F ACTORS AFFECTING THE TIME TO BURST IN EXPLODING WIRES *

Charles P. Nash and Clifford W. Olsen Department of Chemistry University of California, Davis

Studies of AI, Cu, Ag, Au. Pd, and Pb wires are being conducted using a condenser bank of 11.4 kj maximum storage capacity. The order of increasing times to burst, which is not the same as the order of decreasing first-pulse energies, is Pb < Al <Au < Ag < Cu ""Pd. Results with numerous sets of Al samples of constant length but cross sections varying by a factor of about 25 show a linear relationship between the cross-sectional area A and the time to burst, at constant initial voltage. This linearity is shown to be consistent with a theoretical relationship, previously derived, which emphasizes the bydro­dynamic energy per unit length and the radial expansion.

INTRODUCTION

The exploding wire phenomenon proceeds in three more or less well-defined stages [1). At the instant of closure of the circuit, cur­rent flows through the sample. After some time has elapsed the current flow ceases and the "dwell" or "pause" begins. At some later time the discharge reignites and the energy remaining on the condenser bank is dissipated. Under various conditions, of course, one or more of these stages may be absent. Nevertheless, any com­plete theory of the mechanism of the phenomenon must account satisfactorily for all of these processes.

Since all of the subsequent behavior of the exploding wire must be in large measure dependent on its very early history, it is im­portant to study the first pulse in some detail. We have undertaken to examine the way in which the first-pulse durations and energies vary from material to material, as well as with the dimensions of various samples of the same material. The experiments on pulse durations are fairly complete, but the data on first-pulse energies are fragmentary.

On the basis of our data it is possible to give at least a quali­tative interpretation of one of the important aspects of the first pulse, namely, the time to burst.

*Supported by the U.S. Atomic Energy Commission through the Lawrence Radiation Labo­ratory, Livermore.

5

W. G. Chace et al. (eds.), Exploding Wires© Plenum Press New York 1962

6 Nash and Olsen

EXPERIMENTAL

The condenser bank used in these experiments is of conventional design. Voltages up to 20 kv are available, and one to four 14.2-l1f, low-inductance capacitors may be used. The inductance ofthe circuit, based on its ringing frequency ,is 0.3 /Lh. Oscillograms were obtained by using a Tektronix Type 555 Dual Beam Oscilloscope equipped with two Type 22 Time Base Units and two Type L Fast-Rise High-Gain Preamplifiers. With one beam we monitor either the condenser voltage or the voltage across the load, while the other beam displays the voltage induced in a small search coil placed near the sample. The voltage across this coil is proportional to the time derivative of the current in the circuit.

We have exploded (in air) six sizes of copper wire, six sizes of aluminum wire, four sizes of silver wire, and two sizes each of gold, palladium, and lead wires. Whenever possible we have meas­ured the first-pulse energies and the times to burst. We shall henceforth define "time to burst" (TJ as the interval between the first apparent deflection of the dl/dt trace and the apex of the prominent inductive spike.

RESULTS

Figures 1 and 2 present typical data on the time to burst for 7.1-cm lengths of aluminum, copper, and silver wires exploded using 28.4 I1f at various voltages. From these figures it is evident that Tb depends on both the wire cross section and the initial voltage for all three metals. In particular, there is nearly a linear increase in Tb with the mass per unit length for each of the materials. From the data in Fig. 3 it follows that this linear behavior also obtains for other capacitances and wire lengths.

Figures 1 and 2 also show that for a given wire size and initial voltage the order of increasing burst times is Al < Ag< Cu. By com­paring data similar to these for all the metals which we have studied, an order of increasing TbS may be written as follows:

Pb < Al < Au < Ag < eu '" Pd

It is noteworthy that the oscillograms for exploding palladium are rather different from those of the other metals. Figure 4 is a composite of dl/ dt traces for silver and palladium. Here it is clear that a double discontinuity occurs with Pd. A hint of this behavior

Nash and Olsen

0.0451"

<[ ILl a::

BaS ifl I8 <[

-.J I-ALUMINUM· 20 KV <[

2-SILVER-20 KV z 0 3-ALUMINUM -15 KV ~ u 4-SILVER -15 KV ILl (J) 5-ALUMINUM - 10 KV I

(J)

VI 0 a:: u

#20 0 ~

-.J 0.0297" <[ z 0 ~ a:: 0 Q. 0 a:: Q.

ILl #24 ~ <[ z 0 a:: 0

#30

.11134 0 2 3 4 5 6 7 8

Tb ( MICROSECONDS)

Fig. 1. Time to burst as a function of wire size for 7.l-cm lengths of aluminum and silver wires exploded using 28.4-fJf bank at voltages indicated.

7

8 Nash and Olsen

Bas" 18

I-ALUMINUM -20 KV

2-COPPE R - 20 KV

3-ALUMINUM - 10 KV

4-COPPER- 15 KV

5-COPPE R - 10 KV

ex w a:: ex ...J ex z #20 0 I-<.> w (J) , (J)

(J)

0 a:: <.>

0 I-

...J ex z 0 I-a:: 0 0-0 a::

#24 0-

w I-<l

~ 0 a:: 0

# 28

o 2 3 4 5 Tb ( MICROSECONDS)

6 7

Fig. 2. Time to burst as a function of wire size for 7.1-cm lengths of aluminum and copper wires exploded using 28.4- J.Jf bank at voltages indicated.

8

Nash and Olsen

0.0613 "

ALUMINUM

1-7.4 CM ,42.6,uF. 20 KV

2-15.1 eM, 56 .8 ,oF , 20 KV ct ~ 3-7.4 CM. 42.6 pF , 10 KV e;[

-.J e;[ z 0 I-(.) W (/) , (/)

(/)

0 c:: u

0 I-

-.J ct z 0 I-a: 0 a.. 0 c:: a..

W l­e;[ Z o a:

B8S" 18

11'20

o "24

o 4 6 8 Tb (MICROSECONDS)

10 12

Fig. 3. Time to burst as a function of wire size for 15.1- and 7.4-cm lengths of various aluminum wires exploded using 42.6 /If and 56.8 /If at voltages

indicated.

9

10

~ SILVER c( z o ~ PALLADIUM

4. o II: 4.L-~ __ ~ __ ~ __ L-~ __ ~ __ ~~~~ __ ~

Nash and Olsen

Fig. 4. Composite of dl/ dt traces for exploding silver (upper trace)andpalladium (lower trace). Horizontal scale: 1 Jl sec/division; 7.1 em, 8& S 24 gage, 28.4 Jl f,

15 kv.

also occurs with copper, aluminum, and lead, butthe extra "dip" is much less pronounced. Kvartskhava et al. [2] have previously noted that the oscillograms for exploding platinum and nickel, as well as a few other metals, show a region over which the current does not change appreciably. Our results indicate that palladium, which in­terestingly enough is in the same column ofthe periodic table as Pt and Ni, shows the same explosion characteristics.

Table I gives first-pulse energies for the explosion of 7.1-cm lengths of B & S 24 gage samples usingthe 28.4-f.Lf bank at 10 kv. This table also contains the energy required to vaporize the samples com­pletely, as calculated from thermodynamic data for these elements [3].

Table I. Explosion of 7.I-cm Lengths of B&S 24 Gage Wires of Various Metals (28.4 p.f at

10 kv)

Metal E fp• kj 'lb. }J-sec Evap. kj

Al 0.80 3.19 0.539 Ag 1.0 3.43 0.468 Pd 0.74 4.36 0.849 eu 1.2 4.60 0.806

Table II contains the first-pulse energies for 15-cm lengths of various copper wires exploded at 15 kv using42.6 and 56.8 /Lf. From these data it is clear that the energy dissipated in the first pulse increases about as rapidly as the cross-sectional area for the larger wires.

Table III presents data obtained on two pairs of copper wire samples and one pair of silver wire samples having different areas

Nash and Olsen 11

Table II. First-Pulse Energies

B & S gage Diameter, E[p' kj E VBP ' kj

mm (42.6 flf) (56.8 flf)

40 0.080 0.32 0.26 0.0418 34 0.160 0.50 0.74 0.168 28 0.321 0.92 {J.97 0.675 24 0.511 2.2 2.2 1. 70 20 0.812 4.7 5.4 4.32 16 1.29 6.3 10.9

Table III. Explosion of Constant-Mass Samples Using 56.8 Ilf at 10 kv

Wire B&S Length, Mass,

Tb, !-,sec E [p' joules Evap~ joules gage em mg

Ag 24 17.9 385 4.53 1242 1180

Ag 20 7.1 385 6.12 2745 1180

eu 20 7.1 326 7.65 2840 2028

eu 24 17.9 326 5.80 1650 2028

eu 24 7.1 129 3.95 1518 804

eu 28 17.9 129 2.74* 557 804

(eu 34 17.9 32.1 1.20 114 200)

.Interpolated from data on 28 and 34 gage wires using plot of Tb vs area. No burst spike appeared for this wire size.

and lengths but constant masses. It follows that both the burst times and energies are dependent upon the configuration of the samples.

DISCUSSION

A complete theory of the first pulse must be able to cope with the order of TbS for the various metals, and to account for the de­pendences of the first-pulse energies and TbS on sample geometry.

From a survey of various bulk properties (such as resistivity, density, etc.) of the metals in question, we find that the energy of vaporization per unit volume follows most closely the order of TbS

cited above. There is reason to believe, however, that this parallel­ism may be largely accidental. If the thermodynamics alone were responsible for "bursting," samples of a given material having constant mass should show identical first-pulse energies, and Tb for a small-diameter wire should exceed Tb for a large-diameter wire.

12 Nash and Olsen

The experimental facts (d. Table III) are that a (nearly) constant first-pulse energy is obtained only for the two 24 gage copper sam­ples whose masses differ by a factor of 2.5. For the constant-mass systems, the first-pulse energy ratios arenotunity,but range from 1.7 to 3. Furthermore, theTbs are in exactly the wrong order. The variations in the energies which are apparent in the constant-mass experiments cannot be caused by differences in the initial resist­ances of the samples. The (virtual) lack of a dependence of the energy on wire length displayed by the 24 gage copper wires seems to be a general phenomenon. We have observed it for several sizes of both copper and silver wires over a range of lengths from 9 to 50 cm. Accordingly, the magnitudes of the first-pulse energies would not be grossly changed from the values in Table III even if the lengths of, e.g., the 20 and 24 gage samples were adjusted so that they had the same initial resistances rather than the same masses.

In view of the intermingling of the effects of heating and radial expansion on the resistivity of the sample, which in turn affects the instantaneous power dissipation, we cannot at present account for the various features of the first-pulse energies which we have reported.

If we simply accept the experimental facts regarding the ener­gies, we can, however, account for the linear dependence of the time to burst on wire cross section. Ithas been postulated previously [4] that the air-metal interface propagates according to the equation

(1)

Here ~ is the radius expansion ratio

(2)

r 0 is the initial wire radius, r is the radius at time t, Pg and Po are the densities of the surrounding gas and the wire, and E is the hy­drodynamic energy per unit length of cylinder.

It has been shown in numerous photographs [5] that at the instant of "burst" the wire cylinder is in an expanded state, which never­theless has a well-defined radius. Bennett [6] has shown that the efficiency of coupling between the vapor cylinder and its surround­ings decreases as the cross section of the wire increases, for copper wires larger than B&S 34 gage. In equation (1), therefore, the hy­drodynamic energy E could well remain approximately constant in

Nash and Olsen 13

spite of the increase in first-pulse energy with increasing wire diameter.

A possible physical interpretation of the wire "bursting" is that the parameter ~ has reached some constant critical value, which may depend on the material. On this model, equation (1) predicts that the time (Tb) at which ~ reaches ~Critical should be about a linear function of the wire cross section.

If the coupling efficiency is primarily a function of the wire area, then the times required to burst wires having constant diameter but varying lengths should decrease linearly as the square root of the first-pulse energies per unit length. Thus the two samples of 24 gage copper wire described in Table III should have TbS which differ by a factor of 1.52. The experimental value of 1.48 is in good agreement with the prediction based on this simple theory. We have obtained equally good agreement in experiments with other materials besides copper, and for sizes other than 24 gage.

In this model, two parameters which are subject to experimental evaluation turn out to be important. A short burst time may eVidently be obtained by demanding only a small increase in radius; i.e., a small value of ~critical' Alternatively, the coupling efficiency may vary from substance to substance, and a high efficiency, which leads to a large value of E in equation (1), also leads to a small Tb •

We are just now beginning a program designed to evaluate the relative importance of these factors.

REFERENCES

1. W. G. Chace. "Exploding Wires," Vol. 1, W. G. Chace and H. K. Moore [eds.], Plenum Press, New York, 1959, p. 7.

2. I. F. Kvartskhava, A. A. Pliutto, A. A. Chernov, and V. V. Bondarenko, Soviet Physics­JETP Vol. 3, p. 40, 1956.

3. D. R. Stull and G. C. Sinke, "Thermodynamic Properties of the Elements," Advances in Chemistry Monograph No. 18, American Chemical Society, Washington, 1956.

4. C.P. Nash and W.G. McMillan, Phys. Fluids Vol. 4, p. 911,1961. 5. T. Korneff. J. L. Bohn. and F. H. Nadig, in "Exploding Wires," Vol.!, W. G. Chace and

H. K. Moore [eds.], Plenum Press, New York, 1959, p. 104. 6. F. D. Bennett, Phys. Fluids Vol. 1, p. 515, 1958.