Experimental and Numerical Studies on Mild Steel Plates against 7 62 API Projectiles Procedia Engineering 173 ( 2017 ) 369 – 374 Available online at www sciencedirect com 1877 7058 © 2017 The Authors[.]
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 173 (2017) 369 – 374 11th International Symposium on Plasticity and Impact Mechanics, Implast 2016 Experimental and Numerical Studies on Mild Steel Plates against 7.62 API Projectiles K Senthil*a, M A Iqbalb, P Bhargavab, N K Guptac a Department of Civil Engineering, National Institute of Technology Jalandhar, Jalandhar 144011, India b Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India c Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, 110016, India Abstract The ballistic resistance of 12 mm thick mild steel plates has been studied against 7.62 API projectiles through numerical simulations carried out using ABAQUS/Explicit finite element code The incidence angle was varied as 0°, 15°, 30°, 45°, 57° and 59° The material parameters for the JC model proposed by the Authors were employed to predict the material behavior of the target, while the material behavior of the projectile was incorporated from the available literature The numerical results thus obtained have been compared with the experiments reported in earlier study, wherein the incidence velocities of the projectile were considered close to 820 m/s The experimental and numerical results with respect to failure mechanism, residual projectile velocity and critical angle of ricochet have been compared A close correlation between the experimental findings and the predicted results has been found In general, the resistance of the target has been found to increase with increase in target obliquity © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license © 2016 The Authors Published by Elsevier Ltd (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of Implast 2016 Peer-review under responsibility of the organizing committee of Implast 2016 Keywords: Mild steel; Oblique impact; Numerical investigation; ballistic limit; 7.62 API projectiles; Introduction The need for protection against small arms projectiles is very important from a military point of view There are a large number of parameters which may influence the ballistic resistance of metallic plates such as material behavior, target thickness, angle of incidence, nose shape and size of projectile as well as target configuration, [1-15] The *Corresponding Author: Phone: 91-9458948743, 91-8267927382 Email Address: urssenthil85@yahoo.co.in; urssenthil85@gmail.com 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of Implast 2016 doi:10.1016/j.proeng.2016.12.032 370 K Senthil et al / Procedia Engineering 173 (2017) 369 – 374 majority of the ballistic studies are concerned with oblique impact against ordinary hardened steel projectiles, [1-9] Further, the most of studies concerned with worst case scenario, which is normal impact, [10-13] However, most real cases in light of military application, the armour piercing incendiary projectile will strike the target with some degree of obliquity, [14, 15] Therefore, it is concluded that the studies on ballistic resistance at varying angle of incidence against armour piercing projectile is limited In this paper, the ballistic performance of 12 mm thick mild steel targets has been studied against 7.62 AP projectiles at normal and oblique angles of incidence until the occurrence of projectile ricochet by carrying out finite element simulations on ABAQUS/Explicit finite element code The Johnson-Cook [16, 17] constitutive model has been employed for predicting the material behavior of the projectile and mild steel targets The ballistic results thus obtained have been compared with the experiments carried out Gupta and Madhu [14, 15] Constitutive Modeling In order to define the material behavior of mild steel target and armour piercing projectile the Johnson-Cook elasto-viscoplastic material model [16-17] available in ABAQUS finite element code was employed The material model includes the effect of linear thermo-elasticity, yielding, plastic flow, isotropic strain hardening, strain rate hardening, softening due to adiabatic heating and fracture effects The equivalent von- Mises stress ࣌ of the Johnson-Cook model is defined as; ሶ ౦ౢ ୮୪ ሻ ൌ ൣ ሺɂത୮୪ ሻ୬ ൧ ቈͳ ቆக ቇ ൣͳ െ ୫൧ ഥሺɂത୮୪ ǡ ɂሶ ǡ ɐ (1) கሶ బ where A, ܔܘB, n, C and m are material parameters determined from different mechanical tests ઽത ܔܘis equivalent plastic is non-dimensional temperature defined strain, ઽሶ is equivalent plastic strain rate, ઽሶ is a reference strain rate and ܂ as; ൌ ሺ െ ሻΤሺ୫ୣ୪୲ െ ሻ ୫ୣ୪୲ (2) where T is the current temperature, ୫ୣ୪୲ is the melting point temperature and is the room temperature The Johnson and Cook [17] extended the failure criterion proposed by Hancock and Mackenzie [18] by incorporating the effect of strain path, strain rate and temperature in the fracture strain expression, in addition to stress triaxiality The fracture criterion is based on the damage evolution wherein the damage of the material is assumed to occur when the damage parameter, ߱, exceeds unity; ߱ ൌσቆ οகത౦ౢ ఌത ቇ, (3) Where οɂത୮୪ is an increment of the equivalent plastic strain, ߝҧ is the strain at failure, and the summation is performed over all the increments throughout the analysis The strain at failure ߝҧ is assumed to be dependent on a non-dimensional plastic strain rate, ౦ౢ கሶ கሶ బ ; a dimensionless pressure-deviatoric stress ratio, ౣ ഥ (where ɐ୫ is the mean , defined earlier in the ഥ is the equivalent von-Mises stress) and the non-dimensional temperature, stress and ɐ Johnson-Cook hardening model The dependencies are assumed to be separable and are of the form; ɂത ሺ ఙ ఙ ഥ ሶ ౦ౢ ୮୪ ሻ ൌ ቂଵ ଶ ቀଷ ౣቁቃ ቈͳ ସ ቆக ቇ ൣͳ ହ ൧ ǡ ɂሶ ǡ ഥ கሶ బ (4) ୮୪ Where ଵ െ ହ are material parameters determined from different mechanical test, ɂሶ is equivalent plastic strain rate and ɂሶ is a reference strain rate When material damage occurs, the stress-strain relationship no longer accurately represents the material behavior, ABAQUS [19] The use of stress-strain relationship beyond ultimate stress introduces a strong mesh dependency based on strain localization i.e., the energy dissipated decreases with a decrease in element size Hillerborg’s [20] fracture energy criterion has been employed to reduce mesh dependency by creating a stress-displacement response after damage is initiated It also takes into account the combined effect of different damage mechanisms acting simultaneously on the same material 371 K Senthil et al / Procedia Engineering 173 (2017) 369 – 374 Finite Element Modeling The finite element model of the target and the projectile was made using three dimensional modeling approach of ABAQUS The finite element model of the target and projectile is shown in Fig The brass jacket of the projectile has been assumed to have stripped off and it is the steel core which actually hit the target Therefore only the steel core has been modeled for simulating the perforation phenomenon The JC model calibrated by Niezgoda and Morka [21] for the hardened steel core of 7.62 AP projectile was employed in the present study, see Table The shank diameter of the projectile was 6.06 and total length 28.4 mm The length of shank and ogival part was 20.75 and 7.65 mm respectively The target was modeled square, 200 mm x 200 mm, and assigned fixed boundary conditions at the periphery The material parameters of Johnson-Cook constitutive model used to predict the ballistic performance of mild steel target calibrated by Iqbal et al [22-23] are shown in Table The projectile was assigned initial velocities equivalent to those obtained by Gupta and Madhu [14, 15] The contact between the projectile and target was modeled by employing the Kinematic contact algorithm The projectile was considered as master and the contact surface of target as slave surface In the normal direction hard contact was defined and in the tangential direction the effect of friction has been assumed to be negligible The hexahedral elements of constant size mm were used to discretize the projectile The effect of mesh sensitivity of the projectile has not been addressed in this paper The mesh sensitivity in the target was studied by varying the element size as 0.8, 0.6, 0.2 and 0.1 mm in the impact region corresponding to 15, 20, 60 and 120 elements at the target thickness The projectile was impacted normally at an incidence velocity 818 m/s on 12 mm thick target and the residual velocity was found to be 669, 663, 658 and 657 m/s respectively The size of element was therefore considered to be 0.2 mm3 and the aspect ratio unity in all the simulations Away from the impact region, however, the size of element was slightly increased keeping the aspect ratio unity Three planar zones were identified with diameter 6.06, 30 and 50 mm The element size was kept 0.2, 1.0 and 2.0 mm3 respectively The compatibility between the varying sizes of elements was maintained using the tetrahedral elements in the transition zones In order to vary the angle of incidence, the target was rotated about its central axis keeping the axis of projectile horizontal Fig Finite element model of mild steel target and projectile Table Material parameters of mild steel target and projectile Description Modulus of elasticity Poisson’s ratio Density Yield stress constant Strain hardening constant Viscous effect Thermal softening constant Reference strain rate Melting temperature Transition temperature Fracture strain constant Notations E (N/m2) ν ρ (Kg/m3) A (N/m2) Target Material 203 x 109 0.33 7850 304.330 x 106 Projectile Material 202 x 109 0.32 7850 2700 x 106 B (N/m2) 422.007 x 106 211 x 106 n 0.345 0.065 C m ߝሶ 0.0156 0.87 0.0001 s-1 1800 293 0.1152 1.0116 -1.7684 -0.05279 0.5262 0.005 1.17 0.0001 s-1 1800 293 0.4 0 0 ߠ௧ (K) ߠ௧௦௧ (K) D1 D2 D3 D4 D5 372 K Senthil et al / Procedia Engineering 173 (2017) 369 – 374 Results and Discussion The ballistic performance of 12 mm thick mild steel targets has been studied at varying angles of incidence against 7.62 AP projectiles by carrying out finite element simulations on ABAQUS/Explicit finite element code The Johnson-Cook constitutive model has been employed for predicting the material behavior of the target The ballistic results thus obtained have been compared with the experiments carried out Gupta and Madhu [14, 15] The incidence velocities of projectile were considered between 800 to 850 m/s [14-15] The residual velocity of the projectile decreased with increase in the angle of incidence The predicted residual velocities are in close agreement to their actual values, see Table The maximum difference between the actual and predicted residual velocity was found to be 7.6%, at angle of incidence 45° The actual residual velocity was 555.3 m/s and predicted 515.82 m/s The 7.62 AP projectile failed the target through hole enlargement The formation of petals at the front surface and bulge at the rear surface has also been witnessed through experiments, Figs and 3, respectively The numerical simulations accurately predicted the failure mode including the size of hole, petalling at the front and the bulge at the rear surface The hole actually formed in the target was slightly bigger in size at the front than at the rear surface The diameter of the hole in target was 9.6 and 9.0 mm at the front and rear surface respectively A similar variation in the size of hole was predicted through the numerical simulations The predicted diameter of the hole was 9.32 and 7.66 mm at the front and rear surface respectively At 57° obliquity the experimental results suggested perforation of 12 mm thick target with a residual velocity 368.9 m/s At the same angle of obliquity however, the numerical results predicted that the projectile embedded in the target The embedment of the projectile occurred due to change in its trajectory as a result of very high obliquity The projectile penetrated the target and at the same time deviated from its central axis due to the component of resisting force normal to target surface Due to very high obliquity, the resistance normal to target surface deviated the projectile and hence, instead of penetrating through thickness the projectile started penetrating in the plane of target and stuck there, see Fig Thus it may be concluded that the projectile experienced embedment at 57° obliquity The residual velocity, 368.9 m/s, measured during experiments through the optical measurement system could be the velocity of the fragments ejected out of the projectile or target material It should also be noticed that experiments suggested critical ricochet of projectile at 59° obliquity Therefore at 57° obliquity, the residual velocity as high as 318.7 m/s, seems an overestimation of the results The actual and predicted deformation of the target as a result of projectile ricochet has been compared in Fig The projectile has registered an elliptical deformation pattern and erosion of material while sliding over the target surface An exact pattern of deformation and material erosion has been predicted through the numerical simulations Table Resistance of targets against varying obliquity Oblique angle 00 15 30 45 50 53 57 59 (a) Experimental results Impact velocity (m/s) Residual velocity (m/s) 818.0 661.5 842.7 671.6 801.8 598.0 808.0 555.3 808.0 815.3 809.0 368.9 815.3 Ricochet Numerical results Residual velocity (m/s) 658.42 677.73 603.97 515.82 409.59 318.76 0.0 Ricochet (a) Fig Front side target deformed profile of (a) experiment and (b) numerical results K Senthil et al / Procedia Engineering 173 (2017) 369 – 374 (b) (b) Fig Rear side target deformed profile of (a) experiment and (b) numerical results Fig Deformation of target as a result of projectile embedment Fig Deformation of target as a result of critical ricochet at 59° obliquity Conclusions Numerical investigations carried out on 12 mm thick mild steel targets against 7.62 AP projectiles at varying angles of incidence The effect of angle of incidence was studied and the results obtained were compared with the available results and the following conclusions are drawn The simulations at varying angle of incidence accurately predicted with respect to residual projectile velocities, critical angle of ricochet and the failure mechanism of target In general, the resistance of the target has been found to increase with increase in target obliquity The incidence angle up to 30°, the predicted residual velocities are in close agreement to their actual values The incidence angle at 45°, the maximum difference between the actual and predicted residual velocity was found 7.6 % At 57° obliquity, experimentally the target experienced perforation with a residual velocity of 368.9 m/s At the same angle of obliquity however, the numerical results predicted that the projectile embedded in the target The simulations predicted the angle of critical ricochet at 59°, identical to the actual angle of critical ricochet.The numerical simulations accurately predicted the failure mode including the size of hole, petalling at the front and the bulge at the rear surface and the same has also been witnessed through experiments The diameter of the hole in target was 9.6 and 9.0 mm at the front and rear surface respectively A similar variation in the size of hole was predicted through the numerical simulations as 9.32 and 7.66 mm at the front and rear surface respectively 373 374 K Senthil et al / Procedia Engineering 173 (2017) 369 – 374 References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] J Awerbuch, S.R Bodner, An investigation of oblique perforation of metallic plates by projectiles, Exp Mech 17 (1977) 147-53 W 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at the front and rear surface respectively A similar variation in the size of hole was predicted through the numerical simulations as 9.32 and 7. 66 mm at the front and rear