Failure Behavior of Glass and Aluminum Oxynitride (AlON) 

Tiles Under Spherical Indenters 

by Trevor E. Wilantewicz

ARL-TR-5180 May 2010 

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Army Research Laboratory 

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ARL-TR-5180 May 2010 

Failure Behavior of Glass and Aluminum Oxynitride (AlON) 

Tiles Under Spherical Indenters 

Trevor E. Wilantewicz 

ARL/Oak Ridge Associated Universities 

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Failure Behavior of Glass and Aluminum Oxynitride (AlON) Tiles Under 

Spherical Indenters 

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Trevor E. Wilantewicz*

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14. ABSTRACT 

The failure behavior of glass and ceramic tiles during quasi-static loading from spherical indenters is studied. The failure 

behavior is examined on both a micro- and macro-size scale. The former is achieved by using a small spherical diamond 

indenter to study the localized contact behavior, and the latter is achieved by loading large tiles to complete structural failure 

using a unique test configuration. The influence of tile thickness and indenter radius on the failure behavior is also examined. 

Information on fundamental damage mechanisms in glass and ceramic materials subjected to localized contact, including the 

onset of inelastic deformation and the initiation of cracks, may be meaningful in relation to screening and ranking brittle 

materials for failure resistance. 

15. SUBJECT TERMS

ceramics, glass, indentation 

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Trevor E. Wilantewicz 

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iii

Contents 

List of Figures v

List of Tables viii

1. Introduction 1

1.1 Multiaxial Dynamic Failure Modes in Ceramics and Glasses ........................................1

1.2 Objectives ........................................................................................................................1

2. Background Review 2

2.1 Hertzian Contact ..............................................................................................................2

2.2 Cracking Behavior (Elastic Contact) ...............................................................................3

2.3 Cracking Behavior (Elastic-Plastic Contact) ...................................................................3

2.4 Multiaxial Failure ............................................................................................................4

3. Material Selection 5

3.1 Glass Materials ................................................................................................................5

3.2 Ceramic Materials ...........................................................................................................5

4. Experimental Procedures, Results, and Discussion 6

4.1 Instrumented Indentation Testing (IIT) ...........................................................................6

4.1.1 IIT Equipment .....................................................................................................6

4.1.2 Yield Stress Measurements ...............................................................................10

4.1.3 Indentation Damage Patterns .............................................................................14

4.1.4 IIT Load-Displacement Data Analysis ..............................................................25

4.1.5 In-Situ Crack Initiation Observation .................................................................28

4.2 Structural Failure Experiments ......................................................................................34

4.2.1 Tile Preparation and Testing .............................................................................35

4.2.2 Failure Test Results ...........................................................................................37

4.2.3 Flaw Size Estimates ...........................................................................................47

4.3 Other Experiments .........................................................................................................47

5. Summary and Conclusions 49
iv

6. Future Work 50

7. References 51

Appendix. Hertzian Equations 55 

Distribution List 57 
v

List of Figures 

Figure 1. Schematic of Hertzian contact loading. Idealized cross section showing the ringcone crack system and several measurable features. .................................................................2

Figure 2. Schematic of Zwick hardness measuring head. Key components are shown. ...............7

Figure 3. Schematic of a test sequence illustrating how the load and displacement data are 

collected. Also shown are the speeds (V) corresponding to the different steps involved 

for a test......................................................................................................................................7

Figure 4. Load-displacement traces in polycrystalline aluminum from Vickers indentation. ........9

Figure 5. Vickers indentation in polycrystalline aluminum made at 20-N load. ............................9

Figure 6. Residual indentation depth as a function of load for the three glass materials using 

a spherical 500-m-diameter single-crystal diamond indenter. Tin side of the Starphire 

and Borofloat glasses was tested. .............................................................................................10

Figure 7. Straight line fits through high-load data points for determining load at “full” plastic 

yield. The x-intercept marks this load. Error bars are same as in figure 6. ...........................12

Figure 8. Residual indentation depth as a function of load for AlON using a spherical 

500-m-diameter single-crystal diamond indenter. .................................................................13

Figure 9. Straight line fit through high-load data points in AlON for determining load at 

“full” plastic yield. ...................................................................................................................13

Figure 10. Indentation sites in the tin side of Starphire glass produced with spherical 

500-m-diameter single-crystal diamond indenter. .................................................................15

Figure 11. Load-displacement traces for the tin side of Starphire glass. The curves 

correspond to the same indentation sites shown in figure 10. Curves produced with 

spherical 500-m-diameter single-crystal diamond indenter. .................................................16

Figure 12. The 200-N indentation site in tin side of Starphire glass and corresponding loaddisplacement trace for test showing catastrophic failure under indenter. The 500-mdiameter spherical diamond indenter used. ..............................................................................17

Figure 13. Indentation sites in the tin side of Borofloat glass produced with spherical 

500-m-diameter single-crystal diamond indenter. .................................................................19

Figure 14. Load-displacement traces for the tin side of Borofloat glass. The curves 

correspond to the same indentation sites shown in figure 13. Curves produced with 

spherical 500-m-diameter single-crystal diamond indenter. .................................................20

Figure 15. Indentation sites in silica glass produced with spherical 500-m-diameter 

single-crystal diamond indenter. ..............................................................................................21

Figure 16. Load-displacement traces for the silica glass. The curves correspond to the same 

indentation sites shown in figure 15. Curves produced with spherical 500-m-diameter 

single-crystal diamond indenter. ..............................................................................................22

Figure 17. Indentation sites in polycrystalline AlON produced with spherical 500-mdiameter single-crystal diamond indenter. ...............................................................................23
vi

Figure 18. Load-displacement traces for AlON. The curves correspond to the same 

indentation sites shown in figure 17. Curves produced with spherical 500-m-diameter 

single-crystal diamond indenter. ..............................................................................................24

Figure 19. An example of deformation twinning inside a 150-N indentation in AlON 

produced with 500-m-diameter spherical diamond indenter. ................................................25

Figure 20. Elastic recovery and percent elastic recovery as a function of the maximum 

indentation load for glass and AlON materials. Data for tin sides are plotted for Starphire 

and Borofloat glasses. ...............................................................................................................26

Figure 21. Comparison of elastic recovery behavior of tin and air sides of Starphire glass. .......26

Figure 22. Maximum penetration depth as a function of load for the three glass materials 

and AlON. ................................................................................................................................27

Figure 23. Experimental setup for observing the crack initiation behavior of transparent 

materials in real time with the IIT system. ..............................................................................28

Figure 24. In-situ indentation patterns in the tin sides of Starphire (left) and Borofloat (right) 

glasses: (a) F < Fc, (b) F = Fc, (c) F = Fmax = 150 N, and (d) complete unloading 

(F = 0 N) ([a–c] loading cycle and [d] unloading cycle). .......................................................31

Figure 25. In-situ indentation patterns in silica glass (left) and AlON (right): (a) F < Fc, 

(b) F = Fc, (c) F = Fmax, and (d) complete unloading (F = 0 N) ([a–c] loading cycle and 

[d] unloading cycle). ................................................................................................................32

Figure 26. The 150-N indentation sites in Starphire glass for both air and tin sides made 

with 500-m-diameter spherical diamond indenter. ................................................................34

Figure 27. Picture of the experimental setup used to study the structural failure behavior of 

the tiles. ....................................................................................................................................35

Figure 28. Starphire tile both as-received and after 220-grit abrasion: (a) as-received air 

side, (b) after abrasion air side, (c) as-received tin side, and (d) after abrasion tin side. 

All images 250× original magnification. .................................................................................36

Figure 29. Failure load for the 3.2-mm-thick Starphire glass tiles loaded with steel balls of 

different diameter. ....................................................................................................................39

Figure 30. Failure load for the 6-mm-thick Starphire glass tiles loaded with steel balls of 

different diameter. ....................................................................................................................39

Figure 31. Failure load for 12-mm-thick Starphire glass tiles loaded with steel balls of 

different diameter. ....................................................................................................................40

Figure 32. Several failed 3.2-mm Starphire tiles. The star-like fracture patterns are typical of 

biaxial flexural testing. Top row, left to right: 0.125-, 0.25-, and 0.5-in ball. Bottom row, 

left to right: 0.5-in ball and only bottom surface abraded, 0.0625-in ball. Tiles are 4 × 4 

in2. ............................................................................................................................................41

Figure 33. As-received 3.2-mm Starphire tile loaded to failure with 0.5-in steel ball. Tile is 

4 × 4 in2

. ...................................................................................................................................41

Figure 34. Mean contact stress at the initiation load for ring-cone cracks as a function of the 

ball diameter for the tin side of Starphire glass. Data for an unabraded tile. ..........................42
vii

Figure 35. Failed 6-mm Starphire tiles that formed no macro conoid (a) and that did form a 

macro conoid (b). Tension side faces up (a) and compression side faces up (b). Steel ball 

diameter 0.0625 in. Tiles are 4 × 4 in2. ...................................................................................44

Figure 36. Failed 12-mm Starphire tile loaded with a 0.75-in-diameter steel ball. The 

tension side, illustrating the large crater formed from the macro conoid, faces up. The 

chipped away pieces are not shown. ........................................................................................44

Figure 37. A sequence of frames illustrating the formation and growth of the ring-cone crack 

(a–c), and the initiation of the spall failure (d) in the 12-mm Starphire tile (tin side) 

contacted with the 0.25-in-diameter steel ball. Load increases from a to d. ...........................46

Figure 38. Average failure load as a function of tile thickness. Two different curve fits of 

the data show the exponential or power-law dependence on tile thickness. ............................46

Figure 39. Ring crack stress as a function of ball diameter for the tin sides of unabraded 

Starphire and Borofloat glasses. ..............................................................................................47

Figure 40. Ring crack load as a function of ball diameter for the tin sides of unabraded 

Starphire and Borofloat glasses. ..............................................................................................48
viii

List of Tables 

Table 1. Material mechanical data. .................................................................................................5

Table 2. IIT accuracy test results. ...................................................................................................9

Table 3. Residual depth. ................................................................................................................11

Table 4. Yield data. .......................................................................................................................12

Table 5. Deformation and fracture loads. .....................................................................................14

Table 6. Crack initiation summary. ...............................................................................................29

Table 7. Acoustic emission data. ..................................................................................................33

Table 8. Starphire glass failure test results. ..................................................................................38
1

1. Introduction 

1.1 Multiaxial Dynamic Failure Modes in Ceramics and Glasses 

The failure of ceramic and glass materials under ballistic loading is a complex process involving 

a number of distinct multiaxial dynamic failure modes (1–5). These failure modes include, but 

are not limited to, (1) front- and back-face radial cracking, (2) pulverization (comminution) in 

the vicinity of the penetrator, (3) microcracking, (4) steep and shallow cone cracking, and (5) 

lateral cracking. 

These failure modes are not particular to just ballistic impacts, since they are also observed to 

varying extents in dynamic impacts of spheres and rods on ceramics (1, 6–14) and glass 

(8, 15–17) at less than ballistic velocities, and even in quasi-static spherical (Hertzian) and 

cylindrical punch indentation tests (18–26). The formation of very narrow shear bands under 

impact sites in boron carbide has been observed as well and is thought to be the result of 

localized shear failure of the material (12). 

The fact that many of the failure modes seen in ballistic impact tests can be reproduced under 

quasi-static loading conditions under an indenter provides some motivation for the current work. 

Although it is recognized that actual ballistic testing is the definitive way to judge material and 

system performance, it is usually time consuming and costly to conduct, and not possible on 

prototype or experimental materials that may be too small or in limited supply. 

Much effort has been devoted to understanding the material properties that govern ballistic 

performance (27–32) in order to guide research and development of new materials that perform 

better, while still being lightweight and cost-effective to produce. However, one challenge that 

still exists is to create a simple set of experiments that may be used to successfully screen and 

down-rank candidate armor materials in terms of intrinsic (material) performance potential. The 

current work may possibly form part of such a screening test. 

1.2 Objectives 

The failure behavior of glass and ceramic tiles to quasi-static loading from spherical indenters 

forms the basis of the current study. The failure behavior is examined on both a micro- and 

macro-size scale. The former is achieved by using a small spherical diamond indenter to study 

the localized contact behavior, and the second is achieved by loading large tiles to complete 

structural failure using a unique test configuration. 

The influence of tile thickness and indenter radius on the failure behavior is also examined. By 

varying the tile thickness and indenter radius, researchers hope to achieve different failure 

behavior, which might be meaningful in helping to screen candidate materials. Information on 
2

fundamental damage mechanisms in glass and ceramic materials subjected to localized contact, 

including the onset of inelastic deformation and the initiation of cracks, may possibly be 

meaningful in relation to screening and ranking materials for potential ballistic protection design. 

2. Background Review 

2.1 Hertzian Contact 

The contact of an elastic sphere on a rigid elastic body is referred to as Hertzian contact, named 

after Heinrich Rudolf Hertz (33), who first studied this contact situation. A schematic of this 

contact condition is shown in figure 1. If the contact remains entirely frictionless and elastic, 

then the Hertz equations relating the contact load, contact radius, and stress are valid. With 

either the onset of fracture or plasticity, or the presence of friction, the equations are no longer 

strictly valid (22). 

Figure 1. Schematic of Hertzian contact loading. Idealized cross section showing the ringcone crack system and several measurable features. 

However, it is for these reasons the test is used, i.e., to study the deformation and fracture 

response of materials to localized contact. Of the two responses, the onset of plasticity 

invalidates the use of the Hertz equations more than fracture does, since the latter can be nearly 

R 

2a 

2C 



2ri 

c 

specimen 

P 
3

reversible (elastic) under certain conditions. In addition, one is usually concerned with the stress 

level just up to the point of fracture, or yield, where the Hertz equations are valid. 

Indentation contacts can be characterized as either “sharp” or “blunt” depending on whether 

inelastic or elastic deformation of the specimen precedes fracture, respectively (22). Thus, the 

ball indenter radius can be chosen so as to either promote or prevent yield before fracture. For 

Hertzian fracture tests, the ball radius is usually chosen to be large enough to promote fracture 

before yield. However, yielding may occur after fracture if the loads are further increased, since 

the mean contact stress continues to increase with load. 

The indenter material is usually chosen such that its elastic and strength properties considerably 

overmatch the specimen to be examined, e.g., steel or tungsten carbide balls for glass specimens 

and tungsten carbide or diamond balls for ceramic specimens. This ensures that the majority of 

deformation and fracture occurs in the specimen and not the indenter. The appendix defines the 

pertinent Hertzian equations used in this study. 

2.2 Cracking Behavior (Elastic Contact) 

Generally speaking, one of two scenarios with respect to ring and cone crack initiation can occur 

when a ball indenter is loaded onto the surface of a rigid brittle material. The following results 

are primarily based on observations in glass because of its transparency: (1) unstable initiation 

(“pop-in”) of the entire ring-cone crack system or (2) initiation of the ring crack, stable growth of 

the ring crack downward, followed by unstable initiation of the cone crack. 

In both scenarios, after the unstable initiation of the cone crack, the crack grows stably with 

further increase of the load. That is, the strain energy release rate decreases as the crack extends, 

thus making the Hertzian cone a stable crack system. This is to be expected, since the base of 

the cone crack grows larger with increasing load, thus supporting the load. More detailed 

discussions of the initiation behavior can be found elsewhere in several good references (22, 23, 

34–46). 

On unloading, the cone crack is usually observed to retract some, and then at a critical load a 

portion of the cone surface usually detaches itself from the rest. This can generate an intense 

acoustic emission signal. Because of this, the cone crack is highly visible under load, but after 

load removal its visibility decreases, except for the portion close to the surface. 

2.3 Cracking Behavior (Elastic-Plastic Contact) 

If the ball indenter has a sufficiently small diameter, or if a sufficiently high contact load is 

achieved, the material may transition from elastic to elastic-plastic during the course of loading. 

For glasses, the term plastic is being used loosely to indicate inelastic deformation has ensued. 

For example, Swain and Hagan (47) observed plastic yielding and the formation of ring-cone, 

radial, and lateral cracks in soda-lime-silica glass indented with 0.49- and 1.0-mm-diameter 

spherical tungsten carbide indenters and 1.0-mm-diameter spherical diamond indenters. On 
4

loading, elastic deformation took place first, followed by the formation of surface ring cracks, 

and then subsurface plasticity. Occasionally a large cone crack would initiate from the surface 

ring crack, but this usually did not occur. Continued loading produced subsurface median 

cracks. 

On unloading, the median cracks were observed to start closing, and subsequently, radial cracks 

initiated. The radial cracks were sometimes extensions of the median cracks, but in most cases 

they were observed to initiate separately at the edge of the contact impression. Lateral cracks, 

whose orientation are mainly parallel to the surface, were observed to initiate just prior to 

complete load removal. 

Hagan and Swain (48) show evidence that the initiation of median cracks about Vickers and 

small-diameter sphere indentations in soda-lime-silica glass are the result of intersections of 

shear flow lines beneath the surface that occur at high loads, while smaller radial cracks were 

found to extend from the corners of the indentations at the surface for smaller loads. The shear 

flow lines constituted a subsurface region of damage (damage zone) directly below the 

indentation. Subsurface lateral cracks were also observed and found to be extensions of the 

shear faults. 

Lawn et al. (49) show strong evidence that radial cracks in soda-lime-silica glass can also be the 

result of extensions of shear flow lines at the surface. Haranoh et al. (50) have examined the 

initiation of cracks in chemically strengthened (ion-exchanged) glasses with a Vickers indenter 

and found that median and radial cracks did not initiate despite the fact the damage zones 

beneath the indents were deeper than the surface compressive stress layers. They interpreted this 

to mean that radial and median cracks must also form near the surface, since radial and median 

cracks formed in the unstrengthened specimens for the same load. Thus, it appears there is still 

some uncertainty regarding the location of median crack initiation in glass. 

2.4 Multiaxial Failure 

Lardner et al. (51) examined the fracture of glass plates of varying thickness (1, 1.83, and 3 mm) 

supported by 3-mm-thick substrates of glass, steel, and poly(methyl methacrylate) (PMMA) 

using a 12.7-mm-diameter WC-6% Co spherical indenter. Depending on the glass thickness and 

substrate material, different fracture behaviors were observed. 

Lardner et al. found that the fracture patterns fell into four categories: (1) ring, cone, and backface radial cracking, (2) ring cracking and back-face radial cracking, (3) back-face radial 

cracking, and (4) ring and cone cracking. The last mode was seen for the 3-mm-thick glass 

samples regardless of the substrate material. Back-face radial cracking occurred for the 1-mmthick samples, which were supported by steel, indicating that localized bending of the specimens 

can still take place even with rigid support. 

Part of the intent of the current work is to produce a similar variety of failure modes, but with 

thicker specimens that may be more relevant to ballistic protection design.
5

3. Material Selection 

The materials used in this study were transparent, with the exception of the AlON, which was not 

as transparent compared to the glasses. This allowed direct observation of the formation of 

cracks from indentation contact. 

3.1 Glass Materials 

All glass materials examined in the current work were from commercial glass manufacturers. 

The glasses were soda-lime-silica float glass (Starphire*), borosilicate float glass 

(BOROFLOAT†), and vitreous silica. The Starphire and Borofloat materials are produced by 

PPG Industries and Schott Glass, respectively. The vitreous silica specimens were made by 

Corning Inc. 

All glass materials were furnished in the form of 4- × 4-in square tiles with different thickness. 

The Borofloat tiles were 19 mm thick, while the Starphire tiles were provided in thicknesses of 

3.2, 6, and 12 mm with beveled edges. The vitreous silica specimens were provided in 

thicknesses of 6.35, 19.05, and 25.4 mm. Table 1 lists several mechanical properties of the 

glasses as provided by the manufacturers. 

Table 1. Material mechanical data. 

Material 

Young’s 

Modulus, E 

(GPa) 

Poisson’s 

Ratio 

Knoop 

Hardness 

(GPa) 

Density 

(g/cm3) 

Starphire 73.1 0.22 4.6 (500 gf) 2.51 

Borofloat 63 0.20 4.7 (100 gf) 2.23 

Silica glass 72.7 0.16 5.1 (100 gf) 2.201 

AION 323 0.24 18.1 (200 gf) 3.69 

Diamond (indenter) 1141 0.07 ~70 3.52 

Steel (indenter) 200 0.30 ~7 7.5 

3.2 Ceramic Materials 

The ceramic material chosen for study was polycrystalline aluminum oxynitride (AlON). AlON 

is a transparent ceramic with the spinel crystal structure and has a large, average grain size, i.e., 

about 150 m (52). The oxygen and nitrogen anions form a close-packed, face-centered cubic 

lattice (53, 54). 

 *

Starphire is a registered trademark of PPG Industries. 

†

BOROFLOAT is a registered trademark of Schott Glass. 
6

The approximate composition is Al23O27N5. The cubic structure leads to mainly isotropic 

behavior; however, the large grain size can introduce anisotropies on a localized scale. For 

example, microhardness measurements performed on AlON may only sample a single grain 

depending on the indentation load and hence are susceptible to crystallographic effects. 

4. Experimental Procedures, Results, and Discussion 

4.1 Instrumented Indentation Testing (IIT) 

Instrumented indentation testing (IIT) was utilized to study the deformation and fracture 

behavior of the materials to localized indentation contact. In this test format, the load and 

displacement of the indenter into the material are simultaneously, and continuously, monitored 

throughout the load-unload cycle. 

This format provides valuable information on material behavior, including penetration depths, 

hardness under load, elastic recovery, and energy dissipation that cannot otherwise be obtained 

from conventional hardness testing equipment. 

A 500-m-diameter spherical diamond indenter was used. It was made from a single crystal by 

Gilmore Diamond Tools, Inc., (Attleboro, MA) by a special process called precision spindle 

method. This resulted in a surface that was exceptionally smooth and uniform in diameter. 

Temperature and relative humidity were monitored and varied from 22 to 24 °C, and 41% to 

58%, throughout the course of all testing, respectively. 

4.1.1 IIT Equipment 

The IIT equipment consisted of a specialized hardness testing head made by Zwick, Inc., 

attached to a standard universal testing machine (Model Z005), also made by Zwick. A 

schematic of the hardness head is shown in figure 2. 

The hardness head is attached to a cross member (not shown), which is attached to the test frame 

(not shown), which provides the up and down linear motion via a stepping motor. A load cell 

inside the head measured the force, while a transducer measured the displacement to a resolution 

of 0.02 m. The load cell had a 2500-N useable range. 

The entire system was computer controlled. The test software allowed total user control of the 

entire indentation process, including loading rate on both loading and unloading, maximum load, 

hold time at maximum load, type of control (i.e., load or position control), etc. In addition, a 

variety of results could be reported, including the maximum load, maximum displacement depth, 

residual indentation depth, hardness under maximum load, total test time, etc. The load and 

displacement data could be exported for subsequent user analysis as well.
7

Figure 2. Schematic of Zwick hardness measuring head. Key components 

are shown. 

A schematic illustrating the principles of operation is shown in figure 3. At position 1, the head 

is sitting above the sample and moves down toward the sample at speed VLE. At step 2, the unit 

has moved down until the sensor foot contacts the specimen. Further motion downward at speed 

Vpre-test causes the indenter tip to contact the specimen (step 3). However, just before this contact 

occurs, the speed switches to Vcontact. 

Figure 3. Schematic of a test sequence illustrating how the load and displacement data are collected. 

Also shown are the speeds (V) corresponding to the different steps involved for a test. 

The very slight increase in load brought about by the contact establishes the zero point of the 

measurement. The speed at which the indenter approaches the sample during this step (Vcontact) 

is set very low such that the zero point is established very accurately, i.e., with minimal 

overshoot. Once the zero point is established, the test cycle commences at step 4, in which the 

displacement rate is set by the user as Vtest.
8

For spherical indenters a “preload” can be employed at the beginning of step 4, in which a small 

load is applied to “settle” the indenter and specimen for the ensuing major test cycle. The 

preload function does not need to be used but is recommended by the manufacturer. Once the 

desired maximum load, or displacement, is reached, the indenter is withdrawn at Vtest (step 5), 

which can be set different than Vtest on loading. 

At the end of step 5, the load is zero, and if permanent deformation of the sample has occurred, a 

residual depth of hmin is measured. After step 5, the entire hardness head is withdrawn at a rate 

of Vreturn. Note that the permanent indentation depth is given by the difference in displacement 

readings of steps 3 and 5, while the maximum displacement depth is given by the difference in 

readings between steps 3 and 4. The elastic recovery is given by the difference in readings 

between steps 4 and 5. 

Instrument compliance can be a significant factor leading to inaccurate displacement depths, 

where elastic deformations of the machine are superimposed on those from the specimen. Note 

that instrument compliance does not affect the value of hmin, since all elastic deformations of the 

machine and specimen are recovered when the load reaches zero, neglecting any anelastic 

deformations. However, at all other points of the load-displacement curve, the measured depths 

will not necessarily reflect the actual displacement into the sample due to machine compliance. 

Because of the design of the Zwick instrument, the only compliance that is sampled occurs in the 

indenter material located between the sensor foot and the measurement transducer, which is 

relatively small. To account for this, the manufacturer has calculated this compliance and 

factored it out of the displacement readings. The result of this is a displacement measurement 

that accurately reflects only the inelastic and elastic deformations occurring in the sample. 

The compliance factor, as given by the manufacturer, is 0.0049679 m/N. According to the 

manufacturer, the resolution of the displacement measuring system was 0.02 m. 

To test the accuracy of the measurement system, a piece of polycrystalline aluminum metal was 

indented with a Vickers diamond six times at a 20-N load. The diagonals of the resulting 

indentations were measured under an optical microscope equipped with a digital camera and 

measurement software. 

The depth under load was then calculated for each indentation by dividing the average diagonal 

length by seven. This stems from the geometry of the Vickers diamond, where the indentation 

depth is one-seventh the length of the diagonals (49). Since aluminum metal is soft and does not 

undergo significant elastic recovery, particularly along the diagonals where the plastic strain is 

very intense, the measurement of the diagonals of the residual indent can give a good measure of 

the depth under load. 
9

This calculated depth was then compared with the actual depth measured by the IIT. The results 

are shown in table 2. As shown in table 2, the measured depth was about 8 % lower than the 

calculated depth, which amounted to an absolute difference of just 2.2 m. This data is taken as 

evidence that the IIT gives accurate displacement readings. The load-displacement traces for 

these tests are shown in figure 4. An indentation in the aluminum is shown in figure 5. 

Table 2. IIT accuracy test results.a

Diagonal Length 

(μm) 

Calculated Depth 

(μm) 

Measured Depth 

(μm) 

Difference 

(%) 

188.3 ± 1.5 26.9 ± 0.2 24.7 ± 0.3 8.0 ± 1.5 a

Values in table are average ±1 standard deviation 

Figure 4. Load-displacement traces in polycrystalline 

aluminum from Vickers indentation. 

Figure 5. Vickers indentation in polycrystalline 

aluminum made at 20-N load.

Polycrystalline Aluminum

0

5

10

15

20

25

0 5 10 15 20 25 30

Displacement (m)

Load (N)
10

4.1.2 Yield Stress Measurements 

The 500-m-diameter spherical diamond indenter was used to measure the yield stress of the 

three glass materials and the AlON by making indentations at progressively higher loads, starting 

at 2 N up to 200 N. Ten indentations at each load were made. The “tin” and “air” sides of the 

Starphire, and the tin side of the Borofloat glasses, were tested. 

By plotting the average residual indentation depth as a function of load, the onset of inelastic 

deformation can be determined. This method is believed to be more sensitive than trying to 

visually observe when a permanent impression is left in the material, since the deformations may 

be smaller than the wavelength of light and thus impossible to detect. 

According to the manufacturer, the displacement measuring system has a resolution of 0.02 m, 

so in principle, it should be able to detect yielding before optical detection can. The results are 

plotted in figure 6 for the three glass materials. At low loads the materials behave elastic, but as 

the load is increased a permanent set depth begins to appear. Table 3 lists the residual depths as 

a function of load. Differences of residual depth between the materials are more noticeable at 

the higher loads. 

Figure 6. Residual indentation depth as a function of load for the three glass 

materials using a spherical 500-m-diameter single-crystal diamond 

indenter. Tin side of the Starphire and Borofloat glasses was tested. 

Glass Materials

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 50 100 150 200 250

Load (N)

Residual Depth (

m)

Borofloat (Tin)

Starphire (Tin)

Silica Glass

Starphire (Air)
11

Table 3. Residual depth.a

Residual Depth 

(μm) 

Load 

(N) 

Starphire 

(Tin) 

Starphire 

(Air) 

Borofloat 

(Tin) 

Silica Glass AION 

2 0.03 ± 0.01 0.03 ± 0.01 0.04 ± 0.01 0.03 ± 0.01 0.02 ± 0.00 

5 0.03 ± 0.01 0.04 ± 0.01 0.04 ± 0.01 0.03 ± 0.01 0.02 ± 0.01 

10 0.04 ± 0.02 0.05 ± 0.01 0.04 ± 0.01 0.04 ± 0.01 0.03 ± 0.01 

20 0.05 ± 0.01 0.07 ± 0.01 0.05 ± 0.01 0.05 ± 0.01 0.04 ± 0.01 

30 0.07 ± 0.01 0.10 ± 0.00 0.07 ± 0.01 0.06 ± 0.02 0.08 ± 0.05 

35 0.10 ± 0.02 0.11 ± 0.01 0.09 ± 0.01 0.06 ± 0.02 0.07 ± 0.05 

40 0.11 ± 0.01 0.14 ± 0.01 0.11 ± 0.02 0.07 ± 0.02 0.12 ± 0.11 

45 0.15 ± 0.01 0.18 ± 0.01 0.13 ± 0.01 0.07 ± 0.01 0.26 ± 0.14 

50 0.22 ± 0.02 0.23 ± 0.01 0.17 ± 0.01 0.08 ± 0.02 0.33 ± 0.18 

55 0.30 ± 0.01 0.33 ± 0.02 0.21 ± 0.02 0.11 ± 0.02 0.32 ± 0.21 

65 0.54 ± 0.02 0.59 ± 0.03 0.32 ± 0.02 0.11 ± 0.02 0.51 ± 0.19 

75 0.91 ± 0.09 0.96 ± 0.04 0.48 ± 0.03 0.15 ± 0.01 0.72 ± 0.10 

100 2.21 ± 0.24 2.46 ± 0.14 1.16 ± 0.06 0.36 ± 0.02 1.12 ± 0.16 

125 4.00 ± 0.16 4.18 ± 0.06 2.54 ± 0.30 0.90 ± 0.06 1.63 ± 0.20 

150 5.32 ± 0.16 5.62 ± 0.29 4.20 ± 0.29 1.85 ± 0.11 2.11 ± 0.18 

200 8.06 ± 0.54 8.40 ± 0.23 7.30 ± 0.26 4.48 ± 0.34 3.37 ± 0.35 a

Values in table are average ±1 standard deviation. 

As discussed by Tabor (56), initial yielding under a ball indenter occurs at 1.1Y, where Y is the 

yield stress measured in simple uniaxial tension or compression. According to theory, yielding 

begins to take place at a point 0.5a below the surface directly under the indenter, where a is the 

contact radius (18). At this location the shear stress is a maximum, given by 0.48po, where po

is the mean contact stress. Only when the mean stress reaches 3Y does all the material begin to 

yield around the indenter, a condition referred to as “full” plasticity. 

From figure 6, the full plasticity condition is taken to occur in the region where the residual 

depth is linear with the load. Straight line fits through these higher load data points were used to 

determine the loads for full plastic yielding. This is shown in figure 7, where the x-intercept of 

the straight lines corresponds to this load. The Hertz equations (equations 1–3 in the appendix) 

were then used to calculate the mean stress corresponding to these loads. The results are 

summarized in table 4. 

The Vickers hardness of the materials measured at 0.98 N (100 gf), with a 15-s hold time, is 

shown in the last column in table 4. Residual depth data for the AlON is plotted in figures 8 and 9. 

The transition from elastic to elastic-plastic behavior is more well-defined for AlON compared to 

the glasses. Since AlON is a crystalline material, a definite yield stress exists for the movement 

of dislocations and the formation of mechanical twins, and this may result in a more defined 

transition point. 
12

Intercept Load (Glass)

y = 0.0563x - 4.1876 

(Borofloat Tin)

R2 = 0.9856

y = 0.0422x - 4.1729 

(Silica glass)

R2 = 0.9723

y = 0.0569x - 3.2779 

(Starphire Tin)

R2 = 0.9977

y = 0.0591x - 3.3448

(Starphire Air)

R2 = 0.9984

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0 50 100 150 200 250

Load (N)

Residual Depth (

m)

Borofloat (Tin)

Starphire (Tin)

Silica Glass

Starphire (Air)

Figure 7. Straight line fits through high-load data points for determining load at 

“full” plastic yield. The x-intercept marks this load. Error bars are same 

as in figure 6. 

Table 4. Yield data.a

Material 

Yield Load 

(x-Intercept) 

(N) 

Contact 

Radius 

(μm) 

Yield 

Stress 

(GPa) 

Vickers 

Hardness 

(GPa) 

Starphire (tin) 57.6 53.1 6.5 5.1 ± 0.1 

Starphire (air) 56.6 52.8 6.5 4.8 ± 0.1 

Borofloat (tin) 74.3 60.7 6.4 5.3 ± 0.2 

Silica glass 98.8 63.7 7.8 6.8 ± 0.4 

AION 41.9 31.1 13.8 21.3 ± 0.8 *

Values in table are average ±1 standard deviation. 
13

AlON

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 50 100 150 200 250

Load (N)

Residual Depth (

m)

Figure 8. Residual indentation depth as a function of load for AlON using a spherical 

500-m-diameter single-crystal diamond indenter. 

Intercept Load (AlON) 

y = 0.0206x - 0.8649 (AlON)

R2 = 0.9937

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 50 100 150 200 250

Load (N)

Residual Depth (um)

Figure 9. Straight line fit through high-load data points in AlON for determining load 

at “full” plastic yield. 
14

Both slip and mechanical twinning have been shown to occur in the permanent deformation of 

aluminum oxide by indentation (51) and hence are also expected to occur in AlON. In table 5, 

the loads for permanent deformation (dimpling), ring cracking, and radial cracking are shown for 

the three glasses and AlON based on postmortem observations of the indentation sites. 

Table 5. Deformation and fracture loads.a

Material 

Onset 

Dimpling 

(N) 

All Tests 

Dimpled 

(N) 

Onset Ring 

Cracking 

(N) 

All Tests 

Ring Cracked

(N) 

Onset Radial 

Cracking 

(N) 

All Tests 

Radial 

Cracked 

(N) 

Starphire (tin) 30 30 65 75 75 100 

Starphire (air) 20 30 65 100 100 125 

Borofloat (tin) 30 35 30 45 100 200 

Silica glass 75 100 20 30 65 75 

AION 35 45 45 65 40 75 a

Values in table are average ±1 standard deviation. 

Loads are listed for both the onset of this behavior and that for which all tests displayed ring 

cracking, dimpling, and radial cracking. That is, at the onset loads, not all tests may have formed 

dimples, ring cracks, or radial cracks.

The vitreous silica exhibited ring cracking at a much lower load compared to the Starphire and 

slightly lower compared to Borofloat. On the other hand, the silica glass had the highest load for 

which all tests were dimpled, followed by Borofloat, then Starphire. Little difference was seen 

in the deformation and fracture loads for the air and tin sides of the Starphire glass. 

The behavior for the three glasses with increasing load, with respect to the onset of elastic, 

plastic, and fracture responses, can best be described as (1) Starphire: elastic→plastic→fracture; 

(2) Borofloat: elastic→plastic and fracture; or (3) silica glass: elastic→fracture→plastic. Note 

how the silica glass fractures well before yielding, which could be considered a more brittle 

response compared to the other glasses. For AlON, the trend is elastic→plastic→fracture. 

4.1.3 Indentation Damage Patterns 

Figures 10–18 show indentation patterns and corresponding load-displacement traces for the 

three glasses and AlON. 

4.1.3.1 Starphire Glass. Figure 10 shows indentation patterns in the tin side of Starphire glass 

for loads ranging from 35 to 200 N imaged using differential interference contrast (DIC) lighting 

conditions on an optical microscope. At loads from 2 to 20 N, no visual damage (cracking or 

dimpling) was seen in the glass. 
15

Figure 10. Indentation sites in the tin side of Starphire glass produced with spherical 

500-m-diameter single-crystal diamond indenter. 
16

Figure 11. Load-displacement traces for the tin side of Starphire glass. The curves correspond to the 

same indentation sites shown in figure 10. Curves produced with spherical 500-m-diameter 

single-crystal diamond indenter. 

Starphire Tin 2 N

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Displacement (m)

Load (N)

Loading 

Unloading

Starphire Tin 35 N

0

5

10

15

20

25

30

35

40

02468

Displacement (m)

Load (N)

Loading 

Unloading

Starphire Tin 55 N (top indent)

0

10

20

30

40

50

60

0 2 4 6 8 10 12

Displacement (m)

Load (N)

Loading

Unloading

Starphire Tin 75 N

0

10

20

30

40

50

60

70

80

0 5 10 15

Displacement (m)

Load (N)

Loading

Unloading

Starphire Tin 100 N

0

20

40

60

80

100

120

0 5 10 15 20

Displacement (m)

Load (N)

Loading

Unloading

Starphire Tin 200 N

0

50

100

150

200

250

0 10 20 30 40

Displacement (m)

Load (N)

Loading

Unloading
17

Figure 12. The 200-N indentation site in tin side of Starphire glass and corresponding loaddisplacement trace for test showing catastrophic failure under indenter. The 500-mdiameter spherical diamond indenter used. 

The data in table 3 supports these observations for loads up to 10 N, taking the experimental 

scatter into account, where the residual depth is within the limits of detectability of the 

measuring system; recall the resolution of the displacement measuring system was given as 

0.02 m by the manufacturer. 

At 30 N, table 3 shows the residual depth to be 0.07 ± 0.01 m. These 30-N dimples were just 

visible in the glass; however, these could not be seen on a digital image. At 35 N, the dimples 

could be imaged (see figure 10). Note that although the residual depth is 0.10 ± 0.02 m, i.e., 

below the wavelength of visible light, the widths of the dimples are expected to be at least twice 

the depths, and thus begin to be on the cusp of visual detection. The DIC illumination method 

also enhances the detectability by increasing resolution, since the dimples up to 45-N load were 

not seen using ordinary bright-field imaging. 

Load-displacement traces for this glass are shown in figure 11. For loads above 100 N, 

discontinuities (jogs) were observed in the load-displacement traces corresponding to the 

initiation of a large ring-cone crack and/or massive failure below the indenter. The latter would 

produce a loud audible pop, at which point a drastic discontinuity was seen. This was believed 

to correspond to massive failure below the indenter, where the compressive strength of the glass 

was exceeded. An example is illustrated in figure 12. Note how the residual depth goes to zero. 

This is believed to be due to the pulverized material occupying a non-negligible volume due to 

dilatation, which pushed back on the indenter. The 200-N indentation in figure 10 contains a 

small region at the center that is intact, whereas the one in figure 12 does not, thus supporting 

this hypothesis. 

Starphire Tin 200 N

0

50

100

150

200

250

0 10 20 30 40

Displacement (m)

Load (N)

Loading

Unloading
18

4.1.3.2 Borofloat Glass. Figure 13 shows indentation patterns on the tin side of the Borofloat 

glass. The dimples were more difficult to observe compared to the Starphire glass, partly 

because they were shallower. The indentation at 65 N shows that the region of dimpling is 

significantly smaller than the ring crack radius. Since ring cracks tend to initiate just outside the 

contact radius, it is clear that a condition of full plastic flow has not been achieved, otherwise the 

dimple should extend to near the edge of contact. 

At 75 N, the dimple is seen to extend to a larger fraction of the contact radius, closer to a 

condition of full plasticity. However, compared to the Starphire glass, the dimple is still not as 

well developed. These observations support the higher intercept load observed for this glass 

compared to Starphire. Although the stress level for full plasticity is nearly the same for both 

glasses, it takes a higher load to reach this stress level compared to the Starphire glass (see table 4). 

More severe surface spalling also occurred for this glass compared to Starphire (see 150-N 

indentation). Radial cracks were observed for loads of 100 N and above but tended to be 

obscured by the surface spalling. These cracks were shorter compared to Starphire glass, 

indicating a tougher glass. 

Load-displacement traces for the Borofloat are shown in figure 14. Small discontinuities (jogs) 

in these curves were frequently observed for the higher load tests and are believed to result from 

the initiation of particularly severe ring-cone cracks. 

4.1.3.3 Silica Glass. Figure 15 shows indentation patterns in the vitreous silica glass as a 

function of load. In this glass, cracking occurred well before the presence of permanent 

deformation could be observed. The 200-N indentation site is shown in transmitted light, which 

highlights the extensive cracking that occurred, including the well-developed radial cracks. 

Discontinuities in the load-displacement curves tended to occur at lower loads and appear in 

more tests compared to the other glasses. Figure 16 shows plots of the load-displacement curves 

for this glass. 

4.1.3.4 AlON. In figure 17, indentation sites are shown for the AlON material for loads 

ranging from 35 to 200 N. Because the average grain size of the AlON is very large, i.e., 

~150 m, the indentations are primarily within single grains, especially for the lower loads. In 

addition, the cracks are likely contained within single grains, except perhaps at the higher loads, 

e.g., 200 N, where the cracks might span several grains. 

Because the indents lie primarily within single grains, anisotropies in cracking behavior were 

observed, despite AlON being cubic. This is because the crystallographic orientation of the 

indented faces of the grains is different and influences the fracture behavior. Twinning has been 

shown to occur on the fracture surfaces of AlON test specimens (43), and deformation twins can 

also be seen within many of the indentations in figure 17. Figure 18 shows indentation sites in 

AlON as a function of load. 
19

Figure 13. Indentation sites in the tin side of Borofloat glass produced with spherical 500-mdiameter single-crystal diamond indenter. 

40 N 

35 N 
20

Figure 14. Load-displacement traces for the tin side of Borofloat glass. The curves correspond to the 

same indentation sites shown in figure 13. Curves produced with spherical 500-m-diameter 

single-crystal diamond indenter. 

 

Borofloat Tin 2 N

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Displacement (m)

Load (N)

Loading

Unloading

Borofloat Tin 35 N

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10

Displacement (m)

Load (N)

Loading

Unloading

Borofloat Tin 55 N

0

10

20

30

40

50

60

0 5 10 15

Displacement (m)

Load (N)

Loading

Unloading

Borofloat Tin 75 N

0

10

20

30

40

50

60

70

80

0 5 10 15 20

Displacement (m)

Load (N)

Loading

Unloading

Borofloat Tin 100 N

0

20

40

60

80

100

120

0 5 10 15 20 25

Displacement (m)

Load (N)

Loading

Unloading

Borofloat Tin 200 N

0

50

100

150

200

250

0 10 20 30 40

Displacement (m)

Load (N)

Loading

Unloading
21

Figure 15. Indentation sites in silica glass produced with spherical 500-m-diameter singlecrystal diamond indenter. 
22

Figure 16. Load-displacement traces for the silica glass. The curves correspond to the same indentation 

sites shown in figure 15. Curves produced with spherical 500-m-diameter single-crystal 

diamond indenter. 

Silica Glass 35 N

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10

Displacement (m)

Load (N)

Loading

Unloading

Silica Glass 2 N

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Displacement (m)

Load (N)

Loading

Unloading

Silica Glass 55 N

0

10

20

30

40

50

60

0 2 4 6 8 10 12

Displacement (m)

Load (N)

Loading

Unloading

Silica Glass 75 N

0

10

20

30

40

50

60

70

80

0 5 10 15

Displacement (m)

Load (N)

Loading

Unloading

Silica Glass 100 N

0

20

40

60

80

100

120

0 5 10 15 20

Displacement (m)

Load (N)

Loading

Unloading

Silica Glass 200 N

0

50

100

150

200

250

0 10 20 30 40

Displacement (m)

Load (N)

Loading 

Unloading
23

Figure 17. Indentation sites in polycrystalline AlON produced with spherical 500-mdiameter single-crystal diamond indenter. 
24

Figure 18. Load-displacement traces for AlON. The curves correspond to the same indentation sites 

shown in figure 17. Curves produced with spherical 500-m-diameter single-crystal diamond 

indenter. 

AlON 2 N

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4

Displacement (m)

Load (N)

Loading

Unloading

AlON 35 N

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Displacement (m)

Load (N)

Loading

Unloading

AlON 55 N

0

10

20

30

40

50

60

012345

Displacement (m)

Load (N)

Loading

Unloading

AlON 75 N

0

10

20

30

40

50

60

70

80

0123456

Displacement (m)

Load (N)

Loading

Unloading

AlON 100 N

0

20

40

60

80

100

120

01234567

Displacement (m)

Load (N)

Loading

Unloading

AlON 200 N

0

50

100

150

200

250

0 5 10 15

Displacement (m)

Load (N)

Loading

Unloading
25

Figure 19 shows a good example of deformation twinning within a 150-N indentation. In 

addition to slip, twinning in crystals is another way to achieve irreversible deformation. The 

dark bands represent shear failure of material because of twin formation. That is, the material 

twins and then fails along the twin. 

Figure 19. An example of deformation twinning inside a 150-N 

indentation in AlON produced with 500-mdiameter spherical diamond indenter. 

Twinning results from homogeneous shear deformation in which the crystal changes shape at 

fractions of the atomic displacement (Burgers) vector in all planes, in comparison to slip where 

movement occurs in multiples of the Burgers vector along specific planes. Twinning also differs 

from dislocation slip in that a reorientation of the lattice takes place, where twinned atoms are a 

mirror image of those in the untwinned material. In dislocation slip, the lattice orientation 

remains essentially unchanged after the dislocation passes through (58). 

4.1.4 IIT Load-Displacement Data Analysis 

The load-displacement data was examined for each of the materials with respect to the maximum 

displacement and elastic recovery of the indentations in the vertical (depth) direction. The 

results are plotted in figures 20–22. The elastic recovery is seen to increase for all materials with 

increasing maximum load, as seen in figure 20. 

The Borofloat glass showed the most elastic recovery, followed by silica glass, Starphire, and 

then AlON. However, when the percent elastic recovery is plotted, the silica glass has the 

greatest percentage elastic recovery, followed by Borofloat, Starphire, and then AlON.
26

Elastic Recovery vs. Maximum Load

0

5

10

15

20

25

30

2 5 10 20 30 35 40 45 50 55 65 75 100 125 150 200

Load (N)

Elastic Recovery (m)

60

65

70

75

80

85

90

95

100

Percent Elastic Recovery (%)

Starphire Elastic Recovery Borofloat Elastic Recovery

Silica Glass Elastic Recovery AlON Elastic Recovery

Starphire Percent Elastic Recovery Borofloat Percent Elastic Recovery

Silica Glass Percent Elastic Recovery AlON Percent Elastic Recovery

Figure 20. Elastic recovery and percent elastic recovery as a function of the maximum indentation 

load for glass and AlON materials. Data for tin sides are plotted for Starphire and 

Borofloat glasses. 

Elastic Recovery: Starphire Air vs. Tin 

0

5

10

15

20

25

30

2 5 10 20 30 35 40 45 50 55 65 75 100 125 150 200 250

Load (N)

Elastic Recovery (m)

50.0

60.0

70.0

80.0

90.0

100.0

110.0

Percent Elastic Recovery (%)

Starphire (Air) Elastic Recovery Starphire (Tin) Elastic Recovery

Starphire Air Percent Elastic Recovery Starphire Tin Percent Elastic Recovery

Figure 21. Comparison of elastic recovery behavior of tin and air sides of Starphire glass.
27

Figure 22. Maximum penetration depth as a function of load for the three glass 

materials and AlON. 

Figure 21 shows there is no significant difference between the air and tin sides of the Starphire 

glass in terms of elastic recovery behavior. One may note the air side shows slightly more 

percent elastic recovery compared to the tin side. 

In figure 22, the maximum penetration is shown as a function of the load for all materials. The 

Starphire and silica glasses showed similar behavior, and no significant differences between the 

air and tin sides of the Starphire are apparent. 

The Borofloat showed slightly higher penetration compared to the silica and Starphire glasses. 

The higher silica content of the Borofloat glass compared to Starphire yields a more open 

structure capable of deforming more under load, despite the fact these glasses had similar 

Vickers hardness (the greater elastic recovery behavior of the Borofloat may cause more 

contraction of the diagonals in a conventional Vickers indentation test, leading to similar Vickers 

hardness). 

Although the silica glass has the most open structure of the glasses, it has a stronger connected 

network due to the lack of modifier ions and hence shows less penetration under load compared 

to Borofloat, consistent with its higher Vickers hardness. 

The AlON showed the least penetration with load, consistent with its strong intrinsic bonding 

compared to the glasses, as evidence by its high Vickers hardness.

Maximum Penetration vs. Load

0

5

10

15

20

25

30

35

40

0 100 200

Load (N)

Maximum Penetration (m)

Starphire (Air) Starphire (Tin)

Silica Glass AlON

Borofloat (Tin)
28

4.1.5 In-Situ Crack Initiation Observation 

Experiments were conducted on all three glass materials and AlON in which the formation of 

cracks was observed in real time via a unique test configuration that was set up on the IIT tester. 

A picture of the test arrangement is shown in figure 23. 

Figure 23. Experimental setup for observing the crack initiation behavior of 

transparent materials in real time with the IIT system. 

The specimen rested on a 1-in-thick steel plate that had a 0.75-in-diameter hole in the middle to 

allow light to pass through to the glass prism below. The glass prism redirected the light 90° into 

the zoom lens and camera system. A laptop computer and software allowed observation and 

recording of the entire contact process from below. The steel plate was in turn supported by the 

steel sample holder, which was hollow in the middle with a 3-in-diameter support radius. 

The thick steel plate and small circular hole helped ensure rigid specimen support. An acoustic 

emission sensor was attached to the specimen with super glue to record any activity. The 

acoustic emission (AE) system also recorded the load from the IIT tester, so the initiation load 

was recorded for each hit produced. 

Twenty tests were conducted, with a maximum load of 150 N and a displacement rate of 1 m/s 

on both loading and unloading. Table 6 summarizes the crack initiation behavior. Parentheses 

indicate the percentage of tests in which that behavior was observed. 

zoom lens

camera

sample

steel  

plate

hardness test

head

acoustic emission  

sample

holder  

glass prism

and holder

x‐y stage

light
29

Table 6. Crack initiation summary.a

150-N Max. Load Loading Cycle Unloading Cycle 

Material 

Ring/Cone 

Cracking 

(N) 

Radial 

Cracking 

(N) 

Lateral 

Cracking 

(N) 

Radial 

Cracking 

(N) 

Lateral 

Cracking 

Starphire (tin) 39 ± 8 (100%) No No 74 ± 3 (100%) Yes 

Starphire (air) 76 ± 10 (100%) No No 71 ± 7 (100%) Yes 

Borofloat (tin) 50 ± 20 (100%) 60% No 27 ± 18 (100%) Yes 

Borofloat (air) 60 ± 29 (100%) 55% No 25 ± 9 (100%) Yes 

Vitreous silica 24 ± 9 (100%) 24 ± 9 (100%) No 48 ± 12 (100%) Yes 

AION 56 ± 17 (100%) (70%) No (100%) Yes a

Values in table are average ±1 standard deviation. 

All materials had ring-cone cracks initiate on loading. There was a substantial difference in 

initiation loads between the tin and air sides for the Starphire glass but not much difference 

between these sides for the Borofloat. The air side of the Starphire was slightly more resistant to 

ring-cone cracking than the air side of the Borofloat, but the opposite was true for the tin sides. 

The vitreous silica was least resistant to ring-cone cracking of all the glasses. 

The reason for the rather large discrepancy in ring cracking loads in the tin side of Starphire 

between the postmortem observations of cracking conducted from the yield stress tests (table 5), 

i.e., 65 N, and the in-situ measurements, i.e., 39 N, is puzzling, particularly since no significant 

differences were seen between the air sides from the two test techniques. One possibility is that 

the tin side of the sample was unintentionally, and unknowingly, handled roughly after the yield 

stress tests, introducing more severe surface flaws that caused the ring crack initiation loads to 

decrease. 

The AlON material initiated ring-cone cracks on loading, but the overall extent of cone crack 

formation was unclear. In addition, the silica glass, Borofloat, and AlON materials had radial 

cracks initiate on loading. For the silica glass, the radial cracks that initiated on loading did so 

simultaneously with the ring-cone cracks that initiated. Radial cracks were seen to initiate in 

100% of the tests for silica glass and 70% of the tests for AlON. 

For the Borofloat glass, radial cracks initiated on loading for about half the tests, primarily at 

loads higher than the load needed to initiate the first ring-cone crack. For all the glasses, the 

unloading cycle began with the cone crack retracting significantly, but not all the way, and was 

particularly pronounced for the silica glass. This occurred before the initiation of any radial 

cracks on unloading. Some retracting of the cone crack in the AlON was seen as well, though it 

did not appear as pronounced as for the glasses. Radial cracks initiated in all materials on 

unloading; however, for the Borofloat glass only 55% and 60% of the tests had these cracks 

initiate, corresponding to the air and tine sides, respectively, and were the same tests that formed 

these cracks on loading.
30

For the Borofloat and silica glasses, the radial cracks that formed on loading would tend to 

retract slightly on unloading, which was then followed by the initiation of additional radial 

cracks. For the Starphire glass, a drastic cracking event took place on unloading corresponding 

to the partial detachment of the top one-third of the cone crack from the rest of the cone crack. 

This event was accompanied simultaneously by the initiation of the radial cracks and is believed 

to result from the large elastic mismatch between the “plastic” zone and surrounding elastic 

material. 

This type of behavior was significantly reduced in the Borofloat, and especially the silica, glasses 

because of the lower elastic mismatch. This is because these glasses have a more open network 

structure and fewer modifying cations, and hence undergo less shape change beneath the 

indenter. This results in less elastic mismatch and a less intense residual crack opening force 

compared to Starphire glass, where the greater amount of modifier ions allows more shear flow 

to take place, which increases the mismatch. 

The loads at which radial cracks formed in the AlON could not be determined accurately due to 

the translucent nature of the AlON. On the unloading half-cycle, the formation of radial cracks 

at lower loads indicates an increased resistance to cracking. This is because as the indenter is 

removed and the load decreases, the net tensile stress at any fixed location near the surface 

increases as the elastic compressive stresses continually diminish. 

Thus, the Starphire glass had the greatest resistance to radial cracking on loading, since no cracks 

formed. However, on unloading, the Borofloat and silica glasses had greater resistances to radial 

cracking, since these cracks formed at lower loads compared to Starphire. Lateral cracks formed 

in all materials near or just after complete load removal. 

4.1.5.1 In-Situ Indentation Patterns. Figure 24 shows indentation sequences on the tin sides of 

the Starphire and Borofloat glasses. Frames (a) represent contact of the indenter just before 

ring/cone crack initiation. Frames (b) correspond to the exact moment the ring/cone crack 

popped in. The diameter of the cone crack is much larger in the Borofloat glass because the 

average initiation load was greater in the Borofloat tin side compared to the Starphire tin side 

(see table 6), hence the cone crack grew larger at the moment of initiation in the Borofloat glass. 

Frames (c) correspond to the maximum load (150 N). Two small radial cracks can be seen in the 

Borofloat glass, shown by the two small white arrows in this picture. Frames (d) represent 

complete unloading of the indenter, which is when the load is zero. The radial cracks are 

apparent in the Starphire glass in this frame. Radial cracks are seen in the Borofloat, but they are 

smaller due to this glass’ slightly higher toughness and reduced residual crack driving force 

compared to Starphire. 

Figure 25 shows indentation sequences in silica glass and AlON. Radial cracks are visible in the 

silica glass at the moment of ring/cone crack initiation, as seen in frames (c). The cracking 

behavior of the AlON was less pronounced in this example, probably because of anisotropy,
31

Figure 24. In-situ indentation patterns in the tin sides of Starphire (left) and Borofloat (right) 

glasses: (a) F < Fc, (b) F = Fc, (c) F = Fmax = 150 N, and (d) complete unloading (F = 0 

N) ([a–c] loading cycle and [d] unloading cycle). 

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

~ 500 m
32

Figure 25. In-situ indentation patterns in silica glass (left) and AlON (right): (a) F < Fc, (b) 

F = Fc, (c) F = Fmax, and (d) complete unloading (F = 0 N) ([a–c] loading cycle 

and [d] unloading cycle). 

(a) (a)

(b) (b)

(c) (c)

(d) (d)

~ 500 m
33

resulting from the indentations being on the order of the grain size or smaller. In addition, the 

AlON was not fully transparent but was slightly cloudy, which further reduced the clarity of the 

images compared to the glasses. 

4.1.5.2 Acoustic Emission Data. Table 7 summarizes the acoustic emission hit and energy data 

from the crack initiation experiments. In AE, what is being monitored is the sensor’s electrical 

response to a mechanical stimulus, not the actual stimulus itself. Hence, factors such as the 

degree of coupling between the sensor and the test material could potentially affect the results. 

 Table 7. Acoustic emission data.a

Material 

Hits 

Loading 

Hits 

Unloading 

Total 

Hits 

Energy 

Loading 

Energy 

Unloading 

Total 

Energy 

Starphire (tin) 25 ± 10 7 ± 3 31 ± 10 259 ± 114 180 ± 45 439 ± 127 

Starphire (air) 103 ± 37 12 ± 4 103 ± 37 904 ± 363 185 ± 49 1032 ± 366 

Borofloat (tin) 39 ± 14 5 ± 6 44 ± 13 1449 ± 261 65 ± 95 1514 ± 263 

Borofloat (air) 90 ± 37 12 ± 6 101 ± 37 2957 ± 787 99 ± 67 3056 ± 791 

Vitreous silica 83 ± 21 6 ± 4 88 ± 23 1415 ± 232 79 ± 73 1493 ± 275 

AION 21 ± 6 1 ± 1 22 ± 6 350 ± 237 4 ± 9 354 ± 238 a

Values in table are average ±1 standard deviation. 

In this work, a cyanoacrylate-based, fast-acting adhesive was used to couple the sensor to the 

surfaces of the specimens. All AE parameters were kept the same for all materials. The energy 

data is in arbitrary units. Relative comparisons between materials are sought. 

A hit refers to a more-or-less discrete signal detected and processed by the AE computer, and to 

a first approximation the total hit amount can be thought to represent the overall activity 

occurring in the material. The energy measurement is a function of the amplitude and duration 

of a hit and thus indicates the intensity of a hit. 

The data show that the air sides of the Starphire and Borofloat glasses were considerably more 

active than the tin sides, possibly suggesting a greater amount of deformation and microcracking 

activity on the air sides. In addition, this difference in activity primarily arose on the loading 

cycle, since the unloading cycles showed much less difference in the number of hits between the 

air and tin sides. 

Whereas the hits on loading arose from the initiation of ring-cone cracks and possibly other 

smaller microcracking events, e.g., material crushing between surface ring cracks, the unloading 

hits were generated by the initiation of radial and lateral cracks. 

One may thus expect to see a difference between the surface ring cracking behavior between the 

air and tin sides of these two glasses; however, posttest microscopy was unable to reveal any 

differences above the normal test-to-test variations typically seen.
34

This is illustrated in figure 26 for Starphire glass, which shows 150-N indentation sites on both 

the tin and air sides. One possible explanation is that the stress waves are carried more intensely 

(that is, with less attenuation) on the air side than the tin side, allowing more higher-intensity 

signals to pass the threshold requirement for detection. 

Figure 26. The 150-N indentation sites in Starphire glass for both air and tin sides made with 

500-m-diameter spherical diamond indenter. 

4.2 Structural Failure Experiments 

Square tiles of the Starphire glass with nominal dimensions of 4 × 4 in with thicknesses of 3.2, 6, 

and 12 mm were used in the structural failure tests. The tiles were cut from larger sheets of glass 

by Swift Glass Company (Elmira, NY). The eight side edges of the tiles and the four corner 

edges were beveled smooth by Swift Glass in order to minimize the probability of the tiles 

failing from edge defects left over from the tile cutting process. 

In these tests the tiles were centrally loaded with hardened steel spheres (McMaster Carr 

Bearing-Quality Aircraft-Grade E52100 Alloy Steel; Grade 25; ±0.001-in-diameter tolerance; 

±0.000025-in sphericity; 295,000-psi (2.03-GPa) yield strength; Rockwell Hardness C60-67) 

while being supported by the same 3-in-diameter circular sample holder used in the crack 

initiation tests. 

A picture of the assembly is shown in figure 27. Three steel alignment rods ensured the tiles 

were loaded at their center, two of which are shown labeled in figure 25. The third rod is behind 

the sample holder. The sample holder rested on an x-y stage, which allowed further fine-tuning 

of the alignment if necessary. The sample holder was fastened to a steel plate that was fastened 

to the x-y stage, which allowed no movement of the sample holder during testing. 

The whole assembly was attached to the piston of the Instron 1332 hydraulic testing machine 

through several additional pieces. The sample holder was made from 17-4 steel, which can be 

(precipitation) hardened if desired. The holder was not hardened in case further machining 

modifications were deemed necessary after testing was complete. The indenter holder and other 

fixtures made from 17-4 steel were hardened and turned a dark bronze color from the hardening 

process.

Air Tin
35

Figure 27. Picture of the experimental setup used to study the structural failure behavior of the 

tiles. 

The steel balls were held in place by semicircles machined into the indenter holders, which were 

the depth of one-half of the ball diameter. Each diameter ball had its own holder. A small 

amount of superglue held the balls in place. The only exception was the 1.5-in-diameter ball, 

which did not have its own holder. The 0.75-in holder was used to hold this ball in place. 

Not visible in the picture is the hydraulic piston that moved the specimens up into the stationary 

steel ball at a rate of 0.5 mm/min. Any cracks that initiated could be observed with the optical 

setup, as previously described. 

4.2.1 Tile Preparation and Testing 

The majority of the tiles tested were abraded with SiC particles on both the air and tin sides to try 

and ensure a more-or-less uniform flaw size distribution. A set of tiles was also tested in the 

as-received condition in order to determine the effect of the abrasion treatment. 

The tiles were abraded by lapping with 220-grit SiC powder (K.C. Abrasive Company, Kansas 

City, KS) for 4 min on both sides. According to the supplier, this grit size corresponded to ~63-m 

average particle size. 

steel 

alignment 

rods x-y stage 

glass tile 

indenter holder 

zoom lens 

load cell 

digital camera 

Instron

test 

 frame 

sample holder 

steel plate 
36

A stopwatch was used to keep track of time. A 12-in-diameter circular sheet of 1200-grit 

(~3-m average grain size) SiC paper was placed on the aluminum rotating wheel, and then the 

220-grit SiC powder was sprinkled on top and tap water added as a lubricant. A 100-rpm wheel 

speed was used. 

The fine SiC paper was used to protect the softer aluminum wheel from becoming damaged by 

the loose abrasive SiC powder. Note that since the SiC grains on the paper were much smaller 

than the 220-grit SiC powder, they did not cause the major abrasive damage. The tiles were 

rotated 90° every minute, and additional water was added when needed. Tiles were cleaned with 

isopropyl alcohol after abrasion. 

Figure 28 shows a Starphire tile both before and after abrasion, for both tin and air sides. The 

damage consists of scratches/cracks and small chips on the surface. Tiles were aged overnight in 

laboratory air and tested the following day. One set of tiles was prepared and tested at a time. 

Figure 28. Starphire tile both as-received and after 220-grit abrasion: (a) as-received air side, (b) 

after abrasion air side, (c) as-received tin side, and (d) after abrasion tin side. All 

images 250× original magnification.

(a)

(b) (d)

(c)
37

Temperature and relative humidity were monitored at all times. Tiles were cleaned with isopropyl 

alcohol on both sides prior to testing but before taping. The tin sides of the samples were loaded 

with the steel ball, with the air sides facing down and in tension. This was true for all tests.

In order to hold the tiles together after failing, clear plastic tape was placed on the compression 

(top) surface before testing. The tape was arranged in four strips, and the center of the tile was 

free of tape such that the steel ball only contacted the glass. The amount of tape used was kept 

constant for each tile. The actuator displacement rate was 0.5 mm/min for all tests. When 

failure occurred, the test was stopped. 

4.2.2 Failure Test Results 

4.2.2.1 3.2-mm Tiles. Table 8 summarizes the failure test results. Figures 29–31 represent the 

results for the 3.2-, 6-, and 12-mm tile thicknesses, respectively. As seen in figure 29, abrading 

the specimens caused the failure load to decrease, as well as the experimental scatter, compared 

to the as-received samples. 

For example, the failure load for the as-received samples tested with the 0.5-in steel ball was 

1.608 ± 0.590 kN, whereas the samples abraded on the bottom (tension) surface, and also tested 

with the 0.5-in steel ball, had a failure load of 0.445 ± 0.049 kN. 

Thus, the abrasion treatment was effective in producing a more uniform flaw size distribution. 

However, the flaws that were introduced were much larger than the flaws on the as-received 

glasses, causing much lower failure loads. 

However, this is okay, since what is being sought are any differences in failure load due to 

variations in ball diameter and tile thickness, while keeping flaw size more-or-less constant. All 

tiles failed from back-face radial cracks initiated by the equibiaxial tensile stress field. 

Figure 29 shows that the failure loads did not change with ball diameter in the 0.0625- to 0.5-in 

range, despite the fact that ring-cone cracks initiated for the tests conducted with the 0.0625- and 

0.25-in-diameter balls. This indicates that tile failure was still controlled by the back-face radial 

crack tension failures, i.e., the ring-cone cracks played little, if any, role in the overall failure of 

the tiles. 

For those tests where no ring-cone cracks initiated, failure stresses were calculated according to 

(59):

2 2

max 2 22

3 (1 ) (1 ) 1 2ln 1

4 (1 ) 2

P a ba

t b aR

 



 

     

           

 , (1)

with max failure stress, P failure load,  Poisson’s ratio of specimen, t specimen thickness, a

support radius, b radius of uniform stress (~t/3), and R radius of disk (for square specimen R = 

x/2; x = edge length of tile). This equation assumes equibiaxial stress conditions, where the 

radial and tangential stresses are assumed equal.
38

Table 8. Starphire glass failure test results.a

Quantity 

of Tiles 

Evaluated 

No. 

Tiles 

Tested 

Steel 

Ball 

Diameter 

(in) 

Failure 

Load 

(kN) 

Failure 

Stress 

(MPa) 

Ring/Cone

Initiation

Load 

(N) 

Macro 

Conoid 

Backface 

Radial 

Cracks T 

(°C) 

Relative

Humidity

(%) 

3.2-mm-Thick Tiles

As-received 

top and bottom 12 0.5 1.608 ± 0.590 226 ± 83 No No Yes 22 49 

As-received 

top; abraded 

bottom 

12 0.5 0.445 ± 0.049 63 ± 7 No No Yes 18 57 

Abraded top 

and bottom 12 0.0625 0.452 ± 0.061 — 66 ± 12 No Yes 22 47 

Abraded top 

and bottom 10 0.25 0.476 ± 0.054 — 214 ± 42 No Yes 22 48 

Abraded top 

and bottom 11 0.5 0.457 ± 0.051 64 ± 7 No No Yes 22 48 

6-mm-Thick Tiles

Abraded top 

and bottom 12 0.0625 1.580 ± 0.184 — 90 ± 29 Yes (40%) Yesb

 21 24 

Abraded top 

and bottom 12 0.125 1.613 ± 0.163 — 86 ± 13 Yes (60%) Yes 22 46 

Abraded top 

and bottom 8 0.25 1.595 ± 0.173 — 113 ± 13 No Yes 20 37 

Abraded top 

and bottom 12 0.5 1.674 ± 0.169 — 237 ± 27 No Yes 22 48 

Abraded top 

and bottom 10 1.5 1.654 ± 0.207 97 ± 12 No No Yes 22 47 

12-mm-Thick Tiles

Abraded top 

and bottom 12 0.25 9.982 ± 1.029 — 139 ± 50 Yes (100%) Yesc

 22 49 

Abraded top 

and bottom 12 0.5 10.003 ± 0.696 — 336 ± 85 Yes (100%) Yesd

 22 42 

Abraded top 

and bottom 12 0.75 10.529 ± 

1.317 — 454 ± 124 Yes 

(100%) Yesd

 21 25 

Abraded top 

and bottom 12 1.5 10.124 ± 0.75 — 610 ± 105 Yes (100%) Yes 23 45 

Note: Parentheses indicate percentage of tests displaying that behavior. a

Values in table are average ±1 standard deviation. 

b

Surface spalls formed as well (30% of tests). 

c

Surface spalls and surface radials formed as well (100% of tests). 

d

Surface radials formed as well (100% of tests). 
39

Figure 29. Failure load for the 3.2-mm-thick Starphire glass tiles loaded with 

steel balls of different diameter. 

Figure 30. Failure load for the 6-mm-thick Starphire glass tiles loaded with steel 

balls of different diameter.

3.2 mm Starphire Glass

Ball-on-Ring Failure Load

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0 25 50 75 100

Cumulative Frequency

Failure Load (kN)

as-received 0.5 in.

abraded bttm 0.5 in.

abraded top bttm 0.0625 in.

abraded top bttm 0.5 in.

abraded top bttm 0.25 in.

6 mm Starphire Glass

Ball-on-Ring Failure Load 

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0 20 40 60 80 100

Cumulative Frequency

Failure Load (kN)

abraded top bttm 0.5 in.

abraded top bttm 0.125 in.

abraded top bttm 1.5 in.

abraded top bttm 0.0625 in.

abraded top bttm 0.25 in.
40

Figure 31. Failure load for 12-mm-thick Starphire glass tiles loaded with steel balls of 

different diameter. 

Note how the ball size does not enter the equation. As-received specimens had failure stresses of 

226 ± 83 MPa compared to 63 ± 7 MPa for abraded specimens. 

Figure 32 illustrates several failed 3.2-mm Starphire tiles tested with balls of various diameter. 

Back-face radial cracking caused the failures. All tiles shown were abraded on the top and 

bottom surfaces, with the exception of the lower-left tile, where only the bottom surface was 

abraded. Figure 33 is an as-received tile failed by loading with a 0.5-in ball. Note how there are 

many more cracks compared to the abraded specimens, indicating a much greater stress (energy) 

at the time of failure, consistent with the higher failure loads for these tiles (see table 8). 

4.2.2.2 6-mm Tiles. Compared to the 3.2-mm tiles, ring-cone cracks initiated using the 0.5-indiameter steel ball indenter (and all other smaller-diameter indenters as well). However, macro 

conoid cracks formed in 40% and 60% of the tests made with the 0.0625- and 0.125-in balls. 

The macro conoids are thought to be the extensions of the small ring-cone cracks that form early 

on loading but which are then propagated through the specimen thickness at the time of failure. 

The reason for the dependence of macro conoid formation on ball diameter is not entirely 

understood, particularly since the size to which cone cracks grow is not governed by indenter 

diameter, but by material properties and indentation load (22): 

2

3

2

( )

P E f

R



   , (2)

12 mm Starphire Glass 

Ball-on-Ring Failure Load

0.000

2.000

4.000

6.000

8.000

10.000

12.000

14.000

0 10 20 30 40 50 60 70 80 90 100

Cumulative Frequency

Failure Load (kN)

abraded top bttm 1.5 in.

abraded top bttm 0.75 in.

abraded top bttm 0.5 in.

abraded top bttm 0.25 in.
41

Figure 32. Several failed 3.2-mm Starphire tiles. The star-like fracture 

patterns are typical of biaxial flexural testing. Top row, left to 

right: 0.125-, 0.25-, and 0.5-in ball. Bottom row, left to right: 

0.5-in ball and only bottom surface abraded, 0.0625-in ball. Tiles 

are 4 × 4 in2

. 

Figure 33. As-received 3.2-mm Starphire tile loaded to failure with 0.5-in 

steel ball. Tile is 4 × 4 in2

.
42

with P indentation load, R radius of base of cone crack, E Young’s modulus, f fracture surface 

energy, and () a constant dependent on Poisson’s ratio and equal to 2.75 × 10-3 for 0.25. 

Poisson’s ratio for Starphire glass is ~0.22. 

However, one possible explanation is that for these small-diameter indenters (0.0625 and 0.125 in), 

the stress level in the glass is approaching the yield stress, and this alters the trajectory of the 

initially small cone crack, causing it to propagate more steeply compared to conditions of purely 

elastic contact for more blunt indenters. 

In figure 34, the mean contact stress (not the tensile fracture stress) at the moment of ring-crack 

initiation is plotted as a function of ball diameter for the tin side of Starphire glass. The fracture 

stress is lower since the ring cracks form just outside the contact edge. These data were obtained 

from separate experiments in which an unabraded 12-mm-thick Starphire tile was rigidly 

supported. For the 0.125-in-diameter indenter, the mean stress is about 4.5 GPa, which is 

approaching the yield stress based on Vickers hardness measurements (see table 4). 

Figure 34. Mean contact stress at the initiation load for ring-cone cracks as a 

function of the ball diameter for the tin side of Starphire glass. Data 

for an unabraded tile. 

When the power-law curve fit is used (see figure 34), the mean contact stress is estimated to be 

~5.8 GPa for the 0.0625-in-diameter indenter. This value is higher than the Vickers hardness 

and approaches the value of yield stress found from the instrumented tests conducted with the 

500-m-diameter diamond sphere (see section 4.1.2). 

Starphire Glass (Tin Side)

Mean Contact Stress vs. Ball Diameter

y = 1.9446x-0.3974

R2 = 0.983

2

2.5

3

3.5

4

4.5

5

5.5

0 0.1 0.2 0.3 0.4 0.5 0.6

Ball Diameter (in.)

Mean Contact Stress (GPa)
43

Thus, it is possible that yielding is taking place around the same time the ring-cone cracks are 

forming. The yielding may cause the cone cracks to propagate more steeply and penetrate the 

tensile bending region, driving the small conoid into a large conoid that pops out on the tension 

side of the specimen. For the more blunt indenters (0.25 in and larger), the contact stress never 

reaches high enough to cause yielding before failure, hence the ring-cone cracks that initiate are 

not as steep and no macro conoids form. 

Although the mean contact stresses shown in figure 34 are well above the yield stress for the 

steel balls (~2 GPa, see section 4.2), no permanent deformation (dimpling) of the balls was seen, 

although some scratches necessitated rotating or changing the balls periodically. 

Three of the tiles tested with the 0.0625-in ball did not fail, but rather severe surface spalling and 

comminution occurred, causing the ball to be completely buried in the sample, up to the indenter 

holder. These tests were stopped before the tile failed. 

It is very important to point out that the formation of the macro conoids did not affect the failure 

loads above the normal experimental variability seen (see table 8). For example, with the 

0.0625-in ball, one tile that did not form a macro conoid failed at 1.550 kN, whereas another tile 

that did form a macro conoid failed at 1.569 kN. This means the back-face radial cracks are still 

dominating the overall failure behavior. 

Figure 35 (a) and (b) illustrate these two failed 6-mm tiles mentioned previously, without and 

with macro conoid formation, respectively. Cursory fractography revealed that the skirt of the 

macro conoid was discontinuous where it intersected the back-face radial cracks, indicating the 

radial cracks had a slight head start during failure. Much more fractography needs to be done on 

all tiles to confirm these and other observations. 

4.2.2.3 12-mm Tiles. All of the 12-mm-thick tiles formed macro conoid cracks for all ball 

diameters. An example of a macro conoid formation is shown in figure 36 for a tile indented 

with a 0.75-in-diameter steel ball. All of the macro conoids that formed were substantially larger 

than those found in the 6-mm tiles. 

The obvious conclusion is that tile thickness is a key variable in influencing the macro conoid 

formation. A possible explanation is that the cone cracks are able to grow larger in the 12-mm 

tiles, relative to the tile thickness, due to less bending. Greater bending, such as in the 6-mm 

tiles, would presumably reduce cone crack growth via increased surface compression. 

Less bending would allow the cone crack to propagate relatively further into the specimen for a 

given load, compared to the 6-mm tiles. This larger cone crack can then be thrust through once 

the back-face radial cracks start the structural failure process. 
44

Figure 35. Failed 6-mm Starphire tiles that formed no macro conoid (a) and that did form a 

macro conoid (b). Tension side faces up (a) and compression side faces up (b). Steel 

ball diameter 0.0625 in. Tiles are 4 × 4 in2

. 

Figure 36. Failed 12-mm Starphire tile loaded with a 0.75-in-diameter 

steel ball. The tension side, illustrating the large crater formed 

from the macro conoid, faces up. The chipped away pieces are 

not shown.

(a) (b)

cone fragment
45

The fact that large segments of material were removed where the cone crack intersected the rear 

surface tends to confirm that the back-face radial cracks were present before the cone crack 

reached the rear surface. This means the “macro conoid” was probably propagating as separate 

segments, at least during the latter stages of its growth. 

More fractography needs to be done to clarify these and other issues. In addition, by the time the 

macro conoid reached the rear surface, it was nearly parallel to the tile surface, as seen in 

figure 36. This is believed to be caused by the tile bending. 

Regardless of the timing sequence, the formation of a macro conoid will drastically reduce the 

structure’s ability to withstand further impacts, since a major portion of the target will either be 

completely missing or weakly held in place. 

In addition to the macro conoids and back-face radial cracks that formed, surface radial cracks 

also formed for tests performed with the 0.25-, 0.5-, and 0.75-in ball diameters. These cracks 

were small and may not have played a major role in the failures. However, the presence of these 

cracks possibly suggests inelastic deformation occurring, since radial cracks in glass around 

Vickers indentations are thought to arise from inelastic deformation processes, as discussed in 

detail by Lawn and Wilshaw (22). 

For the 0.25-in indenter, surface spalls formed in all tiles prior to failure. These spalls appeared 

to consist of both lateral-type cracks and comminuted material. The small diameter of the 

indenter appeared to generate stresses that would fail material in a localized region before the tile 

failed from the back-face and macro conoid cracks. 

An indentation sequence showing the initiation of a ring-cone crack and the spall failure is 

shown in figure 37 for a test made with the 0.25-in-diameter steel ball. In frame (d), the spall 

failure is visible, and the tile failed completely and catastrophically shortly after.

Figure 38 shows the average failure load for the abraded top and bottom specimens as a function 

of tile thickness. It is apparent that the failure load increases as the square or exponential of the 

tile thickness. 

Finally, the experimental variability in fracture loads was considerably greater compared to the 

3.2- and 6-mm tiles (see table 8). Reasons for this are not entirely known, but perhaps the macro 

conoids are influencing the overall structural failure behavior to a greater extent compared to the 

6-mm tiles. 

It is important to note that in all tests, and for all tile thicknesses, i.e., 3.2, 6, and 12 mm, the ring 

cracks that initiated did so stably, i.e., no abrupt pop-in was observed. This is due to the large 

starting flaw sizes introduced by the abrasion treatment, which stabilizes the initiation process. 

Part of a ring crack would initiate and grow downward while slowly spreading around the rest of 

the contact, as shown in figure 37 (a). When the ring was complete, further load increases 

resulted in just growth of the cone crack.
46

Figure 37. A sequence of frames illustrating the formation and growth of the ring-cone crack (a–c), and 

the initiation of the spall failure (d) in the 12-mm Starphire tile (tin side) contacted with the 

0.25-in-diameter steel ball. Load increases from a to d. 

Figure 38. Average failure load as a function of tile thickness. Two 

different curve fits of the data show the exponential or powerlaw dependence on tile thickness.

Ball diameter: 0.25 in.

ring‐cone crack

(a)

(c) (d)

(b)

y = 0.1715e0.3446x

R2 = 0.9914

y = 0.0279x2.3448

R2 = 0.9927

0

2

4

6

8

10

12

0 5 10 15

Tile Thickness (mm)

Failure Load (kN)

power-law fit

exponential fit
47

4.2.3 Flaw Size Estimates 

An attempt is made to calculate the flaw sizes responsible for failure for the as-received and 

abraded test specimens. Using the failure stress for the as-received samples, i.e., 226 MPa, and 

the fracture mechanics expression for a surface flaw in uniform tension, i.e., 

1.12 K c Ic f    , (3) 

one can solve for the crack depth, c. When a value of 0.70 MPa√m for Starphire glass is used, 

which is reasonable, the flaw size is c  2.4 m. For the abraded specimens with fracture stress of 

64 MPa, the flaw depth is calculated to be c  30 m. 

If to a first approximation the flaws are assumed nearly semi-circular, this depth would 

correspond to a surface flaw length of ~60 m, which approaches the average 220-grit SiC 

particle size of ~63 m. 

4.3 Other Experiments 

Figure 39 shows the ring crack stress as a function of ball diameter for the tin sides of both 

Starphire and Borofloat glasses. This stress was calculated using equation 4 (see the appendix), 

using the measured ring-crack radii obtained from posttest microscopy. The fracture stress 

decreases with increasing ball size in accord with the experimental results of Tillett (25). 

Figure 39. Ring crack stress as a function of ball diameter for the tin sides of 

unabraded Starphire and Borofloat glasses.

Starphire and Borofloat Ring Crack Fracture Stress

y = 0.4168x-0.4243

R2 = 0.9784 

(Starphire)

y = 0.2844x-0.3614

R2 = 0.9736

(Borofloat)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6

Ball Diameter (in.)

Ring Crack Stress (GPa)

Borofloat (tin side)

Starphire (tin side)

Pow er (Starphire (tin side))

Pow er (Borofloat (tin side))
48

This phenomenon is a consequence of the highly inhomogeneous stress field that exists around 

small-sized indenters, causing the stress at fracture to increase with decreasing ball size (40). 

For larger indenters, the stress field is more uniform over the flaw, which gives rise to a nearly 

constant fracture stress. 

It is experimentally observed that the critical load for ring crack formation is proportional to the 

indenter radius, r, for small-sized indenters, i.e., Pc  r, a phenomenon known as Auerbach’s law 

(40). For larger indenters, it is observed that Pc  r

2

. Figure 40 illustrates this for the Starphire 

and Borofloat glasses. 

Figure 40. Ring crack load as a function of ball diameter for the tin sides of 

unabraded Starphire and Borofloat glasses. 

It is important to point out here that the initiation of the cone cracks was simultaneous with the 

initiation of the ring cracks, i.e., an unstable crack system was formed from the start. 

The maximum Hertzian tensile stress can be expressed as (18): 

2/3 1/3

2

12 3

2 4 m

E P

k r







                 . (4) 

This is analogous to equation 4 (the appendix) with = a, i.e., at the contact periphery and with 

the last two terms on the right side of equation 4 substituted in place of po.

Ring Crack Load vs. Indenter Radius

y = 15472x + 113.5

R2

 = 0.9723

(Starphire)

y = 4728x + 139.5

R2 = 0.9732

(Borofloat)

0

1000

2000

3000

4000

5000

6000

0 0.05 0.1 0.15 0.2 0.25 0.3

Indenter Radius, r (in.)

Ring Crack Load, Pc (N)

Starphire (tin)

Borofloat (tin)
49

At fracture, m = f and P = Pc. Since for large indenters Pc  r

2

, equation 4 yields m = 

constant and independent of indenter size. This holds for a given flaw size. In this large 

indenter region, the fracture stress is dependent on flaw size, i.e., Pc  cf

–3/2 (40). That is, Pc

decreases with increasing flaw size in this region. 

For the small indenter (Auerbach) region where Pc r, equation 4 yields m  r 

–1/3. That is, the 

fracture stress is expected to decrease with increasing ball size raised to the negative one-third 

power. In this region the fracture stress is found to be relatively independent of flaw size (40). 

The data in figure 39 were fit with an inverse power law, and the exponents for the Starphire and 

Borofloat glasses were –0.42 and –0.36, respectively. These values are close to the theoretical 

value of –0.33. Of course, plotting the data as stress vs. ball diameter instead of stress vs. ball 

radius has no effect on the value of the exponents. 

If larger-diameter ball indenters were used, the fracture stress is expected to decrease to a moreor-less constant value, similar to what Tillett (25) observed in her experiments. 

It is worthwhile to estimate the flaw size from the 0.5-in ring crack stress for the Starphire glass 

in figure 39. Taking the fracture stress as ~600 MPa (0.6 GPa) from the graph and using 

equation 4 with KIc of 0.70 MPa√m yields c ~0.35 m. This is smaller than the flaw size from 

the equibiaxial flexure tests (c ~2.4 m). 

However, the ring crack stress has not reached its lower plateau value, and a larger value of flaw 

size would be calculated if the failure stress from larger ball diameters had been used. 

5. Summary and Conclusions 

In the current work, IIT was used to study the deformation and fracture behavior of three 

different glass compositions and AlON to localized contact from a 500-m-diameter diamond 

spherical indenter. 

In addition, structural failure experiments were conducted on Starphire glass tiles in which large 

macro conoid cracks were initiated in the thicker specimens. This behavior mimics the large 

conoid cracks sometimes seen in ballistic tests. 

Additional Hertzian fracture tests for measuring ring crack loads and stress were carried out on 

Starphire and Borofloat glass tiles. 

Several conclusions can be made in connection with the work performed here: 

1. IIT can be used to easily measure yield stress at room temperature in glass and ceramic 

materials, and study localized fracture behavior in a controlled manner. These parameters 
50

should be compared to the materials’ actual ballistic performance for the sake of 

determining any correlations. 

2. Large macro conoid cracks, spalls, back-face radial cracks, and smaller surface-localized 

radial cracks can be formed under quasi-static test conditions in tiles of substantial 

thickness when subjected to sufficiently high loads with spherical indenters of appropriate 

size. 

 Failure resulting from such a combination of damage modes may possibly be relevant to 

ballistic performance. Hence, this type of testing should at least be considered, in addition 

to the IIT testing, for the screening of candidate materials. 

3. The macro conoid cracks formed in the 12-mm-thick tiles were nearly parallel to the tile by 

the time they reached and intersected the rear surface. This is believed to be a result of the 

bending of the tile, which “flattens out” the cone crack trajectory. This may be useful 

behavior to exploit.

6. Future Work 

A more in-depth fractographic analysis of the failed tiles would be useful, including 

measurements of the macro conoid diameter. This would help clarify issues relating to the 

sequence of the fracture processes in the case of the thicker tiles. 

In addition, the morphologies of the macro conoids should be examined, with emphasis on the 

angles of these cracks. One way to do this is to make a replica of the cone crack fracture surface, 

possibly using heat-shrink tape, which would yield a positive replica of the cone crack that could 

be easily removed and analyzed. In addition, exploiting tile bending as a way to control the 

angle of the cone crack may be beneficial. 

Additional work should be done to study the influence of indenter diameter and indenter material 

on the yield stress and fracture behavior. 
51

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55

Appendix. Hertzian Equations 

Equation 1. Contact Radius (a)1: 

1/3 4

3

kPR

a

E

       , (A-1) 

where 

a = contact radius,

k = dimensionless constant, 

P = indentation load, 

R = sphere radius, and 

E = Young’s modulus of specimen. 

Equation 2. Dimensionless constant (k)1: 

  2 '2

'

9 1 ) (1 16E k

E

 

        

, (A-2) 

where 

 = Poisson’s ratio of specimen, 

 = Poisson’s ratio of sphere, 

E = Young’s modulus of specimen, and 

E = Young’s modulus of sphere. 

Equation 3. Mean contact stress (po)

1

: 

o 2

P

p

 a  , (A-3) 

where 

po = mean contact stress. 

 1

Lawn, B. R. Indentation of Ceramics With Spheres: A Century After Hertz. J. Am. Ceram. Soc. 1998, 81 (8), 1977–1994. 
56

Equation 4. Tensile stress (T)2

: 

2

1 2

2 T o

a

p







            , (A-4) 

where 

T = tensile stress at surface, and 

 = radial distance along surface from center of contact.

 2

Lawn, B. R.; Wilshaw, R. Review Indentation Fracture: Principles and Applications. J. Mater. Sci. 1975, 10, 1049–1081. 
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