Simulation of Bullet Fragmentation and Penetration in Granular Media

materials

Article Simulation of Bullet Fragmentation and Penetration in Granular Media

Froylan Alonso Soriano-Moranchel 1, Juan Manuel Sandoval-Pineda 1, Guadalupe Juliana Gutiérrez-Paredes 1, Usiel Sandino Silva-Rivera 2 and Luis Armando Flores-Herrera 1,*

1 Postgraduate Studies and Research Section, Instituto Politecnico Nacional, Higher School of Mechanical and Electrical Engineering, U. Azcapotzalco, Av. Granjas 682, Mexico City 02250, Mexico; [email protected] (F.A.S.-M.); [email protected] (J.M.S.-P.); [email protected] (G.J.G.-P.) 2 SEDENA, D.G.E.M., Rectory of the Army and Air Force University, Escuela Militar de Ingenieros, Av. Industria Militar 261, Naucalpan de Juarez 53960, Estado de Mexico, Mexico; [email protected] * Correspondence: laﬂ[email protected]

Received: 30 October 2020; Accepted: 18 November 2020; Published: 20 November 2020

Abstract: The aim of this work is to simulate the fragmentation of bullets impacted through granular media, in this case, sand. In order to validate the simulation, a group of experiments were conducted with the sand contained in two different box prototypes. The walls of the first box were constructed with fiberglass and the second with plywood. The prototypes were subjected to the impact force of bullets fired 15 m away from the box. After the shots, X-ray photographs were taken to observe the penetration depth. Transient numerical analyses were conducted to simulate these physical phenomena by using the smooth particle hydrodynamics (SPH) module of ANSYS® 2019 AUTODYN software. Advantageously, this module considers the granular media as a group of uniform particles capable of transferring kinetic energy during the elastic collision component of an impact. The experimental results demonstrated a reduction in the maximum bullet kinetic energy of 2750 J to 100 J in 0.8 ms. The numerical results compared with the X-ray photographs showed similar results demonstrating the capability of sand to dissipate kinetic energy and the fragmentation of the bullet caused at the moment of impact.

Keywords: impact; sand; bullet penetration; granular media; energy dissipation; transient analysis

1. Introduction The analysis of bullet penetration through different materials is an important issue to achieve adequate safety conditions during the design of containers, pressure vessels, vehicles, armor and other similar products, especially barricades, to protect security forces. These studies have been performed in previous works considering steels and aluminum alloys [1–3]. Børvik carried out several tests with 6082-T651 and 6082-T4 aluminum plates with changes in the angle of impact and plate characteristics [4,5]. In specific defense situations, the behavior of the material supporting bullet impacts is analyzed depending on the crater formation, for example, in continuous media [6]. However, granular media is another option to reduce the kinetic energy of a bullet over short distances [7,8], especially when such media are used in the form of ballistic blocks. The granular nature of sand, its recycling capability combined with its complex interaction dynamics creates unique physical capabilities. The mixture of sand with other construction materials for example, creates important characteristics suitable for several mechanical and construction applications [9–23]. This phenomenon has been studied here as an alternative to achieve the goal of bullet fragmentation. Several containers constructed with fiberglass and considering different geometries have been used as an alternative to

Materials 2020, 13, 5243; doi:10.3390/ma13225243 www.mdpi.com/journal/materials Materials 2020, 13, 5243 2 of 13 constructing ballistic walls [24–30]. Based on these works, samples of ballistic walls were constructed in this research to observe the behavior of a bullet when entering a coupled system. This system is formed by continuous media as the initial impact material and sand as the granular media. The purpose of the present study is to measure the penetration distance of a bullet impacting the materials considered in the continuous system, which are plywood and ﬁberglass shells. The numerical and experimental results obtained with the combination of materials used for the construction of continuous and granular media are the main contributions of this study. A numerical analysis was carried out using ANSYS® 2019R1-AUTODYN to simulate the behavior of the bullet when impacting the samples and to obtain the magnitudes of the kinetic energy absorbed by the coupled system [31]. The dynamic behavior of the granular media as a group of uniform particles transferring the kinetic energy when receiving the 7.62 mm projectile was simulated using the smooth particle hydrodynamics (SPH) model, together with the compaction equations of state (EOS) and the model option MO granular. This transient analysis includes the interaction of the particles inside the coupled system when receiving the impact; in some cases, the bullet deviates with respect to the original trajectory, and in other cases, the bullet is destroyed because of the instantaneous heat and mechanical friction [32].

2. Materials and Methods

2.1. Ballistic Blocks Two types of block prototype were built for the experiment, one that forms the plywood- sand-plywood (PSP) system and another that forms the fiberglass-sand-fiberglass (FSF) system. The construction criteria for the block walls considered the minimum commercial thickness walls required to support 10 kg of sand per block, but also allowing stacking up to 7 blocks to form a 2.1 m high ballistic wall without presenting structural instabilities. As a result of the tests, the resulting wall for the PSP system was 12 mm and for the FSF system it was 6 mm. Finally, a total of 6 blocks were built for each system. The final dimensions of the blocks were 300 300 300 mm in length, × × width and height, respectively. The experiment considered beach-type sand which was first passed through a sieve to eliminate the presence of stones, garbage and other solid objects and it was left to dry in the sun for 10 days, moved with a shovel and covered at night for the purpose of removing traces of moisture. It is very important to remove moisture before the experiments to maintain uniform distribution of the granular media and to avoid a lubricating effect during the friction between the sand and the bullet.

2.2. Ballistic Workbench Figure1 shows the components of the experimental setup. Two types of bullets were used for the experiments, the Full Metal Jacket (FMJ) and the Armor Piercing (AP). An Oehler ballistic chronograph with optical barriers was used to obtain pressure, energy and velocity values. In the figure, the Marlin XL7 rifle is shown on the left side and the ballistic block is located 15 m away on the right side (distance A). Between the rifle and the ballistic block, a pair of infrared frames were located to measure the velocity of the bullet. The first infrared fame which was the start trigger was located 12 m away from the rifle (distance B). The second infrared frame was the stop trigger and it was located 1.5 m from the first one. The rifle was mounted on an adjustable rifle bench rest located 15 m away from the target. This distance reduced the possibility of nutation, yaw or precession of the bullet before the impact. The rifle bench rest was adjusted and used in a fixed position for every shot. Behind the ballistic block, a layer of 0.2 mm of aluminum foil was located to verify the presence of any remaining fragment after the shots. X-ray photographs were taken on the ballistic blocks after the shots with a Vertex II equipment (VJ Technologies, Inc., Suffolk County, NY, USA), with capacity of 160 kV. Materials 2020, 13, 5243 3 of 13 Materials 2020, 13, x FOR PEER REVIEW 3 of 13 Materials 2020, 13, x FOR PEER REVIEW 3 of 13

Figure 1. ConfigurationConﬁguration of the ballistic workbench. Figure 1. Configuration of the ballistic workbench. Figure2 shows a close view of the perforations produced by the impacts in each system. The circular Figure 2 shows a close view of the perforations produced by the impacts in each system. The shapeFigure of the 2 craters shows show a close that view the bullet of the has perforations penetrated produced without inclination, by the impacts this means in each the system. longitudinal The circular shape of the craters show that the bullet has penetrated without inclination, this means the circularaxle of the shape bullet of entersthe craters perpendicular show that withthe bullet respect has to penetrated the wall surface. without It caninclination, be seen inthis (a) means the brittle the longitudinal axle of the bullet enters perpendicular with respect to the wall surface. It can be seen in longitudinalfracture of the axle FSF of system the bullet and enters in (b) theperpendicular ductile hole wi growthth respect of the to PSPthe wall system. surface. It can be seen in (a)(a) thethe brittlebrittle fracturefracture ofof thethe FSFFSF systemsystem andand inin (b)(b) thethe ductileductile holehole growthgrowth ofof thethe PSPPSP system.system.

Figure 2. Resulting crater of the 7.62 mm FMJ (Full Metal Jacket) bullet impacted in (a) the fiberglass- Figure 2. 2. ResultingResulting crater crater of the of 7.62 the mm 7.62 FMJ mm (Full FMJ Metal (Full Jacket) Metal bullet Jacket) impacted bullet impactedin (a) the fiberglass- in (a) the sand-fiberglass (FSF) system and (b) the plywood-sand-plywood (PSP) system. sand-fiberglassﬁberglass-sand-ﬁberglass (FSF) system (FSF) and system (b) the and plywood-sand-plywood (b) the plywood-sand-plywood (PSP) system. (PSP) system.

TableTable 1 11 showsshows thethe the obtainedobtained obtained velocitiesvelocities velocities measurmeasur measurededed asas indicatedindicated as indicated inin “Cartridge,“Cartridge, in “Cartridge, 7.627.62 mm:mm: 7.62 NATO,NATO, mm: Ball-M80MIL-DTL-46931”NATO,Ball-M80MIL-DTL-46931” Ball-M80MIL-DTL-46931” standardsstandards standardsforfor FMJFMJ M80M80 for bubu FMJlletsllets M80andand “MIL-C-60617A”“MIL-C-60617A” bullets and “MIL-C-60617A” forfor armor-piercingarmor-piercing for bullets.armor-piercingbullets. bullets.

Table 1.1. Bullet velocities obtained in the experimental shots.shots. Table 1. Bullet velocities obtained in the experimental shots. Bullet Type Weight (±0.01 g) Energy at 15 m Velocity at 0 m Velocity at 15 m Velocity at 23.77 m BulletBullet Type Type Weight Weight ( 0.01(±0.01 g) g) Energy Energy atat 15 m Velocity Velocity at at0 m 0 m Velocity Velocity at 15 at m 15 m Velocity Velocity at 23.77 at m 23.77 m AP M61 9.75± g 3 481 J 852 m/s 843 m/s 835 m/s AP M61 9.75 g 3 481 J 852 m/s 843 m/s 835 m/s AP M61FMJ M80 9.75 9.65 g g 3 3 481 445 JJ 855 852 m/s m/ s 845 843 m/s m /s 839 m/s 835 m/s FMJ M80 9.65 g 3 445 J 855 m/s 845 m/s 839 m/s FMJ M80 9.65 g 3 445 J 855 m/s 845 m/s 839 m/s 2.3.2.3. NumericalNumerical SimulationSimulation 2.3. Numerical Simulation 3D-CAD3D-CAD modelsmodels werewere constructedconstructed forfor thethe numenumericalrical analysisanalysis simulationsimulation toto observeobserve thethe penetrationpenetration3D-CAD depthdepth models ofof werethethe bulletbullet constructed throughthrough for thethe the conscons numericaltructedtructed analysis systemssystems simulation andand comparcompar to observeee thethe resultingresulting the penetration valuesvalues withdepthwith thethe of experimentalexperimental the bullet through test.test. FigureFigure the 3 constructed3 showsshows thethe coco systemsrrespondingrresponding and compare diagramdiagram forfor the eaea resultingchch system.system. values TwoTwo sidewallssidewalls with the representexperimentalrepresent thethe test. continuouscontinuous Figure3 showsmedia,media, the andand corresponding aa regionregion bebetween diagramtween thethe for wallswalls each system.representsrepresents Two thethe sidewalls granulargranular represent media.media. FiguretheFigure continuous 3a3a showsshows media, thethe FSFFSF and system,system, a region andand between FigureFigure the 3b3b sh wallsshowsows represents thethe PSPPSP system.system. the granular TheThe bulletbullet media. isis locatedlocated Figure3 withawith shows thethe longitudinalthelongitudinal FSF system, axisaxis and perpendicularperpendicular Figure3b shows toto thethe the surfacesurface PSP system. ofof ththee wall,wall, The bullet andand effectseffects is located ofof nutanuta withtion,tion, the yawyaw longitudinal oror precessionprecession axis areperpendicularare notnot included.included. to the surface of the wall, and eﬀects of nutation, yaw or precession are not included.

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(a) (b)

FigureFigure 3. 3. ComponentsComponents of of the the ballistic ballistic blocks blocks in in (a (a) )the the FSF FSF system system and and (b (b) )the the PSP PSP system. system.

TheThe AP AP (M61) andand FMJFMJ (M80) (M80) bullets bullets contain contain an an external external jacket jacket of brass.of brass. The The left sideleft side of each of blockeach blockshows shows the location the location of the of bullet the bullet with with initial initial velocities velocities of 845 of m845/s andm/s 843and m843/s form/s the for lead the lead and steeland steelcores, cores, respectively. respectively. The materialThe material properties properties considered considered for the for simulation the simulation are shown are shown in Table in Table2. 2.

TableTable 2. 2. MechanicalMechanical properties properties required required in in the the simulation. simulation.

MaterialMaterial Media Media Material Material Density Density (kg/m (kg/m33)) Shear Modulus Modulus (GPa) (GPa) BrassBrass Continuous Continuous Orthotropic Orthotropic 8450 8450 35.9 35.9 LeadLead Continuous Continuous Orthotropic Orthotropic 11,350 11,350 4 4 Steel Continuous Orthotropic 7896 81.8 Steel Continuous Orthotropic 7896 81.8 Sand Granular Anisotropic 2641 76.9 Sand Granular Anisotropic 2641 76.9 Plywood Continuous Anisotropic 680 0.75 Plywood Continuous Anisotropic 680 0.75 Fiberglass Continuous Anisotropic 1310 0.82 Fiberglass Continuous Anisotropic 1310 0.82 With respect to the boundary conditions, the ballistic block models were subjected to the same restrictedWith conditions; respect to thethe boundaryhorizontal conditions, displacement the of ballistic the external block faces models of werethe continuous subjected tomedia the samewas restrictedrestricted in conditions; the form theof fixed horizontal support displacement along the ofZ-axis the externalbut not facesfor the of theremaining continuous perpendicular media was directionsrestricted (X in theand formY). The of fixedcreation support of the along resulting the Z -axismesh but for noteach for model the remaining was also perpendicularthe result of improveddirections trials (X and to Y). achieve The creation suitable of values the resulting for the mesh orthogonal for each and model skew was qualities. also the To result improve of improved in the simulationtrials to achieve time, suitablethe bullet values was located for the orthogonal1 mm away and from skew the qualities.contact face, To improve with one in small the simulation timestep simulatedtime, the bulletbefore wasthe impact. located The 1 mm simulation away from scenario the contacts were face,divided with into one 4 smalldifferent timestep cases, simulatedas shown inbefore Table the 3: two impact. for an The initial simulation velocity scenarios of 843 m/s were and divided two for into845 m/s. 4 diff erent cases, as shown in Table3: two for an initial velocity of 843 m/s and two for 845 m/s. Table 3. Bullet velocities considered for each case of analysis. Table 3. Bullet velocities considered for each case of analysis. Case Model Type–Projectile Velocity (m/s) 1Case ModelFSF–AP Type–Projectile (M61) Velocity843 (m /s) 2 1PSP–AP FSF–AP (M61) (M61) 843 843 3 FSF–FMJ (M80) 845 2 PSP–AP (M61) 843 4 PSP–FMJ (M80) 845 3 FSF–FMJ (M80) 845 Figure 4 shows the simulation4 process PSP–FMJ flowchart (M80) as a result 845of the previous research conducted for the construction of the models. The behavior of continuous media considers all the material particlesFigure interconnected4 shows the simulationand working process as a single flowchart piece asin acomparison result of the with previous granular research media conducted in which thefor mechanical the construction property of theof the models. particle The intera behaviorcts and ofreorganizes continuous during media the considers dynamic allprocess. the material particles interconnected and working as a single piece in comparison with granular media in which the mechanical property of the particle interacts and reorganizes during the dynamic process.

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Figure 4. Simulation process flowchart. Figure 4. Simulation process flowchart. This configuration is a combination of selected parameters that involve the material models This configuration is a combination of selected parameters that involve the material models available in the software (ANSYS®2019R1, Canonsburg, PA, USA), and the constants were taken from ® availablethe AUTODYN in the software library. (ANSYS The Smoothed2019R1, Particle Canonsburg, Hydrodynamics PA, USA), Lagrangian and the constantsparticle method were taken(SPH) from the AUTODYNof ANSYS® AUTODYN library. The 2019R1 Smoothed was selected Particle for Hydrodynamics this simulation, the Lagrangian continuous particle media is method considered (SPH) of ANSYSas a® uniformAUTODYN set of particles 2019R1 interacting was selected with for the this energies simulation, created during the continuous the evolution media of the is impact. considered as a uniformMultilinear set isotropic of particles hardening interacting behavior with was the also energies selected created to establish during the the plastic evolution behavior of of the this impact. Multilinearmaterial isotropic [33–38]. hardening behavior was also selected to establish the plastic behavior of this material [33–38]. In the simulation, the effect caused by the angular velocity of the bullet is not considered, and because of that, it was expected that there would be differences between the experimental and Materials 2020, 13, 5243 6 of 13 numerical simulation results. The mechanical behavior of the lead and steel, which are the core materials, were included by considering the Steinberg–Guinan strength formulation. The fiberglass was modeled with the Johnson–Holmquist continuous-strength formulation and the plywood was modeled considering the polynomial Equation of State (EOS) formulation. The behavior of the granular media was modeled as MO Granular Failure Model together with tensile pressure failure and the walls were configured with the shock EOS linear formulation [39–43]. This combination allows the granular media to transfer the load vectors and reorganize the media during the displacement of the bullet. The Grüneisen parameter is conventionally written as a dimensionless combination of the expansion coefficient, bulk modulus, density and specific heat and can also be presented in terms of elastic moduli and their pressure derivatives, providing a quantitative link between thermal and mechanical parameters [44]. The material properties and constant values considered for the simulation are shown in Table4[25,32,45,46].

Table 4. Conﬁguration parameters for the simulation.

Lead Brass Steel Sand Fiberglass Plywood Shock EOS Linear - - - X - X Grüneisen Coefficient 2.74 2.04 2.17 X 1.18 X C1 (m/s) 2006 3726 4569 X 2746 X S1 1.429 1.434 1.49 X 1.319 X Quadratic S2 (s/m) 0 0 0 X 0 X Specific Heat (J/kg C) 124 X 447 X X X Steinberg Giunan Strength - X - X X X MO Granular X X X - X X offset X X X 0 X X Tensile Pressure Failure X X X - X X Max. Tensile Pressure (Pa) X X X 1000 X X Compaction EOS Linear X X X - X X Solid Density (kg/m3) X X X 2641 X X Compaction Path X X X - X X Linear Unloading X X X - X X Johnson-Holmquist Strength X X X X X - Failure type X X X X X Gradual Hugoniot Elastic Limit X X X X X 5.92 109 Pa × Intact Strength Constant A X X X X X 0.93 Intact Strength Exponent N X X X X X 0.77 Strain Rate Constant C X X X X X 0.003 Fracture Strength Constant B X X X X X 0.088 Fracture Strength Exponent m X X X X X 0.35 Max. fracture strength Ratio X X X X X 0.5 Damage constant D1 X X X X X 0.053 Damage constant D2 X X X X X 0.85 Bulking constant B X X X X X 1 Hydrodynamic Tensile Limit X X X X X 0.15 109 Pa − × Bulk Modulus X X X X X 45.4 109 Pa × Shear Modulus X X X X X 15,000 MPa Polynomial EOS X X X X X - Materials 2020, 13, x FOR PEER REVIEW 7 of 13

ThisMaterials combination2020, 13, 5243 of parameters, as shown below, allowed us to observe the fragmentation7 of 13 of the bullet caused by the initial contact with the walls which is of special importance in terminal ballistics andThis military combination medicine of parameters, [47–49]. as shown below, allowed us to observe the fragmentation of the bullet caused by the initial contact with the walls which is of special importance in terminal ballistics 3. Resultsand and military Discussion medicine [47–49]. Figure3. Results 5 shows and Discussion(a) the results of the numerical simulation compared with (b) the experimental X-ray photography.Figure5 shows This (a) figure the results corresponds of the numerical to the simulation FSF AP compared M61 block with (b) (case the experimental 1). The numerical simulationX-ray predicted photography. a penetration This figure corresponds distance to of the 237 FSF APmm M61 and block the (case appearance 1). The numerical of compaction simulation waves along thepredicted penetration a penetration trajectory distance showing of 237 fragmentation mm and the appearance of the brass of compaction after 204 wavesmm. In along the thesimulation penetration trajectory showing fragmentation of the brass after 204 mm. In the simulation and the and the X-ray photograph, an expanded distribution of the compacting wave is observed [50]. Even X-ray photograph, an expanded distribution of the compacting wave is observed [50]. Even when when thethe finalfinal penetration penetration distances distances are not theare same, not boththe circumstancessame, both show circumstances brass jacket fragmentation show brass jacket fragmentationbefore the before steel core the stops. steel The core steel stops. core showedThe steel an additional core showed advance an of additional at least 30 mm advance ahead. In of the at least 30 mm ahead.X-ray In photography, the X-ray aphotography, maximum fragmentation a maximum of the brassfragmentation was 148 mm, of and the an brass additional was advance 148 mm, of and an additionalthe steeladvance core of of 49 the mm whichsteel givescore aof total 49 depthmm ofwhich 197.76 gives mm. In a both total analyses, depth the of final 197.76 position mm. of In both the bullet rotated with respect to the initial entry orientation. analyses, the final position of the bullet rotated with respect to the initial entry orientation.

Figure 5.Figure Comparison 5. Comparison of fragmentation of fragmentation and and penetration penetration depths depths for for the 7.62the mm7.62 APmm bullet AP inbullet the FSF in the FSF block fromblock (a from) numerical (a) numerical simulation simulation and and (b (b)) X-ray X-ray photography.photography.

The results of the fragmentation and penetration distance reached by the 7.62 mm AP projectile for Thethe results PSP AP of M61 the block fragmentation are shown in and Figure penetration6 (case 2). In (a)distance the numerical reached simulation by the and 7.62 (b) mm the X-rayAP projectile for the PSPphotography, AP M61 theblock maximum are shown penetration in Figure distance 6 (case is 183.47 2). In and (a) 200.22 the numerical mm, respectively. simulation The X-ray and (b) the X-ray photography,photography shows the maximum more concentrated penetration compacting distan wavece inis the183.47 upward and direction 200.22 followingmm, respectively. the bullet The X- ray photographytrajectory and shows the ﬁnal more location concentrated of the fragments compacti are veryng closewave to in the the core. upward direction following the bullet trajectory and the final location of the fragments are very close to the core.

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FigureFigure 6.6. Comparison of fragmentation and penetration depths of the 7.62 mm AP bullet in the PSP Figure 6. Comparison of fragmentation and penetration de depthspths of the 7.62 mm AP bullet in the PSP blockblock fromfrom ((aa)) numericalnumerical simulationsimulation andand ((bb)) X-rayX-ray photography.photography. block from (a) numerical simulation and (b) X-ray photography. FigureFigure7 7 shows shows the results of of (a) (a) the the numerical numerical si simulationmulation and and (b) (b) X-ray X-ray photography photography for forthe the7.62 Figure 7 shows the results of (a) the numerical simulation and (b) X-ray photography for the 7.62 7.62mm mmFMJ FMJM80 M80 projectile projectile impacting impacting the theFSF FSF block block (case (case 3). 3).In the In thesimulation, simulation, a penetration a penetration distance distance of mm FMJ M80 projectile impacting the FSF block (case 3). In the simulation, a penetration distance of of116.59 116.59 mm mm was was obtained, obtained, and and in in the the X-ray X-ray photography, photography, a a measured measured distance distance of 126.56 mm waswas 116.59 mm was obtained, and in the X-ray photography, a measured distance of 126.56 mm was obtained.obtained. A widewide compactioncompaction wavewave isis locatedlocated ahead ahead the the core core and and the the expanded expanded fragments fragments showing showing a obtained. A wide compaction wave is located ahead the core and the expanded fragments showing reduceda reduced penetration penetration distance distance with with respect respect to to the the previous previous cases. cases. a reduced penetration distance with respect to the previous cases.

Figure 7. Comparison of fragmentation and penetration depths of the 7.62 mm FMJ bullet in the FSF Figure 7. Comparison of fragmentation and penetration depths of the 7.62 mm FMJ bullet in the FSF Figureblock from 7. Comparison (a) numerical of fragmentationsimulation and and (b) penetrationX-ray photography. depths of the 7.62 mm FMJ bullet in the FSF block from ((aa)) numericalnumerical simulationsimulation andand ((bb)) X-rayX-ray photography.photography. Figure 8 shows the results of case 4 in which an FMJ M80 bullet impacts the PSP box. The Figure 8 shows the results of case 4 in which an FMJ M80 bullet impacts the PSP box. The penetrationFigure8 distancesshows the obtained results of casein (a) 4 inthe which numerica an FMJl simulation M80 bullet and impacts (b) the the PSPX-ray box. photography The penetration were penetration distances obtained in (a) the numerical simulation and (b) the X-ray photography were distances115.47 and obtained 126.07 mm, in (a) respectively. the numerical A unique simulation zone andof extreme (b) the fragmentation X-ray photography was not were identified 115.47 and but 115.47 and 126.07 mm, respectively. A unique zone of extreme fragmentation was not identified but 126.07was the mm, most respectively. extended instead. A unique zone of extreme fragmentation was not identiﬁed but was the most extendedwas the most instead. extended instead.

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Figure 8. Comparison of fragmentation and penetration depths of the 7.62 mm FMJ bullet in the PSP Figure 8. Comparison of fragmentation and penetration depthsdepths of the 7.62 mm FMJ bullet in the PSP block from (a) numerical simulation and (b) X-ray photography. block from ((aa)) numericalnumerical simulationsimulation andand ((bb)) X-rayX-ray photography.photography.

FigureFigure9 a9a9a shows showsshows the thethe numerical numericalnumerical results resultsresults of the ofof penetration thethe penetrationpenetration depth depthdepth with respect withwith respectrespect to the velocity toto thethe startingvelocityvelocity fromstartingstarting the fromfrom penetration thethe penetrationpenetration velocity velocityvelocity for each forfor of theeacheach four ofof thethe cases, fourfour and cases,cases, Figure andand9 FigureFigureb shows 9b9b the showsshows penetration thethe penetrationpenetration depth withdepthdepth respect withwith respectrespect to time. toto time.time.

((aa)) ((bb)) Figure 9. Penetration depth with respect to (a) velocity and (b) time. Figure 9. Penetration depth with respect to (a) velocity andand ((b)) time.time.

FigureFigure 10 1010 shows showsshows the thethe dependence dependencedependence of of theof thethe bullet’s bullet’sbullet’s velocity velocityvelocity inside insideinside the blocksthethe blocksblocks with withwith respect respectrespect to time. toto time. Intime. all cases,InIn allall cases,cases, the velocity thethe velocityvelocity is zero isis after zerozero 0.8 afafterter ms. 0.80.8 Although ms.ms. AlthoughAlthough the spinning thethe spinningspinning effect ofeffecteffect the of bulletof thethe bullet inbullet the in simulationin thethe simulationsimulation is not considered,isis notnot considered,considered, the hardness thethe hardnesshardness and ordering andand orderingordering of each wall ofof eaea materialchch wallwall has materialmaterial an important hashas anan e importantffimportantect on penetration. effecteffect onon Inpenetration.penetration. the case of InIn fiberglass, thethe casecase ofof the fiberglass,fiberglass, fibers do thethe not fibersfibers have dodo a unique notnot havehave arrangement aa uniqueunique arrangementarrangement and the energy andand absorptionthethe energyenergy dissipatesabsorptionabsorption in dissipatesdissipates random in directionsin randomrandom at directionsdirections each instant. atat eaeachch As instant.instant. the bullet AsAs advancesthethe bulletbullet throughadvancesadvances the throughthrough fiberglass, thethe itfiberglass,fiberglass, encounters itit encountersencounters new fibers new everynew fibersfibers layer everyevery reacting layerlayer together reacreactingting with togethertogether the neighboring withwith thethe neighboringneighboring fibers. In the fibers.fibers. plywood, InIn thethe plywood,plywood, thethe fibersfibers areare arrangedarranged inin thethe samesame diredirectionction andand theythey areare allall compressedcompressed togethertogether atat thethe samesame time,time, deformingdeforming andand deflectingdeflecting thethe energyenergy inin aa singlesingle direction.direction. ThisThis alsoalso causescauses anan openingopening ofof

Materials 2020, 13, 5243 10 of 13 the fibers are arranged in the same direction and they are all compressed together at the same time, Materials 2020, 13, x FOR PEER REVIEW 10 of 13 deforming and deflecting the energy in a single direction. This also causes an opening of the fibers duethe to fibers the spinning due to the eff spinningect and allowing effect and the allowing bullet to th advancee bullet withto advance greater with force greater than in force the case than of in the the fiberglasscase of the wall. fiberglass wall.

FigureFigure 10. 10.Numerical Numerical velocity velocity results results with with respect respect to to time time obtained obtained in in the the numerical numerical simulations. simulations.

TableTable5 shows5 shows the the numerical numerical values values obtained obtained in in the the numerical numerical analyses analyses compared compared with with the the experimentalexperimental results, results, the the shortest shortest stopping stopping distance distance was was found found for for case case 4. 4. This This minimum minimum value value was was obtainedobtained in in the the numerical numerical simulation simulation as as well well as as in in the the experimental experimental measurements. measurements.

TableTable 5. 5.Comparison Comparison of of numerical numerical and and experimental experimental results results for for each each case. case.

PenetrationPenetration Depth Depth (mm) (mm) Case Model Type–ProjectileType–Projectile Velocity Velocity (m (m/s)/s) TimeTime (ms) (ms) NumericalNumerical ExperimentalExperimental 11 FSF–APFSF–AP (FMJ) (FMJ) 843 843 237.12237.12 197.76197.76 0.80.8 22 PSP–APPSP–AP (FMJ) (FMJ) 843 843 207.41207.41 200.22200.22 0.80.8 3 FSF–FMJ (M80) 845 116.59 126.56 0.8 3 FSF–FMJ (M80) 845 116.59 126.56 0.8 4 PSP–FMJ (M80) 845 115.35 126.07 0.8 4 PSP–FMJ (M80) 845 115.35 126.07 0.8 4. Conclusions 4. Conclusions During the impact, the bullet entered first into a continuous medium of wood with a thickness of 12During mm and the the impact, penetration the bullet depth entered was ﬁrst reduced into aup continuous to 50.48%medium compared of to wood the withdistance a thickness obtained ofwithout 12 mm the and shells. the penetration A variation depth of 7.53 was m/s reduced between up the to 50.48% experimental compared results to the and distance numerical obtained results withoutwas found. the shells.The numerical A variation and ofexpe 7.53rimental m/s between results theshowed experimental similar fragmentation results and numerical distribution results of the wasbullets found. with The 95.34% numerical similarity and in experimental the penetration results distance showed of the similar FMJ projectile fragmentation and 88.63% distribution for the ofAP theprojectile. bullets withThe 95.34%impact similaritysurface areas in the were penetration 100 mm2 distance and 300 of mm the2 FMJwith projectile a depth andof 300 88.63% mm. forThe 2 2 thenumerical AP projectile. analysis The was impact solved surface with the areas SPH were module 100 mm of ANSYSand 300® Autodyn. mm with It awas depth determined of 300 mm. that ® Thethe numerical initial impact analysis of this was type solved of projectile with the through SPH module a continuous of ANSYS medium,Autodyn. such Itas wasthe 12 determined mm wood thatplate, the reduces initial impact the penetration of this type capacity of projectile by up through to 48.62%. a continuous The presented medium, fragmentation such as the and 12 mm contention wood plate,of the reduces bullet material the penetration can represent capacity a tactical by up to adva 48.62%.ntage The since presented the impact fragmentation of the 7.62 mm and AP contention projectile ofreaches the bullet a maximum material can penetration represent adistance tactical of advantage 52 mm compared since the impact with 100 of themm 7.62 obtained mm AP without projectile the reachesthick initial a maximum continuous penetration medium. distance The use of 52of mmthe comparedfibrous materials with 100 provides mm obtained the advantage without the that thick they initialare cheap, continuous eco-friendly medium. and Theeasy use to repair of the compared ﬁbrous materials to other provides ballistic blocks the advantage based on that ceramics they areand plastics which once fractured cannot be repaired and, in some cases, they must be discarded.

Materials 2020, 13, 5243 11 of 13 cheap, eco-friendly and easy to repair compared to other ballistic blocks based on ceramics and plastics which once fractured cannot be repaired and, in some cases, they must be discarded.

Author Contributions: Conceptualization, L.A.F.-H., methodology and validation, U.S.S.-R. and J.M.S.-P., numerical and experimental analysis, F.A.S.-M. and U.S.S.-R., literature review, F.A.S.-M. and J.M.S.-P., validation, G.J.G.-P. and U.S.S.-R. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Instituto Politécnico Nacional—Secretaría de Investigación y Posgrado through the grant numbers 20200530 and 20200529 of the SIP projects. Acknowledgments: Authors acknowledge the Instituto Politécnico Nacional and the Consejo Nacional de Ciencia y Tecnología (CONACYT). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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