Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures

metals

Article Ballistic Impact Resistance of Bulletproof Vest Inserts Containing Printed Titanium Structures

Pawel Zochowski 1, Marcin Bajkowski 2, Roman Grygoruk 2, Mariusz Magier 2 , Wojciech Burian 3, Dariusz Pyka 4, Miroslaw Bocian 4 and Krzysztof Jamroziak 4,*

1 Military Institute of Armament Technology, Prym. S. Wyszynskiego 7 Str., 05-220 Zielonka, Poland; [email protected] 2 Institute of Mechanics and Printing, Faculty of Production Engineering, Warsaw University of Technology, Narbutta 85 Str., 02-524 Warsaw, Poland; [email protected] (M.B.); [email protected] (R.G.); [email protected] (M.M.) 3 Łukasiewicz Research Network—Institute of Non-Ferrous Metals, Sowinskiego 5 Str., 44-100 Gliwice, Poland; [email protected] 4 Department of Mechanics, Materials and Biomedical Engineering, Wroclaw University of Science and Technology, Smoluchowskiego 25 Str., 50-370 Wroclaw, Poland; [email protected] (D.P.); [email protected] (M.B.) * Correspondence: [email protected]; Tel.: +48-71-320-27-60

Abstract: Finite element modeling of ballistic impact of inserts containing titanium structures were presented in the article. The inserts containing an additional layer made using additive manufacturing technology were analyzed. The layer was created from repetitive elements made without connections (adjacent cells were inseparable). Four variants of printed titanium structures were placed between

layers of Twaron CT 750 aramid fabric to create ballistic inserts. In order to assess the ballistic resistance of the inserts, numerical simulations of ballistic impact phenomenon were carried out

Citation: Zochowski, P.; Bajkowski, using LS-Dyna software. In the simulations the inserts were placed on a steel box filled with ballistic M.; Grygoruk, R.; Magier, M.; Burian, clay and were fired at with the 9 × 19 mm full metal jacket (FMJ) Parabellum projectile. The main aim W.; Pyka, D.; Bocian, M.; Jamroziak, K. of the work was to check the effectiveness of such solutions in soft ballistic protection applications Ballistic Impact Resistance of and to select the most effective variant of 3D printed structure. Results of the numerical analysis Bulletproof Vest Inserts Containing showed a high potential for 3D printed structures made of titanium alloys to be used for bulletproof Printed Titanium Structures. Metals vest inserts. In all analyzed cases the projectile was stopped by the armor. In addition, thanks to 2021, 11, 225. https://doi.org/ the cooperation of adjacent cells, the projectile energy density was distributed over a large area, as 10.3390/met11020225 evidenced by large volumes of hollows in the ballistic clay. The indentations in the ballistic clay obtained in the simulations were significantly lower than the acceptable value for the back face Academic Editor: Thomas Niendorf deformation (BFD) parameter required by international body armor standards. Received: 28 December 2020 Accepted: 22 January 2021 Keywords: ballistic impact; ballistic insert; additive technologies; printed titanium structures; nu- Published: 28 January 2021 merical simulations

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- 1. Introduction iations. The function of a bulletproof vest is to protect the human body from negative effects of an impacting projectile by absorbing and dispersing its kinetic energy. A review of structural and material solutions of ballistic inserts currently used in bulletproof vests shows that layered material systems [1–3], such as ceramic [4,5], ceramic-composite [6–9], Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. titanium [10,11] and polyethylene [12,13] segments, provide effective protection against This article is an open access article small caliber ammunition fired from handguns. Such a shield is used to protect the most 2 distributed under the terms and important internal organs of the human body, which is about 0.5 m of the area [14]. Thanks conditions of the Creative Commons to continuous progress of material engineering [15–17] and production technologies, more Attribution (CC BY) license (https:// efficient bulletproof vests may be developed. Current research projects in the field of creativecommons.org/licenses/by/ personal protection [18], are focused on increasing the protected area and reducing areal 4.0/). density of vests related to the v50 ballistic limit.

Metals 2021, 11, 225. https://doi.org/10.3390/met11020225 https://www.mdpi.com/journal/metals Metals 2021, 11, 225 2 of 23

One of the ways of increasing the protective effectiveness of bulletproof vests may be by using elements made by additive manufacturing technology [19]. Recently, thanks to a wide range of possible additive production methods [20,21], their dynamic development can be observed, especially in medicine [22,23], but also in the defense industry. For example, the stab resistance body armor made of polyamide and carbon fiber plates produced using laser sintered materials technology was analyzed in the paper [24]. The original approach was presented in the paper [25], where a prototype of flexible armor was created on the basis of chitin scales manufactured with the use of 3D printing technology. The armor was composed of segments in the form of scales imitating biological organisms (e.g., crustaceans, fish or chiton). More traditional methods of manufacturing of armor elements were presented in the works [16,26]. In the paper [27], the authors presented a plymetal, which is a new type of composite metal manufactured by a laser-aided additive manufacturing (AM) process using two different metal powders. Ballistic tests were then performed on the structural components made of plymetal with impact velocities of 183–357 m/s. Additive manufacturing technologies were often used to produce porous, honeycomb [28] or cellular structures [29–32]. An interesting example of ballistic inserts produced by using additive technology was presented in the paper [33]. The inserts were made as an array of many loosely intertwined repetitive elements in the form of closed uniform cells. The cells formed a multi-object layer made of sintered powders in one technological operation. Three-dimensional printing technology is poorly described in cases of impact energy dissipative materials. Most studies refer to materials made of sintered metal powders (aluminum or titanium alloys). The remaining group of materials, for example, aramid or polyethylene, still presents a challenge for 3D printing. In the article, numerical simulations were performed to check the possibility of using 3D printed titanium structures as energy absorbing and dissipating layers in bullet-proof vests inserts. On the basis of the literature review, it was noted that there is a lack of information regarding the effectiveness of such structures under ballistic impact conditions. Therefore, the phenomenon of the 9 × 19 mm full metal jacket (FMJ) Parabellum projectile impact into a 100 × 100 mm layered composite armor was modelled using LS-Dyna software. The armor included four variants of 3D printed titanium structures placed between layers of Twaron CT 750 aramid fabric. Results of studies were summarized and conclusions were drawn. On the basis of the simulation results an attempt was made to choose the most effective variant of the analyzed structures, as well as to show directions for further works in the field of 3D printing technology in ballistic applications.

2. Materials and Methods 2.1. Materials Insert Conﬁgurations Four variants of 3D printed titanium structures [33] placed between layers of Twaron CT 750 aramid fabric (Figure1) were analyzed in the study. The structures were made of Ti-6Al-4V titanium alloy with a density of 4.4 g/cm3 and had the form of a grid consisting of many loosely intertwined repeatable components (uniform cells). The whole structure was additively manufactured in one technological operation by sintering powder with laser or electron beam. The grid made in this way may use cells of different geometry (Figure1). The ratio of empty space between the cells to the total volume of the layer may be within the range of 5–60%. All of the analyzed variants of structures had the same areal 2 density (ms = 18.0 kg/m ) which made it easier to compare their effectiveness. MetalsMetals 20212021,, 1111,, x 225x FORFOR PEERPEER REVIEWREVIEW 33 3 ofof 27 2327

((aa)) ((bb)) ((cc)) ((dd))

FigureFigure 1.1. VariantsVariants of ofof 3D 3D3D printed printedprinted titanium titaniumtitanium structures structuresstructures chosen chosenchosen for forfor analyses: analyses:analyses: (a (()aa structure)) structurestructure of ofof the thethe S1 S1S1 type; type;type; (b )((b structureb)) structurestructure of theofof thethe S2 S2 type; (c) structure of the S3 type and (d) structure of the S4 type. type;S2 type; (c) structure(c) structure of the of the S3 typeS3 type and and (d) ( structured) structure of the of the S4 type. S4 type.

TheThe analyzed analyzed ballistic ballistic inserts inserts hadhad dimensionsdimensions of ofof 100 100100 × ×× 100100 mmmm and and a a sandwich sandwich form form (Figure(Figure(Figure 2 2).2).). Each EachEach variant variantvariant of ofof titanium titaniumtitanium structure structurestructure was waswas placed placedplaced between betweenbetween layers layerslayers of Twaron ofof TwaronTwaron CT 750 CTCT 750aramid750 aramidaramid fabric fabricfabric (two (two(two layers layerslayers behind behindbehind and andand two twotwo layers layerslayers in front inin frontfront of the ofof structure). thethe structure).structure).

FigureFigure 2. 2. ConfigurationConﬁgurationConfiguration of of the the analyzed analyzed ballistic ballistic insert. insert.

TwaronTwaron CTCTCT 750 750750 is aisis para-aramid aa parapara‐‐aramidaramid fabric characterizedfabricfabric characterizedcharacterized by favorable byby strengthfavorablefavorable parameters strengthstrength parametersandparameters impact andand resistance impactimpact to resistanceresistance many types toto manymany of threats. typestypes ofof Laminates threats.threats. LaminatesLaminates made of the mademade fabric ofof thethe are fabricfabric often areusedare oftenoften in hard usedused body inin hardhard armors. bodybody Basic armors.armors. parameters BasicBasic parametersparameters of the fabric ofof thethe are fabricfabric presented areare presentedpresented in Table1 . inin TableTable 1.1. Table 1. Properties of Twaron CT 750 aramid fabric [34]. TableTable 1.1. PropertiesProperties ofof TwaronTwaron CTCT 750750 aramidaramid fabricfabric [34].[34]. Type Set (per 10 cm) Areal Density Thickness Minimum Break Strength Style Weave Warp/WeftType Set Warp/Weft(per 10 cm) Areal (g/mDensity2) Thickness(mm) Minimum(N/5 cm Break× 1000) Strength Warp/Weft (N/5 cm  Style Type Weave Set (per 10 cm) Areal Density Thickness Minimum Break Strength (N/5 cm  Style Weave 2 Warp/Weft Warp/Weft (g/m 2) (mm) 1000) Warp/Weft CT 750Warp/Weft 2000 plainWarp/Weft 69/69 (g/m 460) (mm) 0.70 1000) 16.5/18.0 Warp/Weft CTCT 750750 20002000 plainplain 69/6969/69 460460 0.700.70 16.5/18.016.5/18.0

2.2.2.2. ConstructionConstruction of of the the 3D 3D Printed Printed Structures Structures TheThe 3D 3D printed printed structures structures were were made made by by interlacing interlacing many many cells, cells, through through the the inner inner perimetersperimeters of of the the adjacent adjacent repetitive repetitive elements elements (Figure (Figure 3 3).3).). ThatThatThat kindkindkind ofofof grid gridgrid has hashas greater greatergreater strengthstrength and and energy energy-dispersingenergy‐‐dispersingdispersing capacities capacities in in relation relation toto fullfull structures.structures.

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Figure 3. Example of additively manufactured cell interlacing: 1—cells forming the grid structure; Figure 3. Example of additively manufactured cell interlacing: 1—cells forming the grid structure; Figure2—internal 3. Example circuit of of additively the adjacent manufactured grid structure cell element; interlacing: 3—external 1—cells circuit forming of the the adjacent grid structure; grid 2—internal circuit of the adjacent grid structure element; 3—external circuit of the adjacent grid 2—internalstructure element. circuit of the adjacent grid structure element; 3—external circuit of the adjacent grid structurestructure element. element. In the analyzed 3D printed structures, adjacent repetitive components had the possi‐ In theIn analyzed the analyzed 3D printed 3D printed structures, structures, adjacent adjacent repetitive repetitive components components had the had possi the‐ pos- bility of angular movement in relation to each other, which allowed modifying of the bilitysibility of angular of angular movement movement in relation in relation to each to eachother, other, which which allowed allowed modifying modifying of the of the layer’s geometric dimensions within certain limits. Areal density of structures composed layer’slayer’s geometric geometric dimensions dimensions within within certain certain limits. limits. Areal Areal density density of ofstructures structures composed composed of of repetitive elements is smaller than traditional solid composite inserts with similar im‐ of repetitiverepetitive elements elements is is smaller smaller than than traditional traditional solid solid composite composite inserts inserts with with similar similar im impact‐ pact resistance. This feature, together with high flexibility, increases the ergonomics of the pactresistance. resistance. This This feature, feature, together together with with high high ﬂexibility, flexibility, increases increases the the ergonomics ergonomics of of the the user user and the protected area of the body [14]. userand and the the protected protected area area of of the the body body [ 14[14].]. Randomly selected 3D printed components were examined by scanning and light RandomlyRandomly selected selected 3D printed 3D printed components components were were examined examined by scanning by scanning and and light light microscopy. Microstructures were analyzed in order to check the influence of the printing microscopy.microscopy. Microstructures Microstructures were were analyzed analyzed in order in order to check to check the influence the inﬂuence of the of printing the printing process on the quality of generated components. Additive manufacturing using selective processprocess on the on quality the quality of generated of generated components. components. Additive Additive manufacturing manufacturing using using selective selective laser melting (SLM) technology involves multiple cycles with rapid heating and cooling laserlaser melting melting (SLM) (SLM) technology technology involves involves multiple multiple cycles cycles with with rapid rapid heating heating and and cooling cooling in the laser melting zone [35]. Such a dynamic heat transfer affects the microstructure of in thein laser the laser melting melting zone zone [35]. [ 35Such]. Such a dynamic a dynamic heat heat transfer transfer affects affects the themicrostructure microstructure of of thethe printed printed material. material. The metallographic analysis analysis showed showed the the overall overallmorphology morphology and and the the printed material. The metallographic analysis showed the overall morphology and the theeffect effectof of the the β‐βphase-phase diffusionless diffusionless transformation transformation o intoint metastablemetastable martensiticmartensiticα α’-phase’‐phase effect of the β‐phase diffusionless transformation into metastable martensitic α’‐phase (Figure(Figure4). 4). (Figure 4).

Figure 4. Microstructure of the Ti‐6Al‐4V titanium alloy after the selective laser melting (SLM) FigureFigure 4. Microstructure 4. Microstructure of the ofTi‐ the6Al Ti-6Al-4V‐4V titanium titanium alloy after alloy the after selective the selective laser melting laser (SLM) melting (SLM) process (scanning microscopy). Distribution of α’‐phase lath martensite on the background of the processprocess (scanning (scanning microscopy). microscopy). Distribution Distribution of α’‐ ofphaseα’-phase lath martensite lath martensite on the on background the background of the of the β‐phase. β‐phase.β-phase.

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KineticsKineticsKinetics of of the theof transformationthe transformation transformation affected affected affected the the ﬁnalthe final final phase phase phase composition composition composition of of the theof alloy,the alloy, alloy, and and and asas a aas consequence, consequence, a consequence, the the ﬁnalthe final final properties properties properties of of the theof βthe β alloyalloy β alloy [ 36[36,37]., 37[36,37].]. As As a Asa result, result, a result, separations separations separations of of the theof the αα’-phase’‐phaseα’‐phase lath lath lath martensite martensite martensite were were were observed observed observed on on the onthe backgroundthe background background of of the theof βthe β‐-TiTi β‐ phase. phase.Ti phase. During During During the the the metallographicmetallographicmetallographic examination examination examination a a randomly randomly a randomly distributed distributed distributed residual residual residual porosity porosity porosity was was was also also also noticed noticed noticed in in in thethe samplethe sample sample (Figure (Figure (Figure5 ).5). 5).

Figure 5. Microstructure of the Ti‐6Al‐4V titanium alloy after the SLM process (light microscopy) FigureFigure 5. Microstructure 5. Microstructure of the of Ti-6Al-4Vthe Ti‐6Al‐ titanium4V titanium alloy alloy after after the the SLM SLM process process (light (light microscopy) microscopy) etchedetched with with Kroll’s Kroll’s reagent. reagent. etched with Kroll’s reagent.

2.3.2.3.2.3. 9 9 mm mm 9 mm FMJ FMJ FMJ Parabellum Parabellum Parabellum Projectile Projectile Projectile TheTheThe 9 9× × 91919 × mmmm19 mm Parabellum Parabellum Parabellum projectileprojectile projectile was was was used used used in in the thein analyses.the analyses. analyses. The The The projectile projectile projectile was was was developeddevelopeddeveloped by by GeorgeGeorgeby George Luger Luger in 1902. 1902.in 1902. Since Since Since the the the Second Second Second World World World War War War it ithas it has has become become become one one one of the of of the themost mostmost frequently frequentlyfrequently used used ammunitions, ammunitions, fired ﬁredfired with with guns guns and and sub sub sub-machine‐machine‐machine guns. guns. guns. Different Different Different var var‐ ‐ variantsiantsiants of oftheof thethe bullet bulletbullet were were produced produced in morein in more more than than than 70 countries70 70 countries countries around around around the the world. the world. world. The The bullet The bullet bulletbecomebecome become standard standard standard in NATOin NATO in NATO countries. countries. countries. In theIn the Inanalyses theanalyses analyses the the full thefull metal fullmetal jacket metal jacket (FMJ) jacket (FMJ) version (FMJ) version versionof theof the projectile of theprojectile projectile was was used. was used. The used. The projectile The projectile projectile has has a rounded has a rounded a rounded shape shape shape and and consists and consists consists of a of core ofa core a made core made madeof lead/antimonyof oflead/antimony lead/antimony alloy alloy and alloy and jacket and jacket jacketmade made madeof brassof brass of brassor tombacor ortombac tombac plated plated plated steel steel (Figure steel (Figure (Figure 6). 6).6 ).

(a) (a) (b) (b) (c) (c) (d) (d) Figure 6. The 9 19 mm FMJ Parabellum bullet: (a) single cartridge; (b) projectile cross section; (c) projectile and (d) FigureFigure 6. The 6. The 9 ×× 199 × mm 19 mm FMJ FMJ Parabellum Parabellum bullet: bullet: (a) single(a) single cartridge; cartridge; (b) projectile(b) projectile cross cross section; section; (c) projectile (c) projectile and and (d) (d) dimensions of projectile. dimensionsdimensions of projectile. of projectile.

DependingDependingDepending on on type, type,on type, the the massthe mass mass of of the the of projectilethe projectile projectile can can rangecan range range from from from 6.8 6.8 to 6.8to 8 8 g.to g. The8 The g. The projectile projectile projectile cancancan be be ﬁred firedbe fired at at an an at initial initialan initial velocityvelocity velocity ofof 300–420300–420 of 300–420 m/s m/s which which which gives gives gives the the the kinetic kinetic kinetic energy energy energy of of about of about about Ek Ek

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= 600 J. During the analyses the 9 mm projectile with a mass of 8.0 g, muzzle velocity of Ek = 600 J. During the analyses the 9 mm projectile with a mass of 8.0 g, muzzle velocity of 360 m/s and initial energy Ek 518 J was used [38]. 360 m/s and initial energy Ek ~ 518 J was used [38]. 2.4. Determination of Material Characteristics for Numerical Modeling 2.4. Determination of Material Characteristics for Numerical Modeling Experimental tests were carried out to gather data necessary for further validation of Experimental tests were carried out to gather data necessary for further validation numerical models of materials used in the simulation. Three types of experiments were of numerical models of materials used in the simulation. Three types of experiments performed. were performed. Twaron CT 750 aramid fabric was tested in a quasi‐static puncture test of a single layer,Twaron 3 layers, CT 7506 layers aramid and fabric 9 layers. was The tested sample in a quasi-static was fixed peripherally puncture test with of a singlea specific layer, 3 layers,cladding 6 layerspressure and moment, 9 layers. and The penetrated sample was by impactor ﬁxed peripherally moving at with a constant a speciﬁc speed cladding per‐ pressurependicular moment, to the and target penetrated surface. The by impactor force acting moving on the at impactor a constant and speed its displacement perpendicular towere the target recorded. surface. The Theobtained force material acting on characteristics the impactor were and used its displacement as a reference were during recorded. the Thevalidation obtained process material of characteristicsthe fabric numerical were usedmodel. as An a reference example during of a single the validationlayer of Twaron process ofCT the 750 fabric aramid numerical fabric penetration model. An is shown example in Figure of a single 7. layer of Twaron CT 750 aramid fabric penetration is shown in Figure7.

(a) (b)

FigureFigure 7. Experimental 7. Experimental test test of quasi-static of quasi‐static penetration penetration of Twaron of Twaron CT 750 CT aramid750 aramid fabric: fabric: (a) test (a) stand test stand and (andb) example (b) example of results. of results. In order to check the behavior of the 9 mm FMJ Parabellum projectile at different strain rates and to collect data required for validation of its numerical model, a simple experiment In order to check the behavior of the 9 mm FMJ Parabellum projectile at different similar to the classic Taylor test described in the literature [39–41] was proposed. Ballistic strain rates and to collect data required for validation of its numerical model, a simple testsexperiment of the projectile’s similar to impactthe classic into Taylor the polished test described thick non-deformable in the literature Armox[39–41] 500Twas pro armor‐ steelposed. plate Ballistic at appropriate tests of the velocities projectile’s (50–150 impact m/sinto the achieved polished by thick weighing non‐deformable of gunpowder) Ar‐ weremox carried 500T armor out. Results steel plate of theat appropriate projectile impact velocities tests (50–150 and outcomes m/s achieved of the by validation weighing testsof carriedgunpowder) out with were the carried numerical out. Results simulations of the are projectile shown impact in Figure tests8 .and Deformations outcomes of of the the Metals 2021, 11, x FOR PEER REVIEW 7 of 27 projectilevalidation obtained tests carried in simulations out with the and numerical experiments simulations were very are similar,shown in which Figure testiﬁed 8. Defor that‐ selectedmations values of the of projectile parameters obtained in material in simulations models of and projectile experiments components were providevery similar, proper reproductionwhich testified of thethat projectile selected values behavior of parameters at the analyzed in material strain models rates. of projectile compo‐ nents provide proper reproduction of the projectile behavior at the analyzed strain rates.

(a) (b) (c)

FigureFigure 8. Deformations8. Deformations of of the the 9 9 mm mm FMJ FMJ Parabellum Parabellum projectileprojectile obtained in in the the experiments experiments and and simulations: simulations: (a) (impacta) impact velocityvelocity of 100of 100 m/s; m/s; (b ()b impact) impact velocity velocity of of 126126 m/sm/s and and (c (c) )impact impact velocity velocity of of 143.8 143.8 m/s. m/s.

In the last stage of experimental tests response of ballistic clay to specific loads was determined by performing tests recommended by international standards [42]. GM1 0– 0.2 mm ground clay (cyclone) was used. Calibration of the ballistic clay was carried out by simple drop test to confirm a proper plasticity of the material. A cylindrical steel im‐ pactor with spherical frontal part, weight of 1 kg and diameter of 44 mm, was dropped from the height of 2 m onto the clay placed in a container (at least three times). The inden‐ tation in the clay was measured and compared to the proper value of 25 ± 3 mm.

3. Numerical Investigations 3.1. Assumptions Adopted for Modeling Phenomenon of ballistic impact of the 9 × 19 mm FMJ Parabellum projectile into lay‐ ered composite armor consisting of 3D printed titanium structure was modelled with the LS‐Dyna software [43,44]. In the model, the ballistic insert was placed on a steel box filled with ballistic clay. The projectile initial velocity was v0 = 360 m/s. Scheme of the analyzed phenomenon is shown in Figure 9.

Figure 9. Numerical model of the analyzed projectile impact phenomenon.

In order to reduce the time required to complete the calculations, a single symmetry plane was used in the model, thus modelling only half of the system. Due to irregularity of the structures and asymmetry of their interactions with the penetrating projectile, de‐ viation of the projectile from its initial (perpendicular to the target surface) flight path was

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(a) (b) (c)

Metals 2021, 11, 225 7 of 23 Figure 8. Deformations of the 9 mm FMJ Parabellum projectile obtained in the experiments and simulations: (a) impact velocity of 100 m/s; (b) impact velocity of 126 m/s and (c) impact velocity of 143.8 m/s.

InIn thethe lastlast stagestage of experimental teststests responseresponse ofof ballisticballistic clayclay toto specificspecific loadsloads waswas determineddetermined by by performing performing tests tests recommended recommended by international by international standards standards [42]. GM1 [42]. 0–0.2 GM1 mm 0– ground0.2 mm clay ground (cyclone) clay was(cyclone) used. Calibrationwas used. ofCalibration the ballistic of clay the was ballistic carried clay out was by simple carried drop out testby simple to confirm drop a propertest to plasticityconfirm a of proper the material. plasticity A cylindrical of the material. steel impactor A cylindrical with spherical steel im‐ frontalpactor part,with weight spherical of 1 frontal kg and part, diameter weight of 44 of mm, 1 kg was and dropped diameter from of 44 the mm, height was of 2dropped m onto thefrom clay the placed height in of a 2 container m onto the (at leastclay placed three times). in a container The indentation (at least in three the clay times). was The measured inden‐ andtation compared in the clay to the was proper measured value and of 25 compared± 3 mm. to the proper value of 25 ± 3 mm.

3.3. Numerical InvestigationsInvestigations 3.1.3.1. Assumptions AdoptedAdopted forfor ModelingModeling PhenomenonPhenomenon of ballistic ballistic impact impact of of the the 9 9× ×19 19mm mm FMJ FMJ Parabellum Parabellum projectile projectile into into lay‐ layeredered composite composite armor armor consisting consisting of 3D of 3Dprinted printed titanium titanium structure structure was was modelled modelled with with the theLS‐Dyna LS-Dyna software software [43,44]. [43, 44In]. the In model, the model, the ballistic the ballistic insert insert was placed was placed on a steel on a box steel filled box ﬁlledwith ballistic with ballistic clay. The clay. projectile The projectile initial initialvelocity velocity was v0 was= 360v 0m/s.= 360 Scheme m/s. of Scheme the analyzed of the analyzedphenomenon phenomenon is shown isin shown Figure in9. Figure9.

FigureFigure 9.9. NumericalNumerical modelmodel ofof thethe analyzedanalyzed projectileprojectile impactimpact phenomenon.phenomenon.

InIn orderorder toto reducereduce thethe timetime requiredrequired toto completecomplete thethe calculations,calculations, aa singlesingle symmetrysymmetry planeplane waswas used in the model, thus thus modelling modelling only only half half of of the the system. system. Due Due to to irregularity irregular- ityof the of the structures structures and and asymmetry asymmetry of their of their interactions interactions with with the thepenetrating penetrating projectile, projectile, de‐ deviationviation of ofthe the projectile projectile from from its itsinitial initial (perpendicular (perpendicular to the to thetarget target surface) surface) flight ﬂight path path was was predicted. Therefore, it was unreasonable to use two symmetry planes which prevent reproducing this effect. Nodes in the plane of symmetry were deprived of possibility of translation and rotation in the appropriate directions. Use of the symmetry plane excluded the possibility of giving the projectile a rotational velocity, which, however, according to the information available in the literature [45], does not signiﬁcantly affect projectile penetration capability.

3.2. Numerical Models 3.2.1. General Assumptions Discretization of the simulation components is shown in Figures 10–13. It was performed using HyperMesh software. Components of the simulation were meshed by 8-node solid elements with one integration point and a stiffness criterion of hourglass effect control [40]. Size of the elements was selected in such a way that their number did not signiﬁcantly slow down the calculations and, on the other hand, allowed precise reproduce of the geometry of the bodies and obtaining accurate results. In addition, in order to limit the number of elements in the armor model, the mesh of the ballistic clay was reﬁned in the projectile impact point zone. The distance between the neighboring nodes ranged from approximately 0.25 mm in projectile impact zone to 1 mm in non-deformed armor areas. Metals 2021, 11, 225 8 of 23

Several contact models based mainly on the “penalty function” method [43] and considering friction between components were used in the analyses [45,46]. Boundary conditions were set in such a way that the numerical model reproduced features of the real phenomenon as much as possible. The bottom of the box ﬁlled with ballistic clay was ﬁxed.

3.2.2. Projectile Model Half of the 9 × 19 mm FMJ Parabellum projectile was modelled with 71,200 8- node elements. Elastic-plastic projectile behavior was described with the * MAT_107- MODIFIED_JOHNSON_COOK material model [44]. The model included strain hardening, strain rate hardening and thermal softening effects on the material ﬂow stress deﬁned as a function [44]:

( 2 ) m . ∗C T − T σ = A + Brn + Q [1 − exp(−C r)] · 1 + r · 1 − r (1) ∑ i i − i=1 Tm Tr

where: A, B, C, m and n are material constants, Tr, Tm—room and melting temperatures and σ—material strength. . ∗ The normalized damage-equivalent plastic strain rate r is deﬁned by:

. . ∗ r r = . (2) ε0 . where: ε0 is a user deﬁned reference strain rate. The extended Johnson–Cook damage evolution is deﬁned as: ( 0 ; p ≤ pd ∆D = D ∆p (3) c ; p > p p f −pd d

∗ ∗ ∗ where the current equivalent fracture strain p f = p f (σ , ∆p , T ) is deﬁned as: ∗ T − T D3σ ∗ D4 r ε f = D1 + D2e ·(1 + ∆p ) · 1 + D5 (4) Tm − Tr

where: D1–D5 and pd are material parameters. The normalized equivalent plastic strain increment ∆p∗ is deﬁned by:

∗ ∆p ∆p = . (5) ε0 Additionally, the stress triaxiality σ∗ reads:

∗ σH 1 σ = ; σH = tr(σ) (6) σeq 3

Soft lead core of the projectile is usually signiﬁcantly deformed during impact with the target. Therefore, it was modelled with hybrid elements in order to avoid problems related to excessive erosion of ﬁnite elements (lack of system mass preservation, understating the projectile penetration capability). After reaching failure criterion, elements were not removed from the calculations but were replaced by smoothed particle hydrodynamics (SPH) [43]. Material parameters of the projectile components used in the simulations are presented in Table2. Contacts between the lead core and the brass jacket of the projectile were treated as frictionless and described by the * CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43]. Neglection of friction between the projectile components did not negatively affect obtaining proper deformation of the projectile during the validation test. Metals 2021, 11, x FOR PEER REVIEW 9 of 27

∆𝑝 ∆𝑝∗ (5) 𝜀 Additionally, the stress triaxiality 𝜎∗ reads:

∗ 𝜎 1 𝜎 ; 𝜎 𝑡𝑟𝜎 (6) 𝜎 3 Soft lead core of the projectile is usually significantly deformed during impact with the target. Therefore, it was modelled with hybrid elements in order to avoid problems related to excessive erosion of finite elements (lack of system mass preservation, under‐ stating the projectile penetration capability). After reaching failure criterion, elements were not removed from the calculations but were replaced by smoothed particle hydro‐ dynamics (SPH) [43]. Material parameters of the projectile components used in the simulations are pre‐ sented in Table 2. Contacts between the lead core and the brass jacket of the projectile were treated as frictionless and described by the * CONTACT‐ERODING_SURFACE_TO_SUR‐ Metals 2021, 11, 225 FACE algorithm [43]. Neglection of friction between the projectile components did9 ofnot 23 negatively affect obtaining proper deformation of the projectile during the validation test.

Table 2. Parameters of the * MAT_107‐MODIFIED_JOHNSON_COOK model for projectile. Table 2. Parameters of the * MAT_107-MODIFIED_JOHNSON_COOK model for projectile. RO, PR, A, B, n, C, m, D1, D2, D3, D4, D5, Specification E, (MPa) RO, PR, A, B, n, C, m, D1, D2, D3, D4, D5, Speciﬁcation (Tonnes) E, (MPa)(‐) (MPa) (MPa) (‐) (‐) (‐) (‐) (‐) (‐) (‐) (‐) Lead‐Core 1.01(Tonnes) × 10−8 18.4 × 103 0.42 (-)24 (MPa)40 (MPa)1.00 0.01(-) 1.00(-) 3 (-) 0(-) (-)0 (-)0 (-) 0 (-) − BrassLead-Core‐Jacket 8.52×1.01 × 1010−9 811.5×18.4 10×4 100.313 0.42206 24899 0.42 40 0.01 1.00 1.68 0.01 ‐ 1.00WC 3 1414 0 ‐ ‐ 0 0 0 Brass-JacketRO—density;8.52 E—Young’s× 10−9 modulus;11.5× 10 4PR—Poisson’s0.31 206 ratio; A—yield 899 strength 0.42 of 0.01the material; 1.68 B—strain - hardening WC 1414 constant; - - n—strain hardening exponent; C—strengthening coefficient of strain rate; m—thermal softening exponent; D1, D2, D3, RO—density; E—Young’s modulus; PR—Poisson’s ratio; A—yield strength of the material; B—strain hardening constant; n—strain D4hardening and D5—constants. exponent; C—strengthening coefﬁcient of strain rate; m—thermal softening exponent; D1, D2, D3, D4 and D5—constants.

Numerical model of the projectile was validated against experimental data (see Sec‐ Numerical model of the projectile was validated against experimental data (see tion 2.4). Results of the validation indicated that the adopted coefficients of the Johnson– Section 2.4). Results of the validation indicated that the adopted coefﬁcients of the Johnson– Cook material model, mesh size and contact definitions provided a correct representation Cook material model, mesh size and contact deﬁnitions provided a correct representation of the projectile behavior in the analyzed velocity range [47]. of the projectile behavior in the analyzed velocity range [47].

3.2.3.3.2.3. Ballistic Ballistic Clay Clay Model Model HalfHalf of of the the ballistic ballistic clay clay block block was was modelled modelled with with 564,128 564,128 8‐node 8-node solid solidelements elements (Fig‐ ure(Figure 10). The10). mesh The mesh was wasrefined reﬁned in the in projectile the projectile impact impact zone. zone.

(a) (b)

FigureFigure 10. 10. BallisticBallistic clay clay validation: validation: ( (aa) )Initial Initial position position and and ( (bb)) impactor impactor indentation indentation in in clay. clay. The material model *MAT_018-POWER_LAW_PLASTICITY was used to describe the The material model * MAT_018‐POWER_LAW_PLASTICITY was used to describe ballistic clay performance. It is a model of isotropic plastic material considering inﬂuence the ballistic clay performance. It is a model of isotropic plastic material considering influ‐ of strain rate according to power function [44]. Parameters of the material model are listed ence of strain rate according to power function [44]. Parameters of the material model are in Table3. listedFriction in Table between 3. the projectile and the ballistic clay was omitted due to the fact that the projectile was not expected to penetrate the armor and to interact with the clay. The contact was modelled with the *CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43].

Table 3. Parameters of the *MAT_018- POWER_LAW_PLASTICITY model for ballistic clay.

RO, E, PR, K, N, SRC, SRP, SIGY, EPSF, VP, Speciﬁcation Source (Tonnes) (MPa) (-) (MPa) (-) (s–1) (-) (MPa) (-) (-) Ballistic clay 1878 14.2 0.49 0.24 0.014 0 0 0 2.5 1 [48] RO—density; E—Young’s modulus; PR—Poisson’s ratio; K—material constant; N—strain rate sensitivity coefﬁcient; SRC—strain rate parameter C for Cowper–Symonds strain rate model; SRP—strain rate parameter P for Cowper–Symonds strain rate model; SIGY—yield strength; EPSF—plastic failure strain for element deletion; VP—formulation for rate effects.

Results of the validation of the numerical model of the ballistic clay are shown in Figure 10. Validation was performed by numerical reproduction of the calibration test described in Section 2.4. Depth of indentation in the ballistic clay obtained in the FE simulation was 26 mm and was within the acceptable range according to international standards (25 ± 3 mm). Metals 2021, 11, x FOR PEER REVIEW 10 of 27

Friction between the projectile and the ballistic clay was omitted due to the fact that the projectile was not expected to penetrate the armor and to interact with the clay. The contact was modelled with the *CONTACT‐ERODING_SURFACE_TO_SURFACE algo‐ rithm [43].

Table 3. Parameters of the *MAT_018‐ POWER_LAW_PLASTICITY model for ballistic clay.

RO, E, PR, K, N, SRC, SRP, SIGY, EPSF, VP, Specification Source (Tonnes) (MPa) (‐) (MPa) (‐) (s−1) (‐) (MPa) (‐) (‐) Ballistic clay 1878 14.2 0.49 0.24 0.014 0 0 0 2.5 1 [48] RO—density; E—Young’s modulus; PR—Poisson’s ratio; K—material constant; N—strain rate sensitivity coefficient; SRC—strain rate parameter C for Cowper–Symonds strain rate model; SRP—strain rate parameter P for Cowper–Symonds strain rate model; SIGY—yield strength; EPSF—plastic failure strain for element deletion; VP—formulation for rate effects.

Results of the validation of the numerical model of the ballistic clay are shown in Figure 10. Validation was performed by numerical reproduction of the calibration test described in Section 2.4. Depth of indentation in the ballistic clay obtained in the FE sim‐ ulation was 26 mm and was within the acceptable range according to international stand‐ Metals 2021, 11, 225 ards (25 ± 3 mm). 10 of 23

3.2.4. Fabric Model Half of a single aramid layer was modelled with 83,232 8‐node solid elements (Figure 3.2.4. Fabric Model 11a). Due to the local character of the projectile‐fabric interaction, it was decided to model the fabricHalf of at a mesoscale single aramid level layer including was modelled geometry with 83,232of yarns 8-node and solid their elements interlacing(Figure (Figure 11a). 11b).Due to the local character of the projectile-fabric interaction, it was decided to model the fabric at mesoscale level including geometry of yarns and their interlacing (Figure 11b). Contact interaction including friction between yarns (static coefficient of friction μs = Contact interaction including friction between yarns (static coefﬁcient of friction 0.18, dynamic coefficient of friction μd = 0.19) and between the fabric and the other com‐ µs = 0.18, dynamic coefﬁcient of friction µd = 0.19) and between the fabric and the other ponents of the simulation (fabric‐projectile: μs = 0.38, μd = 0.5; fabric‐titanium structure: μs components of the simulation (fabric-projectile: µs = 0.38, µd = 0.5; fabric-titanium structure: = 0.5, μd = 0.5; fabric‐ballistic clay: μs = 0.9, μd = 0.9) was modelled [49]. The contacts used µ = 0.5, µ = 0.5; fabric-ballistic clay: µ = 0.9, µ = 0.9) was modelled [49]. The contacts thes * CONTACTd ‐ERODING_SURFACE_TO_SURFACEs d algorithm [43]. used the * CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43].

(a) (b)

Figure 11. DiscretizationDiscretization of Twaron CT 750 fabric: ( a) Schematic of a plain plain-woven‐woven and ( b) plain woven textile showing the warp and ﬁll.fill. Behavior of aramid fabrics was described by the *MAT_002-ORTHOTROPIC_ELASTIC modelBehavior [44]. In of this aramid model fabrics the elastic was anddescribed shear moduliby the * as MAT_002 well as Poisson’s‐ORTHOTROPIC_ELAS ratios may differ‐ TICfor the model different [44]. In principal this model directions. the elastic The and material shear moduli law that as relates well as stresses Poisson’s to strains ratios may was differdeﬁned for as the [44 different]: principal directions. The material law that relates stresses to strains was defined as [44]: T C = T ·CL·T (7)

where: T—transformation matrix and CL—constitutive matrix deﬁned in terms of the material constants of the orthogonal material axes, {a, b, c}. The inverse of CL for the orthotropic case was deﬁned as [44]:

 1 − vba − vca 0 0 0  Ea Eb Ec  − vab 1 − vcb 0 0 0   Ea Eb Ec   vac vbc 1  −  − − 0 0 0  C 1 =  Ea Eb Ec  (8) L  0 0 0 1 0 0   Gab   0 0 0 0 1 0   Gbc  0 0 0 0 0 1 Gca

where: Ei—Young moduli in principal material directions, νij—Poisson ratios and Gab, Gbc and Gca—shear moduli. In Figure 11 material directions adopted in the simulations are shown. Parameters of the material model are presented in Table4. Metals 2021, 11, 225 11 of 23

Table 4. Parameters of the *MAT_002-OTHOTROPIC_ELASTIC model for Twaron CT 750 fabric.

RO, EA, EB, EC, PRBA, PRCA, PRCB, GAB, GBC, GCA, Speciﬁcation Source (Tonnes) (MPa) (MPa) (MPa) (-) (-) (-) (MPa) (MPa) (MPa) Twaron CT 750 1.158 × 10−9 62,800 628 628 0 0 0 31,000 158 31,000 [50–52] RO—density; EA—Young’s modulus in a-direction; EB—Young’s modulus in b-direction; EC—Young’s modulus in c-direction; PRBA— Poisson ratio, ba; PRCA—Poisson ratio, ca; PRCB—Poisson ratio, cb; GAB—shear modulus, ab; GBC—shear modulus, bc; GCA—shear modulus, ca.

3.2.5. Titanium Structures Model Four variants of 3D printed structures made of Ti-6Al-4V titanium alloy were analyzed in the study (Figure 12). The structures were modelled with 8-node solid elements. Individual variants were modelled with the following number of elements: • 316,080 elements for S1 structure; • Metals 2021, 11, x FOR PEER REVIEW 113,152 elements for S2 structure; 12 of 27 • 199,680 elements for S3 structure; • 352,560 elements for S4 structure.

(a) (b)

Figure 12. Discretization of thethe 3D3D printedprinted structures structures made made of of Ti-6Al-4V Ti‐6Al‐4V titanium titanium alloy: alloy: (a ()a structure) structure S1; S1; (b )(b structure) structure S4; S4; (c) (structurec) structure S2 andS2 and (d) ( structured) structure S3. S3.

ContactContact interaction interaction including including friction friction between between individual individual cells cells of the of structures the structures (μs = 0.36,(µs = μ 0.36,d = 0.3)µd =as 0.3) well as as well between as between the structures the structures and the and other the other components components of simulation of simula- (structuretion (structure-ballistic‐ballistic clay: clay: μs = 0.9,µs = μ 0.9,d = 0.9;µd =structure 0.9; structure-projectile:‐projectile: μs = 0.36,µs = μ 0.36,d = 0.27)µd = [49] 0.27) were [49] modelled with the *CONTACT‐ERODING_SURFACE_TO_SURFACE algorithm [43]. The elastic‐viscoplastic material model *MAT_224‐TABULATED_JOHNSON_COOK [44] was used to describe behavior of titanium structures. In the model plastic heating causes adiabatic temperature increase and material softening. Plastic failure strain can be defined as a function of triaxiality, strain rate, temperature and element size. The user has the ability of direct input of parameters defining curves. The Ti‐6Al‐4V titanium alloy used in the simulations was defined with the following curves:  LCK1: effective stress–effective plastic strain curves for different strain rates (1.0 × 10−4–5.0 × 104 (s−1);  LCKT: effective stress–effective strain curves for different temperature values (223– 2500 K);  LCF: curves that define plastic failure strain as a function of the triaxiality parameter;  LCG: curves that define plastic failure strain as a function of plastic strain rate;  LCH: curves that define plastic failure strain as a function of temperature;  LCI: curves that define plastic failure strain as a function of element size.

Flow stress 𝜎𝑦 expressed as a function of plastic strain 𝜀𝑝, plastic strain rate 𝜀𝑝 and temperature 𝑇 have the following form (using curves LCK1, LCKT) [44]:

Metals 2021, 11, 225 12 of 23

were modelled with the *CONTACT-ERODING_SURFACE_TO_SURFACE algorithm [43]. The elastic-viscoplastic material model *MAT_224-TABULATED_JOHNSON_COOK [44] was used to describe behavior of titanium structures. In the model plastic heating causes adiabatic temperature increase and material softening. Plastic failure strain can be defined as a function of triaxiality, strain rate, temperature and element size. The user has the ability of direct input of parameters defining curves. The Ti-6Al-4V titanium alloy used in the simulations was defined with the following curves: • LCK1: effective stress–effective plastic strain curves for different strain rates (1.0 × 10−4– 5.0 × 104 (s−1); • LCKT: effective stress–effective strain curves for different temperature values (223– 2500 K); • LCF: curves that define plastic failure strain as a function of the triaxiality parameter; • LCG: curves that define plastic failure strain as a function of plastic strain rate; • LCH: curves that define plastic failure strain as a function of temperature; • LCI: curves that define plastic failure strain as a function of element size. . Flow stress σy expressed as a function of plastic strain εp, plastic strain rate εp and temperature T have the following form (using curves LCK1, LCKT) [44]: . kt ε p, T σy = k1 ε p, εp (9) kt(ε1, TR)

Plastic failure strain is deﬁned as a function of triaxiality p/σνm, lode parameter, . plastic strain rate εp, temperature T and initial element size lc (volume over maximum area for solids) by [44]:

p 27J . p = 3 · · ( )· ε p f f , 3 g εp h T i lc, (10) σvm 2σvm σvm using load curves LCF, LCG, LCH and LCI. The default failure criterion of this material model depends on plastic strain evolution . εp and on plastic failure strain εpf and is obtained by accumulation over time: . Z εp F = dt (11) ε p f where element erosion takes place when F ≥ 1. This accumulation provides load-path dependent treatment of failure. An additional, load-path independent, failure criterion can be invoked, where the current state of plastic strain is used [44]:

ε p F2 = (12) ε p f Temperature increase is caused by plastic work [43]:

β Z . T = TR + σyεpdt (13) Cpρ

where: TR—room temperature, β—dissipation factor, Cp—speciﬁc heat and ρ—density. Definitions of the curves used in the model of 3D printed titanium structures were adopted on the basis of works [53,54], where a number of material tests were carried out in order to build an accurate numerical model of Ti-6Al-4V alloy. The material model was validated in the papers [53,55] by conducting dynamic perforation tests of plates made of Ti-6Al-4V alloy and comparing the results of experiments with the results of similar numerical tests.

4. Results and Discussion 4.1. Results of Ballistic Impact Simulations Results of simulations of ballistic impact of the 9 mm FMJ Parabellum projectile into bulletproof vest inserts containing different variants of 3D printed titanium structures Metals 2021, 11, 225 13 of 23

are shown in Figures13–16. Due to speciﬁc shape of the structures (presence of air gaps and denser areas) calculations were carried out for two different and characteristic impact points selected separately for individual variants of structures. The impact points were selected in such a way that they covered two extreme impact scenarios—the maximum and the minimum amount of the structure material in the projectile ﬂight path. Results of the simulations included (Figures 13–16): • Final deformations of the phenomenon components; • Distribution of plastic strain in the 3D printed titanium structures; • Volumes, shapes and dimensions of characteristic deformation parameters of the ballistic clay; • Plots of kinetic energy of the projectile versus time. Results of simulation for the S1 variant of 3D printed titanium structure are shown in Figure 13. Titanium structures were damaged in the direct projectile interaction zone in both variants of impact points (Figure 13c). Results of simulations indicated that structure S1 was very sensitive to location of impact point. During penetration of the S1 structure at impact point 2 the projectile was deformed in a characteristic way. Due to large air gaps between the structure cells, the deformed projectile took the shape of a truncated cone (Figure 13b). This projectile self-sharpening effect was undesirable because it caused concentration of the impact energy on the smaller area. As a consequence, the smallest diameter of indentation (impact point 2) and volumes of hollows in the ballistic clay were observed after the projectile impacted into the S1 variant of structure at impact point 2. On the other hand, the structure showed high effectiveness when the projectile hit at impact point 1. Values of back face deformation (BFD) obtained for the S1 structure were 14.0–16.1 mm (Figure 13d). In the S2 3D printed structure variation, individual cells had toroidal shape (Figure 12c). Thanks to that, the S2 structure showed high capability to dissipate the impact energy of the 9 mm projectile. The smooth shape of the cells prevents their blocking during their movement in relation to each other. Only individual cells were damaged and cracked in the area of the projectile impact (Figure 14c). Taking into account the mushroom shape of the projectile after the impact (Figure 14b), it can be concluded that a significant part of impact energy was dissipated to plastic deformation of projectile. Values of BFD obtained for the S2 structure (14.7–14.0 mm) were significantly smaller than in the case of the S1 structure (Figure 13d). Additionally, volumes and diameters of hollows in the ballistic clay (Figure 14d) were much larger than for the S1 structure. This indicated that the smooth toroidal shape of cells has greater potential in bulletproof vest application. The S3 structure was similar to the S2 variant. The main difference was that individual cells had octagonal forms instead of circular ones (see Figure 12c,d). The S3 structure also showed satisfying energy absorption and dissipation capabilities during the simulations (Figure 15). The depth of indentation in the ballistic clay observed after the impact of the 9 mm FMJ Parabellum projectile was 14.6 mm (Figure 15d) for both impact location points. That indicated that both S2 and S3 structures were much less sensitive to the projectile impact location than variant S1. Significant mushrooming of the projectile demonstrated that the impact energy was dispersed over a larger area. The projectile deformation (Figure 15b) took a similar shape as for the S2 structure. Only individual cells under the projectile impact point were damaged (Figure 15c). In the last 3D printed structure variation—S4 (Figure 16)—cells had the shape of an octagon with an internal scaffold (Figure 12b). Regarding the shape of the cells, it was predicted that the S4 structure would provide the most efficient absorption and dissipation of the projectile energy. However, results obtained for the S4 structure varied greatly. The structure turned out to be very sensitive to the projectile impact location. On the one hand, structure S4 showed the best protection capability when the projectile hit impact point 2. Although a few cells were damaged the greatest diameter (65.8 mm) and the smallest BFD (12.7 mm) was obtained in that case. On the other hand, when the projectile hit impact point 1 the structure showed the worst energy absorption and dissipation capability; depth of indentation in the ballistic clay was the highest (17.2 mm) in that case. It seemed that the main reason for that lay in the specific shape of a single cell of the S4 structure. In some cases when the loads are distributed particularly unfavorably Metals 2021, 11, 225 14 of 23

Metals 2021, 11, x FOR PEER REVIEWon the cell it fractures in a specific way forming fragments with sharp edges (Figure 1615b). of These 27 fragments may cut the aramid layers and significantly decrease their resistance to impact.

Figure 13. Results of simulation for S1 structure: (a) location of the impact point; (b) ﬁnal deformation; (c) distribution of Figure 13. Results of simulation for S1 structure: (a) location of the impact point; (b) final deformation; (c) distribution of effectiveeffective plastic plastic strain strain in in the the titanium titanium structure;structure; ((d)) shapeshape of the hollow in in the the ballistic ballistic clay clay and and (e ()e )plot plot of of the the projectile projectile energyenergy against against time. time. Metals 2021, 11, 225 15 of 23 Metals 2021, 11, x FOR PEER REVIEW 17 of 27

Figure 14. Results of simulation for S2 structure: (a) location of the impact point; (b) ﬁnal deformation; (c) distribution of effective plastic strain in the titanium structure; (d) shape of the hollow in the ballistic clay and (e) plot of the projectile Figure 14. Results of simulation for S2 structure: (a) location of the impact point; (b) final deformation; (c) distribution of energy against time. effective plastic strain in the titanium structure; (d) shape of the hollow in the ballistic clay and (e) plot of the projectile energy against time. Metals 2021, 11, 225 16 of 23

Metals 2021, 11, x FOR PEER REVIEW 19 of 27

FigureFigure 15. 15. ResultsResults of of simulation simulationfor for S3 S3 structure: structure: ( (aa)) location location of of the the impact impactpoint; point; ( (bb)) final ﬁnal deformation; deformation;( (cc)) distribution distribution of of effectiveeffective plastic plastic strain strain in in the the titanium titanium structure; structure; ( (dd)) shape shape of of the the hollow hollow in in the the ballistic ballistic clay clay and and ( (ee)) plot plot of of the the projectile projectile energyenergy against against time. time. Metals 2021, 11, 225 17 of 23 Metals 2021, 11, x FOR PEER REVIEW 21 of 27

Figure 16. Results of simulation for S4 structure: (a) location of the impact point; (b) ﬁnal deformation; (c) distribution of Figureeffective 16. plastic Results strain of simulation in the titaniumfor S4 structure: structure; ( (ad) )location shape of of the the hollow impact inpoint; the ballistic (b) final clay deformation; and (e) plot(c) of distribution the projectile of effectiveenergy against plastic time.strain in the titanium structure; (d) shape of the hollow in the ballistic clay and (e) plot of the projectile energy against time. Metals 2021, 11, x FOR PEER REVIEW 22 of 27

Metals 2021, 11, 225 18 of 23

Comparing the plots of the kinetic energy of projectiles against time it can be noticed that structureComparing S1 theseemed plots to of have the kinetic the lowest energy stiffness. of projectiles The projectile against time was itstopped can be noticedsignifi‐ cantlythat structure later than S1 in seemed the case to of have other the variants. lowest stiffness. Stopping The of the projectile projectile was was stopped observed signifi- in t =cantly 0.2 ms later while than in in the the other case ofvariants other variants. of simulations Stopping the of projectile the projectile velocity was reached observed zero in valuet = 0.2 at ms of whilet = 0.15 in ms the (structures other variants S2, S3) of and simulations t = 0.175 ms the (structure projectile S4). velocity Additionally, reached only zero invalue the case at of oft =the 0.15 S1 structure ms (structures did the S2, projectiles S3) and t come= 0.175 into ms contact (structure with the S4). aramid Additionally, layers. Inonly other in the cases, case the of projectile the S1 structure was stopped did the at projectiles the titanium come layers. into contact It was probably with the aramidcaused bylayers. the significantly In other cases, greater the projectile proportion was of stoppedempty space at the in titanium the total layers.volume It of was the probablytitanium layer.caused by the significantly greater proportion of empty space in the total volume of the titaniumBased layer. on simulation results it can be concluded that the analyzed 3D printed titanium structuresBased together on simulation with additional results it can aramid be concluded layers are that effective the analyzed against 3D the printed 9 mm FMJ titanium Par‐ abellumstructures projectile. together All with the additionalanalyzed structures aramid layers stopped are the effective projectile. against Additionally, the 9 mm thanks FMJ toParabellum the cooperation projectile. of adjacent All the cells, analyzed the concentrated structures stopped energy of the the projectile. projectile Additionally, was distrib‐ utedthanks over to thea much cooperation larger area of adjacentcompared cells, to classical the concentrated systems based energy on of aramid the projectile layers. That was wasdistributed proved overby large a much diameters larger of area hollows compared in the to ballistic classical clay. systems However, based it on should aramid be layers.noted thatThat during was proved the analyses by large the diameters areal density of hollows of structures in the ballistic was not clay. optimized. However, Structure it should var be‐ iantsnoted were that compared during the in analyses order to the select areal the density most efficient of structures shape was of cells not optimized. that show the Structure great‐ estvariants potential were of compared application in in order bulletproof to select inserts the most as a efficient layer with shape high of capability cells that of show absorp the‐ tiongreatest and potentialdissipation of of application the energy in of bulletproof the impacting inserts projectile. as a layer On withthe basis high of capability the simula of‐ tionabsorption results andit was dissipation observed ofthat the variants energy S2 of and the impactingS3 of the structures projectile. showed On the the basis greatest of the capabilitysimulation of results absorbing it was and observed dissipating that variantsof the projectile S2 and S3 impact of the energy. structures Therefore, showed this the structuregreatest capability variant may of absorbing constitute andthe initial dissipating geometry of the used projectile in further impact optimization energy. Therefore, of shape andthis areal structure density variant of 3D may printed constitute structures the initial used geometryin bulletproof used vest in further inserts. optimization of shape and areal density of 3D printed structures used in bulletproof vest inserts. 4.2. Mesh Sensitivity Study 4.2. Mesh Sensitivity Study In order to check the influence of the finite element size on the damage intensity of the titaniumIn order structure to check during the influence the projectile of the impact finite elementthe mesh size sensitivity on the study damage was intensity carried out.of the Additional titanium simulations structure during of the the S2 structure projectile were impact performed the mesh in sensitivity which the studysize of was the elementscarried out. used Additional to describe simulations the cells of the S2structure structure the were projectile performed impact in zone which were the sizede‐ creasedof the elements (Figure used17). It to was describe considered the cells from of the0.5 structureto 0.25 mm the (Figure projectile 17b) impact and from zone 0.5 were to decreased (Figure 17). It was considered from 0.5 to 0.25 mm (Figure 17b) and from 0.5 to 0.125 mm (Figure 17c). 0.125 mm (Figure 17c).

(a) (b) (c)

Figure 17. Variations of discretization used in the mesh sensitivity study: (a (a) base size; ( b) mesh size 0.5–0.25 mm and ( c)) mesh size 0.5–0.125 mm. mesh size 0.5–0.125 mm.

Results of simulations carried out for different mesh size were shown in Figure 18.

Metals 2021, 11, x FOR PEER REVIEW 23 of 27 Metals 2021, 11, 225 19 of 23

Results of simulations carried out for different mesh size were shown in Figure 18.

Figure 18. a b Figure 18. ResultsResultsof of simulations simulations performed performed in in the the mesh mesh sensitivity sensitivitystudy: study:(a () final) ﬁnal deformation; deformation; (b () distribution) distributionof of effective effective plasticplastic strain strainin in the the titanium titanium structure; structure;(c ()c )shape shape of of the the hollow hollowin in the the ballistic ballistic clay clay and and (d (d) )plot plot of of the the projectile projectile energy energy againstagainst time. time.

On the basis of the simulation results it can be concluded that damage intensity of the titanium structures increased together with the decrease of the mesh size (Figure 18b). Metals 2021, 11, 225 20 of 23

As a consequence, the kinetic energy of the projectile was distributed on the smaller area (the smallest indention diameter of 54.7 mm), and the highest back face deformation (BFD) = 16.8 mm was observed in the variant where the cells of the titanium structure were modelled with elements of 0.125 mm size (Figure 18c). The most intense absorption and dissipation of the kinetic energy of the projectile was observed in the variant with the coarsest mesh (Figure 18d). Larger size of the elements increased their stiffness and resulted in the elements being eroded later than in cases with refined mesh. To conclude, the developed model of the ballistic impact phenomenon showed moderate mesh sensitivity. In order to decrease the influence of the mesh size on the failure intensity of titanium structures the curves that define plastic failure strain as a function of element size in the *MAT_224-TABULATED_JOHNSON_COOK should be tuned while taking into account the correlation to experimental data.

5. Conclusions The results of numerical analysis of the ballistic impact of the 9 × 19 mm FMJ Para- bellum projectile into 100 × 100 mm composite layered armor containing four variants of 3D printed titanium structures were presented. Numerical models of the phenomenon were developed. Numerical models of individual components were verified against experimental data from the authors’ own research as well as those available in the literature. The models provide proper representation of the actual behavior of materials. This may indicate that the adopted methodology of numerical analysis was correct, but the final veri- fication of the numerical model of the whole phenomenon will be possible after performing experimental tests. All of the analyzed variants of structures stopped the 9 × 19 mm FMJ Parabellum projectile. Indentations in the ballistic clay after the projectile impact into the analyzed ballistic inserts, were within the range of 12.7–17.2 mm. These values are significantly lower than the limiting BFD value of 44 mm allowed by the standards [42]. On the basis of the simulation results it was observed that variants S2 and S3 of the structures showed the greatest capability of absorbing and dissipating the projectile impact energy. These structures were also less sensitive to the projectile impact location than structures S1 and S4. Therefore, structures S2 and S3 may constitute the initial geometry used in further optimization of shape and areal density of the 3D printed structures used in bulletproof vest inserts. Small indentations in the ballistic clay after the projectile impact into protective structures indicated that they were overweighed and can be optimized to reduce the areal density while providing protection against a 9 × 19 mm FMJ Parabellum projectile. To sum up, it seems justified to continue this project focused on using 3D printed titanium structures in inserts of bulletproof vests protecting against 9 × 19 mm FMJ Parabellum projectiles.

Author Contributions: Conceptualization, P.Z., M.B. (Marcin Bajkowski) and M.M.; methodology, R.G., K.J., W.B. and M.B. (Miroslaw Bocian); software, P.Z., D.P. and M.M.; validation, M.B. (Marcin Bajkowski) and R.G.; formal analysis, P.Z., K.J. and R.G.; investigation, P.Z., M.B. (Marcin Bajkowski) and M.M.; resources, K.J., M.B. (Miroslaw Bocian) and M.M.; data curation, P.Z., K.J., D.P. and M.B. (Marcin Bajkowski); writing—original draft preparation, P.Z., R.G. and W.B.; writing—review and editing, K.J., M.M. and M.B. (Miroslaw Bocian); visualization, P.Z., W.B., K.J. and D.P.; supervision, K.J., M.B. (Marcin Bajkowski) and M.M.; project administration, P.Z., D.P. and M.B. (Miroslaw Bocian); funding acquisition, M.B. (Marcin BajkowskI) and M.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Centre for Research and Development of Poland, grant No. TECHMATSTRATEG 2/410049/12/NCBR/2019. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing is not applicable to this article. Metals 2021, 11, 225 21 of 23

Acknowledgments: Calculations were carried out at the Wroclaw Centre for Networking and Supercomputing (http://www.wcss.pl), grant No. 452. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Pach, J.; Mayer, P.; Jamroziak, K.; Polak, S.; Pyka, D. Experimental Analysis of Puncture Resistance of Aramid Laminates on Styrene-Butadiene-Styrene and Epoxy Resin Matrix for Ballistic Applications. Arch. Civ. Mech. Eng. 2019, 19, 1327–1337. [CrossRef] 2. Clifton, S.; Thimmappa, B.H.S.; Selvam, R.; Shivamurthy, B. Polymer Nanocomposites for High-Velocity Impact Applications—A Review. Compos. Commun. 2020, 17, 72–86. [CrossRef] 3. Benzait, Z.; Trabzon, L. A Review of Recent Research on Materials Used in Polymer–Matrix Composites for Body Armor Application. J. Compos. Mater. 2018, 52, 3241–3263. [CrossRef] 4. Fejdy´s,M.; Ko´sla,K.; Kucharska-Jastrz ˛abek,A.; Łandwijt, M. Hybride Composite Armour Systems with Advanced Ceramics and Ultra-High Molecular Weight Polyethylene (UHMWPE) Fibres. Fibres Text. East. Eur. 2016, 24, 79–89. [CrossRef] 5. Crouch, I.G. Critical Interfaces in Body Armour Systems. Def. Technol. 2020.[CrossRef] 6. Da Luz, F.S.; Filho, F.d.C.G.; Oliveira, M.S.; Nascimento, L.F.C.; Monteiro, S.N. Composites with Natural Fibers and Conventional Materials Applied in a Hard Armor: A Comparison. Polymers 2020, 12, 1920. [CrossRef] 7. Fejdy´s,M.; Ko´sla,K.; Kucharska-Jastrz ˛abek,A.; Łandwijt, M. Influence of Ceramic Properties on the Ballistic Performance of the Hybrid Ceramic–Multi-Layered UHMWPE Composite Armour. J. Aust. Ceram. Soc. 2020.[CrossRef] 8. Kurzawa, A.; Pyka, D.; Jamroziak, K.; Bajkowski, M.; Bocian, M.; Magier, M.; Koch, J. Assessment of the Impact Resistance of a Composite Material with EN AW-7075 Matrix Reinforced with α-Al2O3 Particles Using a 7.62 × 39 mm Projectile. Materials 2020, 13, 769. [CrossRef] 9. Kurzawa, A.; Pyka, D.; Jamroziak, K.; Bocian, M.; Kotowski, P.; Widomski, P. Analysis of Ballistic Resistance of Composites Based on EN AC-44200 Aluminum Alloy Reinforced with Al2O3 Particles. Compos. Struct. 2018, 201, 834–844. [CrossRef] 10. Chusov, S.Y.; Yankov, V.P. Investigation of Properties of Titanium Alloys with Mechanically Stable Beta-Structure for Body Armor Application. Tech. Wyrob.Włók. 2009, 17, 54–57. 11. Cimpoeru, S.J.; Alkemade, S.J.; Szymczak, M.; Rupert, N.L.; Green, W.H.; Wells, J.M. Ballistic Assessment of a Low-Cost Ti-6Al-4V Titanium Alloy. Aust. J. Mech. Eng. 2003, 1, 5–9. [CrossRef] 12. Karahan, M.; Jabbar, A.; Karahan, N. Ballistic Impact Behavior of the Aramid and Ultra-High Molecular Weight Polyethylene Composites. J. Reinf. Plast. Compos. 2015, 34, 37–48. [CrossRef] 13. Shtertser, A.A.; Zlobin, B.S.; Kiselev, V.V.; Shemelin, S.D.; Bukatnikov, P.A. Characteristics of Reinforced Ultra-High Molecular Weight Polyethylene During Its Ballistic Penetration. J. Appl. Mech. Tech. Phys. 2020, 61, 471–478. [CrossRef] 14. Jamroziak, K. Evaluation of Gunshot Wounds in Aspect of Injury Criterion. Aktual. Probl. Biomech. 2016, 11, 33–46. 15. Wang, L.; Kanesalingam, S.; Nayak, R.; Padhye, R. Recent Trends in Ballistic Protection. Text. Light Ind. Sci. Technol. 2014, 3, 37–47. [CrossRef] 16. Baranowski, P.; Płatek, P.; Antolak-Dudka, A.; Sarzyński,M.; Kucewicz, M.; Durejko, T.; Małachowski, J.; Janiszewski, J.; Czujko, T. Deformation of Honeycomb Cellular Structures Manufactured with Laser Engineered Net Shaping (LENS) Technology under Quasi-Static Loading: Experimental Testing and Simulation. Addit. Manuf. 2019, 25, 307–316. [CrossRef] 17. Szymczyk, P.; Hoppe, V.; Ziółkowski, G.; Smolnicki, M.; Madeja, M. The Effect of Geometry on Mechanical Properties of Ti6Al4V ELI Scaffolds Manufactured Using Additive Manufacturing Technology. Arch. Civ. Mech. Eng. 2020, 20, 1–13. [CrossRef] 18. Horn, K.; Biever, K.; Burkman, K.; Sheikh, P.D.; Jamison, L.; Kolb, M. Lightening Body Armor: Arroyo Support to the Army Response to Section 125 of the National Defense Authorization Act for Fiscal Year 2011; Report No. W74V8H-06-C-0001; United States Army: Santa Monica, SM, USA, 2011. 19. Kristoffersen, M.; Costas, M.; Koenis, T.; Brøtan, V.; Paulsen, C.O.; Børvik, T. On the Ballistic Perforation Resistance of Additive Manufactured AlSi10Mg Aluminium Plates. Int. J. Impact Eng. 2020, 137.[CrossRef] 20. Ngo, T.D.; Kashani, A.; Imbalzano, G.; Nguyen, K.T.Q.; Hui, D. Additive Manufacturing (3D Printing): A Review of Materials, Methods, Applications and Challenges. Compos. Part B Eng. 2018, 143, 172–196. [CrossRef] 21. Dunaj, P.; Berczyński,S.; Mi ˛adlicki,K.; Iskra, I.; Niesterowicz, B. Increasing Damping of Thin-Walled Structures Using Additively Manufactured Vibration Eliminators. Materials 2020, 13, 2125. [CrossRef] 22. Garcia-Gonzalez, D.; Rusinek, A.; Jankowiak, T.; Arias, A. Mechanical Impact Behavior of Polyether-Ether-Ketone (PEEK). Compos. Struct. 2015, 124, 88–99. [CrossRef] 23. Szymczyk, P.; Ziółkowski, G.; Junka, A.; Chlebus, E. Application of Ti6Al7Nb Alloy for the Manufacture of Biomechanical Functional Structures (BFS) for Custom-Made Bone Implants. Materials 2018, 11, 971. [CrossRef][PubMed] 24. Yuan, M.Q.; Liu, Y.; Gong, Z.; Qian, X.M. The Application of PA/CF in Stab Resistance Body Armor. IOP Conf. Ser. Mater. Sci. Eng. 2017, 012027.[CrossRef] 25. Connors, M.; Yang, T.; Hosny, A.; Deng, Z.; Yazdandoost, F.; Massaadi, H.; Eernisse, D.; Mirzaeifar, R.; Dean, M.N.; Weaver, J.C.; et al. Bioinspired Design of Flexible Armor Based on Chiton Scales. Nat. Commun. 2019, 10, 1–13. [CrossRef] 26. Costas, M.; Morin, D.; de Lucio, M.; Langseth, M. Testing and Simulation of Additively Manufactured AlSi10Mg Components under Quasi-Static Loading. Eur. J. Mech. A/Solids 2020, 81, 103966. [CrossRef] Metals 2021, 11, 225 22 of 23

27. Masood, S.H.; Ruan, D.; Rajapatruni, P. Mechanical Performance of Plymetal Structures Subjected to Impact Loading. Int. J. Prot. Struct. 2018, 9, 65–76. [CrossRef] 28. Zhao, L.; Qian, X.; Sun, Y.; Yuan, M.; Tang, F.; Zhao, Y.; Zhang, Q.; Chen, Y. Ballistic Behaviors of Injection-Molded Honeycomb Composite. J. Mater. Sci. 2018, 53, 14287–14298. [CrossRef] 29. Płatek, P.; Rajkowski, K.; Cieplak, K.; Sarzyński,M.; Małachowski, J.; Wo´zniak,R.; Janiszewski, J. Deformation Process of 3D Printed Structures Made from Flexible Material with Different Values of Relative Density. Polymers 2020, 12, 2120. [CrossRef] 30. Platek, P.; Sienkiewicz, J.; Janiszewski, J.; Jiang, F. Investigations on Mechanical Properties of Lattice Structures with Different Values of Relative Density Made from 316L by Selective Laser Melting (SLM). Materials 2020, 13, 2204. [CrossRef] 31. Kluczyński,J.; Sniezek, L.; Grzelak, K.; Janiszewski, J.; Płatek, P.; Torzewski, J.; Szachogłuchowicz, I.; Gocman, K. Influence of Selective Laser Melting Technological Parameters on the Mechanical Properties of Additively Manufactured Elements Using 316L Austenitic Steel. Materials 2020, 13, 1449. [CrossRef] 32. Płatek, P.; Baranowski, P.; Janiszewski, J.; Kucewicz, M. Problems of Deformation and Damage Studies of Additively Manufactured Regular Cellular Structures. In Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures; Voyiadjis, G.Z., Ed.; Springer: New York, NY, USA, 2020; pp. 1–33. [CrossRef] 33. Bajkowski, M.; Grygoruk, R.; Nita, Z.; Floriańczyk,A. Method for Producing Additional Ballistic Insert and the Additional Ballistic Insert for Bulletproof. Jackets. Patent PL224964, 28 February 2017. 34. Gmbh, T.A. Teijin Aramid @ Techtextile Middle East Symposium. Available online: https://www.intersecexpo.com/uploads/ editor_images/file/ReneLohmann-DubaiTTS2014_SHOW-locked.pdf (accessed on 20 November 2020). 35. Pawlak, A.; Szymczyk, P.; Ziolkowski, G.; Chlebus, E.; Dybala, B. Fabrication of Microscaffolds from Ti-6Al-7Nb Alloy by SLM. Rapid Prototyp. J. 2015, 21, 393–401. [CrossRef] 36. Del Guercio, G.; Galati, M.; Saboori, A.; Fino, P.; Luliano, L. Microstructure and Mechanical Performance of Ti–6Al–4V Lattice Structures Manufactured via Electron Beam Melting (EBM): A Review. Acta Metall. Sin. (Engl. Lett.) 2020, 33, 183–203. [CrossRef] 37. Cotton, R.; Palanisamy, S.; Avdeev, M.; Jarvis, T.; Henry, C.; Cuiuri, D.; Balogh, L.; Rashid, R.A.R. Diffraction Line Profile Analysis of 3D Wedge Samples of Ti-6Al-4V Fabricated Using Four Different Additive Manufacturing Processes. Metals 2019, 9, 60. [CrossRef] 38. STANAG 4090. Technical Performance Specification Providing for the Interchangeability of 9 mm × 19 Ammunition; North Atlantic Treaty Organization (NATO): Brussels, Belgium, 2020. 39. Panowicz, R.; Janiszewski, J.; Kochanowski, K. Effects of Sample Geometry Imperfections on the Results of Split Hopkinson Pressure Bar Experiments. Exp. Tech. 2019, 43, 397–403. [CrossRef] 40. Chapman, D.J.; Radford, D.; Walley, S.M. A History of the Taylor Test and Its Present Use in the Study of Lightweight Materials. In 3rd Light-Weight Armour Group Workshop. Design and Use of Light-Weight Materials; Teixeria-Dias, F., Dodd, B., Lach, E., Schulz, P., Eds.; Universidade de Aveiro: Aveiro, Portugal, 2005; pp. 12–24. 41. Kruszka, L.; Magier, M.; Zielenkiewicz, M. Experimental Analysis of Visco-Plastic Properties of the Aluminium and Tungsten Alloys by Means of Hopkinson Bars Technique. Appl. Mech. Mater. 2014, 566, 110–115. [CrossRef] 42. Mukasey, M.B.; Sedgwick, J.L.; Hagy, D.W. Ballistic Resistance of Body Armor; U.S. Department of Justice Office of Justice Programs: Washington, DC, USA, 2008; pp. 1–89. 43. LS-DYNA®Keyword User’s Manual; LS-DYNA R12, (r:13109); Livermore Software Technology (LST): Pittsburgh, PA, USA, 2020; Volume I. 44. Materials Modeles. In LS-DYNA®Keyword User’s Manual; LS-DYNA R12, (r:13191); Livermore Software Technology (LST): Pittsburgh, PA, USA, 2020; Volume II. 45. Bocian, M.; Jamroziak, K.; Kosobudzki, M. Analysis of Material Punching Including a Rotational Speed of the Projectile. Solid State Phenom. 2015, 220–221, 571–576. [CrossRef] 46. Mazurkiewicz, Ł.; Małachowski, J.; Baranowski, P. Optimization of Protective Panel for Critical Supporting Elements. Compos. Struct. 2015, 134, 493–505. [CrossRef] 47. Mackiewicz, A.; Pyka, D.; Pach, J.; Jamroziak, K.; Bocian, M. Comparison of Numerical Modelling Methods of Innovative Materials for Ballistic Shields. In Advanced Materials for Defense; Fangueiro, R., Rana, S., Eds.; Springer: Berlin/Heidelberg, Germany, 2020; pp. 119–127. 48. Hernandez, C.; Maranon, A.; Ashcroft, I.A.; Casas-Rodriguez, J.P. Inverse Methods for the Mechanical Characterization of Materials at High Strain Rates. EPJ Web Conf. 2012, 26, 04022. [CrossRef] 49. Coefficient of Friction. Available online: https://www.teachengineering.org/content/nyu_/activities/nyu_heavy/nyu_heavy_ activity1_coftable.pdf (accessed on 8 January 2021). 50. Nilakantan, G.; Keefe, M.; Gillespie, J.W.; Bogetti, T.A. Novel Multi-Scale Modeling of Woven Fabric. In 10th International LS-DYNA®Users Conference; Mindle, W.L., Ed.; Livermore Software Technology Corporation: Dearbon, MI, USA, 2008; pp. 19–38. 51. Nilakantan, G.; Nutt, S. Effects of Ply Orientation and Material on the Ballistic Impact Behavior of Multilayer Plain-Weave Aramid Fabric Targets. Def. Technol. 2018, 14, 165–178. [CrossRef] 52. Nilakantan, G.; Keefe, M.; Bogetti, T.A.; Gillespie, J.W. Multiscale Modeling of the Impact of Textile Fabrics Based on Hybrid Element Analysis. Int. J. Impact Eng. 2010, 37, 1056–1071. [CrossRef] 53. Haight, S.; Wang, L.; Du Bois, P.; Carney, K.; Kan, C. Development of a Titanium Alloy Ti-6Al-4V Material Model Used in LS-DYNA; Report DOT/FAA/TC-15/23; U.S. Department of Transportation: Washington, DC, USA, 2016; 1, p. 353. Metals 2021, 11, 225 23 of 23

54. Burian, W.; Zochowski,˙ P.; Gmitrzuk, M.; Marcisz, J.; Starczewski, L.; Juszczyk, B.; Magier, M. Protection Effectiveness of Perforated Plates Made of High Strength Steel. Int. J. Impact Eng. 2019, 126, 27–39. [CrossRef] 55. Meyer, H.W.; Kleponis, D.S. Modeling the High Strain Rate Behavior of Titanium Undergoing Ballistic Impact and Penetration. Int. J. Impact Eng. 2001, 26, 509–521. [CrossRef]