NEGATIVE PHASE BLAST EFFECTS ONGLASS PANELS

T. KrauthammerThe Pennsylvania State University, USA

andA. Altenberg

Texas A&M University, USA

8th International Symposium on Interaction of the Effects of Munitions with StructuresMcLean, Virginia, 22-25 April 1997

OUTLINE

PROBLEM DESCRIPTION

OBJECTIVE AND SCOPE

BLAST LOADING

DYNAMIC STRUCTURAL ANALYSIS

GLASS FAILURE PREDICTION MODEL

RESEARCH APPROACH

RESULTS AND DISCUSSION

SUMMARY

PROBLEM DESCRIPTION

• WINDOW GLASS BEHAVIOR UNDER BLAST LOADS.

• PREVIOUSLY, STRUCTURAL ANALYSIS MODELS TYPICALLY CONSIDERED ONLY THE POSITIVE PHASE OFTHE BLAST LOAD.

• BOTH THE POSITIVE AND NEGATIVE PHASES OF THE BLAST PULSE ARE CONSIDERED.

OBJECTIVE

EXPLORING HOW GLAZING SYSTEMS COULD BE EITHER PUSHED IN OR PULLED OUT BY THE INCOMING FULL BLASTWAVE.

SCOPE

• A SIMPLE COMPUTATIONAL MODEL HAS BEEN DEVELOPED.

• THE NUMERICAL APPROACH WAS USED TO STUDY THE CONDITIONS UNDER WHICH WINDOW GLASS CANBE EITHER PULLED OUT OF, OR PUSHED INTO THE STRUCTURE.

BLAST LOADING

SCALING LAW

THE MOST COMMON FORM OF BLAST SCALING ISTHE HOPKINSON-CRANTZ OR "CUBE ROOT" SCALING:

E: ENERGY

BLAST PARAMETERS

DRAKE ET AL., PROTECTIVE CONSTRUCTION DESIGNMANUAL, SECTION IV, FINAL REPORT ESL-TR-87-57,AIR FORCE ENGINEERING & SERVICES CENTER,TYNDALL AFB, FLORIDA, NOVEMBER 1989.

BLAST REFLECTION

P C Pr r so= α

0 10 20 30 40 50 60 70 80 90 100

SCALED DISTANCE, z

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

PEAK REFLECTED PRESSURE (psi)

PEAK POSITIVE AND NEGATIVE LOADS

P+

P-

10 20 30 40 50 60 70 80 90 100

SCALED DISTANCE, z

0

5

10

15

20

25

30

PEAK REFLECTED PRESSURE (psi)

PEAK POSITIVE AND NEGATIVE LOADS

P+

P-

HYPOTHESIS

• AN ENHANCED REBOUND RESPONSE MIGHT BEOBSERVED IF THE NEGATIVE PHASE IS APPLIEDDURING THE REBOUND PHASE OF THE GLASSPANEL.

• THE ENHANCED REBOUND IS EXPECTED TO BEMORE SIGNIFICANT FOR LARGER SCALEDRANGES.

• SUCH OBSERVATION CANNOT BE MADE IF THELOAD PULSE HAS ONLY A POSITIVE PHASE.

DYNAMIC STRUCTURAL ANALYSIS

THE DYNAMIC STRUCTURAL ANALYSIS WASPERFORMED USING AN EQUIVALENT SINGLE DEGREEOF FREEDOM (SDOF) SYSTEM.

KM, KR, KL: MASS, RESISTANCE AND LOAD FACTORS

RESISTANCE FACTOR

KM M ˙ ̇ x + KR K x = KL F(t)

THE RESISTANCE FACTOR KR IS EQUAL TO THE LOADFACTOR KL:THE PLATE’S STIFFNESS:

= 252 FOR a/b = 1.0 = 198 FOR a/b = 0.625

a: PLATE’S WIDTH

DAMPING

DAMPING WAS IGNORED BECAUSE:

• VALUES ARE LOW AND NOT WELL KNOWN.

• ONLY ONE CYCLE OF RESPONSE; SMALL EFFECT.

• REASONABLE IN A PRELIMINARY APPROACH.

GLASS FAILURE PREDICTION MODEL(Beason and Morgan, 1984)

AN EQUIVALENT, CONSTANT STRESS OF DURATION td

WITH THE SAME EFFECT ON A SURFACE FLAW AS ANARBITRARY STRESS:

PROBABILITY OF FAILURE

B IS A FAILURE RISK FUNCTION, IT INCLUDESCONSIDERATIONS OF:

• THE MAGNITUDE AND DURATION OF SURFACETENSILE STRESSES.

• PLATE SURFACE AREA OF EXPOSED TO TENSILESTRESS.

• GEOMETRIES AND ORIENTATIONS OF SURFACEFLAWS.

P efB= − −1

APPROACH

• TWO WINDOW GLASS SIZES WERE CONSIDERED:

1,397 ( 1,448 ( 9.63 MM a/b ë11,524 ( 2,438 ( 6.4 MM a/b ë 0.625

• EXPLOSIVE SOURCE: 10 kg AND 100 kg TNT.

• SCALED DISTANCE: VARIED FROM 0 TO 100FT./(LB.)1/3

• A LINEAR STRUCTURAL MODEL WAS CHOSEN.

APPROXIMATE BLAST LOADING

Time

Pressureps

+

T+ T -

p s-

NUMERICAL SOLUTION

• MATHEMATICA WAS USED FOR THE NUMERICALSOLUTION OF THE DIFFERENTIAL EQUATION.

• THE STRESSES IN THE PLATE WERE COMPUTEDAS SHOWN BY TIMOSHENKO AND WOINOWSKI-KRIEGER (1959), AND THE FAILURE CRITERIONWAS USED.

RESULTS AND DISCUSSION

THE RESULTS FROM THE PRESENT STUDY AREPRESENTED, AND COMPARED WITH RESULTSOBTAINED FROM OTHER APPROACHES.

COMPUTATIONAL APPROACHES

PARAMETER BLASTOP WES MODEL PRESENTMODEL

GEOMETRICCONSIDERATIONS

GEOMETRICNONLINEARITIES

GEOMETRICNONLINEARITIES

LINEAR ANALYSIS

SUPPORTCONDITIONS

SIMPLY SUPPORTEDSOME SLIDING ATLARGEDEFLECTIONS

CLAMPED SIMPLY SUPPORTED

DAMPING 2% 3% NO DAMPINGPLATE DIMENSIONS 55.1" X 57.1" X 0.379" 40" X 40" X 0.375" 55.1" X 57.1" X 0.379"

60" X 96" X 0.25"MATERIAL ARCHITECTURAL

LAMINATED GLASSMONOLITHICPOLYCARBONATE

ARCHITECTURAL LAMINATED GLASS

BLAST PULSE NO NEGATIVEPHASE

NO NEGATIVE PHASE FULL BLAST WAVE

FAILURE CRITERION ALLOWABLESTRESS; NORMALDISTRIBUTION OFGLASS PROPERTIES

NONE BEASON AND MORGAN

DATA COMPARISON 1z [ lb/ft^(1/3) ] PEAK DEFLECTION [IN.]

IN THE BLAST DIRECTION 100 KG. TNT, ASPECT RATIO ONEWES Model Present Model

20 4 3.8030 2.6 2.8740 2.2 2.2550 1.72 1.9260 1.37 1.6270 1.19 1.3180 1.14 1.1090 1 0.99100 0.9 0.88

GOOD AGREEMENT FOR POSITIVE PHASE RESPONSE

DATA COMPARISON 2

100 KG. TNT, AND ASPECT RATIO ONEz [ft/lb1/3] BLASTOP PRESENT MODEL

Max.deflectio

n [ in. ]

Prob.failureinward

Prob.failure

outward

Max.deflection [ in. ]

Prob.failureinward

Prob.failure

outward20 2.88 1.000 NONE 3.80 1.00 NA

30 2.20 1.000 2.87 1.00 NA40 1.94 1.000 2.25 0.99 NA50 1.54 0.974 1.92 0.97 NA60 1.21 0.514 1.62 0.71 0.7170 1.00 0.175 1.31 0.48 0.4880 0.94 0.117 1.10 0.32 0.2990 0.84 0.055 0.99 0.24 0.20100 0.77 0.031 0.88 0.16 0.12

DATA COMPARISON 3

10 KG. TNT AND ASPECT RATIO ONE z [ft/lb1/3] BLASTOP PRESENT MODEL

Max.deflection

[ in. ]

Prob.failureinward

Prob.failure

outward

Max.deflection

[ in. ]

Prob.failureinward

Prob.failure

outward

20 1.56 0.980 NONE 2.20 0.80 1.00

30 1.13 0.360 1.70 0.64 1.0040 1.23 0.560 1.40 0.56 0.9650 0.94 0.120 1.20 0.40 0.9060 0.82 0.050 1.00 0.26 0.7070 0.63 0.020 0.85 0.12 0.4680 0.59 0.012 0.70 0.06 0.3290 0.54 0.010 0.60 0.04 0.24100 0.52 0.008 0.55 0.02 0.14

OBSERVATIONS

DATA COMPARISONS 1 - 3 FOR THE PEAK INWARDDISPLACEMENTS SHOW GOOD AGREEMENT BETWEENTHE DATA FROM THE PRESENT APPROACH ANDTHOSE FROM BLASTOP AND THE WES MODEL.

NEITHER BLASTOP NOR THE WES MODEL CAN BEUSED TO COMPUTE THE OUTWARD RESPONSE.

10 20 30 40 50 60 70 80 90 100

SCALED DISTANCE, z

0

10

20

30

40

PEAK DISPLACEMENT (in.)

100 KG, SQ. INWARD100 KG, SQ. OUTWARD100 KG, RECT. INWARD100 KG, RECT. OUTWARD10 KG, SQ. OUTWARD10 KG, SQ. INWARD10 KG, RECT. INWARD10 KG, RECT. OUTWARD

PEAK DISPLACEMENT vs. SCALED DISTANCE

0 1 2 3 4 5

LOAD DURATION TO NATURAL PERIOD RATIO, t/T

0

2

4

6

8

10

12

14

16

PEAK DISPLACEMENT (in.)

100 KG, RECT. INWARD100 KG, RECT. OUTWARD10 KG, RECT. INWARD10 KG, RECT. OUTWARD10 KG, SQ. INWARD10 KG, SQ. OUTWARD100 KG, SQ. OUTWARD100 KG, SQ. INWARD

0.0 REACHED

AT t/T = 17.5

PEAK DISPLACEMENT vs. t/T RATIO

0 10 20 30 40 50 60 70 80 90 100

SCALED DISTANCE, z

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

PROBABILITY OF FAILURE

100 KG, RECT. OUTWARD100 KG, RECT. INWARD100 KG, SQ. INWARD100 KG, SQ. OUTWARD10 KG, RECT. OUTWARD10 KG, RECT. INWARD10 KG, SQ. OUTWARD10 KG, SQ. INWARD

PROBABILITY OF FAILURE vs. SCALED DISTANCE

CONCLUSIONS

• RESULTS BASED ON PEAK DEFLECTION vs. SCALEDRANGE, OR vs. t/T DO NOT SHOW SIGNIFICANT CHANGEIN GLASS PANEL BEHAVIOR.

• RESULTS BASED ON THE PROBABILITY OF FAILUREvs. SCALED RANGE SHOWED BEHAVIORALDIFFERENCES.

• UNDER CERTAIN CONDITIONS, THE NEGATIVE PHASEOF THE BLAST PULSE CAUSES THE WINDOW TO FAILOUTWARD.

• THAT BEHAVIOR WAS ACHIEVED FOR RELATIVELYSMALL OVERPRESSURE VALUES, WHEN THE PARTIALVACUUM INCREASES ITS RELATIVE IMPORTANCE.

SUMMARY

• THIS STUDY WAS AIMED AT ASSESSING THEPOSSIBLE INFLUENCE OF THE NEGATIVE PHASEOF BLAST LOADING ON WINDOW GLASS.

• THE NEGATIVE PHASE MAY HAVE AN IMPORTANTINFLUENCE ON GLASS PANEL BEHAVIOR.

• THE FINDINGS ARE QUALITATIVE, ANDCOMPARISONS WITH TEST DATA ARE NEEDEDBEFORE STRONGER CONCLUSIONS CAN BEDRAWN.

• FURTHER STUDY IS NEEDED FOR A BETTERUNDERSTANDING OF THIS PHENOMENON.