AIAA 98-3467, Proceedings of 34th Joint Propulsion Conference, Cleveland, OH, July 1998.
Selma S. Goldstein,
Donald L. Jackson
Barry T. Neyer,
Barry T. Neyer
1100 Vanguard Blvd
Miamisburg, OH 45342
(937) 865-5170 (Fax)
Explosive performance margins are critical to designing explosive ordnance systems that include transitions along an explosive train from one component to the next. This paper will discuss explosive initiation and the physical parameters that affect it. It will then address the commonly used test methods to evaluate margin in detonation transfers, and review the advantages and disadvantages of each with respect to whether they address the appropriate physical variables. A new method is suggested based on a modern understanding of the detonation process, which was not as well understood at the time that many of the commonly used methods were first developed and adopted.
Explosive ordnance systems usually contain a variety of components that comprise an explosive train. These elements usually include detonators and explosive transfer lines, with various inert connectors or manifolds to link them together in the appropriate geometry.
At each interface between one explosive element and the next, the detonation of the first must be successfully transferred to the next such that reaction of the entire train, and actuation of the end item explosive device, is obtained. Transfer is complicated by the fact that, at most physical interfaces, other materials intrude, through which the shock wave must also pass. These include cups, closures and other barriers that form the containment of the explosive elements in the train in addition to manifold components and safety barriers.
Testing is necessary to verify that the design of an explosive train for an ordnance system includes interfaces between elements that produce reliable detonation transfer in addition to satisfying the requirements of the system geometry. In particular, it is necessary to show that the propagation at each interface has margin, i.e., the impulse transferred from one explosive element to the next is more than sufficient to propagate the detonation across the interface.
This discussion of initiation processes is adapted and summarized from "Detonics of High Explosives" by Johansson and Persson . Only detonation of high explosive elements, such as detonators, explosive transfer lines and confined or flexible detonating cords are addressed. Other interfaces involving low explosives, deflagrating pyrotechnics, or deflagration to detonation transition systems are not considered. Also not considered are designs that transfer detonation by multiple collisions with the acceptor.
Detonation is a specific type of explosive exothermic reaction and is always associated with a shock wave. This reaction may be initiated by heat from shock compression, but then the reaction rate accelerates to the point that sufficient energy is released to sustain a shock wave in the reaction products before any appreciable expansion of those products occurs. Reaction product gases move behind the reaction front, or zone, which moves as a shock wave in the material. The energy transfer from reacted into unreacted explosive material is through these compression waves, and thus the process propagates.
There is a minimum or threshold amount of energy necessary to start this reaction in any explosive. The threshold depends on the chemistry of the material, its density, and any confining materials around it. Since the reaction rate within the reaction zone is affected by the normal variables of temperature and pressure, initiation of detonation in an explosive element will only occur if the initiating shock, whether from an impact or a preexisting detonation process, contains sufficient energy. Energy in a shock is the integral under the pressure profile as a function of time, so the energy available depends both on the amplitude and the time duration of the shock.
However, once a stable detonation wave is propagating through the explosive, the reaction becomes essentially independent of the temperature and pressure in the ambient environment. The energy carried by a shock wave is a function of its velocity and pressure, and to some extent its time duration.
Figure 1: Detonation propagating through an explosive cylinder
The wave propagation nature of a detonation is the key to understanding the physical parameters that will affect detonation transfers. The first element or donor charge must provide enough energy to the next element or acceptor so that it can initiate and attain a steady detonation itself. The donor's detonation energy is a function of its formulation, size, density, and confinement. Similarly, the ability of the acceptor charge to initiate and maintain the chemical reaction is dependent on its formulation, size, density, and confinement. These variables determine the detonation velocity and shock pressure.
A propagating detonation wave is shown in Figure 1. The area between the solid curve and the dashed curve is the reaction zone. The detonation velocity D and the detonation pressure will vary across the wavefront from centerline to edges, depending on distance of a detonating mass element from the surface of the explosive charge.
Shock waves also reflect, transmit, and may be attenuated or amplified across material boundaries. Rarefaction waves, not shown in Figure 1, reflecting back into the explosive from the free surfaces or from the interfaces between the explosive and its confining materials will interact with the compression waves to reduce the amplitude of the detonation shock. The reaction rate and therefore the detonation velocity, and the shock pressure at the detonation front, will be highest in the center of an explosive, on an axis perpendicular to the wavefront, and decrease radially toward the edges.
If the degradation is severe enough, the detonation will die out entirely. At a minimum, the wavefront is curved, as shown in Figure 1, and convex in the direction of propagation. The degree of curvature is related to the dimension of the explosive, giving rise to a critical diameter below which the detonation will lose energy more rapidly from the edges than can be replaced by the reaction zone.
The unsteady waves at the free surfaces of a charge, which affect the strength and stability of the detonation, affect the success of the initiation process as well as the steady propagation process. This is independent of whether the initial shock is generated by a donor explosive charge, a detonator, a booster explosive, a shock from one of these transmitted through a barrier material, or an impacting projectile or flyer plate.
The surface waves, or what are generally referred to as edge effects, also explain the empirical rule used in selecting a configuration of donor and acceptor for the most effective detonation transfer. The generally accepted order of preference is end-to-end, end-to-side, side-to-end, and side-to-side. This is now easily understood in terms of the relative strengths of the output shocks from the donor charge in each of the arrangements.
This picture of the operant mechanism for detonation transfer leads to the following parameters that are important for controlling the performance margin of a given explosive interface:
Detonation transfer interfaces are subjected to various types of tests to determine the margin associated with the transfer of detonation from donor to acceptor charges. Historically, these tests have focused on increasing or decreasing the gap between donor and acceptor or on inserting a barrier between donor and acceptor to attenuate the shock or flyer velocity from the donor. These methods were used in the absence of more sophisticated methods available to the ordnance community today that can provide a more quantitative estimate of the actual margin of donor output to acceptor threshold levels.
The objective of a detonation transfer margin program should be to determine the margin of lowest output level from the donor compared to the highest threshold level of the acceptor. In order to accomplish this, the program must vary the parameters from the list above that are germaine to the particular transfer mechanism.
The user must assess the above parameters plus any additional parameters that may impact the margin associated with the detonation transfer across the given interface and may by analysis or based on past testing determine that some variations in parameters are not relevant to the transfer margin across the interface. The remaining parameters must then be assessed by further analytical or test methods.
The tests mentioned in this section all apply some type of penalty to the transfer mechanism. There are two different approaches to choosing the amount of penalty to apply. Some of the methods apply a fixed penalty: for example increasing the thickness of a barrier by a fixed amount. The increase is usually several times greater than design tolerances allow. A number of devices are tested with this penalty. All must function properly to ensure that the design is robust. If all of the devices function at the large penalty, then it is assumed that there is sufficient margin for the devices to function at the nominal design.
A second approach is to vary the penalty systematically to arrive at the penalty that is just sufficient to cause some fraction of the devices to fail. The penalty that causes a failure is usually called a threshold. This type of test procedure is called a sensitivity test. Sensitivity tests are commonly used to establish the stimulus level to apply to a detonator to ensure its reliable initiation. The same test protocol used to pick the test levels in a detonator sensitivity test can be used to pick the levels for a penalty test. The D-Optimal (Neyer 1994) tests are an efficient procedure for choosing penalties. Once the test series is complete, analysis of the data can determine the probability of explosive transfer as a function of the penalty.
The output from the donor charge is a shock that is attenuated as it travels away from the donor or a flyer or shrapnel that is accelerated by the explosive shock loading to some maximum velocity. The flyer begins to break up into smaller particles and its velocity or the shock pressure decreases with increased travel distance.
As the gap between donor and acceptor increases, at some point the donor will not reliably initiate the acceptor charge. Traditional thinking also implied that small standoffs in which a flyer was the mechanism for detonation transfer would not provide reliable transmission since the flyer would still be accelerating and the velocity would not be sufficient for reliable initiation of the acceptor. In addition, it is recognized that in some applications the orientation of donor with respect to acceptor is critical to reliable transfer, which we now understand as a consequence of the more efficient transfer of shock energy in a "head-on" configuration.
Gap testing was initially established to ensure the standoff distance and orientation between donor and acceptor was in a region of reliable transfer. The assumption of this test method is that an air gap can envelope the effects of any attenuation or distortion of the initiation shock on the detonation transfer. Gap tests are currently defined in the aerospace industry as follows:
The strength of this method for determining margin is that it is relatively simple to define and inexpensive to implement, it can even be performed in an open air setup with the donor and acceptor held in proper orientation. Design of the test setup must, however, take into account other factors in the transfer path such as barriers, shoulders, bores, etc. which affect the shape and strength of transmitted shocks and may impact the applicability and reliability of test results.
The weakness of this method is that it only addresses standoff gap and orientation and does not address actual margin between donor output and acceptor threshold or variations in other parameters such as explosive or flyer properties. If true margin across the interface is to be determined, another test method must be utilized.
Often a detonation transfer interface incorporates a barrier in the transfer path, such as in a safe and arm with an internal detonator and an environmental seal as part of the S&A housing. This seal is typically a metal barrier that is positioned between the detonator and downstream explosive device. The detonator output shock must penetrate this barrier prior to impacting the acceptor of the downstream device.
Currently, testing focuses on performing the varying standoff tests described above. The distance between detonator and barrier is varied with the distance between barrier and acceptor being fixed, then the distance between detonator and barrier is fixed and the distance between barrier and acceptor is varied. In some cases, where the barrier is shown by test to be able to move, then the distance between detonator and acceptor may be fixed and the position of the barrier varied. Like the standoff tests above, this testing is simple to define and reasonably inexpensive to implement. An additional strength of this method is that it can reveal potential design weaknesses regarding the intermediate barrier. For example, testing has shown that if the donor charge is small, e.g., a one grain HNS end tip initiating a larger booster charge, the distance between donor and barrier is large, and the distance between barrier and acceptor is small, reliable transfer may be inhibited. However, as with the standoff tests above, this testing still says nothing about actual margin associated with the detonation transfer.
In this series of tests, cards similar to computer cards are placed in the transfer path, the plane of the card being perpendicular to the transfer path axis. The intent of this method is to attenuate the donor shock or flyer velocity until transfer does not occur. The number of cards through which successful transfer does occur is an indication of margin associated with the transfer interface.
Like the methods above, this test is simple to define and implement. In addition it does give some indication of margin since attenuation of the shock or flyer will occur. However, an actual measurement of margin still is not available, the test only indicates that transfer will occur through some number of cards. In addition, inserting material in the path that is not germane to the actual design interface may introduce variables in the test that are not understood. For example, the card material remains between the flyer and acceptor at impact, an impedance mismatch may occur between flyer, card material, and acceptor. In order to actually understand margin associated with the transfer interface, a different test method must be utilized.
The VariComp method (Ayres et al 1961) varies the composition of the acceptor explosive in an attempt to determine the reliability of explosive transfer. The explosive in the acceptor is replaced with various explosive compositions, having different sensitivities. In the classical performance of this technique, the explosive compositions are chosen by a sensitivity test procedure, similar to the one described in a previous section.
The explosive compositions placed in the acceptors are taken from compositions that have had their sensitivities previously determined. The sensitivities are determined most often by use of a gap test as mentioned previously. Aluminum or steel barriers are placed between a standard donor and the explosive composition to be measured. The gap width is varied to arrive at the mean gap width that is just sufficient to allow detonation of the explosive. The step sizes are usually adjusted logarithmically. The explosive sensitivity is usually determined in proportional aluminum or steel decibangs. The decibang is defined as:
where d is the donor diameter in mils and g is the barrier thickness in mils. Various compositions of explosives have been "calibrated."
The VariComp "calibration" is only valid for the given set of data tested: the explosive donor, the acceptor, the surrounding media, the barrier material, etc. Changing any of these requires a new calibration with the new parameters. However, because the calibration is so expensive, it is usually assumed that the calibration established for one geometry is also true. Once several explosives have been calibrated, mixtures of the explosives are used to fill in the gaps in explosive sensitivity. The calibration is generally established on large batches of explosives that are used over a number of years.
To measure the margin using a VariComp test, the experimenter establishes the explosive mix in the acceptor that is just sufficient to cause detonation transfer. The test is most often performed using a sensitivity test as described previously. The explosive mix used in each test in the series is chosen by the sensitivity test procedure. Analysis of the test data allows for an estimation of the margin for the interface.
There are several difficulties with this approach that have caused it to fall out of favor. One of the main disadvantages is that it is a two step process. A set of explosive mixtures is calibrated using a gap test, and then the calibrated mixtures are used to determine the margin. There is no fundamental reason that the experimenter could not get the same information by performing a gap test directly on the explosive train under study.
The second difficulty is that the calibration is for a certain explosive train design, which is most often different from the explosive train in the actual device. The calibration is performed by measuring the ability to detonate across a metallic barrier, but there is usually a different barrier design in the actual device. It is not at all obvious that the relative ranking of explosive acceptors would be the same for initiation by flying plates.
The final difficulty is that there is no fundamental link between the margin established with this test and the physics of the detonation train. Thus, interpretation of the results is more difficult. It is more meaningful to establish that a flying plate has twice the energy needed to cause detonation, than it is to establish that an interface has a 3 decibang margin.
The VariDrive test method is similar to the VariComp method, except that explosive compositions with variable explosive output or drive are placed in the donor charge. The explosive output of the various compositions can be calibrated using a number of methods. The method used most often is the gap test as mentioned in the previous section.
Once a "calibrated" set of explosive outputs has been established, tests are performed to measure the margin of the interface. The explosive mixes used in the donor charges are chosen with a sensitivity test procedure as described in the previous section.
The VariDrive procedure suffers from the same difficulties as the VariComp method discussed in the previous section. It also is not widely used today.
Figure 2: VISAR Schematic
Many explosive systems are designed to use a flying plate (commonly called a flyer) to transfer the detonation wave from one component to the next. A flying plate system has the advantage that it is not as dependent on the spacing and alignment between the donor and acceptor as direct transfer systems. In principle, it is also easier to understand the initiation mechanism of a flying plate; if and only if the velocity of the flying plate is above a critical value (dependent on the acceptor), the acceptor will detonate. Experiments have shown that the detonation in the acceptor begins promptly upon flyer impact. It is supposed that there is complete decoupling between donor and acceptor. The main thing that determines the probability of detonation in the acceptor is the velocity (and possibly the geometry) of the flyer.
A Velocity Interferometer System for Any Reflector (VISAR) (Barker and Hollenbeck 1972, Barker and Schuler 1974, Hemsing 1979, Neyer 1993v)is a system for measuring the velocity of a flying plate. Figure 2 shows a schematic diagram of a typical VISAR. A laser beam is reflected from a moving object (the flyer). The reflected beam enters the VISAR interferometer. The output of the VISAR is a fringe pattern, where the fringe spacing is directly proportional to the velocity.
Figure 3 shows an example of the velocity of an explosively driven flying plate. The VISAR is capable of measuring the velocity over the entire flight history of the device. The velocity shown in Figure 3 was measured for a distance of 4 millimeters. The oscillations shown during the leading edge of the velocity curve are a direct measure of the change in velocity caused by longitudinal sound waves in the flying plate.
Figure 3: Explosively Driven Flyer Velocity
The VISAR is also capable of indirectly measuring the shock pressure in an interface, by measuring the interface velocity. If a flyer impacts a transparent window, the VISAR measures the velocity of the interface. This velocity is directly related to the pressure via Hugoniot curves for the window material.
Because the VISAR can be used to directly measure the velocity of the flyer, it could determine the probability of causing detonation in the acceptor, if the velocity needed to cause detonation in the acceptor was independently determined. The threshold velocity is determined by performing a sensitivity test as described previously. The work of Harlan (private communication) showed that for a 0.005" thick stainless steel flyer a velocity of 0.7 km/s is the threshold for detonation transfer to a typical confined detonating cord (CDC) endtip. Thus, the VISAR data from this device demonstrates that this donor would reliably detonate a typical CDC endtip.
Previous work (Neyer 1995v) has shown that the VISAR measures different physics than dent block measurements: the VISAR measures the velocity of the flying plate, while a dent test measures the integral of (a complicated function of) the pressure pulse. However, in some cases knowledge of more than the velocity of the flying plate is required to accurately predict the probability of detonation transfer. Studies performed on exploding foil detonators (Neyer et al. 1990) has shown that the threshold velocity required for detonation on a simple system could vary by almost a factor of two, depending on the flight distance. Shorter distances required a lower threshold voltage.
The VISAR method of establishing explosive transfer margin has several advantages. The VISAR directly measures the velocity, the parameter that has the most control on acceptor detonation. Shorter distances required a lower threshold velocity. However, as long as the threshold velocity of acceptor detonation was measured at a similar distance as in the explosive transfer design, the VISAR could be used to establish the reliability. No other measurement technique commonly used has such a clear relationship between measurement and ability to detonate an acceptor.
If the next assembly is a component for which the threshold of detonation has already been established, it only requires a small sample size to establish the probability of explosive transfer. Moreover, the VISAR offers design guidance as to the optimal distance to place the acceptor, subject to the qualification mentioned in the previous paragraph.
The main disadvantage of using a VISAR is that it is a relatively expensive piece of equipment (~100K$) and requires extensive training to achieve reliable results. In addition, because the VISAR is complicated, there will be times when no reliable velocity is recorded. Nevertheless, the VISAR is capable of great precision, and should be considered for measuring the reliability of explosive transfer.
Currently, gap testing is commonly used in the aerospace community for determining margin associated with detonation transfer across an interface. However, this method addresses only the parameter of standoff, i.e., the effect of an air gap, and does not actually consider margin associated with the transfer from donor to acceptor. Nor does it consider the impact of varying donor and acceptor parameters on margin.
In order to adequately assess margin associated with detonation transfer across an interface, two issues must be addressed. First, margin across the interface must be determined with nominal parameters such as donor and acceptor explosive formulations; charge size, density, and confinement; and flyer / interface characteristics. Second, the impact of varying the above parameters to limits at least as great as those associated with design and manufacturing tolerances must be determined and compared with the established margin. The intent of these efforts is to ensure that adequate margin is provided by the interface configuration, given the tolerances allowed in design and manufacturing.
In the two most common explosive train designs, direct contact and flying plate detonation, the explosive transfer process is essentially prompt and one dimensional. In direct explosive transfer, the instantaneous detonation pressure is what causes the acceptor to detonate. In flying plate transfer, the detonation is transferred by the shock of the flyer impact.
Two alternate test approaches can be defined which utilize existing methods and technology to actually address the issue of margin. These tests may not be valid for cases in which there is not prompt detonation transfer.
The first suggested test program is very extensive and potentially costly but will establish the actual margin associated with the interface. This method requires determining the effects of changes in design and manufacturing parameters on the output of the donor and on its ability to transfer detonation to the acceptor. It is essentially the same method that is used to determine the margin for initiation of detonators.
Threshold tests should be performed to determine the stimulus required to transfer detonation to the acceptor. The threshold test should use modified donors or simulators that have variable output. However, it is imperative that the test donor should have the same type of explosive transfer mechanism to the acceptor as the nominal donor. A nominally "worst case" acceptor design should be tested to ensure that the results are meaningful for all acceptors.
The main parameter that should be varied to produce the test donors with variable output is the explosive formulation. Either the density, explosive composition, or percentage of inert material in the composition could be varied to yield variable output. Variation of the explosive diameter or length might produce different output as measured by dent block measurements, but would have little effect on the probability of explosive transfer.
The donor output should be measured by diagnostic techniques that are capable of measuring the physics that controls the detonation transfer. For direct initiation it is the instantaneous pressure, or at least the peak pressure. For flying plate detonators it is the flyer velocity. If it is too expensive to use such techniques, a reasonable ranking of the relative output of a selection of donors might be achieved by the use of dent blocks
To establish margin, it is also necessary to determine the variability of the nominal donor design. Various design parameters of the donor should be varied and the output measured. The variation should be at least a factor of two more than allowed by the manufacturing requirements. Worst case donors should be built by finding the combination of parameters that yield a donor with minimum output.
The margin is determined by computing the ratio of the worst case donor output to the stimulus required for initiation of the acceptor. Usually the stimulus required is stated as a given probability at a given confidence level, e.g. 0.999 probability at 95% confidence. This ratio must be significantly greater than one for a reliable design. The greater this ratio, the greater the margin of the design.
The second test program is less extensive and costly but will not determine actual margin. It will establish that adequate margin is available. This method involves reducing the output from the donor by the same methods discussed above. The output could be measured by VISAR or dent tests. Donor charges with outputs reduced by an agreed upon margin are then assembled with the acceptor and testing is performed. Successful detonation transfer of a number of systems ensures that adequate margin is available.
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