- Email: [email protected]
Simulation of precise setforward and setback experiments
ARTICLE IN PRESS
International Journal of Impact Engineering 32 (2005) 80–91 www.elsevier.com/locate/ijimpeng
Simulation of precise setforward and setback experiments Philip Churcha,, R. Townsleya, T. Bezancea, Bill Proudb, Steve Granthamb, Neil Bournec, Jeremy Milletc a
QinetiQ, Fort Halstead, Modelling & Explosive Applications, Room 18, Building Q14, Sevenoaks, Kent TN14 7BP, UK b Cavendish Laboratory, Physics and Chemistry of Solids (PCS), Madingley Road, Cambridge CB3 OHE, UK c RMCS Shrivenham, Cranfield University, Shrivenham, Swindon SN6 8LA, UK Received 16 September 2004; accepted 28 July 2005 Available online 19 September 2005
Abstract The issue of setback and setforward in gun and penetrator systems is potentially very serious given the drive toward new compositions and higher velocities. The only means of assessing this risk in the real system is through simulations and small-scale testing, since onboard instrumentation is not straightforward and is limited in the data generated. However, for this approach to be successful it is important to validate the models used in the simulations to obtain the necessary degree of confidence. This demands the design of experiments coupled with precise instrumentation to replicate the forces observed in the real system. Precise setback and setforward experiments have been performed aimed at providing validation data and understanding the processes involved and both indicating that little slippage of the filling has occurred. The experiments have been simulated using the QinetiQ GRIM hydrocode using a semi-empirical interim model for the visco-elastic filling material. The results are discussed and future studies are outlined. r 2005 Elsevier Ltd. All rights reserved. Keywords: Setforward; Setback; Explosive; Material model; Simulation
1. Introduction Munitions can be subjected to high accelerations and decelerations such as in gun launch and hard target penetration, respectively. These result in high forces being exerted on the components Corresponding author. Tel.: (44) 1959 514893; fax: (44) 1959 516050.
E-mail address: [email protected] (P. Church). 0734-743X/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2005.07.011
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
81
of the munition and in particular can result in significant setback (in gun launch) and setforward (in penetration) of the explosive filling. The main aim of this research is to determine a methodology for assessing new explosive compositions in the gun systems and penetrators, which are subject to setback and setforward forces respectively. This would enable thresholds (e.g. due to impulse) to be defined, above which an unacceptable event occurs, which can then be used to assess a given concept, before proceeding to full-scale trials. This is very challenging since in the real scenarios, there is little information on the behaviour of a given explosive composition in these environments, primarily due to the difficulty of locating advanced instrumentation into a projectile travelling at high velocities. Therefore, the approach has been to develop different types of testing which replicate the general force history observed in the real situation. These tests range from tests on the actual explosive composition under different loading regimes to small-scale impact tests. They are also specifically designed to enable sophisticated instrumentation techniques to be used effectively. The experimental tests are used to validate the hydrocode simulations. The hydrocodes can then be used to simulate the real scenario and thus gather the necessary information to make a judgement on the suitability of the explosive composition within a given projectile system. For this approach to be successful it is crucial that the instrumentation deployed yields the information needed to provide a quantitative analysis of the behaviour of the composition under these loads. Thus the conceptual leap from defining a measured loading threshold into a material response related threshold is achieved. This enables the hydrocodes to be used effectively in determining whether these thresholds are exceeded in the real application. The general approach adopted was to fully integrate the simulations with precise experimentation and material model development. This is considered crucial since it is very easy to develop models for materials that are difficult to use in the hydrocode. In particular the definition of variables in the model must match those in the hydrocode. The experiments were also considered precise in that the manufacture of components and their general alignment was conducted under strict tolerances, as far as practicable with the nature of these materials.
2. Experiments The experiments were configured such that the impact scenarios were reasonably representative of the actual applications. However, this need was tempered by designing the experiments such that it was relatively straightforward to use advanced instrumentation techniques. These techniques were designed to measure the general movement of the filling and in particular the relative motion of the filling and the case material, in terms of friction or adhesion. In addition for simplicity an inert substitute was used for the experiments. 2.1. Setback experiments These were performed within the Physics and Chemistry of Solids (PCS) group at the Cavendish Laboratory at Cambridge University using the 50 mm gas gun facility. The setback experiments basically comprised a polycarbonate impactor striking a cylindrically filled target. The main instrumentation was a laser interferometer (i.e. VISAR) on the rear of the target (i.e. on
ARTICLE IN PRESS 82
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91 Polycarbonate sorround
SABOT
Filling
Aluminium Annulus
Fig. 1. Impact setup showing impactor (sabot) and filled target, VISAR is used to measure free surface velocity and DSR using X-rays to investigate internal flow field.
axis) to measure particle velocity as well as X-ray digital speckle radiography (DSR) to observe the general motion of the filling. In addition there were some ‘plate impact’ type experiments of a striker hitting a box target featuring the same type of instrumentation. The general configuration for the impact experiments is shown in Fig. 1 and the velocity regime covered was 200–700 m/s, where an inert cylinder impacted the filled cylinder. The filling was based on a PBX inert substitute comprising sugar (crystals) in an HTPB binder matrix, designed to mimic gun-launch type fillings. The general dimensions for the experiment are listed below: The setback/setforward projectiles approximate dimensions, looking at the impact face and going backwards down the barrel, are as follows: Front face overall diameter 49.8 mm. Polycarbonate wall thickness ¼ 5 mm Diameter of filling ¼ 40 mm approx. Length of filling ¼ 75 mm. The aim of the DSR is to provide information of the general 3D internal flow during the impact process. These experiments are carried out using DSR, which is a technique based on digital speckle photography (DSP) combined with flash X-rays and has been tested on polyester, cement [1], sand [2] and glass [3]. 2.1.1. Experimental configuration and results The seeded projectile was suspended in a wire cradle and aligned with a second projectile placed in the end of the gun barrel. A reference X-ray was taken, and then a dynamic image was taken during the experiment at a specified delay after impact. In all the experiments the seeded plane was in the centre of the sample running along its length and the lead filings used for the seeding were 500 mm in size and the layer had 20% coverage. The output from the DSR produces a displacement contour, where one can convert these into strain, for comparison with simulations. The VISAR results are shown in Fig. 2 for the 600 m/s impact and show a linear rise to a constant velocity, which slowly reduces with time. It is interesting and perhaps encouraging that the trace shows no sign of spall or complex wave reflections, which should in principle simplify the simulations. The experiment was repeated with near identical results.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
83
0.5
Velocity / mm s-1
0.4
0.3
0.2
0.1
0 5
10
15
20
25
Time / s
Fig. 2. Measured free surface velocity from rear surface of target with 600 m/s impact using VISAR.
Fig. 3. DSR image of plate impact at velocity of 285 m/s.
An additional experiment was conducted in the plate impact configuration using DSR at low and high velocity. The lower velocity is shown in Fig. 3, where the strain field is seen as being reasonably symmetric and also indicating the intensity of the strain contours at the impact face. At later times, shown in Fig. 4, the presence of the internal lateral release waves is observed, which provides excellent validation of the unloading behaviour in the model and may allow for
ARTICLE IN PRESS 84
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Fig. 4. DSR images plate impact at 600 m/s showing potential lateral releases.
the measurement of the release wave speed. It should be recognised that this is a single result and clearly needs further investigation, in terms of reproducibility, etc. 2.2. Setforward experiments These were performed using the 50 mm gas gun capability at the Royal Military College of Science (RMCS) based at Shrivenham, who have an established track record in terms of impact and Hugoniot behaviour of live explosives and inert substitutes [4,5]. The main aim of these experiments was to represent a setforward scenario, whereby a projectile is impacted against a rigid concrete target. The projectiles were aluminium alloy cylinders 50 mm in diameter and 100 mm in length of wall thickness 2 mm, filled with a PBX inert substitute. Here the inert substitute was based on a barium sulphate/melamine mix, designed to mimic penetrator type fillings. The projectiles were essentially inert filled tubes, with no end plates. The impact velocity was about 300 m/s normally into a semi-infinite concrete block. A 50 mm calibre, 5 m long gas gun was used to deliver the impacts and a Hadland Ultra 68 high-speed camera was used to monitor the event. The projectile case was machined in the form of a slot at the front and rear end, to allow a light path for the camera, enabling the motion of the filling to be monitored relative to the case as shown in Fig. 5. Tests were performed to ensure that there was no significant rotation of the projectile down the gun barrel. Two types of projectile were fired. In the first a cylindrical cavity was machined in the filling at the front of the projectile, whereas in the second there was no cavity machined. The main purpose of the cavity was to investigate its effect on the behaviour of the filling during the penetration process. If the technique proved useful then different shaped cavities could be investigated.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
85
Fig. 5. Schematic of light path to camera through the projectile by means of machined slots in case.
Fig. 6. High-speed photography sequence for deformation of projectile with cylindrical cavity 150,000 fps, velocity 300 m/s.
2.2.1. Results The results for the cylindrical cavity within the filling are shown in Fig. 6 using a framing rate of 150,000 fps. As can be seen the light path at the front of the projectile is clearly visible indicating that there was little rotation.
ARTICLE IN PRESS 86
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Longitudinal Strain
0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 0
5
10
15 20 Time (µs)
25
30
35
Fig. 7. Longitudinal strain gauge trace from gauge in centre of target, impact velocity is 289 m/s.
In contrast, the light path at the rear of the projectile is not visible, thereby demonstrating that no separation occurred between the filler and the cylinder. Between frames 45 (just at impact) and frame 53, the cavity at the front is seen to collapse, but without any obvious effect on the filler itself. This in combination with the lack of separation at the rear suggests that the filler does not experience any slip with the cylinder body. As the filler itself impacts the concrete target, deformation can be observed at the rear of the projectile, which is somewhat concave in nature and persists even to late stages of the impact. The results for the cylinder without any cavity demonstrate similar behaviour in terms of nonslippage between the filling and case and the concavity at the projectile rear. It is interesting that the concavity is characteristic of this type of experiment and not dependent on the cavity at the front. A potential explanation for the concavity is that it is caused by the adhesion between the filler and the case, thereby impeding the flow of the filling near the case, thereby leading to the concavity observed at the projectile rear. This concavity is also observed in a recovered portion of filling. An additional experiment was performed where a copper flyer plate impacted a filled cylinder containing a strain gauge along its axis. The gauge registered a compressive strain, albeit to a relatively low level, as shown in Fig. 7. Although this is an initial result, the result appears to confirm the lack of motion between the filling and the case.
3. Numerical simulations The simulations utilised the QinetiQ Eulerian hydrocode GRIM, which is multi-material and is 3rd order accurate in the advection step, whereby cell variables are transported across cell boundaries. The code also features a very accurate interface algorithm based on Youngs [6]. GRIM has general material descriptions for a wide range of materials, such as metals, ceramics, geological materials and polymer-based materials, including both equations of state and constitutive models incorporating damage and fracture. The work on polymer-based materials is relatively recent and is still very much in progress as described below.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
87
3.1. Material models for polymer-based materials 3.1.1. Equation of state There is an ongoing programme within QinetiQ to develop a better predictive capability for the mechanical and shock response of polymer-based materials. In terms of the equation of state the approach is to use quantitative structural property modelling (QSPM) techniques to generate a table look up of P,V,T over the regime of interest. The technique has been pioneered by Porter and Gould [7] and has been described in detail elsewhere. An example of the improved predictive capability is in the simulation of the stress level attained in plate impact experiments, performed at RMCS on plastic bonded explosives (PBX). This is shown in Fig. 8 for two scenarios, where the stress level is predicted to within 5–10% of these experiments. It should be borne in mind that there is a significant variability of the material. To put this in perspective the results using an empirically derived model for the PBX only predicted half the observed stress level and thus the Porter–Gould equation of state represents a significant improvement in the predictive capability. 3.1.2. Constitutive model The QSPM physically based technique has been expanded to describe the constitutive behaviour through the Porter–Gould model of the material and at present is capable of predicting a quasi-static compression stress/strain curve. However, it does not account for the intermediate strain-rate regime, where there is a well-documented rate dependency observed in polymers [8]. There is work in progress aiming at developing the Porter–Gould constitutive model to account for intermediate rate behaviour. Unfortunately, most of the setback and setforward scenarios of interest are in the intermediate strain rate regime. Therefore, in order to deal with this in the shorter term, an interim model 0.8 Exp Grim
4.0
0.6
3.0
0.5
2.5
Stress (Gpa)
Longitudinal stress (Gpa)
0.7
2.0 1.5 1.0
0.4 0.3 0.2 0.1
0.5
0
0.0
0
0.00
1
2
3
4
5
-0.1
-0.5 0
1
2
3 4 Time (µs)
5
6
7 -0.2 Time (us)
Fig. 8. Comparison of Porter–Gould model and plate impact stress for two different impact velocities.
6
ARTICLE IN PRESS 88
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
approach was adopted. This was basically a semi-empirical fit to quasi-static compression data as well as Hopkinson bar dynamic stress/strain data. The interim model includes the effect of strain rate, temperature and damage and is fitted to both quasi-static and Hopkinson bar data and is applicable in compression only. The model form is as follows s ¼ A1 expðA2 Þ½1 expðA2 Þ A3 þ ð1 þ Þ½1 þ A4 ð1 þ A5 2 Þ2 A1 ¼ A11 _A12 expðA13 TÞ; A3 ¼ A31 _A32 expðA33 TÞ; where, _ is the strain rate, e is strain and T is temperature (K) and A11, A12, A13, A2, A31, A32, A33, A4 and A5 are constants. The main issues with the model are that the unloading behaviour follows the loading curve and there is no account of tension or failure. The model also requires an equation of state. At present the models used in the GRIM hydrocode are based on the Porter–Gould equation of state in conjunction with the interim constitutive model. 3.2. Initial results 3.2.1. Setback simulations GRIM2D has been used to compare directly with the setback experiments described previously. The impact scenario was setup in 2D axisymmetric geometry using a 0.5 mm square mesh. The results presented were largely insensitive to the mesh resolution, subject to the usual caveats of sufficient resolution to resolve the shock wave structure. They were run using the Porter–Gould equation of state and the interim constitutive model for the inert filling. The impact is shown in Fig. 9, where the impact face is heavily deformed and the material is behaving very similar to a symmetric Taylor test experiment. Qualitatively the hydrocode replicates the correct sort of behaviour, although a detailed analysis of the strain map, suggests that the unloading behaviour
Fig. 9. Qualitative GRIM prediction of inert sabot impacting filled cylinder at 600 m/s
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
89
0.52
0.42
0.31
0.21
0.10
0.00 0.00
0.60
1.20 1.80 Time / s*10-4
2.40
3.00
Fig. 10. GRIM prediction of free-surface velocity for inert cylinder impacting filled cylinder at impact velocity of 600 m/s.
in the interim model is crucial and at present incorrect. At present this simply follows the loading behaviour and work is ongoing to define a more accurate unloading path. The predicted free-surface velocity reveals that the maximum level compares reasonably well with the experiment as shown in Fig. 10. However, the simulation predicts significant ‘spikes’ on the trace, which simply are not present in the experiment. The reason for these spikes is unclear, but could be related to the unloading behaviour in the interim model or the tensile cut-off condition (i.e. Pmin) used in GRIM to mimic failure. A sensitivity study of this condition had little effect on the results. This whole aspect requires further investigation. 3.2.2. Setforward simulations In terms of the setforward simulations a similar mesh resolution was utilised and the comparison was with the general shape of the projectile. In addition a sensitivity study was performed covering the projectile geometry in particular focussing on a filled tube and a filled tube with end plates. In terms of the general shape GRIM predicts large deformation at the impact face and the concave region at the back of the projectile occurring at early times in the penetration process (i.e. 20–30 ms) as shown in Fig. 11, compared to the recovered projectiles. The general agreement with the high-speed pictures is reasonable, although further analysis is required. The reason for the concave region at the back is driven by the case interaction with the filling and in the numerical Euler scheme may be influenced by the interfaces ‘sticking’ together, which can be a feature of Euler codes. However, the simulation for the filled case with endplates, shown in Fig. 12, does not exhibit the concave portion at the rear of the projectile. This suggests that the presence of an endplate increases the structural robustness and prevents the concavity at the rear.
ARTICLE IN PRESS 90
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Fig. 11. GRIM prediction of impact of open tube into concrete, showing concavity at rear of projectile using Porter–Gould EOS and interim constitutive model.
Fig. 12. GRIM prediction with impact of filled tube projectile with end plates against concrete, showing no concavity at rear of filling, using Porter–Gould EOS and interim constitutive model.
4. Conclusions The experimental techniques have proved very successful and have demonstrated the value of advanced instrumentation techniques featuring VISAR, gauges, high-speed photography and DSR. In particular they have confirmed that in both setback and setforward there is relatively little motion of the filling relative to the case. The DSR technique has also yielded valuable information on the internal flow field and in principle may be able to resolve the lateral releases. This is important in terms of validation of future models. In addition the use of gauges within the filling has been demonstrated as feasible and gives useful ‘point’ information on strain, for example. The initial simulations have shown promise and given reasonable qualitative agreement using the Porter–Gould equation of state and interim constitutive model for the polymer based inert filling. It is recognised that the models need development to treat the intermediate strain rate regime, unloading and general tensile behaviour including damage and fracture.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
91
Acknowledgements The active support of the Corporate Research Programme in MoD through Chris Leach and Dstl, through Richard Biers is greatly appreciated.
References [1] Synnergren P, Goldrein HT, Proud WG. Application of digital speckle photography to flash X-ray studies of internal deformation fields in impact experiments. Appl Optics 1999;38:4030–6. [2] Goldrein HT, Grantham SG, Proud WG, Field JE. The study of internal deformation fields in granular materials using 3D digital speckle X-ray flash photography. In: Proceedings of the 12th APS topical meeting on shock compression of condensed matter, 2001. [3] Grantham SG, Proud WG. Digital speckle X-ray flash photography. In: Proceedings of the 12th APS topical meeting on shock compression of condensed matter, 2001. [4] Millett J, Bourne N. J. Appl Phys 2001;89:2576–9. [5] Meziere Y, Akhavan, Millett J, Bourne N. The Hugoniot of hydroxy terminated polybutadiene, APS 2003, Portland, USA. [6] Youngs D. In: Morton KW, Baines MJ, editors. Numerical methods for fluid dynamics. 1982. p. 273–285. [7] Porter D, Gould P. Multi-scale modelling for equations of state. J Phys IV 2003;110:809–14. [8] Swallowe G. Mechanical properties and testing of polymers. New York: McGraw-Hill; 1999.
International Journal of Impact Engineering 32 (2005) 80–91 www.elsevier.com/locate/ijimpeng
Simulation of precise setforward and setback experiments Philip Churcha,, R. Townsleya, T. Bezancea, Bill Proudb, Steve Granthamb, Neil Bournec, Jeremy Milletc a
QinetiQ, Fort Halstead, Modelling & Explosive Applications, Room 18, Building Q14, Sevenoaks, Kent TN14 7BP, UK b Cavendish Laboratory, Physics and Chemistry of Solids (PCS), Madingley Road, Cambridge CB3 OHE, UK c RMCS Shrivenham, Cranfield University, Shrivenham, Swindon SN6 8LA, UK Received 16 September 2004; accepted 28 July 2005 Available online 19 September 2005
Abstract The issue of setback and setforward in gun and penetrator systems is potentially very serious given the drive toward new compositions and higher velocities. The only means of assessing this risk in the real system is through simulations and small-scale testing, since onboard instrumentation is not straightforward and is limited in the data generated. However, for this approach to be successful it is important to validate the models used in the simulations to obtain the necessary degree of confidence. This demands the design of experiments coupled with precise instrumentation to replicate the forces observed in the real system. Precise setback and setforward experiments have been performed aimed at providing validation data and understanding the processes involved and both indicating that little slippage of the filling has occurred. The experiments have been simulated using the QinetiQ GRIM hydrocode using a semi-empirical interim model for the visco-elastic filling material. The results are discussed and future studies are outlined. r 2005 Elsevier Ltd. All rights reserved. Keywords: Setforward; Setback; Explosive; Material model; Simulation
1. Introduction Munitions can be subjected to high accelerations and decelerations such as in gun launch and hard target penetration, respectively. These result in high forces being exerted on the components Corresponding author. Tel.: (44) 1959 514893; fax: (44) 1959 516050.
E-mail address: [email protected] (P. Church). 0734-743X/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2005.07.011
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
81
of the munition and in particular can result in significant setback (in gun launch) and setforward (in penetration) of the explosive filling. The main aim of this research is to determine a methodology for assessing new explosive compositions in the gun systems and penetrators, which are subject to setback and setforward forces respectively. This would enable thresholds (e.g. due to impulse) to be defined, above which an unacceptable event occurs, which can then be used to assess a given concept, before proceeding to full-scale trials. This is very challenging since in the real scenarios, there is little information on the behaviour of a given explosive composition in these environments, primarily due to the difficulty of locating advanced instrumentation into a projectile travelling at high velocities. Therefore, the approach has been to develop different types of testing which replicate the general force history observed in the real situation. These tests range from tests on the actual explosive composition under different loading regimes to small-scale impact tests. They are also specifically designed to enable sophisticated instrumentation techniques to be used effectively. The experimental tests are used to validate the hydrocode simulations. The hydrocodes can then be used to simulate the real scenario and thus gather the necessary information to make a judgement on the suitability of the explosive composition within a given projectile system. For this approach to be successful it is crucial that the instrumentation deployed yields the information needed to provide a quantitative analysis of the behaviour of the composition under these loads. Thus the conceptual leap from defining a measured loading threshold into a material response related threshold is achieved. This enables the hydrocodes to be used effectively in determining whether these thresholds are exceeded in the real application. The general approach adopted was to fully integrate the simulations with precise experimentation and material model development. This is considered crucial since it is very easy to develop models for materials that are difficult to use in the hydrocode. In particular the definition of variables in the model must match those in the hydrocode. The experiments were also considered precise in that the manufacture of components and their general alignment was conducted under strict tolerances, as far as practicable with the nature of these materials.
2. Experiments The experiments were configured such that the impact scenarios were reasonably representative of the actual applications. However, this need was tempered by designing the experiments such that it was relatively straightforward to use advanced instrumentation techniques. These techniques were designed to measure the general movement of the filling and in particular the relative motion of the filling and the case material, in terms of friction or adhesion. In addition for simplicity an inert substitute was used for the experiments. 2.1. Setback experiments These were performed within the Physics and Chemistry of Solids (PCS) group at the Cavendish Laboratory at Cambridge University using the 50 mm gas gun facility. The setback experiments basically comprised a polycarbonate impactor striking a cylindrically filled target. The main instrumentation was a laser interferometer (i.e. VISAR) on the rear of the target (i.e. on
ARTICLE IN PRESS 82
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91 Polycarbonate sorround
SABOT
Filling
Aluminium Annulus
Fig. 1. Impact setup showing impactor (sabot) and filled target, VISAR is used to measure free surface velocity and DSR using X-rays to investigate internal flow field.
axis) to measure particle velocity as well as X-ray digital speckle radiography (DSR) to observe the general motion of the filling. In addition there were some ‘plate impact’ type experiments of a striker hitting a box target featuring the same type of instrumentation. The general configuration for the impact experiments is shown in Fig. 1 and the velocity regime covered was 200–700 m/s, where an inert cylinder impacted the filled cylinder. The filling was based on a PBX inert substitute comprising sugar (crystals) in an HTPB binder matrix, designed to mimic gun-launch type fillings. The general dimensions for the experiment are listed below: The setback/setforward projectiles approximate dimensions, looking at the impact face and going backwards down the barrel, are as follows: Front face overall diameter 49.8 mm. Polycarbonate wall thickness ¼ 5 mm Diameter of filling ¼ 40 mm approx. Length of filling ¼ 75 mm. The aim of the DSR is to provide information of the general 3D internal flow during the impact process. These experiments are carried out using DSR, which is a technique based on digital speckle photography (DSP) combined with flash X-rays and has been tested on polyester, cement [1], sand [2] and glass [3]. 2.1.1. Experimental configuration and results The seeded projectile was suspended in a wire cradle and aligned with a second projectile placed in the end of the gun barrel. A reference X-ray was taken, and then a dynamic image was taken during the experiment at a specified delay after impact. In all the experiments the seeded plane was in the centre of the sample running along its length and the lead filings used for the seeding were 500 mm in size and the layer had 20% coverage. The output from the DSR produces a displacement contour, where one can convert these into strain, for comparison with simulations. The VISAR results are shown in Fig. 2 for the 600 m/s impact and show a linear rise to a constant velocity, which slowly reduces with time. It is interesting and perhaps encouraging that the trace shows no sign of spall or complex wave reflections, which should in principle simplify the simulations. The experiment was repeated with near identical results.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
83
0.5
Velocity / mm s-1
0.4
0.3
0.2
0.1
0 5
10
15
20
25
Time / s
Fig. 2. Measured free surface velocity from rear surface of target with 600 m/s impact using VISAR.
Fig. 3. DSR image of plate impact at velocity of 285 m/s.
An additional experiment was conducted in the plate impact configuration using DSR at low and high velocity. The lower velocity is shown in Fig. 3, where the strain field is seen as being reasonably symmetric and also indicating the intensity of the strain contours at the impact face. At later times, shown in Fig. 4, the presence of the internal lateral release waves is observed, which provides excellent validation of the unloading behaviour in the model and may allow for
ARTICLE IN PRESS 84
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Fig. 4. DSR images plate impact at 600 m/s showing potential lateral releases.
the measurement of the release wave speed. It should be recognised that this is a single result and clearly needs further investigation, in terms of reproducibility, etc. 2.2. Setforward experiments These were performed using the 50 mm gas gun capability at the Royal Military College of Science (RMCS) based at Shrivenham, who have an established track record in terms of impact and Hugoniot behaviour of live explosives and inert substitutes [4,5]. The main aim of these experiments was to represent a setforward scenario, whereby a projectile is impacted against a rigid concrete target. The projectiles were aluminium alloy cylinders 50 mm in diameter and 100 mm in length of wall thickness 2 mm, filled with a PBX inert substitute. Here the inert substitute was based on a barium sulphate/melamine mix, designed to mimic penetrator type fillings. The projectiles were essentially inert filled tubes, with no end plates. The impact velocity was about 300 m/s normally into a semi-infinite concrete block. A 50 mm calibre, 5 m long gas gun was used to deliver the impacts and a Hadland Ultra 68 high-speed camera was used to monitor the event. The projectile case was machined in the form of a slot at the front and rear end, to allow a light path for the camera, enabling the motion of the filling to be monitored relative to the case as shown in Fig. 5. Tests were performed to ensure that there was no significant rotation of the projectile down the gun barrel. Two types of projectile were fired. In the first a cylindrical cavity was machined in the filling at the front of the projectile, whereas in the second there was no cavity machined. The main purpose of the cavity was to investigate its effect on the behaviour of the filling during the penetration process. If the technique proved useful then different shaped cavities could be investigated.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
85
Fig. 5. Schematic of light path to camera through the projectile by means of machined slots in case.
Fig. 6. High-speed photography sequence for deformation of projectile with cylindrical cavity 150,000 fps, velocity 300 m/s.
2.2.1. Results The results for the cylindrical cavity within the filling are shown in Fig. 6 using a framing rate of 150,000 fps. As can be seen the light path at the front of the projectile is clearly visible indicating that there was little rotation.
ARTICLE IN PRESS 86
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Longitudinal Strain
0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 0
5
10
15 20 Time (µs)
25
30
35
Fig. 7. Longitudinal strain gauge trace from gauge in centre of target, impact velocity is 289 m/s.
In contrast, the light path at the rear of the projectile is not visible, thereby demonstrating that no separation occurred between the filler and the cylinder. Between frames 45 (just at impact) and frame 53, the cavity at the front is seen to collapse, but without any obvious effect on the filler itself. This in combination with the lack of separation at the rear suggests that the filler does not experience any slip with the cylinder body. As the filler itself impacts the concrete target, deformation can be observed at the rear of the projectile, which is somewhat concave in nature and persists even to late stages of the impact. The results for the cylinder without any cavity demonstrate similar behaviour in terms of nonslippage between the filling and case and the concavity at the projectile rear. It is interesting that the concavity is characteristic of this type of experiment and not dependent on the cavity at the front. A potential explanation for the concavity is that it is caused by the adhesion between the filler and the case, thereby impeding the flow of the filling near the case, thereby leading to the concavity observed at the projectile rear. This concavity is also observed in a recovered portion of filling. An additional experiment was performed where a copper flyer plate impacted a filled cylinder containing a strain gauge along its axis. The gauge registered a compressive strain, albeit to a relatively low level, as shown in Fig. 7. Although this is an initial result, the result appears to confirm the lack of motion between the filling and the case.
3. Numerical simulations The simulations utilised the QinetiQ Eulerian hydrocode GRIM, which is multi-material and is 3rd order accurate in the advection step, whereby cell variables are transported across cell boundaries. The code also features a very accurate interface algorithm based on Youngs [6]. GRIM has general material descriptions for a wide range of materials, such as metals, ceramics, geological materials and polymer-based materials, including both equations of state and constitutive models incorporating damage and fracture. The work on polymer-based materials is relatively recent and is still very much in progress as described below.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
87
3.1. Material models for polymer-based materials 3.1.1. Equation of state There is an ongoing programme within QinetiQ to develop a better predictive capability for the mechanical and shock response of polymer-based materials. In terms of the equation of state the approach is to use quantitative structural property modelling (QSPM) techniques to generate a table look up of P,V,T over the regime of interest. The technique has been pioneered by Porter and Gould [7] and has been described in detail elsewhere. An example of the improved predictive capability is in the simulation of the stress level attained in plate impact experiments, performed at RMCS on plastic bonded explosives (PBX). This is shown in Fig. 8 for two scenarios, where the stress level is predicted to within 5–10% of these experiments. It should be borne in mind that there is a significant variability of the material. To put this in perspective the results using an empirically derived model for the PBX only predicted half the observed stress level and thus the Porter–Gould equation of state represents a significant improvement in the predictive capability. 3.1.2. Constitutive model The QSPM physically based technique has been expanded to describe the constitutive behaviour through the Porter–Gould model of the material and at present is capable of predicting a quasi-static compression stress/strain curve. However, it does not account for the intermediate strain-rate regime, where there is a well-documented rate dependency observed in polymers [8]. There is work in progress aiming at developing the Porter–Gould constitutive model to account for intermediate rate behaviour. Unfortunately, most of the setback and setforward scenarios of interest are in the intermediate strain rate regime. Therefore, in order to deal with this in the shorter term, an interim model 0.8 Exp Grim
4.0
0.6
3.0
0.5
2.5
Stress (Gpa)
Longitudinal stress (Gpa)
0.7
2.0 1.5 1.0
0.4 0.3 0.2 0.1
0.5
0
0.0
0
0.00
1
2
3
4
5
-0.1
-0.5 0
1
2
3 4 Time (µs)
5
6
7 -0.2 Time (us)
Fig. 8. Comparison of Porter–Gould model and plate impact stress for two different impact velocities.
6
ARTICLE IN PRESS 88
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
approach was adopted. This was basically a semi-empirical fit to quasi-static compression data as well as Hopkinson bar dynamic stress/strain data. The interim model includes the effect of strain rate, temperature and damage and is fitted to both quasi-static and Hopkinson bar data and is applicable in compression only. The model form is as follows s ¼ A1 expðA2 Þ½1 expðA2 Þ A3 þ ð1 þ Þ½1 þ A4 ð1 þ A5 2 Þ2 A1 ¼ A11 _A12 expðA13 TÞ; A3 ¼ A31 _A32 expðA33 TÞ; where, _ is the strain rate, e is strain and T is temperature (K) and A11, A12, A13, A2, A31, A32, A33, A4 and A5 are constants. The main issues with the model are that the unloading behaviour follows the loading curve and there is no account of tension or failure. The model also requires an equation of state. At present the models used in the GRIM hydrocode are based on the Porter–Gould equation of state in conjunction with the interim constitutive model. 3.2. Initial results 3.2.1. Setback simulations GRIM2D has been used to compare directly with the setback experiments described previously. The impact scenario was setup in 2D axisymmetric geometry using a 0.5 mm square mesh. The results presented were largely insensitive to the mesh resolution, subject to the usual caveats of sufficient resolution to resolve the shock wave structure. They were run using the Porter–Gould equation of state and the interim constitutive model for the inert filling. The impact is shown in Fig. 9, where the impact face is heavily deformed and the material is behaving very similar to a symmetric Taylor test experiment. Qualitatively the hydrocode replicates the correct sort of behaviour, although a detailed analysis of the strain map, suggests that the unloading behaviour
Fig. 9. Qualitative GRIM prediction of inert sabot impacting filled cylinder at 600 m/s
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
89
0.52
0.42
0.31
0.21
0.10
0.00 0.00
0.60
1.20 1.80 Time / s*10-4
2.40
3.00
Fig. 10. GRIM prediction of free-surface velocity for inert cylinder impacting filled cylinder at impact velocity of 600 m/s.
in the interim model is crucial and at present incorrect. At present this simply follows the loading behaviour and work is ongoing to define a more accurate unloading path. The predicted free-surface velocity reveals that the maximum level compares reasonably well with the experiment as shown in Fig. 10. However, the simulation predicts significant ‘spikes’ on the trace, which simply are not present in the experiment. The reason for these spikes is unclear, but could be related to the unloading behaviour in the interim model or the tensile cut-off condition (i.e. Pmin) used in GRIM to mimic failure. A sensitivity study of this condition had little effect on the results. This whole aspect requires further investigation. 3.2.2. Setforward simulations In terms of the setforward simulations a similar mesh resolution was utilised and the comparison was with the general shape of the projectile. In addition a sensitivity study was performed covering the projectile geometry in particular focussing on a filled tube and a filled tube with end plates. In terms of the general shape GRIM predicts large deformation at the impact face and the concave region at the back of the projectile occurring at early times in the penetration process (i.e. 20–30 ms) as shown in Fig. 11, compared to the recovered projectiles. The general agreement with the high-speed pictures is reasonable, although further analysis is required. The reason for the concave region at the back is driven by the case interaction with the filling and in the numerical Euler scheme may be influenced by the interfaces ‘sticking’ together, which can be a feature of Euler codes. However, the simulation for the filled case with endplates, shown in Fig. 12, does not exhibit the concave portion at the rear of the projectile. This suggests that the presence of an endplate increases the structural robustness and prevents the concavity at the rear.
ARTICLE IN PRESS 90
P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
Fig. 11. GRIM prediction of impact of open tube into concrete, showing concavity at rear of projectile using Porter–Gould EOS and interim constitutive model.
Fig. 12. GRIM prediction with impact of filled tube projectile with end plates against concrete, showing no concavity at rear of filling, using Porter–Gould EOS and interim constitutive model.
4. Conclusions The experimental techniques have proved very successful and have demonstrated the value of advanced instrumentation techniques featuring VISAR, gauges, high-speed photography and DSR. In particular they have confirmed that in both setback and setforward there is relatively little motion of the filling relative to the case. The DSR technique has also yielded valuable information on the internal flow field and in principle may be able to resolve the lateral releases. This is important in terms of validation of future models. In addition the use of gauges within the filling has been demonstrated as feasible and gives useful ‘point’ information on strain, for example. The initial simulations have shown promise and given reasonable qualitative agreement using the Porter–Gould equation of state and interim constitutive model for the polymer based inert filling. It is recognised that the models need development to treat the intermediate strain rate regime, unloading and general tensile behaviour including damage and fracture.
ARTICLE IN PRESS P. Church et al. / International Journal of Impact Engineering 32 (2005) 80–91
91
Acknowledgements The active support of the Corporate Research Programme in MoD through Chris Leach and Dstl, through Richard Biers is greatly appreciated.
References [1] Synnergren P, Goldrein HT, Proud WG. Application of digital speckle photography to flash X-ray studies of internal deformation fields in impact experiments. Appl Optics 1999;38:4030–6. [2] Goldrein HT, Grantham SG, Proud WG, Field JE. The study of internal deformation fields in granular materials using 3D digital speckle X-ray flash photography. In: Proceedings of the 12th APS topical meeting on shock compression of condensed matter, 2001. [3] Grantham SG, Proud WG. Digital speckle X-ray flash photography. In: Proceedings of the 12th APS topical meeting on shock compression of condensed matter, 2001. [4] Millett J, Bourne N. J. Appl Phys 2001;89:2576–9. [5] Meziere Y, Akhavan, Millett J, Bourne N. The Hugoniot of hydroxy terminated polybutadiene, APS 2003, Portland, USA. [6] Youngs D. In: Morton KW, Baines MJ, editors. Numerical methods for fluid dynamics. 1982. p. 273–285. [7] Porter D, Gould P. Multi-scale modelling for equations of state. J Phys IV 2003;110:809–14. [8] Swallowe G. Mechanical properties and testing of polymers. New York: McGraw-Hill; 1999.