N 123-60530S-3825a: T. O. 1 Galcit 90

SOME EXPLORATORY PHOTOELASTIC STUDIES IN

STRESS WAVE PROPAGATION

by

M. L. Williams M. E. Jessey R. R. Parmerter

October 1958

This research was supported by the United States Bureau of Ordnance, through the Naval Ordnance Test Station, China Lake, California, Dr. John Pearson, Project Engineer.

Guggenheim Aeronautical Laboratory

California Institute of Technology

Pasadena, California

SOME EXPLORATORY PHOTOELASTIC STUDIES IN

STRESS WAVE PROPAGATION

* M. L. Williams M. E. Jessey R. R. Parmerter

SUMMARY

During the last three years the Guggenheim Aeronautical Laboratory of the California Institute of Technology (GALCIT) has been conducting a photo-elastic study of stress wave propagation in solids using a high speed framing camera.

This paper presents a technical description of the camera, now operating at 100, 000 35 mm frames per second at one tenth microsecond exposure time for an elapsed time of approximately two milliseconds. The design capability is expected to approach a half million frames per second. This equipment has been used to record dynamic photoelastic stress fringe patterns in various specimens under impact loadings. Typical experimental records of wave propagation in cracked plates, layered media, compressed bars and beams, and cross sections of rocket heads are included in this report.

I. GENERAL DESCRIPTION

In 1955, Sutton ( 1) as part of his doctorate thesis at the

California Institute of Technology presented a series of dynamic photo-

elastic fringe patterns in a rectangular plate under impact compression.

To record the data he made use of a high speed framing camera devel-

oped at the Institute by Ellis (Z) for cavitation studies.

The unique feature used in this equipment was a repeatedly pulsed

Kerr cell which operates as a shutter based upon an electrical rather than

a mechanical time base. The principle of operation is essentially that if

two parallel plates immersed in a closed container of nitrobenzene are

charged, the fluid becomes optically birefringent until the charge is

removed.

*M. L. Williams, Associate Professor; M. E. Jessey, Research Engineer: R. R. Parmerter, Graduate Student, California Institute of Technology.

2

Having a fast shutter thus solves the first problem. Next one

desires stationary film upon which to record the events, thus obviating

the necessity for introducing mechanical motion. The Ellis design used

a circular drum whose longitudinal axis coincided with the optical axis

and was collinear with a shaft driven at high speed by an air turbine.

The end of the shaft was tent- beveled with two 45 degree plane cuts, one

of which was blackened and the other polished to a mirror finish. The

image coming along the optical axis through the Kerr cell was thus

turned at right angles by the mirror and flashed to the stationary film

track. The shuttering of the cell coupled with the rotation of the mirror

printed successive events on the film strip.

Whereas some experimenters have used multiple light flashes,

Ellis achieved satisfactory results using a two millisecond continuous

flashtube light source which operated from the discharge of a bank·of

capacitors.

The last essential ingredient of the first design was a mechanism

to synchronize the timing in order that the light was on and the camera

recording while the desired event was occurring. Ellis solved this

problem by combining a time delay and duration timer.

Upon observing Sutton's results which were not directed toward

studies of stress wave propagation per se, it appeared that the experi-

mental set up could be adapted to investigate stress waves in various

geometries of engineering interest as a primary objective. Accordingly

a second camera assembly has been built incorporating several state of

the art improvements and modifications on the basis of experimental

convenience and solely dynamic photoelastic objectives.

The main features were {l) reasonably high framing rates, of

the order of a half million frames per second, (2) relatively larger

optical field to study larger models, (3) long enough time history of the

events to permit studies of wave reflection and refraction phenomena in

models with low characteristic velocities, (4) a precise start-stop and

timing control, and (5) a reliable, safe, and simply operated design.

The preceding requirements necessitated some changes to the

basic design. For example, the larger field introduced problems of light

3

intensity, already critical because it is necessary to have a very high

film speed or emulsion sensitivity if it is to be activated in exposure

times of 50-100 millimicroseconds. A ten inch diameter field has been

attained by using larger collector lens, opening the gap on the Kerr

cell plates at the expense of increasing the operating voltage to 20, 000

volts, using only one 45 degree planar mirror cut on the turbine shaft -

thus requiring more careful dynamic balance detail design, and

increasing the diameter of the film drum. While 35 mm pictures are

presently being recorded at 100, 000 frames per second, the turbine is

being run at less than half the rated speed and hence 200, 000 frames

per second seems assured. At the expense of reducing the image size

to 16 mm, provisions have been made for printing twice as many

pictures, at the same exposure time, thus again effectively doubling

the framing rate. These last two items have not been demonstrated in

practice however as it has been the experimental philosophy to

increase the turbine speed slowly - and as required for the specimens

under consideration - so as not to come upon a critical vibration speed

unexpectedly.

A magnetic pickup senses the passage of a 128 toothed gear

mounted on the turbine shaft. Each passage generates a pulse which is

amplified and formed into a rectangular shape which activates the Kerr

cell. Exactly 128 pulses are guaranteed by passing the pulses through

a counter containing a gate circuit which closes after the 128 pulses

have passed. Overprinting on the film track is thus prevented.

In over fifty runs on the equipment, there have been two failures

to operate, one due to a burnt out flash tube and one due to a faulty

trigger circuit on the load application mechanism for the model.

II. DETAIL DESCRIPTION

The camera design was broken down into eight major components

as indicated on the block diagram (Figure 1) by appropriate dash numbers:

1 Camera Assembly

2 Kerr Cell

3 Photoelastic Bench

4 Control Chassis

4

5 Pulse Power Amplifier

6 Light Source

7 Initiator Circuit

8 Input Power Control Unit

A isometric drawing of the physical layout is shown in Figure 2.

- 1: Camera Assembly. A schematic drawing of the assembly

is shown in Figure 3. Its main function is to provide a light tight housing

for the pulsed images which have passed through the Kerr cell. After

the images are focused through appropriate lens (Bausch and Lomb,

Baltar, 100 mm, f/ 2. 3) they are reflected through ninety degrees by the

rotating mirror and onto the stationary film track. In Figure 3, most

of the necessary items are shown including the general design of the

mirror itself. Whereas in the earlier Ellis design V-wedge mirror

planes were used, one single plane at forty-five degrees to the turbine

axis was employed. In this manner more light was gathered but the

turbine shaft was unbalanced. A fish-mouthed sleeve with a circular

hole for light passage was therefore designed in order to provide the

necessary dynamic balance. A critical speed calculation, assuming

clamped bearings, carried out in the Analysis Laboratory using the

analog computer indicated that the first or lowest critical bending

frequency would be at approximately 120, 000 rpm.

Located behind the mirror assembly is the timing wheel. As

each of its 128 teeth pass the magnetic pickup - the miniature model

produced by Electro Product Laboratories - a voltage signal is generated.

A typical signal record is shown on the oscilloscope record (Figure 4a).

While it may be remarked that the record has marked deviation in peak

outputs as well as a general overall oscillatory character, the control

chassis will accept and easily distinguish voltage signals from 10

millivolts to 10 volts. Such four decade sensitivity has proven more

than adequate.

The images reflected from the mirror fall upon the film track,

wherein the film lies stationary during a run. The Tri-X or Ilford 35

mm high sensitivity film with a rated speed of 200-400 ASA is stored in

100 foot rolls in a manually, or optionally a motor driven, operated

5

Mitchell camera magazine. The sprocket assembly from a Cunningham

Combat Camera was modified to feed the film into the film track. After

some experimentation it was found satisfactory to push the film through.

Considering that there was nearly 10 feet to feed, the success of this

operation seemed to hinge upon holding the film track dimensions and

not permitting local buckling of the strip. After the initial 10 feet was

loaded, the cranks on the Mitchell film holder of course permitted the

remainder of the roll to be pulled through without difficulty.

As will be observed on Figure 3, a prism was installed on the

front plate to permit focusing the image. The dimensions are adjustable

on the adapter so that the light path to the film track and to the frosted

glass on the adapter were the same. It was also found convenient to

design the adapter to accomodate a 35 mm single frame Leica camera

to record trial runs to check light intensity without exposing, and

developing, a complete 10 foot film strip.

As shown in the photograph (Figure 5) the entire camera

assembly was rigidly constructed of metal, except the front plate which

was made of plywood to minimize the weight, and was mounted on three

adjustable legs to provide levelling and height adjustment.

- 2: Kerr Cell. This component (Figure 6) was fabricated in

the Chemistry Department and operated as designed. It is not a new

development( 3 ) and its principle of operation is described in most text-

books in physics. Certain substances become birefringent when they

are placed in an electric field. This is the well known "Kerr effect".

The birefringence is proportional to the strength of the electric field,

and thus, for a given geometry, to the applied voltage. By appropriate

choice of voltage, the cell can be made to act as a half-wave plate, and

will rotate the plane of polarization of the light through 90°, provided

the plane of polarization of the incident light is 45° to the principle

optical axis of the cell.

The light from the photoelastic set up is therefore polarized at

45° to the principle axis of the Kerr cell. It passes through the cell

and is blocked by a polaroid which is oriented at 90° to the plane of

polarization of the light (In Figure 7, the top of this polaroid is just

6

visible behind the mounting block). However, when the Kerr cell is

pulsed, the light is rotated 90° in the cell, and is able to pass through

this polaroid.

The device thus acts as a shutter, with a speed which is deter-

mined by the length of the applied pulse and the relaxation time of the

nitrobenzene. As the relaxation time is many orders of magnitude less

than the currently used 10-7

second pulse, it has no effect in our case.

At the other extreme, if the cell is open too long - many orders more

than in this design - a lower limit of operation is reached at which the

nitrobenzene boils due to the applied voltage and causes optical

distortion of the transmitted image.

The 128 signals per revolution which are sensed by the magnetic

pickup from the timing disk, are chopped, formed, amplified, and

ultimately applied to the Kerr cell. Thus the time between the one tenth

microsecond pulses is determined by the turbine speed alone, and is

always in precise syncronization with the rotating image so that

uniformly spaced frames, without overlap, are obtained.

Besides polarizing the light when the voltage is imposed, the cell

has the additional feature of filtering the white light source to the extent

of giving nearly monochromatic light without the necessity of introducing

additional filters which would of course reduce the already marginal

light intensity.

It might also be mentioned that while the liquid is sealed within

the cell, nitrobenzene is somewhat toxic and consequently the experiments

are conducted in a ventilated room.

- 3: Photoelastic Bench. The optical system (Figure 9) is

standard and self-explanatory except that the lens used are not believed

optimum for the set up. They are mainly GALCIT equipment from stock

and it is anticipated that improvements can be made by designing new

items for this application. The present system has, however, operated

satisfactorily, and the question is merely one of potential improvement.

When the light source is fired, it remains lit for approximately

two milliseconds, the middle portion of which is essentially flat. The

light is collected by a 10 inch lens and a non-parallel beam passes through

7

the model area. Quarter plates are used to give circularly polarized

light. The converging beam is passed through another lens and quarter

plate and thence into the Kerr cell, through the Kerr cell polarizer, and

into the camera.

Through the tests to date there has been no noticeable distortion

of the image due to using converging light either through the model or

the Kerr cell.

In most of the tests conducted so far the drop rig, shown in

Figure 9, was employed. While other loading devices are deemed more

appropriate in further experimentation, the drop rig was the simplest

with which to carry out the initial tests. A steel ball was restrained by

a magnetically operated plunger at the top of a vertical tube. Upon its

release downward to impact upon the specimen, it interrupted a photo-

cell circuit which provided the input to an initiator circuit to be

described presently. Other loading mechanisms would likewise provide

an initial signal to trigger subsequent action.

4: Control Chassis. Returning to the magnetic signal picked

off the timing disk, it is fed into the control chassis (Figure 1) to be

amplified and formed into a rectangular pulse on its way toward the Kerr

cell. From the original signal given in Figure 4a the resultant signal

shown in Figure 4b is generated. Each pulse rises to an amplitude of

10 volts and returns to zero in one microsecond. The rise time may be

observed in the figure. After forming, the pulse, which is monitored by

a Berkeley Universal Counter (Model 550 I) for the visual information of

the experimenter, is fed into the gate circuit which, when triggered,

passes into a seven stage binary strip. The binary count is displayed

on the control panel (Figure 10) and runs through 128 counts - the number

of teeth on the timing wheel. When the count is complete, the gate circuit

closes, the pulses stop and the Kerr cell remains closed thus preventing

overprinting inasmuch as the camera dimensions are such to provide 128

* 35 mm pictures around the periphery •

Actually four or five pictures at an indeterminant point during the run are lost due to the cut out for the film magazine and blanketing by the prism.

8

- 5: Pulse Power Amplifier. Inasmuch as the 10 volt signal

from the control chassis is considerably less than that required to open

the Kerr cell, it is amplified to approximately 20 kilovolts. With the

exception of the 21 kilovolt, 1. 5 Mfd capacitors and the Solar regulating

transformer, all components were GALCIT designed and represented a

significant amount of time devoted to electronics. The amplifier is

separately controlled as a safety precaution. Its general layout and

size may be observed in Figure 5 or Figure 10 where it lies to the left

of the control panel.

These signals then are those which open and close the Kerr cell

electrical shutter for the camera.

- 6: Light Source. The light source is another important

component inasmuch as a critical problem in high speed photography is

a proper matching of light intensity and film speed. Following Ellis'

experience, a xenon-filled General Electric Model FT 524 Flash tube

rated at 5 kilovolts, 250 Mfd was us ed. The power supply consisted of

a bank of 10 kilovolt, 25 Mfd capacitors; when the design voltage of

5000 was reached, the light, coordinated with the drop rig photocell

signal by appropriate time delay units, was fired.

A photograph of the unit (Figure 11) shows the coiled nature of

the flashtube geometry which did not give uniform intensity and led to

streaks on some of the resulting pictures. At the expense of losing

light a frosted glass was inserted between the source and the collector

lens in later tests to provide diffused light.

The spectral distribution of intensity for the source is given in

Figure 12 and is seen to be relatively flat over the light sensitivity band

of the film. The life of the flash tube for this type operation seems to

be in the vicinity of 100 firings when operated intermittently at voltage

dis charges of 5000 volts and below. The light will not fire if the voltage

is lower than 2000 volts.

- 7: Initiator Circuit. The photocell circuit (Figure 1) is a

standard GALCIT item and has been used successfully for several years.

One unusual feature incorporated into the drop rig pick up (Figure 9) is

the relatively small light source used. Its focal point is interrupted by

the ball to trigger the circuit. In the first tests two pickups four inches

9

apart were used and the velocity of the one inch diameter 0. 15 lb. steel

ball at impact was determined to be 155 inches per second.

- 8: Input Power Control Unit. The last major component of

the camera is the power routing control. The entire system operates

from 120 volt AC, 60 cycle; power is routed to the various individual

power supplies, Berkeley counter, and auxiliary equipment by

appropriate cables.

Generally speaking, with the exception of the separate safety

control on the pulse power amplifier, all controls are centralized in

the control panel (Figure 10) which contains the time delay units, light

source and initiator triggers, the counter, turbine speed control and

lubrication indicator, and auxiliary power. This arrangement has

considerably simplified checkout prior to testing as well as permitting

direct control during experiments.

III. PRELIMINARY RESULTS

The camera has been used over the last few months to perform

a number of exploratory experiments. The specimens tested have been

made from one of the standard photoelastic plastics, CR- 39(4

). When

this plastic is loaded and ¥iewed in circularly polarized light through a

quarter-wave plate and polaroid, light and dark lines or fringes appear.

For CR- 39 subjected to dynamic loading, a given fringe is a line of

constant difference in principal strain(Z), which itself is proportional to

the maximum shearing strain. In order to determine the complete stress

field as a function of time, further measurements and analysis of the

data is necessary. Our program however has attempted to obtain

qualitative data for a number of problems, the most interesting of which

are to be discussed.

A drop rig (Figure 9) was chosen as the simplest method of

applying a dynamic load in these tests. AO. 15 lb. steel ball is held at

the top of a 41 inch tube by a solenoid. Closing the circuit to the solenoid

releases the ball, which falls freely down the tube and strikes the speci-

men at 155 inches per second. The ball trips a photocell, which is

located just above the specimen, and this signal opens the gate circuit to

the Kerr cell amplifier after a suitable time delay.

10

Two fields of view have been used, a 2 1I2 inch diameter field

and a 10 inch diameter field. The 2 1/ 2 inch field provides higher

resolution of fringes, while the 10 inch field allows a longer time to

observe the fringes without interference from the reflection of the stress

wave by the boundary. All pictures included are 35 mm and have been

taken at 70, 000 or 100, 000 frames per second.

Fracture

Because of the interest at GALCIT in fracture and stress distri-

butions at the point of a crack, it was of interest to see if the dynamic

fringe pattern was similar to the static one, predicted by theoretical

analysis(S)• as well as to compare it with the data obtained by Wells

and Post(6), using individual spark photographs. For this reason a

1. 2 x 2. 5 inch rectangular specimen 1I4 inch thick was prepared. A

small slot 1/ 4 inch deep and ten thousandth of an inch wide was cut in

the top to accommodate a Shick razor blade, chosen for its low aspect

ratio and consequent rigidity (Figure 13). The blade protruded

approximately 1/ 16 inch over the top of the specimen and was contacted

by the falling steel ball. Figure 13 shows interesting sections of the

complete record obtained.

First of all it is observed that as the force introduced by the ball

is transmitted to the specimen, the stress gradually builds up without

any immediate fracture. Furthermore the gross appearance of the

fringe pattern possesses the characteristic "bug-eye" appearance

predicted for the static case(S) (Figure 14), spoiled somewhat of course

in sharpness because the width of the crack is actually finite, and hence

the vertex is rounded. With time the load builds up as indicated by the

increasing number of fringes until at about the third or fourth picture

(separated timewise by 14. 5 /.). seconds) the ultimate load is reached

and the crack appears to accelerate. The time of running is affected by

many factors of course, not the least of which are the generally compres-

sive nature of the stress field, the local stress condition after machining,

and the interference of reflected waves which take approximately 20

microseconds to cross the specimen.

11

The first clear indication of the propagation may be noted on

the ninth frame after contact where the gross "bug-eyes" have given

way to an elliptic-like shape. This qualitative characteristic pattern

predicted statically (Figure 14) may be associated with an antisymmetric

stress field due to the blade not being precisely centered in the slot and

hence contributing a high localized shear stress. In the eleventh frame

the "bug-eyes 11 are beautifully reestablished at the crack front and

carry very plainly through six frames until the crack breaks through

and the stress field unloads completely in the latter frames of the

second row.

Returning to the first frame for a moment it will be noted that

the ball emerging from the tube is pressing upon the razor blade.

Beginning in the third row, where several frames are missing as may

be noted by the coded numbers on the film strip, the ball has now pushed

the blade into the plastic and has itself contacted the specimen. Due to

a slight antisymmetry the dynamic Boussinesq fringes are not perfectly

paired, although the second frame is coincidentally remarkably

continuous across the crack (as it should be because the fringe value or

shear is zero at the crack). These latter frames are included to give a

striking visual illustration of the complex interaction to be expected

when the waves have time to reflect from free and fixed boundaries.

Before making any semi-quantitative deductions at all from the

strips, consider the next specimen, shown in Figure 15. In contrast to

the previous case where the crack was loaded, an experiment was tried

wherein a similar specimen was inverted and simply supported with the

crack on the bottom. It was then impacted on the top as indicated in the

figure with the resulting 100, 000 frames per second fringe pattern as

shown. (The striations observed, as mentioned earlier, are due to the

undiffused helical light source.) Reading from the top left down, the

characteristic Boussinesq pattern is exhibited. As it progresses to the

supports and across the bar sensing the presence of the crack, a

reflected signal observable at strip number 38 and firmly established at

39 indicates the crack progressing toward the load. While the pattern

is complex it appears that the crack accelerated too quickly for the

quasi-static "bug-eyes" to appear before complete fracture.

12

In order to explore this point a bit further, a crack front

position vs. time plot was prepared based upon reading the film strip

in an enlarger and gave the data shown in Figure 16. It is immediately

noticed that for this geometry, the loaded crack reached a maximum

speed only half that of the unloaded crack. It is interesting to observe

the very rapid acceleration in the latter case and the quantitative value

of the propagation - 17, 700 inches per second. If one uses Clark's

value(4

) of the sound velocity, viz. 60, 000 inches per second, the

propagation speed can not be less than 30 per cent of the sound velocity,

or approximately 50 per cent of the shear velocity.

Considering the qualitative nature of this experiment, the values

are in reasonably close agreement with Wells and Post's, although the

records seem to indicate that the acceleration - for the unloaded crack -

was a bit more rapid than their case which would tend a bit more toward

their theoretical expectations.

Layered Media

Another set of experiments pertained to layered media. Such

geometries are of fairly wide concern in aeronautics, civil engineering

and atomic warfare. Generally theoretical treatment is difficult if not

impractical, but the initial tests indicated that two-dimensional tests at

least could be conducted simply with quantitative interpretation. In

Figure 17, the same drop rig has been used to apply a load to a

rectangular specimen of CR- 39 which was separated into two pieces

separated by a section of electrical tape having of course a different

modulus. It was desired to examine the feasibility of recording wave

transmission phenomenon such as is illustrated in the figure. To add

a bit of additional practical interest, a circular hole was cut in the

lower piece of CR- 39 and consequently the results show not only a

transmission delay but also the pas sage of the transmitted wave

around the inclusion giving rise to a dynamic stress concentration

factor. The stress pattern is quite symmetrical with the expected

clover-leaf pattern very apparent. Inspection of the film strip in an en-

larger indicates that quantitative analysis is perfectly feasible. Hence

the effect of parametric changes in materials, relative thicknesses and

changes in the shape of the inclusion can be evaluated without undue

difficulty.

13

Simulated Head Studies

The third set of tests to be described relates to the impact of

ogive type specimens with variable head angles. Figure 18 shows a

set of data using the drop rig and a 70, 000 framing rate which was

among the earliest records obtained. Here a qualitative idea of the

cone angle magnitude was desired for which the wave front remained

essentially planar. In the limit for very small included angles or

wedges, one would normally treat the problem theoretically as a

* one-dimensional wave by simply replacing.:_ dC by.:! • From the records it appears the one-dimensional assumption be-

comes increasingly accurate for included wedge angles less than 60 degrees.

Following up the wedge tests, another series was run at 70, 000

frames per second for a 90 degree included angle with a rectangular "after-

body" (Figure 19) which was used to compare with the same geometry

except it was notched symmetrically (Figure 20). The constricting effect

of the notch is quite evident by simply comparing the fringe density in the

upper and lower sections. While data interpretation in the vicinity of the

corners would be difficult more generous fillets in this region would

permit straightforward quantitative analysis inasmuch as the fringe

patterns are satisfactorily distinct.

For the final test in this set, the previous specimen was again

used except the central part was removed to simulate the cross section

of a rocket head (Figure 21 ), although it hardly need be remarked that

the wall thickness is relatively oversize. Again the steel ball was

dropped on the point of the head and the resulting fringe pattern observed.

The separation and diffusion of the load down the two legs of the "tuning-

fork" in a most symmetric fashion is easily observed. Moreover the

skew wave front indicates the bending or flexural character of the wave

transmission which proceeds through the length of the specimen in very

close to the 50 microseconds expected. A fracture occurs at about the

fifth frame and the propagating crack runs into the reflected stress field

from the maximum stress point at the radius of the inside ogive contour.

Fracture is complete by the ninth frame and in all the subsequent pictures

the two legs are behaving as two independent bodies.

*While ·it is to be emphasized that the fringes are not necessarily dilitational - actually they are maximum shear strain lines, considerations of symmetry and boundary conditions usually permit proper interpretation without additional data such as the dynamic isoclinics . This point deserves careful consideration for quantitative analysis however.

14

IV. CONCLUSIONS

In reviewing the program, it is believed that the exploratory

studies have established that the camera design is satisfactory to

achieve quantitative dynamic design data for a considerable number

of engineering problems.

It is, of course, obvious that there are places where improve-

ments can be made, most particularly in the optical system where it

is known that the optimum system has not been used. Furthermore, a

more appropriate loading mechanism should be designed to simplify

quantitative analysis; also certain state of the art improvements can

be introduced in any research tool. In addition, certain advancements

will be required in the theoretical area as well as in determining and

interpreting material property data, especially if other than CR-39 is

contemplated.

Nevertheless it is the opinion of the authors that an important

and convenient tool has been dem·onstrated for dynamic analysis. The

proper quantitative exploitation remains.

ACKNOWLEDGMENT

The authors wish to acknowledge the able assistance of other

present and former members of GALCIT who have contributed to this

program. In particular the consultations with Prof. E. E. Sechler

and the mechanical design work of Mr. A. E. Gaede has been

especially helpful.

15

V. REFERENCES

1. Sutton, G. W.: Study of the Application of Photoelasticity to the Investigation of Stress Waves. Thesis in Mechanical Engineering, California Institute of Technology, June 1955. See also an abbreviated version, A Photoelastic Stud of Strain Waves Caused by Cavitation. Journa of App ied Mechanics, ept. 19 no. 3, p 340.

2. Ellis, A. T.: Observations on Cavitation Bubble Collapse, Thesis in Mechanical Engineering, California Institute of Technology, 1953.

3. White, H. J.: The Technique of Kerr Cells, Review of Scientific Instruments, v. 6, 1935, pp 22-26. See also: Kingsbury, Rev. Sci. Instr., v. 1, 1930, p 22. Beams, Rev. Sci. Inst., v. 1, 1930, p 780. Dunnington, Phys. Rev., v. 38, 1931, p 1506.

4. Clark, A. B. J.: Static and Dynamic Calibration of a Photoelastic Material, CR-39, Report 4779, Naval Research Laboratory, June 1956. See also Soc. Exp. Stress Analysis, vol. 14, n. 1, 1957, pp 195-204.

5. Williams, M. L.: The Stress Distribution at the Base of a Stationary Crack, Journal of Applied Mechanics, March 1957.

6. Wells, A. A. and Post, D.: The Dynamic Stress Distribution Surrounding a Runnin Crack - A Photoelastic Analysis, Report 4935, Nava R ...::search Laboratory, Apri 19 ee a so Soc. Exp. Stresd Analysis, vol. 12, n. 1, 1954, pp 99-116.

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Mitchell Camera Model 54 L

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Typical of 8 Bolts Securing Front Plate. Note Front Plate Is Removable .

Figure 3. Camera Assembly - Schematic .

19

Figure 4.

a. Magnetic Pickup Output. b. Control Chas sis Output.

20

Figure 5, General View of Pulse Power Amplifier,

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Figure 9. General View at Drop Rig Showing Typical CR-39 Specimen

in Place.

25

Figure 10. General View of the Camera, Amplifier and Control Panel.

From Top to Bottom on the Panel: Two Delay Timers,

Light Source Capacitor Control, Firing Panel, Counter,

Turbine Control, Photo-cell Control.

26

Figure 11. Close up of the Light Source and Collector Lens.

14

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Figure 14. Static Isochromatic Fringe Patterns.

n II ,, {' (j {j {J ,, ,, ,~

30

{~~~~EL BALL 0 .15LB. 155 IN./SEC. T L2"

o.010"--n:.10.2s " .l

MATERIAL, CR 39 1/4" THICK

FRAMING RATE

100,000 FRAMES/SEC .

Figure 15. Dynamic S tr e ss D istribution f or an Unloaded Crack.

Framing Rat e 100, 000 F r a m e s p er Second

31

I. 0 (/) Maximum Velocity Q)

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[7 Ref. Fig. 15 -- -

0 50 100 150 200

Time - fl Seconds

Figure 16. Crack Length vs. Time.

ELECTRICAL

TAPE -

32

~.....:;...._,_r:-112"

T, .. 0 114

l/4"DIA. _l 1-1·~

MATERIAL, CR 39 114" THICK

FRAMING RATE

70,000 FRAMES/SEC. LOAD, I" STEEL BALL 0 .15 LB. 155 IN./SEC.

Figure 17. Dynamic Stress Distribution in a Layered Media Having

an · rnclusion.

33

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Figure 18. Wedge Angle Effect Under Impact .

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