n 123-60530s-3825a: t. o. 1 stress wave propagation...used to record dynamic photoelastic stress...
TRANSCRIPT
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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
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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.
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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
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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
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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
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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
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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
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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.
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- 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
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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.
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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.
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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.
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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.
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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.
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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.
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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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IT 9
0
Fig
ure
1.
Blo
ck
Dia
gra
m o
f H
igh
Sp
eed
Ph
oto
ela
stic
Cam
era
Dra
win
g
Seri
es
X-2
92
.
...... "'
-
P
Po
lari
ze
r
QP
Q
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rte
r P
late
A
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aly
zer
s S
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men
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l _t1
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lse
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s 9
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it
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sing
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Film
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Fra
me
A
sse
mb
ly
Fig
ure
2.
Sch
em
ati
c L
ay
ou
t o
f th
e C
am
era
Ass
em
bly
.
......
--.I
-
----Back Plate
Turbine Assembly
Magnetic Pickup,
Ai research Turbine
18
Mitchell Camera Model 54 L
Box With Cunningham Sprocket Assembly
Prism For Focussing and Single Frame Recording.
\Adopter For Mounting Leica Single Frame Camera . Frost Gloss and Cover Plate Not Shown .
Front Plate
°'"\ Lens Mount Kerr Cel I
.------./ 1 t
LL ens Assembly Bausch 8 Lomb Balter IOOmm, f/2 .3
..--+--1--- Fi Im Track
Rubber Tubing Seal
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,
Kerr Cell and Camera.
-
T
15
/161
1 1
u ..----~1
I --
---
-· ' -
----
, I
II
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J:
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er
to
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x
,...
11/16~
Nic
kel
Pla
tes
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e 11
Fi 1
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to
9
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m e
W
ith
N
itro
B
en
zen
e
(Ea
stm
an
K
od
ak
38
7 )
Fig
ure
6.
Kerr
Cell
.
Silv
er
So
lde
r
N ,_.
-
22
Figure 7. Close up of Kerr Cell.
-
Fro
sted
G
loss
I011
Dio
. Pol
aroi
d
22
11F
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/2.2
C
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nser
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2 i'2
D
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roid
Axi
s 4
5 °
To K
err
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laro
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In
cid
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31
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L. f /.
75
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culo
rily
Po
lari
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2 V2
Dia
. Qu
art
er
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1
00
mm
. F
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14
011
=
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Fig
ure
8.
Ph
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ela
stic
Ben
ch
, 1
011
F
ield
.
N
VJ
-
24
~ :-1
:11
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
0 --~~~---,,--~~~--.-~~~~~~~~~-.--~~~~-,.--~~~~~
Xen
on
Fla
shtu
be
~
0 ...
10
0 ~<
l
Blo
ck
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y S
pe
ctr
um
Fo
r 7
00
0 °
K
Q) ~
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Q) >
-6
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40
20
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00
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To
tal
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tpu
t 3
00
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att
-Se
c.
G.E
. F
lash
tub
e N
o. F
T 5
24
Re
f: G
en
era
l E
lectr
ic C
o.
60
00
Wov
e le
ng
th -
An
gst
rom
s
Fig
ure
12
. S
pectr
al
Dis
trib
uti
on
fo
r th
e F
T 5
24
Fla
sh
Tu
be.
70
00
N
...J
-
SC
HIC
K
RA
ZO
R ~----
i" S
TE
EL
BA
LL
B
LA
DE
T
r===
=z=,
0
.15
LB
1.20
" -l~o.010"
155
IN /
SE
C.
_J_
.__
__
_ ~
MA
TE
RIA
L,C
R 3
9
FR
AM
ING
RA
TE
1
/4"
TH
ICK
7
0,0
00
FR
AM
ES
/SE
C.
NO
TE
: S
IX F
RA
ME
S A
RE
MIS
SIN
G
BE
TW
EE
N
24
A A
ND
35
A
Fig
ure
1
3.
Dy
nam
ic S
tress D
istr
ibu
tio
n f
or
a L
oad
ed
Cra
ck
.
Fra
min
g R
ate
70
, 0
00
Fra
mes p
er
Sec
on
d.
N
00
-
~I o Crock 'O c:
6 8 CD
IX= Xo I
2. 9
y
r
x
14 o - GEOMETRY
Crock
14 b- SYMMETRIC FRINGES
Grae
n"'r-1/2
14 c -ANTI - SYMMETRIC FRINGES
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)
.c 8 600 ln./Sec. (.) 0.8 c
..c ..... 0.6 O'l c: Q) _J
..x 0.4 (.)
0 ..... 0
0.2 Ref. Fig. 13
0 50 100 150 200
Time - fl Seconds
(/) I. 0
Q)
..c (.)
c 0.8
..c ..... 0 .6 OI
c Q) _J
~ /7
..x 0.4 (.)
0 ..... 0
0.2 I Maximum Velocity 17,700 In. /Sec .
[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
•
Figure 18. Wedge Angle Effect Under Impact .
-
LO
AD
, I
11 S
TE
EL
B
AL
L
0.1
5 L
B.
15
5
IN./
SE
C.
17
,, 2.
0 1~
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.94
7"
r-
MA
TE
RIA
L,
CR
3
9
1/4
11
TH
ICK
70
,00
0
FR
AM
ES
I S
EC
ON
D
Fig
ure
19.
D
yn
amic
Fri
ng
e P
att
ern
s fo
r a
45
° W
edg
e-B
od
y C
on
fig
ura
tio
n.
VJ
~
-
LO
AD
I"
S
TE
EL
B
AL
L
0.1
5 L
B
15
5
IN./
SE
C.
L o.~ t
o.n +
0.4
0· t
o.sr
· _
L..
..._
__
-..J
0. 2
.
--i
0.9
47
r-
MA
TE
RIA
L,
CR
3
9
70
,00
0
FR
AM
ES
/SE
CO
ND
Fig
ure
20.
D
yn
amic
Fri
ng
e P
att
ern
s fo
r a
45
° N
otc
hed
Wed
ge-
Bo
dy
Co
nfi
gu
rati
on
.
UJ
U1
-
t
45° T~
-
2.0
" 0
.32
8"
l ~
--1
0.9
4if
---
MA
TL
., C
R
39
1
/4"
TH
ICK
FR
AM
ING
RA
TE
7
0,0
00
FR
AM
ES
/ S
EC
LO
AD
, 1"
ST
EE
L B
AL
L
0.1
5 LB
15
5 IN
./S
EC
.
Fig
ure
21
. D
yn
am
ic F
rin
ge P
att
ern
s in
th
e C
ross
-Secti
on
of
a
Sim
ula
ted
Ro
ck
et
Head
.
w
O'