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Transient response of steel plates subjected to close proximity explosive detonations in air
International Journal of Impact Engineering 102 (2017) 102116
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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Transient response of steel plates subjected to close proximity explosive detonations in air TagedPD1X XR.J. CurryD2X X*, D3X XG.S. LangdonD4X X TagedPBISRU Department of Mechanical Engineering, University of Cape Town, Rondebosch 7700, South Africa
TAGEDPA R T I C L E
I N F O
Article History: Received 14 September 2016 Revised 2 December 2016 Accepted 4 December 2016 Available online 14 December 2016 TagedPKeywords: Blast loading Transient response Plates Deformation Digital image correlation
TAGEDPA B S T R A C T
The permanent deformation and failure of steel plates subjected to air-blast loading has been the subject of numerous investigations. The transient deformation of such intensely loaded plates has been difficult to obtain due to experimental difficulties. In recent times, high speed imaging and digital image correlation techniques have enabled reliable non-contact measurement of deformation and strain in various applications, such as tensile testing and far-field impulsive loading response of large plated structures. This paper investigates the transient deformation and strain evolution of a deformable plate subjected to air blast loading arising from explosives detonated in close proximity to the plates. The experiments made use of a blast pendulum to measure the impulse imparted on the plates. The pendulum modifications required to accommodate the high speed camera system are described. Results from blast experiments are used to show the influence of stand-off distance on the transient response and permanent deformation of thin steel plates subjected to air blast loading. The difference between maximum transient mid-point deflection and final deformation decreased with an increase in charge mass and global deformation. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction TagedPDue to the current global social and political climate, explosive threats loom larger in the public consciousness than ever before. Explosive threats can be either accidental (such as a gas explosion aboard an offshore platform) or deliberate (such as terrorist activity or military action). The common thread in deliberate explosions is an explosive substance connected to a detonation device, with examples being pipe bombs, improvised explosive devices (IEDs) and landmines. TagedPIn the interests of public safety and security, the need to protect people, equipment and structures from explosions has greatly increased. A great deal of effort has gone into preventing an explosive detonation, such as improving screening at airports and active mitigation methods in military systems. However, active mitigation techniques are not practicable for everyday situations and screening methods will not always work perfectly. Hence, there is a need to understand the loading arising from an explosive detonation and the damage that is sustained by structures subjected to blast loading from close proximity explosive detonations. This improved understanding will assist in efforts made to prevent injury or loss of life during explosions. TagedPThere is little full-scale explosion test data available as full scale *
Corresponding author. E-mail address: [email protected] (R.J. Curry).
http://dx.doi.org/10.1016/j.ijimpeng.2016.12.004 0734-743X/© 2016 Elsevier Ltd. All rights reserved.
tTagedP ests are prohibitively expensive and time consuming to perform, and often the findings are classified by the military. Small scale testing offers a number of advantages such as reducing the expense, allowing better control of the test process variables (explosive size and geometry, accurate positioning of the explosive, stand-off distance to target structure) and potentially improved measurement of parameters such as impulse, pressure and structural response. The link between the small scale experimental and the full scale testing is being able to scale the work. TagedPExtensive laboratory scale experimental studies were performed by Nurick and Martin [1] with the aim of understanding the large permanent ductile deformation and rupture of plates, beams and shells due to air-blast loading. Jones [2] and Nurick and Martin [1,3] present overviews of theoretical and experimental studies of plates subjected to uniformly distributed impulsive loading. Further studies were reported, examining the influence of boundary conditions (clamped or built-in) [4,5] and the spatial distribution of the loading. In each case, the loading was assumed to be impulsive and reported on the permanent deformation and failure of the structures. Many of these make use of a blast pendulum in order to measure the impulse imparted on the plates outlined by Nurick [1]. TagedPMenkes and Opat [6] were the first to define the failure modes of blast loaded clamped beams. Three modes were observed as the applied uniform impulse was increased:
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TagedP
Fig. 1. Photograph of the modified pendulum hanging in blast chamber. Clearly showing the 300 mm circular exposed test area on the plate.
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TagedP Mode I - Large inelastic deformation TagedP Mode II - Tensile tearing at the supports TagedP Mode III - Transverse shear failure at supports
TagedPUnderstanding the transient deformation history of plates prior to failure would add valuable insight to the mechanisms which may influence and drive the different modes of deformation. TagedPCapturing transient test data by placing instrumentation on or in close proximity to a test plate poses a problem where the instrumentation itself may influence the plate response. Simple tools such as the deformation combs described by Neurberger [7] have yielded valuable insight into maximum transient deflection of plates but were unable to provide information about transient deformation profiles or time to peak deflection. Non-contact measurement techniques such as light interference and high speed filming have proved the most successful in previous works when trying to extract richer data. TagedPThe use of 3D Digital Image correlation for displacement measurement has become a well established technique [8] used in many different applications [9,10]. Fourney et al. [11] used a 3D DIC system to measure the transient response of test plates under blast conditions. Velocity and acceleration profiles were both reported. An issue noted in this work was the constraint of camera resolution and lighting of the specimen as the experimental setup tracked an
Fig. 2. Schematic drawing of modified pendulum, showing internal arrangement (shroud removed for clarity).
Fig. 3. The Modified pendulum with shrouds removed to show the inside.
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Fig. 4. Charge configuration.
Fig. 5. Ballistic pendulum geometry.
Fig. 6. Typical displacement versus time output from the displacement sensor.
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TagedPunconstrained plate and clamp frame. The rigid body motion of the clamp frame was removed to determine the motion of the test specimen. One particular problem with this method was that the camera must focus on a larger area (including the clamp frame and the surrounding area to ensure the plate could be tracked once it started moving). This resulted in much smaller apertures set on the lenses to ensure sufficient depth of field and more challenging lighting conditions. This was further aggravated by the changing light conditions on the specimen as it moved. This work by Fourney et al.was expanded together with Sutton and Tiwari et al. [12] increasing the charge mass slightly and reported a circular deformation wave moving radially outward from the centre of the plate. TagedPWork by Borvik et al. [13] proposed the use of a stationary rigid clamp frame with the cameras filming from some distance away (but in the same room as the test). It was noted by Borvik et al. [13] that the movement of the cameras as the blast wave impinged on them caused the DIC technique to stop working, limiting the duration of data. Borvik et al. [13] also reported inconsistencies in the trigger system and problems with the adhesion of the painted speckle pattern on the test plate. As a result successful data capture was achieved for a limited number of tests. One further complication in the technique presented is that the impulse of the plate is not a direct measurement but rather an inferred value based on pressure sensor readings during calibration tests. TagedPIn an effort to overcome some of these difficulties reported in previous work, an improved technique has been developed. In this paper, the transient response of Domex steel to air-blast loading arising from detonations of plastic explosive at two different standoff distances (SODs) is reported. Firstly, the experimental method for close proximity air-blast testing using high speed imaging is reported, including detail about the modification of the pendulum system to incorporate the camera system. Secondly, details regarding the digital image correlation technique are reported. Thirdly, the results of the material characterisation and air-blast loading experiments are reported. The influence of charge mass and stand-off distance on the transient response and permanent deformation of steel plates is discussed. 2. Experimental method TagedPThe experimental method comprises three distinct areas: blast test specimen description, modifications to the conventional blast pendulum and transient response measurement.
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Fig. 7. The 400 mm £ 400 mm test plate used, showing the bolt holes with the preparation steps to create the DIC speckle pattern.
TagedP ith a side length of 400 mm. When placed in the clamp frame, w the plates had a exposed circular area with a diameter of 300 mm, as shown in Fig. 1. 2.2. Experimental arrangement TagedPExperiments were performed at the Blast Impact and Survivability Research Unit (BISRU) at the University of Cape Town. Each test plate was bolted into the clamp frame with 12 bolts evenly spaced around the circular exposed area at a pitch circle diameter of 350 mm. The clamp frame is chamfered at a 45° angle around the edge of the plate to reduce pressure build up and recirculation [4,5]. The clamp frames and test plates were mounted to a modified pendulum, which was used to determine the impulse and house the cameras used for transient measurements. The experimental arrangement is shown in Figs. 1 and 2.
2.1. Blast test specimens T he test plates were made from 3 mm thick Domex 355MC, a agedPT high strength hot rolled low alloy steel. The plates were square
TagedP2.2.1. Modification of the pendulum to incorporate high speed imaging TagedPThe horizontal pendulum used at BISRU for many years [1,5,14,15]consisted of an I-beam suspended from four cables with a
Fig. 8. The calibration target shown together with the software identified markers.
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Fig. 9. The DIC stereo subsets.
Fig. 10. The Z Displacement field obtained from the correlation seen overlayed on the left(top) and right (bottom) images shortly after detonation.
Fig. 11. The gauge point and line extracted in the DIC.
TagedPmounting frame at the front to support the test specimen and a counterbalance mass at the rear. It was not possible to mount the cameras to this pendulum as it would have provided no protection from the intense light burst during an explosion, or the ensuing blast wave. The light would have saturated the camera sensor, making it impossible capture images of the deformation response, and the blast wave would have caused considerable damage to the camera body and lenses (and the electronic systems and cabling). TagedPIn order to protect the camera system, a new pendulum was constructed from Mild Steel with a shroud seen around it to protect the cameras from the blast. The shroud isolated the cameras from the blast loading and protected the cameras from the intense light emissions that could saturate the camera sensor. The modified pendulum is shown in Figs. 1 and 2. Fig. 1 is a photograph of the pendulum prior to a test, showing the steel shrouding in place. Fig. 2 is a schematic drawing of the pendulum, shown without the shroud to allow viewing of the internal arrangement. Part of the web was removed in order to give the cameras a direct line of sight to the rear surface
Fig. 12. Typical example of the engineering strain field in the radial plate direction extracted from the DIC.
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Table 1 Table of chemical Ladle analysis of Domex 355MC steel [19]. C (max %)
Si (max %)
Mn (max %)
P (max %)
S (max %)
Al (min %)
Nb (max %)
V (max %)
Ti (max %)
0.10
0.03
1.50
0.025
0.010
0.015
0.09
0.20
0.15
Table 2 Table of experimental results. Date
*Pendulum
Charge mass (g)
SOD (mm)
Impulse (Ns)
dPerm (mm)
2015-09-14 2015-09-11 2016-02-18 2016-02-18 2016-02-18 2016-02-17 2016-02-17 2015-09-14 2015-09-14 2016-02-18 2015-11-11 2015-10-05 2015-11-11 2015-09-17 2016-02-18 2016-02-18 2015-11-11 2015-10-01 2015-10-01 2016-02-17 2016-02-12 2015-11-11 2015-10-02 2015-10-01 2015-11-11 2015-09-14
Horizontal Horizontal DIC pendulum DIC pendulum DIC pendulum DIC pendulum DIC pendulum Horizontal Horizontal DIC pendulum Horizontal DIC pendulum Horizontal Horizontal DIC pendulum DIC pendulum Horizontal Horizontal Horizontal DIC pendulum DIC pendulum Horizontal Horizontal Horizontal Horizontal Horizontal
50 30 25 20 20 15 10 10 30 25 20 20 20 20 20 20 15 15 15 15 10 10 10 10 10 10
50 50 50 50 50 50 50 50 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
67.4 41.5 41.0 34.1 32.2 23.1 16.7 17.6 46.6 40.0 34.5 34.7 34.4 36.1 33.5 33.2 26.6 27.5 26.5 25.8 19.1 19.1 18.1 18.0 18.2 17.8
40.68 24.19 25.46 20.99 18.06 16.13 11.26 10.61 39.00 31.34 28.72 26.04 25.87 25.60 25.25 24.78 22.00 21.98 21.64 19.24 16.24 16.01 14.05 13.76 13.60 13.15
dPeak (mm)
30.46 26.16 23.16 21.74 16.84
36.27 31.10
30.67 30.24
25.28 22.02
*Pendulum type Horizontal D Pendulum with cameras removed DIC Pendulum D Pendulum with cameras inserted and DIC data available.
TagedPof the test specimens and also provide space to mount a lighting system, as shown in Fig. 3. The cameras were mounted on a rail system to isolate them from vibration and positioned appropriately for the focal distance of the lenses selected, as shown in Fig. 3. The mass of the modified pendulum increased to 308 kg due to the changes (the previous pendulum was less than 30kg when unladen).
TagedPSince the pendulum is at rest at its lowest position prior to the explosion, the maximum forward displacement, X1 will occur at T D 1 4 and the maximum backwards displacement will occur at X2 at T D 34. Therefore:
TagedP2.2.2. Loading conditions TagedPSmall disks of 38 mm diameter PE4 plastic explosive were detonated in the centre of the back face using instantaneous electrical detonators (type M2A3). Two stand off distances of 40 mm and 50 mm were used; the stand-off distance was determined by placing the charge on a polystyrene bridge, as shown in Fig. 4a, and adjusting the length of the bridge legs. A template was used to mark the position of the polystyrene bridge (markers are shown in the photograph in Fig. 4b) to ensure that the centres of the plate and the explosive charge were co-axial (Figs. 5 and 8).
x2 D ¡
x1 D
T x_ 0 ¡bT e 4 2p T x_ 0 ¡3bT e 4 2p
2.3. Impulse measurement TagedPSimple pendulum theory is applied to the motion of the ballistic pendulum. The equation of motion assuming viscous damping can be written as: €x C 2bx_ C v2n x D 0
ð1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 , vn D and vd D vn ¡b where b D TagedPC is the damping coefficient, M is the total mass of the pendulum, experimental rig and T is the natural period of the pendulum motion. C 2M
2p T
Fig. 13. Quasistatic test data showing material response.
ð2Þ ð3Þ
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Fig. 14. Graph of Impulse Vs Charge Mass.
Fig. 15. Graph of permanent mid-point Deflection Vs Impulse.
TagedPRelating x1 and x2 to solve for b produces: 2 x b D ln 1 T x2
ð4Þ
TagedPNow that b can be determined, the initial velocity, x_ 0 ; can be determined from: x_ 0 D
bT
2p x1 e 4 T
ð5Þ
T ultiplying the total loaded mass of the pendulum, mp, with the agedPM initial velocity of the pendulum, x_ 0 ; gives the Impulse, I, imparted onto the test plate by the explosive charge. I D mp x_ 0
ð6Þ
TagedPThe swing of the pendulum was recorded using a laser displacement sensor (CP35MHT80) during each test, and the impulse was determined using the pendulum swing recorded by an oscilloscope. A typical output from the oscilloscope is shown in Fig. 6.
TagedPThis data was processed to determine values for X1 and X2 of the swing of the pendulum and then used to calculate the impulse of the pendulum.
2.4. Transient response measurement TagedP2.4.1. Specimen preparation TagedPThe rear surface of each test plate was painted with a random speckle pattern which was used in the DIC procedure to determine the spatial deformation of the plate. Prior to applying the speckle pattern, the plates were thoroughly cleaned and abraded to ensure that the paint remained adhered plate during testing. The surface was degreased with acetone and then painted with a thin layer of white primer before a black speckle pattern was added. The surface preparation procedure is illustrated in Fig. 7.
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TagedP2.4.2. High speed imaging TagedPTwo IDT vision NR4 S3 high speed cameras were mounted to a vibration isolated aluminium rail system and installed in the modified pendulum, as described in Section 2.2.1. This mounting method, shown in Fig. 3, ensured that the two cameras did not move independently during the test (independent camera movement would have invalidated the calibration of the DIC system before the test). This movement became more challenging to prevent as the charge mass increased. The two cameras were separated and make an approximate 30° included angle. The central web of the pendulum was removed to ensure the view was not obstructed when the camera position changed. The method of two cameras was specifically chosen due to the increase in resolution achieved with the existing hardware. Alternate methods of image splitting such as those described by Rijensky and Rittel [16] would have significantly reduced the frame rate or the available resolution for image capture. This also has the benefit of increasing the achievable DIC resolution by increasing the pixel density in the acquired images. TagedPThe images from the two cameras were synchronised by means of a synchronising cable that connected the two camera control boxes. The cameras were triggered with a custom built TTL trigger circuit that was activated by the detonation of the charge. TagedP35 mm fixed focus lenses were used on each camera and the views were set at 1024 £ 76 pixels. The allowed a full width strip along the mid-line of each plate to be filmed by both cameras (25 £ 300 mm). The frame rate of the cameras were set at 30 000 Fps with the exposure set at 31 m s (which was limited by the available light). At this short exposure a lot of extra illumination was required on the specimen and two custom built LED lights were focused on the test plate during testing. It was found that diffusers were needed for the lighting to ensure uniform specimen illumination and prevent hot spots where the image would appear overexposed. 3. Processing DIC data TagedPThe camera images were post processed using the Dantec Dynamics Istra 4D DIC software package, to calculate the displacement field for the view of the cameras. Prior to testing, calibration was required and was used as an input to the post-processing analysis. The calibration steps were performed prior to each test to account for any movement that may have occurred between experiments. TagedPThe process identifies object points in the images of the two cameras by applying the correlation algorithm and finding homologous points. Taking the imaging parameters into account the contour of the object and the displacements were subsequently calculated. 3.1. Calibration of DIC system TagedPPrior to testing, the projection parameters (intrinsic and extrinsic imaging parameters) were determined from the calibration process. Multiple images of the calibration target were captured in different positions using the cameras set in their respective positions. The calibration target had a known accurate pattern which was recorded with both cameras simultaneously. TagedPThe software then processed these images to locate the target markers from the sequence of images at different positions. From the located target markers, the projection parameter of the whole system, with additional distortion parameters, were calculated based on the pinhole model [17]. A bundle-adjustment algorithm within the software calculated the intrinsic parameters (focal length, principal point, distortion parameter) for each camera, their respective orientation and the extrinsic parameters (translation vector and rotation matrix). The intrinsic and extrinsic calibration values for the system were stored in a calibration file and imported into the analysis. The quality of the measurement was directly related to the
Fig. 16. Permanent deformation profiles along the centre line of the blasted plates obtained by 3D scanning. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
TagedP ccuracy of the projection parameters. By simplifying the calibration a process and providing quality feedback, accurate measurements could be assured. Typically eight images were sufficient to calculate all calibration parameters accurately. 3.2. Correlation method TagedPThe correlation algorithm was based on the tracking of the grey value pattern G(x,y) in small local neighbourhood facets seen in Fig. 9. TagedPDue to a loading of the specimen, this pattern was transformed into a deformed shape. Within the correlation algorithm the difference of these patterns was minimised. By varying the illumination parameters and the parameters of the affine transformation, a matching accuracy of better than 0.08 pixel could be achieved, but
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Fig. 17. Transient plate deformation data from DIC for 10 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPthis varied (up to 5 pixels) during the deformation of the test plates in the worst case example during this experimental set. For this set of tests, an equivalence of 1 pixel D 0.3 mm meant that the worst uncertainty in the DIC data would give an equivalent error of less than 1.5 mm in the deformation data. Subset sizes were fixed at 19 pixels with a grid spacing of 5 pixels to ensure overlap in the subsets. An example of the displacement field which is extracted from the correlation is shown in Fig. 10. Once this displacement field has been calculated for the area of interest, other information such as the strain field, velocity and acceleration field could be calculated based on the displacement field. It should be noted that due to subsets being bigger than a single pixle the technique of correlation reduces the displacement value of a subset to the centre point of each subset. Due to the high resolution of the cameras and the fine speckle pattern used this effect was minimised in the this investigation and all data presented here is raw and unfiltered as exported from the correlation.
3.3. Gauge points and lines TagedPData was extracted from two separate gauge points on each test plate so that easily comparable analysis was possible. To ensure the centre line of each plate was measured, small markers (in form of a small cross) were placed 20 mm from the clamp frame on the centre line of each test plate. These small markers were then used in the DIC analysis to define a gauge line across the centre of each plate as shown in Fig. 11. The gauge point for the midpoint of the plate was defined as the midpoint of this centre line. It was found that if the markers were made too large they would interfere with the DIC analysis. Information such as displacement and strain were extracted at discrete points along the line. Each data point in the field is representative of a facet and any irregularities in the pixels of that facet (associated with motion blur for example), may cause variations in the readings at that point. Once the displacement information for each line is extracted the data is post processed using a
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Fig. 18. Transient plate deformation data from DIC for 15 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPcustom python script to align and plot the information together with the 3D scans of the plates. TagedPFrom the Displacement field a strain field is generated with reference to the undeformed plate as seen in Fig. 12. This strain field represents the strain observed in individual subsets of the correlation. This data often appears more noisy than the displacement field due to the small subset size. 4. Blast test plate material description TagedPThe blast test plates were machined from 3 mm thick Domex 355MC hot rolled low alloy steel, sourced from SSAB. The chemical composition of the steel is shown in Table 1. Quasi-static uni-axial tensile tests were performed on dog bone specimens cut from the
sTagedP ame sheets as the plates, in three different orientations. These tests indicate the level of isotropy in the material and the degree to which rolling has affected the material properties. Because the specimens were cut from different regions of the original plate they also indicate the consistency of the material properties through the width and length of the plate. The longitudinal axes of the dog bone specimens were oriented relative to the rolling direction at 0, 45 and 90°. The specimens were designed according to ASTM E8 [18] and had overall dimensions of 200 mm by 25 mm wide, while the reduced section was 80 mm long and 12.5 mm wide. The specimens were tested at crosshead speeds of 2 mm/min and 150 mm/min (corresponding to engineering strain rates of 4.17 £ 10¡4 s¡1 and 3.12 £ 10¡2 s¡1 respectively). No significant difference in material response was observed between these two testing strain rates.
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Fig. 19. Transient plate deformation data from DIC for 20 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPThe mean average specimen thickness was 3.00 § 0.01 mm. Typical true stress-strain curves are shown in Fig. 13. As expected, the material properties were very consistent in within a set and also across the three orientations. The mean average yield strength of the Domex 355 MC was 444 MPa, ultimate tensile strength was 627 MPa and the percentage elongation at failure was 20%. 5. Experimental results and discussion TagedPThe results of the 26 air-blast experiments are summarised in Table 2. A graph of impulse versus charge mass is shown in Fig. 14. The results of tests at two stand off distances (40 and 50 mm) are indicated in two series for a charge mass range of 1050 g. The
rTagedP esults presented in Fig. 15 show an approximately linear trend of increasing deflection with increasing charge mass, although there is some scatter in the 20 g detonations at a 50 mm SOD. The impulses obtained from the 50 mm stand-off were slightly lower than the 40 mm stand-off impulses. TagedPThe post-test inspection of the plates revealed that all plates exhibited Mode I (that is, large plastic deformation) failure without any indication of tearing or shearing failures. Membrane action and shear stresses would be present as deformation increases in the plate section but without any evidence of rupture due to these internal forces. This was desirable for tests involving high speed cameras, as torn pieces of the plates could have damaged the camera system, and discontinuities such as cracks would have been difficult to process during digital image correlation.
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Fig. 20. Transient plate deformation data from DIC for 25 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPA graph of permanent mid-point displacement versus impulse is shown in Fig. 15. The results show the expected trend of increasing displacement with increasing impulse, and also show that the permanent midpoint displacements exhibited by plates tested at 40 mm stand-off were larger than those exhibited by plates tested at a stand-off distance of 50 mm. The differences in displacement shown in Fig. 15 are greater than the small differences observed in the global impulse transfer at the two stand-off distances. This is attributed to the significant variation in the spatial distribution of the loading at the two stand off distances.
5.1. Final deformation of specimens TagedPThe rear surfaces of the blasted plates were 3D scanned and processed to extract the cross-sectional deformation profile. The permanent displacements along the mid-line of the blasted plates are plotted in Fig. 16a and b, for SODs of 40 mm and 50 mm respectively. The plates are stacked in order of increasing charge mass from bottom to top with charge mass indicated on the left hand side. As expected, the larger charges masses produced larger permanent deformation in the plates. It is also evident from Fig. 16a that the 10 g, 15 g and 20 g tests gave very repeatable profiles shown by the
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Fig. 21. Mid-point transient deflection - time histories for various charge masses.
Fig. 22. Plate strain through the plate centres at 0.7 ms (point of maximum transient deflection).
TagedPoverlapping curves of the repeated tests. The 10 g repeat test at 50 mm SOD, shown in Fig. 16b, also shows excellent repeatability. This indicated that the applied loading and response of the system was repeatable. TagedPAn inspection of the permanent displacement profiles of the plates in Fig. 16a and b shows that the deformation at the 40
TagedPmm (closer) stand-off distance was larger in the plate centre, indicating that the blast loading was more locally applied. This is consistent with observations from previous work by Jacob et al. [14], who noted a change in plate response from localised to more uniformly distributed with increasing stand-off distance and is clearly seen in Fig. 16c.
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TagedPThe general plate deformation profiles are observed to be similar at the different charge mass between the 40 and 50 mm SOD, with the main deviation happening locally under the charge in a 100 mm diameter of the centre of the plate. The deformation of the 50 mm SOD was always found to be lower than the deformation of the 40 mm SOD tests. TagedPWhen comparing the mid point deflection for each of the SODs a linear increase in the mid point deflection is observed with an increase in charge mass.
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Table 3 The maximum centre point strain along the centre line of the test plates. Maximum central strain value (mstrain) Charge mass (g)
40 SOD
50 SOD
10 15 20 25
154 119 177 210
65 83 99 140
5.2. Transient deformation response TagedPThe DIC data is presented in two different ways. Firstly the evolution of the plate profile can be seen by looking at the Z-displacement (out of plane) of the plate. This is shown at discrete points in time together with the observed final deformation profile of the each plate shown in black in Figs. 1720. Secondly, the transient deformation time histories of the midpoint of the plate are shown in Fig. 21. Four charge masses (10, 15, 20 and 25 g) were chosen to show the mid-point deformation-time response at these different charge masses. TagedPAs the deformation of the plate was tracked using the images captured by the high speed camera, it is important to keep in mind the frame rate of the camera was limited to 30 000 fps due to the amount of light needed to illuminate the specimen. Due to this restriction each frame of data is captured at 33 m s intervals. In regions of high plate velocity motion blur was evident, causing irregularities in the DIC data. In frames affected by the motion blur, the profile of the plate may be partially captured resulting in displacement profiles which are irregular or exhibit artificial discontinuities. TagedPThe transient deformation profiles at discrete times are compared in Figs. 1720. From the transient profiles for each of the 40 and 50 SOD tests it can be observed that at 66 ms (blue curve) there is consistently more localised deformation in the 40 SOD series. These profiles are also the most irregular due to motion blur. The deformation appears to be localised to a 100 mm diameter plastic hinge in the centre of the plate for both SODs with a higher midpoint deflection in the 40 SOD series. Similar observations with regard to the radially expanding deformation are mentioned by Tiwari et al. [12] looking at a much smaller area of test plate. At 165 ms the plastic hinge has moved out towards the clamp frame and appears at around 150 mm diameter, the shape of the deformed section is conical between the midpoint and the plastic hinge. By 297 ms, the plastic hinge has reached a diameter of approximately 250 mm and the general shape is bell-shaped with a point of inflection at approximately the 100 mm diameter around the centre. This point of inflection becomes more noticeable as the plate approaches its maximum transient deformation and at about 561 ms is the most pronounced. By the time the plates reach their maximum transient deformation the point of inflection has become less significant and is almost undetectable by the time the plate reaches its final shape . During the evolution of the plate profile there is a very localised initial deformation with a radially outward moving plastic hinge that transitions into a more global and final profile after 198 ms. TagedPThe transient midpoint deflection time histories shown in Fig. 21, show that there is a consistent time to reach peak transient deflection of 0.7 ms. This was observed through both the experimental series together with very similar oscillations of the mid point with a period of 2.82 ms. The midpoint oscillates around the final deformation point illustrated by the dashed lines. Fig. 21 also shows very good repeatability of the transient midpoint displacement at different charge masses. The displacement histories produce very similar profiles at each charge mass. TagedPThe difference in the transient mid point deflection and final mid point deflection, seen in Table 2 for both stand off distances, can be seen to decrease from a maximum of approximately 5.8 mm at the
sTagedP maller charge masses of 10 g down to approximately 5 mm at the larger charge mass of 25 g. This decrease could also be seen in data presented by Neurberger et al. [20]. TagedPIt is further noted that up to the point of maximum transient midpoint displacement the general plate profile does not match the final deformed shape at any point. This implies that any measurements extracted from numerical simulations or DIC measurements might not match the final deformation profile until the plate has been allowed to settle. TagedPThe strain along the centre line of the plates (at the point of maximum transient deflection) is shown in Fig. 22. It can be clearly seen in the Fig. 22 that the strain along the mid line is localised at the centre of the plate. The strain peaks at the centre and decayed to a very small value at appropriately 50 mm from the centre. The minimum point appeared to co-incide with the point of inflection in the permanent deflection profile seen in Fig. 16. The maximum strain increased with a decrease in Stand Off Distance and an increase in charge mass. Representative values of the maximum central strain value along the centre line of the plates are shown in Table 3, grouped by SOD. 6. Conclusions TagedPThe transient response and permanent deformation of fully clamped, circular, Domex 355MC steel plates to air-blast loading is reported. The loading was generated by detonating various quantities of PE4 at 40 mm and 50 mm SODs. The blast pendulum was modified to incorporate the camera system and lighting which moves with the pendulum as it swings allowing for simultaneous measurements of impulse and transient deformation. A blast shroud was added to the pendulum to protect the camera system from the explosive flash and the subsequent pressure loading. The high speed images were processed using digital image correlation techniques to obtain the transient deformation profiles of the plates. The transient plate deformation profiles do not match the final plate profiles during the period of recorded data. The difference between the measured transient mid-point displacement and final mid-point of each test was observed to decrease with an increase in charge mass and an increase in global deformation. Permanent deformation increased linearly with increasing impulse and decreased with increasing stand-off distance, as indicated by previous work. Acknowledgements TagedPThe authors are grateful to the UCT University Research Committee, The David and Elaine Potter Foundation and the National Research Foundation (NRF) of South Africa for their financial support. Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. The donations of Domex steel from SSAB and Vulcan Steel are gratefully acknowledged. The authors would also like to thank the staff of the Mechanical Engineering workshop at UCT for their assistance in machining the specimens and pendulum parts.
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References TagedP [1] Nurick G, Martin J. Deformation of thin plates subjected to impulsive loading - a review. part 2: experimental studies. Int J Impact Eng 1989;8:171–86. TagedP [2] Jones N. Structural impact. Cambridge University Press; 1989. TagedP [3] Nurick G, Martin J. Deformation of thin plates subjected to impulsive loading - a review. part 1: theoretical consideration. Int J Impact Eng 1989;8:159–69. TagedP [4] Bonorchis D. Analysis and simulation of welded plates subjected to blast loading. University of Cape Town Ph.D. thesis; 2007. TagedP [5] Bonorchis D, Nurick G. The influence of boundary conditions on the loading of rectangular plates subjected to localised blast loading - importance in numerical simulations. Int J Impact Eng 2009;36:40–52. TagedP [6] Menkes S, Opat H. Tearing and shear failures in explosively loaded clamped beams. Exp Mech 1973;13:480–6. TagedP [7] Neuberger A, Peles S, Rittel D. Scaling the response of circular plates subjected to large and close-range spherical explosions. part 1: air-blast loading. Int J Impact Eng 2007;34:859–73. TagedP [8] Sutton M, Wolters W, Peters W, Ranson W, McNeill S. Determination of displacements using an improved digital correlation method. Image Vis Comput 1983;1 (3):133–9 http://dx.doi.org/10.1016/0262-8856(83)90064-1. TagedP [9] He ZH, Sutton MA, Ranson WF, Peters WH. Two-dimensional fluid-velocity measurements by use of digital-speckle correlation techniques. Exp Mech 1984;24(2):117–21. doi: 10.1007/BF02324993. TagedP[10] Chu TC, Ranson WF, Sutton MA. Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech 1985;25(3):232–44. doi: 10.1007/ BF02325092.
TagedP[11] Fourney W, Leiste U, Bonenberger R, Goodings D. Mechanism of loading on plates due to explosive detonation. Fragblast 2005;9:205–17. TagedP[12] Tiwari V, Sutton MA, McNeill S, Xu S, Deng X, Fourney WL, et al. Application of 3d image correlation for full-field transient plate deformation measurements during blast loading. Int J Impact Eng 2009;36(6):862–74 http://dx.doi.org/10.1016/ j.ijimpeng.2008.09.010. TagedP[13] Aune V, Fagerholt E, Hauge K, Langseth M, Børvik T. Experimental study on the response of thin aluminium and steel plates subjected to airblast loading. Int J Impact Eng 2016;90:106–21. TagedP[14] Jacob N, Yuen SCK, Nurick G, Bonorchis D, Desai S. Scaling aspects of quadrangular plates subjected to localised blast loads - experiments and predictions. Int J Impact Eng 2004;30:1179–208. TagedP[15] Langdon G, Yuen SK, Nurick G. Experimental and numerical studies on the response of quadrangular stiffened plates. part ii: localised blast loading. Int J Impact Eng 2005;31(1):85–111. TagedP[16] Rijensky O, Rittel D. Polyurea coated aluminum plates under hydrodynamic loading: does side matter? Int J Impact Eng 2016;98:1–12 http://dx.doi.org/ 10.1016/j.ijimpeng.2016.07.006. TagedP[17] Thorsten~Siebert MJC. Application of high speed digital image correlation for vibration mode shape analysis (white paper). Technical report. Dantec Dynamics; 2010. TagedP[18] ASTM. E8/e8m-15a standard test methods for tension testing of metallic materials. Technical report. ASTM International; 2015. TagedP[19] SSAB. Domex 355mc material data sheet. Technical report. SSAB; 2015. TagedP[20] Neuberger A, Peles S, Rittel D. Springback of circular clamped armor steel plates subjected to spherical air-blast loading. Int J Impact Eng 2009;36(1):53–60.
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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Transient response of steel plates subjected to close proximity explosive detonations in air TagedPD1X XR.J. CurryD2X X*, D3X XG.S. LangdonD4X X TagedPBISRU Department of Mechanical Engineering, University of Cape Town, Rondebosch 7700, South Africa
TAGEDPA R T I C L E
I N F O
Article History: Received 14 September 2016 Revised 2 December 2016 Accepted 4 December 2016 Available online 14 December 2016 TagedPKeywords: Blast loading Transient response Plates Deformation Digital image correlation
TAGEDPA B S T R A C T
The permanent deformation and failure of steel plates subjected to air-blast loading has been the subject of numerous investigations. The transient deformation of such intensely loaded plates has been difficult to obtain due to experimental difficulties. In recent times, high speed imaging and digital image correlation techniques have enabled reliable non-contact measurement of deformation and strain in various applications, such as tensile testing and far-field impulsive loading response of large plated structures. This paper investigates the transient deformation and strain evolution of a deformable plate subjected to air blast loading arising from explosives detonated in close proximity to the plates. The experiments made use of a blast pendulum to measure the impulse imparted on the plates. The pendulum modifications required to accommodate the high speed camera system are described. Results from blast experiments are used to show the influence of stand-off distance on the transient response and permanent deformation of thin steel plates subjected to air blast loading. The difference between maximum transient mid-point deflection and final deformation decreased with an increase in charge mass and global deformation. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction TagedPDue to the current global social and political climate, explosive threats loom larger in the public consciousness than ever before. Explosive threats can be either accidental (such as a gas explosion aboard an offshore platform) or deliberate (such as terrorist activity or military action). The common thread in deliberate explosions is an explosive substance connected to a detonation device, with examples being pipe bombs, improvised explosive devices (IEDs) and landmines. TagedPIn the interests of public safety and security, the need to protect people, equipment and structures from explosions has greatly increased. A great deal of effort has gone into preventing an explosive detonation, such as improving screening at airports and active mitigation methods in military systems. However, active mitigation techniques are not practicable for everyday situations and screening methods will not always work perfectly. Hence, there is a need to understand the loading arising from an explosive detonation and the damage that is sustained by structures subjected to blast loading from close proximity explosive detonations. This improved understanding will assist in efforts made to prevent injury or loss of life during explosions. TagedPThere is little full-scale explosion test data available as full scale *
Corresponding author. E-mail address: [email protected] (R.J. Curry).
http://dx.doi.org/10.1016/j.ijimpeng.2016.12.004 0734-743X/© 2016 Elsevier Ltd. All rights reserved.
tTagedP ests are prohibitively expensive and time consuming to perform, and often the findings are classified by the military. Small scale testing offers a number of advantages such as reducing the expense, allowing better control of the test process variables (explosive size and geometry, accurate positioning of the explosive, stand-off distance to target structure) and potentially improved measurement of parameters such as impulse, pressure and structural response. The link between the small scale experimental and the full scale testing is being able to scale the work. TagedPExtensive laboratory scale experimental studies were performed by Nurick and Martin [1] with the aim of understanding the large permanent ductile deformation and rupture of plates, beams and shells due to air-blast loading. Jones [2] and Nurick and Martin [1,3] present overviews of theoretical and experimental studies of plates subjected to uniformly distributed impulsive loading. Further studies were reported, examining the influence of boundary conditions (clamped or built-in) [4,5] and the spatial distribution of the loading. In each case, the loading was assumed to be impulsive and reported on the permanent deformation and failure of the structures. Many of these make use of a blast pendulum in order to measure the impulse imparted on the plates outlined by Nurick [1]. TagedPMenkes and Opat [6] were the first to define the failure modes of blast loaded clamped beams. Three modes were observed as the applied uniform impulse was increased:
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TagedP
Fig. 1. Photograph of the modified pendulum hanging in blast chamber. Clearly showing the 300 mm circular exposed test area on the plate.
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TagedP Mode I - Large inelastic deformation TagedP Mode II - Tensile tearing at the supports TagedP Mode III - Transverse shear failure at supports
TagedPUnderstanding the transient deformation history of plates prior to failure would add valuable insight to the mechanisms which may influence and drive the different modes of deformation. TagedPCapturing transient test data by placing instrumentation on or in close proximity to a test plate poses a problem where the instrumentation itself may influence the plate response. Simple tools such as the deformation combs described by Neurberger [7] have yielded valuable insight into maximum transient deflection of plates but were unable to provide information about transient deformation profiles or time to peak deflection. Non-contact measurement techniques such as light interference and high speed filming have proved the most successful in previous works when trying to extract richer data. TagedPThe use of 3D Digital Image correlation for displacement measurement has become a well established technique [8] used in many different applications [9,10]. Fourney et al. [11] used a 3D DIC system to measure the transient response of test plates under blast conditions. Velocity and acceleration profiles were both reported. An issue noted in this work was the constraint of camera resolution and lighting of the specimen as the experimental setup tracked an
Fig. 2. Schematic drawing of modified pendulum, showing internal arrangement (shroud removed for clarity).
Fig. 3. The Modified pendulum with shrouds removed to show the inside.
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Fig. 4. Charge configuration.
Fig. 5. Ballistic pendulum geometry.
Fig. 6. Typical displacement versus time output from the displacement sensor.
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TagedPunconstrained plate and clamp frame. The rigid body motion of the clamp frame was removed to determine the motion of the test specimen. One particular problem with this method was that the camera must focus on a larger area (including the clamp frame and the surrounding area to ensure the plate could be tracked once it started moving). This resulted in much smaller apertures set on the lenses to ensure sufficient depth of field and more challenging lighting conditions. This was further aggravated by the changing light conditions on the specimen as it moved. This work by Fourney et al.was expanded together with Sutton and Tiwari et al. [12] increasing the charge mass slightly and reported a circular deformation wave moving radially outward from the centre of the plate. TagedPWork by Borvik et al. [13] proposed the use of a stationary rigid clamp frame with the cameras filming from some distance away (but in the same room as the test). It was noted by Borvik et al. [13] that the movement of the cameras as the blast wave impinged on them caused the DIC technique to stop working, limiting the duration of data. Borvik et al. [13] also reported inconsistencies in the trigger system and problems with the adhesion of the painted speckle pattern on the test plate. As a result successful data capture was achieved for a limited number of tests. One further complication in the technique presented is that the impulse of the plate is not a direct measurement but rather an inferred value based on pressure sensor readings during calibration tests. TagedPIn an effort to overcome some of these difficulties reported in previous work, an improved technique has been developed. In this paper, the transient response of Domex steel to air-blast loading arising from detonations of plastic explosive at two different standoff distances (SODs) is reported. Firstly, the experimental method for close proximity air-blast testing using high speed imaging is reported, including detail about the modification of the pendulum system to incorporate the camera system. Secondly, details regarding the digital image correlation technique are reported. Thirdly, the results of the material characterisation and air-blast loading experiments are reported. The influence of charge mass and stand-off distance on the transient response and permanent deformation of steel plates is discussed. 2. Experimental method TagedPThe experimental method comprises three distinct areas: blast test specimen description, modifications to the conventional blast pendulum and transient response measurement.
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Fig. 7. The 400 mm £ 400 mm test plate used, showing the bolt holes with the preparation steps to create the DIC speckle pattern.
TagedP ith a side length of 400 mm. When placed in the clamp frame, w the plates had a exposed circular area with a diameter of 300 mm, as shown in Fig. 1. 2.2. Experimental arrangement TagedPExperiments were performed at the Blast Impact and Survivability Research Unit (BISRU) at the University of Cape Town. Each test plate was bolted into the clamp frame with 12 bolts evenly spaced around the circular exposed area at a pitch circle diameter of 350 mm. The clamp frame is chamfered at a 45° angle around the edge of the plate to reduce pressure build up and recirculation [4,5]. The clamp frames and test plates were mounted to a modified pendulum, which was used to determine the impulse and house the cameras used for transient measurements. The experimental arrangement is shown in Figs. 1 and 2.
2.1. Blast test specimens T he test plates were made from 3 mm thick Domex 355MC, a agedPT high strength hot rolled low alloy steel. The plates were square
TagedP2.2.1. Modification of the pendulum to incorporate high speed imaging TagedPThe horizontal pendulum used at BISRU for many years [1,5,14,15]consisted of an I-beam suspended from four cables with a
Fig. 8. The calibration target shown together with the software identified markers.
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Fig. 9. The DIC stereo subsets.
Fig. 10. The Z Displacement field obtained from the correlation seen overlayed on the left(top) and right (bottom) images shortly after detonation.
Fig. 11. The gauge point and line extracted in the DIC.
TagedPmounting frame at the front to support the test specimen and a counterbalance mass at the rear. It was not possible to mount the cameras to this pendulum as it would have provided no protection from the intense light burst during an explosion, or the ensuing blast wave. The light would have saturated the camera sensor, making it impossible capture images of the deformation response, and the blast wave would have caused considerable damage to the camera body and lenses (and the electronic systems and cabling). TagedPIn order to protect the camera system, a new pendulum was constructed from Mild Steel with a shroud seen around it to protect the cameras from the blast. The shroud isolated the cameras from the blast loading and protected the cameras from the intense light emissions that could saturate the camera sensor. The modified pendulum is shown in Figs. 1 and 2. Fig. 1 is a photograph of the pendulum prior to a test, showing the steel shrouding in place. Fig. 2 is a schematic drawing of the pendulum, shown without the shroud to allow viewing of the internal arrangement. Part of the web was removed in order to give the cameras a direct line of sight to the rear surface
Fig. 12. Typical example of the engineering strain field in the radial plate direction extracted from the DIC.
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Table 1 Table of chemical Ladle analysis of Domex 355MC steel [19]. C (max %)
Si (max %)
Mn (max %)
P (max %)
S (max %)
Al (min %)
Nb (max %)
V (max %)
Ti (max %)
0.10
0.03
1.50
0.025
0.010
0.015
0.09
0.20
0.15
Table 2 Table of experimental results. Date
*Pendulum
Charge mass (g)
SOD (mm)
Impulse (Ns)
dPerm (mm)
2015-09-14 2015-09-11 2016-02-18 2016-02-18 2016-02-18 2016-02-17 2016-02-17 2015-09-14 2015-09-14 2016-02-18 2015-11-11 2015-10-05 2015-11-11 2015-09-17 2016-02-18 2016-02-18 2015-11-11 2015-10-01 2015-10-01 2016-02-17 2016-02-12 2015-11-11 2015-10-02 2015-10-01 2015-11-11 2015-09-14
Horizontal Horizontal DIC pendulum DIC pendulum DIC pendulum DIC pendulum DIC pendulum Horizontal Horizontal DIC pendulum Horizontal DIC pendulum Horizontal Horizontal DIC pendulum DIC pendulum Horizontal Horizontal Horizontal DIC pendulum DIC pendulum Horizontal Horizontal Horizontal Horizontal Horizontal
50 30 25 20 20 15 10 10 30 25 20 20 20 20 20 20 15 15 15 15 10 10 10 10 10 10
50 50 50 50 50 50 50 50 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
67.4 41.5 41.0 34.1 32.2 23.1 16.7 17.6 46.6 40.0 34.5 34.7 34.4 36.1 33.5 33.2 26.6 27.5 26.5 25.8 19.1 19.1 18.1 18.0 18.2 17.8
40.68 24.19 25.46 20.99 18.06 16.13 11.26 10.61 39.00 31.34 28.72 26.04 25.87 25.60 25.25 24.78 22.00 21.98 21.64 19.24 16.24 16.01 14.05 13.76 13.60 13.15
dPeak (mm)
30.46 26.16 23.16 21.74 16.84
36.27 31.10
30.67 30.24
25.28 22.02
*Pendulum type Horizontal D Pendulum with cameras removed DIC Pendulum D Pendulum with cameras inserted and DIC data available.
TagedPof the test specimens and also provide space to mount a lighting system, as shown in Fig. 3. The cameras were mounted on a rail system to isolate them from vibration and positioned appropriately for the focal distance of the lenses selected, as shown in Fig. 3. The mass of the modified pendulum increased to 308 kg due to the changes (the previous pendulum was less than 30kg when unladen).
TagedPSince the pendulum is at rest at its lowest position prior to the explosion, the maximum forward displacement, X1 will occur at T D 1 4 and the maximum backwards displacement will occur at X2 at T D 34. Therefore:
TagedP2.2.2. Loading conditions TagedPSmall disks of 38 mm diameter PE4 plastic explosive were detonated in the centre of the back face using instantaneous electrical detonators (type M2A3). Two stand off distances of 40 mm and 50 mm were used; the stand-off distance was determined by placing the charge on a polystyrene bridge, as shown in Fig. 4a, and adjusting the length of the bridge legs. A template was used to mark the position of the polystyrene bridge (markers are shown in the photograph in Fig. 4b) to ensure that the centres of the plate and the explosive charge were co-axial (Figs. 5 and 8).
x2 D ¡
x1 D
T x_ 0 ¡bT e 4 2p T x_ 0 ¡3bT e 4 2p
2.3. Impulse measurement TagedPSimple pendulum theory is applied to the motion of the ballistic pendulum. The equation of motion assuming viscous damping can be written as: €x C 2bx_ C v2n x D 0
ð1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 , vn D and vd D vn ¡b where b D TagedPC is the damping coefficient, M is the total mass of the pendulum, experimental rig and T is the natural period of the pendulum motion. C 2M
2p T
Fig. 13. Quasistatic test data showing material response.
ð2Þ ð3Þ
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Fig. 14. Graph of Impulse Vs Charge Mass.
Fig. 15. Graph of permanent mid-point Deflection Vs Impulse.
TagedPRelating x1 and x2 to solve for b produces: 2 x b D ln 1 T x2
ð4Þ
TagedPNow that b can be determined, the initial velocity, x_ 0 ; can be determined from: x_ 0 D
bT
2p x1 e 4 T
ð5Þ
T ultiplying the total loaded mass of the pendulum, mp, with the agedPM initial velocity of the pendulum, x_ 0 ; gives the Impulse, I, imparted onto the test plate by the explosive charge. I D mp x_ 0
ð6Þ
TagedPThe swing of the pendulum was recorded using a laser displacement sensor (CP35MHT80) during each test, and the impulse was determined using the pendulum swing recorded by an oscilloscope. A typical output from the oscilloscope is shown in Fig. 6.
TagedPThis data was processed to determine values for X1 and X2 of the swing of the pendulum and then used to calculate the impulse of the pendulum.
2.4. Transient response measurement TagedP2.4.1. Specimen preparation TagedPThe rear surface of each test plate was painted with a random speckle pattern which was used in the DIC procedure to determine the spatial deformation of the plate. Prior to applying the speckle pattern, the plates were thoroughly cleaned and abraded to ensure that the paint remained adhered plate during testing. The surface was degreased with acetone and then painted with a thin layer of white primer before a black speckle pattern was added. The surface preparation procedure is illustrated in Fig. 7.
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TagedP2.4.2. High speed imaging TagedPTwo IDT vision NR4 S3 high speed cameras were mounted to a vibration isolated aluminium rail system and installed in the modified pendulum, as described in Section 2.2.1. This mounting method, shown in Fig. 3, ensured that the two cameras did not move independently during the test (independent camera movement would have invalidated the calibration of the DIC system before the test). This movement became more challenging to prevent as the charge mass increased. The two cameras were separated and make an approximate 30° included angle. The central web of the pendulum was removed to ensure the view was not obstructed when the camera position changed. The method of two cameras was specifically chosen due to the increase in resolution achieved with the existing hardware. Alternate methods of image splitting such as those described by Rijensky and Rittel [16] would have significantly reduced the frame rate or the available resolution for image capture. This also has the benefit of increasing the achievable DIC resolution by increasing the pixel density in the acquired images. TagedPThe images from the two cameras were synchronised by means of a synchronising cable that connected the two camera control boxes. The cameras were triggered with a custom built TTL trigger circuit that was activated by the detonation of the charge. TagedP35 mm fixed focus lenses were used on each camera and the views were set at 1024 £ 76 pixels. The allowed a full width strip along the mid-line of each plate to be filmed by both cameras (25 £ 300 mm). The frame rate of the cameras were set at 30 000 Fps with the exposure set at 31 m s (which was limited by the available light). At this short exposure a lot of extra illumination was required on the specimen and two custom built LED lights were focused on the test plate during testing. It was found that diffusers were needed for the lighting to ensure uniform specimen illumination and prevent hot spots where the image would appear overexposed. 3. Processing DIC data TagedPThe camera images were post processed using the Dantec Dynamics Istra 4D DIC software package, to calculate the displacement field for the view of the cameras. Prior to testing, calibration was required and was used as an input to the post-processing analysis. The calibration steps were performed prior to each test to account for any movement that may have occurred between experiments. TagedPThe process identifies object points in the images of the two cameras by applying the correlation algorithm and finding homologous points. Taking the imaging parameters into account the contour of the object and the displacements were subsequently calculated. 3.1. Calibration of DIC system TagedPPrior to testing, the projection parameters (intrinsic and extrinsic imaging parameters) were determined from the calibration process. Multiple images of the calibration target were captured in different positions using the cameras set in their respective positions. The calibration target had a known accurate pattern which was recorded with both cameras simultaneously. TagedPThe software then processed these images to locate the target markers from the sequence of images at different positions. From the located target markers, the projection parameter of the whole system, with additional distortion parameters, were calculated based on the pinhole model [17]. A bundle-adjustment algorithm within the software calculated the intrinsic parameters (focal length, principal point, distortion parameter) for each camera, their respective orientation and the extrinsic parameters (translation vector and rotation matrix). The intrinsic and extrinsic calibration values for the system were stored in a calibration file and imported into the analysis. The quality of the measurement was directly related to the
Fig. 16. Permanent deformation profiles along the centre line of the blasted plates obtained by 3D scanning. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
TagedP ccuracy of the projection parameters. By simplifying the calibration a process and providing quality feedback, accurate measurements could be assured. Typically eight images were sufficient to calculate all calibration parameters accurately. 3.2. Correlation method TagedPThe correlation algorithm was based on the tracking of the grey value pattern G(x,y) in small local neighbourhood facets seen in Fig. 9. TagedPDue to a loading of the specimen, this pattern was transformed into a deformed shape. Within the correlation algorithm the difference of these patterns was minimised. By varying the illumination parameters and the parameters of the affine transformation, a matching accuracy of better than 0.08 pixel could be achieved, but
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Fig. 17. Transient plate deformation data from DIC for 10 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPthis varied (up to 5 pixels) during the deformation of the test plates in the worst case example during this experimental set. For this set of tests, an equivalence of 1 pixel D 0.3 mm meant that the worst uncertainty in the DIC data would give an equivalent error of less than 1.5 mm in the deformation data. Subset sizes were fixed at 19 pixels with a grid spacing of 5 pixels to ensure overlap in the subsets. An example of the displacement field which is extracted from the correlation is shown in Fig. 10. Once this displacement field has been calculated for the area of interest, other information such as the strain field, velocity and acceleration field could be calculated based on the displacement field. It should be noted that due to subsets being bigger than a single pixle the technique of correlation reduces the displacement value of a subset to the centre point of each subset. Due to the high resolution of the cameras and the fine speckle pattern used this effect was minimised in the this investigation and all data presented here is raw and unfiltered as exported from the correlation.
3.3. Gauge points and lines TagedPData was extracted from two separate gauge points on each test plate so that easily comparable analysis was possible. To ensure the centre line of each plate was measured, small markers (in form of a small cross) were placed 20 mm from the clamp frame on the centre line of each test plate. These small markers were then used in the DIC analysis to define a gauge line across the centre of each plate as shown in Fig. 11. The gauge point for the midpoint of the plate was defined as the midpoint of this centre line. It was found that if the markers were made too large they would interfere with the DIC analysis. Information such as displacement and strain were extracted at discrete points along the line. Each data point in the field is representative of a facet and any irregularities in the pixels of that facet (associated with motion blur for example), may cause variations in the readings at that point. Once the displacement information for each line is extracted the data is post processed using a
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Fig. 18. Transient plate deformation data from DIC for 15 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPcustom python script to align and plot the information together with the 3D scans of the plates. TagedPFrom the Displacement field a strain field is generated with reference to the undeformed plate as seen in Fig. 12. This strain field represents the strain observed in individual subsets of the correlation. This data often appears more noisy than the displacement field due to the small subset size. 4. Blast test plate material description TagedPThe blast test plates were machined from 3 mm thick Domex 355MC hot rolled low alloy steel, sourced from SSAB. The chemical composition of the steel is shown in Table 1. Quasi-static uni-axial tensile tests were performed on dog bone specimens cut from the
sTagedP ame sheets as the plates, in three different orientations. These tests indicate the level of isotropy in the material and the degree to which rolling has affected the material properties. Because the specimens were cut from different regions of the original plate they also indicate the consistency of the material properties through the width and length of the plate. The longitudinal axes of the dog bone specimens were oriented relative to the rolling direction at 0, 45 and 90°. The specimens were designed according to ASTM E8 [18] and had overall dimensions of 200 mm by 25 mm wide, while the reduced section was 80 mm long and 12.5 mm wide. The specimens were tested at crosshead speeds of 2 mm/min and 150 mm/min (corresponding to engineering strain rates of 4.17 £ 10¡4 s¡1 and 3.12 £ 10¡2 s¡1 respectively). No significant difference in material response was observed between these two testing strain rates.
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Fig. 19. Transient plate deformation data from DIC for 20 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPThe mean average specimen thickness was 3.00 § 0.01 mm. Typical true stress-strain curves are shown in Fig. 13. As expected, the material properties were very consistent in within a set and also across the three orientations. The mean average yield strength of the Domex 355 MC was 444 MPa, ultimate tensile strength was 627 MPa and the percentage elongation at failure was 20%. 5. Experimental results and discussion TagedPThe results of the 26 air-blast experiments are summarised in Table 2. A graph of impulse versus charge mass is shown in Fig. 14. The results of tests at two stand off distances (40 and 50 mm) are indicated in two series for a charge mass range of 1050 g. The
rTagedP esults presented in Fig. 15 show an approximately linear trend of increasing deflection with increasing charge mass, although there is some scatter in the 20 g detonations at a 50 mm SOD. The impulses obtained from the 50 mm stand-off were slightly lower than the 40 mm stand-off impulses. TagedPThe post-test inspection of the plates revealed that all plates exhibited Mode I (that is, large plastic deformation) failure without any indication of tearing or shearing failures. Membrane action and shear stresses would be present as deformation increases in the plate section but without any evidence of rupture due to these internal forces. This was desirable for tests involving high speed cameras, as torn pieces of the plates could have damaged the camera system, and discontinuities such as cracks would have been difficult to process during digital image correlation.
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Fig. 20. Transient plate deformation data from DIC for 25 g charge detonations. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TagedPA graph of permanent mid-point displacement versus impulse is shown in Fig. 15. The results show the expected trend of increasing displacement with increasing impulse, and also show that the permanent midpoint displacements exhibited by plates tested at 40 mm stand-off were larger than those exhibited by plates tested at a stand-off distance of 50 mm. The differences in displacement shown in Fig. 15 are greater than the small differences observed in the global impulse transfer at the two stand-off distances. This is attributed to the significant variation in the spatial distribution of the loading at the two stand off distances.
5.1. Final deformation of specimens TagedPThe rear surfaces of the blasted plates were 3D scanned and processed to extract the cross-sectional deformation profile. The permanent displacements along the mid-line of the blasted plates are plotted in Fig. 16a and b, for SODs of 40 mm and 50 mm respectively. The plates are stacked in order of increasing charge mass from bottom to top with charge mass indicated on the left hand side. As expected, the larger charges masses produced larger permanent deformation in the plates. It is also evident from Fig. 16a that the 10 g, 15 g and 20 g tests gave very repeatable profiles shown by the
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Fig. 21. Mid-point transient deflection - time histories for various charge masses.
Fig. 22. Plate strain through the plate centres at 0.7 ms (point of maximum transient deflection).
TagedPoverlapping curves of the repeated tests. The 10 g repeat test at 50 mm SOD, shown in Fig. 16b, also shows excellent repeatability. This indicated that the applied loading and response of the system was repeatable. TagedPAn inspection of the permanent displacement profiles of the plates in Fig. 16a and b shows that the deformation at the 40
TagedPmm (closer) stand-off distance was larger in the plate centre, indicating that the blast loading was more locally applied. This is consistent with observations from previous work by Jacob et al. [14], who noted a change in plate response from localised to more uniformly distributed with increasing stand-off distance and is clearly seen in Fig. 16c.
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TagedPThe general plate deformation profiles are observed to be similar at the different charge mass between the 40 and 50 mm SOD, with the main deviation happening locally under the charge in a 100 mm diameter of the centre of the plate. The deformation of the 50 mm SOD was always found to be lower than the deformation of the 40 mm SOD tests. TagedPWhen comparing the mid point deflection for each of the SODs a linear increase in the mid point deflection is observed with an increase in charge mass.
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Table 3 The maximum centre point strain along the centre line of the test plates. Maximum central strain value (mstrain) Charge mass (g)
40 SOD
50 SOD
10 15 20 25
154 119 177 210
65 83 99 140
5.2. Transient deformation response TagedPThe DIC data is presented in two different ways. Firstly the evolution of the plate profile can be seen by looking at the Z-displacement (out of plane) of the plate. This is shown at discrete points in time together with the observed final deformation profile of the each plate shown in black in Figs. 1720. Secondly, the transient deformation time histories of the midpoint of the plate are shown in Fig. 21. Four charge masses (10, 15, 20 and 25 g) were chosen to show the mid-point deformation-time response at these different charge masses. TagedPAs the deformation of the plate was tracked using the images captured by the high speed camera, it is important to keep in mind the frame rate of the camera was limited to 30 000 fps due to the amount of light needed to illuminate the specimen. Due to this restriction each frame of data is captured at 33 m s intervals. In regions of high plate velocity motion blur was evident, causing irregularities in the DIC data. In frames affected by the motion blur, the profile of the plate may be partially captured resulting in displacement profiles which are irregular or exhibit artificial discontinuities. TagedPThe transient deformation profiles at discrete times are compared in Figs. 1720. From the transient profiles for each of the 40 and 50 SOD tests it can be observed that at 66 ms (blue curve) there is consistently more localised deformation in the 40 SOD series. These profiles are also the most irregular due to motion blur. The deformation appears to be localised to a 100 mm diameter plastic hinge in the centre of the plate for both SODs with a higher midpoint deflection in the 40 SOD series. Similar observations with regard to the radially expanding deformation are mentioned by Tiwari et al. [12] looking at a much smaller area of test plate. At 165 ms the plastic hinge has moved out towards the clamp frame and appears at around 150 mm diameter, the shape of the deformed section is conical between the midpoint and the plastic hinge. By 297 ms, the plastic hinge has reached a diameter of approximately 250 mm and the general shape is bell-shaped with a point of inflection at approximately the 100 mm diameter around the centre. This point of inflection becomes more noticeable as the plate approaches its maximum transient deformation and at about 561 ms is the most pronounced. By the time the plates reach their maximum transient deformation the point of inflection has become less significant and is almost undetectable by the time the plate reaches its final shape . During the evolution of the plate profile there is a very localised initial deformation with a radially outward moving plastic hinge that transitions into a more global and final profile after 198 ms. TagedPThe transient midpoint deflection time histories shown in Fig. 21, show that there is a consistent time to reach peak transient deflection of 0.7 ms. This was observed through both the experimental series together with very similar oscillations of the mid point with a period of 2.82 ms. The midpoint oscillates around the final deformation point illustrated by the dashed lines. Fig. 21 also shows very good repeatability of the transient midpoint displacement at different charge masses. The displacement histories produce very similar profiles at each charge mass. TagedPThe difference in the transient mid point deflection and final mid point deflection, seen in Table 2 for both stand off distances, can be seen to decrease from a maximum of approximately 5.8 mm at the
sTagedP maller charge masses of 10 g down to approximately 5 mm at the larger charge mass of 25 g. This decrease could also be seen in data presented by Neurberger et al. [20]. TagedPIt is further noted that up to the point of maximum transient midpoint displacement the general plate profile does not match the final deformed shape at any point. This implies that any measurements extracted from numerical simulations or DIC measurements might not match the final deformation profile until the plate has been allowed to settle. TagedPThe strain along the centre line of the plates (at the point of maximum transient deflection) is shown in Fig. 22. It can be clearly seen in the Fig. 22 that the strain along the mid line is localised at the centre of the plate. The strain peaks at the centre and decayed to a very small value at appropriately 50 mm from the centre. The minimum point appeared to co-incide with the point of inflection in the permanent deflection profile seen in Fig. 16. The maximum strain increased with a decrease in Stand Off Distance and an increase in charge mass. Representative values of the maximum central strain value along the centre line of the plates are shown in Table 3, grouped by SOD. 6. Conclusions TagedPThe transient response and permanent deformation of fully clamped, circular, Domex 355MC steel plates to air-blast loading is reported. The loading was generated by detonating various quantities of PE4 at 40 mm and 50 mm SODs. The blast pendulum was modified to incorporate the camera system and lighting which moves with the pendulum as it swings allowing for simultaneous measurements of impulse and transient deformation. A blast shroud was added to the pendulum to protect the camera system from the explosive flash and the subsequent pressure loading. The high speed images were processed using digital image correlation techniques to obtain the transient deformation profiles of the plates. The transient plate deformation profiles do not match the final plate profiles during the period of recorded data. The difference between the measured transient mid-point displacement and final mid-point of each test was observed to decrease with an increase in charge mass and an increase in global deformation. Permanent deformation increased linearly with increasing impulse and decreased with increasing stand-off distance, as indicated by previous work. Acknowledgements TagedPThe authors are grateful to the UCT University Research Committee, The David and Elaine Potter Foundation and the National Research Foundation (NRF) of South Africa for their financial support. Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. The donations of Domex steel from SSAB and Vulcan Steel are gratefully acknowledged. The authors would also like to thank the staff of the Mechanical Engineering workshop at UCT for their assistance in machining the specimens and pendulum parts.
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