desensitized by the weaker parts of the blast wave. However, experimental studies investigating the initiation of a booster device do not exist in the literature. Experiments utilizing x-ray or proton radiography can be performed to analyse the extent of reactions within the detonator and booster configuration and provide valuable insight into the influence of shock desensitization during the initiation of the booster.
This study employs numerical simulations to study the detonator and booster configuration based on a design that is used by the mining industry. We consider the detonators used in the previous chapter inserted within the booster device and examine their ability to initiate the booster explosive as well as the effect of shock desensitization on this process. The reactive model is extended with a desensitization model to account for the effect of shock desensitization. This extension is required for the Ignition and Growth model to capture dead zone formation as has been shown by previous studies [23, 14]. The shock desensitization effect and the related model are discussed in the next section along with extensive validation. Following this, the booster configuration is presented and examined in several configurations. The study considers the initiation process of the booster with and without the desensitization model, for different types of detonators, and for a case of different positioning of the detonator.
5.2
Shock desensitization of solid explosives
Shock desensitization is the phenomenon where the sensitivity of an explosive is decreased by the passage of a shock wave that is not strong enough to ignite it. The degree of desensitization increases with the strength of the shock and can have different manifestations depending on the setup. For example, desensitization effects include the delay of shock to detonation transition in the case of double shock initiation and the quenching of an established detonation when it encounters a desensitized region. The physical processes behind this phenomenon are quite intricate and despite studies spanning over five decades, there has not been a consensus on the underlying causes. However, it is a subject of great interest to the explosives community because of its wide reaching implications ranging from being a useful safety feature for rendering explosives difficult to initiate to being a highly undesirable effect in applications concerned with the performance and efficiency of explosive devices.
Shock desensitization of solid explosives was first mentioned in a study by Campbell et al. [71] in which they performed experiments on shock initiation of heterogeneous explosives. The authors observed that the layer of the explosive which was first to
5.2. Shock desensitization of solid explosives
experience the shock did not proceed to complete reaction and it was deduced that the shock had desensitized that region.
Subsequent investigations have distinguished between different manifestations of shock desensitization [72, 5]. In the context of shock initiation, desensitization is observed in double (or reflected) shock initiation where there is a delay in the transition to detonation of the explosive compared to single shock case. This suggests that the first shock has desensitized the explosive making it harder for the second shock to ignite it. When considering detonation propagation, shock desensitization is expressed as the quenching of detonation in parts of the explosive that have been previously shocked. In many occasions, detonation will propagate around these regions and will leave portions of non-reacted or partially reacted explosive, commonly called “dead zones”.
Multiple experimental studies have investigated shock desensitization and a useful aggregation of the experimental evidence is provided in the study of Hussain et al. [72]. Double shock initiation experiments have found that if the first shock induces no reactions by the time the second shock catches it, then the time or distance to initiation is increased. However, when measured from the catch point, it is almost the same as initiation from a single shock of the same pressure as the second one. In cases where the second shock never overtakes the first, such as in reflected shock scenarios, no reactions are induced in the explosive. This suggests that the initiation of an explosive requires a single shock of strength above a certain threshold, while splitting it to multiple shocks will not ignite the explosive even if the final shock is above the initiation threshold.
On the aspect of detonation quenching, Drimmer and Liddiard [73] performed one of the first experiments involving detonation failure in pre-shocked HMX-based explosives. Campbell and Travis [74] performed similar experiments on RDX-based explosives and more recently Vandersall et al. [75] studied the interaction of detonation with weak shocks in TATB-based explosives. All studies reported that detonation degenerated into an inert shock for a range of pre-shock pressures that were weak enough not to induce reactions in the explosive. However, detonation did proceed for shock pressures below a minimum value. The studies concluded that desensitization is a time dependant phenomenon were strong shocks lead to faster desensitization and by extension, faster failure of detonation.
Advances in experimental diagnostics have enabled the study of dead zone formation and have shown that they occur for all polymer bonded explosives [5]. The usual setup used in such studies involves an abrupt change in geometry such as an increase in charge radius which forms a corner. As the detonation moves into the wider explosive region, it is diffracted and may propagate in the radial direction usually referred to as
5.2. Shock desensitization of solid explosives
“turning the corner”. In most cases, the detonation in the radial direction is established at some distance from the corner which results in some parts of the explosive not reacting. Cox and Campbell [25] performed one of the earliest experiments involving detonation diffraction and reported dead zone formation in TATB-based explosive. Similar experiments performed by Held [76] showed dead zone formation in an RDX-based explosive.
The formation of dead zones in charges with sharp corners is a result of a weak shock propagating radially as the detonation expands into the wider explosive region. This shock is not strong enough to induce prompt reactions and results in desensitizing the explosive. The detonation continues to propagate in the initial direction as well as expanding radially, at a rate faster than the weak shock. It eventually reaches the outer boundary of the corner but it is unable to penetrate the desensitized region resulting in a pocket of non-reacted explosive. The dead zone is more extensive if the corner is covered with a high sound speed confining material. In this case, the shock wave formed in the confining material is transmitted into the explosive region along the corner much earlier than the detonation is able to diffract and reach it. This results in the desensitization of a large region of the explosive along the corner which might not be consumed by the detonation.
The processes involved in the formation of dead zones are the result of the complex interactions between the rarefaction, shock, and detonation waves. The resulting size and shape of the dead zone is heavily dependant on the fine details of relative timings and strengths of these interactions. As mentioned in the review paper by Handley et al. [5], detonation diffraction experiments are very sensitive to initial conditions and explosive composition and show significant variability between similar experiments. This sensitivity is observed in the numerical simulations as well which has made this class of experiments an ideal case for assessing the accuracy and capabilities of reactive models.
All of the effects of shock desensitization described above have been explained by the simple notion that shocks which are too weak to induce reactions will instead desensitize the explosive and that the degree of desensitization will vary depending on the strength of the shock. However, the underlying cause of shock desensitization of explosives is still debated between two concepts.
The classic view [74, 77] considers the hotspot mechanisms and advocates that the weak first shock activates the hotspots in the explosive to a small degree that does not lead to hotspot coalescence and ignition. When the second shock arrives, the hotspots are no longer available and initiation fails. This view resides heavily on the