figure 5-2B and Figure 5-2C). In the interior region, a low level of near-constant tensile stress was observed, as revealed by the small number of fringes and the small variation in the fringe colors. In previous studies, Jannotti et al.[9, 26] evaluated the severe compressive stress gradient for this strengthened glass and measured a maximum compressive stress of around 1075 MPa at the glass surface. This value decreased rapidly to around 500 MPa within 6 microns depth and to less than 250 MPa within 25 microns from the glass surface. In the current study, only the residual stress profiles extending from ~50 microns depth into the interior of the glass were examined. The residual stress profiles are illustrated in Figure 5-3. The measured stress profiles were superposed with the near-surface stress profile measured previously [9, 26] with an inset revealing the residual stress magnitude within 25 microns from the surface. For the two glass bars examined in this study, a black photoelastic fringe (zero stress) appeared at 0.8 mm and 0.9 mm depth when viewed through a polished surface of 7.6 mm and 12.1 mm height, respectively. This solid black fringe denoted the case-depth or depth of the compressive zone. Due to the requirement of force equilibrium across the glass cross-section, interior balancing tension must prevail in the central region of the bar.

Thus, increased specimen height led to a larger tensile region and a lower magnitude of interior balancing tension. When viewed through a surface of 7.6 mm height, the maximum tensile stress was 44 MPa at 1.4 mm depth, which fell to a constant value of 37 MPa throughout the glass interior. Comparitively, for a glass of 12.1 mm height, the maximum tensile stress in the glass interior was 27 MPa at a depth of 1.3 mm, which then dropped to a constant tensile stress of 22

MPa throughout the glass interior. The strain energy density of the glass bar was estimated for an equibiaxial state of stress using the elasticity solution [91] combined with the measured residual stress profiles from Figure 5-3. The average elastic strain energy density of the strengthened glass bar was thus computed to be 9.0x104 J/m3. The average strain energy density values in the compressive and tensile regions were 8.0x104 J/m3 and 0.5x104 J/m3, respectively, with maximum values of strain energy density on the order of 107 J/m3 at glass the surface

(compressive) and 103 J/m3 in the glass interior (tensile).

Mechanical Properties

The bulk material properties of the as-received and strengthened glass bars are displayed in Table 5-1. Recall that chemical strengthening by ion exchange (“ion-stuffing”) results in the outer glass regions becoming a stuffed-derivative of the parent glass. Although the influence of the ion exchange process may be more pronounced locally, the effect on the bulk properties of the strengthened glass were still noticeable. It was found that the wedging of Na+ and K+ into the glass matrix yielded an increase of 1.7% in the bulk density (ρ) of the strengthened glass compared to the as-received glass. Also, ultrasonic measurements revealed that the ion exchange process resulted in an increase of 4.6% in the elastic modulus (E) and 5.3% in shear modulus (G) of the strengthened glass. The Poisson’s ratio (ν) of the strengthened glass was found to be 3.6 % lower than the as-received glass. The increase in elastic impedance, (Eρ)1/2, due to the increase in

density and elastic modulus resulted in an increase in the elastic wave velocities – longitudinal by 1.7%, shear by 2.6%, and Rayleigh by 2.3% – in the strengthened glass compared to the as- received glass.

Damage Morphology

Figure 5-4A illustrates a sequence of images revealing the damage propagation in the as- received glass at a ball impact velocity of 261 m/s. Damage was initiated at the impact-end and then propagated for a short distance of 27 mm before it was fully arrested within 25 µs.

However, the compressive wave generated due to the impact continued to travel towards the rear-end of the bar, where it reflected as a tensile wave and propagated back toward the impact- end. Due to the greater sensitivity of defects to tensile stresses, a secondary damage front was initiated at the rear-end of the bar and then propagated inwards. The nature of damage caused by the reflected tensile wave (damage formed perpendicular to the bar axis) was visibly different compared to the damage at the impact-end (axial cracks parallel to the bar axis). At the impact- end, the damage was in the form of polygonal and needle-like fragments aligned with the bar axis which increased in size with distance away from the impact site, consistent with axial splitting (Figure 5-4B). On the other hand, the cracks at the rear-end were formed perpendicular to the axis of the bar (tensile cracking) and cleaved away large fragments from the bar (i.e., spallation). Each of these large fragments contained extensive networks of internal cracks

(Figure 5-4C). Also, the central section of the bar remained intact with no visible internal cracking.

On the contrary, the abundance of damage and propagation characteristics (path, duration, etc.) in the chemically strengthened glass were noticeably different (Figure 5-5). Once initiated at the impact site, the damage front propagated in a self-sustained manner until the

entire bar was consumed. The observed damage propagation could be separated into two modes: planar and oscillatory. Initially, the damage front appeared planar, i.e., parallel to the impact plane, up to 11.4 µs (the first three images in Figure 5-5A). At some distance away from the impact site the damage front diverged as seen in the images at 18.6 µs and beyond. Damage along the top and bottom regions of the bar merged periodically via transverse bridging cracks

(more clearly visible in the shadow light images shown in Figure 5-6 and Figure 5-7), resulting in oscillatory damage front propagation in the remainder of the bar. This mode of damage resulted in a mix of polygonal and needle-like fragments along the glass periphery (Figure 5-5B) and the formation of damage-free islands of glass in the central tensile zone of the bar (Figure 5-

5C). This process repeated until the entire bar was completely fragmented. Unlike the as- received glass, a secondary damage front initiating from the rear-end of the bar was not observed. Recall that for the as-received glass, damage growth from the rear-end of the bar was observed from t = 24.4 µs to 56.5 µs (Figure 5-4A). The images shown in Figure 5-5A during this time frame only showed damage propagating from the impact-end towards the rear-end of the bar, implying that the strengthened glass did not exhibit damage due to the reflected tensile wave. To verify the lack of reflected wave damage initiation from the rear-end of the bar, an additional test was performed at an impact velocity of 334 m/s on the strengthened glass where the entire- bar was viewed during the impact process with shadow lighting. It is clear from the sequence of images in Figure 5-6 that, unlike the as-received glass, no visible damage or spallation was observed from the rear-end of the strengthened glass bar. Moreover, only the damage initiated from the impact site was seen to propagate in a self-sustained fashion towards the rear-end. Although no secondary damage front was initiated by reflected stress waves, they were observed to interact with damage propagating from the impact-end. As the reflected tensile

wave interacted with the advancing damage front near the midpoint of the bar, a loss of the periodic or oscillatory damage mode was witnessed (similar to that seen in Figure 5-5A at t =

36.3 µs), i.e., damage island formation at regular intervals was inhibited. Also, a second stress wave interaction was observed between the reflected shear wave and the advancing damage front

(at t = 44.2 µs). In both cases, the moving damage front was observed to experience intensified cracking, damage front deceleration and a disruption of the initial oscillatory mode of damage propagation. Note that due to camera limitations, increased viewing domain came at a loss in resolution for comparable frame rates and increased parallax effects.

Interestingly, it was observed in Figure 5-5 and Figure 5-6 that the damage front propagated preferentially and at a faster rate along the periphery of the bar, compared to the interior regions. Compared to the photoelastic images in Figure 5-2B and Figure 5-2C, the damage appeared to travel predominantly through the compressively stressed regions. It was not definitively clear if the damage propagated in a similar fashion on all planes, suggesting that the damage front may preferentially propagate faster along the edges (or corner regions), as opposed to the top and bottom surfaces as it appeared when viewed through one plane only (Figure 5-7A).

To clarify the damage mode, the optical arrangement was altered with the use of mirrors to allow the damage front propagation to be viewed simultaneously through two adjacent perpendicular faces of the bar (Figure 5-7B). Utilizing mirrors, both the front and top surfaces of the glass bar were imaged simultaneously which allowed for a pseudo-three-dimensional perspective of the damage propagation, as shown in Figure 5-7C. Again, the initially planar damage front propagation (up to t=6.9 µs) became divergent (at t=10.7 µs) and the previously observed oscillatory mode of self-sustained damage was observed where bridging cracks directed the damage from the outer regions into the interior of the glass. Thus, the dominant path of damage

front propagation was determined to be along the bar edges. However, based on the time and spatial resolution limits of the high-speed imaging system, it was difficult to conclude whether the damage front propagation occurred first in the compressive layer or the tensile region. This issue was further complicated by the fact that the technique provides two-dimensional projections of the three-dimensional specimen and the associated complex fracture process.

Observation of the damage zone in the strengthened glass bars through high-speed imaging

(Figure 5-5 , Figure 5-6, and Figure 5-7) revealed that the damage developed within ~0.5-2.0 mm from the edges. Thus, the damage zone extends into both the compressive zone and the outer part of the tensile zone. Hence, it is inferred that the stress gradient plays a role in the self- sustained damage process. The implications of these observations are discussed in more detail in the later sections. The drawback of the optical arrangement shown in Figure 5-7B was that the image resolution and the associated frame rate were significantly reduced due to the increased viewing area. It is interesting to note that even when the normal impact was not centered on the impact face (Figure 5-7A), the damage observed was similar to that shown in Figure 5-5 and

Figure 5-6. Additionally, the damage along the top and bottom edges was approximately even despite being initiated close to the top edge.

Damage Front Velocity Characteristics

Ball impact experiments were conducted at a range of velocities to understand the damage propagation characteristics in the as-received and strengthened glasses. In each experiment, the damage front velocity was measured along the length of the bar. The damage propagation behavior was visualized by plotting the damage front velocity profiles as a function of the damage front position from the impact-end (Figure 5-8). The position of the damage front was normalized by the bar length. For the as-received glass, the damage front velocity reached a

maximum value ranging between 1626-2135 m/s immediately after impact, depending on the ball impact velocity (52-287 m/s). The damage front velocity then dropped quickly to zero as the damage front arrested within a short distance from the impact-end, i.e., not self-sustaining. From

Figure 5-8, it was noted that for the as-received glass, both the depth of damage and the maximum damage front velocity were dependent on the ball impact velocity. On the other hand, for the strengthened glass, the damage front velocity reached an initial velocity ranging between

1791-2275 m/s, depending on the impact velocity (62-245 m/s). The damage front velocity then stabilized to around 1920 m/s within 3-5 μs (Figure 5-8), and remained approximately constant for the residual duration of the damage propagation. Thus, the damage in the strengthened glass was observed to be self-sustaining and the damage front velocity had only an initial dependence on the impact velocity. Notice that for impact velocities above a threshold velocity (e.g., 162 m/s), the maximum damage front velocity was the same as the initial velocity, and then the damage front velocity rapidly decreased to the self-sustained (constant) velocity, VC, of 1920 m/s. For impact velocities below a threshold impact velocity (e.g., 62 m/s), the initial front velocity was less than the VC, and the damage front velocity then quickly increased to VC. The threshold velocity was determined to be approximately 95 m/s at which the initial and maximum damage front velocities were predicted to be equal. Occasional dips and jumps in the damage front velocity profiles were attributed to instabilities in fast fracture and damage front deflections due to bridging cracks to form damage-free islands (Figure 5-5, Figure 5-6, and Figure 5-7).

Some variation in damage front velocity along the bar length may also be due to the fact that the maximum damage front positions were measured in each frame parallel to the bar length, i.e., along the dominant path of propagation, in order to determine the average (interframe) velocity.

When the cracks deflected transversely towards the interior of the bar, some loss in the measured velocity was inevitable.

It is instructive to compare the measured damage front velocities of the as-received and strengthened glasses with the Rayleigh wave (CR) velocities (given in Table 5-1). It is generally accepted that the theoretical limiting velocity of propagating cracks approaches the Rayleigh

(surface) wave velocity, as predicted from continuum wave propagation theories of dynamic fracture [92]. Considering that most of the energy to drive crack extension is delivered along the internal surfaces of the crack, the maximum bound for the crack velocity is then the Rayleigh wave velocity (CR) [90]. For the examined ball impact velocities, the maximum observed damage front velocities for the as-received glass ranged from 0.48-0.64CR, while for the strengthened glass the maximum velocities were between 0.57-0.66CR. As the impact velocity increased, the maximum damage front velocities were observed to asymptotically approach a limiting velocity, approximately 0.64CR (2135 m/s) and 0.66CR (2275 m/s) for the as-received and strengthened glasses, respectively. These measured values agree well with limiting crack velocities for a variety of glasses in literature [93]. Comparing the self-sustained damage velocity, VC, and elastic wave velocities for the strengthened glass, the self-sustained velocity was found to be on average 0.56CR (1920 m/s). This constant velocity, which is independent of the impact energy and is directly related to the strengthening process, was only slightly lower than the maximum damage front velocity of 2275 m/s observed in the strengthened glass.

Although the maximum velocities for the as-received and strengthened glass were not dramatically different, the additional stored energy contribution in the strengthened glass allowed the damage front velocity to more quickly reach a given velocity. For the as-received glass, a maximum damage front velocity of ~2100 m/s was not reached until the ball impact velocity was

raised to 287 m/s, whereas, the stored energy in the strengthened glass allowed the damage front to reach the same velocity at an impact velocity of only 162 m/s.

Discussion

The differences in damage propagation behavior between the two examined glass bars can be explained by considering the available stored elastic energy in the strengthened glass bar.

For example, consider the trends in the depth of damage and damage front propagation velocity

(Figure 5-8). For the as-received glass, the damage induced was solely due to the kinetic energy of the impacting steel ball. The maximum depth of damage and the initial (maximum) damage front velocity both increased with increasing impact energy in the as-received glass and then fell rapidly to zero as this energy was consumed. For the strengthened glass, the damage front velocity exhibited only an initial dependence on the impact velocity and within a few microseconds the velocity reached a constant value (VC = 1920 m/s), reflecting that it was independent of the impact energy (Figure 5-8). This behavior in the strengthened glass is directly attributed to the stored elastic strain energy developed during the ion exchange process.

Recall that during the ion exchange process, larger Na+ and K+ ions were substituted in place of smaller Li+ ions in the glass, therby generating large surface compressive stresses (up to

1 GPa at the glass surface) to a depth of around 0.8 - 0.9 mm (Figure 5-3) with low levels of interior balancing tension. This residual stress development translates to stored elastic energy.

Once damage initiated at the impact surface reached the interior tensile zone, a sudden release of stored energy occurred, leading to self-sustained damage growth [63]. This was verified from

Figure 5-8 based on the attainment of the self-sustained velocity due to the stored energy release.

For the lowest impact velocity (e.g., 62 m/s) on the strengthened glass, it was observed that a damage front velocity of VC was not reached immediately after impact (Figure 5-8). Due to the

large case-depth and finite time required to propagate damage through the thick compressive layer, initiation of the cascading release of stored energy depends on the impact velocity. Thus, for a low impact velocity, i.e., reduced damage velocity, a delay in the attainment of VC was expected, as seen in Figure 5-8. However, once the damage had penetrated though the compressive layer and catastrophic energy release was initiated, the continued availability of stored energy and its progressive release along the bar length facilitated self-sustained damage front propagation at a constant velocity (VC). Although rapidly propagating cracks typically branch out (to cause net energy decrease) such that the crack velocities of the two are slower than the original crack [94], in the presence of sufficiently high levels of stored elastic energy, crack branching occurred while maintaining a near constant propagation velocity. If one extends this logic, it can be inferred that even at a low impact velocity, as long as the initial loading damage penetrates through the compressive layer, then self-sustained failure can be initiated in the strengthened glass, and the damage front velocity should tend to the constant velocity, VC, and propagate indefinitely.

The damage path in these experiments is contrary to that observed in previous studies which describe that damage propagation and growth should be dominant in the glass interior which is dominated by tensile stresses compared to the exterior compressive layers [63, 88]. To explain the observed damage path in our experiments, i.e., predominantly along the edges and close to the surface, several possible mechanisms are discussed, each of which may act independently or in concert with other factors. Firstly, a region of localized tensile stresses close to corners/edges is proposed, with a much greater magnitude compared to the interior tensile stresses observed by photoelasticity. Note, these localized stresses and distributions are not easily captured by typical photoelastic methods. The in-plane residual stress state analyzed in the

previous section (Residual Stress Distribution) using photoelasticity is typically taken through two parallel polished faces along the polished face centerline and away from the ends to mitigate edge effects. However, one can gain an idea of the edge effects by examining the complex fringe patterns in corners in Figure 5-2E, where symmetry is observed along a line bisecting the corner.

Based on previous computational studies [65, 95], a slight expansion of the glass due to ion exchange results in a “dog-ear” shape at surface intersection points (i.e., edges or corners).

Compared to regions away from the edges/corners, the localized stress state is marked by lower surface compression, a shallower compression depth, and greater levels of tension oriented along the direction bisecting the edge/corner. It could then be expected that the damage would be preferential to the edge regions compared to the interior regions due to the greater level of residual tension. Based on the single-plane and dual-plane (mirror) observations given in Figure

5-7, this mechanism seems viable. Indeed, greater damage propagation velocities and fragmentation were observed near the edges with less damage occurring near face centers and interior regions of the glass bar. Although this preferential damage mode along edges has not been directly observed previously, similar rationale has been suggested by Tandon and Glass

[96] to explain their observation of edge-concentrated powdering compared to the interior tensile zones away from the edge regions where much larger fragments were found. Additionally, recognize that due to processing inhomogeneities in the edges/corners, lower case-depths and decreased levels of residual compression may create more favorable conditions for damage nucleation compared to surface regions away from the edges which are under increased levels of beneficial compression and have larger case-depths. This emphasizes a possible weak-link in strengthened glasses.

From Figure 5-3A, it is seen that the maximum amplitude of tensile stress occurs just beyond the case-depth (1.3-1.4 mm from the surface), close to the point of zero residual stress

(0.8-0.9 mm from the surface). The near-edge damage front appears to follow this line of maximum residual tension. Once impact damage reaches the tensile zone and initiates the self- equilibration process, the stress released at one location is followed by a similar rapid stress release in the neighboring regions. As the regions ahead of the fracture front equilibrate, the residual compression near the edges immediately reduces to zero allowing for easier crack propagation through the case-layer and damage development along the bar edges. In the interior region of the bar, similar damage severity was not observed due to the low stress levels and the low available stored (strain) energy.

Other factors could be influencing the observed damage propagation behavior as well.

For example, boundary reflections of the stress waves generated by the impact and dynamic fracture can influence additional crack initiation, crack path stability and trajectories, and cause intensified cracking due to interactions with the advancing damage front. Due to increased elastic impedance (square-root product of the local density and elastic modulus) in the compressive regions, stress waves and therefore the damage can travel faster within the exterior glass layers.

Recall that the values in Table 5-1 are based on bulk measurements and should be expected to vary more widely on a local scale, especially in the outer layers where the stress gradients are the steepest due to the increased concentration of wedged ions. The cascading effect may be further amplified by the relative abundance of defects (inherent surface cracks as well as the wedged foreign ions) close to the outer surfaces and edges which may become damage nucleation sites ahead of the advancing damage front.

The results of this study emphasize the critical need for a better understanding of the local variations in the stress state and boundary-effects on self-sustained damage growth which are lacking in current literature. Previous studies [63, 88, 96] have primarily focused on the influence of bulk residual stress distributions and have homogenized the damage process to a one-dimensional process fueled only by interior (uniform) tensile stresses. Hence, it is suggested that more in-depth analysis should be undertaken with special emphasis on the influence of local variations in the residual stress state along edges and corner and specimen three-dimensionality.

Finally, a brief discussion of the utility of the ion-exchanged glasses with ultrahigh residual stresses is given. The results of this study did not allow for overarching conclusions to be drawn as to whether the impact response of the strengthened glass was superior or inferior to the as-received glass. However, a clear benefit of glass strengthening was the prevention of damage due to the reflected tensile stress wave from the rear-end of the bar (i.e., increased spall strength), as shown in Figure 5-6. Additionally, note that the impact conditions in the current study were such that the induced stress levels quickly over-stressed the compressive layer and resulted in catastrophic failure. Thus, strengthened glasses should be limited in use to low velocity direct impact applications where the impact stresses are below the critical level to cause catastrophic failure. For moderate or high impact velocities, strengthened glasses may be used as intermediate layers in laminate plates where sufficient stress attenuation has taken place, as previously suggested by Strassburger et al. [84].

Conclusions

Ball impact experiments at velocities between 52-345 m/s were utilized to assess the damage morphology and damage front propagation characteristics of as-received and strengthened glass bars. The presence and distribution of stored elastic energy in the

strengthened glass had a profound influence on the nature of the damage propagation and fragmentation compared to the as-received glass. The high levels of residual surface compression were observed to prevent secondary damage front initiation due to the reflected tensile wave for ball impact velocities up to 334 m/s (i.e., increased spall strength). However, the damage in the strengthened glass was found to be catastrophic and encompassed the entire specimen once the compressive layer was penetrated and stored energy release was initiated. Additionally, the initial damage front velocity in both glasses showed a clear correlation to the impact velocity; however, notable differences in damage front propagation velocities were found between as- received and strengthened glasses once the influence of the impact energy had diminished.

Unlike the as-received glass which experienced a maximum damage front velocity immediately upon impact and a sudden decrease to zero within a short distance, the strengthened glass exhibited a self-sustained (constant) damage front which quickly stabilized at a velocity close to

1920 m/s and consumed the entire glass bar. Furthermore, the damage front propagated at a greater velocity in the near-surface regions along glass edges compared to interior tensile zones.

Lastly, based on the current study, it appears that one may derive significant benefit from strengthened glass if the induced tensile stress levels to be accommodated are below a critical level (i.e., low velocity direct impact or as an interlayer in a laminate window panel).

Table 5-1. Bulk material properties of the as-received and strengthened glass bars. Property As-received Glass Strengthened Glass Steel Ball Density (g/cc), ρ 2.41 [1] 2.46 [1] 7.87 [2] Elastic Modulus (GPa), E 81.4 [1] 85.0 [1] 213.0 [2] Poisson’s Ratio, ν 0.22 [1] 0.21 [1] 0.30 [2]

Longitudinal Wave Velocity 6.13 [1] 6.23 [1] 5.20* (km/s), CL Shear Wave Velocity (km/s), 3.69 [1] 3.79 [1] 3.19* CS Rayleigh Wave Velocity 3.36 [1] 3.44 [1] 2.95* (km/s), CR * Computed using Equation (A-3)

Figure 5-1. Schematic of the setup used for the ball impact experiments.

Figure 5-2. Images of the glass bars when viewed in a circular polariscope under white light. Photoelastic fringes seen for the A) as-received, B) strengthened glass bars , C) an enlarged image of the fringes near the strengthened glass edge, D) and a generalized schematic of how the fringes were viewed in the strengthened glass bars. The high density of fringes along the periphery of the strengthened glass in C indicate a high magnitude of surface compression and a steep compressive stress gradient close to the edge. E) The complex stress state arising in the corner regions of the glass and the symmetry which evolves along the line bisecting the corner.

Figure 5-3. Residual stress profiles determined by photoelasticity. A) The full stress profile is as viewed through glass bars of approximately 7.6 mm and 12.1 mm height is shown, including B) an inset containing a magnified view of the near-surface stress profile [9, 26]. Note the severe stress gradient within 25 microns from the glass edge (inset) where the maximum compressive stress was up to 1075 MPa. On the other hand, tensile stresses in the glass interior ranged between 22-44 MPa and were approximately constant.

Figure 5-4. Impact damage due to ball impact at 261 m/s on an as-received glass bar. A) High-speed white light images of the damage propagation, B) small fragments near the impact site and coarser fragments away from impact-end, and C) large fragments due to tensile fracture initiated from the rear-end of the bar. Note that only 75 mm of the glass bar was visible in the high-speed images.

Figure 5-5. Impact damage due to ball impact at 345 m/s on a strengthened glass bar. A) High-speed white light images of the damage propagation, B) polygonal and needle-like fragments formed near the glass exterior, and C) the damage-free fragments (i.e., islands) formed in the center of the glass bars. Note that only 75 mm of the glass bar was visible in the high-speed images.

Figure 5-6. High-speed shadow light images of the damage propagation in a strengthened glass bar due to ball impact at 334 m/s. Only damage initiated by the impact was observed to propagate along the bar length and no damage initiation was seen from the rear-end of the glass bar. Note that the entire 100 mm glass bar is visible.

Figure 5-7. High-speed imaging of impact damage. A) Shadow light images of the damage propagation in a strengthened glass bar due to ball impact at 162 m/s imaged through the front surface. B) A schematic of the modified (mirror) optical arrangement to view damage evolution through the front and top surfaces (simultaneously), and C) the associated high speed shadow light images due to ball impact at 252 m/s on a strengthened glass bar. Note in A and C that only 37 mm and 29 mm of the glass bars were visible, respectively.

Figure 5-8. Plot of the damage front velocity profiles for both as-received and strengthened glass bars as a function of the damage front position. The damage velocity profiles are plotted starting from the impact-end. Note that the damage position is normalized by the respective glass bar length.

CHAPTER 6 IMPACT-INDUCED DEFORMATION AND ENERGY DISSIPATION MECHANISMS

Background

Studies performed on glasses and ceramics to determine material properties that can serve as performance metrics often do not always indicate a direct link between properties and impact performance [97]. Edge-on impact experiments on plates or rods coupled with high-speed photography have been identified as a suitable means of exploring the impact response and damage mechanisms of transparent materials [77, 78, 81, 98]. However, limited experiments have been performed on the impact response of strengthened glasses [63, 83, 84, 98].

In Chapter 6, an in-depth examination of the influence of chemical strengthening on the deformation mechanisms is presented for a range of impact velocities. Additionally, the fractional energy absorbed by various deformation modes was estimated by means of an overall energy balance to determine key energy dissipations modes and apparent differences between the as-received and strengthened glasses.

Materials

As-received and chemically strengthened glass bars of 100 mm (length) x 7.6 mm (depth) x 8.6, 10, or 12 mm (height) were obtained from Saxon Glass Technologies, Alfred, NY, USA.

The glass in its “as-received” form was a lithium aluminosilicate glass procured from Nippon

Electric Glass, Tokyo, Japan. The as-received glass bars were chemically strengthened by Saxon

Glass Technologies using a patented ion exchange process and the resulting glass was trade- named Ion-Armor®. The as-received bars were placed into a bath of mixed molten salts

(NaNO3-KNO3) for up to 24 hours. During this time, exchanges occurred between the lithium

(Li+) ions in the parent glass and the sodium (Na+) and potassium (K+) ions in the salt bath. As the glass substrate cooled, the larger salt ions became “wedged” into the spots once filled by the 95

smaller glass ions. Thus, in the exchanged outer layers of the glass a residual state of compression was developed with a balancing interior residual tension. The exchange process resulted in a thick near-surface compressive layer consisting of two sub layers: a thin (~25 micron) outer layer of ultrahigh residual compressive stress up to approximately 1 GPa and a thick inner layer (0.8-0.9 mm) of moderate residual compressive stress up to ~250 MPa [9, 26,

98]. In the interior of the bar, tensile stresses ranging from 22-47 MPa were developed to satisfy equilibrium conditions. For a 12 mm x 7.7 mm x 100 mm strengthened bar, the residual stresses developed within the strengthened glass bars translated to a total stored elastic strain energy density of 8.5x104 J/m3 (8.0x104 J/m3 due to residual compressive stress and 0.5x104 J/m3 due to residual tensile stress) [98]. This corresponded to approximately 0.74 J of residual compressive strain energy and 0.04 J of residual tensile strain energy, based on the volume of the glass bar in a state of residual compression and tension, respectively. The implications of this residual stress and stored strain energy on the observed damage mechanisms will be discussed.

Selected material properties of relevance in this study for the as-received glass, strengthened glass, and the steel projectiles are provided in Table 6-1. Clearly, the strengthening process can result in an increase in the strengthened glass properties compared to the as-received glass, most notably the fracture strength which can generally be considered as the level of residual compression that must be overcome to cause failure [11]. These properties were used to better understand the impact-induced damage evolution and to calculate discrete values for the observed energy dissipation modes, as discussed in the Results and Discussion section.

Experimental Method

Ball impact experiments were conducted at a range of impact velocities from 52-345 m/s on as-received and strengthened glass bars. The experimental method is a modified version of

the Edge-On Impact (EOI) technique developed by the Ernst-Mach-Institut (EMI) [81]. In the current study, normal impact occurs on the edge face of a long rectangular glass bar which allows damage front propagation along its length. The long dimension in the impact direction allows for separation of the impact-damage from the damage developed due to stress wave reflections at the rear-end. The experimental setup, shown in Figure 6-1, illustrates a freely supported glass bar impacted by a steel spherical impactor of diameter 4.76 mm and weight 0.44 mg. By freely supporting the bars, the rigid body motion of the target material can also be captured and accounted for rather than the energy being dissipated into the rigid supports. The damage characteristics were captured using a high-speed camera (Vision Research® Phantom v710®) at frame rates up to 500,000 frames per second (fps) with minimum interframe time of

2.0 microseconds. Two different optical configurations were used: reflected light and transmitted light. The reflected light arrangement exploited light reflections from the developing cracks and damaged regions to observe the fracture development and damage make-up. Transmitted light relied on the disruption of the light transmission by damage formation and provided improved contrast between damaged and intact glass regions.

Results and Discussion

Impact Damage Evolution

The damage developed in the as-received and strengthened glass bars was analyzed from the high-speed images, shown in Figure 6-2 and Figure 6-3. The operative damage mechanisms were found to be highly dependent on the impact velocity and the available stored energy to activate the damage. Thus, two regimes were classified as low velocity impact (~50-60 m/s) and moderate velocity impact (~150-350 m/s). For reference, note that the impact generates a longitudinal compressive wave, a transverse shear wave, and a Rayleigh surface wave in the

glass bar, whose elastic wave velocities for the as-received and strengthened conditions are given in Table 6-1.

Low velocity impact

For a low velocity impact (52 m/s) on the as-received glass bar, fracture surface creation was the only observable inelastic deformation mechanism (Figure 6-2A). The damage propagation velocity quickly reached a maximum velocity of 1627 m/s (Fig. Figure 6-4A), and arrested rapidly within 10 µs and at a distance of 11 mm from the impact-end. Also, it was observed that a well-defined cone crack was formed during the early stage of damage development. The ball was then observed to penetrate slowly into the bar with a residual velocity of ~16 m/s (~31% of the initial velocity). Here, once structural cohesion was lost the large macroscopic fragments were simply pushed out of the way, allowing the ball to slowly penetrate the debris.

In contrast, for a 62 m/s impact on the strengthened glass, no well-defined cone-crack was observed, perhaps due to an increased level of fragmentation fueled by the additional stored elastic energy (residual stresses) (Figure 6-2B). However, cone-shaped damage was observed to partially extend from the impact plane during the early stage of damage development. Instead of large cracks, a highly comminuted fracture zone developed over the entire impact plane. Rather than quickly subsiding as in the case of the as-received glass, the available stored energy in the strengthened bar fueled self-sustained damage propagation and complete fragmentation of the bar. Shortly after the impact, the ball was observed to rebound outward at 33 m/s (~53% of the initial velocity). The fractured material at the impact site was similarly thrown outward at a comparable velocity, possibly due to an elastic recovery mode of the underlying (intact) material and the dilatant nature of the fragment bed at the impact site. Clearly, the strengthening process

and the ultrahigh residual surface compression improved the elastic response of the glass bar, i.e., reduced the ability of the hardened steel projectile to penetrate the glass bar due to its increased hardness [98] and fracture strength [3]. Also, the increased level of fragmentation at the impact plane may act to oppose the incoming projectile. The ball then rebounded. However, the minimum requirement for the initiation of catastrophic or self-sustained failure of the strengthened glass was merely the initial damage penetration beyond the depth of the compressive layer. This behavior was observed even for a low velocity impact of 62 m/s, where the damage penetrated the compressive layer at 1791 m/s, before stabilizing to a self-sustained velocity (VC) of ~1928 m/s, as seen in Figure 6-4A. As the self-sustained damage advanced along the bar, the outer compressive layers were observed to dilate at ~12 m/s along the entire bar length. This damage mode is termed “uniform dilation” (Figure 6-2) because the expansion occurs at a near constant rate along the entire bar length. Similar to the self-sustained damage growth, the uniform nature of this dilation over the entire bar length suggests that it is independent of the impact velocity and is solely dependent on the stored elastic energy due to the strengthening process.

Moderate velocity impact

At greater impact velocities (~150-350 m/s), a greater level of damage and additional energy dissipation modes were observed, i.e., high velocity jetting of fine particles (ejecta) from the impact site and non-uniform radial dilation of the glass bar near the impact-end (Figure 6-3).

For both the as-received and strengthened glasses, a dense network of microcracks and splinter- shaped fragments were observed to form at the impact site. This mode of damage in glass is different from that typically seen for low impact velocities and quasi-static indentation experiments [99, 100]. The microcracking is due to a low level of confinement by the

surrounding material and high shear at the impact site leading to pulverization of the material at the impact site (discussed in more detail in the Energy Balance section).

For moderate velocity impacts on the as-received glass bars, the maximum damage propagation velocities ranged from 1910-2135 m/s (Figure 6-4A) before the damage front fully arrested within 24-27 µs or 24-30 mm from the impact-end. The longitudinal compressive wave which travels at the fastest speed reached the free end and reflected as a tensile wave, thereby initiating secondary damage from the rear-end of the bar at ~3190 m/s. The tensile cracking at the rear-end (i.e., spallation) formed perpendicular to the axis of the bar (consistent with principles of brittle fracture), and resulted in the cleavage of large sections of glass from the rear- end of the bar (Figure 6-3A). Next, a dominant crack in the center of the bar and parallel to the bar axis was observed, likely due to the reflected shear wave. This observation was based on calculations using the wave velocity and the time when the crack growth was observed.

Simultaneously, the tensile stress wave continued toward the impact-end and interacted with the impact-end damage, causing further cracking in the form of transverse (fan-shaped) cracks. A portion of this wave was reflected from the damaged material (due to negligible impedance) back towards the rear-end causing further damage at the rear-end. At the impact-end, significant fine particle jetting and radial dilation was observed. Ejected fine particles were measured to reach average velocities of 280-525 m/s (depending on the impact velocity), quickly obscuring any measurement of the residual ball velocity (Figure 6-4B). The mode of radial dilation near the impact-end was termed “non-uniform” as the maximum dilation velocity occurred at the impact plane (86-91 m/s) and decreased almost linearly to zero within ~13-18 mm from the impact plane (Figure 6-4C and Figure 6-4 D), for the range of impact velocities used. Interestingly, long

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after the impact (hundreds of microseconds later), rigid body motion at ~5 m/s of the remainder of the intact as-received bar could be measured in the high-speed images.

For moderate velocity impacts on the strengthened glass bars, the initial damage due to the impact was similar to that observed in the as-received glass, i.e., highly comminuted and planar damage zone at the impact-end (Figure 6-3B). However, the maximum damage front reached an initial velocity of 2051-2275 m/s and then continued to propagate the full length of the glass bar at an average velocity of 1870-1937 m/s (Figure 6-4A). This behavior of self- sustained damage propagation seen in Figure 6-3B was also seen previously in Figure 6-2B for a lower velocity impact, where the presence of stored elastic energy allowed for sustained damage propagation at 1928 m/s. Unlike the as-received glass, no spallation was observed due to the reflected tensile stress wave in the strengthened glass. This behavior is due to the high level of residual compression along the glass periphery which prevented the secondary damage formation. The stress waves reflected from the rear-end were, however, observed to interact with the advancing self-sustained damage front (based on the wave travel time), causing intensified damage and momentary deceleration of the failure front by a factor of almost two (from VC down to ~980 m/s). This deceleration only lasted a few microseconds before recovering to VC.

Note that as the reflected tensile wave travelled towards the impact-end, some portion of the wave was reflected from the advancing damage front (neglible impedance) as a recompression.

This was observed as a displacement of the rear-end of the strengthened bar by ~0.5 mm in the impact direction at t = 44.1 µs (verified by the computed wave travel time). This recompression wave is commonly observed when analyzing failure waves in glass by plate impact experiments

[101]. The residual ball velocity could not be determined due to fine particle ejection from the impact site at an average velocity of 336-721 m/s (depending on the impact velocity). Non-

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uniform dilation in the vicinity of the impact-end was observed for the strengthened glass, similar to that of the as-received bar (Figure 6-3). The non-uniform dilation velocity was maximum at the impact plane (72-93 m/s), and decreased in a linear fashion to zero within a short distance (10-15 mm) from the impact-end, for the range of impact velocities used. In addition to non-uniform dilation, as the damage extended into the bar, the entire bar exhibited a uniform dilation at 12-13 m/s along its entire length similar to that observed for a low velocity impact on strengthened glass, as shown in Figure 6-2B.

Summary of the impact damage

The impact damage characteristics observed from the high-speed images as a function of impact velocity are shown in Figure 6-4. The fracture front propagation velocities for the as- received and strengthened glass bars [98], as well as the average self-sustained damage front velocity for the strengthened glass are shown in Figure 6-4A. As the impact velocity increased the damage front velocity also increased, with maximum velocities reaching 2135 m/s and 2275 m/s, or 62% and 66% of the Rayleigh wave velocity, for the as-received and strengthened glass, respectively. These values are at the upper-end of the typical limiting crack velocities for glasses

(i.e., ~40-60% of the Rayleigh wave velocity [102]). This indicates that once a critical impact velocity (imparted energy) is reached, the damage at the impact-end will develop at the limiting rate of an individual crack. However, at lower impact velocities and away from the impact

(reduced stress levels and energy), the damage develops at lower speeds. For the as-received glass, the imparted energy for damage propagation (due to ball impact) quickly diminished within a short distance from the impact-end and the damage front velocity fell to zero for all impact velocities. The secondary damage from the rear-end, i.e., damage growing into a primarily tensile-field, had a much greater damage velocity (~3190 m/s or 95% of the Rayleigh

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wave velocity) compared to that generated into a primarily compressive-shear field from the impact-end. This velocity is greater than the typical value of limiting crack velocities. However, note that the damage from the rear-end was observed to be due primarily to the nucleation of cracks from the surfaces and edges of the bar which linked together to form a cohesive zone of tensile damage. This damage is clearly not continuous, but intermittent with damage-free material in between, leading to a greater apparent damage velocity (thus, it is not shown in

Figure 6-4A). This manner of noncontiguous damage, with damage nucleating ahead of the advancing front, allows the damage front to move faster than is allowed by continuous crack extension. This type of tensile cracking was not witnessed for the lowest impact velocity (52 m/s) due to the insufficient amplitude of the reflected tensile wave. In the strengthened glass, the trend in damage front velocities was the same as that of the as-received glass, but was slightly increased due to the added influence of the stored elastic energy from chemical strengthening.

Once the influence of kinetic energy of the impactor (steel ball) was diminished at some distance away from the impact site, the damage front in the strengthened glass propagated at a self- sustained velocity which was independent of the impact energy until the bar was fully consumed

(Figure 6-2B and Figure 6-3B).

In Figure 6-4A, the self-sustained damage front velocity (VC) appears to be approximately constant (1870-1937 m/s), irrespective of the impact velocity. Instead, it is primarily dependent on the stored elastic energy. In order to determine if the sample dimensions affect VC, it is plotted as a function of the cross-sectional area of the bar (Figure 6-5). Notice that ion-exchanged glasses develop the same surface compressive stress profile (depth and magnitude) for identical processing conditions. However, increased cross-sectional area results in reduced (near-constant) tensile stress magnitudes in the bar interior in order to balance the

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compression and to satisfy the stress equilibrium. Thus, increased cross-sectional area will yield a lower tensile stress over a larger volume resulting in reduced tensile strain energy density. In

Figure 6-5, VC decreased with increasing cross-sectional area (i.e., decreased tensile strain energy density), and vice versa. The trend suggests that the velocity of the self-sustained damage front may not inherently propagate at a constant value equal to the limiting (terminal) velocity, but shows a weak correlation to the internal tensile strain energy density. This is consistent with a study by Takahashi [18] using thermally tempered glass plates, which described a weak dependence of the self-sustained crack velocities on the interior residual tensile stress. However, other studies by Chaudhri [19, 20] have described that the self-sustained fracture front should inherently propagate at the limiting velocity of the given material (material constant), i.e., the velocity at which crack bifurcation is observed.

Figure 6-4B shows the influence of impact velocity on the ejecta velocity at the impact site. At the lowest impact velocities of 52 m/s and 62 m/s, no particles were observed to be ejected from the impact site. As the impact velocity increased, small comminuted particles

(ejecta) were ejected at high velocities up to 525 m/s for the as-received glass and 656 m/s for the strengthened glass at comparable impact velocities of 287 m/s and 283 m/s, respectively. The increased ejecta velocity for the strengthened glass suggested perhaps a difference in the conditions imposed on the fine particle movement from beneath the impact site (e.g. ease of particle movement/flow, impact-induced pressure, etc.) before eventual high-rate ejection. The implications of such differences will be discussed in more detail in the next section, Energy

Balance.

Upon impact, axial splitting along the compression direction caused a non-uniform lateral bulking or a radial increase in the volume of the glass bar. The trends in non-uniform dilation

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depth and velocity are plotted in Figure 6-4C and Figure 6-4 D, respectively, as a function of impact velocity. Additionally, the uniform dilation velocities observed for the strengthened glass are also shown in Figure 6-4D. At low impact velocities of around ~50-60 m/s, no measurable non-uniform dilation occurred at the impact-end in both glasses. As the impact velocity increased, the zone of non-uniform dilation grew. This zone of dilatancy extended from the impact-end to a short distance into the bar, up to 17.9 mm in the as-received glass compared to

13.6 mm in the strengthened glass at comparable velocities of 287 m/s and 283 m/s, respectively.

The depth of uniform dilation in the strengthened glass is not shown as it encompasses the entire specimen length (i.e., 100 mm) in every test regardless of the impact velocity. In Figure 6-4D, the maximum non-uniform dilation velocity (at the impact plane) showed a sharp increase with increasing impact velocity, reaching 91 m/s and 86 m/s for the as-received and strengthened glasses, respectively. Despite similar non-uniform dilation velocities, the non-uniform dilation zone was larger for the as-received glass compared to the strengthened glass. This behavior was perhaps caused by the additional fragmentation and the mode of uniform dilation observed in the strengthened glass (due to inherent strain energy). As the strengthened bar experienced a sudden loss of structural cohesion by uniform dilation, it could no longer effectively support energy transfer from the impacting ball. However, regardless of the impact velocity, the uniform dilation velocity was approximately constant at ~12 m/s, and is related to the strengthening-induced stored energy. As the stored energy in the form of residual stresses is released just ahead of the failure front, fracture energy for crack growth and kinetic energy for uniform dilation are immediately available. Thus, once damage passed through a region it can be assumed that bulking and a sudden redistribution of stored energy into kinetic energy of radial expansion has taken place.

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Interestingly, although the measured uniform dilation velocity was nearly constant along the bar length, when viewed at greater magnification for bars of various cross-sectional dimensions, the damage revealed a periodic relief, where certain sections experienced increased bulking or lateral expansion than others (Figure 6-6). This damage mode is a result of a stress wave phenomenon which is prevalent in impact scenarios and is called “wave splitting” [21-23].

To satisfy lateral stress-free boundary conditions, e.g., when a single stress wave (either longitudinal or shear) reaches a free boundary at an oblique angle, it can trigger both a longitudinal and a shear wave reflection, which is the case for a spherically divergent wave generated by ball impact. This can result in surface strains up to twice that in the bar interior and can lead to the bar section being cleaved along the mid-plane into two halves. If fracture along the mid-plane does not take place, surface normal displacements are directed into the bar causing increased relief normal to the surfaces and initiating a periodic oscillation of the two surfaces.

Thus, as seen in Figure 6-6, the shape of the uniformly dilated zone shows indications of the wave splitting phenomenon, i.e., radial expansion is not entirely uniform and the bulked outer perimeter is not fully parallel to the surface, i.e., “wavy”.

The above discussion focused primarily on damage modes directly measured from the high-speed images, i.e., fracture propagation, ejecta and radial bar dilation. Additional mechanisms of energy dissipation such as frictional contact, fracture surface creation, and elastic wave propagation, cannot be easily determined directly from the high-speed images and require in-depth post-mortem assessment as well as specific defining assumptions. These contributions will be discussed in more detail in the next section, Energy Balance. In order to better understand the deformation mechanisms at high-velocity, an in-depth review of the overall system energy balance was explored.

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Energy Balance

In the previous section, Impact Damage Evolution, noticeable differences in the damage morphology were observed between the as-received and strengthened glasses which were attributed to the additional stored elastic energy in the strengthened glass. However, to better understand the influence of strengthening on the overall (system) energy balance, a comprehensive examination of the operative energy dissipation mechanisms in the two glasses was performed. To simplify the comparison, one set of high-velocity impacts at comparable impact velocities, i.e., kinetic energies of the impacting balls (KB), were considered. The selected impacts were at 287 m/s (17.8 J) and 283 m/s (17.3 J) on the as-received and strengthened glass bars, respectively. Upon impact, energy transfer between the steel ball and glass bars was both elastic and inelastic. The mechanisms of energy dissipation considered were radial dilation (KED) of the glass bars, kinetic energy of fine ejected fragments (KEE) expelled from the impact site, frictional contact (UF), fracture surface creation (UFS), and elastic wave propagation energy

(UEW). Thus, the energy balance equation can be written as

KEB= KED + KEE + UF + UFS + UEW + other (6-1)

Other minor energy loss mechanisms such as light, heat, and acoustic emission are considered negligible and were not considered. All material properties used in the following calculations are provided in Table 6-1.

Kinetic energy of bar dilation

As the damage propagated into the material, the as-received and strengthened glass bars were observed to rapidly dilate near the impact site (Figure 6-7). The maximum non-uniform dilation velocity, V1, MAX, was seen near the impact-end where the impact energy density and fragment density were the highest. However, for both glasses, the dilation velocity decayed

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almost linearly from the impact-end and became zero at a distance, x1 , denoting the maximum extent of the dilatant zone (Figure 6-7). For the strengthened glass, additional ‘uniform dilation’ occurred along the full length of the bar (Figure 6-7B). The kinetic energy of non-uniform

dilation (KED1) was computed as function of the dilation velocity (V1) over length x1 , whereas the kinetic energy of uniform radial dilation (KED2) was based on a near constant dilation

velocity, V2, along the entire bar length, x2 = 100 mm (Figure 6-7). For the strengthened glass, the two forms of dilation (KED1 and KED2) were observed to occur simultaneously and were thus superimposed. Therefore, V1, MAX in the strengthened glass is calculated as the maximum dilation velocity at the impact plane subtracted by the uniform dilation velocity. The equations to calculate the kinetic energies associated with the two bar dilation mechanisms are given by,

x1 V KE0.5 ab V dx ; where V  V  1,MAX x D1 1 1 1, MAX x 0 1 (6-2)

2 KED2 0.5 abx 2 V 2 (6-3) where  is the material density (Table 6-1), a and b are the cross-sectional dimensions of the glass bars and x refers to the position along the bar length from the impact-end. For the as- received bar, the maximum non-uniform dilation velocity was 91 m/s at the impact end, decaying linearly to zero at around 17.9 mm from the impact-end. Therefore, radial dilation accounted for

5.4 J of kinetic energy, or 29.5% of the available energy. For the strengthened glass, the maximum non-uniform dilation velocity was around 86 m/s which decayed to zero at around

13.6 mm, equating to 3.8 J (20.4 % of the total energy). In addition, the average velocity of fragments due to uniform dilation was measured to be close to 13 m/s along the entire bar length,

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resulting in 0.65 J of kinetic energy (3.5% of the total energy). These two forms of dilation encompassed a total kinetic energy of 4.2 J (23.8% of the total energy) in the strengthened glass bar.

For the mode of uniform dilation in the strengthened glass, the uniformly dilating volume was approximated to consist only of regions which were initially in a state of residual compression, taken as an outer skin of thickness ~0.85 mm from the outer surface (approximate depth of compression) [98]. It was verified from the high-speed images that long after the impact

(hundreds of microseconds) the outer regions of the bar initially in compression experienced radial dilation ,while the interior region remained held together as a fragmented skeleton and underwent no outward expansion (not shown for brevity). Additionally, recall that the value of stored compressive strain energy for the strengthened glass bar was found to be ~0.74 J

(Materials section). This value is in good agreement with the computed kinetic energy for uniform dilation (0.65 J). Thus, it was determined that during the equilibration process, the regions initially in compression experienced an expansion, and the stored compressive strain energy is redistributed into uniform particle motion (kinetic energy). In literature, the energy associated with equilibration-related dilation has been broadly assigned to the total stored energy release [86, 103], neglecting individual contributions of the compressive and tensile strain energies. Note that the disparity between the computed values of compressive strain energy and the kinetic energy of uniform dilation may stem from several sources. For example, complete strain energy release during equilibration is assumed; however, some energy may be retained in the fragments as residual energy. Also, inhomogeneities in the residual stress state near sharp corners/edges result in a lower magnitude of compression, a decreased compression depth, and increased localized tension values. This would result in an overestimation of the compressive

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strain energy and an underestimation of the tensile strain energy by ~10%. Lastly, wave-splitting may locally alter the uniformity of the dilation along the bar length, thereby leading to some level of measurement variance.

Kinetic energy of ejecta

From the high-speed images, it was observed that fine particles were ejected from the impact site at high velocities, resulting in kinetic energy being carried by a small volume of comminuted particles (ejecta) (Figure 6-8). As the material ahead of the projectile becomes fragmented, the ball advances into the glass bar. A small localized volume beneath the advancing ball experiences low confinement, but high shear, which comminutes this zone into fine fragments [97]. With continued penetration, the comminuted particles experience high pressure and are extruded around the ball through a more coarsely fragmented tunnel region, causing significant wear to the incoming projectile (ball) nose. The wear surfaces on the recovered balls are defined by inner and outer contact radii, as shown in Figure 6-9. The smaller inner contact radius for the strengthened glass is likely due to the increased penetration resistance as a result of the ultrahigh residual surface compression, which has been shown to increase the glass hardness

(Table 6-1) [26]. The mass of the ejecta was approximated based upon the calculated volume of the comminuted zone using the measured contact radii and Hertzian contact theory [104-106].

The comminuted zone initiates at the point of maximum elastic shear stress beneath the contact surface and then grows towards the loaded surface [106]. The maximum depth of the comminuted zone was estimated based on the outer contact radii of the recovered balls as 1.98 mm and 1.94 mm for the as-received and strengthened glasses, respectively (Figure 6-9).

According to Hertzian elastic contact theory [104], the maximum elastic shear stress is located at a depth below the contact surface of around one-half the contact radius, R, [105, 107], which

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yields a depth, h, of 0.95 and 0.91 mm for the as-received and strengthened glasses, respectively.

The comminuted zone which emanates from a depth (h) and grows up to meet the contact surface was idealized as an elliptical cone with volume (∀),

2휋푅2ℎ ∀= (6-4) 3

Multiplying this value by the glass density (given in Table 6-1), the mass of the comminuted particles (m) was found. By tracking the jets of ejected particles, the average ejecta velocities (VE) for the as-received and strengthened glasses were found to be 525 m/s and 656 m/s, respectively. Notice the large difference in ejecta velocities between the two glasses. This difference may be attributed to two factors which may be interconnected: (i) The additional fragmentation, bulking, and uniform dilation in the strengthened glass may allow more favorably oriented macrocracks in the tunnel region which aid particle flow out of the projectile path and may give rise to easier penetration; and (ii) the ultrahigh residual surface compression may also lend itself to greater sustainable impact pressures (i.e., due to increased fracture strength [3] and hardness [98]) and hence increased ejecta velocities. The kinetic energy of the ejecta is given by,

1 퐾퐸 = 푚푉2 (6-5) 퐸 2 퐸 where m is the mass of ejecta, VE is the average velocity of ejecta. For the as-received and strengthened glass, the energy carried by ejecta was calculated to be 2.6 J and 3.6 J (14.2% and

19.5% of the total energy), respectively. Thus, the energy associated with ejecta is an important factor, which is consistent with literature [108]. However, these fine ejected particles also cause significant frictional contact (and wear) with the incoming projectile, which is discussed in the next section, Frictional energy.

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Frictional energy

As noted above from Figure 6-9, there are clear indications of wear and erosion of the impacting ball. Wear marks appear as radial striations or grooves and are formed as a direct result of frictional contact between the impacting ball and the comminuted particles. Here, exact values of the friction coefficient could not be determined from the experiments. The maximum normal force, 퐹푚푎푥, was estimated by the following impact equation [63].

1 8퐻휌 퐹 = ( )2 휋푅2푉 (6-6) 푚푎푥 3 where ρ is the density of the ball, R is the ball radius, V is the impact velocity, and H is the glass hardness (given in Table 6-1). Assuming that the average normal force, Favg, during penetration to be half the maximum value calculated using Eq. (6), this gives a force of 28.6 kN and 29.3 kN, for the as-received and strengthened glass, respectively. Due to crushing and inelastic deformation, the magnitude of the force is likely much lower. In fact, by making deceleration measurements (from the high-speed images) for both glasses and applying Newton’s second law, the force values are closer to an average force, Favg, of ~10 kN. Limited time and spatial limitations do not permit differentiation between the average force applied to the as-received and strengthened glasses. However, due to a increased fracture strength and a greater hardness value

[98], it would be expected that the impact force for the strengthened glass would be slightly greater. A friction coefficient (휇) from the literature for steel-on-glass contact was found to be

~0.56 [109]. Particle flow was taken to be primarily in a circumferential path around the ball as it penetrated the glass bar. The arc length between the inner and the outer contact radii was 0.56 mm and 0.75 mm for the as-received and strengthened glasses, respectively. It is assumed that the comminuted material flows outward from the point of maximum stress, thereby travelling the arc length of the wear zone, a. Thus, the energy consumed by friction can be computed by [110], 112

푈퐹 = 휇퐹푎푣𝑔푎 (6-7)

The frictional energy in the as-received and strengthened glasses was determined to be

3.1 J and 4.2 J (or 17.1% and 22.5% of total energy), respectively. This large disparity between the as-received and strengthened glasses may be due to enhanced fragmentation in the strengthened glass which leads to increased frictional contact (i.e., contact length, a).

Energy due to fragmentation

The impact process creates a large number of fragments, thereby dissipating a finite amount of impact energy in fracture surface creation. Through an image-based analysis of the collected glass fragments using ImageJ (image processing program), the distributions of fragment sizes and aspect ratios as well as the projected surface area of the fragments was directly measured. The mean values of fragment sizes (s) and fragment aspect ratio (AR) for both glasses were found to be ~1 mm and ~2, respectively, for both glasses (Figure 6-10). Despite the similarities in the particle size and aspect ratio distributions, the strengthened glass had significantly more fragmentation compared to the as-received glass (1-2 orders of magnitude).

From the image analysis, the projected surface area of the fragments for the as-received and the strengthened glasses was 0.9x10-2 m2 and 1.7x10-2 m2, respectively. This area is directly proportional to the total energy in fracture surface creation. Multiplying the surface area by 2 times the fracture energy per unit area, (3.7 J-m-2 [11]), the fracture energy for the as-received and strengthened glass were calculated to be 0.07 J and 0.13 J (or 0.4% and 0.7% of the total available energy), respectively. Thus, despite the large amount of fragmentation observed, very little energy was actually consumed by fracture surface creation, which is concurrent with previous studies in literature due to ballistic impact [108, 111]. More importantly, the sole contribution of the stored elastic energy (due to chemical strengthening) can be derived from

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these experiments by simply taking the difference between the energy consumed by fracture between the as-received and strengthened glasses at comparable impact velocities. As both experiments involve impact energy contributions, the difference in fracture energy consumption between the two glasses describes the contribution of stored elastic energy to fragmentation, which was found to be 0.06 J. This value matches well with the computed stored tensile strain energy which was 0.04 J (given in the Materials section), but not the stored compressive strain energy which was 0.74 J. This agreement further confirms that the energy stored in residual tension will dictate the extent of the fragmentation process.

The energy contribution of macrocracking (bulk fragmentation and mm-size fragments) is well-approximated by the optical approach described above, but microcracking (um-scale and nm-scale size fragments) is not accounted for by the analysis. The imaging method utilized to assess the fragment morphology and fracture area is limited by its inability to accurately quantify microfracture and particle comminution. Finely comminuted particles are highly concentrated to a region near the tip of the projectile during the impact [112]. Once these fragments reach the surface, they were ejected at high-velocity (>500 m/s), and are difficult to collect and measure due to the small volume fraction. However, to compute the contribution of comminution (i.e., micro-fracture) to the energy balance, the average comminuted particle size was approximated.

By measuring the adhered fragments on the steel balls, the average particle size was found to be

~1 um for both glasses. Using the previously computed volume of comminuted material and assuming a predominantly cuboidal fragment morphology, the total number of fragments was estimated to be ~109 and the cumulative fracture area of fine particles was computed to be ~10-2 m2. This yielded a total energy in comminution of 0.32 J and 0.23 J (1.8% and 1.3%) for the as- received and strengthened glasses, respectively. Despite the large number of comminuted

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particles and corresponding surface area generated by crushing the glass into micron and submicron particles, the energy required for this process was found to still be small relative to the total impact energy.

Elastic wave energy

The energy dissipated by elastic wave propagation was computed using equations derived by Reed et al.[113]. The fractional kinetic energy dissipated by the elastic wave propagation is given by,

2 1/2 훿 1−휈2 −1/5 −6/5 3/5 휆 = 7.267 3 (1 + 휈2) ( ) 휌1 퐾 푉 (6-8) 휌2퐶0 1−2휈2 where 퐶0 is the longitudinal wave velocity of the target body, 푉 is the ball impact velocity, and

휌1, 휌2, 휈1, 휈2 are the densities and Poisson’s ratios of the steel ball and target, respectively, and 훿 is a dimensionless quantity dependent only on target Poisson’s ratio. The quantity 퐾 is a parameter computed using,

−1 4 1−휈2 1−휈2 퐾 = ( 1 + 2) (6-9) 3 퐸1 퐸2 where 퐸1 and 퐸2 are the Young’s moduli of the impacting ball and target, respectively. The equations above provide for the total energy dissipated by elastic waves for elastic impact. It is acknowledged that the force-time profile will likely change based on the local state

(elastic/plastic) at the impact site. Thus, the computation is used for the purpose of determining an upper bound of elastic wave dissipation. Due to the violent nature of the impact process, it is assumed that the elastic loading profile will terminate to zero upon reaching the maximum load, translating to a sudden loss of structural cohesion and load bearing capacity. The fractional energy (dimensionless) absorbed by the elastic wave propagation was thus found to be approximately 0.35 and 0.33, for the as-received and strengthened glasses, respectively.

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Multiplying the fractional energy values by the initial kinetic energy of the impacting steel ball yielded the amount of energy dissipated for the as-received and strengthened glasses to be 6.2 J and 5.7 J (35.0% and 33.1% of the total energy), respectively.

Other

Lastly, the glass bars used in this study were freely supported such that exterior boundary conditions would not significantly modify the nature of damage propagation inherent to the tested materials. From the high-speed images, it was found that the bar section beyond the impact-end damage (Figure 6-3) moved at a constant velocity of ~5 m/s, roughly translating to

0.23 J of energy, or 1.3% of the total energy. Thus, more energy went into rigid body motion of the glass bar than into fracture surface creation.

Other factors not included in this energy balance were tensile fracture at the rear-end of the bar during spallation in the as-received glass bar, heat generation, light and acoustic emissions, etc. Tensile cracks near the rear-end of the bar did not always fully cleave sections of glass from the bar, instead only a dense network of internal cracking was observed which could not be accurately quantified. However, as noted above, fragmentation is a small source of energy dissipation and thus little contribution of tensile fracture is anticipated in the overall energy balance. At increased impact velocities, a bright emission of light was observed at the impact- end. Despite the possibility of localized heat generation and light emission due to melting or luminescence (of mechanical or fracture origins), the bright spots are speculated to be due to the deflection of external light at the impact-end causing a saturation of select image sensor pixels in the camera. Finally, plastic deformation and erosion of the steel ball was minimal and was thus not computed.

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Summary of the energy balance

Figure 6-11 illustrates a pie chart for each glass, summarizing the contributions of various energy dissipation modes. Radial expansion (dilation), ejecta, frictional contact, and elastic wave propagation were the most dominant among the considered energy dissipation mechanisms for both the as-received and strengthened glass. These mechanisms encompassed 95% of the total dissipated energy. While the dominant mechanisms in each glass were the same, the as-received bar dissipated 6% more energy by non-uniform dilation, whereas the strengthened bar dissipated more energy by ejecta and frictional contact. In particular, due to the increased ejecta velocities and larger frictional path for the strengthened glass, the individual contribution of ejecta and friction was 5% greater compared to the as-received glass. Due to the complete fragmentation of the strengthened glass, the energy component associated with rigid body motion was not observed. Interestingly, while fracture appears to dominate the impact process, it contributes only ~2% of the total energy dissipated (for both glasses). For both glasses, this leaves less than

1% of unaccounted energy due to neglected dissipation modes and uncertainty in the analysis. It is proposed that self-equilibration mechanisms of strengthened glass which lead to increased fragmentation and uniform radial dilation may reduce the intensity of damage modes such as non-uniform dilation and rigid body motion. Therefore, it is suggested that strengthened glasses may be useful as interlayer window panels in their ability to protect subsequent (regions) layers from impact energy transfer.

Conclusions

Ball impact experiments were performed on as-received and strengthened glass bars to assess the deformation mechanisms as a function of impact velocity. Over the range of impact velocities considered, it was found that the strengthened glass differed from the as-received glass

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as follows: (i) greater damage propagation velocities, (ii) sustained damage growth (complete fragmentation) due to stored tensile strain energy, (iii) suppression of spall fracture, (iv) increased ejecta velocities, (v) comparable non-uniform dilation velocities and reduced depth of non-uniform dilation, and (vi) an additional mode of uniform dilation due to stored compressive strain energy.

Analysis of the contributions of various energy dissipation modes to the overall energy balance were quantified for comparable impact velocities. The analysis revealed that the primary energy dissipation mechanisms were radial dilation, ejecta, frictional contact, and elastic wave propagation. It is proposed that enhanced fracture surface creation and the additional mode of uniform dilation led to increased frictional contact and increased ejecta velocities for the strengthened glass. Thus, the strengthened glass absorbed ~5% more energy by ejecta and by frictional contact. Conversely, the as-received glass dissipated ~6% more of the total energy by non-uniform radial dilation compared to the strengthened glass. As anticipated, the strengthened glass exhibited almost two times the (macro-) fragmentation compared to the as-received glass due to additional stored strain energy. However, the fragmentation characteristics (size and aspect ratio distributions) did not differ significantly for both glasses.

Finally, for the strengthened glass, it was quantitatively verified that the stored tensile energy was well-correlated to the level of fragmentation, while the stored compressive energy matched the magnitude of uniform dilation velocity in the outer (compressive) layers of the strengthened glass. Additionally, a weak correlation was observed between the self-sustained damage velocity and the internal tensile strain energy density for the strengthened glasses.

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Table 6-1. Selected material properties for the as-received glass, the strengthened glass, and the steel ball. As-received Strengthened Steel Property Glass Glass Ball Density (g/cc), 휌 2.41 [98] 2.46 [98] 7.87 [78] Elastic Modulus (GPa), 퐸 81.4 [98] 85.0 [98] 213.0 [78] Shear Modulus (GPa), 퐺 33.3 [98] 35.0 [98] 80.0 [114] Poisson’s Ratio, 휈 0.22 [98] 0.21 [98] 0.30 [78] Vickers Hardness (GPa), 퐻 6.0* [26] 6.5* [26] 5.9 [114]

Fracture Strength (MPa), 휎퐹 14-70 [11] >1000 [9, 26, 98] 2150 [114] † Longitudinal Wave Velocity (km/s), 퐶퐿 6.13 [98] 6.23 [98] 5.20 † Shear Wave Velocity (km/s), 퐶푆 3.69 [98] 3.79 [98] 3.19 † Rayleigh Wave Velocity (km/s), 퐶푅 3.36 [98] 3.44 [98] 2.95 * Dynamic Vickers hardness values † Computed using Equation (A-3)

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Figure 6-1. Schematic of the test setup used for ball impact experiments.

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Figure 6-2. High-speed images of the damage induced by low velocity impacts. Impact A) at 52 m/s on the as-received bar and B) at 62 m/s on the strengthened bar.

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Figure 6-3. High-speed images showing damage evolution due to moderate velocity impacts. Impact A) at 261 m/s on as-received glass [98] and B) at 334 m/s on strengthened glass bars.

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Figure 6-4. Trends in deformation mechanisms as a function of impact velocity. A) Damage front propagation velocity, B) ejecta velocity, C) dilation depth, and D) dilation velocity.

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Figure 6-5. Plot of the average self-sustained damage front velocity for strengthened glass bars of varying cross-sectional dimensions. Note that cross-sectional area is inversely proportional to stored tensile strain energy density.

Figure 6-6. High-speed images of the periodic relief induced in the strengthened glass bars due to wave splitting. Impact at A) 334 m/s and B) 345 m/s. Note that the first relief from the impact-end is likely due to the impact-induced waves while the subsequent relief damages are due to interactions between the stress waves induced at the impact-end and rear-end reflections. The periodic relief is indicated by arrows.

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Figure 6-7. High-speed images revealing the representative dilation behavior observed. Dilation behavior for the the A) as-received and B) strengthened glass bars at comparable impact velocities of 287 m/s and 283 m/s, respectively. The selected frames show the approximate time that both glasses exhibited similar size non- uniform dilation zones, and when the uniform dilation was clearly perceivable.

Figure 6-8. High-speed images illustrating the fine particles ejected from the impact site. Ejecta for the A) as-received and B) strengthened glasses for comparable impact velocities of 287 and 283 m/s, respectively.

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Figure 6-9. Images of steel ball after impact. A) Side-view and B) top-view of the ball which impacted the as-received glass. C) Side-view and D) top-view of the ball which impacted the strengthened glass. The eroded zone is between the inner and outer radii as denoted by the two white circles. E) Fine glass particle adhered to the steel balls and F) the radial grooves due to frictional contact between ejected particles and the steel ball. The wear markings and adhered glass particles are similar for both glasses. 126

Figure 6-10. Fragment characteristics for the as-recevied and strengthened glasses. A) Particle size and B) aspect ratio distributions.

Figure 6-11. Summary of the contributions of various elastic and inelastic deformation mechanisms to the overall energy balance. The breakdown of energy dissipation modes is given for the A) as-recevied and B) strengthened glasses.

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CHAPTER 7 SUMMARY

Residual Stress

Chemically strengthened glasses have become increasingly popular for protecting display screens for electronics such cell phone, TVs, and laptops due to their improved resistance to scratches and fracture. This is accomplished by introducing residual compression into the surface of the glass. The means of characterizing the stress distribution has become problematic due to the enormous compressive stresses (over 1 GPa) and steep stress gradient that are generated.

A simple birefringence method was developed to characterize the high levels of stress and severe stress gradients present in chemically strengthened glasses. By using specimens of different thicknesses, the fringe density was manipulated to produce the ideal number of fringes for a given stress magnitude and stress gradient. The method and analysis make residual stress measurements in strengthened glass simple and approachable. The resultant ability to readily obtain residual stress magnitudes and profile of stresses are of paramount importance to understanding the mechanical behavior of the strengthened glass.

Properties

Multiple experimental techniques were employed to characterize the properties of the strengthened glass compared to its as-received form. Bulk properties such as elastic modulus and density were determined by ultrasonic measurements and Archimedes’ principle, respectively.

The results revealed that the strengthened glass exhibited a greater density and elastic modulus compared to the as-received glass due to the exchange of denser ions in the outer ~1 mm of the glass specimen. Quasi-static and dynamic indentation tests were performed on as-received and strengthened glass surfaces to examine the influence of surface compressive stresses and strain rate on the indentation hardness and cracking behavior. It was found that both compressive 128

stresses and increased strain rate yielded increased hardness values as well as an increase in the resistance to cracking (especially radial cracking). Residual compressive stresses were shown to enhance shear deformation, while increased strain rate promoted densification. Lastly, a novel method was proposed to characterize the residual stress profile based on the influence of the residual stresses on the hardness values. It was found that the residual compressive stresses slightly increased the hardness values, while tensile stresses dramatically decreased the measured hardness.

Impact Response

Ball impact tests were performed to provide insight into the influence of strengthening on the impact-induced damage propagation and impact-induced damage mechanisms. The damage in as-received glass was characterized by limited damage propagation at the impact-end followed by spall fracture at the rear-end. On the other hand, strengthened glasses exhibited continuous oscillatory damage propagation from the impact-end, with no tensile cracks (spallation) forming at the rear-end of the bar. Additionally, stored energy due to the residual stresses fueled sustained damage front propagation once released by the impact damage. The self-sustained damage wave appeared different than traditional explanations would predict. Rather than maximum damage velocities coinciding with the central tension, the damage observed in the current work propagated fastest near the glass edges. It has been proposed that because the central tension magnitude of chemically strengthened glasses is relatively low, the considerably higher residual tension found near glass edges dominates the damage propagation.

In addition to damage propagation, the operative energy dissipation modes were characterized and influence of residual stresses was determined. Over the impact velocities examined it was found that the damage in strengthened glass differed from the as-received glass

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as follows: (i) higher damage propagation velocities, (ii) sustained damage growth (complete fragmentation) due to stored tensile strain energy, (iii) suppression of spall fracture, (iv) higher ejecta velocities, (v) reduced depth of non-uniform dilation, and (vi) an additional mode of uniform dilation due to stored compressive strain energy. Analysis of the fractional contributions of the various energy dissipation mechanisms to the overall energy balance revealed that bar dilation, ejecta, and frictional contact were the primary inelastic mechanisms. It was suggested that enhanced fragmentation and the additional mode of uniform dilation in the strengthened glass led to increased frictional contact, increased ejecta velocities, and a reduced zone of non- uniform dilation compared to the as-received glass. For the strengthened glass, it was also quantitatively verified that the residual stored tensile strain energy correlated with the energy consumed by fracture surface creation, while the compressive strain energy dictated the uniform dilation velocity.

Future Work

High Compression, Low Case-Depth Strengthened Glasses

Through microscale indentation studies presented in Chapter 4, strengthened glasses have been shown to clearly outperform its as-received counterpart with greater hardness values and increased resistance to fracture. However, macroscale ball impact experiments shown in Chapter

5 have demonstrated that this improvement is limited to a practical mechanical limit. Once damage is initiated and extends beyond the case-depth, catastrophic and self-sustained failure ensues. The energy balance calculations shown in Chapter 6 have identified that the catastrophic damage wave that consumes the strengthened bar is driven by strain energy stored in the residual tensile zones. Thus, residual tension in strengthened glasses should ideally be minimal.

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The magnitude of the interior tensile stress is a function of sample thickness and the compressive stress profile. Recall that the chemical strengthening process develops a pre- determined compressive stress profile (maximum compressive stress and depth of compressive layer) in the surface layer of the glass article. The tensile stress profile and magnitude develops in response to balance the compressive stress. The thicker the glass article, the larger the area over which to balance the compressive stress, leading to reduced levels of tension. Similarly, a reduced magnitude of maximum compressive stress and shallower depth of compression both decrease the balancing tension which is generated.

As the dimensionality of the sample cannot always be altered, it would be of specific interest to determine how the self-sustained fracture propagation could be influenced or limited by reducing the level of interior tension across a constant cross-section, i.e. modify the tensile strain energy density. This would be accomplished by using strengthened glasses with a shallow fixed case-depth and varied levels of compression (moderate to high compression). This would also present further exploration into the weak correlation observed between the self-sustained damage velocity and the internal tensile strain energy density for the strengthened glasses.

Raman Spectroscopy

Raman spectroscopy is a useful non-destructive tool for evaluating material

“microstructure”, which highlights the nature of bonding and structure of a given material. The spectrum produced by a typical scan is composed of Raman peaks which are characteristic of various bonding and vibrational modes. Despite the lack of crystallinity or crystal structure in glass, the short-range order of the glass structure still produces characteristic peaks, albeit broad peaks or bands. Raman spectra for an as-received (untreated) glass and a strengthened glass are given in Figure 7-1. The peak at ~476 cm-1 is present in both glasses and is relatively insensitive

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to the differences between the glasses, i.e., stress and alkali dopant atoms (Na+ and K+). Slight shifting of ~1.5 cm-1 towards higher wavenumbers is indicative of structural (bond length) shortening due to increased density and residual compressive stress.

Previous work [115-117] has demonstrated the ability of Raman spectroscopy to evaluate indentation-induced densification in glass. This work discusses densification in a variety of different normal and anomalous glasses; however, no work has demonstrated whether elastic stresses or structural modification by ion exchange may present an influence on the densification behavior. Furthermore, no Raman work has analyzed the influence of strain rate on densification.

Recall that indentation deformation proceeds through a combination of volume-conserving

(deviatoric) shear flow and volume-reducing (hydrostatic compression) densification. It has been presented in Chapter 4 that residual stress and strain rate dramatically influenced the shear deformation behavior observed in as-received and strengthened glass, but it is unclear how the densification component of the deformation process was affected. Thus, future studies aimed at revealing this information through densification maps are vital to better understanding the underlying mechanisms of deformation which result from chemically strengthening glass.

Preliminary Raman mapping studies have been conducted and are presented in Figure 7-

2). Figure 7-2A and Figure 7-2C show line scans which extend ~25 µm from the indents apex towards the edge of indent and terminate outside the indent impression (virgin material) for as- received and strengthened glass, respectively. The analysis focused on the position of the peak

-1 close to ~476 cm , which is related to the 3-D bond-rocking mode of the SiO2 bonds [118]. Note that the virgin peak position in both glasses was slightly lower (~464 cm-1) for the mapping scans compared to the point scans. This is attributed to determining the peak position from lower resolution scans, which was necessary for minimizing scan duration and drift. For the as-

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received glass (Figure 7-2B) and the strengthened glass (Figure 7-2D), it can be observed that the peak is maximally shifted towards higher wavenumbers near the indent apex (by 24 and 38 cm-1 for the as-received and strengthened glass, respectively). Because the pressure is highest at the center of the indent and quickly diminishes towards the indent perimeter, this indicates that maximum densification occurs at the point of maximum applied pressure. Moving away from the indent apex, the peak position exhibited less shifting denoting less densification as the deformation intensity was reduced near the indent perimeter. The primary finding is that the densification-induced shifting was much more pronounced in the strengthened glass under comparable loads. Recall that the strengthened glass exhibited greater shear-induced faulting during indentation compared to the as-received glass (Chapter 4). It can be inferred that along with greater shear deformation comes a greater level of densification, suggesting that increased shear may play a role in and/or enhance the densification process.

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Figure 7-1. Raman spectra for as-received and strengthened glass. The A) characteristic spectra are overlaid with the peak positions denoted. The peaks were determined by curve-fitting the profile in order to determine the underlying peak structure for the B) as-received and C) strengthened glass.

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Figure 7-2. Raman map data for static indentations. A) Line map on as-received glass and B) Raman peak position profile. C) Line map on strengthened glass and D) Raman peak position profile. The color-coding in the line scan corresponded to the peak position.

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APPENDIX: ELASTIC WAVE VELOCITIES

퐸 0.5 Longitudinal Wave Velocity, 퐶 = ( ) [35] Equation (A-1) 퐿 휌

퐺 0.5 Shear Wave Velocity, 퐶 = ( ) [35] Equation (A-2) 푆 휌

0.862+1.14휈 Rayleigh Wave Velocity, 퐶 = 퐶 [35] Equation (A-3) 푅 1+휈 푆

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BIOGRAPHICAL SKETCH

Phillip A. Jannotti graduated Summa Cum Laude with B.S. in Mechanical Engineering from the University of Florida in 2010. He began his research on strengthened glasses with

Professor Ghatu Subhash during his undergraduate tenure in the Spring of 2010, and continued this research as his thesis project during his Ph.D. studies in mechanical engineering. Beginning in 2011, Phillip also worked on a separate project developing microstructure-property relationships for advanced boron carbide-based structural ceramics. In 2014, he began working on a project seeking to manufacture novel boron carbide crystal structures with enhanced structural stability and mechanical properties. During his graduate studies, he published 4 journal papers and 2 conference papers related to his glass work. Additionally, he published 2 journal papers and 2 conference papers on structural ceramics. Finally, he collaborated with Sanika

Subhash, a high school student, leading to a co-authored journal paper and conference paper on the unique mechanical response of coquina rock. Mr. Jannotti graduated in Spring of 2015 with a Ph.D. in Mechanical Engineering and a minor in Materials Science and Engineering. His research interest are focused on the characterization of advanced materials using static and dynamic mechanical testing in order to develop microstructure-property relationships and to identify the underlying deformation mechanisms.

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