ARL-TN-0756 ● MAY 2016

US Army Research Laboratory

Stress Optical Coefficient, Test Methodology,

and Glass Standard Evaluation

by Clayton M Weiss and Parimal J Patel

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ARL-TN-0756 ● MAY 2016

US Army Research Laboratory

Stress Optical Coefficient, Test Methodology,

and Glass Standard Evaluation

by Clayton M Weiss

Oak Ridge Institute for Science and Education (ORISE), Belcamp, MD

Parimal J Patel 

Weapons and Materials Research Directorate, ARL

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4. TITLE AND SUBTITLE

Stress Optical Coefficient, Test Methodology, and Glass Standard Evaluation

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Clayton M Weiss and Parimal J Patel

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14. ABSTRACT

The photoelastic behavior of transparent materials under stress, which is represented by the material property of stress optical 

coefficient, can be used to evaluate glass samples of known and unknown composition. Using a polariscopic and load frame, 

we were able to create and observe the conditions of stress-induced birefringence. A modification of an ASTM testing 

procedure for determining stress optical coefficient is described. Stress optical coefficient data for several types of glasses are 

computed for comparison and standardization purposes. 

15. SUBJECT TERMS

glass, stress optical coefficient, SOC, photoelasticity, fringe

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Clayton M Weiss

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Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Photoelasticity 2

3. ASTM Testing 3

4. SOC Experimental Evaluation 4

5. New Method for Evaluation 5

6. Experimental Results 9

7. Conclusions 10

8. References 11

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List of Figures

Fig. 1 Beam stressing and polarimeter arrangement........................................3

Fig. 2 Loading configuration of glass beams adapted from the ASTM 

standard. The glass beams used are to have a width b) of 20–30 mm, 

thickness d) of 6–10 mm, and a length within the range 120–130 mm. 

The top and bottom surfaces of the specimen are prepared with a fine 

grind. The faces normal to the light transmission direction (L × d) are 

polished. The 4 faces, excluding the ends, are flat and parallel to 

within 0.050 mm. Annealing of the specimens should be performed if 

the neutral fringe is excessively curved. The 4-point bend loading 

fixture uses a support span L) of 115 mm and a moment arm a) of 

45 mm (a = (L-Li)/2). The loading points are approximately 5 mm in 

radius......................................................................................................4

Fig. 3 Color scale showing the relationship among retardation, fringe order, 

and displayed color through crossed polarizers (adapted from MicroMeasurements).......................................................................................6

Fig. 4 A) A glass specimen in a 4-point bend with no load applied, a dark 

field image. B) 0-order (black) fringe at position 1, the first-order 

fringe (indigo to violet) at position 2, the second-order fringe (red to 

green) at position 3 and the third-order fringe (red to green) at position 

4. C) A beam overloaded so that the blue appears (position 1). D) 

Relaxation of the applied stress so only the first transitional fringe is 

shown (position 2). E and F) Repeat of this procedure so that the 

second-order fringe can be identified with position 1 being overloaded 

and position 2 showing the transition point at the extreme tensile 

fiber........................................................................................................8

Fig. 5 The slope of each linear fit line represents the SOC for each glass type 

tested ......................................................................................................9

List of Tables

Table 1 Material properties of glass....................................................................2

Table 2 SOC determined experimentally from the retardation and stress values 

from 4-point bending. Values are shown when the 1.5-order fringe is 

included and when it is excluded.........................................................10
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Acknowledgments

This research was supported in part by an appointment to the Postgraduate Research 

Participation Program at the US Army Research Laboratory (ARL) administered 

by the Oak Ridge Institute for Science and Education through an interagency 

agreement between the US Department of Energy and ARL.
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INTENTIONALLY LEFT BLANK.
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1. Introduction

Glass is a widely used material in transparent armor systems due to its low cost and 

availability. Some types of glass that are used include soda lime silica (float glass), 

borosilicate glass, fused silica, and glass ceramics.1 These materials demonstrate

properties to meet the ballistic requirements and are used, in practice, because of

their wide availability and their low cost. The major uses of these glasses are 

architectural, automotive, and specialty applications such as semiconductor, photovoltaic, mirrors, and optics. These commercial applications drive the need for these 

materials, and armor designers use the materials to develop transparent armor. 

The recent focus to improve and understand the behavior of glasses has been the 

investigation of glass under high-strain conditions. These investigations are 

difficult to conduct, so there is a need to assess glasses in the quasi-static regime. 

There has been extensive research on ceramic and glass materials to correlate 

materials properties to ballistic performance. Some properties of these materials are 

shown in Table 1. The hardness of the striking ply material relative to the projectile 

hardness has been found to be an important property to rank different striking ply 

materials.2 However, using hardness to rank materials is not adequate when 

comparing similar materials such as glasses. Hardness differences for various glass 

systems are not large enough to observe a change in ballistic performance. Thus, 

there have been ongoing studies to characterize and understand these commercial 

glasses.3–10 One of the critical parameters often overlooked is the surface condition 

of glass. The numerous surface flaws can affect ballistic performance. Wereszczak 

et al.10 scanned the surface of borosilicate and soda lime silica glass and found 

upward of 730 and160 surface flaws, respectively on a 75- × 75-mm square area. 

There have been several investigations11–18 to improve the surface strength of 

glasses using coating and etching techniques. 
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Table 1 Material properties of glass

Material Type Density Young’s 

modulus

Knoop 

hardness

Poisson’s 

ratio

Starphirea Soda lime silica 2.51 73.1 470 0.22

Borofloatb Borosilicate 2.23 64 480 (0.1/20) 0.2

BK-7c Borosilicate 2.53 81 520 0.206

Corning 7740d Borosilicate 2.23 63 418 0.2

Fused quartz Silica 2.2 72 570 0.17

Notes:

a

PPG Industries, Inc. Starphire property data sheet. Pittsburgh (PA): PPG Industries, Inc. 2016 [accessed 

2016 Mar 17] http://www.jnsglass.com/pdf/Starphire.pdf. b

Schott North America, Inc. Schott Borofloat 33 glass data sheet. Louisville (KY): Schott North America, 

Inc. 2016 [accessed 2016 Mar 17]. http://www.us.schott.com/borofloat/English/attribute/mechanical

/index.html. c

Esco Optics, Inc. BK-7 glass property data sheet. Oak Ridge (NJ): Esco Optics, Inc. 2016 [accessed 2016 

Mar 17]. https://www.escooptics.com/material-data/bk7-optical-glass.html. dMatWeb, LLC. Corning Pyrex 7740 borosilicate glass data sheet. Blacksburg (VA): MatWeb, LLC. 2016 

[accessed 2016 Mar 17]. http://www.matweb.com/search/datasheet.aspx?MatGUID=5bb651ca58524e7

9a503011b2cd8083d.

The properties listed in Table 1 are measured under ambient, quasi-static 

conditions. Pressure and temperature influence high-strain-rate events and there is 

limited correlation between high-strain-rate behavior and any of these properties. 

There is a need to determine critical material parameters that can bring insight into 

the behavior of different materials. One property that has not been investigated for 

correlation is the stress optic coefficient as a method to differentiate glasses. Upon 

review of commercial glasses properties, US Army Research Laboratory (ARL)

researchers noted that the stress optic coefficient might correlate to the performance 

of these glasses. It is unknown if this is happenstance or true dependence. It is not 

believed the stress optic coefficient is the actual cause of the change in 

performance. Rather, the stress optic coefficient is an indirect measure of the glass

composition and structure. This report discusses the development of an apparatus 

to measure the stress optic coefficient of different glasses and the results of 

commercially available glasses. 

2. Photoelasticity

Materials that are transparent to visible light can be analyzed through the evaluation 

techniques of photoelasticity. Materials that are transparent and demonstrate 

birefringence only when under stress can be looked at with a series of polarizing 

filters to reveal information about the stress state of the material. A transparent 

material under a certain given loading and viewed through a polariscope, with 

crossed polarizing plates so that there is a net extinguishing of the illuminating 

light, is known as a dark field. In a dark field, configuration regions of constant 

stress will display a band of a single color and known wavelength. When light is 
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passed through a stressed, optically transparent material the theory of 

photoelasticity dictates that the light passing through will show constructive and 

destructive interference within the material itself. This leads to a known wavelength 

sequence, where each wavelength corresponds to a certain degree of relative

retardation of the light. 

3. ASTM Testing

ASTM C770, Measurement of Glass Stress–Optical Coefficient,19 outlines a 

procedure for identifying the stress optical coefficient (SOC) of bars in 4-point 

bending, fibers in tension, and bars in compression. In all instances the optical 

retardation is calculated in response to a number of fixed loads. The measurement 

apparatus used in the evaluation of these techniques is described. A mechanism for 

stressing the glass and a polarimeter are used together to evaluate the retardation,

which is then used to calculate the SOC.

The polarimeter and loading mechanism described in the ASTM standard, shown 

in Fig. 1, is as follows: A light source, preferably a single wavelength source A), is 

followed by an adjustable aperture B), a polarizer C), a loading frame D), a Babinet 

compensator E), an analyzer (polarizer) F), and telescope with an angular scale G). 

The polarizer and analyzer are mounted at 45° from the vertical and at right angles 

from each other creating a full extinction of the transmitted light, or dark field 

image. 

Fig. 1 Beam stressing and polarimeter arrangement

This study is an alternate method of calculating the stress optical condition of stressbirefringent glass material. The beam loading configuration of the ASTM standard 

is used (Fig. 2). 
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Fig. 2 Loading configuration of glass beams adapted from the ASTM standard. The glass 

beams used are to have a width b) of 20–30 mm, thickness d) of 6–10 mm, and a length within 

the range 120–130 mm. The top and bottom surfaces of the specimen are prepared with a fine 

grind. The faces normal to the light transmission direction (L × d) are polished. The 4 faces,

excluding the ends, are flat and parallel to within 0.050 mm. Annealing of the specimens 

should be performed if the neutral fringe is excessively curved. The 4-point bend loading 

fixture uses a support span L) of 115 mm and a moment arm a) of 45 mm (a = (L-Li)/2). The 

loading points are approximately 5 mm in radius.

The polariscope setup is also in accordance with the ASTM standard. The system 

is set up as a plane polariscope, which means that the polarizer and the analyzer are 

at 90° to each other. The system is set up with the broadband light source and 

polarizer positioned behind the load frame with a glass sample in 4-point bend 

configuration. The analyzer is situated after the load frame and closest to the 

observer. Each polarizing plate is set up at 45° from the vertical and so 90° from 

each other. The system will display a dark field view due to the full extinction of 

crossed polarizers. Any stress in the test material will create colored fringes that 

will help to identify the stress state of the material. 

4. SOC Experimental Evaluation

The SOC is a material property, independent of sample geometry, that is used in 

the photoelastic analysis of glass and other transparent materials with stressinduced birefringence. When light passes through a transparent medium, with 

principle stresses in the plane normal to the propagation direction, it is resolved into 
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slow and fast waves along the principle stress directions. These waves show a 

relative angular phase difference or retardation (δ). This property is insensitive to 

wavelength. The SOC (sometimes referred to as C and sometimes K) is a property 

that relates stress to the retardation in a specific material system. The unit for C is 

the Brewster (10-12 m2/N) and is used in the relationship 

Stress = retardation/(thickness * C), or σ (MPa) = δ (nm)/(b (mm) * C (Brewster)). (1)

This relationship can also be expressed in terms of fringe order (N) and wavelength 

(λ 565 nm for glass)20,21:

σ =N* λ /b*C . (2)

In the case of a beam in 4-point bending loading configuration, the value of the 

maximum tensile or compressive stress is given as

σ = [3(L – Li)W]/(2b*d2

). (3)

In this study L is 115 mm; Li is 25 mm, the width in the light-propagating direction;

b is 25 mm; and the thickness d is 10 mm. W represents net loading in newtons and 

the stress σ is in MPa.22

5. New Method for Evaluation

The SOC measurement in the ASTM standard is made by applying a series of fixed 

weights, measuring the retardation, and then calculating the SOC through these 

measurements. An alternative method for this calculation is the use of a variable 

load, such as that provided by a computer-controlled load frame, and an 

identification of the level of retardation. When fixed loads are used, the exact 

amount of retardation must be evaluated. This is accomplished using a polariscope 

and a Babinet compensator. The alternative method proposed does not require the 

use of a Babinet compensator but does need highly controllable loading 

capabilities. This fine control over loading can be accomplished with a load frame.

The evaluation of the first, second, third, and potentially subsequent order 

transitions can be used to determine the extent of retardation. A specific color 

sequence can be observed in photoelastic materials with varying degrees of stress. 

Crossed polarizers set up to create a dark field image will display a zero stress state 

as dark (black). Even in material that has some degree of residual stress, the neutral 

fiber, the transition point from compression to tension, will appear as black. 

Depending on the state of the polarizing equipment, this black color can appear 

gray, but it will be equivalent to the fully extinguished dark field background. This 

central black band is known as the 0-order fringe. The first-order fringe is indigoviolet (transitional purple in some descriptions). The second-order fringe is the 
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transition from red to green, and the third-order fringe is the transition from light 

red to green. These colors can be difficult to ascertain in isolation but can be 

identified by their proximity to other colors on the scale. The color scale shown in 

Fig. 3 is representative of the constructive and destructive interference that is 

created as incoming light is broken into 2 paths, each parallel to the principle 

stresses. The light retardation or relative delay is proportional to the principle stress 

difference.23

Fig. 3 Color scale showing the relationship among retardation, fringe order, and displayed 

color through crossed polarizers (adapted from Micro-Measurements24

)
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In the ASTM test method, fixed weights are used so that the measurable quantity 

in the analysis is the precise degree of retardation. In the method used for this study,

it is possible to shift quantity of interest to the exact loading that produces a known 

amount of retardation. To achieve this, it is necessary to determine the stress in the 

sample corresponding to a known retardation value. With a sample bar loaded into 

a 4-point bend fixture and the polarizer showing the isochromatic fringes, the load 

is incrementally increased until the fringe color of interest is present at the extreme 

tensile fiber. It is sometimes hard to determine this exactly but it is possible to 

observe the transition by surpassing the transition and then decreasing the load until 

the posttransition color is seen at the extreme fiber. For example, to identify the 

indigo-to-violet transition that occurs at a retardation value of 575 nm, the load can 

be increased until blue is distinctly observed and then the load decreased until the 

blue is extinguished (Fig. 4). 
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Fig. 4 A) A glass specimen in a 4-point bend with no load applied, a dark field image. B)

0-order (black) fringe at position 1, the first-order fringe (indigo to violet) at position 2, the 

second-order fringe (red to green) at position 3 and the third-order fringe (red to green) at 

position 4. C) A beam overloaded so that the blue appears (position 1). D) Relaxation of the 

applied stress so only the first transitional fringe is shown (position 2). E and F) Repeat of this 

procedure so that the second-order fringe can be identified with position 1 being overloaded 

and position 2 showing the transition point at the extreme tensile fiber. 
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6. Experimental Results

SOC was calculated for various glass samples and 4 samples were prepared for 

each glass type: fused silica, borosilicate float, Supremax, Starphire, borosilicate, 

and BK-7. Each sample was tested by 4-point bend. The samples were loaded so 

that the retardations of 565, 850, 1,130, and 1,695 nm (1-, 1.5-, 2-, 3-order fringes) 

could be observed by interpreting isochromic fringes. The load at each retardation 

value was taken 5 times and the corresponding maximum tensile stress calculated 

from the loading data averages. Plotting the data with the quantity (Stress*thickness 

in the light propagation direction) with the units of MPa*mm along the X and 

retardation (nm) on the Y is shown below a linear fit was applied. The slope of the 

trend line represents the quantity of SOC for each glass type (Fig. 5). Table 2 

summarizes the experimental results.

Fig. 5 The slope of each linear fit line represents the SOC for each glass type tested
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Table 2 SOC determined experimentally from the retardation and stress values from 4-point 

bending. Values are shown when the 1.5-order fringe is included and when it is excluded.

Glass type SOC

(1-, 1.5-, 2-, and 3-order fringe)

SOC

(1-, 2-, and 3-order fringe)

Fused silica 3.86 3.81

Borofloat 4.18 4.15

Supremax 4 3.92

Starphire 2.63 2.59

Borosilicate 3.96 3.9

BK-7 2.79 2.73

7. Conclusions

SOC can be a tool to help characterize glass samples. The methodology discussed 

in this report is useful if a load frame is available. The human eye can be used to 

identify the transitions that occur at known retardation values. If more precise 

values are needed for the retardation measurement, a Babinet compensator can be 

used as described in the ASTM specification19. Comparing the glass to existing 

sample values can help to confirm an unknown glasses composition. Because the 

SOC is a material property, it can be used as an additional glass characterization 

method. If the SOC of a glass sample is known, the stress state of a glass specimen 

can be evaluated through photoelastic methods both qualitatively and 

quantitatively.
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8. References

1. Sands J, Patel P, Dehmer P, Hsieh A, Boyce M. Transparent materials 

safeguard the Army’s vision. The AMPTIAC Quarterly 2004;8(4):28–36.

2. Hilton CD, McCauley JW, Swab JJ, Shanholz ER, Chen MW. Using hardness 

tests to quantify bulk plasticity and predict transition velocities in SiC 

materials, International. Journal of Applied Ceramic Technology.

Feb 2013;10(1):114–122. 

3. Becker, R. Formulation of a glass model to capture observations from highrate ballistic penetration. Aberdeen Proving Ground (MD): Army Research 

Laboratory (US); 2012 Aug. Report No.: ARL-TR-6086.

4. Grujicic M, Bell WC, Pandurangan B, Cheeseman BA, Patel P, Gazonas GA.

Inclusion of material non-linearity and inelasticity into a continuum-level 

material model for soda-lime glass. J Mater and Des. 2012;35:144–155.

5. Izvekov S, Rice BM. Mechanism of densification in silica glass under pressure 

as revealed by bottom-up pairwise effective interaction model. J Chem Phys. 

2012;136(13):134508.

6. Weingarten NS, Izvekov S, Rice BM. Mechanism of densification in silica

glass under pressure as revealed by a bottom-up pairwise Effective interaction 

model. Presented at: 22nd International Workshop on Computational 

Mechanics of Materials; 2012 Sep 24–26; Baltimore, MD.

7. Strassburger E. Stress wave and damage propagation in transparent laminates 

at elevated temperatures. Aberdeen Proving Ground (MD): Army Research 

Laboratory (US); 2010 Mar. Report No.: ARL-CR-639.

8. Strassburger E, Patel P, McCauley JW, Templeton DW. Wave propagation and 

impact damage in transparent laminates. In: Gálvez F, Sanchez-Gálvez V, 

editors. Proceedings of the 23rd International Symposium on Ballistics; 2007

Apr 16–20; Tarragona, Spain. Madrid (Spain): np; c2007. p. 1381–1388.

9. Strassburger E, Patel P, McCauley JW, Templeton DW, Varshneya A. Highspeed photographic study of wave propagation and impact damage in novel 

glass laminates. In: Bless S, Walker J, editors. Proceedings of the 24th 

International Symposium on Ballistics; 2008 Sep 22–28; New Orleans, LA. 

Lancaster (PA): Destech Publications; c2008. p. 548–555.
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10. Wereszczak AA, Ferber MK, Musselwhite W. Method for identifying and 

mapping flaw size distributions on glass surfaces for predicting mechanical 

response. International Journal of Applied Glass Science. 2014;5(1):16–21.

11. James PF, Chem M, Jones FR. Strengthening of soda lime silica glass by sol 

gel and melt-derived coatings. J of Non-Crystalline Solids. 1993;155:99–109.

12. Wu LYL, Tan GH, Qian M, Li TH. Formulation of transparent hydrophobic 

sol-gel hard coatings. SIMTech Technical Reports. 2005 Jul–Sep;6(2):1–4.

13. Greene CH. Flaw distribution and the variation of glass strength with 

dimensions of the sample. J of American Ceramic Society. 1956;39:66–72.

14. Fabes BD, Doyle WF, Zelinski BJJ, Silverman LA, Uhlmann DR. 

Strengthening of silica glass by gel-derived coatings. J of Non-Crystalline 

Solids. 1985;82:349–355.

15. Greene CH. Surface flaws in glass and the statistics of flaw distribution. Glass 

Technology. 1966;7:54–65.

16. Proctor BA. The effect of hydrofluoric acid etching on the strength of glasses.

Phys Chem Glass. 1962;3(1):7–27.

17. Vlasov AS, Zilberbrand EL, Kozhushko AA, Kozachuk AI, Sinan AB.

Stepanov MI. In: Carleone J, Orphal D, editors. Ballistic behavior of 

strengthened silicate class. Proceedings of the 20th International Symposium 

on Ballistics; 2002 Sep 23–27; Orlando, FL. Lancaster (PA): Destech 

Publications; c2002. Vol 2, p. 982–987.

18. Vlasov AS, Zilberbrand EL, Kozhushko AA, Kozachuk AI, Sinan AB.

Behavior of strengthened glass under high velocity impact. Strength of 

Materials. 2002;34(3):266–268.

19. ASTM C770. Standard test method for measurement of glass stress—optical 

coefficient. West Conshohocken (PA): ASTM International; 2013.

20. Wilson T. Measuring residual stress in glass. Strainoptics, Inc. North Wales 

(PA): Strainoptics, Inc.; nd.

21. Strainoptics, Inc. PS-100 Polarimeter quick-start guide. North Wales (PA): 

Strainoptics, Inc.; nd.

22. Van Zee AF, Noritake HM. Measurement of stress-optical coefficient and rate 

of stress release in commercial soda-lime glasses. Journal of the American 

Ceramic Society. 1958;41(5).
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23. Doyle JF, Phillips JW. Manual on experimental stress analysis. Seattle (WA): 

Society for Experimental Mechanics; 1998.

24. Micro-Measurements. Introduction to stress analysis by the photostress 

method. Wendell (NC): Vishay Precision Group; 2011 Jun 29. Technote TN702-2.
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