Dynamic Loading of Thin-Walled Cylinders with Detonation Waves
Basic data for design of equipment to withstand high transient pressures
SOME
processes which operate a t high temperatures and pressures involve the use of explosive or detonable gases. I n designing equipment to withstand detonations, data are needed concerning pressures developed by stable normal detonations, as well as pressures arising when stable detonation waves are reflected from a n obstacle and during formation of detonations. Also, information is required concerning stressstrain behavior of materials of construction. Data concerning pressures developed by stable normal detonations and by the reflection of these waves from an obstacle are available (7, 2, 4 ) . However, data for pressures during formation of detonations are meager, although it has been sho\+n that pressures higher than those for normal stable detonation are developed ( 3 . 8- 70). I n one study of stress-strain behavior for materials subjected to dynamic loading (6) rupture disks were loaded with reflected detonation waves to determine the relationship between static and dynamic impact bursting pressures. The present report is a related study in detonative loading of thin-walled cylinders.
JAMES A. LUKER and STANLEY A. MOSIER' Syracuse University, Syracuse, N. Y.
HOT WIRE IGNITER7
7 D . C . SOURCE
TO GAS CONTROL SYSTEM RECORDING CAMERA
DETONAT'ION TUBE
CATHODE RAY OSCl LLOSCOPE
1
e
3-STAGE AMPLIFIER /
TEST SPECIMEN WITH
Apparatus
Seamless tubing (Superior Tube Co.) of Type 304 stainless steel, used for test specimens, was thin-walled so that lower detonation pressures could be used without reducing precision of measurement.
STRAIN GAGE T BRIDGE Present address, Pratt and Whitney Aircraft Co., Hartford, Conn.
LDETONATION TUBE EXTENDER
Figure 1 . Two major parts of the dynamic measuring system supplied detonative force and measured deformations VOL. 51, NO. 4
APRIL 1959
589
Tubing Specifications Nominal o.d., inch
0.75
-0.000
Nominal i.d., inch Nominal wall thickness, inch Commercial straightness tolerance
0.710 f 0.000 -0.005
0.020
POSITION OF S R - 4 GAGE
,/-
4-0 . 0 0 5
* 10% 1/600
Analysis
Element C Mn Si P S Cr Ni
Max. % 0.08 2.00 1 .oo
Figure
0.03 0.03 18-20 8-11
3.
Strain gage for indicating deformation was attached t o specimens
T h e dynamic measuring system consisted of two major parts (Figure 1)-
f DETONATION TUBE BAR
EXTENDED DETONATION TUBE
-
Figure 2. Specimen adapter was constructed so that internal diameters o f specimen and detonation tubes matched
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INDUSTRIAL AND ENGINEERING CHEMISTRY
equipment for supplying detonative force and that for measuring the resulting deformation. The detonating agent, a stoichiometric mixture of hydrogen and oxygen contained in a specially designed high pressure storage tank, was fed to the loading tube through Type 304 stainless steel pressure tubing (0.25 and "32 inch in outside and inside diameter, respectively) and 30,000 p.s.i. stainless steel needle valves. The loading, or detonation tube, was an 8-foot section of seamless steel tubing, 0.687-inch inside diameter, with a wall thickness of 0.313 inch. Its length was such that a stable normal detonation wave could be established (5). T h e specimen tube adapter, detonation tube extender, and rupture disk assembly were located at one end, and a t the other end were the source of ignition (hot wire) and the gas entry tube. Because the detonation wave had to travel unrestricted with no discontinuities in the loading tube, the specimen adapter (Figure 2) had to be constructed so that the internal diameters of the specimen tube and the detonation tube matched almost exactly. T h e specimen also had to be held flush to the detonation tube while acting as an extension of the original tube. Also, the adapter had to retain an initial gas pressure of around 300 p.s.i. By employing a double O-ring seal in a steel cylinder that was in turn welded to the detonation tube, a satisfactory adapter was obtained. T h e downstream specimen adapter was identical to that of the upstream, except that it had a 13-inch detonation tube estender of the same diameter as the original welded to it (Figure 2). These two parts of the adapter assembly held the specimen in place by the use of steel flanges and stringers. A standard 0.75-inch rupture disk assembly was screwed to the end of the tube extender. It was thus possible to study the effect of normal waves and the combination of normal and reflected waves simply by using either a weak or strong disk.
E Q U I P M E N T TO WITHSTAND D E T O N A T I O N system. The desired pressures were obtained by manipulating the series of control valves and reading the pressure on either a 0 to 60 or a 0 to 400 p.s.i. pressure gage. When the detonation tube was filled with the detonable gas mixture at the desired pressure, energy was supplied to the hot wire igniter by a battery booster. The strain set up in the specimen from the resulting detonation was recorded on the oscilloscope using the Polaroid Land Camera. This procedure was repeated with stepwise increases in the initial gas pressure until the “dynamic elastic limit” of the specimen was reached. The specimen for studying the plastic region was basically the same as that described above for the elastic region. However, instead of a strain gage being applied a t the center of the specinlen, the periphery at that point was divided into 10 increments. Then the diameter a t each of these points was measured with a micrometer. The specimen was
STRAIN LINE
STRAIN AMPLITUDE ( A )
I
I
I
I
I
I
1
-TIME Figure 4. Typical oscillogram of dynamic elastic strain shows large vibrations resulting from “overshoot” caused by detonative loading force
The type of strain gage chosen for indicating instantaneous average deformation was the Baldwin-Lima-Hamilton SR-4, Type PA-3 gage. T h e strain gage was attached to the 6-inch tubing specimens as sholvn in Figure 3. The nucleus of the dynamic strain measuring system was the Dumont 324 cathode ray oscilloscope equipped with a fixed-focus Polaroid Land camera. The oscilloscope frequency response was flat to 100.000 c.p.s. EmpIoyed in conjunction with this oscilloscope was the Ellis Associates BA-12 strain gage bridge. The frequency response of the Ellis a.c. amplifier was flat u p to 25,000 C.P.S. Because the frequency response of the strain gages when subjected to detonation loading was assumed to be above 25,000 c.P.s., the amplifier in the BA-12 was not utilized. Instead, a Fairchild Decade amplifier Model 203 rated at ( 1 0 . 5 db.) from 5 C.P.S. to 3.0 mc. with a pulse response rise time less than 0.1 microsecond was used. The static system was essentially the same as the dynamic system except for the method of loading. Force for the static loading was supplied by a handoperated .4merican Instrument Co. hydraulic pump.
strain gage. T h e detonation tube and specimen were evacuated after which the detonable gas mixture was fed into the
Procedure
Dynamic Loading. Six-inch tubular specimens with Type P,4-3 strain gages bonded to them were inserted into the specially prepared adapters (Figure 2), and the stringers were tightened until just taut. The active gage was then adjusted to zero by manipulating the oscilloscope! amplifier, and Ellis BA-12 until no deflection on the oscilloscope was observed with zero load on the active
NOMINAL FIBER STRAIN, 1NJIN.x 10Figure 5. Stress-strain curves for elastic region were obtained by two methods, and in one case ( B ) had to b e shifted because a finite strain a t zero stress resulted A.
Static.
8.
Dynamic.
C.
Shifted dynamic, no points
VOL. 51, NO. 4
APRIL 1959
591
inserted into the adapters and was subjected to a dynamic load. T h e stress resulting from the detonation was from either a normal detonation wave or a normal plus reflected detonation wave combination. For this case where the former was to be studied, a low-rated rupture disk was employed
described for the static region. Readings of applied pressure us. deformation were then taken up to the breaking pressure of the sample tubes which was 3850 p.s.i.g. These readings were then converted into nominal static hoop stress and nominal static strain in a manner described later.
Discussion of Results
/
~
/
I
/
€in STRAIN,
Stable normal detonation pressures were taken from the calculated parameters of Luker, McGill, and Adler (7). Their results were plotted as normal detonation pressure us. initial knallgas pressure, and a least regression line was fitted. The equation of the line was P, = 19.6 PO. This relationship was used throughout to determine the loading force due to the normal detonation wave.
etn
E
100
Figure 6. Above 1470 p.s.i.a. the strain gage did not function properly and instantaneous strain was obtained graphically as shown
in the assembly at the terminus of the detonation tube extender. For the latter, a high-rated rupture disk was used. The strain created by either of the above stresses was determined by the difference in the dimension of the tube diameter at the center of the specimen before and after the detonation. This difference divided by the original outside diameter of the tube was equal to the residual strain set up in the tube from the detonation wave. Static Loading. T h e specimen for this investigation was identical to the sample employed in the study of the dynamic elastic region. When the specimen was in position, the active gage was then balanced out in the same manner as in the dynamic elastic study. High pressure oil was fed through the system to flush out any air, then the pressure was increased to the desired level by manipulating the hydraulic pump. Readings of internal pressure were made on either a 0 to 4000 or a 0 to 20,000 p.s.i.g. pressure gage. Strain readings at desired pressures were obtained from the strain gage, BA-12, and oscilloscope system. Readings were obtained in this manner for applied pressure us. deformation up to the elastic limit for this particular set of circumstances. Beyond the static elastic limit, the specimen employed and the method for determining the strain in the specimen were basically the same as those used for studying the dynamic plastic region. T h e method of applying stress to the specimens was the same as the method
592
Strain gages used in the elastic region were calibrated using the standard simulated static-strain calibration technique. This procedure is questionable for the dynamic phase of the investigation, but the dynamic stress-strain curves should yield the proper slope even if the quantitative value of true strain is in error. Oscillograms which related deformation as a function of time were employed to determine the dynamic strain when the specimen was subjected to a detonative force. A typical oscillogram is shown in Figure 4. The signal oscillations formed an envelope and appeared to vibrate about a mean that was above the datum line of the oscillogram. These large oscillatory vibrations were considered to be the result of “overshoot” created by the detonative loading force.
90
-
80
0 X
a:
70
m”
a
60
l-
tn
&
50
0 I E
w 40 m -
LL
5
30
Z
0
20 IO
0 -
IO
0
20
30
40
50
NOMINAL FIBER STRAIN,
60 70 80 I N . / I N . X 103
90
Figure 7. Stress-strain curves for elastic and plastic regions showed that normal detonation wave caused little damage to specimens up to 58,000-p.s.i. stress
INDUSTRIAL AND ENGINEERING CHEMISTRY
A.
Static us VS. e t b
B.
Dynamic uIIVI.
~t(,,+~)
C.
Dynamic u s vs.
et,
E Q U I P M E N T TO W I T H S T A N D D E T O N A T I O N
NOMINAL FIBER STRAIN,
IN./IN. x IC
Figure 8. Tubular specimens showed remarkable hyperelastic resiliencewhen subjected to normal detonative loading
Because the initial strain was considered to be of greatest importance, two schemes were employed to obtain this strain. I n the first scheme, the initial strain signal \vas arbitrarily bisected, and the strain corresponding to this amplitude was obtained from the calibration curve of strain LIS. deflection. This was done for each dynamic loading in the elastic region. These results are presented in Figure 5 > c:urve B , and show a finite X intercept. Because a finite strain at zero stress is impossible, the stress-strain line was shifted parallel to itself so that it passed through the origin. I n the second scheme, the above procedure was verified. The 10 consecutive oscillations on a n oscillogram from the second to the 11th were bisected as shown in Figure 4. T h e strain line was drawn through the points of bisection and extrapolated to zero time. T h e amplitude of the extrapolated strain line a t zero t i n e was taken as the measure of strain. In every case tried using this scheme, the results agreed within experimental accuracy with the corrected stress-strain line (Figure 5 , curve C). SR-4 strain gages could not be used to indicate deformation for normal detonation pressures higher than approximately 1470 p.s.i.a. Above this pressure the strain signal was distorted and non-
intelligible. T h e inability of the strain gage signal to function was probably due to failure of the Type PA-3 bonding cement as the elastic limit was approached. Thus, for loadings in the postyield region at pressures greater than 1470 p.s.i.a. the technique as illustrated in Figure 6 was used. The residual strain e
