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MEMORANDUM REPORT NO. 1461MARCH1963

c= THE RESPONSE OF CYLINDRICAL SHELLS TO

EXTERNAL BLAST LOADING

______William J. Schuman, Jr.

RDT & E Project No. 1M0I0501A006

BALLISTIC RESEARCH LABORATORIES

ABERDEEN PROVING GROUND, MARYLAND

ASTIA AVAILABILITY NOTICE

Qualified requestors may obtain copies of this report from ASTIA.

The findings in this report are not to be construedas an official Department of the Ar=y position.


MEMORANDUM REPORT NO. 1461

MARCH 1963

THE RESPONSE OF CYLINDRICAL SHELLSTO EXTERNAL BLAST LOADING

William J. Schuman, Jr.

Terminal Ballistics Laboratory

Funded Under DASA NWER Sub-Task 02.053

RDT & E Project No. 1M5OlOO1A006

ABERDEEN PROVING GROUND, MARYLAND


wimMN 4 REPORT NO. 1461

WJSchuman/cetAberdeen Proving Ground, Md.Nku ch 1963

THE RESPONSE OF CYLINDRICAL SHELLSTO EXTERNAL BLAST LOADING

ABSTACT

A method of predicting permanent deformation of thin-walled unstiffened

cylindrical shells to external blast loading from charges of high explosives

in presented. Empirical relations are derived from a series of firings con-

ducted at Aberdeen Proving Ground against scaled shells. The average deviation

between the predicted and the actual blast pressures required for permanent

deformation is 1i.

3 Ii

bTTABLE OF CONTNTS

SAB87RACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

INTR C•X•TION. . . . . . . . . . . . .. . . . . . . . . . . . 7

TEST A•RAENES AND PROCEDURES .... o. . .. .. 8

TE.ST RESULTS AND DISCUSSION ... . . . .. . . . . .. . . . o 1

PREDICTION OF DEFO•MATION ...

CONCLUSIONS .. . . .. ... .. ... .. ... ... . . . ... o 9

A C 1 XOWLEIDGEMNENNS . . . .. .. .. .. -o

AP PNIDICES ....... ....... . o 45

REFERENCES ............ . ..... . 169

DISTRIBUTION LIST ... ............. ...... . .. . 171

5

INTRODUCTION

The problem of missile vulnerability is quite complex, involving many

factors. A quick resume of these factors will establish the relationship ofthe present report to the overall problem.

Missile Condition - A missile may be in the storage, transport, launch,

in-flight, or re-entry condition. The missile was considered to be

in an unhardened, launch !ondition in this study.

Kill Mechanisms - A missile is vulnerable in varying degrees to fragments,

x-rays, thermal inputs and blast. Blast is the mechanism of concern

in this study and it may be further divided into: overturning of

the complete missile, excess acceleration loading of internal struc-

tural and electrical components, and crushing of the basic structure

and internal components. This report will be limited to considera-

tions of crushing damage to the basic structure.

Approach - The problem may be treated theoretically or experimentally.

A survey of previous work indicated that some analytical studies had

been made at Brooklyn Polytechnic InstituteI* and Columbia Univer-

sity 2 for various loading and boundary conditions. The Space Tech-nology Laboratories 3 have conducted tests on mylar cylinders with

uniform compressive loadings and rise times much slower than those

obtained from blast. Avco Corporation4 has used sheet explosive

applied to segments of the surface of a cylinder to obtain deforma-

tion. Southwest Research Institute5 is also studying this problem

and has conducted some experimental work with flexural type loadings.

Suffield Experimefital Station is investigating the details of blast

loading of various simple structures, including cylinders.

The lack of experimental data, the complexity of the required

theoretical analyses and the urgent need for design data were impor-

tant factors in deciding that both an experimental and theoretical

approach be taken, with the experimental phase receiving precedence.

Only the experimental phase of the study will be reported at this

time.

* Superscripts refer to references listed at end of report.

S~7

Targets - There are three types of targets that might be chosen: actual

hardware, scaled-models and simplified models. It was decided to

utilize simplified models to define the basic parameters and their

relatiorships before proceeding to the more sophisticated models and

actual hardware. The simplified model chosen was a right-circular,

thin-walled, unstiffened cylinder.

The primary goal of the first phase of this study was to develop an

empirical method of predicting the blast parameters necessary to cause perma-

nent deformation of a wide spectrum of cylinder geometries and materials. The

secondary goal was to obtain details of loading and response for correlation

and to aid in further studies.

TEST ARRANGEMENTS AND PROCEDURES

Preparation of Models

The cylindrical shells were fabricated from steel and aluminum foil, sheet

and tubing. The steel shells were formed from 1040 hot-rolled sheet and butt-

welded. The aluminum shells were either sections of 6061-T6 seamless tubing

or formed from ±100-0 or 5052-H3' foil and fastened by solder or by cloth-

backed adhesive tape. The shell diameters varied from 3 to 24 inches, the

lengths from 2 to 48 inches, and the thicknesses from 0.003 to 0.136 inches.

These dimensions provided shells that were geometrically scaled and have length-

to-diameter ratios of 0.7 to 10 and diameter-to-thickness ratios of 60 to 2000.

The dimensions of the shells used are presented in Table I.

A few representative shells were instrumented internally with Baldwin-

Lima-Hamilton FAB-25-35, 350-ohm foil strain gages for measuring details of

response. One gage pattern is shown in Fig. 1. A solid cylinder (non-

responsive) was instrumented with flush-mounted piezoelectric gages for measur-

ing details of loading. The gage pattern is shown in Fig. 2.

The shells were fastened to heavy end caps and this assembly then was

fastened over a rigid tube. This tube prevented rotation of the end caps

about an axis perpendicular to the longitudinal axis of the shell and there-

fore minimized bending in the shell. A schematic of the shell and support

tube assembly is shown in Fig. 3.

8

TABLE ICylindri•al •hell Diaensiano

* 1 Disimter Length ThLokaess L/D D/t MiterialD L t(in.) -. a

1 ,. 2 3.0 6.0 0.019 2.0 158 Steel Sheet -1003 - 6 3.o 8.62 0.019 2.87 158

7 3.0 9.0 0.019 3.0 158 H

8,9 3.0 11.62 0.019 3.87 158 H

op, 11 3.0 1A4.62 0.019 4.87 158Its, 13 3.0 18.0 0.019 6.0 158 "24, 15 3.0 24.0 0.019 8.o 15816, 17 3.0 8.6a 0.035 2.87 86

18 3.0 9.0 0.035 3.0 8619 3.0 18.0 0.035 6.0 86

2D, 21 6.0 18.0 0.019 3.0 31622, 23 6.0 17.5 0.035 2.91 172

A 6.o 18.0 0.035 3.0 17225, 26 6.o 17.5 0.076 2.91 79 "

27 6.o 18.o 0.076 3.0 79 "26, 29 12.0 35.38 0.076 2.94 158

30 12.0 35.38 o.136 2.94 8831, 32 214.0 147.25 o.136 1.98 176

33 3.0 6.0 0.003 2.0 100 Alum.Foll 5052 - E383- 3.0 9.0 0.003 3.0 Woo

37 3.0 15.0 0.003 5.0 1000 "3 -ho 3.0 9.0 o.006 3.0 5oo "

4i 3.0 15.0 o.oo6 5.0 500 "23.0 23.0 0.006 7.67 5o034, 3.0 30.Q o.oo6 10.0 500 "3- 46 3.0 9.0 0.012 3.0 250 H47 - 49 3.0 9.0 o.o214 3.0 125 "

50 - 53 6.0 18.0 0.003 3.0 2000S- 5 6.0 18.0o o.o6 3,0 1000 .57, 58 3.0 9.0 o.o22 3.0 136 Alum.Tubing - 6061 - T6

(O, 6D 3.0 9.0 0.0o2 3.0 716, 6.o 18.o o.042 3.0 114363 3.0 2.0 0.006 0.67 500 Alum.Fotl - 1300 - 0S3.0 2.0 0.006 1.0 50 "

53.0 5.0 o.oo6 1.67 500663.0 6.0 o.oo6 2.0 50o 0

67'-7 3.0 9.0 o.oo6 3.0 5o076 3.0 12.0 0.006 4.0 500

77, 78 3.0 15.0 o.6 5.0 5o79 3.0 23.0 o.=o6 7.67 500

s -82 3.0 9.0 0.010 3.0 30083, 8' 3.0 2.0 0.012 0.67 250 "85- a7 3-. 3.0 0.012 1.0 250 "

8691 3.0 9.0 0.012 3.0 250S6.0 9.0 0.006 1.5 iooo m93 6.0 11.0 o.006 1.83 100094 6.0 4.0 0.012 0.67 500 "95 6.0 6.o 0.012 1.0 50096 6.o 9.0 0.012 3.0 500

97, 96 6.o 11.0 o.012 1.83 500 H99 7.5 7.5 o.o63 1.0 119 Alm. (Poastinn Arsa)* 7.5 7.5 0.125 1.0 60 Alum. (Piostimy Arseasl)

9i

4L AR2

C14

IL _ /IC 4~3C

I CHARGE

NOTE:

L - LONGITUDINAL STRAINC - CIRCUMFERENTIAL STRAIN

IL _ _ 3L3C _

IC& 44C CHARGE

21LI 2C

FIG. t. STRAIN GAGE PATTERN

10

L .- 4 ..

"cI.__ __ ____________L90 90

4 + 00100 + 0 + 0

SEC A-A SEC B-B SEC C-C

FIG. 2. PRESSURE GAGE PATTERN

11

FTHICKNESS If IT D IAMETER (0)

END CAPSHELL

SUPPORT TUBE

LENGT (

FIG. 3 - TYPICAL SHELL SPECIMEN

1

12

Test Arrangements

The blast loading was provided by detonating charges of high explosive

(HE) ranging in weight from one pound to 216 pounds. The smaller charges of

bare spherical Pentolite was suspended as shown in Fig. 4. The larger charges

were placed on the ground. The free air blast parameters; overpressure,

impulse, and duration are determined by use of tabulated data7' 8 . (References 9

and 10 define and discuss the various blast parameters.)

The shell and support tube assemblies were mounted on portable stands at

a height of 6 feet to minimize ground effects as shown in Figs. 4 and 5. They

were oriented with respect to the charge so that the blast impinges on the

shells either along a line perpendicular to the longitudinal axis (lateral

loading) or along an extension of the longitudinal axis (longitudinal loading).

A nose cone was added to the shell for the longitudinal loading orientation to

minimize the disturbance of the flow.

Test Procedure

A group of uninstrumented shells were positioned about an explosive charge

at various distances such that the pressure levels would be below that required

to cause permanent deformation. The shells were then repositioned in incre-

ments until optimum deformation - defined in this study as approximately 5% to

10% of the original diameter - was obtained.

The instrumented cylinders were fired on individually because of instru-

mentation requirements. The signals from the strain gages were recorded by a

16 channel CEC Miller Recording Oscillograph that has a maximum writing speed

of 400 in/sec and a frequency response of DC to 200 KC. The signals from the

pressure gages were amplified, presented on cathode ray tubes and recorded by

General Radio streak cameras. This system has a maximum writing speed of 2500

in/sec and a frequency response of DC to 100 KC.

TEST RESTTLTS AND DISCUSSION

Uninstrumented Shells

Values of overpressure and impulse for the shells fired on are listed in

* Tables II and III for the lateral and longitudinal loading orientations.

13

LATERAL LOADING

CHARGE STAN

FIG. 4 -TYPICAL FIELD ARRANGEMENT

14I

15

U, CI W,

M~U~t-. - - -

0 0 UOsrOD 0a "*0 104 0

000 0'. OD O ., C CO00 OD OD O oSO

AIR~~~~~~~~~0~ r0C 16%Dt-D'N91%QArqA:c0,4RgF

416

4-)

ax aa.0 Lr, 0- -0 a

L(%ju~ UNU ^U %c-2% ý S~ P zPaZ

.. 4t- CD.-~t- ' Ž

0; uý W%,g ý ý,CM c r-lLf% cu0Lý ~ -A - m . , - wcu

'44tp' C lJ 04 U C.-.4

r- C4 C 4 6 .1 4 -L%

t Cý 4 H W Ltzktz 0 ON ooo _;r1

.43

17

41

2 aj* I In Il ia i IIto*.* F~"~

~F

v4 RVVuI jr^*,Co 0W,71.78N 4 coDt-co

~~Aq 4 0 cJO O ..4. e-C4 NN * J !**-

'R ~ 4.f R 8 U%'- it U

Uýe-O . .. ... l 199. . . .l -- UUg A E-:~ t.:.: ~ t-Ao * u C4 Uý ý44

18

L ii

1 4 )

to~ 0,

k m

t. 41

*ý 9 0l 9q NC\U

I.I CID

-4A -r

419

Plots of incident impulse (Ii) vs. incident pressure (pi) for the shells

listed in Table II as having approximately the optimum deformation are pre-

sented in Fig. 6. Iso-damage curves are drawn through these points that

represent the various combinations of pressure and impulse for equivalent

deformation of a given shell material and configuration (see points 4-5-6-7,54-55-56, etc., Fig. 6). These curves form the boundaries between regimes of

deformation and non-deformation.

The effect of variations of explosive weight on the blast parameters can

easily be determined from these curves. As the explosive weight increases,

moving from right to left along one of these curves, the impulse increases

but the pressure decreases. For very large explosive weights the pressure-

time histories will approach a step function (long durations, high impulse

values) and the iso-damage curves should approach asymptotically some minimum

value of pressure that will cause deformation.

If curves are drawn through different sets of points (i.e., 4-8-10, etc.)

the effects of changes in length of the shells can be determined. In this

case, the curve appears as a straight line. As length is increased, moving

from right to left (all other parameters constant) the required values of

pressure and impulse decrease. It is expected that an increase in length

beyond a certain minimum value will not produce a further reduction in pres-

sure and impulse values. At this point, the shell can be considered infinite

and end conditions will not influence the deformation at the center. This

minimum length has not been determined at this time.

In like manner, the variation of pressure and impulse values for changes

only in diameter, thickness or type of material can be determined. As expected,

an increase in pressure and impulse values is required if either the thickness

is increased oz the diameter decreased.

Having a family of iso-damage curves and the variation of the significant

parameters, it is possible to generate a method of predicting deformation of

cylindrical shells. The details of the method will be presented in the next

section, "Prediction of Deformation."

2

20

II

21

The nearly vertical, dotted lines on Fig. 6 show that shells of differentconfigurations will be deformed at the same pressure level by unlike explosive

weights. A close examination of the connected points indicates that "geomet-

rical" modeling laws apply for these large deformations. For example, refer

to Fig. 6 and Fig. 7 - Scaling Parameters, and Table II: Point 5 on Fig. 6represents a cylinder of given geometry (3 in. diameter, 8.62 in. length,

0.019 in. thickness) laterally loaded by an explosive weight of 8.4 lbs.

positioned at a distance of seven feet. The equivalent deformation of a shell

whose geometry has been scaled by the factor K = 2 (Point 23 - 6 in. diameter,

17.50 in. length, 0.035 in. thickness) exposed to an explosive weight of

64 lbs. (i.e., W oc or Doc v¶ or Dwo 0 oc 2 and, therefore,

W2oc K 3 Dw3 c (2)3 . (2)3 oc 64) located at a distance of 2d = 2 x 7 = 14 ft.

validates this conclusion as do the other sets of points.

There are two general deformation patterns arising from lateral loadings:

a single transverse crease or multiple longitudinal lobes. Typical transverse

and longitudinal patterns are shown in Figs. 8 - 10 and i. and 12. A typical

deformation pattern resulting from longitudinal loading is shown in Fig. 13.

Photographs of all shells are presented in Appendices A and B for the lateral

and longitudinal loadings respectively.

The two lateral loading patterns seem to be primarily a function of the

shell geometry. The thicker shells deform with a transverse crease while the

thinner form a lobe pattern. However, one of the shell. deformed in a com-

pound pattern when the explosive weight was increased. (See Fig. 14.) Further

investigation is required to define the applicable parameters and their vari-

ation.

One shell was tested statically to compare its pattern with those shown

in Figs. 8 - 10. The shell and support tube assembly was mounted on v-blocks

in a testing machine. The line load was applied perpendicular to the center-

line of the shell at the center with a 1/4 x 4 inch striker plate. The

deformation pattern Is similar to that of the transverse crease (see Figs. 15

and 16). The shell cmmenced to deform at 3 lb. load and the load increased

22

t9

t d

CHARGE OF HIGH EXPLOSIVE

WD3D

kLW cDw N TE

W-WEIGHT OF EXPLOSIVECHARGE

k- SCALE FACTOR

SCALED CHARGEkDw OF HIGH EXPLOSIVE

kD

WaCkDw )3

We k 3 Dw3

FIG. 7- SCALING PARAMETERS

23

. .0 2 3 4 5 6 7 8 9 to 12

FIG. 8 -DEFORMATION PATTERN -SHELL NO. 9

FIG. 9 - DEFORMATION PATTERN - SHELL NO. 22

25

, kk

0 6 12,

A*SCALE I N INCHESFIG. I10- DEFORMATION PATTERN - SHELL NO. 28

0 I 2 3 4 5 6

FIG, 11 DEFORMATION PATTERN -SHELL NO. 88

4" JI 0 i 2 3 4 5 6

INCHES

FIG. 12 - DEFORMATION PATTERN - SHELL NO. 66

CjLO

dz

LLJm

zcrLLJ

z0

cr0LLL.LiaILo

0LL

CDC*j

"t

Ld

Q)0 -

,FIG. 15- DEFORMATION PATTERN - SHELL NO. 75

FIG. 16- DEFORMATION pATTERN -SHELL No. 75

continuously as the deformation increased. The load was increased to a maxi-

mum value of 10 lb. and then removed. This requirement that the load must be

increased in order to increase the deformation also agrees with the blast

loading results.

Instrumented Shells

The results of exploratory firings for checking out the strain gage

recording system are presented in Table IV. Only peak strains were read.

Additional firings will be conducted and the results coordinated with similar

investigations being carried out at the Suffield Experimental Station.

A number of firings have been made against the solid loading cylinder,

but calibration difficulties preclude presenting the data at this time.

PREDICTION OF DEFORMATION

A semi-graphical method for predicting the critical incident pressure

required to cause permanent deformation for a cylindrical shell in the lateral

loading orientation has been generated. The necessary curves are shown in

Figs. 17 - 20.

The four curves of Fig. 17 are plots of the length-to-diameter ratio -

L/D - vs. critical incident pressure pcr for the four materials tested: steel

and the three types of aluminum alloy. Each of these curves is based on a

change of L/D for a constant explosive weight of one pound, a diameter of three

inches and a thickness of 0.019 in. for steel and 0.006 in. for aluminum.

If the explosive weight, diameter, or thickness are different from the

above standard values, the value of critical incident pressure pcr must be

adjusted. The necessary correction factors have been determined from the inde-

pendent effect of each of these factors on the critical pressure and are given

in Figs. 18 - 20. The required pressure is then:

Pcr = Pcr KD Kt K

where P = Critical Incident Pressure for lateral loadingcr

Pcr = Critical Incident Pressure (for standard conditions) (Fig. 17)

Kw = Correction factor for explosive weight 'Fig. 18)

33

TABLE IV

Strain Data for Lateral Loading of Shell*

Round No. 106 107 109 110 111

Explosive Wt. (lb) 1.06 1.O6 1.07 8.19 8.19

Explosive Dist. (ft) 3.75 3.75 3.5 8.0 8.0

Press. pi (psi) 69.2 69.2 82.4 58.8 58.8

Gage Position Maximum Strain (it in/in)

1U 603 551 61u --

lC 1635 1281 1749 1923 --

2L 559 536 752 581 633

2C 790 752 1112 656 894

3L 909 668 1308 726 983

3C 1065 663 646 1749 151 3

4L 577 57 4 74 5 612 656

4C 641 514" 790 734 1013

*Shell Dimensions - Diameter - 3", Length - 9", Thickness - .019", Material -

.teel

34

loo?

5004-

3-

200

I00_9-S7-

50\N

z 2_1040 STEELo 20

lot9

7 6061- T66- ALUMINUM

54 STANDARD CONDITIONS ALUMINUMH 38

3-EXPLOSIVE WEIGHT- I LB.

2 WALL THICKNESS - 10.019 #STEEL ____

2 0.O06#ALUM

1100-0ALUMINUMI

0.1 0.2 3 4 0.56 71691.0 2.0 3 4 5,06 79910 20 3 4 506 7 19100

L/D

FIG. 17 LENGTH -TO-DIAMETER RATIOVS

CRITICAL INCIDENT PRESSURE FOR STANDARD CONDITIONS

35

K

I U U

I0

-W.

10J

C-

N w K

-- 2

* .

-V€)

Y.- z

0

U, 00.

w

0

w

/0

(I,

0 0

•36

_ _ _ __ Xu

108 -

76

54

3-

2

9-

* 0.5

"4-3

'0.2

0.1

7-6-

0.05

4-

3-

0.02

0.1 0.2 3 40.5 1.0 2.0 5.0 71890 20 450 7 8ý100D/3

FIG. 19. CORRECTION FACTOR FOR VARIATIONS OF DIAMETER

37

1009-

a--

76

50 -0____ ____ ___ __

4-

Kt3-

20

10 /9- /

7-6-

4-

3-

Kt

.7-

.4-

.3-

0.2

0 .1 1 1 It l lI l I i I

0.1 0.2 3 40.567631.0 2 3 4 5 6 To910 20 3 4 506769100

t /0.019-STEEL ; t/0.0O6-ALUMINUM

FIG. 20. CORRECTION FACTOR FOR VARIATIONS OF WALL THICKNESS

38

KD = Correction Factor for Diameter (Fig. 19)

Kt = Correction Factor for Thickness (Fig. 20)

As an example, consider Shell No. 30. It is steel and L/D 2.94 (Table I).

Therefore pcr = 150 psi

also D = 12.0 in.,-2 = 4 and KD = 0.27

t 0.136 in., 0 = 7.17 and Kt = 24.2

W = 389 lb., K = 0.265

Therefore Pcr = Pcr KD Kt Kw

= (150) (0.27) (24.2) (0.265)

P = 26 0 psicr

The actual pressure was pi = 257 psi. Therefore, the deviation of the

predicted value from the actual value is + 1.2%.

The average deviation between predicted and actual pressures for the

laterally-loaded cylinders listed in Table V is 12% with a spread of -40%

to + 40%.

If the shell is exposed to longitudinal loading, the pressure required

for deformation is higher. The data presently available seem to follow the

general trend of the other set of iso-damage curves. Therefore, the critical

pressure for the lateral loading should be determined and multiplied by a

factor of X where X : 6.0 for steel, and X *2.0 for aluminum.

CONCLUSIONS

The primary goal of the first phase of an investigation of the response

of thin walled cylinders exposed to external blast loading has been achieved.

An empirical method of predicting the critical incident blast pressure required

to cause permanent deformation has been presented. The correlation of pre-

dicted and actual pressure values is satisfactory (average deviation of 12%).

However, there are several areas requiring further investigation. It is

planned to conduct a series of firings in the 1000 lb. to 30,000 lb. explosive

weight range at the Yuma Test Station the early part of 1963. This will help

define the iso-damage curves at much higher impulse levels.

39

TAB3I V

Cciw•rison of Actual and Predicted Pressures for Optima Deformt ion

Shell Incident Predicted Deviation RemarksNo. Pressure* Critical Pressure (M)

Ag Peý(pal) 51

1 117 .114 -2.62 48.5 58.2 +20.0

14148 894*** - No Deformation3b** 1463 144*** .4.64 159 149 -6.35 82.4 80.6 -2.26 58 52.6 -9.37 39.7 39.7 08 118 111 -5.99 6o.3 59.8 -0.8

10 82.h 86.5 +5.011 44.8 46.8 +4.512 36.0 37.9 +5.313 17.14 19.3 +11.014 27.9 28.6 +2.515 2.9 14.5 - No Deformation16 213 217 +1.917 166 1143 -16.118 96.7 107 +12.119 172 103 -o.0020 36.o 40.6 +12.821 21.8 20.7 -5.022 130 112 -13.823 91.3 73.0 -20.124 63.6 55.9 -1-325 463 389 -16.o26 209 2514 - No Deformation27 171. 195 +12.028 83.7 102 +22.129a** 617 612*** - No Deformation29b** 544 786*** - No Deformation30 257 260 4-1.231 83.7 196 - Less Than Optimu32** 404 1176*** - " Deformation33 1.87 2.21 +18.234 5.05 5.06 +0.235 3.04 2.74 -9.936 1.62 1.8o +11.137 1.65 1.37 -16.9 Greater Than Optima38 12.1 12.2 +0.8 Deformation39 7.94 6.59 -17.040 4.26 4.33 +1.641 2.94. 3.30 - No Deformation12 1.06 2.63 - No Deformation

.43 2.0 P.27 +13.5S22.1 29.2 ,Am0.

45 13.5 15.8 +17.016 11.5 lo. 4 -9.647 58.8 69.5 +18.2

40o

TABLE V (Cont'd)

shell Incident Predicted DeviationNo. Pressure* Critical Pressure () Re-ks

P1 Per(psi) (psi)

48 45.6 37.6 -17.549 35.0 24.7 -30.650 2.50 2.53 +1.251 1.50 1.42 -4.552*'* 1.84 i.87*•* +1.653 0.82 .935 +16.554 7.94 6.30 -20.755 5.14 3.40 -33.956 2.47 2.24 -9.357 57.5 92.0 - No Deformation58 45.6 49.6 +8.859 264 205 -22.460 107 115 +7.561 113 107 -5.362 57.5 57.5 063 12.4 11.0 - Excess Deformation64 7.80 7.88 +1.065 7.80 5.38 - Excess Deformation66 3.97 4.61 +16.167 3.53 3.46 -2.068 1.91 1.76 -7.869 12.9 1.95 - Excess Deformation70 7.65 1.49 - Excess Deformation71 4.18 1.42 - "72 1.07 1.28 +19.673"* 46.3 6.92*** - Excess Deformation74** 34.5 3.00*** - "75 - " - Static Test76 2.57 2.95 +14.877 4.85 2.40 - Excess Deformation78 2.50 1.35 - "79 1.91 1.73 -9.80 7.80 6.4o -17.981 5.68 3.60 -36.682 3.24 3.27 +1.083 11.5 12.9 No Deformation84 9.4 9.38 -0.385 12.4 18.8 - No Deformation86 7.35 9.63 -87 7.20 6.99 -2.988 7.80 8.3 +6.489 7.65 4.65 - Excess Deformation90 3.97 4.23 +6.591 2.16 3.07 - No Deformation92 1.40 1.55 +10.793 1.54 1.33 -13.694 2.32 4.86 - No Deformation95 2.16 3.63 "96 5.28 2.20 - Excess Deformation

411

TABLE V (Cont'd)

Shell Incident Predicted Deviation Remarks5O. Pressure* Critical Pressure (%)

Pi Per(psi) (psi)

97 5.28 3.18 - Excess Deformation98 1.76 2.30 +30.799 83.7 91.0 +8.7

100 218 217 -0.5

* From Tables II & III** Longitudinal Loading Orientation (all others are lateral loading

orientation)*** Predicted Critical Pressures for Lateral Loading Orientation have been

Multiplied by 6.0 for Steel, 2.0 for Aluminum

42

Shells are being fabricated with greater lengths to determine at what

point end conditions may be neglected. The variation in deformation patterns

will be studied further. The iso-damage curves for the longitudinal loading

orientation will be defined more accurately. The effects of free-body motion

of the shell are now being studied.

Continuation of study of the instrumented shells will provide valuable

data for analytical correlation of the loading and response.

Future work with actual hardware will determine the degree of applicabil-

ity of these simplified models.

This is an interim report released at this time so that Government and

private agencies may integrate these results into overall vulnerability

analyses.

ACKNOWLEDGMENTS

The assistance afforded the author by Professor Norman Davids, Department

of Mechanics, the Pennsylvania State University in the planning of these tests

and in the preparation of this report is gratefully acknowledged.

Acknowledgment is also made of the assistance of Miles Lampson, Harry

Goldstein and the many members of the BRL field crew in conducting experiments

at BRL ranges.

WILLIAM JAC JR.

4~3

APPENDIX A

DEFORMATION OF LATERALLY LOADED SHELLS

45

100 Y" 4 5 6

FIG. I. -SHELL NO. I

2INCHES

FIG. 2. - SHELL NO. 2

............

SCALE IN INCHES .i

FIG. 3 - SHELL NO. 4 -- SIDE VIEW

48

I

o I 2 3 4 5 6*I I a a I I I

SCALE IN INCHES .

FIG. 4 - SHELL NO. 4 - FRONT VIEW

"49

-o-j

0 1 2 4 5 6 7 8 9 1 0 II 12

FIG. 5 -SHELL NO. 5 -SIDE VIEW

50

0 I 2 4 5 ~' 7 8 9 10 I 2

F{G6 -SHELL NO. 5 -FRONT VIEW

51

FIG,? -SHELL NO. 6 SIDE VIEW

52

tO I A

HCEL NO. 6 -. ,"

FIG. 8- SHELL NO. 6- FRONT VIEW

53

z

-J

Ia)

FIG. 10-SHELL NO. 8- SIDE VIEW

FIG. 11 SHELL NO. 8 -FRONT VIEW

56

FIG. 12- SHELL NO. 9 - SIDE VIEW

I t -

FIG. 13- SHELL NO.9- FRONT VIEW

58

(2i

FIG. 14- SHELL NO.1IO- SIDE VIEW

I 5

FI

• .If

FIG. 15- SHELL NO. I0 - FRONT VIEW

0 1 2 3 4 5 6~

SCALE IN INCHES

FIG. 16- SHELL NO. If

m

FoG. 0 I S 3 4 5 6

FIG. 17- SHELL NO. 12

m0

Tr7'

47-t, -1-7

R-7

101

188 1 3

FIG. 19- SHELL NO. 13 REAR VIEW

102A

FIG. 21 -SHELL NO. 16

66


1030 2 3 4 5 6

IN H- F

FI.23 - SHELL NO. 19

VI

104B30 1 2 3 4. 5 6

INCHFS

/FIG. 24- SHELL NO. 20

184 1 2 3 4 5 6INCHES

FIG. 25-SHELL NO.21-FRONT VIEW

70

184 0 1 2 3 4 5 6IN rHFq

IG. 26- SHELL NO. 21 SIDE VI

1840 1 2 3 5 6

FIG. 27- -SHELL NO. 21 -REAR VIEW

0 I 2 5 4 5 6 7 8 9 10 I '

A I I I I S, I 2 I S II V

a FIG 8- HELL NO. 22.- SIDE VIEW-

FIG. 29 -SHELL NO. 22- FRONT VIEW

A irfoi

A 4111 M

a tr SIR IN

a

An 4,

As

Is Is

It %U

lot

aw

go

Oki

am

B 14ý A'011ý Vro,

FIG. 30 - SHELL NO. 23 SIDE VIEW

ir'

4pd

Ift

FIG. 32 - SHELL NO.2

A

FIG. 33-SHELL NO. 25

N~ wiCln >W w

aa

w

0(/))

LL

C\j

Cl

Now*

LAJ

CY

ODMow N

d

UJ_j LLJ

ch

LL

4 wzn

uP OD

ii ~ /

w r w At it IL

db

NA

44

tIV 0

w amp EML

zOV w

0 is,

wT-

ODlie I K)

W& or AN

40 of M

ok

r

40

VA M

1

96

lot

N

LIJ

I~lk

I' 84

196 oINrHFS


85

380A 0 2 3 4 5 6

INCHES

FIG. 41 - SHELL NO. 34-FRONT VIEW

86

INCHES /FIG. 42- SHELL NO. 34- REAR VIEW

By(

"1l' 012 5 2AphirmES


LA)

rf)

uj

T-

Y)

qt

200 2 3 4 5 6


1,38 B 0 2 34 5I

FIG 46- SHELL NO- .8 - FRONT IV

-K-I-.

HG 46- SHELL NO 36 - EROt'JT �R�v

038 2 3 4 5 6

FIG. 47- SHELL NO. 38 -REAR VIEW

FIG. 48-- SHELL NO. 39

690 I 2 3 4 5 6

INCHES

FIG. 49- SHELL NO. 40- FRONT VIEW

FIG. 50-SHELL NO. 40- REAR VIEW

0 12 3 4 5 6

INCHES


96

U

1I. 2 3 4 5 N


72

INCHES

98

72A 1 2 3 4 5 61 N rHF7S

FIG. 54-SHELL NO. 46-REAR VIEW

DoZ 012 3 45 6INCHES


100

88~)

83 ~~INCHES456

FI.57 -SHELL NO. 50

890 1 2 3 4 5 6

INCHfS

58- SHELL NO. 51

OD(D

al

0 1 4 5 6m ~~IN H

60- SHELL NO. 54

FIG. 61 -SHELL NO. 55--FRONT VIEW'

146 ,,0 1 2 3 4 1) C

C~-j

... .. .

M

C',

(0L

FIG 64- SHELL NO. 58

400 .,4I 2 3 4 5 6


401 3 4

FIG. 66- SHELL -NO. 60

93

FI.67- SHELL NO. 61

FIG 68 - SHELL NO. 62

FIG 6 2 N3 -F VIINCHES

FIG. 69- SHELL NO. 63-FRONT VIEW

0 I 2 3 4 5 6


270 I 2 3 4 5 6

INCHES

FIG. 71- SHELL NO. 64-FRONT VIEW

0 1 2 3 4 5 6INCHES

I4 !

FIG 2 3 4 5

FI.73- SHELL NO. 65

NC, 2 3* INCHES

FIG. 74-SHELL NO. 66-FRONT VIE_..W

474. 0 i 2 3 4 5 6

INCHES

FIG. 75-SHELL NO.66-REAR VIEW

25G

FIG. 76- SHELL NO. G7-FRONT VIEW

25C

0 2 3 4 5 6


S N IN

62A 62BFIG. 78-SHELL NO. 68-FRONT VIEW

i 123

o 4 25~ 6

FIG. 79 -SHELL NO, 68- REAR VIEW

FIG. 80- SHELL NO.69-FRONT VIEW

125

I

FIG. 81 -SHELL,,. NO. 69-SIDE VIEW

5F

0 1 2 3 4 5 6

INCHES

ll l/iI.82- SHELL NO. 71- SIDE VIEW

INCHES

FIG.~~~~~ 83-HLN.7-REA

uj

N

-Now 6

co0U-

c -ow

LiiJw

w

Lc)m O-

= 0L

0 2 6

FIG. 87- SHELL NO. 76-RERVW

I I 3 4 5 0

133

FG -8-SHELL No. 781

FIG.• • 90-2 3 N 79

FG90- SHELL N.7

S0 1 2 3 4 5 6

FIG. 91 - SHELL NO, 80-FRONT VIEW

137

/

0 I 2 3 4 5 6


63

SCALE IN INCHES

0 I 2 3 4 5 69 HI I I I I82

-0-J

"W4 4-'

I I1 ~(D

0 2 3 4 5 6INCHES

FIG. 97- SHE'LL NO.88- FRONT VIEW

- I T

0 1 2 3 4 5 6

FIG.98-HELL NO. 88- SIDE VIEW

I

FIG. 99- SHELL NO. 89 -FRONT VIEW

1-45

5ýý9 A 59 590C

SCAL IN INCHES

SCALE IN INCHES

FG. 103 - SHELL NO. 92 -FRONT VIEW

14,'

SCALE IN INCHES

FIG 1.0 - SHL NO 2; I D VIE

• IA W5

SCALE IN INCHES

0 I 2 3 4 5 6I 5I I S I I I I

FIG. 105-SHELL NO.93FOTVE

FIG. 106-SHELL NO. 9-3- REAR VE

1~51

F IG -I

SCALE IN INCHES

0 1 2 3 4 5 6

LFIG 107 SHL N -FON VIE

SCALE IN INCHES

0 1 2 3 4 5 6

SHELL NO. 96- REAR

155

SCALE IN INCHES

o 1 2 3456F IN I9 HES

F IG 09 SHL NO 95 FRN6VE

.. . . .... ..

IJ

IL-

N-J

156

tj

w

5;w

co(D

Lli

z

LAJ

cli

J6-

Lj

LL

C5

LAJ

C/)

158

I 59J

APPENDIX E,

DEFORKATION OF LONGITUDINJALLY LOADED SHELLS

161

/

FIG. I- SHELL NO.3b-FRONT VIEW

162

FIG. 2- SHELL NO. 3b-END VIEW

163

00 - I

A-s-

jogj

-LJ

It)

164

CMjC

165)

1alp

FG - IHL N .(

It


REFERENCES

1 1. Hodge, P. G. Impact Pressure Loading of Rigid-Plastic Cylindrical ShellsPolytechnic Institute of Brooklyn Report No. 255, MAy 1954.

Hodge, P. G. Ultimate Dynamic Load of a Circular Cylindrical ShellPolytechnic Institute of Brooklyn Report No. 265, November 1954.

Hodge, P. G. The Influence of Blast Characteristics on the Final Deforma-tion of Circular Cylindrical Shells Polytechnic Institute of BrooklynReport No. 266, December 1954.

Sankaranarayanan, R. Dynamic Response of Plastic Circular CylindricalShells Under Lateral and Hydrostatic Pressures Polytechnic Institute ofBrooklyn Report No. 573, June 1961.

2. Mindlin, R. D. and Bleich, H. H. Response of an Elastic Cylindrical Shellto a Transverse Step Shock Wave Technical Report No. 3, ContractNonr-266(08), Columbia University, March 1952.

Baron, M. L. and Bleich, H. H. Further Studies of the Response of aCylindrical Shell to a Transverse Shock Wave Technical Report No. 10,Contract Nonr-266(08), Columbia University, December 1953.

Bleich, H. H. and Dimaggio, F. L. Dynamic Buckling of Submerged Platesand Shells Technical Report No. 12, Contract Nonr-266(O8), ColumbiaUniversity, September 1954.

3. Seide, P., Weingarten, V. I., and Morgan, E. J. Final Report on theDevelopment of Design Criteria for Elastic Stability of Thin Shell Struc-tures Space Technology Laboratories, AFBMD/TR-61-7, December 1960.

Final Report on Buckling of Shells Under Dynamic Loads Final Report,Contract NASr-56, Space Technology Laboratories, October 1961.

4. Radkowski, P. P. et al Studies on the Dynamic Response of Shell Structuresand Materials to a Pressure Pulse AVCO Corporation, AFSWC-TR-61-31 (II),July 1961.

5. DeHart, R. C. and Basdekas, N. L. Response of Aircraft Fuselages andMissile Bodies to Blast Loading Southwest Research Institute, ASD-TDR-62 -Preprint, March 1962.

6. Scientific- Observations on the Explosion of a 20 Ton TNT Charge, VolumeOne, General Information and Measurements Report No. 203, SuffieldExperimental Station, Ralston, Alberta, September 1961.

7. Goodman, H. J. Compiled Free-Air Blast Data on Bare Spherical Pentolite,BRL Report No. 1092, February 1960.

S-. 'Ecaker, 'W. E. and Schuman, W. J. Air Blast Data for Correlation with MovingAirfoil Tests BRL Technical Note No. 1421, August 1961.

169

9. Kinney, G. F. Explosive Shocks in Air The MacMillan Company, 1962.

10. Cole, R. H. Underwater Explosions Princeton University Press, 1948.

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