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The Ballistic Performance of Thin Aluminium Plates Against Blunt-Nosed Projectile
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 21 (2020) 1763–1771
www.materialstoday.com/proceedings
ISFM-2018
The Ballistic Performance of Thin Aluminium Plates Against BluntNosed Projectile S. Shrivastavaa, *, G. Tiwaria, M.A. Iqbalb, P.K. Guptab
a
Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440010, India b Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India
Abstract In present study a three-dimensional finite element simulations were carried out to explore the perforation behaviour of aluminium1100-H12 plates by varying thickness 1, 2, 3, 4 and 5 mm keeping diameter identical, 255 mm, against impact with blunt-nosed projectile having diameter of 19 mm. The numerical results were validated through experimentation (for 1-2 mm thickness) and theoretical results (for 1-5 mm thickness) addressed in the literature and found to be close to each other. The commercial finite element code LS-DYNA was employed to carry out the numerical simulations. It was observed that as the thickness increases ballistic limit increases drastically. © 2019 Elsevier Ltd. All rights reserved. Peer-review under responsibility of the scientific committee of the International Symposium on Functional Materials (ISFM-2018): Energy and Biomedical Applications. Keywords: ballistic limit;LS-DYNA;blunt-nosed projectile;
1. Introduction The application of aluminium alloys in today’s era grown widely in the industries like aerospace, transportation and defence. It is one of the most widely used metal due to its high strength to weight ratio and excellent workability. In the defence industry, the choice of the armour material depends upon the ballistic resistance, thickness, and energy absorption capacity. The science of ballistic impact mechanics was far more complex than the normal impact mechanics.
* Corresponding author. Tel.: +9197138 12578
E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Peer-review under responsibility of the scientific committee of the International Symposium on Functional Materials (ISFM-2018): Energy and Biomedical Applications.
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As precisely explain impact mechanics is the branch of science which deals with the forces on and motion of objects. According to different literature “The action of one object coming forcibly into contact with other is an impact”. The parameters which differentiate between the impact and ballistic impact are high strain rate, large strain and temperature characteristics of the target body The performance of the target body mainly depends on its material, span, thickness and strength and parameters of the projectile such as velocity, mass and nose shape etc. The number of literature are available that addresses the impact response of various materials, mechanism of penetration and various parameters which governs the performance of material under high strain rate loading. Iqbal et. al. [1] numerically and experimentally concluded for aluminium targets and steel projectile that with the increase in target diameter(D) to the projectile diameter(d) ratio (D/d) the ballistic limit increases consistently against the projectile impact. According to Ansari et al. [2] study over aluminium plates and different nosed projectile, as the projectile nose shape changes from conical to blunt, damage in the target increases. Recht and Ipson [3] studied the ballistic-penetration resistance for steel plates against the blunt and conical nosed projectile and found that for thicker target blunt nosed projectile was more efficient. Flores et al. [4] explored the behaviour of the plates of materials like steel and aluminium with single and multilayered arrangement and concluded that for monolithic material the ballistic performance of single layer in comparison with multi layered arrangement is far better. Iqbal et al. [5] studied the influence of the double nosed projectile on the ballistic response of thin aluminium plates. Dev et al. [6] studies various constitutive relationship of projectile impacted over steel plates and explored that for real life practical applications, constitutive relationship and fracture criterion given by the Johnson-Cook gives exceptional congruence with the results obtained experimental for the impact of the projectile on steel plates which concludes that Johnson-cook model is a good choice for impact related problems. Borvik et al. [7] performed an experimental study over steel plate with different nosed projectile and it was concluded that the failure mode and energy absorption mechanism of the target plate during failure was considerably affected by the projectile nose shape. The effect of varying target thickness over the ballistic performance, deformation, energy absorption, and other influencing parameters over the same projectile was still under study. With increase in the plate thickness failure characteristics changes from thin plate to thick plate. In thin plate membrane stretching was there which enhance the bending of the plate after impact this increase the deformation characteristics of the plate and ultimately shearing occurs. In the thick plate membrane stretching is not that much significant which decreased the deformation characteristics of the plate which ultimately leads to shearing without much bending of the plate. In this study, the influence of varying target thickness of the monolithic plate of aluminium 1100-H12 on the residual velocity, ballistic limit, energy absorption, deformation and perforation time over blunt-nosed projectile has been studied. The projectile impact velocities were varied and ballistic limit and other influencing parameters were analysed. Numerical simulations were performed to know the effect of thickness on response of aluminium plate with varying thickness as 1, 2, 3, 4 and 5 mm. The projectile diameter kept constant as 19 mm. The numerical results were validated and strengthened out by conducting experiments for 1-2 mm thickness whereas analytical model of Richet and Ipson [3] was employed for validation of the results of 1-5 mm thick target. 2. Numerical and Experimental Investigation The commercial finite element code ANSYS / LS-DYNA was employed to carry out the numerical simulations. The thickness of the plate varied as 1, 2, 3, 4, 5 mm plate keeping the blunt-nosed projectile same. Figure 1 shows the three-dimensional meshed model of the blunt projectile and the target plate. As there is surface contact (because of flat faces) between the target and the projectile due to blunt-nosed shape and so contact algorithm of Automatic_Surface_To_Surface was assigned. The material of projectile was considered steel having diameter 19 mm, length 50.8 mm and mass 52.5 gm and considered as rigid in the simulation. The diameter of the target plate was kept constant as 255mm and considered as a deformable body. The plate was finely meshed at the centre because the impact took place at the centre of the plate which acted as a critical zone (slightly larger than the projectile diameter). The aspect ratio was kept unity at the critical zone. The mesh density has varied from fine to coarser from center to the outer periphery of the plate. Eight node brick element meshing was used in the numerical study and similar type of meshing was done in all the plates for doing the comparative study. Due to the rigid nature of the projectile it was considered as master part and plate was considered as slave part due to deformable nature. A mesh convergence study was also carried out by Tiwari et al.
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[8] and the most optimum results obtained by considering 6 elements along the thickness of 1mm plate and similarly 12 elements for 2 mm and so on till 30 elements in 5mm plate with the corresponding size of cubic element 0.16 mm in the contact region. The experimental study was carried out using the experimental setup shown by schematic diagram of a pneumatic air gun in Figure 2 which comprises with a compressor working pressure of 60 kg/cm2, a valve that trigger out the blunt projectile from a 1.5 m long barrel over the target and a projectile catcher which is placed to safeguard the projectile after impact. A high speed fps video camera was used to measure the velocity of the projectile before and after the impact. The steel projectile of mass 52.5 oil quenched and then annealed to release the internal stresses. The target plates were fully clamped in the periphery of the plate and the projectile was normally impacted. After passing through the plate the projectile was caught by the catcher, it is made up of cotton rag to safeguard the projectile after perforation.
Figure 1:Meshed plate and projectile.
Figure 2: Schematic diagram of the experimental Setup.
3. Constitutive Modelling The mathematical modelling of any ballistic impact is very complex and difficult because of phenomena like yielding, perforation, spring back, hardening, heating and shearing. The mathematical model which comprises of this process along with high strain rate behaviour generally employed for monolithic isotropic material like aluminium 1100-H12 (Table 1). A constitutive relationship and fracture criterion developed by Johnson and Cook [8] or J-C model (MAT-015) was widely used to capture high strain rate, large strain behaviour of the metals. The Johnson-Cook model gives exceptional congruence with the results obtained experimental for the impact of projectile on monolithic plates which concludes that Johnson-cook model is a good choice for impact related problems. The ballistic impact characteristics like high strains, large strain rate, heating and failure mechanism of the monolithic target body was correctly approximated by this relationship.
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The equivalent von misses stress constitutive J-C model was expressed below: ̍
σ̅ ( 𝜀̅ , 𝜀̅̍ , Ť) = [𝐴̅ + 𝐵( 𝜀̅ ) ][ 1+ 𝐶̅ ln ( )] [1 - Ť ] (1) ̍ ̅ ̅ where 𝐴 , 𝐵 , 𝐶 ,n and m are material characteristics parameters 𝜀̅̍ was equivalent plastic strain rate, 𝜀̍ was a reference strain rate , 𝜀̅ was equivalent to plastic strain, and Ť is the temperature defined as:Ť = (T -T )/(T
− T) T ≤ T ≤ T
(2)
is the melting temperature and T was the room temperature. where T is the existing temperature, T According to this model the failure occurs when the parameter 𝐷 also known as damage parameter go above unity; 𝐷(𝜀̅ , 𝜀̅ ̍ , T, 𝜎 ∗ ) = ∑
∆ (̍ ,
,
(3)
∗)
Where, ∆ 𝜀̅ was an rise of equivalent plastic strain during an integration cycle and 𝜀̅ level. The equivalent fracture strain 𝜀̅ was expressed as:𝜀̅ (
σ
, 𝜀̅ ̍ , Ť) = [D + D exp(D
σ
)] [1 + D ln (
̍ ̍
)] × [1 + D Ť]
was the critical failure strain
(4)
is the ratio of stresses and 𝜎 is the mean or average where D , D are material characteristic parameters, σ stress. The material parameters where 𝐴̅ , 𝐵 and n were obtained from cylindrical cross section specimen by doing uni-axial tension tests whereas D , D & D were obtained from artificial notched specimens by performing uniaxial tension test. The material parameter 𝐶̅ and D were obtained from Hopkinson pressure bar tension test whereas D and m from tension test at high temperature. The projectile having rigid characteristics MAT_RIGID (MAT-020) was used as material model. Table 1: Material properties of aluminium 1100-H12 Plate [8] Modulus of ℯlasticity, E(N/mm2) 𝑃oison’s ratio, 𝜈 𝐷ensity, 𝜌 (kg/m3) 𝑌ield stress, 𝐴̅ (N/mm2) 𝐵 (N/mm2) Reference strain rate , 𝜀̍ (s-1) n M T (K) T (K) 𝑆pecific heat, Cp (J/kg-K) 𝐼nelastic heat fraction, 𝛼 D D D D D
65.762 .3 2700 148.361 345.513 .001 .183 .859 893 293 920 .9 .071 1.248 -1.142 .0097 0
4. RESULTS AND DISCUSSION Results obtained by the numerical simulations in LS-DYNA for the ballistic impact were discussed in the subsequent section. Modes of failure due to the impact of projectile of blunt-nosed shape, Variation in the ballistic limit, deformation, energy absorption of the plate and velocity and acceleration characteristics of the projectile as the function of thickness of the projectile were discussed.
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4.1. Modes of failure Figure 3 Shows the impact of the blunt-nosed projectile over 2 mm plate with velocity of 102.63 m/s. When the projectile strikes the plate it first deforms and after deformation a critical zone was created at the point of a strike which increases the stresses of the plate at that zone. The induced stress by the impact was the collaborative effect of the shear, tensile as well as compressive stress. Once the stress exceeds the strength of the plate the plate gets shear off in the form of plug having equivalent cross section as that of projectile i.e. circular. The plug having a diameter approximately same as diameter of the projectile, the thickness of the plug was approximately (not equal due to local stretching) same as that of the plate thickness. As the thickness of the plate varied similar perforation mechanism takes place i.e. the formation of the plug as shown in the Figure 4. After perforation, the velocity of plug and the bullet was approximately same. The stress was distributed in the form of circular fringes having the maximum value at the contact zone and decreases radially.
Figure 3: Stress Distribution over the plate
(a)
(b) Figure 4: Perforation mechanism observed in the plate due to impact of blunt projectile, (a) Numerical, (b) Experimental
4.2. Ballistic limit The ballistic limit or velocity is the average of the maximum velocity of the projectile which creates initial indentation over the target and the minimum velocity of the projectile at which perforation occurs in the target. Generally denoted by V50 or Vb. In other words, projectile velocity below the ballistic limit will not be able to perforate the target. With increase in the thickness of the target plate the ballistic limit increased significantly shown in the figure 5. The increment in the ballistic limit was highest from 1mm to 3 mm plate and then the increment decreased. The ballistic resistance increased from 49.68% for 1 & 2 mm plate, 49.88 for 2 & 3 mm plate, 15.38% for 3 & 4 mm plate, 11.11% for 4 & 5 mm plate. Due to the increase in the thickness, the resistance offered by the plate in perforation by the bullet increases as more area was there for shearing which increases the capacity of the plate. This increase the ballistic limit of the thicker plate. Because of the increase in thickness, the weight of the plate also increases significantly. Among the 5 different plates, 3 mm plate justifies the increase in the thickness for the optimum variation of the ballistic limit.
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Figure 5: Ballistic Limit for different thickness of the plate
4.3. Energy Absorption and deformation of the plate When the projectile strikes the target the plate first significantly deforms(stretch) and vibrate in order to absorb the impact energy and once the threshold energy of plate reaches the plate gets shear off and forms a plug. Due to elastic nature of the plate, spring back action takes place and plate try to regain its original configuration, but due to locking of stresses plate get permanently deforms as shown in the figure 6 and figure 7. As the thickness increases the energy absorption capacity of the plate increases and the deformation due to impact decreases. Due to the increase in thickness, stiffness and strength of the plate increase because of that the damping characteristics increases and as a result ability to dissipate energy increases and resistance towards deformation increases. The maximum deformation of the plate at velocity just above the ballistic limit is 3.85, 3.2, 2.43, 2.17 and 1.73 mm for 1, 2, 3, 4 and 5 mm thickness respectively. It was observed that there was a considerable decrease in the deformation. Similarly, Fig. (6) shows the energy absorbed by the target plate and energy loss by the projectile. From figure 7 it is observed a spring back action of the plate after the removal of the plug by the projectile. The plate tries to regain its original shape due to internal stresses developed in the plate. But due to inelastic nature the plate not be able to reshape its original configuration. As we can see from the figure the spring back action is maximum for 1mm plate and then decreases this is due to decrease in stiffness of the plate as we increase the thickness. 4.4 Velocity & Acceleration Behaviour of the Bullet The velocity of the projectile plays a significant role in the perforation mechanism. Most of the other parameters depend on the velocity of the projectile. The velocity lower than the ballistic limit was not being able to perforate the plate but deformation of the plate takes place. Figure 7 for 1mm plate, it can be seen that at first the deformation increases and become maximum at the ballistic limit and then as the velocity increases it decreases. A similar pattern was followed by all the plates of different thickness. The velocity after perforation was called residual Velocity (Vr). Below ballistic limit, Vr is equals to zero. Figure 8 shows the variation of the Vr with respect to the impact velocity(Vi) for different thickness of the plate. As the thickness increases residual velocity decreases. Due to the change in velocity, acceleration comes into the picture and it varies as shown in the figure 9. Acceleration varies maximum for 5mm plate and reduces significantly as the thickness decreases. This variation was due to the momentum exchange between the plate and projectile and by increasing thickness exchange of momentum exceeds and so more velocity was lost in perforation and due to which residual velocity decreases and acceleration increases 5.Validation of the Results The experimental study was carried out for 1 & 2 mm plates having the same diameter of 255 mm with the blunt projectile of diameter 19 mm and mass 52.5 gm. As shown in the figure 4(b) the plate was clamped and the projectile was impacted, the plate deforms and plug forms, see Fig. 4(a). Similar deformation and plug formation takes place in the numerical simulation. Similarly, the theoretical model given by Recht and Ipson [10], where law of conservation of momentum and energy is used to determine the velocity after perforation, i.e. residual velocity of the projectile. With the help of method of least squares the model constants 𝑎 and p are found and this empirical
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relationship gives the residual velocity for 1, 2, 3, 4 and 5 mm plates: υ =
0
0≤υ ≤υ
𝑎 (υ − υ )
υ
υ
𝑎 =
, 𝑚
𝜋𝑟 𝜌 ℎ
(5)
On comparing the numerical, experimental and theoretical results for the ballistic limit and residual velocity for 1mm and 2 mm plates, see figure 10 and Table (2), the results were found in close agreement with each other. Also, numerical and theoretical results were validated for 1, 2, 3, 4 and 5 mm plate as shown in figure 11 and in Table 3.
(a)
(b)
Figure 6: Total Energy variation for, (a) plate and (b) bullet with varying thickness
(a)
(b)
Figure 7: Variation of deformation of plate with varying, (a) Time and (b) Thickness
Figure 8: Variation of Residual velocity v/s Impact velocity.
Figure 9: Variation of Acceleration v/s Time.
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Figure 10: Validation of the result for 1mm and 2mm plates experimentally, numerically and analytically.
Figure 11: Validation of the result for 1, 2,3,4,5 mm plates numerically and analytically.
Table 2: Comparison of the residual velocity for 1mm and 2mm plates numerically, analytically and experimentally. Plate Thickness
1mm
2mm
Impact Velocity(Vi) m/s 101.28 81.02 70.9 57.51 52.15 51.75 190.31 162.43 102.63 78.06
Numerical 81.03 64.82 48.61 28.75 --180.15 144.115 60.04 0
Residual Velocity (Vr) m/s Analytical 86.093 61.844 48.283 25.709 0 0 163.142 131.652 48.6885 0
Experimental 87.36 62.337 50.215 24.633 0 0 165.09 136.92 55.031 0
Table 3: Comparison of the Residual Velocity of the bullet for different thickness of plate analytically and numerically Impact Velocity (Vi)
1mm
2mm
3mm
4mm
5mm
81.02 70.9 57.51 52.15 190.31 162.43 102.63 78.06 156 143 130 117 175 160 150 135 225 200 170 150
Numerical 65.811 51.368 24.785 0 165.09 136.92 55.031 0 110.2 92.869 6.582 0 122.71 96.01 77.36 0 187.38 156.32 96.595 0
Residual Velocity (Vr) m/s Analytical 61.844 48.283 25.709 0 163.142 131.652 48.6885 0 105.897 87.449 66.23 0 117.0463 96.0059 80.3224 0 171.2946 141.8332 102.367 0
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6. Conclusion The influence of thickness on ballistic performance of aluminium plate against blunt projectile was explored by carrying out numerical simulations and experiments. The projectile of 52.5 g mass and 19mm diameter was hit over the target of Aluminium 1100-H12 plate with varying thickness of 1,2,3,4,5 mm. The parameters like deformation, ballistic limit, energy absorption etc. were analyzed which influence the perforation mechanism of the thin plate of aluminium. By varying the thickness, the failure mode remains the same, all targets failed due to shearing of plug. The ballistic limit of the plate increased significantly as the thickness of the plate increases with linear relationship initially and after that a steep slope was observed which showed a nonlinear relationship between the thickness and the ballistic limit. Thin plate failed mainly due to membrane stretching which causes the bending of the plate whereas the major factor responsible for thick plate was shearing. Spring back action was observed due to the stresses developed inside the plate which try to regain its original configuration and it decreased with the increase in the target thickness. The numerical results were validated both experimentally and numerically with a close agreement. The most optimum increase in the ballistic limit with respect to the weight was found for the thickness 3mm which showed the highest ballistic limit to weight ratio. References [1] M.A. Iqbal, G. Tiwari, P.K. Gupta, P. Bhargava. Ballistic performance and energy absorption characteristics of thin aluminium plates. International Journal of Impact Engineering 77 (2015) 1e15. [2] M.A. Iqbal, S.H. Khan, R. Ansari, N.K. Gupta. Experimental and numerical studies of double-nosed projectile impact on aluminium plates. International Journal of Impact Engineering 54 (2013) 232e245. [3] T. W. Ipson and R. F. Recht. Ballistic-penetration Resistance and Its Measurement. Journal of Applied Mechanics. 30. 10.1115/1.3636566. [4] E.A. Flores-Johnson, M. Saleh, L. Edwards. Ballistic performance of multi-layered metallic plates impacted by a 7.62-mm APM2 projectile. International Journal of Impact Engineering 38 (2011) 1022e1032. [5] M.A. Iqbal, S.H. Khan, R. Ansari, N.K. Gupta. Experimental and numerical studies of double-nosed projectile impact on aluminium plates. International Journal of Impact Engineering 54 (2013) 232e245. [6] S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth. On the influence of constitutive relation in projectile impact of steel plates. International Journal of Impact Engineering 34 (2007) 464–486. [7] T. Børvik, M. Langseth, O.S. Hopperstad, K.A. Malo. Perforation of 12mm thick steel plates by 20mm diameter projectiles with flat, hemispherical and conical noses Part I: Experimental study. International Journal of Impact Engineering 27 (2002) 19–35. [8] G. Tiwari, M.A. Iqbal, P.K. Gupta. Energy absorption characteristics of thin aluminium plate against hemispherical nosed projectile impact. Thin-Walled Structures 126 (2018) 246–257.
ScienceDirect Materials Today: Proceedings 21 (2020) 1763–1771
www.materialstoday.com/proceedings
ISFM-2018
The Ballistic Performance of Thin Aluminium Plates Against BluntNosed Projectile S. Shrivastavaa, *, G. Tiwaria, M.A. Iqbalb, P.K. Guptab
a
Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440010, India b Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India
Abstract In present study a three-dimensional finite element simulations were carried out to explore the perforation behaviour of aluminium1100-H12 plates by varying thickness 1, 2, 3, 4 and 5 mm keeping diameter identical, 255 mm, against impact with blunt-nosed projectile having diameter of 19 mm. The numerical results were validated through experimentation (for 1-2 mm thickness) and theoretical results (for 1-5 mm thickness) addressed in the literature and found to be close to each other. The commercial finite element code LS-DYNA was employed to carry out the numerical simulations. It was observed that as the thickness increases ballistic limit increases drastically. © 2019 Elsevier Ltd. All rights reserved. Peer-review under responsibility of the scientific committee of the International Symposium on Functional Materials (ISFM-2018): Energy and Biomedical Applications. Keywords: ballistic limit;LS-DYNA;blunt-nosed projectile;
1. Introduction The application of aluminium alloys in today’s era grown widely in the industries like aerospace, transportation and defence. It is one of the most widely used metal due to its high strength to weight ratio and excellent workability. In the defence industry, the choice of the armour material depends upon the ballistic resistance, thickness, and energy absorption capacity. The science of ballistic impact mechanics was far more complex than the normal impact mechanics.
* Corresponding author. Tel.: +9197138 12578
E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Peer-review under responsibility of the scientific committee of the International Symposium on Functional Materials (ISFM-2018): Energy and Biomedical Applications.
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As precisely explain impact mechanics is the branch of science which deals with the forces on and motion of objects. According to different literature “The action of one object coming forcibly into contact with other is an impact”. The parameters which differentiate between the impact and ballistic impact are high strain rate, large strain and temperature characteristics of the target body The performance of the target body mainly depends on its material, span, thickness and strength and parameters of the projectile such as velocity, mass and nose shape etc. The number of literature are available that addresses the impact response of various materials, mechanism of penetration and various parameters which governs the performance of material under high strain rate loading. Iqbal et. al. [1] numerically and experimentally concluded for aluminium targets and steel projectile that with the increase in target diameter(D) to the projectile diameter(d) ratio (D/d) the ballistic limit increases consistently against the projectile impact. According to Ansari et al. [2] study over aluminium plates and different nosed projectile, as the projectile nose shape changes from conical to blunt, damage in the target increases. Recht and Ipson [3] studied the ballistic-penetration resistance for steel plates against the blunt and conical nosed projectile and found that for thicker target blunt nosed projectile was more efficient. Flores et al. [4] explored the behaviour of the plates of materials like steel and aluminium with single and multilayered arrangement and concluded that for monolithic material the ballistic performance of single layer in comparison with multi layered arrangement is far better. Iqbal et al. [5] studied the influence of the double nosed projectile on the ballistic response of thin aluminium plates. Dev et al. [6] studies various constitutive relationship of projectile impacted over steel plates and explored that for real life practical applications, constitutive relationship and fracture criterion given by the Johnson-Cook gives exceptional congruence with the results obtained experimental for the impact of the projectile on steel plates which concludes that Johnson-cook model is a good choice for impact related problems. Borvik et al. [7] performed an experimental study over steel plate with different nosed projectile and it was concluded that the failure mode and energy absorption mechanism of the target plate during failure was considerably affected by the projectile nose shape. The effect of varying target thickness over the ballistic performance, deformation, energy absorption, and other influencing parameters over the same projectile was still under study. With increase in the plate thickness failure characteristics changes from thin plate to thick plate. In thin plate membrane stretching was there which enhance the bending of the plate after impact this increase the deformation characteristics of the plate and ultimately shearing occurs. In the thick plate membrane stretching is not that much significant which decreased the deformation characteristics of the plate which ultimately leads to shearing without much bending of the plate. In this study, the influence of varying target thickness of the monolithic plate of aluminium 1100-H12 on the residual velocity, ballistic limit, energy absorption, deformation and perforation time over blunt-nosed projectile has been studied. The projectile impact velocities were varied and ballistic limit and other influencing parameters were analysed. Numerical simulations were performed to know the effect of thickness on response of aluminium plate with varying thickness as 1, 2, 3, 4 and 5 mm. The projectile diameter kept constant as 19 mm. The numerical results were validated and strengthened out by conducting experiments for 1-2 mm thickness whereas analytical model of Richet and Ipson [3] was employed for validation of the results of 1-5 mm thick target. 2. Numerical and Experimental Investigation The commercial finite element code ANSYS / LS-DYNA was employed to carry out the numerical simulations. The thickness of the plate varied as 1, 2, 3, 4, 5 mm plate keeping the blunt-nosed projectile same. Figure 1 shows the three-dimensional meshed model of the blunt projectile and the target plate. As there is surface contact (because of flat faces) between the target and the projectile due to blunt-nosed shape and so contact algorithm of Automatic_Surface_To_Surface was assigned. The material of projectile was considered steel having diameter 19 mm, length 50.8 mm and mass 52.5 gm and considered as rigid in the simulation. The diameter of the target plate was kept constant as 255mm and considered as a deformable body. The plate was finely meshed at the centre because the impact took place at the centre of the plate which acted as a critical zone (slightly larger than the projectile diameter). The aspect ratio was kept unity at the critical zone. The mesh density has varied from fine to coarser from center to the outer periphery of the plate. Eight node brick element meshing was used in the numerical study and similar type of meshing was done in all the plates for doing the comparative study. Due to the rigid nature of the projectile it was considered as master part and plate was considered as slave part due to deformable nature. A mesh convergence study was also carried out by Tiwari et al.
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[8] and the most optimum results obtained by considering 6 elements along the thickness of 1mm plate and similarly 12 elements for 2 mm and so on till 30 elements in 5mm plate with the corresponding size of cubic element 0.16 mm in the contact region. The experimental study was carried out using the experimental setup shown by schematic diagram of a pneumatic air gun in Figure 2 which comprises with a compressor working pressure of 60 kg/cm2, a valve that trigger out the blunt projectile from a 1.5 m long barrel over the target and a projectile catcher which is placed to safeguard the projectile after impact. A high speed fps video camera was used to measure the velocity of the projectile before and after the impact. The steel projectile of mass 52.5 oil quenched and then annealed to release the internal stresses. The target plates were fully clamped in the periphery of the plate and the projectile was normally impacted. After passing through the plate the projectile was caught by the catcher, it is made up of cotton rag to safeguard the projectile after perforation.
Figure 1:Meshed plate and projectile.
Figure 2: Schematic diagram of the experimental Setup.
3. Constitutive Modelling The mathematical modelling of any ballistic impact is very complex and difficult because of phenomena like yielding, perforation, spring back, hardening, heating and shearing. The mathematical model which comprises of this process along with high strain rate behaviour generally employed for monolithic isotropic material like aluminium 1100-H12 (Table 1). A constitutive relationship and fracture criterion developed by Johnson and Cook [8] or J-C model (MAT-015) was widely used to capture high strain rate, large strain behaviour of the metals. The Johnson-Cook model gives exceptional congruence with the results obtained experimental for the impact of projectile on monolithic plates which concludes that Johnson-cook model is a good choice for impact related problems. The ballistic impact characteristics like high strains, large strain rate, heating and failure mechanism of the monolithic target body was correctly approximated by this relationship.
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The equivalent von misses stress constitutive J-C model was expressed below: ̍
σ̅ ( 𝜀̅ , 𝜀̅̍ , Ť) = [𝐴̅ + 𝐵( 𝜀̅ ) ][ 1+ 𝐶̅ ln ( )] [1 - Ť ] (1) ̍ ̅ ̅ where 𝐴 , 𝐵 , 𝐶 ,n and m are material characteristics parameters 𝜀̅̍ was equivalent plastic strain rate, 𝜀̍ was a reference strain rate , 𝜀̅ was equivalent to plastic strain, and Ť is the temperature defined as:Ť = (T -T )/(T
− T) T ≤ T ≤ T
(2)
is the melting temperature and T was the room temperature. where T is the existing temperature, T According to this model the failure occurs when the parameter 𝐷 also known as damage parameter go above unity; 𝐷(𝜀̅ , 𝜀̅ ̍ , T, 𝜎 ∗ ) = ∑
∆ (̍ ,
,
(3)
∗)
Where, ∆ 𝜀̅ was an rise of equivalent plastic strain during an integration cycle and 𝜀̅ level. The equivalent fracture strain 𝜀̅ was expressed as:𝜀̅ (
σ
, 𝜀̅ ̍ , Ť) = [D + D exp(D
σ
)] [1 + D ln (
̍ ̍
)] × [1 + D Ť]
was the critical failure strain
(4)
is the ratio of stresses and 𝜎 is the mean or average where D , D are material characteristic parameters, σ stress. The material parameters where 𝐴̅ , 𝐵 and n were obtained from cylindrical cross section specimen by doing uni-axial tension tests whereas D , D & D were obtained from artificial notched specimens by performing uniaxial tension test. The material parameter 𝐶̅ and D were obtained from Hopkinson pressure bar tension test whereas D and m from tension test at high temperature. The projectile having rigid characteristics MAT_RIGID (MAT-020) was used as material model. Table 1: Material properties of aluminium 1100-H12 Plate [8] Modulus of ℯlasticity, E(N/mm2) 𝑃oison’s ratio, 𝜈 𝐷ensity, 𝜌 (kg/m3) 𝑌ield stress, 𝐴̅ (N/mm2) 𝐵 (N/mm2) Reference strain rate , 𝜀̍ (s-1) n M T (K) T (K) 𝑆pecific heat, Cp (J/kg-K) 𝐼nelastic heat fraction, 𝛼 D D D D D
65.762 .3 2700 148.361 345.513 .001 .183 .859 893 293 920 .9 .071 1.248 -1.142 .0097 0
4. RESULTS AND DISCUSSION Results obtained by the numerical simulations in LS-DYNA for the ballistic impact were discussed in the subsequent section. Modes of failure due to the impact of projectile of blunt-nosed shape, Variation in the ballistic limit, deformation, energy absorption of the plate and velocity and acceleration characteristics of the projectile as the function of thickness of the projectile were discussed.
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4.1. Modes of failure Figure 3 Shows the impact of the blunt-nosed projectile over 2 mm plate with velocity of 102.63 m/s. When the projectile strikes the plate it first deforms and after deformation a critical zone was created at the point of a strike which increases the stresses of the plate at that zone. The induced stress by the impact was the collaborative effect of the shear, tensile as well as compressive stress. Once the stress exceeds the strength of the plate the plate gets shear off in the form of plug having equivalent cross section as that of projectile i.e. circular. The plug having a diameter approximately same as diameter of the projectile, the thickness of the plug was approximately (not equal due to local stretching) same as that of the plate thickness. As the thickness of the plate varied similar perforation mechanism takes place i.e. the formation of the plug as shown in the Figure 4. After perforation, the velocity of plug and the bullet was approximately same. The stress was distributed in the form of circular fringes having the maximum value at the contact zone and decreases radially.
Figure 3: Stress Distribution over the plate
(a)
(b) Figure 4: Perforation mechanism observed in the plate due to impact of blunt projectile, (a) Numerical, (b) Experimental
4.2. Ballistic limit The ballistic limit or velocity is the average of the maximum velocity of the projectile which creates initial indentation over the target and the minimum velocity of the projectile at which perforation occurs in the target. Generally denoted by V50 or Vb. In other words, projectile velocity below the ballistic limit will not be able to perforate the target. With increase in the thickness of the target plate the ballistic limit increased significantly shown in the figure 5. The increment in the ballistic limit was highest from 1mm to 3 mm plate and then the increment decreased. The ballistic resistance increased from 49.68% for 1 & 2 mm plate, 49.88 for 2 & 3 mm plate, 15.38% for 3 & 4 mm plate, 11.11% for 4 & 5 mm plate. Due to the increase in the thickness, the resistance offered by the plate in perforation by the bullet increases as more area was there for shearing which increases the capacity of the plate. This increase the ballistic limit of the thicker plate. Because of the increase in thickness, the weight of the plate also increases significantly. Among the 5 different plates, 3 mm plate justifies the increase in the thickness for the optimum variation of the ballistic limit.
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Figure 5: Ballistic Limit for different thickness of the plate
4.3. Energy Absorption and deformation of the plate When the projectile strikes the target the plate first significantly deforms(stretch) and vibrate in order to absorb the impact energy and once the threshold energy of plate reaches the plate gets shear off and forms a plug. Due to elastic nature of the plate, spring back action takes place and plate try to regain its original configuration, but due to locking of stresses plate get permanently deforms as shown in the figure 6 and figure 7. As the thickness increases the energy absorption capacity of the plate increases and the deformation due to impact decreases. Due to the increase in thickness, stiffness and strength of the plate increase because of that the damping characteristics increases and as a result ability to dissipate energy increases and resistance towards deformation increases. The maximum deformation of the plate at velocity just above the ballistic limit is 3.85, 3.2, 2.43, 2.17 and 1.73 mm for 1, 2, 3, 4 and 5 mm thickness respectively. It was observed that there was a considerable decrease in the deformation. Similarly, Fig. (6) shows the energy absorbed by the target plate and energy loss by the projectile. From figure 7 it is observed a spring back action of the plate after the removal of the plug by the projectile. The plate tries to regain its original shape due to internal stresses developed in the plate. But due to inelastic nature the plate not be able to reshape its original configuration. As we can see from the figure the spring back action is maximum for 1mm plate and then decreases this is due to decrease in stiffness of the plate as we increase the thickness. 4.4 Velocity & Acceleration Behaviour of the Bullet The velocity of the projectile plays a significant role in the perforation mechanism. Most of the other parameters depend on the velocity of the projectile. The velocity lower than the ballistic limit was not being able to perforate the plate but deformation of the plate takes place. Figure 7 for 1mm plate, it can be seen that at first the deformation increases and become maximum at the ballistic limit and then as the velocity increases it decreases. A similar pattern was followed by all the plates of different thickness. The velocity after perforation was called residual Velocity (Vr). Below ballistic limit, Vr is equals to zero. Figure 8 shows the variation of the Vr with respect to the impact velocity(Vi) for different thickness of the plate. As the thickness increases residual velocity decreases. Due to the change in velocity, acceleration comes into the picture and it varies as shown in the figure 9. Acceleration varies maximum for 5mm plate and reduces significantly as the thickness decreases. This variation was due to the momentum exchange between the plate and projectile and by increasing thickness exchange of momentum exceeds and so more velocity was lost in perforation and due to which residual velocity decreases and acceleration increases 5.Validation of the Results The experimental study was carried out for 1 & 2 mm plates having the same diameter of 255 mm with the blunt projectile of diameter 19 mm and mass 52.5 gm. As shown in the figure 4(b) the plate was clamped and the projectile was impacted, the plate deforms and plug forms, see Fig. 4(a). Similar deformation and plug formation takes place in the numerical simulation. Similarly, the theoretical model given by Recht and Ipson [10], where law of conservation of momentum and energy is used to determine the velocity after perforation, i.e. residual velocity of the projectile. With the help of method of least squares the model constants 𝑎 and p are found and this empirical
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relationship gives the residual velocity for 1, 2, 3, 4 and 5 mm plates: υ =
0
0≤υ ≤υ
𝑎 (υ − υ )
υ
υ
𝑎 =
, 𝑚
𝜋𝑟 𝜌 ℎ
(5)
On comparing the numerical, experimental and theoretical results for the ballistic limit and residual velocity for 1mm and 2 mm plates, see figure 10 and Table (2), the results were found in close agreement with each other. Also, numerical and theoretical results were validated for 1, 2, 3, 4 and 5 mm plate as shown in figure 11 and in Table 3.
(a)
(b)
Figure 6: Total Energy variation for, (a) plate and (b) bullet with varying thickness
(a)
(b)
Figure 7: Variation of deformation of plate with varying, (a) Time and (b) Thickness
Figure 8: Variation of Residual velocity v/s Impact velocity.
Figure 9: Variation of Acceleration v/s Time.
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Figure 10: Validation of the result for 1mm and 2mm plates experimentally, numerically and analytically.
Figure 11: Validation of the result for 1, 2,3,4,5 mm plates numerically and analytically.
Table 2: Comparison of the residual velocity for 1mm and 2mm plates numerically, analytically and experimentally. Plate Thickness
1mm
2mm
Impact Velocity(Vi) m/s 101.28 81.02 70.9 57.51 52.15 51.75 190.31 162.43 102.63 78.06
Numerical 81.03 64.82 48.61 28.75 --180.15 144.115 60.04 0
Residual Velocity (Vr) m/s Analytical 86.093 61.844 48.283 25.709 0 0 163.142 131.652 48.6885 0
Experimental 87.36 62.337 50.215 24.633 0 0 165.09 136.92 55.031 0
Table 3: Comparison of the Residual Velocity of the bullet for different thickness of plate analytically and numerically Impact Velocity (Vi)
1mm
2mm
3mm
4mm
5mm
81.02 70.9 57.51 52.15 190.31 162.43 102.63 78.06 156 143 130 117 175 160 150 135 225 200 170 150
Numerical 65.811 51.368 24.785 0 165.09 136.92 55.031 0 110.2 92.869 6.582 0 122.71 96.01 77.36 0 187.38 156.32 96.595 0
Residual Velocity (Vr) m/s Analytical 61.844 48.283 25.709 0 163.142 131.652 48.6885 0 105.897 87.449 66.23 0 117.0463 96.0059 80.3224 0 171.2946 141.8332 102.367 0
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6. Conclusion The influence of thickness on ballistic performance of aluminium plate against blunt projectile was explored by carrying out numerical simulations and experiments. The projectile of 52.5 g mass and 19mm diameter was hit over the target of Aluminium 1100-H12 plate with varying thickness of 1,2,3,4,5 mm. The parameters like deformation, ballistic limit, energy absorption etc. were analyzed which influence the perforation mechanism of the thin plate of aluminium. By varying the thickness, the failure mode remains the same, all targets failed due to shearing of plug. The ballistic limit of the plate increased significantly as the thickness of the plate increases with linear relationship initially and after that a steep slope was observed which showed a nonlinear relationship between the thickness and the ballistic limit. Thin plate failed mainly due to membrane stretching which causes the bending of the plate whereas the major factor responsible for thick plate was shearing. Spring back action was observed due to the stresses developed inside the plate which try to regain its original configuration and it decreased with the increase in the target thickness. The numerical results were validated both experimentally and numerically with a close agreement. The most optimum increase in the ballistic limit with respect to the weight was found for the thickness 3mm which showed the highest ballistic limit to weight ratio. References [1] M.A. Iqbal, G. Tiwari, P.K. Gupta, P. Bhargava. Ballistic performance and energy absorption characteristics of thin aluminium plates. International Journal of Impact Engineering 77 (2015) 1e15. [2] M.A. Iqbal, S.H. Khan, R. Ansari, N.K. Gupta. Experimental and numerical studies of double-nosed projectile impact on aluminium plates. International Journal of Impact Engineering 54 (2013) 232e245. [3] T. W. Ipson and R. F. Recht. Ballistic-penetration Resistance and Its Measurement. Journal of Applied Mechanics. 30. 10.1115/1.3636566. [4] E.A. Flores-Johnson, M. Saleh, L. Edwards. Ballistic performance of multi-layered metallic plates impacted by a 7.62-mm APM2 projectile. International Journal of Impact Engineering 38 (2011) 1022e1032. [5] M.A. Iqbal, S.H. Khan, R. Ansari, N.K. Gupta. Experimental and numerical studies of double-nosed projectile impact on aluminium plates. International Journal of Impact Engineering 54 (2013) 232e245. [6] S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth. On the influence of constitutive relation in projectile impact of steel plates. International Journal of Impact Engineering 34 (2007) 464–486. [7] T. Børvik, M. Langseth, O.S. Hopperstad, K.A. Malo. Perforation of 12mm thick steel plates by 20mm diameter projectiles with flat, hemispherical and conical noses Part I: Experimental study. International Journal of Impact Engineering 27 (2002) 19–35. [8] G. Tiwari, M.A. Iqbal, P.K. Gupta. Energy absorption characteristics of thin aluminium plate against hemispherical nosed projectile impact. Thin-Walled Structures 126 (2018) 246–257.