Dynamics of Window Glass Fracture in Explosionsprod.sandia.gov/techlib/access-control.cgi/1998/980598.pdfSAND98-0598 Distribution Unlimited Release Category UC–700 Printed May 1998

SANDIA REPORT SAND98-0598 ● UC-700 Unlimited Release Printed May 1998

Dynamics of Window Glass Fracture in Explosions

Edwin K. Beauchamp and Rudolph V. Matalucci

Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Liverrnore, California 94550 for the United States Department of Energy under Contract DE-AC04-94AL85000

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Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation.

NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States government, any agency thereof or any of their contractors.

SAND98-0598 DistributionUnlimited Release Category UC–700Printed May 1998

Dynamics of Window Glass Fracturein Explosions

Edwin K. BeauchampMaterials Joining Department

Rudolph V. MatalucciSecurity Systems and Survivability Department

Sandia National LaboratoriesP.O. Box 5800

Albuquerque, NM 87185-0761

Abstract

An exploratory study was conducted under the Architectural Surety {sm} Program to examine thepossibility of modifying fracture of glass in the shock-wave environment associated with terroristbombings. The intent was to explore strategies to reduce the number and severity of injuries resultingfrom those attacks. The study consisted of a series of three experiments at the Energetic MaterialsResearch and Testing Center (EMRTC) of the New Mexico Institute of Mining and Technology atSocorro, NM, in which annealed and tempered glass sheets were exposed to blast waves at severaldifferent levels of overpressure and specific impulse. A preliminary assessment of the response oftempered glass to the blast environment suggested that inducing early failure would result in loweringfragment velocity as well as reducing the loading from the window to the structure. To test thatpossibility, two different and novel procedures (indentation flaws and spot annealing) were used toreduce the failure strength of the tempered glass while maintaining its ability to fracture into smallcube-shaped fragments. Each experiment involved a comparison of the performance of four sheets ofglass with different treatments. In the test, incident blast pressures were measured adjacent to thefront surface of the window. The fragments were captured in a backstop consisting of layers of rigidpolyurethane foam. A grid with one-foot spacing on the backstop provided an approximate measureof lateral translation of fragments during flight. Penetration depth provided an approximate measureof kinetic energy of the fragments. Fractographic techniques were used in posttest analyses to obtaindetails of the fracture process in the different glasses.

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One of the unexpected results is that the depth of penetration of tempered glass fragments into thefoam was essentially the same as that of the annealed glass. Tempered glass had been regarded asintrinsically less likely to cause injuries than annealed glass because of its small fragment size andblunt shape. The apparent reason for the penetration in these tests is that the tempered glass failed tocompletely disintegrate into small fragments. The glass fractured into small fragments as expected,but those fragments remained coupled into assemblages with lengths of two or more inches andsufficient strength to survive the blast loading and impact on the foam backstop. Penetration occurredwhen those assemblages contacted the foam surface edge on.

Another unexpected result is that while the pretest introduction of indentation cracks as flaws tolower strength in the tempered glass did decrease the failure stress as expected, the decreasedepended on the rate of increase of the pressure pulse as well as on the magnitude. This dependencesuggests that the indentation flaws may have been modified during the four-day delay between theirintroduction and the test. The modification, which effectively decreased the flaw severity, probablyresulted from blunting at the flaw tip as a result of chemical corrosion by water vapor. Theconsequence of the blunting is that flaws might not propagate under very dynamic loading at stresslevels that would cause failure in quasistatic testing where the crack has time to resharpen. Thus itmay not be appropriate to use strength data obtained by quasistatic testing to predict failure in blastloading.

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AcknowledgmentsThe authors would like to recognize the significant contributions to this report made by Director VanRomero and the staff, including Mike Stanley, of the Energetic Materials Research and TestingCenter (EMRTC) of the New Mexico Institute of Mining and Technology. EMRTC provided theexplosive environment testing facility, including the firing system, the explosive material, test control,high-speed photography capabilities, and the styrofoam backstop employed to capture the glassfragments. The authors appreciate the support of the EMRTC staff in performing these experiments.

The authors also wish to thank Sharon O’Connor of Tech Reps, Inc., for editorial support and JohnHurtado, then with the Experimental Structural Dynamics Department at Sandia NationalLaboratories, for supplying a data acquisition system (DAS) for use in these experiments. The glass-testing data acquired by this DAS served as a confirmation of the test environment.

U.S. Department of Energy funding for this work was provided through the Sandia NationalLaboratories Strategic Surety Program managed by Laura Gilliom.

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Intentionally Left Blank

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Contents1.0 INTRODUCTION......................................................................................................................................... 9

1.1 Background ................................................................................................................................................ 91.2 An Alternative Approach.......................................................................................................................... 10

2.0 OBJECTIVES ............................................................................................................................................. 13

2.1 Dynamics of Glass Fracture in Explosive Shock Loading.......................................................................... 132.2 Evaluation of Analytical Procedures ......................................................................................................... 13

3.0 TEST PROCEDURES (GENERAL) .......................................................................................................... 19

4.0 EXPERIMENT NO. 1................................................................................................................................. 21

4.1 Test Plan .................................................................................................................................................. 214.2 Results...................................................................................................................................................... 22

4.2.1 General ............................................................................................................................................. 224.2.2 Local Stress Determination ............................................................................................................... 23

5.0 EXPERIMENT NO. 2................................................................................................................................. 27


5.2.1 General Observations (Posttest)......................................................................................................... 275.2.2 Phenomenology of Fracture Initiation................................................................................................ 275.2.3 Crack Growth (Fragmentation) and Local Stresses ............................................................................ 285.2.4 Fragment Penetration into the Foam Backstop................................................................................... 30

6.0 EXPERIMENT NO. 3................................................................................................................................. 33


6.2.1 Sources for Fracture Initiation at Low Blast Pressure......................................................................... 336.2.2 Capture of Fragments in the Foam Backstop ..................................................................................... 336.2.3 Stress Measurements......................................................................................................................... 34

7.0 VELOCITY MEASUREMENTS ............................................................................................................... 43

8.0 DISCUSSION .............................................................................................................................................. 47

8.1 Penetration of Foam Boards by Tempered Glass ....................................................................................... 478.2 Reduction of Failure Stress in Tempered Glass ......................................................................................... 488.3 Location of Fracture Origins in Shock-Loaded Windows .......................................................................... 498.4 Indent Crack Length................................................................................................................................. 508.5 Future Work ............................................................................................................................................. 51

9.0 REFERENCES............................................................................................................................................ 53

APPENDIX: TECHNIQUES FOR DETERMINATION OF APPLIED AND RESIDUALSTRESS FROM FRACTURE FEATURES .............................................................................. 55

Applied Stress from Mirror Radius.................................................................................................................. 55Tempering Stress from Fragment Size............................................................................................................. 56Shift in Position of Features (in Tempered Glass) ............................................................................................ 56Indentation Crack Length................................................................................................................................ 58References....................................................................................................................................................... 62

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FiguresFigure 1. Reduction of Strength of Tempered and Annealed Glass by Introduction

of Indentation Flaws8....................................................................................................................... 14Figure 2. Dependence of Particle Count (size) on Central Tension in Thermally

Stressed Glass10 ............................................................................................................................... 16Figure 3. Explosive Test Facility at Energetic Materials Research and Testing Center,

Socorro, NM.................................................................................................................................... 19Figure 4. Schematic of Window Test .............................................................................................................. 20Figure 5. Fracture Origin (indentation flaw) in Annealed Glass, Experiment No. 1 ........................................ 24Figure 6. Fracture Origin (indentation flaw) in Tempered Glass, Experiment No. 1........................................ 24Figure 7. Fragment from Annealed Glass Showing Cracks That Had Penetrated Partway

Through Thickness, Experiment No. 2 ............................................................................................ 29Figure 8. Penetration of Glass Fragments into Right Side of Backstop, Experiment No. 2............................... 31Figure 9. Areal Distribution of Fragments Captured in Backstop from the Center Section

of the Annealed Sheet, First Foam Layer ......................................................................................... 37Figure 10. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide

Edge of the Annealed Sheet, First Foam Layer ................................................................................ 37Figure 11. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide

Edge of the Annealed Sheet, Second Foam Layer ............................................................................ 38Figure 12. Areal Distribution of Fragments Captured in Backstop from the Center Section

of the Tempered and Indented Sheet, First Foam Layer ................................................................... 39Figure 13. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide

Edge of the Tempered and Indented Sheet, First Foam Layer........................................................... 39Figure 14. Areal Distribution of Fragments Captured in Backstop from the Center Section

of the Tempered and Indented Sheet, Second Foam Layer ............................................................... 40Figure 15. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide

Edge of the Tempered and Indented Sheet, Second Foam Layer....................................................... 40Figure 16. Areal Distribution of Fragments Captured in Backstop from the Tempered

and Spot-Annealed Sheet, First Foam Layer .................................................................................... 41Figure 17. Areal Distribution of Fragments Captured in Backstop from the Tempered

and Spot-Annealed Sheet, Second Foam Layer ................................................................................ 41Figure 18. Areal Distribution of Fragments Captured in Backstop from the Tempered,

As-Received Sheet, First Foam Layer .............................................................................................. 42Figure 19. Areal Distribution of Fragments Captured in Backstop from the Tempered,

As-Received Sheet, Second Foam Layer .......................................................................................... 42Figure 20. Horizontal Position vs. Time for Glass Fragment Clusters ............................................................... 44Figure 21. Wide-angle Photograph of Glass Fragments Moving from Window at Right.................................... 44Figure A.1 Stress Profiles in Thermally Tempered Glass Sheet with Applied Bending Stress ............................ 59Figure A.2 Fracture Surface in Thermally Tempered Sheet with No Applied Stress........................................... 60Figure A.3 Fracture Surface in Thermally Tempered Sheet with Applied Bending Load ................................... 60Figure A.4 Schematic of Indentation Crack Formation...................................................................................... 61Figure A.5 Indentation Crack in Annealed Glass............................................................................................... 61

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TablesTable 1. Glass Sheet Placement..................................................................................................................... 22Table 2. Sandia Glass Experiments: Shock Conditions.................................................................................. 23Table 3. Stress Values for Experiment No. 1 ................................................................................................. 25Table 4. Experiment No. 3: Stresses Calculated from Fracture Features ....................................................... 36

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9

1.0 Introduction

1.1 BackgroundOne of the concerns raised by terrorist bombingsis the large number of casualties caused by flyingglass. In the Oklahoma City Federal Buildingbombing, many injuries were caused far from thesite of the explosion by shards of glass projectedat high velocity by the blast wave.1 A major issuein current Architectural Surety {sm} Program*efforts to mitigate the effects of terroristactivities and natural disasters is how to reduceinjuries from flying glass.

One proposed approach is to use thermallytempered or otherwise prestressed glass inwindows. The presumed advantage of highlyprestressed (fully tempered) glass over annealedglass in typical glazing applications is that, infracturing, the prestressed glass is very rapidlyconverted into a weakly coupled assembly ofsmall fragments. The planar orientation of theresidual stresses in the tempered glass results infragments that have a roughly cubic shape withright-angle corners on the fragment edges. Thiscubic shape has led to the use of the term“dicing” to describe the fracture process forprestressed glass.

*For further information, see R. V. Matalucci and D. S.Miyoshi, An Introduction to the Architectural Surety{sm} Program, in the proceedings of Assuring thePerformance of Buildings and Infrastructures: AConference on Architectural Surety, held inAlbuquerque, NM, May 14-15, 1997, Sandia NationalLaboratories Security Systems and Technology Center,Albuquerque, New Mexico.

In contrast, the fracture of annealed (stress-free)glass commonly produces substantially largershards with lance shapes. When annealed glassfails under a bending load such as that producedby an impact or a pressure wave, the resultingshards often have very sharp cutting edges thatcan produce severe wounds even at low velocity.In conventional glazing applications such aspatio doors, fatalities have occurred as a resultof injuries caused by those shards. The muchsmaller size of the fragments from temperedglass plus the lesser damage from contact withthe 90-degree edges has led the constructionindustry to recommend the use of tempered glass(or laminated glass) in commercial buildings andhomes. In recommending the use of temperedglass for structures vulnerable to bombing, thereis a tacit assumption that the blast environmentwill also yield the very small fragment sizeproduced in the more usual failures.

However, the advantages of tempered glass inthe more benign structural applications do notnecessarily make it the preferred choice forreducing the injury potential in the event of anearby explosion. A possible disadvantage is thatthe residual stress system that produces dicingfragmentation could also provide high strengthto the glass sheet. High strength assures that thewindow will sustain much higher blast-pressureloading before it fails, creating potentialproblems. In one scenario, the resistance tofailure of the glass could drive the sheet out ofthe frame as a single unit. This large projectilecould cause much more damage than if the glasshad fragmented. Several studies have shown thatat a given velocity, the severity of injuriesincreases rapidly as the mass of the projectileincreases.2,3,4,5 In another scenario, the blastwave would bow the glass inward until it fails,then drive it forward with much higher velocitythan if it had failed at a lower loading.

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Furthermore, in either of these scenarios,retention of the glass sheet in the frame until ahigh blast pressure is reached can put highloading into the glass frame assembly and thesurrounding structure. That higher loadingincreases the possibility of collapse of thebuilding structure.

Another proposed approach to reducingcasualties from flying glass is to contain the glassby laminating it to an elastomer layer, forexample, or by applying a protective film to thesurfaces of a single sheet. Either of thesecontainment methods might be used with asystem that would anchor the glass sheet bymechanically constraining it within the frame.Particularly with a system that anchors the sheetto the structure, increased structural loadingwould be anticipated from blast overpressure.Without anchoring, the blast wave mightseparate the glass sheet from the structure andcarry it forward as a large projectile. In one setof tests, sheets of ½-inch-thick glass, 75.5 by 49inches (150 pounds of glass) coated with a0.007-inch-thick film were propelled as far as 16to 20 feet after ejection from their frames.6

1.2 An Alternative ApproachA better blast response for both the structure andits occupants might result from taking advantageof the small fragment size of fractured temperedglass while promoting its fracture at low appliedstress. Thus the tempered plate would fail duringthe early stages of loading by the blast wave. Acrack velocity of 5000 feet per second duringfragmentation of the tempered sheet means thatthe sheet would lose its strength in less than onemillisecond, and thus the blast-wave loading onthe sheet would no longer be transferred to thestructure.

If the glass plate fails before a substantial bowingof the plate occurs, the blast wave should initiallymove the fragmented sheet forward as a planarassembly. The velocity vector imparted by the

residual compressive stress in the sheet would betransverse to the forward motion of the blast-wave direction. That velocity vector shouldseparate the dicing fragments in the plane of theplate, reducing the areal density of the fragmentsas they move forward. Presumably, the lowerdensity of the fragments impinging on a bodywould mean less damage to the body.

A computer modeling program generated byACTA, Inc. indicates that it may also be possiblethat early separation into dicing fragments resultsin substantially lower energy transferred to theparticles by the blast wave so that their forwardvelocity is reduced.7 Thus it may not benecessary to provide a shield to stop thefragments; at the least, it may be much easier toreduce the velocity of fragments produced byearly failures.

Providing a means for the early onset of dicingduring blast loading should be relatively easy.One approach would be to sensitize a spot on thesheet so that a very low applied load wouldresult in fracture. This could be accomplished by:

• shielding the spot from quenching during thetempering process, so that the magnitude ofthe surface compressive stress is reduced;

• annealing the spot after tempering; or

• introducing a flaw into the surface of thesheet after tempering.

One problem with these approaches is that thesheet would be somewhat more vulnerable toaccidental breakage during handling before andduring its insertion into the structure. However,for ordinary glazing procedures, it should beacceptable to adjust the strength reduction sothat the sheet retains the strength of untempered(annealed) glass during installation and use. Thatstrength should also be sufficient for the sheet tosurvive ordinary wind loads.

An alternative to a sustained loss of strength ofthe window might be to introduce a critical flawinto the sheet at the moment of arrival of the

11

blast wave. This could be accomplished byinstalling an indenter in the window frame, sothat the blast wave drives the tempered glassplate against it, creating a flaw that leads to rapidfracture. A more reliable procedure would be toprovide a spring-loaded device activated bymotion of the window or in some other way bythe blast wave that would drive a sharp projectileinto the glass.

To evaluate these concepts for reducing theinjury potential by promoting early fracture intempered glass, Sandia National Laboratoriesarranged a series of tests to be conducted inconjunction with ongoing explosive tests at theNew Mexico Institute of Mining andTechnology, Socorro, NM. The series ofpreliminary experiments described in this reportwere intended as an introductory exploration ofthose concepts. The experiments also providedthe opportunity to examine the dynamics of glassfracture during explosive loading and to evaluatetechniques of fractographic analysis in posttestexamination of windows exposed to explosiveshock waves. These experiments were conductedat the Energetic Materials Research and TestingCenter (EMRTC).

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13

2.0 Objectives

2.1 Dynamics of Glass Fracture inExplosive Shock Loading

The experiments at EMRTC were intendedprimarily as an exploratory attempt to describethe interaction between a blast wave and glasswindows in a frame. An assessment of thefactors that govern the potential for injury fromfragments of broken glass was of particularinterest. The size and shape of fragments as wellas their velocity are important parameters fordefining the injury potential.3,4,5,6 Consequently,there is great interest in the pattern of fracture inannealed glass as compared with that intempered glass and also in the dynamics ofinteraction of the blast wave with fragments thatdetermine the kinetic energy of the fragments.The primary subject of the experiments is acomparison of the fragmentation of temperedglass and annealed glass and the subsequentinteraction of the fragments with the blast wave.

Two different approaches were used to promoteearly fracture in the glass. The first was theintroduction of strength-reducing defects byindenting the glass at high applied indentationloads. Each of the three tests included samplesthat had been indented prior to testing. Thereduction of strength with indent flaws waspreviously studied and reported in Reference 8.Figure 1 is a plot of the data showing the effectof flaws introduced with a Vickers indenter (atvarious indenter loads) on the strength of soda-lime glass with two different levels of tempering.The figure also includes a plot of failure stressvs. indentation load for annealed glass.

The second approach for reducing the effectivefailure strength of tempered glass while retainingits ability to disintegrate into fine fragments wasto reduce the tempering stress in selected areas.

This was done by heating a spot until part of thecompressive surface stress was reduced.

Among the issues to be addressed in theexperiments was the question of whetherfragments from the test windows could becaptured in a way that would provideinformation on the potential for producing injuryto building occupants. The fragments werecaptured in a backstop consisting of two outerlayers of 1-inch-thick polyurethane foam backedwith three layers of 2-inch foam. Depth ofpenetration through these layers was determinedby velocity and mass of fragments as well as theirorientation when they contacted the backstop.By placing a grid on the backstop, the position ofthe captured fragments could be obtained andused to provide a rough indication of thetrajectories of those fragments. After calibration,in future work in which penetration of fragmentswith known velocity will be measured, velocitydata obtained from the penetration will becompared with that gained from high-speedphotography. Predictions from computermodeling also will be compared to thepenetration-derived velocity data.

2.2 Evaluation of AnalyticalProcedures

The Sandia National Laboratories experiments atEMRTC also provided an opportunity toevaluate fractographic techniques forcharacterizing the response of glass to shockloading. Reference 9 provides an excellentintroduction to the use of fractography inanalyzing fracture.

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= Pre-etched glass

= As-received glass

= Pre-abraded glass

Figure 1. Reduction of Strength of Tempered and Annealed Glass by Introduction ofIndentation Flaws8

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The techniques involve examination of thefracture patterns and features on fracturesurfaces after the event to determine the level ofstress present at a selected point on a glass sheetat the moment of failure.9 By observing thegrowth of indentation flaws, it might also bepossible to determine maximum tensile stress at aspecified point even when failure did not occur.The techniques for these stress determinationsare outlined below and presented in more detailin Appendix A.

One technique for estimating the tensile stress atfailure involves measuring the branchingdistance, i.e., the distance between points wherethe crack branches into multiple paths.9 Thisdistance decreases as the maximum tensile stresspresent in the glass at failure increases. Thistechnique is exemplified for tempered glass inFigure 2.10 That figure shows the dependence ofthe number of fragments per unit area producedin the fracture of tempered glass on themagnitude of the central tension, i.e., themaximum tensile stress produced by the

tempering process. These data can be used todetermine the maximum tensile stress fromfragment size (and plate thickness). Fragmentsize (or particle size) is equivalent to branchingdistance.

The plots in Figure 2 assume no applied stress atfracture. However, additional applied stress,which increases or decreases the maximumtensile stress, will affect the branching distanceand hence the size of fragments. For example, ifsimple bending is applied to a tempered sheetduring failure, the particle shape will changefrom essentially bilaterally symmetrical(equiaxed) to shortened parallel to the appliedstress. It should be possible to estimate themagnitude of the applied stress from thedimensional changes. The results of thebranching process can also be used for analysisof fracture in annealed glass. The distancebetween branches provides a measure of themagnitude of the stress, while the branchingangle provides information on the type ofloading.

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Figure 2. Dependence of Particle Count (size) on Central Tension in ThermallyStressed Glass10

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When the origin of failure can be located, thefracture surface near that location will usuallyshow a “mirror” region where the fracturesurface is very smooth and, adjacent to that, a“mist” region where the fracture surface gives adiffuse reflection. The distance from the centerof the originating flaw to the boundary betweenthe mirror and mist regions, the mirror radius,can provide an estimate of the stress at failure.9

Another technique for analysis of stresses,applicable only to tempered glass, evaluates thechange in the stress distribution produced by theblast loading. The evaluation is possible becausecrack growth in tempered glass producesunusual features on the fracture surfaces. Highcompressive stress on the surface of a temperedsheet results in a tensile stress in the interiorlayer. In tempered glass with no applied stress,the first stage of crack growth involves veryrapid propagation through that tensile layer.Subsequently, the crack extends toward theouter surfaces of the sheet, propagatingperpendicularly to its original direction. Theresult is a clear line of demarcation on thefracture surface where no stress was presentbefore fracture. When a flexural stress is appliedto the sheet during fracture, the lines ofdemarcation shift. That shift can be used to inferthe magnitude of the applied stress.

Another procedure that provides a measure ofthe maximum local stress during shock loadinguses cracks produced by an indenter. In soda-lime silicate glasses like those used in typicalglazing, these cracks are obtained at loads ofabout 100 grams or greater using a Vickersindenter; the cracks extend from the diagonals ofthe indent. When moderate tensile stresses aresubsequently applied to the glass, these crackswill grow in a stable manner; i.e., they will growuntil the intensity of the local stress field at thecrack tip, KI, drops below the critical value, KIc.If subcritical crack growth is possible, growth

continues until KI decreases to the thresholdvalue for that process. The increase in length ofthe cracks provides a useful measure of themagnitude of the stress even if the cracks do notreach the critical size necessary to propagatethrough the glass plate.

In principle, one of the possible applications ofthe procedure in which the growth of indentationcracks is used to determine applied stress wouldbe to obtain a map of maximum tensile stressesproduced on the surface of a glass sheet duringshock loading. That map would be obtained byintroducing indents at various spots on the sheetand shock loading it at a pressure that wasslightly too low to cause failure. Because theVickers indenter produces a pair of orthogonalcracks, values for the orthogonal planar stressescould be obtained.

In the event that an indent crack was the originof failure, the data in Figure 1 could be used toobtain a value for the local stress at that point.The dimensions of the fracture mirror could alsobe used to obtain a value for the failure stress.Moreover, as will be seen in the results of thecurrent experiments, even when one of the indentflaws causes failure, the extension of otherspresent on the sheet can be used to measure thestress at the locations of those flaws at themoment of failure.

The Sandia National Laboratories experiments atEMRTC were also intended to demonstrate theutility of these techniques and advocate their usein other experimental studies of this type. Oneuse for these procedures would be to obtaindetailed maps of stress distributions in glasssheets at the moment of failure to validatecomputer stress analyses. Currently, thelaboratories engaged in the study of glassfracture by explosive shock do not appear to betaking advantage of the insight and knowledgethat could be provided by these procedures.

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19

3.0 Test Procedures (General)The three tests were conducted at EMRTC usingthe structure shown in Figure 3. The walls of thisbuilding are 12-inch-thick reinforced concretebacked with steel plate. The window opening atthe center of the wall is 36 inches wide by 48inches high. A window frame constructed ofangle iron, 1 inch wide by ¼ inch thick,accommodated four panes of glass, 17.5 incheswide and 23.5 inches in width. The open area foreach pane of glass was 16 inches by 22 inches.Glass sheets were held in the frame with softputty. A 1-inch-wide, 1/8-inch- thick layer offoam separated the glass surface from the angleiron. As shown schematically in Figure 4,explosive charges were placed on a line normal

to the plane of the window and passing throughthe center of the window.

Within the building, a backstop, intended tocapture glass fragments, was placed parallel toand behind the window. In Experiment Nos. 1and 2, the backstop was 4 feet to the rear of thewindow. In Experiment No. 3, it was 6 feet tothe rear. The backstop consisted of two sections,each made from 4-foot by 8-foot polyurethanefoam panels backed by a ¾-inch-thick plywoodsheet. Those two sections will be referred to asthe right and left sections as viewed from thefront.

Figure 3. Explosive Test Facility at Energetic Materials Research and TestingCenter, Socorro, NM

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Window

Backstop

Figure 4. Schematic of Window Test (Explosive is placed on line normal tobackstop surface and passing through window center.)

The two sections of the backstop were placedside by side with their common edge parallel tothe vertical center line of the window and on theline from the explosive charge through the centerof the window. A grid with 1 foot spacingbetween elements was drawn on the front foampanels. The grid was intended to permit a roughmeasure of the dispersion of fragments as theyleft the window and were captured in thebackstop. The center of the grid was on the linepassing through the window center and theexplosive charge.

For the first two experiments, shock conditionswere measured with pressure monitors outsidethe building (near the vertical edges of thewindow) and with strain gages mounted on the

interior surface of the wall facing the explosive.In all three experiments, high-speed cameraswere positioned to record the motion of theglass fragments toward the backstop and providea measure of fragment velocity. However, in thefirst two experiments, the cameras failed tofunction and in the third experiment, the lightlevel was too low to obtain useful pictures.Subsequent to the three Sandia experiments, anadditional test of annealed glass of severaldifferent thicknesses was conducted using thesame blast conditions as those in Experiment No.3. Additional lighting in that test resulted inhigh-speed photographs that were used forestimating fragment velocity.

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4.0 Experiment No. 1

4.1 Test PlanBecause the researchers had minimal experiencein conducting this type of test, the selectedapproach was very conservative. Earlierexperiments by others suggested that at about 2psi overpressure, windows would break andsome kinetic energy would be imparted to theglass fragments. For a preliminary experimentwith the primary interest in the fracture processin annealed and tempered glass sheets and howthat might be affected by the presence ofindentation flaws in the glass, shock conditionswere selected that would provide overpressureonly slightly in excess of 2 psi.

For small deformations of a plate (deflection atthe plate center less than 1.5 times thethickness), the maximum tensile stress on a platesimply supported and loaded with uniformpressure, w, is given by the linear equation (fromReference 11, p. 225):

σσ = ββwb2/t2 [1]

where b is the plate width, t is the thickness, andββ is a correction factor that depends on the ratioof the width to length of the plate. For thewindows in these tests, it has a value of 0.425.This equation indicates that, to obtain amaximum tensile stress of at least 8,000 psi in awindow with an opening of 16 inches by 22inches at 2 psi pressure, the thickness must beless than 0.165 inch. The thinnest glass sheetavailable with full tempering was 4 mm (0.157inch) thick. All experiments were conductedwith tempered glass of that thickness and, exceptfor the first experiment, the annealed sheets usedin the experiments were 4 mm thick.

To try to obtain fracture of the 4-mm-thicktempered glass at 2 psi pressure, five indentation

flaws were introduced, 1 inch apart on the platevertical center line, using a 30-kilogram load onthe Vickers indenter. Even with this high load,the data in Figure 1 indicated that it would bequestionable whether fracture could beproduced. For the 4-mm annealed glass, a 3-kilogram load was used on the indenter toproduce a line of five flaws. The data in Figure 1indicate a nominal failure stress of about 4 ksiwith that load. To enhance recovery offragments in the indented zone after theexperiment, a 2-inch by 2-inch piece of duct tapewas applied to those areas after the indents wereintroduced.

To discriminate between fragments from thetempered sheet and the annealed sheet duringrecovery, the sheets were coated with MagicMarkers™ of different colors. On theexpectation that the trajectories of fragmentsfrom the edges of the sheets would besignificantly different from those from the center,a four-inch-wide band at the sheet edge wascolored differently than the center section.

To evaluate the procedure for using theextension of indent cracks to measure localstress during the shock, indents of various sizeswere introduced in ¼-inch- and ½- inch-thicksheets. Except for the 10-kilogram load on the¼-inch sheet, none of the loads on the indenter(1, 3, and 10 kilogram on the ¼-inch sheet and3, 10, and 30 kilogram on the ½- inch sheet)should have caused catastrophic failure at 2 psipressure. To keep these two sheets together inthe event the glass fractured, plastic adhesivetape was applied to the entire sheet surface (onthe indented side) after the sheets were indented.The thin, low-modulus tape would have only avery minor effect on the stresses generated in theglass. Locations of the four sheets of glass

22

within the frame for each of the experiments areshown in Table 1.

Table 2 shows the explosives used in each of thethree experiments and the nominal shockconditions anticipated at the window. Thesenominal conditions were obtained fromhandbook data for the explosives used in theexperiments. As shown, in the first experiment,0.22 pound of C4 explosive was used to obtain ashock with nominal peak overpressure of 2.52psi and specific impulse of 2.09 psi-msec at thefront surface of the window. The peakoverpressure measured by two gages at the frontof the window was 4 psi.12

4.2 Results

4.2.1 General

The 4-mm annealed and tempered sheetsfractured and, except for a few fragments held in

the frame by the putty, all glass from thesesheets was ejected from the window. However,no fragments penetrated the foam in thebackstop. Judging from the position of thefragments between the window and the backstopafter the test, it is doubtful that any fragmentsreached the backstop. In fact, most fragmentsfrom both sheets were found in front of the testbuilding, i.e., between the window and theexplosive. The implication is that the sheetsfractured under the initial positive overpressure,when tensile stress was generated at the surfacecontaining the indentation flaws, but were notseparated from the frame until loaded by therelease wave, i.e., a negative differential pressureat the end of the shock wave. Although the ¼-inch annealed glass sheet also fractured, it andthe unfractured ½-inch sheet remained in theframe.

Table 1. Glass Sheet Placement

Upper Left Lower Left Upper Right Lower Right

ExperimentNo. 1

Annealed 4 mm,indented at center

Annealed ¼ inch,indented at center

Annealed ½ inch,indented at center

Tempered 4 mm,indented at center

ExperimentNo. 2

Tempered 4 mm,flame annealedspot at center

Tempered 4 mm,indented at center

Annealed 4 mm,indented at center

Tempered 4 mm,as received

ExperimentNo. 3

Tempered 4 mm,indented at

corners and center

Tempered 4 mm,laser-annealed

spots at cornersand center

Tempered 4 mm,as received

Annealed 4 mm,indented at

corners and center

23

Table 2. Sandia Glass Experiments: Shock Conditions

Explosive Peak Overpressure(psi)

Specific Impulse(psi-msec)

ExperimentNo. 1

C4,a 0.22 lb

@ 12.0 ft

2.52 2.09

ExperimentNo. 2

ANFO,b 25 lb

@ 20 ft

12.7 20.22

ExperimentNo. 3

ANFO, 13 lb

@ 20 ft

8.22 13.41

aComposition 4bAmmonium nitrate and fuel oil

4.2.2 Local Stress Determination

Both the annealed 4-mm sheet and the tempered4-mm sheet failed from indentation flaws at thesheet center. Figure 5 shows the fracture surfaceat the failure origin in the 4-mm-thick annealedsheet. The arrows indicate the limits of themirror region at the tensile surface. The indentflaw is midway between those arrows. Thefailure stress was calculated using half thedistance between those points as the mirrorradius (approximately 2.2 mm). Procedures fordetermining the local stress from the dimensionsof the mirror are described in Appendix A. Table3 shows the results of the analyses. As shown inthat table, a value of 5.9 ksi was obtained for thefailure stress using the mirror radius equationand a value of 5.6 ksi was obtained for the localstress at failure using a data plot from Reference13. Assuming that the plate deformed linearly tofailure so that Equation 1 represents therelationship between maximum tensilestress andpressure, the pressure at which it failed wasabout 1.3 psi.

Figure 6 shows the fracture surface near thefailure origin of the indented tempered glasssheet. The central tension was determined to be8.3 ksi from the mirror dimensions, specificallyfrom half the distance between the pointsmarked with the arrows in the micrograph.Assuming that the tempering stress distributionwas parabolic, the surface compression was 16.6ksi. The failure stress was determined to be 7.8ksi from the shift in the position of the tensilestress maximum in an adjacent part of thefracture surface as described in Appendix A.Figure 1 includes a plot of failure stress as afunction of indentation load for fully temperedglass (surface compressive stress of 128 MPa{18.3 ksi}). There is considerable scatter in thefailure stress data for indentation loads in therange of the 30 kilogram but no value less than100 MPa (14.3 ksi). The value of 7.8 ksiobtained in Experiment No. 1 for glass withnearly the same compressive surface stress issubstantially lower.

24

Figure 5. Fracture Origin (indentation flaw) in Annealed Glass, Experiment No. 1(Arrows indicate limits of mirror region at tensile surface.)

Figure 6. Fracture Origin (indentation flaw) in Tempered Glass, Experiment No. 1(Arrows indicate mirror/mist boundary.)

25

Table 3. Stress Values for Experiment No. 1

Crack LengthChange(Indent)

MirrorRadius

Equation

MecholskyPlot

Shift inFeaturePosition

Predictiond

Tempered a

Central TensionFailure StressPressure

8.3 ksi7.8 ksi1.74 psi

22.5 ksi (30 kg)5.1 psi

Annealed (4 mm)b

Failure StressPressure

5.87 ksi1.31 psi

5.6 ksi1.25 psi

3.8 ksi (10 kg)0.85 psi

Annealed (¼ in)c

Failure StressMaximum StressPressure

2.44 ± 0.1 ksi1.08 psi

4.7 ksi

2.07 psi

2.99 ksi (10 kg)

1.28 psia3.95 mm thick. Vickers indent with 30-kg load.b3.95 mm thick. Vickers indent with 3-kg load.c0.219 inch thick. Vickers indent with 10-kg load.dBased on data in Figure 1.

For the ¼-inch annealed sheet, one of the 10-kilogram-load indent flaws propagated andcaused extensive fracture. The tape kept thefragments together and the sheet remained in theframe. The failure stress for that flaw wasdetermined (from the mirror radius equation) tobe 4.7 ksi, indicating a pressure of 2.1 psi atfailure. Three of the other indent cracksproduced with the 10-kilogram load also showedsome growth during the test. Stresses calculatedfrom the crack length changes are shown inTable 3. None of the 3-kilogram-load or 1-kilogram-load indent cracks in the ¼-inch-thicksheet showed any growth. As noted in AppendixA, the lack of growth during the blast loading isattributed to the fact that the indentation crackshad the opportunity to grow subcritically priorto that loading. If that subcritical growthexceeded the crack length that could have beenproduced in the blast loading, no additionalgrowth would have occurred. To determine

whether crack growth would occur from theapplied stress (of the blast loading), that stressvalue is inserted into Equation A-8 (AppendixA). If the KI value exceeds the critical stressintensity, KIc, crack growth can occur.

In the ½-inch-thick sheet, which did not fracture,only the 30-kilogram-load indent cracks showedany growth during the test. To determinewhether crack growth should have occurred forthese indents, the pressure determined from the10-kilogram-load indents in the ¼-inch-thicksheet was used to calculate the tensile stressgenerated in the ¼-inch and ½-inch sheetsduring the shock loading. The stress was theninserted into Equation A-8 (Appendix A) and theK value was calculated. For the 1-kilogram-loadindentation flaw in the ¼-inch sheet and for the3-kilogram-load and 10-kilogram-load flaws inthe ½-inch-thick sheet, the K values were lessthan KIc (0.7 MPa.m1/2); thus no additional crackgrowth would have been possible during the

26

shock loading. For the 3-kilogram-load indent inthe ¼-inch sheet, the K value was 0.7; thus a

small increase in crack length should have beenpossible.

27


5.1 Test PlanThe second experiment did not include the ¼-and ½-inch-thick plates of annealed glass thatwere used in the first experiment. Instead, theexperiment was designed to compare thefracture and subsequent transport, by the blastwave, of an as-received tempered plate with twoother tempered plates that were weakened toinitiate failure early in the blast loading. Thebehaviors of those sheets would be comparedwith that of an annealed sheet. All plates were 4mm thick. As noted above, two differentprocedures were used to reduce the failurestrength. In one of the plates, the strength wasdiminished by reducing the compressive stress ina small area in the center of the plate. The low-strength area was produced by annealing with apropane torch. In the other plate, the strengthwas reduced by indenting with a Vickersindenter at a load of 30 kilogram. In theannealed sheet, indentation flaws wereintroduced at the sheet center using a load of 3kilogram. Positioning of the sheets in thewindow is noted in Table 1.

The amount of explosive used in this test wassubstantially greater than that in the first test.Moreover, to provide a higher impulse from theshock wave, the explosive type was changedfrom C-4 to ANFO (ammonium nitrate/fuel oil).With 25 pounds of ANFO at 20 feet from thewindow, the peak incident overpressure waspredicted to be 12.7 psi, while the impulse waspredicted to be 20.22 psi-msec.

5.2 Results

5.2.1 General Observations (Posttest)

The 25 pounds of ANFO proved to be excessivefor the experimental setup. The right section ofthe backstop was found lying on its front face.Apparently the lower support failed, the blastrotated that section around the upper support,and the section then dropped to the floor. Theleft section of the backstop rotated about avertical axis so that it was oriented about 90degrees from its original location but remainedstanding. The displacements of the backstopsections occurred after the glass fragments werecaptured in the backstop.

The two front foam panels (1 inch thick) on theleft side of the backstop were so severelyfragmented that an area approximately 18 incheswide and 3½ feet high was torn from both ofthose panels. As a consequence, all glassfragments that had impacted that area were lost(for the purposes of determining penetrationdepth and trajectory). The right section of thebackstop was not quite as severely damaged;thus it was possible to obtain some data onpenetration.

5.2.2 Phenomenology of Fracture Initiation

A comparison of the first two experimentsyielded a very surprising result. Althoughfracture initiated at indents in the center of boththe annealed and tempered glass sheets in thefirst experiment, that was not the case in thesecond. Instead, in every glass sheet, fractureinitiated at one of the corners, presumably fromflaws on the edge of the sheet. These flawswould likely have been produced in cutting theglass or subsequent handling. In typical windowapplications, these types of flaws are responsiblefor failure.

28

The difference in location of the fractureorigination between Experiment No. 1 andExperiment No. 2 is apparently a result of thehigher pressure and the rapid rise in pressure inExperiment No. 2. At low applied pressure withdeflection less than the plate thickness, stressesin the sheet are described as bending stresses. Inthat event, the resultant tensile stress is amaximum at the center of the sheet. However, ifthe deflection at the center of the plate exceedsthe thickness of the sheet, the plate is treated asa membrane in stress analysis. The nonlinearstress analysis that is then applicable shows thatthe maximum tensile stress is at the corners ofthe plate and results from local bending.11 Thetensile stress near the center of the sheet is lowerthan at the corners and nearly uniform throughthe thickness. Therefore, particularly because theworst defects in a sheet are ordinarily at thesheet edges, failure would typically start at acorner. The surprise in considering the results ofExperiment Nos. 1 and 2 comes from the factthat indent flaws at the sheet centers had resultedin crack origination at the sheet center for the 4-psi overpressure experiment, but those sameindent flaws were ineffective in the 12.7-psioverpressure experiment. Possible explanationsfor this phenomenon will be presented below.

5.2.3 Crack Growth (Fragmentation) andLocal Stresses

The membrane deformation behavior of the glasssheets in Experiment No. 2 was also evident inthe fragmentation of the sheets and in the localstresses in the sheets. For the annealed glasssheet, a different color had been used on a 4-inchband at the edge of the sheet than had been usedin the center, permitting a comparison of thecrack propagation details in the different parts ofthe sheet. Fragments from the peripheral area

ranged from more than 2 inches to less than 0.2inch in length and from about 0.8 inch to lessthan 0.1 inch in width. This small fragment sizeindicates a high tensile stress at fracture. Most ofthe larger fragments from the periphery hadadditional cracks extending approximatelyhalfway through the thickness. These crackswere present as a roughly parallel array runningon the long dimension of the fragment as shownin the example in Figure 7. Separation of thesepartial cracks was in the range of 0.1 inch.

Fracture in the central area of the annealed sheethad a very different character. The areasurrounding the indent flaws at the sheet centerhad been taped prior to the shot so that an areaof more than 6 square inches was recovered.Most of the fragments in this area were muchlarger than those from the edge of the plateMoreover, most of the fracture that producedthis fragmentation was produced by a bendingstress with opposite sign from that at theperiphery; i.e., the surface of the sheet facing theexplosive was in tension, not compression.Apparently, this area did not fragment when theperiphery did. Instead, it remained essentiallycrack-free as it separated from the periphery.The fragmentation probably occurred when thatlarge piece struck the backstop or some otherobject, creating a bending load leading to theunusual stress condition.

As noted above, fracture of the annealed sheetdid not initiate at any of the indents at the centerof the plate. Nevertheless, some crack growthoccurred at three of the five indents; thus ameasure of the maximum tensile stress at thoseflaws during the blast loading could be made.The values for the applied tensile stresscalculated from the crack extensions at thoseflaws were 3.5, 3.2, and 3.3 ksi.

29

Figure 7. Fragment from Annealed Glass Showing Cracks That Had PenetratedPartway Through Thickness, Experiment No. 2

This pattern of fracture of the annealed sheet isconsistent with a fracture mode in blast loadingreferred to as circumferential in Reference 14.That mode results from membrane deformationof the sheet with very large strains at theperiphery and small strains at the center. In thehigh-strain regions, where the maximum tensilestress is high, the sheet disintegrates into smallfragments; in the low-strain region, little or nofragmentation occurs.

For the as-received (no deliberate reduction instrength) tempered sheet, tape had been applied

at the corners as well as at the center prior to thetest in an effort to capture the material in thevicinity of the origin for subsequent examination.Although unsuccessful in capturing the origin inany of the recovered areas, preserving thoseareas did provide the opportunity to compare thefracture behavior of the center with that of thecorners. As with the annealed sheet, it was clearthat the stress from the blast wave was muchlower at the center than at the corners. At thecenter, the shift of the demarcation linesindicated an applied tensile stress of 42 MPa (6.1

30

ksi) in one fragment, 58 MPa (8.5 ksi) in anotherfragment, and effectively zero in a third fragmentfrom the taped area. In contrast, a sample in thelower left corner showed a shift correspondingto 198 MPa (28.7 ksi) applied stress, while theapplied stress in the upper left corner wasmeasured at 221 MPa (32 ksi).

5.2.4 Fragment Penetration into the FoamBackstop

The damage to the backstop during this testforced a change in the strategy for analyzing thepenetration. Only the right side of the backstopsurvived the explosion. Rather than attemptingto map the areal distribution of fragments fromthe four glass sheets captured in that side, a plotwas made of the total mass of glass from eachsheet that penetrated through different layers ofthe foam. In that plot, shown in Figure 8, thesheet identities are Annealed, Temper.nopo (notreatment after tempering; i.e., as received),Temper.inde (indented), and Temper.anne(annealed center spot). On the Position axis,Sheet #1 refers to fragments captured in the first1-inch sheet of foam, Interface 1/2 refers tofragments that penetrated the first foam sheet(Sheet #1) but were not trapped in the second(Sheet #2), and so forth.

The most obvious feature of these data is thatmost of the captured fragments came from theAnnealed and Temper.nopo sheets. Thishappened simply because those two glass sheetswere mounted in the right side of the window.The very small quantity of the glass from theother two glass sheets indicates very little lateral

dispersion as the glass moved from the windowto the backstop.

The other unexpected observation is that thepenetration of the tempered glass fragments isessentially the same as that of the annealed glass.The apparent reason for that penetration is that,like the annealed glass fragments, the temperedglass fragments were large pieces withdimensions up to two inches. These large piecesshowed the extensive fracturing expected fromthe dicing process in tempered glass, but noseparation at the fracture surfaces. The pieceswere actually assemblages of dice fragments.These smaller fragments were coupled stronglyenough that they survived the transit by the blastwave and the impact on the backstop.

Note that the total mass of the annealed and as-received tempered glass sheets that was capturedwas only a small fraction (about 5% of the total)of the mass of the original sheets. Those glasssheets weighed about 2.34 kilogram, and only129 grams of the annealed glass and 100 gramsof the as-received tempered glass were capturedin the backstop. Some additional material wouldhave been captured in the left side of thebackstop, but most of the rest of the fragmentspresumably reached the backstop and bouncedoff without penetrating. Most of that materialwas found on the floor in front of the backstopand most of the tempered sheet material on thefloor was in the form of small fragments, i.e.,single dice fragments or small clusters.

31

Interface 2/3

Sheet #2

Interface 1/2

Sheet #1

Annealed

Temper.inde

Temper.nopo

50

20

30

40

10

Mas

s -

gra

ms

0

Temper.anne

Figure 8. Penetration of Glass Fragments into Right Side of Backstop, ExperimentNo. 2 (As-received tempered and annealed sheets were also on right sideof window. Temper.nopo = tempered, as received; Temper.inde =tempered, indented; Temper.anne = tempered with annealed spots.)

32


33


6.1 Test PlanFor Experiment No. 3, the amount of explosivewas reduced to 13 pounds of ANFO. As notedin Table 1, at a distance of 20 feet from thewindow, that quantity of explosive was expectedto produce a peak overpressure at the windowof 8.22 psi and a specific impulse of 13.41 psi-msec. Pressure was not monitored in thisexperiment. As in Experiment No. 2, the foursheets of glass included one sheet of annealedglass of 4 mm thickness. The other three werefully tempered glass sheets, also 4 mm thick, twoof which were treated before the test (indentedor spot-annealed) to reduce the pressurerequired to initiate failure. In Experiment No. 2,in which the backstop was 4 feet behind thewindow, the captured fragments wereconcentrated near the center of the backstop. Toobtain a somewhat broader dispersion inExperiment No. 3, the backstop was located 6feet from the window. To ensure that thebackstop would fall face up after capturingfragments, the bottom rear of the backstop washeavily braced while the top was held in placewith strips of duct tape.

6.2 Results

6.2.1 Sources for Fracture Initiation at LowBlast Pressure

In Experiment No. 2, the fractures initiated atthe corners of each of the plates. That happeneddespite the introduction in three of the plates offeatures to reduce the local failure stress in thecenter of the plate. Fractures were expected toinitiate at those weak spots; because of thenature of the plate deformation, fractures did notoriginate at the expected locations (theweakened spots in the centers of the plates). In

Experiment No. 3, weak spots were placed atthe four corners as well as the center of theplates to try to ensure that failure would initiateat deliberately introduced weak spots. For thetempered sheet with indentation flaws, threeindents (using a 30-kilogram load) were placednear each corner on a vertical line at 2 inchesfrom the vertical edge of the plate and at thevertical center line of the plate. Similarly for theannealed plate, three indentation flaws (using a3-kilogram load) were placed at each of the fourcorners and at the center.

For the fourth plate, the failure stress wasreduced by annealing a small circular spot at thecenter of the plate and near the corners of theplate (approximately 2 inches from the plateedges). A polariscope ascertained that thetreatment produced stress changes; however, noattempt was made to measure those stresses.Although no obvious change was observable onthe plate surface immediately after the heattreatment, some very shallow cracking wasobserved several hours later. This crackingindicates that the heat treatment did more thanreduce the local compressive tempering stress; itprobably developed tensile stress in a shallowlayer at the surface of the sheet.

To permit recovery of the glass in the vicinity ofthe flaws after the explosion, 2-inch-wide andabout 3-inch-long strips of duct tape were placedover the areas where the flaws had beenintroduced. Strips of tape were also placed in thesame areas on the as-received tempered glass.

6.2.2 Capture of Fragments in the FoamBackstop

As intended, the backstop tipped over during thetest so that both sections were found face up onthe floor. The front surfaces of both sectionsshowed fragments captured in the top layer of

34

foam and holes indicating deeper penetration ofother fragments. As in Experiment No. 2, thesefeatures were concentrated near the center of thebackstop.

As noted earlier, the glass sheets were coatedwith different Magic MarkerTM colors so that itwould be possible to identify fragments from agiven sheet after fragmentation. For the annealedsheet and the tempered sheet with indentationflaws, a 4-inch-wide band at the edge of theplate was coated with a different color than thecenter of the sheet. The lateral spread of glassfragments from each of the plates during theflight to the backstop was monitored byremoving the fragments from each of therectangular sectors in the backstop and weighingthe total mass of particles from a given glasssheet that were found in each sector.

Plots of the distributions of the mass captured ineach of the grid sectors are shown in Figures 9to 19. For the annealed sheet and the temperedsheet with indentation flaws, separate plots areincluded for fragments from the edge and fromthe center. The plots are oriented so that the gridcoordinates (horizontal A to H, vertical 1 to 7)correspond with those of the grid on thebackstop. To provide a reference for the relativeposition of the corresponding plate in thewindow, the projection of that plate on thebackstop is indicated by filling that area with adarker tone. The total mass of fragments from agiven glass sheet captured in a given foam layeris indicated next to the plot. Separate plots showpenetration into the second foam layer. Nofragments penetrated into the third layer. Notethat the scale for the mass data in Figure 9 isslightly different from the scale in the otherplots.

As in the results from Experiment No. 2, thepenetration of fragments from the temperedsheets is not much different from that offragments from the annealed sheet. In fact, themass captured from the tempered glass withindentation flaws was slightly greater than that

of the annealed sheet. As in the prior experiment,the deeply penetrating segments of temperedglass were assemblages of smaller fragments. Inall tempered sheets, these fragments containedarrays of cracks consistent with that expectedfrom the central tension in the tempering stressprofile.

Comparing the plots for the center of the sheetwith those for the edge of the sheet for theannealed sheet (Figures 9 through 11) and thetempered sheet with the indent flaws (Figures 12though 15), fragments from the edge of a sheetspread more than those from the center. Theinference is that the fragments from the edgehave a larger lateral velocity component thanthose from the center. That larger component isprobably associated with the membranedeformation mode for these sheets. In thatmode, the edge of the sheet bows out while thecenter section is relatively flat and parallel to theplane of the window. The bowing at the edgeleads to a load component parallel to the planeof the window, hence an acceleration in thatplane. For the tempered sheet with indent flaws,fragments from both the center and the edgeshow a broader dispersion than for the annealedsheet. That greater dispersion is consistent withseparation of the fragments in the plane of thetempered sheet as a result of the compressivetempering stresses. Note also, in comparing thetotal mass of edge fragments and centerfragments captured in the foam, that the 4-inch-wide region of the sheet had a mass of about1600 gm compared with about 1000 gm for thecenter portion.

6.2.3 Stress Measurements

Table 4 shows the values of local stress at failurecalculated for the various glass sheets inExperiment No. 3. Note that local stress atfailure is calculated from the shift in the positionof the center line of the fracture surface features.That calculation assumes that the applied stressis a bending stress and thus the stress profilethrough the thickness is linear. That is not

35

necessarily the case everywhere in a sheet inthese experiments. If the deflection of the sheetcenter is large enough that the deformation mustbe described in terms of membrane deformationbehavior, the local stress will vary in profile aswell as in magnitude. At the center of the sheet,for example, the stress will be nearly uniformtension through the thickness, while at the edge,

stresses will be primarily flexural. Table 4 alsoshows values of the central tension, i.e., themaximum tensile stress, as determined fromfragment size or from the mirror radius. In thesecases, the mirror radius was taken as half thedistance between the mirror/mist boundaries asmarked by the arrows in Figure 6.

36

Table 4. Experiment No. 3: Stresses Calculated from Fracture Features

CentralTension (ksi)

Center(ctr)(ksi)

Upper Left(ul)(ksi)

UpperRight(ur)(ksi)

Lower Left(ll)

(ksi)

LowerRight

(lr)(ksi)

Tempered,as received

8.7 (FS) 10.3 (CLS) 16.9 (CLS) 23.4 (CLS) 23.1 (CLS)

Tempered,indented

9.6 (FS)(ctr)10.0, 9.6, 11.0(MR)(ctr)

19.6 (CLS)15.7 (CLS)

25.57 (CLS) 13.4 (CLS) 17.7 (CLS) 35.1, 31.3(CLS)

Tempered,annealed

spot

5.0 (MR)(ur)7.0 (FS)4.5 (MR)(ll)6.4 (MR)(ul)

5.1 (CLS) 1.64 (CLS) 3.8 (CLS) 3.35 (CLS) 2.89 (CLS)

Annealed N/A < 2 (FS) 3.9, 4.5(FS)*

6.3 (MR)

Methods for stress determination

1. FS = Fragment size

2. CLS = Center line shift (Applied tensile stress at surface during failure)

3. MR = Mirror radius (at origin)

* At corner of center section (4 inches from edge of sheet)

37

TTotal Mass = 97.1 g

Figure 9. Areal Distribution of Fragments Captured in Backstop from the CenterSection of the Annealed Sheet, First Foam Layer

Total Mass = 87.7 g

Figure 10. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide Edge of the Annealed Sheet, First Foam Layer (Darker zone onbackstop is the projection of the annealed window opening on thebackstop.)

38

Total Mass = 18.8 g

Figure 11. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide Edge of the Annealed Sheet, Second Foam Layer

39

Total Mass = 121.0 g

Figure 12. Areal Distribution of Fragments Captured in Backstop from the CenterSection of the Tempered and Indented Sheet, First Foam Layer

Total Mass = 46.2 g

Figure 13. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide Edge of the Tempered and Indented Sheet, First Foam Layer

40

Total Mass = 57.8 g

Figure 14. Areal Distribution of Fragments Captured in Backstop from the CenterSection of the Tempered and Indented Sheet, Second Foam Layer

Total Mass = 1.5 g

Figure 15. Areal Distribution of Fragments Captured in Backstop from the Four-Inch-Wide Edge of the Tempered and Indented Sheet, Second Foam Layer

41


Figure 16. Areal Distribution of Fragments Captured in Backstop from the Temperedand Spot-Annealed Sheet, First Foam Layer

Total Mass = 18.8 g

Figure 17. Areal Distribution of Fragments Captured in Backstop from the Temperedand Spot-Annealed Sheet, Second Foam Layer

42


Figure 18. Areal Distribution of Fragments Captured in Backstop from theTempered, As-Received Sheet, First Foam Layer

Total Mass = 26.3 g

Figure 19. Areal Distribution of Fragments Captured in Backstop from theTempered, As-Received Sheet, Second Foam Layer

43

7.0 Velocity MeasurementsAlthough the efforts to obtain high-speedphotographic records of the glass fragmenttransport during the three Sandia NationalLaboratories experiments were unsuccessful, asubsequent non-Sandia test with improvedlighting was successfully photographed. In thatexperiment, which used the same explosivematerials and blast conditions as those inExperiment No. 3, only annealed glass was usedin the window. Two sheets each of 1/8-inch-thick and ¼-inch-thick glass were placed so thatsheets of the same thickness were locateddiagonally in the window.

The horizontal translation of the fragments fromthe four sheets was determined from theirposition relative to a grid. Those data are plottedas a function of time in Figure 20. In this plot,zero time corresponds to the instant when theexplosive detonated. That instant was recordedas a bright flash in one frame of the film. Thewindow was 20 feet from the explosive. The factthat no motion of the glass occurred until 0.015second later indicates that the blast-wavevelocity was at least 1300 feet per second.

In Figure 20, the higher velocities were attainedby the 1/8-inch-thick glass, as expected. Thehighest of the velocities was attained by the 1/8-inch-sheet lower in the window. Note that thereis essentially no change in velocity with distance.The terminal velocity was reached very early,perhaps by the time that fragmentation of thesheets had been completed.

The high-speed images also provided someuseful information on the trajectories of thefragments. Figure 21 is a frame from the filmtaken with a second camera, placed abouthalfway between the window and the backstop,that viewed a larger area than the one used for

the velocity measurements. In this view, theglass fragments are moving from the window atthe right toward the backstop at the left. Thedark vertical streak at the lower center of thepicture is a cluster of fragments from the lower1/8-inch-thick sheet. At about 2 feet from thewindow, the fragments were still orientedapproximately as they were when the sheetfractured. The frames used for the velocitymeasurements showed that by the time thefragments had moved 5 feet from the window,most had rotated out of their original plane.However, few of these fragments had rotated sothat their long axes are oriented normal to thebackstop; i.e., they did not have an orientationthat would be expected to produce maximumpenetration of the foam in the backstop.

Although the fragments in this cluster slowlyrotated, there was very little separation in theplane of the cluster. At 5 feet from the window,the vertical dimensions of the cluster were nearlythe same as at 2 feet from the window.

A careful examination of frames early in theflight of the glass fragments showed that thecluster in Figure 21 was from the center of thesheet. The motion of that cluster contrastedsharply with that of fragments from theperiphery (an estimated 2-inch-wide strip) of thesheet. Fragments from that strip separatedrapidly from the central cluster, indicating largevelocity components in the original plane of thesheet. These fragments also had lower horizontalvelocity, so that they quickly lagged behind thecentral cluster and they rotated much morerapidly. Some of those fragments can be seenbelow and behind the cluster in Figure 21.

44

Figure 20. Horizontal Position vs. Time for Glass Fragment Clusters (From high-speed photography frames obtained in a test subsequent to ExperimentNo. 3.)

Figure 21. Wide-angle Photograph of Glass Fragments Moving from Window atRight Toward Backstop at Left (Grid spacing is 1 foot.)

45

This general behavior was also seen in themotion of the other three sheets; however, theupper sheets showed somewhat more separationof fragments from the center of the sheet thanthe lower sheets showed. The fragments fromthe upper sheets are difficult to see in Figure 21because they are a lighter color than the twolower sheets. (The lower ¼-inch-thick sheet is inthe dark zone nearer the window and is difficultto see in this picture.)

The motion of the glass sheet fragments in thistest is consistent with membrane deformation ofthe sheets prior to fracture. As noted above, inthat type of deformation the center of the sheetis nearly planar, while the edge curves,producing a shape similar to a shallowrectangular, flat-bottomed tub. At the moment offracture, the velocity vectors produced by thepressure loading are essentially normal to thesurface at that point. As a consequence, the

fragments at the center of the plate will movehorizontally with no strong tendency to separate.On the other hand, fragments from the peripherywill have velocity components in the plane of thesheet. Moreover, those velocity components willvary with position away from the frame; thusfragments from the periphery will have a strongtendency to rotate.

The observation that the center of the sheets inthis test remained in a cluster of fragments withlittle rotation may explain the fact that only asmall fraction of the mass of any of the sheets inthe earlier experiments was captured in thebackstop. Apparently, most of the fragmentsstruck the backstop flat (i.e., with an orientationthat precluded penetration) and they bouncedoff.

46


47

8.0 Discussion

8.1 Penetration of Foam Boards byTempered Glass

One of the unexpected results from theseexperiments was the deep penetration into thefoam boards by the tempered glass fragments. InFigure 8, which shows the results fromExperiment No. 2, there are some differences indetail, but the overall conclusion is that thetempered glass and the annealed glass showednearly the same degree of penetration. InExperiment No. 3, the total mass of fragmentsfrom the tempered, indented sheet thatpenetrated the foam was slightly greater than themass from the annealed sheet. The masses fromthe as-received tempered sheet and from thetempered sheet with the annealed spots wereslightly less. On the basis of earlier work thatshowed rapid fragment separation duringfracture of prestressed sheets,2-5 a much smalleramount of penetration from fragments of thetempered sheets had been expected. Thatexpectation was based on the assumption thatthe small fragments produced by dicing of thetempered glass would separate from one anotherand impact the foam as individual fragments.Instead, large areas (dimensions of 2 to 3 inchesor more) of the tempered glass impacted thefoam and penetrated it. These areas showed theclosely spaced branching fractures expected fordicing, but separation did not occur at thosefractures.

Although these assemblages of smaller fragmentssurvived the stresses associated with moving outof the window and impacting the foam, theywere not exceptionally strong. In manyinstances, they disintegrated as they were beingremoved from the foam. Their survival duringimpact with the foam may be attributed to thenature of the loading during that impact. Alllarge segments that penetrated the backstop had

impacted the foam surface essentially edge-on;thus the loading in the plane of the segment wascompressive. In contrast, an impact at a smallangle between the plane of the glass fragmentand the backstop could produce some tensilestress. Pieces with that impact mode would beexpected to fragment either during the collisionor after rebounding and hitting the floor.

The failure of the tempered glass to separateconsistently into smaller fragments during thefracture process was unexpected. The stressprofile usually assumed to exist in a temperedglass sheet includes a compressive stress layer inwhich the magnitude of the stress increasesmonotonically toward the sheet surfaces. Thecontinuous redistribution of stresses as the crackgrows through the compressive region shouldcause the crack to penetrate almost to the sheetsurface. The strain energy in a tempered sheet iscalculated by integrating σ2/E through the sheetthickness, assuming a parabolic profile for thestress distribution. In that equation, σ is the localstress and E is Young’s modulus. Thatcalculation showed that the strain energy in thecompressive stress region of a tempered sheet is60% greater than that in the tensile stress region.However, the fracture surface produced by thatenergy is only 2/3 that produced in the tensilestress region. The implication is that substantiallymore energy is available in the compressiveregion than necessary to generate the fracturesurfaces during dicing. Much of that extra strainenergy was expected to be converted into kineticenergy of the individual fragments in a mannerthat would separate them with some velocity.

The conversion of strain energy from thecompressive stress region into kinetic energy ofdicing fragments has been observed in chemicallystrengthened glasses and glass-ceramics.15 Forthe more energetic materials tested (higher

48

residual compressive stresses), particle velocitiesof greater than 40 feet/second were measured.Finite element calculations showed that greaterthan 60% of the original strain energy wasreleased in the dicing process and about half ofthat was converted to kinetic energy of thefragments.

In the tempered glass used in this study, thetempering process apparently did not produce astress profile that was conducive to rapid andcomplete separation of the dicing fragments.One possible explanation for the failure toseparate may be that the stress profile was notmonotonically increasing to the surface, butrather had a maximum within the sheet. Thetwo-stage cooling process used in temperingwindows for general use may cause such aturnover in the stress profile.16 However, thesheets used in these experiments were temperedat a local custom-glass supplier. The variationbetween sheets in dicing size and central tensionindicates that the processing of these sheets wasnot precisely controlled. It is possible that theperformance of these sheets is not typical ofstandard tempered glass manufactured on aproduction line. It is also possible that standardtempered glass does not result in completeseparation of dicing fragments. Further testing isindicated to resolve this question.

It is possible that the presence of the flexuralstresses from the blast loading could affect thepropagation of the fracture to the sheet surfacesas well as the energy imparted to the fragments.However, during tests to determine a suitableheat treatment for spot-annealing the temperedglass, a companion sheet to those used in theseexperiments was fractured. With no appliedstress except that at the annealed spot, the samepattern of fracture was observed: many pieceswith dimensions of 2 to 3 inches that containedfracture patterns with separations of 0.2 to 0.4inch. Blast loading was expected to enhance theseparation rather than limit it. At the surfacewhere the bending load produces the tension, it

would be much easier to propagate the crack tothe surface, even if the tempering stress did notmonotonically increase to the surface. At thesurface where the bending load producescompressive stress, fracture should also beenhanced, once the fracture at the tensile side iscompleted. The extra compressive stress fromthe bending load should also result in moreenergy for separating the particles.

Note that penetration into a foam board may notprovide an accurate measure of the potential forproducing injury to the human body. If theperformance of the tempered glass in theseexperiments is representative of thermallytempered glass, the assumption that temperedglass would produce fewer injuries than annealedglass in a blast environment requires furtherstudy. If the current procedures for temperingglass typically result in fragment clusters,modification may be required so that separationinto small fragments can be assured in a blastenvironment.

8.2 Reduction of Failure Stress inTempered Glass

Both techniques intended to reduce the failurestress for tempered glass proved successful.Indentation flaws were more effective thanpredicted by the data8 shown in Figure 1. InExperiment No. 1, the tempered sheet had acentral tension of 8.3 ksi and a compressivestress at the sheet surface of 16.6 ksi (115 MPa).(If it had not been indented, the failure stresswould have been substantially greater than 16.6ksi.) In the experiment, failure originated withan applied tensile stress of 7.8 ksi (54 MPa) atan indentation flaw produced with a 30-kilogramload at the center of the sheet. In Figure 1, thelarge arrow on the line drawn through the datafor the fully tempered glass (128 MPacompressive stress on the surface) indicates afailure stress of slightly over 150 MPa (21.8 ksi)with an indentation flow introduced with a 30-

49

kilogram (294 N) load. The lowest data point inFigure 1 for that load is about 110 MPa (16 ksi),twice the stress at which the sheet in ExperimentNo. 1 failed. In contrast, the 3- kilogram-loadindentation flaw in the annealed glass inExperiment No. 1 reduced the failure stress toabout 5.6 ksi (39 MPa), only slightly greaterthan the value marked by the arrow on theannealed glass plot in Figure 1.

The data in Table 4 contradict the results inExperiment No. 1. In Table 4, most stress valuesfor the as-received sheet are actually lower thanthose for the indented sheet. The onlyexplanation for the contradiction is that the as-received sheet had an unusually severeprocessing flaw that lowered its strength. Themost likely place for such a flaw would be thesheet edge. The membrane deformation wouldenhance the likelihood of activating such a flaw.Unfortunately, the fracture origin was notpresent in any of the taped areas that wererecovered so that possibility could not besubstantiated.

In Experiment No. 3, three of the corner areas ofthe tempered sheet with annealed spots wererecovered for subsequent examination. In allthree of those areas, fracture had propagatedfrom the annealed spots. As a result,fragmentation of the sheet occurred byessentially simultaneous development of cracknetworks from at least those three sites. Asshown in Table 2, shifts in the center line of thefracture surface features indicated local tensilestresses (i.e., the effective failure stresses) fromthe blast loading ranging from 3.8 ksi down to1.64 ksi in the vicinity of those flaws. Centraltension from tempering, determined fromfragment size, was between 4.5 and 7.0 ksi; thusthe surface compressive stress (except at thespots that had been annealed) was at least 9.0 ksi(63 MPa). The failure stress without the inducedflaws would have been substantially greater than9.0 ksi. This very substantial reduction of failurestress suggests that the annealing treatment may

have gone beyond reducing the magnitude of thecompressive tempering stress at those spots. Itmay have produced some tensile stress. Thepresence of shallow cracks at these annealedspots after the treatment but before the testsupports that possibility.

Reduction of the failure stress in the temperedsheet with annealed spots was accompanied by asignificantly lower penetration of fragments fromthat sheet (Figures 16 and 17) compared to allother sheets. The total mass of fragments fromthis glass sheet captured in the foam was 140grams compared with 225 grams for thetempered sheet with no posttreatment. Thisreduced penetration mass may be a consequenceof the substantial reduction in the failure stressfor this sheet that resulted in a reduction of thevelocity of the fragments.

8.3 Location of Fracture Origins inShock-Loaded Windows

The observation in Experiment No. 2 that failureinitiated at the corners of all four glass sheets,despite three of the sheets having severe flaws inthe center, has important implications forwindow failure in a blast environment. It isunlikely that the shock pressure could increaseto the 12.7 psi maximum value without firstcreating a condition in the glass sheet with stressin the center of the sheet at least as high as inExperiment No. 1. Why then didn’t the indentflaw propagate and cause failure? The answermay be in the behavior of a crack held at lowstress intensity (K) values in conditions wherevery slow subcritical crack growth could occur(at what is referred to as the stress corrosionlimit). Reference 17 showed that under suchaging conditions water vapor acting on the cracktip can effectively blunt it, so that the stressnecessary to restart the crack growth increasessubstantially with aging time. Moreover, theonset of crack growth would be delayed until thecrack tip was resharpened. That delay time

50

decreases as the applied K value increases(beyond the K value at which the aging tookplace). All data reported in Reference 17 wereobtained during testing under quasistaticconditions and do not provide a basis forestimating the response of a blunted crack tovery rapid loading.

The implication of the Reference 17 results forthe tests described here is that during the 3 to 5days between indenting the sheets and runningthe tests, the cracks probably grew until the Kvalue dropped to the stress corrosion limit andthen the crack tips blunted. During Test No. 2,the stress acting on the indent flaws increasedrapidly, then dropped off as the deformation ofthe sheet changed from linear to membranedeformation mode. The prior blunting of theflaws prevented them from propagating underthe short-term, high tensile stress present duringthe linear mode loading. After the transition tomembrane deformation, the higher stress at thecorners resulted in a shorter delay time topropagation than at the center. As aconsequence, the failure started there, eventhough the fabrication flaws at the corners mighthave been less severe than the indent flaws at thecenter.

Blunting at the crack tip and the consequentfailure to respond to applied stress may alsoexplain why some of the indent cracks failed togrow in the test. In the ¼-inch sheet, forexample, four of the five 10-kilogram-loadindent cracks grew, but one did not. For stressesonly slightly greater than that necessary topropagate an indent crack with a sharp crack tip,there is simply not enough time for theresharpening of the crack that must precede itsgrowth.

The importance of these observations inunderstanding the response of windows to shockloading is that data obtained in quasistatic testingof windows may have little relevance to thebehavior of identical windows in the shockenvironment. In quasistatic testing, strain rates

are much lower; thus the delay of a bluntedcrack in responding to the applied stress wouldprobably not even be apparent. The flaws thatlimit glass strength during quasistatic testing maybe from an entirely different population thanthose that initiate failure in blast loading. Usingprocedures that try to account for subcriticalcrack growth would be inappropriate forprojecting failure probabilities under blastloading. Because of crack tip blunting, theeffective strength of blast-loaded windows maybe much greater than any projection based onsubcritical crack growth. The response of glassunder dynamic loading requires more studybefore its behavior can be predicted.

This result (failure initiating in sheet corners)also suggests a strategy for the proposed use ofindentation or annealing flaws to lower strengthof tempered glass in the blast environment. Theflaw should be placed in the corner where it canrespond to the stresses generated duringmembrane deformation by the high differentialpressures produced near explosions. On theother hand, corner flaws are not likely to beactivated by stresses generated in natural eventssuch as tornadoes.

8.4 Indent Crack LengthThe growth of indent cracks in Experiment No.1 showed promise as a method for determiningthe maximum local applied tensile stressproduced during the shock loading of the glasssheets. The values from this approach agreereasonably well with those derived using othertechniques. Better agreement may be possible byobtaining more accurate values of the parametersin the equations used for the calculations. Valuesacquired in other studies for the residual stressparameter, χ, the critical stress intensity factor,KIc, and the KI value after subcritical crackgrowth were used in the calculations for Tables3 and 4.

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In Experiment No 1, the indents introduced withlower loads in both the ¼-inch and ½- inchannealed glass sheets did not show any growth.The reason these sheets showed no growthduring shock loading is that the cracks wereallowed to grow subcritically during the 3 to 5days between their introduction into the glassand the shock loading. For the smaller indentloads, that growth was greater than that possibleduring shock loading. In shock loading, thecrack would have stopped growing when Kdropped below KIc. It would be highly desirableto prevent subcritical crack growth betweenintroduction of indent cracks and application ofthe load. Smaller indent loads could then be usedto obtain useful data and, for larger loads, thelarger length changes during shock loadingwould provide greater precision in thedetermination of local stresses.

Preventing subcritical crack growth in glass forlong periods of time is very difficult. The mostcommon agent that makes subcritical crackgrowth possible is water, usually in vapor form.Even at dew points below -90°C, significantgrowth rates can be obtained from the watervapor in air. For short-term experiments, likethose described in Reference 8, materials such asparaffin oil have been applied to the surface priorto indenting and left until the experiment isconducted. This approach is reasonablyeffective, but even paraffin oil has somepermeability to water. To measure accuratelystress from crack growth during blast loading, animpermeable coating must be developed toprevent subcritical crack growth. This coatingcould be applied to the flaw zone, but it wouldnot interfere with the crack length measurement.

8.5 Future WorkAlthough inferences have been drawn from theobservations made in this series of experiments,it is important to recognize that the processes forfracture and for the subsequent flight of

fragments in the blast wave are stochastic. Thedetails of differences in the dispersion and thepenetration of fragments from annealed andtempered glass may be a result of therandomness of the process rather than of thenature of the stresses and flaws present in thesheets prior to the experiments. Thus thepossibility that the potential for injury by glassfragments from tempered glass may be the sameas that from annealed glass requires furtherinvestigation. Whether the results in theexperiments described here were a consequenceof a particular tempering stress profile thatprevented the crack from propagating to thesurface of the sheets or had some other basisshould be investigated. It would be useful todetermine if a stress profile with compressivestress peaking away from the sheet surface isresponsible for the failure of the temperedfragments to dice and, if so, whether thetempering process can be modified to produce aprofile that assures separation and subsequentlateral motion of the fragments.

The current experiments showed clearly that thefailure stress of tempered glass sheets can besubstantially reduced by either of the procedurestested. The loading of the support structure bythe pressure on the windows can be reduced. InExperiment No. 3, the fragments from thetempered sheet with the annealed spots showedsignificantly reduced penetration of the foamboards compared with fragments from the as-received tempered sheet. That differencesuggests that lowering the failure stress of thetempered glass (1.64 ksi with annealed spotscompared with at least 16.9 ksi in the as-received sheet) can be effective in reducing thekinetic energy of fragments. However, failure oftempered sheets to separate into individualfragments prevented any real test of the thesisthat deliberately induced early fracture oftempered glass can reduce the potential forinjury from fragments.

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53

9.0 References1. S. Mallonee, S. Shariat, G. Stennies, R.

Waxweiler, D. Hogart, and F. Jordan,“Physical Injuries and Fatalities ResultingFrom the Oklahoma City Bombing,” JAMA,Vol. 276, p. 382, August 7, 1996.

2. D. N. Neades and R. R. Rudolph, “AnExamination of Injury Criteria for PotentialApplication to Explosive Safety Studies,” inMinutes of the Explosives Safety Seminar(21st) held at Houston, TX, pp. 1343-1354,August 28-30, 1984.

3. I. G. Bowen, D. R. Richmond, M. B.Wetherbe, and C. S. White, “BiologicalEffects of Blast from Bombs: GlassFragments as Penetrating Missiles and Someof the Biological Implications of GlassFragmented by Atomic Explosions,” AECU-3350, Lovelace Foundation for the AEC,June 1956.

4. R. E. Fletcher, D. R. Richmond, and J. T.Yelverton, “Glass Fragment Hazard fromWindows Broken by Airblast,” Report No.DNA-IACRO-76-634 (DNA Report No.55931), Lovelace Biomedical andEnvironmental Research Institute,Albuquerque, NM, May 30, 1980.

5. S. Glasstone and P. J. Dolan, “The Effects ofNuclear Weapons,” 3rd Ed., United StatesDepartment of Defense and Department ofEnergy, Washington, DC, 1977.

6. N. J. Glover, “Report on GSA ProtectiveGlazing Tests No. 4 & 5, 7 & 9, August1996, Range 19, Fort Polk, LA,” August 15,1996.

7. A. I. Bodner, J. D. Chrostowski, M. R.Legg, K. B. Overbeck, and J. R. Westlake,“Program Description Document for theBLASTC Computer Model,” Tech. Rpt. No.93-282/31-04.2, ACTA Inc., 1993.

8. D. B. Marshall and B. R. Lawn, “StrengthDetermination of Thermally Tempered GlassPlates,” J. Am Ceram. Soc. 61 [1-2], pp. 21-27, 1978.

9. V. D. Frechette, Failure Analysis of BrittleMaterials, Adv. In Ceramics, Vol. 28,Amercian Ceramic Soc., 1991.

10. K. Akeyoshi et al., Rept. Res. Lab., AsahiGlass Company, Ltd., Vol. 17 (No. 1), pp.23-36, 1967.

11. R. J. Roark, Formulas for Stress and Strain,4th Ed., McGraw-Hill, Inc., 1965.

12. J. E. Hurtado, “Sensor Readings from GlassFracture Dynamics Experiments at Socorro:Experiments 1 & 2,” Sandia NationalLaboratories internal report, April 29, 1997.

13. J. J. Mecholsky, S. W. Freiman, and S. M.Morey, “Fracture Surface Analysis of OpticalFibers,” in Fiber Optics, B. Bendow and S.S. Mitra, eds., Plenum Press, NY, 1979.

14. R. J. Harris, M. R. Marshall, and D. J.Moppett, “The Response of Glass Windowsto Explosion Pressures,” I. Chem. E. Symp.Series No. 49, pp. 83-97, 1997.

15. E. K. Beauchamp, “Fracture and StrainEnergy Release in Prestressed Glass andGlass-Ceramics,” Fracture Mechanics ofCeramics, Vol. 3, R. C. Bradt, D. P. H.Hasselman, and F. F. Lange, eds., PlenumPress, NY, p. 823, 1978.

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16. Robert Gardon, personal communication toEdwin K. Beauchamp, May 19, 1997.

17. T. A. Michalske, “The Stress CorrosionLimit: Its Measurement and Implications,” inFracture Mechanics of Ceramics, Vol. 5, R.C. Bradt, D. P. H. Hasselman, and F. F.Lange, eds., Plenum Press, NY, pp. 277-289,1973.

Other Recent Sandia Publications on GlassFracture

S. Nicolaysen and M. J. Readey, “Strength-Limited Weaklink Feasibility Study,” SandiaInternal Report, August 8, 1994.

S. D. Nicolaysen and P. J. Skogmo, “A Reviewof Shock Weaklink Technology forImproving Nuclear Weapon Safety,”SAND94-2109, UC-744, September 1994.

E. K. Beauchamp, “Mechanisms for HackleFormation and Crack Branching,” Ceram.Trans. 64, pp. 409-445, 1996.

E. K. Beauchamp, “Crack Front Stability andHackle Formation in High-Velocity GlassFracture,” J. Am. Ceram. Soc. 78 [3], pp.689-697, 1995.

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Appendix: Techniques for Determinationof Applied and Residual Stress FromFracture Features

Applied Stress from Mirror RadiusDuring the passage of a crack front through abrittle material like glass, a variety of featuresare formed on the fracture surface that provide arecord of the progress of the crack. From thesefeatures it is possible to determine the localstress at the moment of failure, the distributionof stresses along the crack path, the location andnature of the origin, and the velocity ofpropagation of the crack, as well as some of thedetails of environmental effects. Reference A-1is a good introductory text describingfractographic analysis, the general methodologyfor examining and interpreting these features.For prestressed glass, such as the thermallytempered glass used in the current work, with awell-defined residual stress distribution presentprior to fracture, some additional features aregenerated that can aid in understanding thefailure. The interpretation of those features isdescribed below.

One commonly used procedure in fractographicanalysis is the determination of failure stress (thetensile stress present at the point of origin of thefracture) from the mirror radius. This procedurewas used for analysis in this report. In fracture ofhomogeneous, isotropic brittle materials likeglass, the fracture surface in the immediatevicinity of the origin of the crack is very smooth(hence the term mirror). If the crack acceleratesas it propagates away from the origin, thesurface develops visible features that arecharacterized as mist. The features grow in sizeas the crack progresses farther, resulting in azone characterized as the hackle region.

Ultimately, the crack branches. A description ofthe processes at the crack tip during generationof these features is given in Reference A-2.

When a crack grows in a uniform tensile stressfield, so that propagation is the same in alldirections from the origin, the mirror region, themist region, and the hackle region haveboundaries that are circular arcs. The distancefrom the origin to the mirror/mist boundary iscalled the mirror radius, Rm. Similarly, thedistance to the mist/hackle boundary ischaracterized by Rh and the distance to thebranching point is Rb.

The mirror, mist, and hackle features(collectively known as velocity hackle features)are important in the analysis of fracture becausethere is an inverse relationship between thetensile stress at failure, σf, and a given boundaryradius, Rj:

σσf = Aj / Rj1/2 [A-1]

where Aj are constants for a given material. Thuswith a knowledge of Aj, measurement of themirror radius or one of the other radii canprovide an estimate of the failure stress.Reference A-3 shows that this equationdescribed data for cracks with mirror sizesranging from 0.5 µm to more than 5 mm.

For some analyses of failure stress in this report,the plot in Figure 1 of Reference A-3 that showsfailure stress as a function of mirror radius wasused. Although those data were obtained onfused silica glass, the fracture behavior of the

56

soda-lime silica glasses used in the currentexperiments is similar. No significant errorresults from the use of that plot.

Tempering Stress from FragmentSizeIn tempered glass with a residual tensile stresspresent in the interior of the glass sheet, thebranching distance (i.e., the size of the fragmentsproduced in fracture of the sheet) depends onthe magnitude of the residual tensile stress. Inparticular, it depends on the maximum tensilestress at the central plane of the sheet (thecentral tension). It also depends on the thicknessof the sheet. That dependence is shown in Figure2 of this report. (For the determination of centraltension in this report, values for 4-mm glasswere obtained by interpolating between the 3.4-mm and 4.9-mm curves.)

More accurately, the fragment size is determinedby the maximum tensile stress in the sheet sothat an applied stress can influence the size. Inthe event that the applied stress increases themaximum tensile stress above the value of thecentral tension, the branching distance will beshortened. Similarly, if the applied stress reducesthe maximum tensile stress, the branchingdistance will be lengthened. Those lengthchanges can be used to obtain a quantitativeestimate of the magnitude of the applied stress.They also can be used to qualitatively evaluatethe nature of the stress. As an example, if thebranching distance is shortened in one directionbut is not affected in the orthogonal direction,the applied stress can be assumed to be uniaxialtension.

Shift in Position of Features (inTempered Glass)Fracture of tempered glass occurs in two stages.In the first stage, fracture is limited to the centralzone of the sheet where residual tension ispresent. Because of the high tensile stress, that

fracture is very rapid. The entire fracture patternin the tensile zone of a one-meter-square sheet iscompleted in less than a millisecond. In that briefinterval, the stress in the tensile zone adjacent tothe fracture surfaces is reduced; however,because the inertial mass of the plate severelylimits the separation of the fragments, there islittle change in the stresses in the compressivezone. Subsequently, in the second stage offracture, the fragments begin to separate as thecompressive stress in the outer layer pushes thefragments apart. The fracture velocity for thisstage is much slower.

The transition from the fast-fracture stage to theslow-fracture stage often results in well-definedlines of demarcation on the fracture surfacebetween the tensile stress zone and thecompressive stress zones. These lines ofdemarcation result from the propagationdifferences in the two stages of fracture. In thefirst stage, the fracture direction is parallel to theplate surface with the highest velocity at thecentral plane of the plate and the lowest at thezero stress plane. In the second stage of fracture,the fracture propagates toward the surfaces ofthe plates, i.e., perpendicular to the direction ofthe first stage crack growth. A common result ofthis change in direction is the formation of twisthackle linear features oriented perpendicular tothe plate surface.

Usually tempering stresses are symmetrical withrespect to the midplane of the sheet; thus thelines of demarcation between the two stages offracture will be equidistant from the central planeof the sheet. However, if a bending stress isapplied to the sheet when the glass is fractured,the lines of demarcation will be shifted towardthe surface of the sheet that is put into tension bythe applied load. That shift is shownschematically in Figure A-1.

In the thermal tempering process, the temperingstress profile is usually nearly parabolic. In thatevent, the central tension is about one-half themagnitude of the compressive stress at the

57

surface of the sheet. The stress distribution canthen be described by the function:

σσ(x) = ax2 + b [A-2]

where x is the distance from the central plane ofthe sheet. Because the stress at x = 0 is thecentral tension, b is equal to the central tension.Consequently, with the surface compressionequal to -2 times the central tension, CT,Equation A-2 becomes:

-2 CT = a (t/2)2 + CT [A-3]

where t is the sheet thickness, so that:

a = -3 CT / (t/2)2 [A-4]

Most failures of windows are caused by bendingloads for which the applied stress can berepresented by:

σσ(applied) = mx [A-5]

When that stress is added to the temperingstress, Equation A-2 becomes:

σσ(x) = ax2 + mx + b [A-6]

In Figure A-1, the application of a bending stressmoves the point of maximum tensile stresstoward the surface where the applied stress istensile. The points on the resultant curve withzero stress are also moved toward that surface.Assuming that a value for the central tension ofthe unloaded plate has been determined (fromthe fragment size or some other technique), thedistance from the central plane to one of thesenew lines of demarcation on the fracture surfacecan be measured. That x value can be insertedinto Equation A-6 to obtain a value for m,noting that at that x value, σ(x) = 0. Themagnitude of the applied stress at the sheetsurface is then obtained by inserting t/2 intoEquation A-5.

An alternative to using the shift of the lines ofdemarcation to determine the applied stress is touse the shift in position of the maximum tensilestress. In a symmetric stress field, even if thetempering stress is not parabolic, the minimum isat x=0 in the unstressed sheet. An appliedbending load moves the minimum toward thetensile stress side associated with the bendingload. For parabolic stress, the first derivative ofEquation A-5 is:

dσσ/dx = 2ax + m [A-7]

For dσ/dx = 0, x = -m/2a is the distance of thenew minimum from the central plane. (SeeFigure A-1.) Thus if the value of the centraltension is known, the value of the applied stressfrom the shift in the position of the minimum canbe calculated, the value for m can be obtained,and Equation A-5 can be used to calculate thevalue for the applied stress. For the stressdeterminations in this report, the position of theminimum was taken to be midway between thelines of demarcation. The central tension wasdetermined from the fragment size using theplots in Figure 2.

Figure A-2 is an example of a fracture surfaceshowing the lines of demarcation in a temperedsheet that fractured with no applied stress.Figure A-3 shows a similar surface in which thelines of demarcation have been shifted by anapplied bending stress. The lines of demarcationare marked with the short, blunt arrows. Thelarger arrows show the position of the sheetsurface.

For the tempered glass used in the current tests,the lines of demarcation were not in thepredicted location (i.e., where they should havebeen if the stress profile were truly parabolic andthe first stage of fracture terminated at the pointwhere the stress was zero). One possibleexplanation is that the tempering process usedfor these plates did not generate a parabolicdistribution. In that case, Equations A-2 through

58

A-6 above could not be used to determine thestress. The other possibility is that the stressprofile was parabolic, but the crack did not stopwhere the stress was zero. In that event, theapplied stress could not be directly determinedfrom the shift of the lines of demarcation.However, it would still be valid to use the shiftof the stress minimum to calculate the appliedstress. The tables in this report are based on thesecond explanation. The midpoint between thepositions of the lines of demarcation areconsidered to be the position of the stressminimum.

Indentation Crack LengthThis procedure for determining the applied stressinvolves the growth of cracks emanating fromthe corners of indentations produced at the glasssurface by Knoop or Vickers indenters, as shownschematically in Figure A-4. The cracks appearin glass at an indenter load in excess of about100 grams. If no other stress field is present, thedriving force for the generation of the cracks atthe indent is a consequence of compaction of thematerial under the indenter during loading. Whensufficient force is applied to the indenter, apermanent depression remains when the indenteris removed from the surface. When the indenteris unloaded, the material immediately beneaththat depression is constrained from recoveringits original volume by the surrounding material.As a consequence, that zone develops residualcompressive stress while the surroundingmaterial is placed in tension. Because of thegeometry of the indenter, the tensile stress hasits maximum value perpendicular to the planespassing through the diagonals of the indent; thuscracks generated by that stress arepredominantly oriented along those diagonals.Figure A-5 shows a glass surface with an indentand cracks running from the indent diagonals.

The stress produced by the indent decreases withdistance from the indent. As a consequence, acrack propagated by that stress initially growsrapidly, then slows, and finally stops growing.

Growth stops when the stress intensity, KI, dropsto the critical stress intensity, KIc. In the eventthat subcritical crack growth is possible, thecrack will continue to grow. The rate of growth(the crack velocity) decreases as the crackgrows; crack growth finally stops when KI dropsto the threshold value for subcritical crackgrowth.

The effect of an applied stress is to change thelength of the crack emanating from the indent. Ifthe stress is present when the surface is indented,tensile stress raises the KI value, increasing thecrack length; conversely, a compressive stressshortens the cracks. The equation for calculatingthose stresses is derived from fracture mechanicsand based on the assumption that the crackgrows until the stress intensity at the crack tipdrops to KIc. The net stress intensity, whichincludes contributions from the residual stress atthe indent and the stresses, σa, present fromother sources, is expressed by:

K1 = χχr P / c3/2 + σσa ΦΦ c1/2 [A-8]

where χr, the residual stress parameter, isassociated with the compaction of material underthe indent. Φ is a parameter that accounts for thegeometry of the crack, and c is the crack lengthmeasured from the center of the indent.A-4

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Figure A.1 Stress Profiles in Thermally Tempered Glass Sheet with AppliedBending Stress (Note the shifts of the zero stress points and the stressminimum toward the surface where bending stress is tensile.)

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Figure A.2 Fracture Surface in Thermally Tempered Sheet with No Applied Stress(Small, blunt arrows indicate line of demarcation between tensile andcompressive region. Note band of mist and hackle at center of sheet.)

Figure A.3 Fracture Surface in Thermally Tempered Sheet with Applied BendingLoad (Note shift of lines of demarcation and mist band toward upper(tensile) surface.)

61

Figure A.4 Schematic of Indentation Crack Formation: a) Cross Section ThroughIndent Zone Showing Radial Crack Limits (dashed line), b) Intersectionof Radial Cracks with Surface of Sheet, c) Dependence of Crack Size onLocal Stresses

Figure A.5 Indentation Crack in Annealed Glass (3-kg load on indenter)

62

Rearrangement of Equation A-8 yields anexpression for the applied stress of:

σσa = (K1c - χχr P / c3/2 ) / ΦΦ c1/2 [A-9]

where it is assumed that crack growth stoppedwhen KI was no longer greater than KIc. Theparameter χr is a constant for a given materialusing the Vickers indenter. For most materials, areasonable value for χr is represented by:

χχr = 0.015 (E/H)1/2 [A-10]

where E is Young’s modulus and H is theVickers hardness. A value of 0.034 for χr,calculated in an earlier experimental study ofindentation fracture in soda-lime glass, was usedin the calculations in this report.

If subcritical crack growth had been possible,calculation of σa directly from Equation A-9would not be appropriate. Instead, it would benecessary to replace KIc with the value of KI

present at the crack tip at the moment that thecrack length was measured.

In the indent measurements in this report, theindents were introduced in the annealed glasssheets while no stress was applied.Subsequently, the sheets were shock-loaded tocreate a local tensile stress for a short time. Inthis situation, a stress is applied after the indentis introduced into the surface; thus it is possibleto obtain a value for the applied stress using theincrease in length of the crack even if a value forχr is not available. For the indent without appliedstress:

K1(initial) = χχr P / ci3/2 [A-11]

so that:

χχr P = K1(initial) ci3/2 [A-12]

where ci is the initial crack length. Substitutingthis into Equation A-9 yields:

σa = (K1c - K1(initial) ci3/2 / cf

3/2 ) / ΦΦ cf1/2 [A-13]

where cf is the final crack length.

The identity of the initial KI value is retainedbecause it is not necessarily the same as thatexisting at the crack tip when the stress, σa, isapplied. In a controlled experiment, subcriticalcrack growth is prevented (by coating thesurface with paraffin oil and measuring the cracklengths immediately, for example), and it can beassumed that the initial and final KI values bothequal KIc. For the experiments described here,the delay between introducing the indent cracksand shock-loading the glass was three or moredays. It was impractical to prevent subcriticalcrack growth during that time; rather it wasassumed that crack growth had occurred. Usingdata for subcritical crack growth from ReferenceA-5, the KI value at the end of three days ofcrack growth would have been about 0.41MPa•m1/2. That value for K(initial) is used inEquation A-13.

On the other hand, in the explosive testsdescribed in this report, the stress was appliedfor too short a time to permit subcritical crackgrowth: thus it could be assumed that the final KI

value as a result of that loading was equal to KIc.However, if the applied stress had beenmaintained long enough that subcritical crackgrowth occurred, KIc in Equation A-13 would bereplaced by KI (final), i.e., the KI value at the endof that subcritical crack growth.

ReferencesA-1. V. D. Frechette, Failure Analysis of Brittle

Materials, Adv. In Ceramics, Vol. 28,American Ceramic Soc., 1991.

A-2. E. K. Beauchamp, “Mechanisms forHackle Formation and Crack Branching,”Ceram. Trans. 64, pp. 409-445, 1996.

A-3. J. J. Mecholsky, S. W. Freiman, R. W.Rice, “Fracture Surface Analysis ofCeramics,” J. Mater. Sci., 11, pp. 1320-1329, 1976.

63

A-4. R. F. Cook and G. M. Pharr, “DirectObservation and Analysis of IndentationCracking in Glasses and Ceramics,” J. Am.Ceram. Soc. 73 [4], pp. 787-817, 1990.

A-5. S. Wiederhorn, J. Amer. Ceram. Soc. 50,p. 407, 1967.

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