This protocol details the use of Hopkinson pressure bars to measure reflected blast loading from near-field explosive events. It is capable of interpolating a pressure-time history at any point on a reflective boundary and as such can be used to fully characterize the spatial and temporal variations in loading produced.
Near-field blast load measurement presents an issue to many sensor types as they must endure very aggressive environments and be able to measure pressures up to many hundreds of megapascals. In this respect the simplicity of the Hopkinson pressure bar has a major advantage in that while the measurement end of the Hopkinson bar can endure and be exposed to harsh conditions, the strain gauge mounted to the bar can be affixed some distance away. This allows protective housings to be utilized which protect the strain gauge but do not interfere with the measurement acquisition. The use of an array of pressure bars allows the pressure-time histories at discrete known points to be measured. This article also describes the interpolation routine used to derive pressure-time histories at un-instrumented locations on the plane of interest. Currently the technique has been used to measure loading from high explosives in free air and buried shallowly in various soils.
Characterizing the output of explosive charges has many benefits, both military (defending against buried improvised explosive devices in current conflict zones) and civilian (designing structural components). In recent times this topic has received considerable attention. Much of the knowledge gathered has aimed at the quantification of the output from charges to enable the design of more effective protective structures. The main issue here is that if the measurements made are not of high fidelity then the mechanisms of load transfer in these explosive events remain unclear. This in turn leads to problems validating numerical models which rely on these measurements for validation.
The term near-field is used to describe blasts with scaled distances, Z, less than ~1 m/kg1/3, where Z = R/W1/3, R is the distance from the center of the explosive, and W is the charge mass expressed as an equivalent mass of TNT. In this regime the loading is typically characterized by extremely high magnitude, highly spatial and temporally non-uniform loads. Robust instrumentation is hence required to measure the extreme pressures associated with near-field loading. At scaled distances Z < 0.4 m/kg1/3, direct measurements of the blast parameters are either non-existent or very few1 and the semi-empirical predictive data for this range is based almost entirely on parametric studies. This involves using the semi-empirical predictions given by Kingery and Bulmash2, which is outside of the author's intended scope. Whilst tools based on these predictions3,4 allow for excellent first-order estimations of loading they do not fully capture the mechanics of near-field events, which are the focus of the current research.
Near-field blast measurements have in recent times focused on quantifying the output from buried charges. The methodologies employed vary from assessing the deformation caused to a structural target5-7 to direct global impulse measurement8-13. These methods provide valuable information for the validation of protective system designs but are not capable of fully investigating the mechanics of load transfer. Testing can be done at both laboratory scales (1/10 full scale), or at near to full scale (> 1/4), with pragmatic reasons such as controlling burial depth or ensuring no inherent shape of the shock front is generated by the use of detonators rather than bare charges14. With buried charges the soil conditions need to be highly controlled to guarantee the repeatability of the testing15.
Independent of the whether the charge is placed in free air or is buried, the most fundamental issue in measuring the resulting blast is ensuring the validity of measurements made by the instrumentation deployed. In the designed test apparatus16 a fixed 'rigid' target plate is used to shield the Hopkinson pressure bars17 (HPBs) whilst at the same time ensuring that the ends of the bars can only record the fully reflected pressures. The authors have previously shown that measurement of reflected pressure from a rigid target is more accurate and repeatable than incident, or 'free-field' measurements18-20. The geometry of this plate is such that any pressure relief generated by clearing or flow around the target edge21 would be negligible. This new test apparatus has been constructed at 1/4 scale. At this scale tight control over the burial conditions and the explosives can be ensured, with the full scale charge size of 5 kg scaled down to 78 g, at a burial depth of 25 mm.
1. Rigid Reaction Frame
Figure 1. Schematic of the test frame. (A) Overall arrangement, (B) plan of target plate, (C) close-up view of target plate. The Hopkinson pressure bars are hung from the bar assembly receiver so that they sit flush with the face of the target plate. This allows the fully reflected pressure acting on the target plate to be recorded. Please click here to view a larger version of this figure.
2. Load Cell Design
Figure 2. Diagram of the in-house fabricated load cells. (A) Side elevation, (B) end elevation. The dark grey cylinder is a thick wall steel tube which strains under loading. This strain is recorded using a single strain gauge as no rotation is experienced during the loading. From the calibration of the load cell the strain can be related back to the stress applied. Please click here to view a larger version of this figure.
3. Hopkinson Pressure Bar Design
4. Experimental Setup & Data Acquisition
Note: With the reaction frame, target plate, load cells and HPBs designed and fabricated, assembly can begin as shown in Figure 1, and designed in protocol section 1.
Figure 3. (A) Diagram of a HPB fitted into the target plate, (B) section through HPB at gauge location, (C) example Wheatstone bridge circuit. Two strain gauges are used in the Wheatstone bridge so that and bending of the Hopkinson bar is cancelled out. Please click here to view a larger version of this figure.
5. Explosive preparation
6. Firing sequence
Note: there is a small amount of overlap with protocol section 5 due to the nature of the testing. The firing sequence should aim to minimize risk and should only be conducted by suitably trained staff.
7. Numerical interpolation for a 1D HPB array
Figure 4. Interpolation sequence for 1D HPB array. (A) Original data, (B) time-shifted data, (C) shock front arrival times, and (D) final interpolated pressure time data16. The discrete nature of the pressure time histories can clearly be seen in (A) with there being no continuity between the peak pressures at each of the five gauge locations. When aligned by peak pressure as in (B) the interpolation of pressure at any radial distance (assuming the same arrival time) is possible. By recording the time shift required to align the peak pressures the arrival time of the shock front can be calculated as shown in (C). This then allows the arrival time and pressure time history to be calculated for any radial distance be interpolation of pressure from (B) and time from (C) giving the final interpolated pressure as seen in (D). Please click here to view a larger version of this figure.
8. Numerical interpolation for a 2D HPB array
Note: The code used to run the interpolation in Matlab has been provided along with an example results file which will be referred to in this section.
Figure 5. Interpolation sequence for 2D HPB array. (A) Sign conventions used, (B) original data mm, (C) time-shifted data mm, and (D) arrival times for each radial direction16. For a 2D array of bars the pressure time history at any point is dependent on both radial distance and which quadrant the point of interest is located. If the blast were perfectly symmetric then the pressures in (B) would form vertical lines as shown in (C). In (B) it can be seen that the shock front is reaches the 50 mm location on axis first.
Please click here to view a larger version of this figure.
An effectively rigid reaction frame needs to be provided. In the current testing a total imparted impulse of several hundred Newton-seconds needs to be resisted with minimal deflection. An illustration of the rigid reaction frame used is given in Figure 1. In each frame a 50 mm steel 'acceptor' plate has been cast into the base of the cross beams. Whilst not explicitly required, this allows for easy fixing of the load cells / target plate and provides added protection to the face of the concrete beam. The closest scaled distance currently conducted has been 0.15 m/kg1/3.
The current frame has been tested up to 500 Ns, and has 500 mm square columns with a 750 mm deep, 500 mm wide beam spanning the columns as shown in shown in Figure 1A. The critical element in the design is the target plate which is 100 mm thick mild steel, this was estimated to deform 0.3 mm when resisting a 100 g spherical free air blast at 75 mm stand-off (using the LS-DYNA28 routine load_blast4). The construction of the frames was performed by a specialist concrete contractor who provided site equipment and formwork. The factors applied in the design stage very much depend upon the nature of the testing and whether any further safety factors will be applied by the structural engineer. A safety factor of 10 was used in the current work.
Indications of the equipment used have been given in the main protocol sections where appropriate. To provide representative results a single test with 17 HPBs configured in a 2D array as shown in Figure 1B was conducted. In the current work the bars utilized are 3.25 m long with a radius of 5 mm, with the strain gauge being attached 0.25 m from the loaded face as shown in Figure 3A. The spacing of the HPBs in the target was chosen to be 25 mm as shown in Figure 1B.
The test conducted used a 78 g PE4 3:1 squat cylinder buried at 28 mm in saturated Leighton Buzzard sand15. The sand had a bulk density of 1.99 Mg/m3 and moisture content of 24.77%. The stand-off between the finished soil surface and the target plate was 140 mm.
Once the test had been conducted the individual pressure-time histories were run through a simple 5 point moving average smoothing algorithm to remove any high frequency noise from the data. It was noted when collating the data that the 75 and 100 mm bars in the array had not recorded the data properly. This was likely due to the glue of the strain gauge de-bonding from the HPB giving false readings. To compensate for this the data from the 75 and 100 mm bars were used instead. The data from each of the 4 radial arrays are plotted in Figure 6, with the central (0 mm) HPB being common to all plots. In the saturated soil a very clear shock front is seen, with the pressure decaying slowly with radial distance.
The recorded pressure-time histories were then run through the 2D interpolation routine, with the zone of interest being set as a 200×200 mm square (-100 to 100 mm). This zone was subdivided into a 5 mm grid, which was deemed fine enough to capture the shock front propagation across the target plate accurately. Plots of the interpolated pressure acting on the target plate at selected times are shown in Figure 7. The ≈ 20 msec delay in the arrival of the shock front is the time taken for the shock wave to cover the distance between the charge and the target plate. The asymmetric nature of the loading shown in the recorded data (Figure 6) can be seen clearly in the and axes. This is especially clear at msec.
Figure 6. Recorded pressure-time histories for a single test with a 2D HPB array. (A) (B) (C) (D) . This figure shows the processed trace for each bar location. The black central bar trace is common to all plots to indicate the arrival of the shock front. The non-continuous nature of the shock front is again clearly visible as there is little overlap between the peak stress zone for each bar. The lower pressure in the 25 mm bar has an interesting effect on shape of the shock front as plotted in Figure 7. Please click here to view a larger version of this figure.
Figure 7. Interpolated pressure distribution plots at specified times16. The horseshoe shape of the shock front can be seen in the t = 0.22-0.23 plots. This is caused by the dip in pressure seen in the 25 mm bar shown in Figure 6. By 0.3 sec after detonation the shock front is almost symmetric along all axes. Please click here to view a larger version of this figure.
Using the protocol outlined above the authors have shown that it is possible to get high fidelity measurements of the highly varying loading from an explosive charge, using an array of Hopkinson pressure bars. Using the interpolation routine outlined the discrete pressure-time histories can be transformed into a continuous shock front which is usable directly as the loading function in numerical modelling or as validation data for the output of such models.
When using buried charges the methodology used for preparing the soil containers outlined in protocol section 5 must be checked to ensure sufficient compaction energy is provided to reach the target density. If the target density is not reached then the lift height should be reduced to increase the effectiveness of the compaction. From previous research it has been seen that uniform soil types provide more repeatable test data than tests conducted with well-graded soils15. Tests with soils at full saturation are also prepared with a slightly different methodology as outlined in the authors' previous work15.
For all tests with explosive charges it has been shown in previous studies16,29,30 that the location of the detonator in near-field tests is critical to producing repeatable tests which are free from signal noise. In this respect the detonator should always be placed into the bottom of the charge (furthest from the target plate) so that any fragments from the detonating assembly will not strike the HPBs ahead of the main shock front.
Whilst every attempt is made to ensure the testing is as robust as possible, data loss does still occur. This is usually due to the strain gauges partially de-bonding from the HPBs which can be a particular problem in cold weather (the current apparatus is set up in an unheated building). Great care must also be taken when setting up the break wire as this not only allows the recording of the detonation time but also provides the signal that triggers the data recording. A loss of this signal or error in setup can cause all data from a test to be lost. In regard to data management, the data from the tests are immediately duplicated from the recording computer to a USB drive to ensure no data is lost once the testing is complete.
In the current testing the load cells attach the target plate to the rigid reaction plate and are used to measure the total impulse imparted to the target plate (as the HPBs only cover a limited area). If quantification of only the localized loading (and not global data) is required then the target plate can be mounted directly to the rigid reaction frame.
With the HPB pressure-time histories being only applicable to known points on the target plate an interpolation routine is required to evaluate the pressure-time history for any point on the target plate, and hence to calculate the total recorded impulse.
If only a single radial array has been utilized in the testing, interpolation is still possible by assuming the point HPB loadings to be indicative of the loading at any polar rotation at the same radius on the target plate. Time shifting is also required to interpolate across the discontinuous data (Figure 4A).
The main advantage of using a 2D HPB array is the ability to capture asymmetry in the pressure-time histories. This requires a more complex interpolation routine. In principal this theory can be applied to any number of radial arrays. In the current research this has been limited to four arrays (, , , ) from 0 to 100 mm with the central HPB being common to all (Figure 5A). A total of 17 HPBs have been used in each test.
The interpolation routine in the form presented here assumes that for each pressure-time history there is a single well-defined pressure spike which corresponds with the arrival of the shock front. It can be seen in Figure 6 that for all the bars this is a good assumption. In certain test conditions however this assumption may not be valid and so thought should be given on how best to align the pressure-time histories to allow for the most representative interpolation of pressure.
Modifications can be easily made to cater for different scaled distances (Z) in the current protocol by moving the charge further away from the target plate. Care however must be taken if the scaled distance is brought down below 0.15 to ensure that the loading will not damage the face of the HPBs. The shape of explosive and explosive type may also be changed, with the caveat that the initial modelling done to validate the experimental design will have to be checked.
The authors have nothing to disclose.
The authors wish to thank the Defence Science and Technology Laboratory for funding the published work.
Load Cell | RDP | RSL0960 | This is only indicative, the exact load cell should be able to resolve the required loading |
Steel target plate / HPBs | Garratts | N/A | Fabricated to order |
Strain gauge | Kyowa | KSP-2-120-E4 | To use with steel HPBs |
Cyanoacrylate | Kyowa | CC-33-A | Check with manufacturer depending on mar material to be used |
Digital Oscilloscope | TiePie | HS4 16-bit Handyscopes | 6 used in parallel in current testing |
Leighton Buzzard sand | Garside sands | Garside 14/25 | Uniform silica sand |