SPH Simulation Of Ballistic Impact On Ceramic Plate

SPH Simulation of Ballistic Impact on Ceramic PlateChetan Swaroop, Arunesh Kumar Srivastave & K. N. PandeyMechanical Engineering Department, MNNIT AllahabadE-mail : swaroopchetan@hotmail.com, arunesh srivastava15@yahoo.com, knpandey@mnnit.ac.inmany complex mechanisms, e.g. large deformations,crack and fracture of both bullet and armor [3].Abstract - This paper studies the use of smooth particlehydrodynamics (SPH) numerical technique to simulate theimpact, penetration and perforation of Ceramic plate(Al2O3-99.7%) by Lead Round Nose (LRN) projectile. Thegeneral discussion of the SPH solver is introduced firstthen AUTODYN 2D simulation of penetration andperforation of ceramic plate. The numerical prediction ofthe time history of velocity of bullet is investigated for arange of impact velocity between 400m/s to 800m/s and anempirical relation is derived between impact velocity andresidual velocity. For this type of problem, the SPHapproach can provide significant advantages over moretraditional numerical methods.Armors ceramics are available as pressure lesssintered (lower cost) or hot pressed (higher cost). Armorceramics are normally produced via powder processingroutes.II. SPH SOLVERSPH is a mesh free method that can be applied tonon-linear problems with large deformation and largestrains, especially for impact and penetration of solidstructure. SPH holds premise to overcome many of theinherent limitation with classical Lagrange and EulerApproaches. In penetration problems severe meshdistortion is typical difficulty evident with a classicalLagrange Solver. Such mesh distortion can result ininefficient small time steps and inaccurate results. Toavoid this mesh distortion problem, and erosionmechanism is introduced to remove highly distortedelement and allow the calculation to continue [4].Keywords: ballistic impact, ceramic, lead round nose (LRN).I.INTRODUCTIONDevelopment of light weight armor structure is veryimportant with respect to saving energy and increasingmobility of the defense system. Armors containingceramic front layer and a metallic or composite backinglayer offer a significant weight saving compared to steelfor the same ballistic threat. In the composite armor theceramic plate breaks up and erodes the projectile, meantime broken ceramic form a conide which distribute aforce over a larger area and reduce the pressure on thebacking plate [1].In impact and penetration problem, all theequilibrium equation of continuum dynamics andconservation laws are represented by group of partialdifferential equations. Traditional finite differencemethod transforms the partial differential equation into asystem of Algebraic equation by writing the partialdifferentiation in an incremental form of field variablesand time. In SPH Solver these partial differentialequations are transformed into integral equationsthrough the use of interpolation function. Interpolationfunctions give a "Kernel Estimate" of the field variableat each interpolation point by evaluating the integrals assums over neighboring interpolation point. Theseinterpolation points are called SPH nodes therefore aphysical object is represented by a field of SPH nodesinstead of cells (elements) as in traditional LagrangeSolver. In the SPH solver there is no "Mesh tangling"and mesh degeneration so that a numerical erosionmodel is not needed. AUTODYN is a general finiteelement/ finite difference/ finite volume computer codeProperties that make ceramic efficient include lowdensity, high hardness, high compressive strength andhigh modulus however, the low tensile strength typicalof ceramic severally limits their performance. Theprimary role of the armor ceramic is to convert theprojectile KE into elastic stored energy or plastic workon the projectile. For brittle projectiles the elastic storedenergy can result in projectile fragmentation. As a resulteither plastic work or fragmentation the failed projectileremnants may also disperse which distribute theprojectile KE over a greater target area [2].During ballistic impact between bullet and armor,the bullet tries to punch through the plate and maydisintegrate in the process. This phenomenon involvesISSN : 2319 – 3182, Volume-2, Issue-1, 201384

International Journal on Theoretical and Applied Research in Mechanical Engineering (IJTARME)for the non-linear analysis of solids, fluids and theinteraction between the solid and fluids [5].The projectile was impacted for a range of velocityfrom 400m/s to 800m/s on a 6mm thick Ceramic plate(Al2O3 99.7%) and corresponding residual velocity wasobserved as shown in Fig.1(a),(b),(c),(d),(e). Anempirical relation is derived between Impact velocityand residual velocity from simulation result.In the present paper the SPH processor in AUTODYN isapplied to the penetration and perforation ceramic plateby Lead round nose (LRN) Projectile.Table I: Material Name – LEADIII. AUTODYN SIMULATIONIn the numerical simulation presented the projectileare made of Lead. The lead material properties are fromthe AUTODYN Material Library. The size andgeometry of projectile is equivalent to 9mm lead roundnose (LRN) bullet. The projectile's Equation of state isshock while the Strength model is Steinberg-Guinan.The Geometrical Erosion strain is taken as 2.0(Instantaneous). The Lagrange solver is applied to theprojectile. The Alumina (Al2O3) ceramic plate ismodeled by SPH Nodes. The ceramic plate equation ofstate is polynomial while the strength model is JohnsonHolmquist (JH2). The Geometrical Erosion strain istaken as 2.0 (Instantaneous).Equation y1.13400E 01(g/cm3 )ShearModulus8.60000E 06(kPa )Gruneisencoefficient2.74000E 00(none )Yield Stress8.00000E 03(kPa )Parameter C12.00600E 03(m/s )MaximumYield Stress1.00000E 05(kPa )Parameter S11.42900E 00(none )ErosionGeometricStrainIn order to account for contact/penetration behaviorbetween the Lagrange projectile and the SPH plate, thegap interaction logic of AUTODYN has been activatedbetween the SPH nodes and Lagrange cells [5].AUTODYN has a contact logic wherein object use asmall gap to determine if interaction exists. enetration interface" for the SPH solver toavoid excessive noise on the impact surface [6].ParameterQuadratic S20.00000E 00(s/m )ErosionStrain2.00000E 00(none )The SPH solver has been implemented in both 2D and3D. AUTODYN 2D is used here for simplicity and easefor demonstration.Table II: Material Name - Al203 - 99.7%IV. PROJECTILE (LEAD) IMPACT ON CERAMIC PLATE(Al2O3 99.7%)The Projectile modeled in AUTODYN 2D usingaxial symmetry about the axis with Lagrange solver.The total length is 29.69mm and the diameter is 9mmwith round nose. The effective material property aretaken from AUTODYN Material Library as shown inTable -I.Equation ofStatePolynomialParameter B10.00000E 00(none )Referencedensity3.80000E 00(g/cm3 )Parameter T12.00000E 08(kPa )BulkModulus A12.00000E 08(kPa )Parameter T20.00000E 00(kPa )ParameterA20.00000E 00(kPa )StrengthJohnsonHolmquistParameterA30.00000E 00(kPa )ShearModulus1.35000E 08(kPa )ParameterB00.00000E 00(none )Model rain2.00000E 00A 6mm thick ceramic plate of size 100 mmdiameter clamped on the ends. The effective materialproperties used in AUTODYN simulation for thismaterial are taken from AUTODYN Material Libraryshown in Table -II. The equation of state of the ceramicplate is shock with bulk modulus 200 GPa and JohnsonHolmquist strength model is used. The total number ofSPH nodes in the plate is 30,000 and 60 SPH nodesthrough thickness. The fixed boundary condition isapplied on outer edge of the plate.Fig. 1(a)Fig. 1(b)ISSN : 2319 – 3182, Volume-2, Issue-1, 201385

International Journal on Theoretical and Applied Research in Mechanical Engineering (IJTARME)These points are fitted in MATLAB with linear fit andcorresponding equation is:𝑉𝑟 0.94𝑉𝑝 10-----------(1)where 𝑉𝑟 Residual Velocity(m/s)𝑉𝑝 Impact Velocity (m/s)This equation holds good agreement with the impactvelocity ranging from 400-800m/sFig. Fig. (d)Table III.Sr.no.Impact Velocity(m/s)Residual 743Fig. 1 (e)To verify equation (1) for above velocity rangeanother simulation was executed with projectile impactvelocity 560 m/s and the residual velocity fromnumerical simulation was found 518m/s as shown inFig.-3, which is in close agreement with the aboveempirical relation of equation (1).V. EMPIRICAL RELATIONFrom the numerical simulation of 6 mm thickceramic plate impacted with LRN projectile. From theabove figures residual velocity of projectile is found andshown in the Table -III. Residual velocities were plottedagainst the corresponding impact velocities inMATLAB as shown in Fig.-2 with '*'.Fig. 3Fig. 2ISSN : 2319 – 3182, Volume-2, Issue-1, 201386

International Journal on Theoretical and Applied Research in Mechanical Engineering (IJTARME)The AUTODYN simulation results are shown inFig. 4 to Fig. 5. The Fig. 4 shows the general setup ofLagrange grid of Projectile interacting ceramic platefilled with SPH Nodes. Fig. 5 (a),(b),(c) shows theinteraction and penetration of ceramic plate by projectileand crack conide formation and crack propagationphenomenon occurred in different time intervals. Fig. 6shows the Perforation of ceramic plate.Fig. 5 (c)Fig. 4Fig. 6VI. CONCLUSIONIn the present paper the SPH solver inAUTODYN has been employed to simulate the ballisticimpact behaviour of ceramic plate (Al 2O3-99.7%). Thesimulations studied impact model of 9mm LRN bulletwith impact velocity ranging from 400-800m/s onceramic plate. With the help of time history of projectilevelocity, the corresponding residual velocities werefound. An empirical relation is derived between impactvelocity and corresponding residual velocity for 6 mmthick ceramic plate (Al2O3-99.7%) for the above impactvelocity range with linear fit with good agreement.Fig. 5 (a)VII. REFERENCES[1]Mustafa Ubeyli, R. Orhan Yildirim, BilgehanOgel,"Investigation on the Ballistic Behavior ofAl2O3/Al-2024 laminated composite, Journal ofMaterial Processing and Technology, vol.196,pp356364, 2008[2]Christain E. Grethlein, "Army Material Research,Advance Material and Process Technology InformationFig. 5 (b)ISSN : 2319 – 3182, Volume-2, Issue-1, 201387

International Journal on Theoretical and Applied Research in Mechanical Engineering (IJTARME)AnalysisCentre (AMPTIAC)", Vol. 8,pp2127,November 2004,[3][4]Tarin Vanichayangkuranont, Kuntinee Maneeratanaand Nuwong Chollacoop,"Numerical Simulation ofLevel 3A Ballistic Impact on Ceramic/SteelArmor",20th conference on Mechanical EngineeringNetwork of Thailand, October 2006Century Dynamics, Inc. 2005. "SPH User Manual andTutorial for AUTODYN Interactive NonlinearDynamic Analysis Software",Century Dynamics, Inc.,San Ramon, California, U.S.A.[5]Xiangyang Quan, Naury Birnbaum,"SPH Simulation ofthe Ballistic Perforation of GFRP", 18th InternationalSymposium and Exhibition of Ballistics, November15-19, 1999, Texas U.S.A.[6]Century Dynamics, Inc 1999. "AUTODYN TheoryManual". Century Dynamics. Inc., San Roman,California, USA.[7]MJ Iremonger "Disruption of Small Arms Bullets usingThin Metal Plates", Proceeding of the 11thInternational Symposium on Interaction of the many ISSN : 2319 – 3182, Volume-2, Issue-1, 201388

AUTODYN has been employed to simulate the ballistic impact behaviour of ceramic plate (Al 2 O 3-99.7%). The simulations studied impact model of 9mm LRN bullet with impact velocity ranging from 400-80