December 2011 

NASA/TP–2011-217322 

Examination of Relationship Between Photonic 

Signatures and Fracture Strength of Fused Silica 

Used in Orbiter Windows 

William T. Yost and K. Elliott Cramer 

Langley Research Center, Hampton, Virginia 

Linda R. Estes 

Johnson Space Center, Houston, Texas 

Jonathan A. Salem 

Glenn Research Center, Cleveland, Ohio 

James Lankford, Jr. 

Southwest Research Institute, San Antonio, Texas 

Jon Lesniak 

Stress Photonics, Inc., Madison, Wisconsin 
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December 2011 

NASA/TP–2011-217322 

Examination of Relationship Between Photonic 

Signatures and Fracture Strength of Fused Silica 

Used in Orbiter Windows 

William T. Yost and K. Elliott Cramer 

Langley Research Center, Hampton, Virginia 

Linda R. Estes 

Johnson Space Center, Houston, Texas 

Jonathan A. Salem 

Glenn Research Center, Cleveland, Ohio 

James Lankford, Jr. 

Southwest Research Institute, San Antonio, Texas 

Jon Lesniak 

Stress Photonics, Inc., Madison, Wisconsin
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

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National Aeronautics and Space Administration. 
5 

Examination of Relationship between Photonic Signatures and Fracture Strength of Fused 

Silica Used in Orbiter Windows 

William T. Yost and K. Elliott Cramer, NASA-Langley Research Center 

Lynda R. Estes, NASA-Johnson Space Center 

Jonathan A. Salem, NASA-Glenn Research Center 

James Lankford, Jr.-Southwest Research Institute 

and 

Jon Lesniak-Stress Photonics, Inc. 

Abstract 

A commercially available grey-field polariscope (GFP) instrument for photoelastic 

examination is used to assess impact damage inflicted upon the outer-most pane of the 

orbiter windows. Four categories of damage: hyper-velocity impacts that occur during 

space-flight (HVI); hypervelocity impacts artificially made at the Hypervelocity Impact 

Technology Facility (HIT-F); impacts made by larger objects falling onto the pane 

surface to simulate dropped items on the window during service/storage of vehicle 

(Bruises); and light scratches from dull objects designed to mimic those that might occur 

by dragging a dull object across the glass surface (Chatter Checks) are examined. The 

damage sites are cored from fused silica window carcasses, examined with the GFP and 

other methodologies, and broken using the ASTM Standard C1499-09 to measure the 

fracture strength. A correlation is made between the fracture strength and damage-site 

measurements including geometrical measurements and GFP measurements of 

photoelastic retardation (stress patterns) surrounding the damage sites. An analytical 

damage model to predict fracture strength from photoelastic retardation measurements is 

presented and compared with experimental results, where a power-law correlation 

between the measurements and fracture strengths, σf , is shown to give the best fit. The 

best-fit results are found to be: 

σf = 43.7 (ε)

-0.127 R2

= 0.997 (HVI-photoelastic retardation) 

σf = 181 (ε)

-0.351 R2

= 0.955 (HIT-F-GFP measured inner diameter damage) 

σf = 37.2 (ε)

-0.282 R2

= 0.981 (Bruises-photoelastic retardation) 

σf = 117 (ε)

-0.099 R2

= 0.334 (Chatter Checks-outer length of scratch) 

where ε is the corresponding damage parameter (e.g. photoelastic retardation) 

measurement. Based on the analytical damage model a general experimental procedure 

outline is presented. The GFP is shown to be a viable instrument for use in the estimation 

of damage effects on the mechanical integrity of the outer-most window for manned 

space vehicles 

I. INTRODUCTION 

During storage and flight, windows on space vehicles are subjected to sometimes 

harsh and damaging conditions capable of impairing their mechanical performance. The 

outer windowpanes on a spacecraft encounter high velocity impacts (HVI) from debris 

and micrometeoroids from vehicle launch to landing. During vehicle re-entry these 

windowpanes are subjected to high temperatures. While in storage and during preparation 

for launch, windows sometimes encounter accidental collision events, such as a dropped 

tool or a tethered device striking its surface. 
6 

Fused silica, which is the primary material of choice for crewed spacecraft 

windows for the manned spacecraft programs at NASA1

, has significant advantages over 

other transparent materials. These include thermal shock tolerance and optical 

performance. With these advantages, however, are properties that make engineering with 

this material very difficult. Fused silica, like other silica-based glasses, is a brittle 

material, whose strength can be degraded considerably by sharp object impacts2,3. Other 

characteristics of engineering significance include a large scatter in material and fracture 

properties. In particular, fracture strength exhibits a strong dependence on surface quality 

(e.g. presence of micro-cracks and other flaws) and the inevitable internal flaws that are 

distributed through the volume. 

From launch to landing the windowpanes on a spacecraft are subjected to 

aggressive conditions and events that degrade mechanical performance and affect vehicle 

safety. The vehicle’s re-entry into the atmosphere subjects these windowpanes to high 

temperatures4

. As a consequence of the temperature ranges encountered, the mounts must 

place the glass panes under minimum mechanical stresses (sufficient to seal the glass to 

the vehicle). When damaged by impacts and placed under tensile stresses, these panes 

can suddenly fail. All accumulated damage sites, whether from the active (launch to 

landing) period or from storage and maintenance period, must be identified, measured, 

evaluated, and continually monitored for their effects on the pane’s structural 

performance. Since the service life of a pane is shortened by damage causing events, 

engineers must ensure that the glass surfaces are carefully inspected prior to every active 

cycle for safety assurance. 

To date, the U.S Space Program has never lost a spacecraft to window failure. 

This is due in large part to a carefully designed program and execution of window 

maintenance procedures. During each mission, thousands of new damage sites are added 

to each pane. A crew dedicated to window maintenance conducted thorough post flight 

examinations of the Shuttle windows. The examination procedure used various and 

sometimes specially designed optical instruments. During the inspection the emphasis 

was placed on accurate measurements of the damage surface features (a daunting 

problem requiring human judgment and estimation due to typical damage site 

irregularity). Each damage site was characterized by measurements of mold impressions 

(damage depth, damage area) and was recorded on maps of damage site locations. Depth 

features as small as 15μm (0.0006 inches) were recorded and mapped for further 

examination and analysis. The molds were measured with an optical comparator to 

determine damage size (cross-section and depth) at each impact site. 

 Stress analysis uses flaw depths in a static fatigue analysis that give a 

conservative estimate of the residual strength5

. An assessment of remaining life was made 

in light of the residual strength and the pressure load encountered during launch, orbit, 

and reentry (glass loses strength when subjected to static stresses and pressure 

gradients6

). On the basis of this analysis, a decision on window replacement was made. 

 As the Shuttle program progressed, studies of the effects of hypervelocity impacts 

continued for improvement of analytical approaches. 7

 Hypervelocity impacts were made 

on silica blanks at the NASA Johnson Space Center Hypervelocity Impact Technology 

Facility (HIT-F) located at the White Sands Test Facility in Las Cruces, New Mexico. 

Generally, NASA defines hypervelocity impacts as impacts involving velocities greater 

than 5 km/s. Typically these impacts were made with a two-stage light-gas gun launcher. 

The impacts were made under various conditions, with the firings of impacters of various 

materials and at a variety of angles. 

 During the operations outlined in Reference 4, damages to shuttle windows other 

than from hypervelocity impacts have also been noted. Specifically bruises, a class of 
7 

(low velocity) impacts that cause underlying damage, do not create surface disruptions 

with the same characteristics of the damage accumulation associated with higher velocity 

impacts. Examples of the causes of this damage classification include the dropping of an 

object or tool onto the window and a tool swinging from a tether that collides with the 

windowpane during vehicle servicing. Still other damage includes the dragging of a dull 

object across the glass surface. This type of damage falls under a specific category, 

“chatter checks”, and is characterized by a linear series of small bruises of similar 

diameter caused by the friction contact between the glass and the object in contact with it. 

The purpose of this work is to investigate and report on an alternative, more 

reliable, and more accurate inspection method with improved reliability for location and a 

predictive assessment of loss of fracture strength caused by windowpane damage in 

aerospace vehicles. Further, we compare the capability of this new technique with the 

currently used inspection techniques to predict loss of fracture strength. This new 

technique uses a Grey Field Polariscope (GFP) to measure stress birefringence8

, the 

photoelastic response to stress fields in glass. When the glass is damaged, light waves 

passing through the damage regions have different velocities according to the local 

stresses associated with the damage and their alignments with the light’s polarization 

states. Hence, one easily locates and characterizes damage regions by noting locations 

and variations of light speed with polarization direction. Moreover, the photoelastic 

region surrounding the damage site extends over much larger distances than the damage 

site itself, thus making detection easier. Once located the photoelastic response 

determines the residual stress field around the damage site. 

An orbiter window inspection system based on the GFP principle was designed 

and built to perform this inspection.9

 This scanning system allows single-sided inspection 

of windows and mounts to an x-y articulated translation mechanism capable of examining 

each windowpane in place and hence without the necessity of the pane’s removal from 

the vehicle. By combining the outputs from the GFP and the coordinate information this 

instrument makes an accurate map of damage site locations. The map includes 

coordinates, the optical image, and the strain patterns of each detected damage site for 

future reference, comparisons, and analysis, including differential analysis. 

In this investigation, we test the ability of the GFP-based measurements to predict 

fracture strength on a series of specimens with damage sites that are cored from shuttle 

window material. Measurements were taken with a GFP inspection system at and near 

regions of damage caused by the four different damage classifications under test10 (HVI, 

HIT-F, Bruises, and Chatter checks). The standard (depth and size) measurements taken 

during inspection are included in this study. We compare measurements of photoelastic 

retardation (PER) around damage sites and the standard measurements, and correlate 

these with the measured fracture strength11 of the specimens. We develop an analytical 

model that suggests and outlines the basic aspects of a PER measurement procedure 

leading to the prediction. 

We assume that PER is related to the residual stress field surrounding the damage 

site. The progenitor of the stress-field is the energy of the incoming collider or particle. 

Depending upon path and initial conditions the causes of fracture strength reduction are 

also related to the particle energy. Such colliding particle properties as coefficients of 

restitution, diameter, angle of impact, density, etc. also affect fracture strength of the 

window. We therefore derive an expression that relates fracture strength loss in the 

window as a result of a colliding particle to the energy imparted to the plastic strain in the 

glass at the damage site, which is then related to the measurement of the photoelastic 

response. This plastic strain at the damage site in turn causes an elastic stress field in the 

surrounding region measured with PER, which is then related to fracture strength through 
8 

the expression for the energy imparted to the plastic strain. We simplify the case by the 

limiting assumption that the particle speed is small enough that rate dynamics associated 

with glass impacts do not appreciably affect the outcome12. The PER, averaged around 

the damage site, is checked against the tested strength in shuttle glass specimens with 

damage. Data analysis confirms that the GFP, which is a nondestructive, non-contacting 

measurement system based on relating residual stress fields surrounding damage sites in 

glass to optical birefringence measurements, is more accurate than the other 

measurements used in this study in predicting fracture strength in annealed fused silica 

with damage (HVI and Bruises). This technique is less labor intensive, removes many 

ambiguities associated with the previously used characterizations, and is more accurate in 

predicting fracture strength degradation for HVI and Bruise damage. 

II. THEORY OF COLLISIONS OF PARTICLES WITH GLASS 

 This section is divided into four segments. The first segment considers the 

activation of a critical size flaw within the glass by a collision process. Specifically this is 

a derivation of the loss in strength of an annealed fused silica specimen caused by a 

collision with a particle, which we treat from the plastic deformation caused by a 

sequence of differential quasi-static indentations. The energy thus imparted has a 

multitude of paths that depend on parameters of the colliding particle at impact. These 

include material transformations, shock wave formations with consequent damage 

initiation, etc. The second segment derives a relationship from the output of the GFP to 

the strain field caused by the damage. The third segment develops the relationship 

between damaged glass fracture strength and the specific measurements from the GFP. In 

the fourth segment, we outline the foundation for a general experimental approach to 

nondestructively measure the parameters capable of predicting the fracture strength in 

annealed fused silica. This foundation is based on the analysis presented in the first three 

segments. 

IIA. Particle Collisions with Glass. 

 We begin the discussion with a particle of mass m moving toward and colliding 

with the windowpane fabricated from annealed fused silica. The particle velocity (relative 

to the window), u, is normal to the window surface. As it collides with the surface, the 

glass undergoes a deformation, of which part is plastic and part is elastic. In this case we 

are interested in the plastic component, as it contains a shift in the glass molecular 

structure, which causes a residual variation of index of refraction as a function of the 

polarization direction of light. We neglect rate-dependent processes and treat the collision 

as a series of differential quasi-static processes by time-sequencing an indentation caused 

by the colliding particle as the prototypical source of the damage13. We also assume that 

the colliding particle loses no mass as a result of the collision. 

 Consider a particle moving vertically toward the glass window, considered 

infinitely massive in this case, with a speed, u. The particle collides with the glass surface 

and rebounds with a speed v. The particle energy before collision Tinitial is 

 (1) 

After the rebound the particle energy Tafter is 
9 

 (2) 

The energy imparted to the glass, T is 

 (3) 

where e is the coefficient of restitution of the collision process associated with the 

deformation. If the collision is completely elastic, then e = 1. If the collision is 

completely inelastic, then e=0. In the case that we examine here, 0<e<1. The remaining 

analysis considers what changes occur in the glass from the collision process. For this 

process, we specify the coefficient of restitution as being associated in part with the 

plastic deformation and its effects within the glass14. 

 We next examine the effects of the indenter’s collision and consequent 

indentation of the glass surface. We simplify by assuming a completely rigid sharp 

indenter so that e represents the damage caused by the energy lost in the glass. Therefore, 

a portion of the kinetic energy of the indenter is dissipated by the mechanisms used for 

the local molecular rearrangement in the glass as the indenter penetrates into the glass. 

This rearrangement also causes an elastic residual field outside the damage site. 

We begin from the perspective of indenting the surface. In this case hardness is 

the significant parameter. We start with a general definition of hardness, derive the 

energy deposition into the damage site, and analyze effects on strength by using fracture 

mechanics. Finally, we apply these results to effects on optical birefringence of glass, and 

deduce the connection between strength and photoelastic retardation measured with a 

modified grey-field polariscope. 

Following an approach presented in Reference 2, Figure 1 is a schematic diagram 

of an idealized damage infliction with coordinates shown. The projectile tip formed by an 

angle of 2ψ penetrates a distance z into the glass surface. The penetration profile on the 

glass surface is circular with a radius a. The penetration causes the formation of the 

plastic zone in the glass ahead of the projectile, which is treated as an indenter. 

 We begin with the geometrical relationship between the penetration profile and 

the indenter angle: 

 (4) 

The mean stress pmean is given by 

 (5) 

where H is the hardness, F is the force exerted by the projectile on the glass, and Λ is a 

geometrical factor that depends upon the projectile’s shape. We assume that the mean 

stress remains constant throughout the process. By combining Eq. (4) and (5) and solving 

for the force, we obtain 
10

 (6) 

Figure 1. Diagram showing the projectile during collision with the glass target. 

The work performed in forming the indentation in the glass is 

 (7) 

where Fm is force at maximum indentation. 

We equate the kinetic energy of the projectile imparted to the glass (impact 

energy), 

 (8) 

to the plastic work done when penetrating the glass, and solve for the force 

 (9) 

The dynamics of crack evolution from a stress caused by a sharp contact are 

covered elsewhere15. As the indenter penetrates the glass surface, a tensile stress 

concentration builds at the elastic-plastic interface, which extends outward from the 

impact site. At some critical force, Fcritical , a subsurface flaw located within the field will 

experience sufficient stress over a large enough portion of the flaw that it will become 

unstable16 . The critical force at which this occurs is 
11 

 (10) 

where ae/p is an empirical factor that depends upon the indenter and the glass target, and 

Kc is the fracture toughness of the glass. This condition represents a minimum condition 

for crack initiation. The cracks thus initiated expand as half pennies centered at the point 

of impact and normal to the impact surface. 

 From fracture mechanics17 one obtains a relationship between the crack depth, D, 

and the force exerted by the projectile (indenter) on the glass. 

 

 (11) 

where ξF is another empirical factor related to the projectile. The relationship between 

the maximum tensile stress (tensile strength σ) and the dominant flaw length lflaw is given 

by 

 (12) 

Below threshold speeds, u0, no damage greater than flaw lengths that are already present 

in the glass is created. Above speeds of u0 an indentation flaw (crack) of length D

dominates the maximum tensile strength. Hence we write the dominant flaw length in the 

two cases: 

 (13) 

where Ω is a geometric constant (4/π

2

 for penny cracks18). The fracture stress (strength) 

σfracture then becomes 

 (14a) 

 (14b) 

For the data presented here we consider the case of where T>T*, where T* is a minimum 

energy below which damage is not added to the glass. As outlined in the derivation the 

impacts of high velocity particles with the glass surface causes localized damage sites 

that affect the glass target’s fracture strength. 

 Several observations from the derivation may be made at this point. First, some 

collisions below a threshold energy, even though they may cause plastic deformations, do 

not appreciably alter glass strength, since any crack formed does not exceed naturally 

occurring flaw lengths already in the glass. Secondly, as the particle impact speed 
12

increases within a range above a minimum speed (determined by the threshold energy), 

the fracture strength decreases inversely with impact energy to the 2/9 power. Thirdly, 

one generalizes the impact process by noting that any energy imparted to the glass, 

including the work of dragging a blunt object across the surface, can suffice in causing 

damage that results in a decrease in fracture strength. Regardless of the damage source, 

damage accumulation that affects strength results in the displacement of atomic 

arrangements within the glass volume. Therefore any inspection method that responds to 

displacement of material arrangements in glass, even at the atomic level, is useful in 

assessing changes in the fracture strength of glass. 

To gain insight into collision damage, an X-ray computed tomography was made 

of a damage site (one of several sites) in a specimen cut from a shuttle window. 

Figure 2. An X-Ray tomographic view (slice) of a damage site in shuttle glass specimen 

27-165. Within the region of this slice are characteristics showing regions of differing 

density to x-ray transmission. It is thought that this slice shows a compressive stress field 

that surrounds the damage site. 

Figure 2 is a slice of the x-ray computed tomographic image (negative presentation), 

which shows the damage in a plane within the fused silica shuttle glass specimen. In this 

presentation, lighter regions indicate more x-ray absorption, where darker regions 

indicate relatively less x-ray absorption. The slice shown is relatively close to the surface 

where some material has been knocked away, and thus leaves a void (black center). The 

region surrounding the black center extends a distance of 1.3 mm edge-to-edge (a factor 

of ~ 2.7 larger than the void) and shows a higher density (indicated in the image by 

lighter shades and shading). Marked on the diagram are regions of various densities. 

Extending from the perimeter of the damage site outward into the material is a diffused 

increase in density over the background, thus possibly indicating a region of some strain. 
13 

A zone of demarcation is outlined by the slightly brighter regions marked by clusters of 

moderately higher density. Between the demarcation zone and the black interior are 

regions with clusters of highest density. This diagram is consistent with compressive 

stress fields surrounding the damage site. 

While manufacturing techniques vary, fused silica is a super-cooled state of 

melted silicon dioxide (silica) with various levels of impurities and, depending on 

application, additives. Without additives it is an amorphous structure of silicon dioxide, 

another form of which is crystalline quartz. 

Fused silica is in a configurational state with higher energy than the lowest energy 

for silica, a quartz state, α-quartz. α-quartz is a trigonal trapezohedral crystal class 3 2, or 

crystalline form. Other forms include β-quartz, which includes a hexagonal 622 form 

with melting points of 1670C [β tridymite] and 1713C [β cristobobalite]. Both β forms 

have configurational energies above α-quartz, but lower than amorphous silica. Because 

of the high activation energies of the different forms of silica, it is possible for these 

forms to be present in metastable states19 even at standard temperatures and pressures. 

Since local energy densities from the impact are quite high, it may be energetically 

possible that silica progresses locally (at the atomic level) from the amorphous state to 

other forms (as might be included in the density changes shown in the X-ray CT in Figure 

2) when damaged. Regardless of whether the impact, which causes local atomic 

rearrangements, is the source, or the extended (elastic) stress field is the source, the 

birefringent properties of fused silica offer the possibility of a quantitative assessment 

and characterization of these fields. 

IIB. Principle of grey-field photoelasticity. 

We next measure the effect of stress fields left in the glass by the impact. The 

process that we use is governed by the fact that regions surrounding damage sites in glass 

become photo-responsive to polarized light. The degree of responsiveness is directly 

related to the magnitude and extent of the plastic stress field and the elastic stress field 

that extend beyond the immediate damage site. The first stress field is close to the 

damage site, and is largely due to plastic –related effects in the glass from the projectile, 

which affect local volume. Away from the damage site there is an elastic stress field 

caused by this volume change. This field extends for some distance from the damage site. 

The visible light GFP was originally developed by Stress Photonics, Inc. for 

NASA20 to provide high-resolution full-field subfringe photoelastic stress analysis in 

materials transparent to visible light21. In photoelasticity, the stress field of a test article 

is evaluated through the use of polarized light. The GFP performs this evaluation by 

combining a circularly polarized light source with a linearly polarized analyzer. As the 

analyzer is rotated, data is acquired with a video camera that uses synchronous 

(synchronized with the rotation of the analyzer) demodulation. 

Figure 3 shows a schematic representation of grey-field polariscope using 

photoelasticity to inspect a specimen that exhibits birefringence when strained. Circularly 

polarized light is represented by two orthogonal linear polarized light vectors that are out 

of phase by π/2 radians.
14

Figure 3. Schematic representation of the grey-field polariscope. 

It has been shown by Horn22 that for the GFP configuration described above, the 

intensity of the transmitted light is: 

I = κ E A2(1+ sin{2(α − β)}sinΔ) (15) 

where A is amplitude of the circularly polarized light, α is the angular orientation of the 

analyzer, β is the orientation of the fast axis of the resulting elliptical light, Δ is the phase 

lag of the slow axis of the ellipse due to the stress-birefringence of the specimen, and κE

is a constant of proportionality. When α−β=0, the intensity I=κE A2

. This condition 

marks the alignment of fast-axis orientation with the analyzer angle (α=β). When α−β is 

±45° the intensity I= κE A2

(1± sinΔ), which determines Δ experimentally.

For the elastic case of birefringent retardation we define Δ, 

 (16) 

where C is the elastic stress-optic coefficient, λ is the wavelength of the light, l is the 

thickness of the plate and σ1 and σ2 are the first and second principal stresses23. 

The damage site specifically will have a plastic rearrangement of atomic 

structures around the damage site, and a region (far field) surrounding the damage site 

where atomic position shifts are elastic. This study utilizes the elastic stress field for 

analysis. 
15 

 By dividing Eq. (15) by κEA2

, and using a trigonometric identity to rewrite the 

RHS in terms of the angular orientation α, one obtains 

 I

κ E A2 =1+ Ica cos2α + Isa sin2α (17) 

where the (dimensionless) normalized intensities are 

 Ica = −(sinΔ)sin2β (18a) 

 

 (18b) 

and Δis the birefringent or photoelastic phase retardation, PERφ.

The first principal stresses are related directly to the sine and cosine amplitudes 

(Ica, Isa) by 

 

 (19) 

 (20) 

For most applications of interest the shear stresses encountered are small. Therefore the 

PERΦ are small (subfringe). Equation (19) can be simplified further by using the 

relationship sin Δ ≈ Δ. We combine this with Equation (16) to give: 

 (21) 

Horn gives a geometric interpretation of Eq. (21) by using a Mohr’s circle24, with 

a radius of (σ1 - σ2)/2 for the case of elastic deformation. This allows for the following 

relationships to be directly developed from the sine and cosine intensities (Isa and Ica

respectively) discussed above: 

 (22) 

 (23) 

 The analysis for the elastic case was generated for the commercially developed 

unit, currently marketed by Stress Photonics20-23. This laboratory instrument is a 

transmission system that has a spatial resolution determined by the diffraction limits of 

the lens system.

IIC. The relationship between collision dynamics and photoelastic retardation 

measured in this study. 

When silica is in the annealed amorphous state, it is not birefringent. As stresses 

increase, there becomes a directional dependence of the electric field vector’s speed of 

propagation through the glass. Since impacts cause plastic (irreversible) deformation 
16 

(leading to crack formation) around the impact site, there is a residual stress field and an 

accompanying PERΦ surrounding the damage site. The birefringence begins at the 

periphery of the damage site affected zone, and increases as the stress increases, 

throughout the damage zone of depth l. 

 Damage sites in orbiter windows always occur on the outer surface of the 

window. Where impact occurs, the surrounding volume becomes stressed, while the 

remaining material beneath the damage zone is less affected. Figure 4 (ahead in Section 

IID) shows a schematic of an impact site cross-section, where regions near the center 

show compressions as indicated by the increased density to x-radiation (Figure 2. An 

elastic residual stress field surrounds the impact site and extends radially for a substantial 

distance into the elastic zone. 

 Consider a ray of circularly polarized light passing through the stress field 

surrounding the damage site as shown in Figure 4. Since the extent of the residual stress 

field (and hence PERΦ) is related to the impact energy, we assume that the fracture 

strength varies (as shown in the low velocity impact case) with the amplitude of the PERΦ

(averaged around a path in the elastic zone). Therefore, the magnitude of the PERΦ as 

averaged around the damage site in this study, is experimentally shown to be an indicator 

of breakage strength. The plastic deformation from the damage affects PERΦ in the 

elastic zone. In turn, the PERΦ , which is related to the principal stresses at each point in 

the stress field, is related to the impact energy. 

In this section we outline the mechanisms and derive expressions that relate the 

PERΦ associated with the stress pattern in the elastic region, where Equation (16) applies, 

to the plastic deformation at the collision site. We model the formation of the plastic 

(damage) zone by a network of radially oriented edge dislocations, each with a Burgers 

vector of b, which we represent as a set of dislocations that are aligned in a uniform, 

radially symmetric pattern about the origin. We define an effective Burgers vector to 

represent the effect of the plastic deformation on the stress fields. We write plane stress 

fields in the elastic region. We recast PERφ to PER (with units of nanometers) to 

correspond with experimental measurements. We use Mohr’s Circle analysis to 

determine the relationship of PER to principle stress fields at each point in the elastic 

stress field. We sum PER contributions to each illuminating ray, passing near the 

damage-affected zone, and parallel to the damage axis. Then we perform an integral of 

PER at points on a circular path with the plastic zone site at the center, and relate this to a 

product, Nbl, which is a measure of the plastic deformations inflicted at the damage site. 

From this analysis, we construct an experimental procedure to measure this product, and 

apply these measurements to the four classes of inflicted damage to orbiter windowpanes. 

We write an energy expression for the plastic zone and relate it to the energy of the 

incoming particle and the PER measurements in the elastic field. Finally, we apply the 

previous analysis to predict fracture strength based on the PER measurements. 

Consider that the plastic deformation zone results from a process where atomic 

planes are forced in a close-packed configuration until the penetrating particle energy is 

dissipated25. We model the process as the generation of fields of edge dislocations with 

the extra planes inserted radially outward from the impact site, and distributed throughout 

the damage-affected volume. Let the number of edge dislocations inserted be N, so that 

the number of dislocations between θ and θ+dθ equals (N/2π)dθ. The Burger’s vector 

contribution to the stress field between θ and θ+dθ is then (Nb/2π) dθ. Adopting the 

hollow core model26,27 of Volterra, we write the elastic-zone stress in cylindrical 

coordinates by summing the distribution of Burger’s vectors contributions to the stress 

fields. At a distance r from the z-axis (in cylindrical coordinates)28, 
17 

σ rr = σθθ = −GNb

4π2

(1− ν)r

sinθdθ

θ =−π

2

θ =

π

2

∫ = 0 (24) 

σ rθ = GNb

4π2(1− ν)r

cosθdθ

θ =−

π

2

θ =

π

2

∫ = GNb

2π2(1− ν)r

 (25) 

where G is the shear modulus, ν is Poisson Contraction. Calculation of Mohr’s Circle 

parameters from these values gives a center location, σ , and radius R, respectively, of 

 

σ = σrr +σθθ

2 = 0

R = (

σrr −σθθ

2 )

2 +σrθ2 = GNb

2π2

(1−ν)r

 (26) 

The instrument measures the photoelastic retardation PER in units of nanometers. From 

Equation (16) we write 

 

PER = λ

2π

PERφ = λ

2π

Ica

2 + Isa2

PER = Ica,nm

2 + Isa,nm2

 (27) 

 

where Ica,nm and Isa,nm are Ica and Isa respectively, converted to nanometers. Substituting 

2R for the principal stress differences, σ1-σ2, into Equation (21), then substituting in 

Equation (27), and solving for Nb gives 

 Nb = r

π2

Cl

(1− ν)

G

Ica,nm

2 + Isa,nm2 (28) 

Next we average around the circumference of radius ξ chosen for 

measurement. This averaging is to compensate for asymmetries that may be encountered 

in the damage sites. 

 

 (29) 

Solving for <Nb >l gives an average value over the path of measurement 

 

 (30)

Equation (30) shows that, for any experimental set-up to measure PER, the measurements 

of radius ξ, the material properties, ν, G, and C, one can determine a property of the 
18 

plastically deformed volume represented by the product, <Nb>l. For any damage site, 

one can assume that <Nb>l remains fixed, so the measurement of PER averaged around 

the radius ξ is directly proportional to the accumulated plastically stressed material. 

 Recalling Equation (7), we calculate the indentation depth from 

 

 (31)

where lp is the indentation depth. We assume that lp is related to the compression beneath 

the collision to give an effective damage length29, which we equate to the damage zone 

depth l, where l=κlp

ζ

 . We equate Wplastic to the plastically deforming component of the 

collision particle energy, T, given in Equation (8) and solve for l to obtain 

 

 (32)

where υ is the fractional component of the particle energy imparted to the glass, T, 

utilized in the plastic deformation processes. We assume the compressed region below 

the indentation also contributes to the effective distance l and hence the cumulative PER . 

Combining with 

Equation (30) we solve for <Nb>

 

 (33)

The derivation above identifies the variables and parameters so that an 

experimental procedure can be developed to measure the quantities shown in Equation 

(33), and related to the fracture strength. We include contributions to PER from plane 

stresses that exist well below the disruption zone normally measured with other optical 

instruments such as microscopes including those with special illumination features. The 

extent of the increase of PER from the region below the disruption zone is not examined 

here. This area is one for future exploration and experimental confirmation. Using the 

results of Equation (33) in Equation (14b) we get the dependency of the fracture strength 

of glass in terms of PER measured in this investigation. 

 (34) 

Combining the constants and solving for T gives 
19 

 

Ξ = Nb GC

ξπ2(1− ν)

3υκ

3

ζ

ΛπH tan2ψ

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

ζ

3

T = (

PER

Ξ )

3

ζ

 (35) 

Substituting into Equation (14b) gives the relationship between the fracture strength and 

PER as 

σ fracture = A(PER)

− 2

3ζ

σ fracture = ( 1

9π11/ 2 )

1/9( ξF

3

Λtan2ψ

)

1/9 ( Kc

4/3

Ω1/2H1/9 )(Ξ)

2

3ζ

⎡

⎣

⎢

⎤

⎦

⎥(PER)

− 2

3ζ (36) 

While this equation was derived under the assumption that the indenter was of uniform 

shape as outlined in Section IIA, we extend the approach by noting that ζ is expected to 

change for each class of damage accumulation, whether caused by a colliding particle or 

an indentation from another object. Some of this change is due to various shapes and 

sizes of indenter. Other parameters expected to alter ζ include speed, impact angle, etc. 

 Each class of collision will have a value of ζ because each path classification will 

have a differing plastic deformation associated with the path30. The effect on the 

prediction of fracture strength depends upon what path is followed. 

IID. Energy Considerations in the Elastic Zone Stress Field 

 The general expression for the energy density U0 for a stress field in an isotropic 

material is written as 

 (37) 

For the plane stress case we obtain the following in cylindrical coordinates 

U0 = 1

2E (σ rr

2 + σθθ

2 ) − ν

E (σ rrσθθ ) +

1

2G (τ rθ

2 ) (38)

Writing the energy density in terms of principal stresses using Mohr Circle parameters 

we obtain 
20 

U0 = 1

2E [(σ + R)

2 + (σ − R)2

]− ν

E [σ2 − R2

]

= 1

2G [R2 + (

1− ν

1+ ν

)σ2]

 (39)

 where , and E = 2G(1+ ν). Applying Equation (39) to the elastic 

zone for this case gives 

 U0 = R2

2G (40) 

Substituting the value for R from Equation (26) gives an expression for energy density in 

the elastic stress field of 

 U0 = GN2

b2

8π4(1− ν)

2

r

2 (41) 

Integrating over the elastic volume one obtains the energy stored in the elastic stress 

field, 

 Uelastic = GN2

b2

8π4(1− ν)

2

r

2 (2πrldr)

r=rref

r=Rmax

∫ = GN2

b2l

4π3

(1− ν)

2 ln Rmax

rref

 (42) 

where Rmax in this application is the maximum extent of a measurable PER, and rref is the 

radius at the boundary between the elastic and plastic zones. Next one writes the 

maximum energy available for plastic compression as 

 Uplastic = T − Uelastic (43) 

where, as before, other modes of energy transformations are assumed to be small by 

comparison. The particle energy spent on plastic deformation, equal to Uplastic , can be 

estimated using Equation (32) for l in Equation (42). Then Equation (43) is written as 

 Uplastic = T − ( GN2

b2

4π3(1− ν)

2 ln Rmax

rref

) 3υκ

3

ζ T

ΛπH tan2

ψ

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

ζ

3

 (44) 

This estimate establishes the variables that affect plastic damage formation in the glass in 

terms of glass properties and particle energy and path characteristics. Substituting the 

measurements from GFP, and factoring gives 

 Uplastic = T

−

ζ

3 (T

3+ζ

3 − πξ2

4GC2 χ

−

ζ

3 Ica,nm

2 + Isa,nm2 ln Rmax

rref

) (45) 

where 
21 

 (46) 

IIE. Experimental Design 

Damage sites in orbiter windows always occur on the outer surface of the 

window. Where impact occurs, the surrounding volume becomes stressed, while the 

remaining material beneath the damage zone is less affected. Figure 4 shows a schematic 

of an impact site cross-section, where regions near the center show compressions as 

indicated by the increased density to x-radiation (Figure 2). An elastic residual stress field 

surrounds the impact site and extends radially for a substantial distance into the elastic 

zone. 

 Since the extent of the residual stress field (and hence PERΦ) is related to the 

impact energy, we assume that the fracture strength varies (as shown in the low velocity 

impact case) with the amplitude of the PERΦ (averaged around a path in the elastic zone). 

Therefore, the magnitude of the PERΦ as averaged around the damage site in this study, is 

experimentally shown to be an indicator of breakage strength. The plastic deformation 

from the damage affects PERΦ in the elastic zone. In turn, the PERΦ , which is related to 

the principal stresses at each point in the stress field, is related to the impact energy. 

 Consider a ray of circularly polarized light passing through the fused silica and 

into the damage-affected zone of depth l. Referring to the diagram in Figure (4) the 

measurement arrangement is shown on a fused silica specimen with a damage site 

extending from the specimen surface and into the specimen. Close to the impact surface 

the stress field begins to contribute to the photoelastic retardation. The damage-affected 

volume consists of a plastic zone, characterized by effects of the damage from the 

collision process, and an elastic zone which extends for a large distance from the site. 

This is labeled as the "Damage-affected volume" in the diagram. We examine and 

measure the cumulative effect on the ray from the birefringence caused by the residual 

stress field, which is in the "Elastic Zone" and radially outward from the "Plastic Zone" 

caused by the particle collision energy. The "Circularly Polarized Ray", parallel to the 

damage site axis and passing through the "Measurement Circumference" is well within 

the elastic zone and lies on the cylindrical surface defined by the Measurement 

Circumference and damage depth l. Since fused silica is optically inactive until subjected 

to stress, the ray is only affected at and near the elastic portion of the damage-affected 

zone. By examination of Equation (30) we note that averaging the measured PER at any 

radius around the damage site center, one obtains a quantity which is proportional to the 

damage within the damage volume. Since this is the case, the experimenter may choose 

any radius that is experimentally convenient, without appreciably affecting the analysis. 

 As the circularly polarized ray passes into and through the damage-affected 

elastic zone, it accumulates retardation effects of the stress on the wave speed of the light 

polarized in the direction of the compression. The ray emerges from the glass along with 

the direction-dependent polarization retardations, which gives a phase shift between the 

different polarization directions. The rotating analyzer and video imaging system with 

appropriate software decodes the phase shift into the retardation (PER) and records it as 
22

part of an image. For each damage site PER was calculated and compared with breakage 

strength. 

In the experimental design used to collect data for this paper, we kept the 

measurement radius constant and sufficiently large so that the circumference was always 

larger than the plastic damage zones31 for all damage sites except chatter checks32

Measurements of PER were taken and averaged around the measurement circumference, 

as shown in the diagram. The measurement technique was applied to damage sites of 

different damage classifications. 

Figure 4. A schematic diagram of the elements to illustrate the technique for measuring 

the photoelastic retardation around a damage site in fused silica. The measurement is 

made in the elastic zone. 

III. MEASUREMENTS AND ANALYSIS 

Specimens were prepared from windows taken from shuttle vehicles. The four 

general classes of damage in this study are (1) HVI , hyper velocity impacts encountered 

during shuttle flight , (2) HIT-F, lab created hypervelocity impacts from uniform shaped 

projectiles at the Hypervelocity Impact Technology Facility, (3) Bruises, impacts from 

low-velocity masses, and (4) Chatter Checks, a linear series of bruises inflicted by dull 

and slow objects moving across the glass surface. Specimens from each class were 

measured with various tools to record the size and the depth of the damage site. 

Measurements were also taken with the grey-field polariscope images using a Stress 

Photonics, Inc. device (GFP 2400 Camera) to determine the PER and to obtain an image 

of the damage site in circular polarized light. Then the specimens were broken to measure 

the fracture strength. 
23 

 We use the standard methods to analyze empirical data: the linear fit, the two 

semi-log fits (logarithm and exponential, depending on axis orientation), and the log-log 

plot or power law fit. The linear fit is given by the form (y=Bx+A). Similarly, the 

exponential fit is given by (y=AeBx); The log fit is given by (y=A+Blogx); and the powerlaw fit is given by (y=AxB

). In these cases, y is the fracture strength. 

 From the extensive records kept on each window, natural HVI sites that occurred 

during shuttle missions were identified and cored from retired windowpanes. Protection 

was provided at the damage site with cardboard and tape or suction cups. Then the pane 

was placed on a water knife where the core was removed, leaving the remaining pane (the 

“carcass”) undamaged. The core diameter was dictated by parameters provided in the 

ASTM1499-C specification for ring-ring bi-axial strength testing. The remaining parts of 

pane carcasses could then be inflicted with other classes of damage for testing. 

HIT-F # Projectile 

Material 

Projectile 

Diameter 

(mm) 

Shot 

Velocity 

(km/s)

Impact 

Angle 

(deg) 

Surface 

damage X 

(mm) 

Surface 

damage Y 

(mm) 

Depth of 

crater 

(mm) 

HITF05186 GLASS 0.2 4.16 60 3.1 3.7 0.12 

HITF05190 ALUMINUM 0.2 6.82 45 5.0 5.4 0.25 

HITF05195 ALUMINUM 0.2 4.04 60 2.15 2.5 .1 

HITF05202 GLASS 0.1 6.81 60 1.4 1.9 0.04 

HITF05305 SAPPHIRE 0.2 5.03 0 4.7 4.5 0.4 

HITF05310 SAPPHIRE 0.2 6.91 60 6.5 7 0.22 

HITF05314 STEEL 0.25 4.97 0 10.7 9.4 0.72 

HITF05329 GLASS 0.05 4.0? 45 0.34 0.33 0.03 

HITF03021 ALUMINUM 0.6 7.06 0 27.5* 27.5* 1.950 

HITF03051 ALUMINUM 0.4 6.88 0 16* 16* 1.220 

Table 1. Data from HIT-F collisions. Included are parameters associated with the 

collisions, and measurements of surface damage. Not shown in this table are the 

photoelastic retardation measurements. * indicates that measurement is a diameter. 

 In the HIT-F case, the inflicted damage came from colliding projectiles fired 

from a light gas gun at the Hypervelocity Impact Technology Facility at the White Sands 

Test Facility (Las Cruces, NM). The projectile mass, profile, and speed were controlled 

and measured. The projectile materials, sizes, velocities, and angles of impact for some of 

the HIT-F specimens included in this research are provided in Table 1. 

 For the Bruise category, each specimen was damaged by dropping various sized 

metal bearings on the glass, causing low-speed (Hertzian) impacts to the pane surface. 

The bearing drop was controlled by rolling it down a metal channel with one end placed a 

prescribed distance from the surface of the glass. Various impact velocities (not 

measured or recorded) were obtained by placing the bearings at various distances up the 

channel for release. This category of damage is intended to simulate dropped items on 

the window during servicing of the vehicle. 

The last damage type, Chatter Checks, was formed by placing a sheet of paper on 

the glass and simply drawing a line on that sheet with a ball-point pen. The metal ball of 

the pen produced enough friction between the glass and paper to inflict remarkably 

consistent width chatter checks. The lengths of the chatter checks were varied, as this 

was (erroneously) thought to be the controlling feature for strength. The chatter check 

category simulates damage that might be inflicted during storage and preparation for 

flight. Of all the damage inflicted, the chatter check damage type appeared to cause the 

least damage. 
24 

 

Figure 5. Experimental arrangement set-up for inflicting bruise damage on glass panes. 

Once the bruises and chatter checks were inflicted on the windowpane carcasses, 

the panes were shipped to Southwest Research Institute for measurements of breakage 

strength. Similar to the HVI and HIT-F specimens, the damage sites were protected, and 

the cores were cut from the carcass with a water knife. During the cutting process, the 

diameters were controlled to meet the parameters outlined in ASTM1499-C. 

 Figure 6a. Inflicting chatter check damage on a shuttle windowpane with a ball-point 

pen acting through a paper sheet on pane surface. 
25

Figure 6b33. (Top) Photo showing chatter check damage inflicted in windowpane. 

(Bottom) Chatter Check measurement diagram. 

Each damage site was measured using mold impressions and an optical 

micrometer, photographed, and imaged using the GFP device (Figure 7). The images 

were used to measure the PER amplitudes used in the stress analysis of regions 

surrounding the damage sites. 

IIIA. Procedure with the GFP Device. 

Circularly polarized light was used to form images of the damage sites, with the 

optical birefringence measurements from the GFP associated with each site being 

measured and recorded for each specimen. The birefringence measurements were 

converted into PER and averaged over a closed path that surrounds the damage site but 

far enough away to be in the elastic stress field around the damage site. This procedure 

was designed to specifically avoid optical discontinuities at the actual damage site. The 

resulting PER measured in this way and used in the analysis is proportional to the stress 

field at each damage site. The same technique was applied to all measured damage sites, 

regardless of classification. The same circumference was used for each set of 

measurements. 

 Geometrical measurements of the damage sites were also made with the GFP. 

The outer diameter of the damage site was determined by highlighting surface and 

internal damage by measuring loss of light intensity at the surfaces (internal and 

external). An analysis was made on a construct, which circumscribed the damage. The 

“diameter” of the construct was calculated by averaging a number of chord lengths across 

the construct, or by measuring the construct area, Ac, and determining the diameter by 

d = 2 A

π

 . The chatter-check dimensions were similarly determined. The shadow of the 

defect was filtered and a threshold was determined. The length was measured from tip to 

tip of the chatter check damage. The width was determined by the width of the shadow. 

The shadow was edge-detected, and dilated by 7 pixels to create an area mask for the 

stress calculation.
26

Figure 7. Engineer imaging and measuring PER at a damage site. A commercially 

available GFP with special software was used for these measurements. 

Figure 8. Ring-ring biaxial strength measurement of a specimen. In this figure the 

fracture strength of Specimen 27-159-27 (a Bruise specimen) is under measurement. 

The fracture strength for each specimen was measured. Correlations were run 

between the fracture strength and the optical measurements including the results from the 

GFP. 

IIIB. Results. The GFP Measurements. 

1. HVI. 

Patterns from a typical hyper velocity impact (HVI) are shown in Figure 9. The 

analysis is shown graphically in Figure 10. In Figure 9, the image color shows the two 

states discussed in Eqs. (22) and (23). The color indicates the PER in nanometers 

associated with each stress state as labeled. The image shows the retardation in a colorcoded format with the scale shown in the center. Further analysis of the image is shown 
27

in Figure 10 (top), where the PER due to the total stress amplitude is shown as a function 

of r, the distance from the center of the damage site. One notices that the PER is largely 

radially symmetric with some structure that is azimuthally dependent. Within the image 

one also notices radially dependent structures of lower PER values that are formed. 

Beneath the image is a plot of the magnitude of the in-plane shear, σ1-σ2 ,versus r. Based 

on the character of variations within the top image and the graph, one notices three zones 

in this diagram. In Zone 1, surrounding the impact site and extending out approximately 

1.5 mm, we observe a center region where the PER is positive, followed by a region 

where PER is nearly zero. Within the near zero portion we see islands of large stress. 

Zone 2, [1.5 mm <r<~2.8 mm], is characterized by a mottled appearance, where we note 

concentric structures that appear to be separated by radial line segments, consistent with 

the generation of fields of edge dislocations where the extra planes are inserted radially 

outward from the impact site, and distributed throughout the damage zone. The 

appearance has a somewhat randomly appearing “clamshell” variation as indicated in the 

top of Figure 10. Zone 3, [r > 3 mm] has a relatively smooth appearance and a gradual 

decrement in magnitude that extends out for a large distance from the center. Even in this 

region one observes substantial fluctuations. By using GFP technology, we observe that 

the measurable stress field extends far from the visible damage site. 

HVI Specimen 27-135-1 

Figure 9. Stress-field image of the damage site from high velocity impact damage 

occurring in space, Specimen HVI 27-135. In the center of the color images is the 

photoelastic retardation –to-color scale in nanometers. 
28

Beneath the graph is an optical image of a typical damage site taken in circularly 

polarized light. In this view a dark center appears, surrounded by less pronounced 

structures noted above. There is no view of the center structure that is so clearly evident 

in the PER image at the top. Close examination in the GFP image reveals a shadowy 

network with a grain boundary-like appearance near the prominent central feature. This 

indicates that patterns, within the plastic region, that become prominently visible in 

birefringence at and near the damage site. 

 HVI Specimen 27-135-1 

 Maximum in-plane shear (σ1−σ2) 

Figure 10. Photoelastic Retardation analysis for HVI Specimen 27-135-1 constructed 

from the data shown in Figure 9. Below graph is optical image of the damage site taken 

in circularly polarized light. 
29 

 

 We analyze the HVI measurement results by least-squares fittings of the fracture 

strength (dependent variable) against 6 different independent variables. The results are 

given in Table 2. The dependent variable, fracture strength, is Y and the independent 

variable is x. The x-variables are given in the top row, and (in order) are the outer 

diameter and inner diameter of the damage site (as measured with the illumination from 

the circularly polarized light source from the grey-field polarizer), the PER measurement, 

the defect depth and defect depth to specimen thickness ratio, both measurements taken 

from the mold casting, and the defect size, taken from a measurement with an optical 

magnifier and scale. The equations used for the fits are shown in the extreme left column. 

The equation parameters are given for each fit. 

x

 Y 



Outer 

Diameter 

(GFP) 

Inner 

Diameter 

(GFP) 

Photoelastic 

Retardation 

(GFP) 

Defect 

Depth 

(Mold) 

Depth to 

Thickness 

(Mold) 

Defect Size 

(Optical) 

Bx+A 

A=45.8 

B=-0.029 

R2

=0.532 

A=40.29 

B=-0.076 

R2

=0.648 

A=39.5 

B=-0.247 

R2

=0.805 

A=45.73 

B=-35.2 

R2

=0.595 

A=45.61 

B=-221.95 

R2

=0.588 

A=32.31 

B=-0.513 

R2

=0.122 

AeBx 

A=47.2 

B=-0.00086 

R2

=0.548 

A=40.44 

B=-0.0023 

R2

=0.653 

A=39.3 

B=-0.0075 

R2

=0.843 

A=47.04 

B=-1.036 

R2

=0.609 

A=46.88 

B=-6.526 

R2

=0.602 

A=32.00 

B=-0.017 

R2

=0.112 

A+Blog(x) 

A=106.0 

B=-28.0 

R2

=0.581 

A=50.13 

B=-9.545 

R2

=0.472 

A=43.1 

B=-9.793 

R2

=0.991 

A=21.04 

B=-24.53 

R2

=0.632 

A=1.505 

B=-24.39 

R2

=0.627 

A=30.32 

B=0.4039 

R2

=0.002 

AxB 

A=274.2 

B=-0.356 

R2

=0.593 

A=55.21 

B=-0.13 

R2

=0.431 

A=43.7 

B=-0.127 

R2

=0.997 

A=22.85 

B=-0.310 

R2

=0.635 

A=12.94 

B=-0.308 

R2

=0.631 

A=30.00 

B=0.003 

R2

=0.002 

Table 2. Relationships between fracture strength of HVI-damaged specimens and six 

selected independent variables. Included are the fitting equation and the square of 

correlation coefficient (R2

) for each fit. 

 The rankings of the correlation coefficients for each independent variable 

category in descending order of correlation are Photoelastic Retardation (GFP), Inner 

Diameter (GFP), Defect Depth (Mold), Defect depth to thickness ratio (Mold), Outer 

Diameter (GFP), and Defect Size (Optical). Within the equation types the power law best 

predicts the fracture strength except for the Defect Size (Optical), where the linear fit is 

slightly better. We suspect that this discrepancy is caused by the measurement 

uncertainty with the optical magnifier induced by variations of light paths caused by the 

optical disruptions at the damage site. The table shows that the best correlation occurs 

with a power-law fit of the fracture strength to the photoelastic retardation, thus affirming 

the results from theoretical predictions. 

 We further analyze the power-law fit between the Fracture Strength and PER. In 

Figure 11 we calculate the least squares power-law fit and obtain a square of the 

correlation coefficient R. As predicted by the theory, this is the best fit with a correlation 

coefficient of 0.998 (R2 =0.9967). Thus the theoretical analysis for the relationship 

between fracture strength and PER is confirmed for HVI damage. 
30

Figure 11. A plot of measured fracture strength versus photoelastic retardation for hyper 

velocity impacts . 

2. Bruises. 

In Figure 12, we have images from a typical measurement obtained from a 

bruised specimen. The figure shows the stress image of a bruised specimen (left) and an 

optical image (right) taken with circularly polarized light. The stress image also shows 

relatively low values of stress-induced birefringence (SIB) in the central zone. Outside 

the center zone we find regions of low SIB in the positive (red in color) regions , and 

regions of much higher SIB (white) in both the positive and negative regions. Separation 

zones between positive and negative stresses are curled, where in the HVI, the 

separations were straight. Many of the same prominences appear in the optical image 

(circularly polarized illumination) of the bruise as well, but are less pronounced. In both 

images the center is slightly affected, with a positive SIB showing in the PER image. 

Most of the damage appears around the perimeter of the center zone. A slight SIB 

variation in the central feature appears across the central zone. Just beyond the central 

zone regions (corresponding to Zone 2 in the HVI), the SIB shows some features that 

stand out from the background. These features fall into two different shape 

classifications. Some features follow a circular or radially symmetric appearance. Other 

features appear to have a dependency that has a spiral or involuted appearance. Both 

features show that the strain pattern has regions with prominences, indicating substantial 

localized strains. But in comparison to the typical HVI pattern, the PER range is similar. 

The damage site was also measured with an optical micrometer with the aid of a 

Surface Light Optimization Tool (SLOT), which directs high intensity light into the plane 

of the glass, at the damage site. These data were used in compiling the comparisons in 

Table 3. 
31

Bruise 27-139-15 

Figure 12. Stress Field Image (left) and visual image under circularly polarized light 

(right) of a typical bruised specimen. At the left of the color image is the photoelastic 

retardation –to-color scale in nanometers. 

Table 3 gives the least-squares fit of the fracture strength (dependent variable) of a set of 

specimens, each with a bruise damage site, to different measurements taken for the 

independent variable. Correlation coefficients are relatively high for the Outer Diameter 

measured with circularly polarized light illumination from the GFP and the Photoelastic 

Retardation measurement. Additionally for these two independent variable choices the 

power law is the best fit. The highest correlation coefficient, R=0.990 (R2

=0.981) occurs 

between the Fracture Strength and the PER measured with the GFP. A closer examination 

of the fit is shown in Figure 13, which is a plot of the fracture strength versus the 

Photoelastic Retardation for the bruise specimens. 

3. HIT-F 

This class of damage is inflicted with hyper velocity projectiles of varying 

materials, sizes and shapes and at various angles (See Table 1 for the details). The 

velocity at impact can be varied and measured precisely, so that projectile energy is 

known. The typical resulting damage site is shown in Figure 14, which shows the stressinduced birefringence image (left) and an image taken with circularly polarized light 

(right). There is substantial clamshell cracking, called conchoidal spall, that a subatantial 

distance from the impact site. The site appears to have a bright center surrounded by a 
32

x

 Y 



Outer 

Diameter 

(GFP)

Inner 

Diameter 

(GFP)

Photoelastic 

Retardation 

(GFP)

Ave. Outer 

Diameter. 

(Slot+Edge)

Ave. Inner 

Diameter. 

(Slot+Edge)

Bx+A 

A=50.09 

B=-0.0658 

R2

=0.679 

A=59.53 

B=-0.305 

R2

=0.333 

A=37.26 

B=-1.199 

R2

=0.625 

A=48.16 

B=-137.4 

R2

=0.651 

A=53.17 

B=-639.6 

R2

=0.311 

AeBx 

A=58.54 

B=-0.00247

R2

=0.794 

A=93.96 

B=-0.012

R2

=0.304 

A=36.32 

B=-0.0455

R2

=0.735 

A=54.66 

B=-5.19

R2

=0.748 

A=72.96 

B=-26.37

R2

=0.272 

A+Blog(x) 

A=177.45 

B=-59.859 

R2

=0.816 

A=182.9 

B=-77.20 

R2

=0.312 

A=39.42 

B=-19.11 

R2

=0.973 

A=-19.44 

B=-54.70 

R2

=0.775 

A=-58.01 

B=-60.67 

R2

=0.274 

AxB 

A=5686.8 

B=-0.941 

R2

=0.913 

A=14946 

B=-1.38 

R2

=0.273 

A=37.16 

B=-0.282 

R2

=0.981 

A=4.513 

B=-0.866 

R2

=0.861 

A=0.7362 

B=-1.09 

R2

=0.221 

Table 3. Relationships between fracture strength of bruised specimens and selected 

independent variables. Included with the equation for each fit is the square of correlation 

coefficient (R2

) for the fit. 

Figure 13. A plot of fracture strength versus photoelastic retardation for bruise damage in 

glass. 
33

dark central region. Directly beyond this is a region where concentric bands appear and 

extend beyond what appears as impact-related patterns in the glass. This is prominent in 

both images, as are a series of radial patterns emanating from the impact center. This 

appears in both the SIB image and the image formed by circularly polarized light. As in 

the other images, the strain field extends far from the impact site. In this case, however, 

more structure also appears in the image taken with circularly polarized light. In both 

images (SIB and circularly polarized light) sharp variations in radial directions appear. 

Figure 14. Stress induced birefringence image (left) and visual (right) of a typical 

impacted site. At the left of the color image is the photoelastic retardation –to-color scale 

in nanometers. 

We analyze the five specimens, which were used in this study. Only three 

specimens had PER data. Even though the data is statistically insignificant, we include 

the HIT-F data for completeness. The HIT-F measurements are evaluated by forming a 

least-squares fits of the fracture strength (dependent variable) against 6 different 

independent variables. The results are given in Table 4. As before, the dependent 

variable, fracture strength, is Y and the independent variable is x. The x-variables are (in 

order) the outer diameter and inner diameter of the damage site (as measured with the 

illumination from the circularly polarized light source from the grey-field polarizer), the 

PER measurement, the defect depth taken from the mold casting, and the defect size, 

taken from a measurement with an optical magnifier and scale. Each set is analyzed for 

best-fit correlation, with the equation parameters given for each fit. The equations used 

for the fits are shown in the extreme left column. The top row gives the independent 

variable used for the fit. 

The rankings of the correlation coefficients for each independent variable 

category (best to worst) are Inner Diameter (GFP), Defect Size (Optical), Outer Diameter 

(GFP), Defect Depth (Mold), Defect to thickness (Mold), and Photoelastic Retardation 

(GFP). The exponential and log fits appear to be the best of the equation forms evaluated 

against the fracture strength. The power law is not the best except for the PER. Although 
34 

not the best match, the inner diameter has a good correlation coefficient of R=0.977 

(R2

=0.955) shown in Figure 15. We are unable to draw conclusions because of the 

paucity of data, especially for the Photoelastic Retardation measurements (3 points), 

since only three of the specimens were able to render a PER reading because surface 

spalling caused excessive light path scattering. However, a graph of fracture strength vs. 

PER is included, (Figure 16) even though the least squares fit (and hence its Correlation 

Coefficient) is not sufficiently representative of the process to be able to draw 

conclusions. 

x

 Y 



Outer 

Diameter 

(GFP) 

Inner 

Diameter 

(GFP) 

Photoelastic 

Retardation 

(GFP)* 

Defect 

Depth 

(Mold) 

Defect 

Length/Dia. 

(Mold) 

Defect 

Size 

(Optical) 

Bx+A 

A=41.36 

B=-0.0068 

R2

=0.860 

A=41.39 

B=-0.035 

R2

=0.882 

A=41.70 

B=-0.374 

R2

=0.234 

A=40.95 

B=-12.29 

R2

=0.876 

A=47.24 

B=-211.85 

R2

=0.841 

A=42.44 

B=-0.957 

R2

=0.901 

AeBx 

A=42.47 

B=-0.00025 

R2

=0.846 

A=43.00 

B=-0.0013 

R2

=0.917 

A=41.27 

B=-0.0089 

R2

=0.243 

A=41.93 

B=-0.450 

R2

=0.865 

A=52.05 

B=-7.56 

R2

=0.798 

A=44.35 

B=-0.035 

R2

=0.902 

A+Blog(x) 

A=81.00 

B=-17.175 

R2

=0.865 

A=82.29 

B=-22.74 

R2

=0.967 

A=44.77 

B=-8.409 

R2

=0.487 

A=24.72 

B=-14.60 

R2

=0.865 

A=2.172 

B=-23.74 

R2

=0.743 

A=49.44 

B=21.03 

R2

=0.905 

AxB 

A=166.2 

B=-0.259 

R2

=0.856 

A=180.99 

B=-0.351 

R2

=0.955 

A=44.52 

B=-0.0887 

R2

=0.516 

A=23.53 

B=-0.218 

R2

=0.836 

A=11.12 

B=-0.346 

R2

=0.691 

A=55.55 

B=0.319 

R2

=0.875 

Table 4. Relationships between fracture strength of HIT-F-damaged specimens and 

selected independent variables. Included with the equation for each fit is the square of 

Correlation Coefficient (R2

) for the fit. Three points were used for the determination of 

fits to the Photoelastic Retardation, and is indicated by *. 

 We further note that the accuracy of optical measurements with this damage are 

less because light is badly scattered by the crazing that extends from the center to a good 

distance from the damage site. Depending on surface disruptions, significant portions of 

the light beam may be scattered from the site. 

4. Chatter Checks

 This class of damage is inflicted with dull object pulled across the surface of the 

glass. Other than the force necessary to hold the object to the surface, no particular 

normal force is applied to the dull object as it scrapes across the glass surface. The 

typical resulting damage site is shown in Figure 17, which shows the stress-induced 

birefringence image. The site appears to have a bright centerline with indications of strain 

patterns extending, somewhat randomly, normal to the line. In contrast to the other 

images, the strain fields do not extend far from the scratch (damage site). 
35

Figure 15. A plot of fracture strength as a function of GFP measurement of damage site 

inner diameter in HIT-F-damaged specimens. 

We analyze twelve specimens that were used in this study. The Chatter Check 

measurement results are analyzed by forming least-squares fits of the fracture strength 

(dependent variable) against 5 different independent variables. The results are given in 

Table 5. As in the earlier classifications, the dependent variable, fracture strength, is Y 

and the independent variable is x. The x-variables are (in order) the outer length (GFP 

measurement), outer breadth (GFP measurement) of the damage site (as measured with 

the illumination from the circularly polarized light source from the GFP), the PER

measurement, the outer length from an optical micrometer aided by the SLOT. 

Each set is analyzed for best-fit correlation, with the equation parameters given for each 

fit. As before, the equations used for the fits are shown in the extreme left column. The 

top row gives the independent variable used for the fit. 

The rankings of the correlation coefficients for each independent variable 

category (best to worst) are Outer Length from SLOT Measurement, Outer Length 

(GFP), Area from Slot Measurement, Photoelastic Retardation (GFP), and Outer Breadth 

(GFP). The power law equation form best predicts the fracture strength (has the higher 

correlation coefficient), except for outer breadth, where the linear form is the best fit. 

Whether measured with the GFP or the SLOT measuring instrument, the outer length 

appears to be the best predictor, with a correlation coefficient of 0.578 (R2

=0.335). 

Generally, the low correlation parameters suggest that none of these variable are 

predictive of the fracture strength. It is instructive to examine a graph of fracture strength 

vs. PER (Figure 18) even though the least squares fit (and hence its correlation 

coefficient) is not the best in the list. We find that most of the scatter appears with 

specimens where the PER is less than 1 nm. For comparison fracture strength plotted 

against outer length is shown in Figure 19. Unfortunately, most of these data lies in the 

range where PER is less than 1 nm. 
36

Figure 16. A plot of fracture strength of HIT-F-damaged specimens as a function of 

photoelastic retardation. Only 3 points available make plot inconclusive. 

x

 Y 



Outer Length 

(GFP) 

Outer 

Breadth 

(GFP) 

Photoelastic 

Retardation 

Outer Length 

from Slot 

Measurement 

Damage Area 

from Slot 

Measurement* 

Bx+A 

A=70.617 

B=-0.117 

R2

=0.205

A=76.85 

B=-0.827 

R2

=0.109

A=69.404 

B=-8.558 

R2

=0.147

A=70.31 

B=-26.702 

R2

=0.184

A=69.98 

B=-5.17 

R2

=0.159

AeBx 

A=70.43 

B=-1.77x10-4 

R2=0.212

A=77.56 

B=-0.013 

R2

=0.108

A=69.208 

B=-0.132 

R2

=0.149 

A=70.07 

B=-0.403 

R2

=0.192 

A=69.73 

B=-0.0782

R2=0.167 

A+Blog(x)

A=104.74 

B=-15.173 

R2

=0.321

A=94.60 

B=-25.76 

R2

=0.099

A=60.072 

B=-14.66 

R2

=0.167

A=53.69 

B=-14.793 

R2

=0.321

A=63.9 

B=-14.96 

R2

=0.306 

AxB 

A=117.22 

B=-0.0986 

R2

=0.334

A=102.15 

B=-0.173 

R2

=0.097

A=59.89 

B=-0.099 

R2

=0.167

A=54.65 

B=-0.096 

R2

=0.335

A=63.58 

B=-0.0971 

R2

=0.322

Table 5. Relationships between fracture strength of specimens with chatter-check 

damage sites and selected independent variables. Included with the equation for each fit 

is the square of correlation coefficient (R2

) for the fit. * indicates a calculated value 

(length x width*1000 ; arb. Units . See Fig. 6b for detail used to calculate area) 
37 

Chatter Check Specimen 26-210-30 

 

Figure 17. Stress-field image of Chatter Check, showing effects of stress fields around 

the damage (line). To the right of the image is the PER color scale in nanometers. 

 
38

Figure 18. A plot of fracture strength versus average photoelastic retardation for Chatter 

Checks. 

Figure 19. A plot of fracture strength versus outer length for chatter checks. 
39 

IV. DISCUSSION 

 We began this project to improve the location and detection of damage sites as an 

aid to technicians who examined each window on returning shuttles for damage. As the 

data were collected we observed that PER measurements were predictive. At this point 

we developed an analytical model to relate fracture strength of fused silica to PER 

measurements. Furthermore, we checked the fracture strength of a somewhat randomly 

selected (within each category) sampling of specimens against their PER measurements. 

We used the somewhat random selection of the data to establish parameters against 

which the remaining data can be compared. The results of this comparison will be the 

basis of a later study. The random selection of the data was chosen for this work so that 

an estimate of uncertainty can be made. The uncertainties are estimated by comparing 

values calculated from the least-squares power fits with the measured data against the 

PER measurements. Table 6 gives the results of the estimates of uncertainty of PER

measurements for each damage classification. 

Damage Classification HVI Bruise HIT-F Chatter Check 

Uncertainty (MPa) ±0.8 ±1.8 ±4.2 ±6.5

Table 6. Uncertainties for calculations from least-squares fits of the fracture strength to 

the photoelastic retardation for each damage type. 

 Table 7 (below) gives the constants associated with the least-squares data analysis 

for fracture strength versus PER. In the first two rows the constants are given for the 

power law (y=AxB

) fit, determined by theory to be the best functional form for relating 

fracture strength to damage. 

Damage 

Type 



 Constants 

 

HVI Bruise HIT-F Chatter Check 

A 43.71 37.16 44.52 59.89

B -0.127 -0.2817 -0.0887 -.0099

ζ 5.25 2.37 7.52 6.73 

χ 43.71 37.16 44.52 59.89 

Table 7. A Summary of constants associated with the different damage classifications in 

this study. χ is equal to A and is repeated here for emphasis. 

 For each of the damage types listed, the constant χ (= Α in Equation 36)is the 

value of the fracture strength (in MPa) for one nm of photoelastic retardation. χ shows a 

very small difference for the hyper-velocity impacts (HVI and HIT-F damage), while 

showing substantially more difference for the bruises and chatter checks. The origin of 

this variation is suspected to be differences in the constant factors (shape factors and 

other geometrically-related constants, photo-elastic constants, energy threshold effects 

and load rates) that contribute to χ. Based on the present data, Eqs. (14b), and (36), 
40 

particle shape has little effect on χ for high velocity regimes, since the hyper velocity 

impacts (HVI) and impacts from the Hypervelocity Impact Technology Facility (HIT-F) 

appear to nearly match in value of χ. However within the same regime, impactor 

characteristics such as shape and composition appear to affect the dynamics of the 

conversion process within the glass, as seen with the variation inζ for HVI and HIT-F 

inflicted damage. The constant ζ shows a variation in effective lengths of plastic strain 

regions. This is not surprising since a large number of possible paths are available for the 

conversion process within the glass from differing indenter shapes and properties 

(density, hardness, etc.). 

 

Damage Type

Minimum 

PER 

HVI Bruise HIT-F Chatter Check 

Imin (nm) 0.456 0.323 0.399 8.81

Table 8. Minimum PER for each of the Damage Classifications for a fracture strength 

equal to the published tensile strength for fused silica. 

It is instructive to determine the values of PER for each classification at which the 

fracture strength is no more than the published tensile strength of 48.3 MPa34, for fused 

silica. Table 8 shows the values for each type of damage classification analyzed here. We 

also note that an examination of Chatter Check Damage (Figure 18) shows an interesting 

feature about the relationship between strength and the degradation threshold for PER. 

The fracture strength appears random for values of PER below ~0.6 nm, indicating a 

possible minimum damage below which the fracture strength is not affected. Thresholds 

for degradation for chatter checks indicate that PER sensitivity is adequate for a 

nondestructive methodology to inspect windows for aerospace usage for this 

classification of damage. It therefore is an area for further investigation to determine a 

minimum PER in each classification below which impact damage does not exceed the 

effects of inherent flaws in the glass on strength.

 HIT-F inflicted damage analysis shows that PER is unable to give measurements 

if the physical disruption of the surface leads to excessive light scatter. Unless one 

develops a technique to avoid the surface scattering at the damage site, another technique 

would need to be employed for analysis of such damage. Our data suggest that the inner 

diameter of the damage site gives best predictive results for this type of damage. In this 

case, the inner diameter measured with the GFP system gave the most reliable 

predictions. The optically-measured defect size and the defect depth (mold) also gave 

good results. 

 Bruise damage shows a center where PER is largely unaffected. Most of the large 

variation in birefringence occurs at the perimeter of the physical damage site. 

Measurements other than PER, but made with the GFP optical instrument also show 

promise for bruise damage assessment as well. The GFP optical image measurements of 

outer diameter damage of bruises are a good predictor of fracture strength. 

 The depth measurement using molds (HVI) appear to provide the next most 

reliable indications of fracture strength in glass. Chatter Checks do not show the same 

reliability of prediction in any of the measurement techniques that were tested. But of all 

measurements on Chatter Checks, the outer length appears to be the most predictive. Part 
41 

of the reason for this is that the effect of chatter checks on the fracture strength was much 

less than the other modes of damage, and the size of each craze-site along the length was 

uniform. 

 We again point out that the theory developed for the relationship between PER 

and fracture strength depends upon the theory for collision kinetic energies and fracture 

strength, which is based on a quasi-static analysis, and hence is limited. Since this 

analysis is applied to a very dynamic situation, the framework is missing rate-related 

elements. While it allows for different collision classifications, it doesn’t analytically 

treat the different pathways by which energy is imparted by the particle to the glass. 

None-the-less, its predictive power is quite good, as is its ability to assist in the 

development of solid and reliable experimental procedures. It predicts the power-law 

dependence, which is consistent with current damage models for glass. This quasi-static 

analysis introduces a damage response mechanism of dislocation formations within the 

glass in response to damage-causing impacts. Furthermore this work points to a basis for 

a systematic treatment of damage analysis and fracture strength prediction from grey field 

polariscope-based measurements in annealed fused silica. 

V. CONCLUSIONS 

 Measurements on shuttle windows were taken to determine the geometrical and 

the birefringence characteristics of different types of inflicted damage with various 

optical devices. Measurements of each site were taken with a variety of techniques, 

including the use of various magnifiers for geometrical optical image analysis that 

included direct measurements and measurements on molds made of damage sites. A 

commercially available grey-field polariscope was also used to measure simultaneously 

an image of the damage site and the photoelastic retardations at each damage site. After 

these measurements were made, each specimen was broken in accordance to ASTM 

Standard C1499-09. The fracture strength for each specimen was curve-fitted to four 

standard functions by using least-square fitting routines, and the correlation coefficients 

were compared. Consistent with the theory relating fracture strength to photoelastic 

retardation measurements as prescribed, the power law fit gives the best results for Hyper 

Velocity Impact damage and bruise damage. Chatter check damage correlation with 

fracture strength was best predicted by damage length because a well-defined crack 

length is formed. HIT-F-inflicted damage correlated best with inner diameter 

measurements of the damage sites.

 The results show that, as predicted by theory, the power-law correlation between 

the GFP measurements and fracture strengths σf gives the best fit, with the results as 

follows: 

σf = 43.7 (ε)

-0.127 R2

= 0.997 (HVI-photoelastic retardation) 

σf = 181.0 (ε)

-0.351 R2

= 0.955 (HIT-F-inner diameter damage) 

σf = 37.2 (ε)

-0.282 R2

= 0.981 (Bruises-photoelastic retardation) 

σf = 117.2 (ε)

-0.099 R2

= 0.334 (Chatter Checks-outer length of scratch) 

where ε is the corresponding damage parameter (e.g. photoelastic retardation) 

measurement. Both the theoretical and experimental components of this study clearly 

establish the fact that photoelastic retardation is a valid technique to assess fracture 

strength degradation of annealed fused silica from high velocity impacts encountered 

during flight. This study further outlines the framework of an experimental analysis for a 

photoelastic retardation-based method to accomplish this. This study also affords a 

comparison of the effectiveness of different evaluation techniques to assess effects of 
42 

impact damage on the service life of fused silica windows. We conclude that the optical 

birefringence assessment of damage sites is a good indicator of fracture strength in 

annealed fused silica and hence a good inspection technique for aiding in the 

determination of retirement-for-cause for annealed fused silica windows used for space 

applications. This conclusion is based on correlations among different measurements 

with the fracture strength measured in specimens prepared from shuttle windowpanes. 

VI. ACKNOWLEDGEMENTS 

The authors wish to acknowledge and thank the following, who helped with this work. 

Brad Boyce (Stress Photonics) wrote much of the data collection software used with the 

GFP system. Marshall Neipert (NASA/JSC), systematically created the bruises and 

chatter checks that were used in this study. Ray Parker (NASA/LaRC) took the x-ray 

tomographic data on a damage site in silica. Karen Bernstein (NASA/JSC) held up a 

significant portion of her study so that we could collect the GFP data on the HVI and 

HIT-F damaged specimens. We also wish to thank Richard W. Russell (NASA/KSC) for 

funding the Stress Photonics portion of the data collection. 

VII. REFERENCES AND NOTES 

1 In the past, these panes have been manufactured from Corning 7940/7989 Fused Silica glass.

2

 S. M. Wiederhorn and B. R. Lawn, “Strength Degradation of Glass Impacted with Sharp 

Particles: I, Annealed Surfaces”, J. Am. Ceram. Soc., 62, pp. 66-70, (1979). 

3

 B. R. Lawn, D. B. Marshall, and S. M. Wiederhorn, “Strength Degradation of Glass Impacted 

with Sharp Particles: II, Tempered Surfaces”, J. Am. Ceram. Soc., 62, pp. 71-74, (1979). 

4

 Edelstein, Karen S. “Orbital impacts and the Space Shuttle windshield”, NASA-TM-110594, 

NASA. Johnson Space Center, 1995. 

5

 For example of an analysis, see S. M. Wiederhorn, A. G. Evans, E. R. Fuller, and H. Johnson, 

“Application of Fracture Mechanics to Space-Shuttle Windows”, J. Am. Ceram. Soc., 57, pp. 

319-323, (1974). 

6

 B. A. Proctor, I. Whitney, and J. W. Johnson, “The strength of fused silica”, Proceedings of the 

Royal Society of London, Series A, Mathematical and Physical Sciences, 297, pp. 534-557, 

(1967). 

7

 An example of this is Richard R. Burt, and Eric L. Christiansen, “Hypervelocity Impact Testing 

of Transparent Spacecraft Materials”, Intl. J. Impact Engineering, 29, pp. 153-166, (2003). 

8

 Max Born and Emil Wolf, “Principles of Optics”, 4th Edition, Pergamon Press, Oxford, UK, pp. 

703-718, (1970). 

9

An orbiter window inspection system was designed and built by ASRC (Artic Slope Resource 

Corp.) and NASA Kennedy Space Center. This design used a modified GFP unit based largely on 

the Stress Photonics GFP-2400 commercially modified, built, and tested by Stress Photonics.

10 The damage classifications were developed to cover the range of damage infliction to the 

window. All but the naturally occurring High Velocity Impacts (HVI) are idealized. 

11 “Standard Test Method for Monotonic Equibiaxial Flexural Strength of Advanced Ceramics at 

Ambient Temperatures”, ASTM Standard C1499-09, ASTM International, Conshohoken, PA 

(2009). 

12 This assumption is restrictive because damage caused by different speeds of particles has 

different energy dependencies. In this case we use a quasi-static approach, which limits its 

applicability. However, the power-law dependency on energy appears to be broadly applicable, 

even though the power-law parameters change under the differing initial conditions (velocity, 

particle diameter, etc). 

13 Estes, Lynda R., “Strength Design and Verification Criteria for Glass, Ceramics, and Windows 
43 

in Human Space Flight Applications”, NASA Technical Standard, NASA-STD-5018, Oct, 2010. 

Also See Reference 2. 

14 There are various energy-loss mechanisms. The list includes sound-wave generation, modal 

vibrations and heat generation. 

15 B. R. Lawn and D. B. Marshall: pp. 205-229 in Fracture Mechanics of Ceramics, Vol. 3, edited 

by R. C. Bradt, D. P. H. Hasselman, and F. F. Lange, Plenum, New York, (1978). 

16 B. R. Lawn and A. G. Evans, “A Model for Crack Initiation in Elastic/Plastic Indentation 

Fields,” J. Mater. Sci., 12 [11] 2195-2199, (1977). 

17 B. R. Lawn and E. R. Fuller, “Equilibrium Penny-Like Cracks in Indentation Fracture”, J. 

Mater. Sci, 10 [12] 2016-2024, (1975). 

18 B. R. Lawn, E. R. Fuller, and S. M. Wiederhorn, “Strength Degradation of Brittle Surfaces: 

Sharp Indentors”, J. Am. Ceram. Soc., 58, pp. 193-197, (1976).

19 Wright, A. F., and Leadbetter, A. J. , “The structures of β-cristobalite phases of SiO2 and 

AlPO4”, Phil. Mag. 31, pp. 1391-1401, (1975).

20 J.R. Lesniak, STTR Final Report (Contract No. NAS1-97036, 2000). The initial support for its 

development came from Langley Research Center to Stress Photonics through the STTR 

Program. 

21 J.R. Lesniak, M.J. Zickel, C.S. Welch, and D.F. Johnson, “An Innovative Polariscope for 

Photoelastic Stress Analysis”, Proceedings of the Society of Experimental Mechanics Annual 

Conference, Bellevue, WA (June 2-4, 1997), pp. 219-224, (1997). 

22 G. Horn, J. Lesniak, T. Mackin, B. Boyce, Rev. Sci. Instrum., 76, 045108, pp. 1-10, (2005). 

23 For a more complete discussion see K. Ramesh, “Digital Photoelasticity – Advanced 

Techniques and Applications”, Berlin, Springer (2000). 

24 There are a number of references on Mohr’s Circle and the application to stresses. For 

example, one using SI units is Ferdinand P. Beer, E. Russell Johnston, Jr., and John T. DeWolf, 

“Mechanics of Materials” Third Edition, McGraw-Hill, NY (2001). 

25 While beyond the scope of this work, there are several approaches to build up a structure of 

short aggregates of dislocations to describe the damage strength. Because fused silica has shortrange order and long-range disorder, we use Burgers vectors as a basis for this analysis. One can 

consider the damage site as a density of edge dislocations, where the extra planes point radially 

outward (radial symmetry). We assume a collection of edge dislocations with a set of Burgers 

vectors radially symmetric about the origin, and each of value b. A reference for dislocations in 

systems with short-range order (liquids) is given in A. H. Cottrell, “Theory of Dislocations” 

Gordon and Breach, New York and London, p. 35, (1964). 

26 Lee A Segel, “Mathematics Applied to Continuum Mechanics”, Dover, Mineola, NY, pp. 241-

248, (1987). 

27 R. W. Lardner, “Mathematical Theory of Dislocations and Fracture”, University of Toronto 

Press, Toronto, p. 75 (1974).

28 R. W. Lardner, pp. 77-78, (1974).

29 Plastic strain depends upon the path leading to the deformation (i.e. the loading path). We 

introduce ζ as an exponent in the effective length to account for the different paths or classes of 

impacters, since each shape will have a different dynamic of compression. This is consistent with 

a power-law expression for the flow curve used in plasticity. See: Dieter, George E, “Mechanical 

Metallurgy” Third edition, McGraw-Hill, New York, pp.70-72, (1986); and A. Kelly and N. H. 

Macmillan, “Strong Solids”, 3rd Edition, Clarendon Press, Oxford, p.140ff, (1986). 

30 Dieter, George, p. 88, (1986). 

31 After the derivation above, we realize that it is probably not necessary to hold the radius 

constant, although this point needs to be checked experimentally. 
44 

32 Each chatter check was an elongated damage site created by dragging a stylus across the glass 

surface. It consisted of a sequence of small indentations in the surface along the stylus path. 

Consequently the stylus path exceeded the measurement path circumference. 

33 From a process specification for window inspection, Report MT0501-514 “Requirements for 

Inspection of Orbiter Windows” (Rev G). The Boeing Company, Feb 15, 2008.

34 This value was found at many internet sites. For example, Proscitech.com, PROPERTIES OF 

FUSED QUARTZ. 
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Technical Publication

 4. TITLE AND SUBTITLE

Examination of Relationship Between Photonic Signatures and Fracture 

Strength of Fused Silica Used in Orbiter Windows 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Yost, William T.; Cramer, K. Elliott; Estes, Linda R.; Salem, Jonathan A.; 

Lankford, James, Jr.; Lesniak, Jon

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20101

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified Unlimited

Subject Category 37 

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

A commercially available grey-field polariscope (GFP) instrument for photoelastic examination is used to assess impact damage inflicted upon the outer-most 

pane of the orbiter windows. Four categories of damage: hyper-velocity impacts that occur during space-flight (HVI); hypervelocity impacts artificially made 

at the Hypervelocity Impact Technology Facility (HIT-F); impacts made by larger objects falling onto the pane surface to simulate dropped items on the 

window during service/storage of vehicle (Bruises); and light scratches from dull objects designed to mimic those that might occur by dragging a dull object 

across the glass surface (Chatter Checks) are examined. The damage sites are cored from fused silica window carcasses, examined with the GFP and other 

methodologies, and broken using the ASTM Standard C1499-09 to measure the fracture strength. A correlation is made between the fracture strength and 

damage-site measurements including geometrical measurements and GFP measurements of photoelastic retardation (stress patterns) surrounding the damage 

sites. An analytical damage model to predict fracture strength from photoelastic retardation measurements is presented and compared with experimental results. 

15. SUBJECT TERMS

Fracture strength; Fused silica; Hypervelocity impact; Impact damage; Photoelastic

18. NUMBER

 OF 

 PAGES

45

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

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3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

604746.02.22.07.01.01.04 

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/TP-2011-217322

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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 12 - 2011