Penetration resistance of joint joints of constrained ceramic-metal composite structures

Penetration resistance of joint joints of constrained ceramic-metal composite structures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Penetration resistance of joint joints of constrained ceramic-metal composite structures Hao Wu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3872452/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Aiming at the problems of edge weakening effect and gap defects in ceramic metal composite structure, the anti-penetration performance of ceramic metal composite structure was studied. Based on the experimental study of ceramic metal composite structure against 7.62 mm armor-piercing incendiary projectile penetration, the numerical model of ceramic metal composite structure against penetration was established. According to the experimental results, the reliability of the numerical simulation method was verified, and the anti-penetration performance at the ceramic joint was analyzed. The results show that the aluminum alloy sandwich plate can provide effective support for the ceramic. With the increase of the thickness of the aluminum alloy sandwich plate, the anti-penetration performance of the composite structure is improved. The anti-penetration performance of the composite structure increases with the increase of the thickness of the UHMWPE backplane. When the backplane reaches a certain thickness threshold, increasing the thickness of the backplane cannot significantly improve the anti-penetration performance of the composite structure. Adding a certain thickness of metal separator at the joint can effectively reduce the damage of ceramics. Physical sciences/Engineering Physical sciences/Engineering/Mechanical engineering ceramics anti-penetration performance aluminium alloy sandwich plate UHMWPE Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Individual protective equipment is an important equipment to improve the combat capability and production capacity of soldiers in modern battlefield. The bulletproof insert plate is mainly composed of ceramic, metal and UHMWPE plate. The characteristics of high hardness and high compressive strength of ceramics make the projectile passivated and broken, consuming its energy. The fiber backplane plays a role in supporting the ceramic plate and absorbing the residual kinetic energy of the projectile [ 1 ] . Ceramic constraints are divided into two categories, namely impedance constraints and pressure constraints. The impedance constraint refers to the material with different wave impedances to limit the deformation of the ceramic, and the impedance constraint is formed by the ceramic plate superimposed with the support side plate, the support back plate and the support panel. The pressure constraint refers to the pre-stress applied to the ceramic before penetration.Shockey [ 2 ] , fi.Orphal [ 3 ] , Espinosa [ 4 ] and Anderson [ 5 ] used long-rod projectiles to penetrate ceramic materials to measure DOP. The results show that : for ceramic materials with cover plate, side plate and back plate constraints, ceramic fragments cannot be spattered, and the friction between ceramic fragments makes its anti-elastic performance significantly improved.Cao et al. [ 6 – 7 ] used DOP test to show that under three conditions, the order of ceramic protection coefficient is unconstrained < prestressed constraint < prestressed constraint. Sun Juan [ 8 – 10 ] studied the anti-elastic properties of ceramic targets under different constraints, and showed that the anti-penetration performance of ceramics with lateral constraints was improved. Runqiang Chi et al. [ 11 ] used AUTODYN to simulate the impact of long rod projectile ( LRP ) on the prestressed confined ceramic target. The results show that the elastic resistance of the confined SiC target with radial and hydrostatic prestress does not increase monotonously with the increase of radial and axial prestress. There is an optimal value for the prestress value related to the highest level of ballistic performance.Wu et al. [ 12 – 13 ] showed that there is an optimal matching relationship between the magnitude of prestress and its anti-penetration performance. When the prestress exceeds a certain value, the anti-penetration ability of ceramics decreases. Xia [ 14 ] and other studies have shown that the lateral restraint steel ring is subjected to radial pressure caused by ceramic expansion in the early stage of the projectile invading the target plate, delaying the formation of cracks in the ceramic. Based on the research of scholars at home and abroad, adding lateral constraints to ceramics can improve the anti-penetration performance of ceramic-metal composite structures. However, there is a weak protection area at the edge of ceramic units, that is, there is an edge weakening effect [ 15 – 16 ] .While increasing impedance constraints, the anti-penetration performance at ceramic joints has not been studied in depth. In this paper, the influence of different backplanes on the anti-penetration performance of ceramic composite protection is studied by means of experiment and numerical simulation, and the influence of constrained ceramics on weakening the edge weakening effect is verified, which provides support and guidance for optimizing the structure of ceramic units and enhancing the anti-penetration performance of weak areas of splicing ceramic composite protection. 2. Numerical Modeling In order to explore the anti-penetration performance of the ceramic-metal composite structure joints, based on the reliability of the numerical simulation method, the lsdyna finite element software was used to establish a numerical model of 7.62 mm penetrator penetrating different positions of the ceramic-metal composite structure. The relationship between the structural characteristics such as the thickness of the metal layer of the composite structure and the thickness of the UHMWPE back plate and the anti-penetration performance was analyzed by using the characteristic quantities such as the back convex of UHMWPE, the residual velocity of the steel core and the residual mass of the steel core. On this basis, the anti-penetration performance at the ceramic joint was further explored. 2.1. Establishment of geometric model The bullet of 7.62 mm armor-piercing incendiary bullet of 53 type is shown in Fig. 1. The bullet is composed of steel core, bullet shell, lead sleeve, incendiary agent, etc., with a length of 37.88 mm and a diameter of 7.92 mm. The warhead parameter index is shown in Table 1 , and the initial velocity of the warhead is 878 ± 8m / s. Although the mass of the steel core is only half of the total mass of the warhead, the terminal trajectory analysis value of the steel core penetrating the target plate is still close to the test result of the warhead penetrating the armor, and the difference of the ballistic limit is less than 10%. This shows that the contribution of the steel core is the most important in the process of the warhead penetrating the target plate, and the influence of the steel shell, the lead sleeve and the base on the penetration of the warhead is limited. Therefore, the numerical simulation of the projectile is simulated by the steel core [ 17 ] . Table 1 Parameter index of 53 type 7.62mm armor-piercing incendiary bomb [ 18 – 19 ] . Argument Numerical value Argument Numerical value Bullet shell mass /g 2.84 ~ 3.04 Total warhead mass /g 10.18 ~ 10.72 Casing mass /g 1.35 ~ 1.4 Steel core length /mm 27.4 Burner mass /g 0.19 ~ 0.23 Steel core diameter /mm 6.17 Steel core mass /g 0.19 ~ 0.23 In order to reduce the amount of calculation, 1/2 model calculation will be carried out according to the penetration position. The ceramic panel is composed of B 4 C ceramic units with a size of 50×50×6mm, and the mesh size of the ceramic model is controlled at 0.5mm. The aluminum alloy sandwich plate is added between the ceramic panel and the UHMWPE back plate, and the aluminum alloy separator is added in the middle of the ceramic panel. The aluminum alloy sandwich plate is locally densified. The mesh size near the penetration area is 0.5mm, and the mesh size in the remaining area is 1mm.UHMWPE plate is selected as the back plate. For the modeling of the finite element model of UHMWPE plate, considering that the UHMWPE plate is composed of numerous prepregs obtained by unidirectional arrangement and bonding of fibers, and in order to balance the influence of calculation efficiency and calculation accuracy, UHMWPE plate adopts layered modeling. When establishing the numerical model, the thickness of 0.5mm is used for layered modeling. The finite element model of the target plate is shown in Fig. 2 . The parameters of steel core and 5083 aluminum alloy are shown in Table 2 . The Johnson _ Cook constitutive model is used for metal materials [ 20 ] : $${\sigma }=\left(\text{A}+\text{B}{{\epsilon }}^{\text{n}}\right)\left(1+\text{C}{\text{ln}\dot{{\epsilon }}}^{\ast }\right)\left(1-{\text{T}}^{\ast \text{m}}\right)$$ 1 , In the formula : σ is the stress ; A is yield strength ; B is the hardening coefficient ; n is the hardening index ; plastic strain ; C is the strain sensitivity coefficient ; m is the temperature sensitivity coefficient ; \({\dot{{\epsilon }}}^{\ast }=\dot{{\epsilon }}/{\dot{{\epsilon }}}_{0}\) is the equivalent plastic strain rate, \({\dot{{\epsilon }}}_{0}\) take the static test strain rate of 1 * 10-3s-1 ; \({\text{T}}^{\ast }=\left(\text{T}-{\text{T}}_{\text{r}}\right)/\left({\text{T}}_{\text{m}}-{\text{T}}_{\text{r}}\right)\) , T is the ambient temperature of the sample, T m is the melting point of the material, and T r is room temperature. Table 2. Metal material Johnson_Cook model parameters. Material ρ(g/cm3) A(MPa) B(MPa) C m n steel core 7.85 975 810 0.016 1.09 0.27 5083 aluminum alloy 2.7 167 596 0.001 0.859 0.551 As a typical brittle material, ceramics have the characteristics of small failure strain, short failure process time, strong sensitivity to initial material defects, and strong pressure sensitivity. The Johnson _ Holmquist _ ceramic constitutive model, referred to as the JH-2 model, is used. The specific parameters are shown in Table 3. The model takes into account the relationship between the strain, strain rate, pressure and equivalent stress of the material [ 21] : \({{\sigma }}^{\ast }={{\sigma }}_{\text{i}}^{\ast }-\text{D}\left({{\sigma }}_{\text{i}}^{\ast }-{{\sigma }}_{\text{f}}^{\ast }\right)\) , (2) \({{\sigma }}_{\text{i}}^{\ast }=\text{A}{\left({\text{p}}^{\ast }+{\text{T}}^{\ast }\right)}^{\text{N}}\left(1+\text{C}\text{ln}{\dot{{\epsilon }}}^{\ast }\right)\) , (3) \({{\sigma }}_{\text{f}}^{\ast }=\text{B}{\left({\text{p}}^{\ast }\right)}^{\text{M}}\left(1+\text{C}\text{ln}{\dot{{\epsilon }}}^{\ast }\right)\) , (4) \(\text{D}=\sum \varDelta {{\epsilon }}_{\text{p}}/{{\epsilon }}_{\text{p}}^{\text{f}}\) , (5) \({\epsilon }_{p}^{f}={D}_{1}{\left({p}^{\ast }+{T}^{\ast }\right)}^{{D}_{2}}\) , (6) \({p}^{\ast }=p/{p}_{HEL}\) , (7) \({T}^{\ast }=T/{p}_{HEL}\) , (8) \(p={K}_{1}\mu +{K}_{2}{\mu }^{2}+{K}_{3}{\mu }^{3}\) , (9) In the formula : \({{\sigma }}^{\ast }\) is the equivalent stress of the material ; \({{\sigma }}_{\text{i}}^{\ast }\) 、 \({{\sigma }}_{\text{f}}^{\ast }\) are complete equivalent strength and damage equivalent stress, respectively ;D is the material damage factor, \({\text{p}}^{\ast }\) is the equivalent hydrostatic pressure, p is the hydrostatic pressure, and p HEL is the hydrostatic pressure in the HEL state of the material ; \(\varDelta {{\epsilon }}_{\text{p}}\) is the single-step plastic strain, \({{\epsilon }}_{\text{p}}^{\text{f}}\) is the damage plastic strain under hydrostatic pressure p ;A, N, C, B, M, D 1 and D 2 are dimensionless parameters. K 1 is the bulk modulus, K 2 and K 3 are the fitting modulus parameters ; µ is volume strain. Table 3 JH-2 model parameters of B 4 C ceramic [ 21 ] . ρ(g/cm3) G(GPa) K1(GPa) K2(GPa) K3(GPa) HEL(GPa) PHEL(GPa) T(GPa) 2.510 197 233 -593 2800 19 8.71 0.26 A(GPa) B(GPa) C M N D1 D2 β 0.927 0.7 0.005 0.85 0.67 0.001 0.5 1 The back plate of UHMWPE was modeled by COMPOSITE _ FAILURE _ SOLID _ MODEL constitutive model. The model is based on elastic-plastic theory, which is applicable to both shell element and solid element. The stress-based strength criterion is used for solid element simulation, which can simulate transverse and longitudinal tensile compression failure, compression failure along the thickness direction and shear failure along the thickness direction. The specific parameters are shown in Table 4 . Table 4 Model parameters of UHMWPE [ 22 ] . Sign Implication Material parameter ρ(g/cm 3 ) Density 0.97 EA、EB、EC(GPa) Three-dimensional direction elastic modulus 97、93、11.5 PRBA、PRCA、PRCB(GPa) Three-dimensional direction poisson 's ratio 0.006、0.06、0.06 GAB、GBC、GCA(GPa) Three-dimensional direction shear modulus 4.6、5、5 SBA、SCA、SCB(GPa) Three-dimensional direction shear strength 0.5、0.5、0.5 XT、YT、ZT(GPa) Three-dimensional direction tensile strength 3、3、2 XC、YC、ZC(GPa) Three-dimensional direction compressive strength 3、3、2 In the numerical simulation of this paper, ERODING _ SURFACE _ TO _ SURFACE contact is defined between steel core and ceramic panel, aluminum alloy sandwich panel and UHMWPE backplane, and penetration algorithm is defined in contact. The bonding effect between ceramic block and aluminum back plate, aluminum alloy sandwich plate and UHMWPE back plate is simulated by adding AUTOMATIC _ SURFACE _ TO _ SURFACE _ TIEBREAK fixed failure contact between layers to simulate the bonding effect of bonding layer. 2.2. Model validation The projectile used in the test is a 7.62 mm armor-piercing incendiary projectile, which is launched by a 7.62 mm ballistic gun device. The ceramic metal composite target plate is located at 15 m from the muzzle, and its damage effect is observed by penetrating the center of the target plate. Figure 3 is the test results of 6mm ceramic + 3mm aluminum alloy sandwich plate + 8mmUHMWPE. The projectile hits the central area of the ceramic, and the ceramic in the central area is broken and spattered. The projectile and ceramic fragments continue to penetrate the aluminum alloy sandwich plate. When the deformation of the sandwich plate reaches a certain limit, the tensile strain increases sharply, resulting in radial cracks and radial bending deformation, thus forming a petal-shaped breach. The maximum diameter of the breach is 15 mm.The black fracture of UHMWPE back plate is due to the mutual abrasion between the projectile and the ceramic fragments, the aluminum alloy sandwich plate, and the combustion effect of the penetrator. The temperature in the fracture is high, and the UHMWPE fiber is melted and fractured. The back of the UHMWPE back plate presents a conical bulge along the diagonal ridge. At the same time, the edge necking occurs in the middle part of the UHMWPE plate edge, and the necking amount is about 3mm.This is caused by the extreme deformation of the fibers in the center of the UHMWPE plate. The UHMWPE back convex is 15.7mm, and the back convex area is about 110 * 110mm. The numerical simulation model is used to reproduce the anti-penetration process of 6mm ceramic + 3mm aluminum alloy sandwich plate + 8mmUHMWPE. Figure 4 is the damage evolution of ceramics during the whole penetration process. 0 ~ 2 µs. The compressive stress of the contact surface rises rapidly at the moment when the steel core hits the ceramic bullet face. When the ceramic bullet face exceeds the ultimate compressive strength, pits appear on the surface. 2 ~ 8 µs. The steel core continues to impact the ceramic, blunting the tip of the steel core head, and absorbing energy in the process of crushing the ceramic surface to form small and hard fragments. 8 ~ 25 µs. The steel core impacted and plugged the ceramic. After the ceramic formed a penetrating damage, the crack extended to the boundary. Table 5 Scheme 1 ballistic test and numerical simulation data. Scheme Residual mass of steel core The maximum diameter of the break of the sandwich plate UHMWPE back convex Test 3.8g 15mm 15.7mm Simulation 4.17g 11mm 14.9mm Table 5 and Fig.5 are the comparison between experiment and simulation. Fig.9 ( a ) is the comparison of steel core abrasion. The numerical simulation model effectively simulates the morphology of steel core abrasion. The residual mass of the steel core is 3.80 g, and the residual mass of the steel core is 4.17 g, and the error rate is 8.9 %. The experimental results show that the outer edge of the aluminum alloy sandwich plate is a petal-shaped break, and the maximum break diameter is 15 mm. The numerical simulation results show that the maximum break diameter of the aluminum alloy sandwich plate is 11 mm, and the error rate is 26 %. ( c ) For the comparison of UHMWPE backplane, because the thermal effect caused by the combustion of the armor-piercing incendiary bomb is not considered, there is an error between the shape of the bullet hole of the UHMWPE backplane in the numerical simulation and the test. The conical bulge along the diagonal ridge can be well presented. The test results show that the UHMWPE back convex is 15.7mm, the numerical simulation UHMWPE back convex is 14.9mm, and the error rate is 5.1 %. Therefore, the numerical simulation results are close to the experimental results, and the validity of the model is verified. 3. Analysis of anti-penetration ability of ceramic composite target plate at joint 3.1. The failure effect of normal penetration ceramic center On the basis of verifying the reliability of the numerical simulation method, the finite element models of 1mm, 2mm, 3mm aluminum alloy sandwich plate and 8mm, 10mm, 12mm UHMWPE backplane composite target plate against 7.62mm penetrator penetration were established respectively. The anti-elastic properties of ceramic, aluminum alloy sandwich plate and UHMWPE backplane composite structure under different thickness of aluminum alloy sandwich plate and different thickness of UHMWPE backplane were studied. By comparing Fig. 6 and Fig. 7 , the aluminum alloy sandwich plates with different thicknesses provide support for the ceramic back. As the thickness increases, the steel core accelerates more during the penetration process and the kinetic energy decreases faster. The main reason is that the projectile is more resistant to the ceramic panel during the penetration process, the contact time between the ceramic and the projectile increases, and the projectile is fully eroded. At the same time, the metal plate can absorb the projectile energy through compression, shear and bending deformation, thereby improving the anti-penetration ability of the composite structure. Table 6 UHMWPE back convex under different UHMWPE back plate thickness conditions. Thickness of UHMWPE backplane UHMWPE back convex 8mm 14.9mm 10mm 8.8mm 12mm 8.0mm The shear fracture and tensile fracture of UHMWPE backplane are the main failure mechanisms. In the process of projectile penetration, energy is mainly dissipated by friction with fibers, tensile deformation, tensile fracture and other deformation forms. After the abrasion of the ceramic panel and the metal sandwich plate, the residual projectile continues to penetrate the UHMWPE back plate, and the fiber shear fracture dominates the invasion area. This is because the kinetic energy of the projectile is still high, but as the projectile penetration speed decreases, the fiber failure mode gradually changes from shear fracture to tensile fracture. By comparing the influence of UHMWPE backplanes with different thicknesses on the anti-penetration ability of ceramics in Table 6 , the back projection of UHMWPE gradually decreases with the increase of UHMWPE backplane thickness. When the backplane reaches a certain thickness threshold, increasing the backplane thickness cannot significantly improve the anti-penetration performance of the composite structure. 3.2. Damage effect of penetrating ceramic joints Through the above exploration, the optimal scheme is selected as 6mm ceramic + 3mm aluminum alloy sandwich plate + 10mmUHMWPE. On the basis of the optimal scheme, the anti-penetration ability of the joint of the composite target plate is deeply explored. The aluminum alloy partitions of 2mm, 1mm and 0mm are set at the joints. The schematic diagram is shown in Fig. 8 .By simulating the vertical penetration of 7.62mm penetrator into the ceramic joint position, the residual kinetic energy of the projectile, the residual mass of the projectile, the crack extension of the ceramic and the deformation of the back plate are obtained, and the anti-penetration performance of the ceramic joint position is studied. Figure 9 shows the process of steel core penetrating into 2mm aluminum alloy clapboard joints. Ceramic materials have the characteristics of high hardness, low density and high compressive strength. Aluminum alloy materials are softer and lower in strength than ceramics. The compressive strength of ceramic materials is much higher than the impact load generated by projectiles, while the compressive strength of aluminum alloy materials is less than the impact load generated by projectiles. In the pit-opening stage, the steel core is less resistant when it hits the aluminum alloy material, and the steel core head only undergoes small deformation without erosion. In the coarse stage of the pier, the areas on both sides of the steel core head are eroded by ceramics, but the overall kinetic energy is large. Due to the lack of anti-penetration ability at the joint, the residual velocity of the projectile is high, and the penetration of the projectile into the aluminum alloy sandwich plate and UHMWPE is mainly perforation damage. Table 7 Comparison of simulation results under different working conditions. Thickness of aluminum alloy partition UHMWPE back convex Residual speed of steel core Residual mass of steel core 2mm penetration 500m/s 4.72g 1mm 6.4mm 4.00g 0mm 6.2mm 3.98g Comparing the kinetic energy time history curves of steel core under three different working conditions in Fig. 10 and the simulation results under different working conditions in Table 7 , the resistance and erosion of steel core under the working condition of 2mm aluminum alloy baffle are much smaller than those under the other two working conditions, so the kinetic energy attenuation of steel core is much smaller than that under the other two working conditions. The anti-single penetration ability of 1mm aluminum alloy clapboard and 0mm aluminum alloy clapboard is not much different, but the ceramic damage of 0mm aluminum alloy clapboard is more serious after being impacted by steel core, while the ceramic damage of 1mm aluminum alloy clapboard is weakened after the shock wave passes through different wave impedance media of ceramic-metal-ceramic, and the ceramic damage cloud diagram is shown in Fig. 11. 4. Conclusions Based on the experiment of 7.62 mm penetrator penetrating ceramic-metal composite structure, the numerical model of the joint position of 7.62 mm penetrator penetrating ceramic-metal composite structure is established and verified. The anti-penetration performance of the splicing ceramic-metal composite structure is studied, and the relationship between the composite structure and the anti-penetration performance is analyzed. The main conclusions are as follows. (1) The aluminum alloy sandwich plate can provide effective support for the ceramic back. The projectile is more resistant to the ceramic panel during the penetration process. The contact time between the ceramic and the projectile increases, and the projectile is fully eroded. At the same time, the metal plate can absorb the energy of the projectile through compression, shear and bending, thereby improving the ballistic resistance of the overall structure. (2) The anti-penetration performance of the composite structure increases gradually with the increase of the thickness of the UHMWPE backplane. When the thickness of the backplane reaches a certain threshold, the anti-penetration performance of the composite structure cannot be significantly improved by continuously increasing the thickness of the backplane. (3) Adding a certain thickness of the metal partition at the joint can effectively reduce the damage of the ceramic, and there is an optimal range of the metal partition. Declarations Funding: This research was funded by National Defense Basic Research Program of China, grant number JCKY2019209C001 Data Availability The datasets generated and analysed during the current study are not publicly available due but are available from the corresponding author on reasonable request. Conflicts of Interest: The authors declare no conflicts of interest. Author Contribution WuHao wrote the main manuscript text References Wang D.Z.; Qin R M.Experimental and Numerical Simulation Study on Anti-Projectile Penetration Performance of Ceramic /Fiber Composite Armor. Journal of Materials Science 2021, 35 ( 18 ), 18216–18221. Shockey D.A.; Marchand A.H.Failure phenomenology of confined ceramic targets and impacting rods. International Journal of Impact Engineering 1990, 9 ( 3 ), 263–275. Franzen D.L.Penetration of confined silicon carbide targets by tungsten long rods at impact velocities from 1.5 to 4.6 km/s. 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Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBACgxsJQPIAEDMzNz5IqLAhSQtjs8GDM2mkaGFgbJN82HaIGC05ho8rzthE87cztlUksB1g4G/vTsCrxez+G2PDMzfScmccZmy7kcBzh0HizNkN+LXcyN0m2fDhcG4DWIvEMwYDiVyitPzPnQ/UUpBgcJiwFnuwlhsHcjcAtTAkJBChxfJG/mfDhjPJuRsPMzZLJBxI4yHoF4MbaYkPG47Z5c47f/jgx5//bOT423vxa8EAPKQpHwWjYBSMglGAFQAAcWxYGr7gISgAAAAASUVORK5CYII=","orcid":"","institution":"North University of China","correspondingAuthor":true,"prefix":"","firstName":"Hao","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2024-01-17 09:31:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3872452/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3872452/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50795775,"identity":"efb05845-e046-457f-8a9a-c5570cd802eb","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":110205,"visible":true,"origin":"","legend":"\u003cp\u003ewarhead model\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/c25512f69e6cd0c0796e105b.png"},{"id":50795997,"identity":"25c9caa0-89a5-424d-929a-5bfb23bdb2a7","added_by":"auto","created_at":"2024-02-07 12:08:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":132433,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element model of target plate\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/af78ee1db8caf13c01031fcf.png"},{"id":50795781,"identity":"ff5a52e6-abfa-4517-b0e7-04fd32221380","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1465569,"visible":true,"origin":"","legend":"\u003cp\u003eTest results of 6mm ceramic +3mm aluminum alloy sandwich plate +8mmUHMWPE.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/275953977b3b0312fb835732.png"},{"id":50795777,"identity":"4ccc63d5-bf3d-4fed-b055-828b3d9d5df0","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":63802,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 1 Ceramic damage evolution.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/35d2989894978c683267e92b.png"},{"id":50795999,"identity":"0a4fb81b-8893-485a-8afe-9fdae0ff8b51","added_by":"auto","created_at":"2024-02-07 12:08:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":406949,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 1 Ballistic test and numerical simulation.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/1f28698a4719c6b4d3e84841.png"},{"id":50795998,"identity":"49d26201-3393-4bc1-937b-593ac6e758f4","added_by":"auto","created_at":"2024-02-07 12:08:59","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":22668,"visible":true,"origin":"","legend":"\u003cp\u003eThe acceleration time history curve of steel core under different thickness of aluminum alloy sandwich plate.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/7500eab357e8c5764116009b.png"},{"id":50795785,"identity":"a1d30031-5160-4b93-8d2c-6eb737c8dd9a","added_by":"auto","created_at":"2024-02-07 12:01:00","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":13149,"visible":true,"origin":"","legend":"\u003cp\u003eThe kinetic energy time history curve of steel core under different thickness of aluminum alloy sandwich plate.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/a70ecc9d54b7d0146f2f5855.png"},{"id":50795778,"identity":"6feee6a7-924c-4a16-83d1-5f374386581f","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":26106,"visible":true,"origin":"","legend":"\u003cp\u003eA schematic diagram of penetrating the joint of special-shaped ceramics.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/c141d5b34874f137d28f2d00.png"},{"id":50795783,"identity":"3af4c8dc-4720-4b4d-9069-516be2debcaa","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":44398,"visible":true,"origin":"","legend":"\u003cp\u003eThe anti-penetration process of 2mm aluminum alloy clapboard under working condition.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/9f304e3575471cb116bad579.png"},{"id":50795782,"identity":"66e1370f-fde0-442b-b1b1-f50f0775098e","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":13495,"visible":true,"origin":"","legend":"\u003cp\u003eThe kinetic energy time history curve of steel core under three different working conditions.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/4e7ca1768906fb7fc743615f.png"},{"id":50795784,"identity":"58ccf2c5-cb92-4154-be2a-81e85ee06a8b","added_by":"auto","created_at":"2024-02-07 12:00:59","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":121540,"visible":true,"origin":"","legend":"\u003cp\u003eCeramic damage cloud picture.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/49b53fe05ec14575b10fdbc9.png"},{"id":52006595,"identity":"e57e95fd-56c4-4eb3-8e81-65696ab7f3fa","added_by":"auto","created_at":"2024-03-05 09:19:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2515543,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3872452/v1/6e553506-705c-4518-b34d-8083363f80ba.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Penetration resistance of joint joints of constrained ceramic-metal composite structures","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIndividual protective equipment is an important equipment to improve the combat capability and production capacity of soldiers in modern battlefield. The bulletproof insert plate is mainly composed of ceramic, metal and UHMWPE plate. The characteristics of high hardness and high compressive strength of ceramics make the projectile passivated and broken, consuming its energy. The fiber backplane plays a role in supporting the ceramic plate and absorbing the residual kinetic energy of the projectile \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eCeramic constraints are divided into two categories, namely impedance constraints and pressure constraints. The impedance constraint refers to the material with different wave impedances to limit the deformation of the ceramic, and the impedance constraint is formed by the ceramic plate superimposed with the support side plate, the support back plate and the support panel. The pressure constraint refers to the pre-stress applied to the ceramic before penetration.Shockey \u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e, fi.Orphal \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e, Espinosa \u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e and Anderson \u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e used long-rod projectiles to penetrate ceramic materials to measure DOP. The results show that : for ceramic materials with cover plate, side plate and back plate constraints, ceramic fragments cannot be spattered, and the friction between ceramic fragments makes its anti-elastic performance significantly improved.Cao et al. \u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e used DOP test to show that under three conditions, the order of ceramic protection coefficient is unconstrained\u0026thinsp;\u0026lt;\u0026thinsp;prestressed constraint\u0026thinsp;\u0026lt;\u0026thinsp;prestressed constraint. Sun Juan \u003csup\u003e[\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e studied the anti-elastic properties of ceramic targets under different constraints, and showed that the anti-penetration performance of ceramics with lateral constraints was improved. Runqiang Chi et al. \u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e used AUTODYN to simulate the impact of long rod projectile ( LRP ) on the prestressed confined ceramic target. The results show that the elastic resistance of the confined SiC target with radial and hydrostatic prestress does not increase monotonously with the increase of radial and axial prestress. There is an optimal value for the prestress value related to the highest level of ballistic performance.Wu et al. \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e showed that there is an optimal matching relationship between the magnitude of prestress and its anti-penetration performance. When the prestress exceeds a certain value, the anti-penetration ability of ceramics decreases. Xia \u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e and other studies have shown that the lateral restraint steel ring is subjected to radial pressure caused by ceramic expansion in the early stage of the projectile invading the target plate, delaying the formation of cracks in the ceramic. Based on the research of scholars at home and abroad, adding lateral constraints to ceramics can improve the anti-penetration performance of ceramic-metal composite structures. However, there is a weak protection area at the edge of ceramic units, that is, there is an edge weakening effect \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e.While increasing impedance constraints, the anti-penetration performance at ceramic joints has not been studied in depth.\u003c/p\u003e \u003cp\u003eIn this paper, the influence of different backplanes on the anti-penetration performance of ceramic composite protection is studied by means of experiment and numerical simulation, and the influence of constrained ceramics on weakening the edge weakening effect is verified, which provides support and guidance for optimizing the structure of ceramic units and enhancing the anti-penetration performance of weak areas of splicing ceramic composite protection.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"2. Numerical Modeling","content":"\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIn order to explore the anti-penetration performance of the ceramic-metal composite structure joints, based on the reliability of the numerical simulation method, the lsdyna finite element software was used to establish a numerical model of 7.62 mm penetrator penetrating different positions of the ceramic-metal composite structure. The relationship between the structural characteristics such as the thickness of the metal layer of the composite structure and the thickness of the UHMWPE back plate and the anti-penetration performance was analyzed by using the characteristic quantities such as the back convex of UHMWPE, the residual velocity of the steel core and the residual mass of the steel core. On this basis, the anti-penetration performance at the ceramic joint was further explored.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Establishment of geometric model\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe bullet of 7.62 mm armor-piercing incendiary bullet of 53 type is shown in Fig. 1. The bullet is composed of steel core, bullet shell, lead sleeve, incendiary agent, etc., with a length of 37.88 mm and a diameter of 7.92 mm. The warhead parameter index is shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, and the initial velocity of the warhead is 878\u0026thinsp;\u0026plusmn;\u0026thinsp;8m / s. Although the mass of the steel core is only half of the total mass of the warhead, the terminal trajectory analysis value of the steel core penetrating the target plate is still close to the test result of the warhead penetrating the armor, and the difference of the ballistic limit is less than 10%. This shows that the contribution of the steel core is the most important in the process of the warhead penetrating the target plate, and the influence of the steel shell, the lead sleeve and the base on the penetration of the warhead is limited. Therefore, the numerical simulation of the projectile is simulated by the steel core \u003csup\u003e[\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameter index of 53 type 7.62mm armor-piercing incendiary bomb\u003csup\u003e[\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eArgument\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumerical value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eArgument\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumerical value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBullet shell mass /g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.84\u0026thinsp;~\u0026thinsp;3.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal warhead mass /g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.18\u0026thinsp;~\u0026thinsp;10.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCasing mass /g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.35\u0026thinsp;~\u0026thinsp;1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSteel core length /mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBurner mass /g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u0026thinsp;~\u0026thinsp;0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSteel core diameter /mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSteel core mass /g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u0026thinsp;~\u0026thinsp;0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eIn order to reduce the amount of calculation, 1/2 model calculation will be carried out according to the penetration position. The ceramic panel is composed of B\u003csub\u003e4\u003c/sub\u003eC ceramic units with a size of 50\u0026times;50\u0026times;6mm, and the mesh size of the ceramic model is controlled at 0.5mm. The aluminum alloy sandwich plate is added between the ceramic panel and the UHMWPE back plate, and the aluminum alloy separator is added in the middle of the ceramic panel. The aluminum alloy sandwich plate is locally densified. The mesh size near the penetration area is 0.5mm, and the mesh size in the remaining area is 1mm.UHMWPE plate is selected as the back plate. For the modeling of the finite element model of UHMWPE plate, considering that the UHMWPE plate is composed of numerous prepregs obtained by unidirectional arrangement and bonding of fibers, and in order to balance the influence of calculation efficiency and calculation accuracy, UHMWPE plate adopts layered modeling. When establishing the numerical model, the thickness of 0.5mm is used for layered modeling. The finite element model of the target plate is shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThe parameters of steel core and 5083 aluminum alloy are shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. The Johnson _ Cook constitutive model is used for metal materials\u003csup\u003e[\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e :\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${\\sigma }=\\left(\\text{A}+\\text{B}{{\\epsilon }}^{\\text{n}}\\right)\\left(1+\\text{C}{\\text{ln}\\dot{{\\epsilon }}}^{\\ast }\\right)\\left(1-{\\text{T}}^{\\ast \\text{m}}\\right)$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e,\u003cp\u003e\u003c/p\u003e\n \u003cp\u003eIn the formula : \u0026sigma; is the stress ; A is yield strength ; B is the hardening coefficient ; n is the hardening index ; plastic strain ; C is the strain sensitivity coefficient ; m is the temperature sensitivity coefficient ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\dot{{\\epsilon }}}^{\\ast }=\\dot{{\\epsilon }}/{\\dot{{\\epsilon }}}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the equivalent plastic strain rate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\dot{{\\epsilon }}}_{0}\\)\u003c/span\u003e\u003c/span\u003e take the static test strain rate of 1 * 10-3s-1 ; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{T}}^{\\ast }=\\left(\\text{T}-{\\text{T}}_{\\text{r}}\\right)/\\left({\\text{T}}_{\\text{m}}-{\\text{T}}_{\\text{r}}\\right)\\)\u003c/span\u003e\u003c/span\u003e, T is the ambient temperature of the sample, T\u003csub\u003em\u003c/sub\u003e is the melting point of the material, and T\u003csub\u003er\u003c/sub\u003e is room temperature.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e2.\u003c/strong\u003e Metal material Johnson_Cook model parameters.\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\" valign=\"top\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026rho;(g/cm3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003eA(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003eB(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003em\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003en\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\" valign=\"top\"\u003e\n \u003cp\u003esteel core\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\" valign=\"top\"\u003e\n \u003cp\u003e7.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003e975\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003e810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e0.016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e1.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\" valign=\"top\"\u003e\n \u003cp\u003e5083 aluminum alloy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\" valign=\"top\"\u003e\n \u003cp\u003e2.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003e167\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\" valign=\"top\"\u003e\n \u003cp\u003e596\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e0.859\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.34020618556701%\" valign=\"top\"\u003e\n \u003cp\u003e0.551\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003eAs a typical brittle material, ceramics have the characteristics of small failure strain, short failure process time, strong sensitivity to initial material defects, and strong pressure sensitivity. The Johnson _ Holmquist _ ceramic constitutive model, referred to as the JH-2 model, is used. The specific parameters are shown in Table 3. The model takes into account the relationship between the strain, strain rate, pressure and equivalent stress of the material \u003csup\u003e[\u003c/sup\u003e\u003csup\u003e21]\u003c/sup\u003e :\u003c/p\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003c/caption\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tabb\" border=\"1\"\u003e\n \u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}^{\\ast }={{\\sigma }}_{\\text{i}}^{\\ast }-\\text{D}\\left({{\\sigma }}_{\\text{i}}^{\\ast }-{{\\sigma }}_{\\text{f}}^{\\ast }\\right)\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{i}}^{\\ast }=\\text{A}{\\left({\\text{p}}^{\\ast }+{\\text{T}}^{\\ast }\\right)}^{\\text{N}}\\left(1+\\text{C}\\text{ln}{\\dot{{\\epsilon }}}^{\\ast }\\right)\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{f}}^{\\ast }=\\text{B}{\\left({\\text{p}}^{\\ast }\\right)}^{\\text{M}}\\left(1+\\text{C}\\text{ln}{\\dot{{\\epsilon }}}^{\\ast }\\right)\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{D}=\\sum \\varDelta {{\\epsilon }}_{\\text{p}}/{{\\epsilon }}_{\\text{p}}^{\\text{f}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\epsilon }_{p}^{f}={D}_{1}{\\left({p}^{\\ast }+{T}^{\\ast }\\right)}^{{D}_{2}}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}^{\\ast }=p/{p}_{HEL}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(7)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}^{\\ast }=T/{p}_{HEL}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(8)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p={K}_{1}\\mu +{K}_{2}{\\mu }^{2}+{K}_{3}{\\mu }^{3}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIn the formula :\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003eis the equivalent stress of the material ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{i}}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003e、\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{f}}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003eare complete equivalent strength and damage equivalent stress, respectively ;D is the material damage factor, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{p}}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003e is the equivalent hydrostatic pressure, p is the hydrostatic pressure, and p\u003csub\u003eHEL\u003c/sub\u003e is the hydrostatic pressure in the HEL state of the material ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {{\\epsilon }}_{\\text{p}}\\)\u003c/span\u003e\u003c/span\u003e is the single-step plastic strain, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\epsilon }}_{\\text{p}}^{\\text{f}}\\)\u003c/span\u003e\u003c/span\u003e is the damage plastic strain under hydrostatic pressure p ;A, N, C, B, M, D\u003csub\u003e1\u003c/sub\u003e and D\u003csub\u003e2\u003c/sub\u003e are dimensionless parameters. K\u003csub\u003e1\u003c/sub\u003e is the bulk modulus, K\u003csub\u003e2\u003c/sub\u003e and K\u003csub\u003e3\u003c/sub\u003e are the fitting modulus parameters ; \u0026micro; is volume strain.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eJH-2 model parameters of B\u003csub\u003e4\u003c/sub\u003eC ceramic\u003csup\u003e[\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026rho;(g/cm3)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eG(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK1(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK2(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK3(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eHEL(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePHEL(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eT(GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.510\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e197\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eB(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eD1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eD2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026beta;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.927\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThe back plate of UHMWPE was modeled by COMPOSITE _ FAILURE _ SOLID _ MODEL constitutive model. The model is based on elastic-plastic theory, which is applicable to both shell element and solid element. The stress-based strength criterion is used for solid element simulation, which can simulate transverse and longitudinal tensile compression failure, compression failure along the thickness direction and shear failure along the thickness direction. The specific parameters are shown in Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eModel parameters of UHMWPE\u003csup\u003e[\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSign\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eImplication\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial parameter\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026rho;(g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDensity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEA、EB、EC(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction elastic modulus\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97、93、11.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePRBA、PRCA、PRCB(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction poisson \u0026apos;s ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.006、0.06、0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGAB、GBC、GCA(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction shear modulus\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.6、5、5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSBA、SCA、SCB(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction shear strength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5、0.5、0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eXT、YT、ZT(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction tensile strength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3、3、2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eXC、YC、ZC(GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree-dimensional direction compressive strength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3、3、2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIn the numerical simulation of this paper, ERODING _ SURFACE _ TO _ SURFACE contact is defined between steel core and ceramic panel, aluminum alloy sandwich panel and UHMWPE backplane, and penetration algorithm is defined in contact. The bonding effect between ceramic block and aluminum back plate, aluminum alloy sandwich plate and UHMWPE back plate is simulated by adding AUTOMATIC _ SURFACE _ TO _ SURFACE _ TIEBREAK fixed failure contact between layers to simulate the bonding effect of bonding layer.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Model validation\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe projectile used in the test is a 7.62 mm armor-piercing incendiary projectile, which is launched by a 7.62 mm ballistic gun device. The ceramic metal composite target plate is located at 15 m from the muzzle, and its damage effect is observed by penetrating the center of the target plate. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e is the test results of 6mm ceramic\u0026thinsp;+\u0026thinsp;3mm aluminum alloy sandwich plate\u0026thinsp;+\u0026thinsp;8mmUHMWPE. The projectile hits the central area of the ceramic, and the ceramic in the central area is broken and spattered. The projectile and ceramic fragments continue to penetrate the aluminum alloy sandwich plate. When the deformation of the sandwich plate reaches a certain limit, the tensile strain increases sharply, resulting in radial cracks and radial bending deformation, thus forming a petal-shaped breach. The maximum diameter of the breach is 15 mm.The black fracture of UHMWPE back plate is due to the mutual abrasion between the projectile and the ceramic fragments, the aluminum alloy sandwich plate, and the combustion effect of the penetrator. The temperature in the fracture is high, and the UHMWPE fiber is melted and fractured. The back of the UHMWPE back plate presents a conical bulge along the diagonal ridge. At the same time, the edge necking occurs in the middle part of the UHMWPE plate edge, and the necking amount is about 3mm.This is caused by the extreme deformation of the fibers in the center of the UHMWPE plate. The UHMWPE back convex is 15.7mm, and the back convex area is about 110 * 110mm.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThe numerical simulation model is used to reproduce the anti-penetration process of 6mm ceramic\u0026thinsp;+\u0026thinsp;3mm aluminum alloy sandwich plate\u0026thinsp;+\u0026thinsp;8mmUHMWPE. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e is the damage evolution of ceramics during the whole penetration process. 0\u0026thinsp;~\u0026thinsp;2 \u0026micro;s. The compressive stress of the contact surface rises rapidly at the moment when the steel core hits the ceramic bullet face. When the ceramic bullet face exceeds the ultimate compressive strength, pits appear on the surface. 2\u0026thinsp;~\u0026thinsp;8 \u0026micro;s. The steel core continues to impact the ceramic, blunting the tip of the steel core head, and absorbing energy in the process of crushing the ceramic surface to form small and hard fragments. 8\u0026thinsp;~\u0026thinsp;25 \u0026micro;s. The steel core impacted and plugged the ceramic. After the ceramic formed a penetrating damage, the crack extended to the boundary.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eScheme 1 ballistic test and numerical simulation data.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eScheme\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eResidual mass of steel core\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThe maximum diameter of the break of the sandwich plate\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eUHMWPE back convex\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.8g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.7mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimulation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.17g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.9mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable 5 and Fig.5 are the comparison between experiment and simulation. Fig.9 ( a ) is the comparison of steel core abrasion. The numerical simulation model effectively simulates the morphology of steel core abrasion. The residual mass of the steel core is 3.80 g, and the residual mass of the steel core is 4.17 g, and the error rate is 8.9 %. The experimental results show that the outer edge of the aluminum alloy sandwich plate is a petal-shaped break, and the maximum break diameter is 15 mm. The numerical simulation results show that the maximum break diameter of the aluminum alloy sandwich plate is 11 mm, and the error rate is 26 %. ( c ) For the comparison of UHMWPE backplane, because the thermal effect caused by the combustion of the armor-piercing incendiary bomb is not considered, there is an error between the shape of the bullet hole of the UHMWPE backplane in the numerical simulation and the test. The conical bulge along the diagonal ridge can be well presented. The test results show that the UHMWPE back convex is 15.7mm, the numerical simulation UHMWPE back convex is 14.9mm, and the error rate is 5.1 %. Therefore, the numerical simulation results are close to the experimental results, and the validity of the model is verified.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Analysis of anti-penetration ability of ceramic composite target plate at joint","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. The failure effect of normal penetration ceramic center\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eOn the basis of verifying the reliability of the numerical simulation method, the finite element models of 1mm, 2mm, 3mm aluminum alloy sandwich plate and 8mm, 10mm, 12mm UHMWPE backplane composite target plate against 7.62mm penetrator penetration were established respectively. The anti-elastic properties of ceramic, aluminum alloy sandwich plate and UHMWPE backplane composite structure under different thickness of aluminum alloy sandwich plate and different thickness of UHMWPE backplane were studied.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eBy comparing Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, the aluminum alloy sandwich plates with different thicknesses provide support for the ceramic back. As the thickness increases, the steel core accelerates more during the penetration process and the kinetic energy decreases faster. The main reason is that the projectile is more resistant to the ceramic panel during the penetration process, the contact time between the ceramic and the projectile increases, and the projectile is fully eroded. At the same time, the metal plate can absorb the projectile energy through compression, shear and bending deformation, thereby improving the anti-penetration ability of the composite structure.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eUHMWPE back convex under different UHMWPE back plate thickness conditions.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThickness of UHMWPE backplane\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eUHMWPE back convex\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.9mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.8mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.0mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThe shear fracture and tensile fracture of UHMWPE backplane are the main failure mechanisms. In the process of projectile penetration, energy is mainly dissipated by friction with fibers, tensile deformation, tensile fracture and other deformation forms. After the abrasion of the ceramic panel and the metal sandwich plate, the residual projectile continues to penetrate the UHMWPE back plate, and the fiber shear fracture dominates the invasion area. This is because the kinetic energy of the projectile is still high, but as the projectile penetration speed decreases, the fiber failure mode gradually changes from shear fracture to tensile fracture. By comparing the influence of UHMWPE backplanes with different thicknesses on the anti-penetration ability of ceramics in Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the back projection of UHMWPE gradually decreases with the increase of UHMWPE backplane thickness. When the backplane reaches a certain thickness threshold, increasing the backplane thickness cannot significantly improve the anti-penetration performance of the composite structure.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Damage effect of penetrating ceramic joints\u003c/h2\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThrough the above exploration, the optimal scheme is selected as 6mm ceramic\u0026thinsp;+\u0026thinsp;3mm aluminum alloy sandwich plate\u0026thinsp;+\u0026thinsp;10mmUHMWPE. On the basis of the optimal scheme, the anti-penetration ability of the joint of the composite target plate is deeply explored. The aluminum alloy partitions of 2mm, 1mm and 0mm are set at the joints. The schematic diagram is shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e.By simulating the vertical penetration of 7.62mm penetrator into the ceramic joint position, the residual kinetic energy of the projectile, the residual mass of the projectile, the crack extension of the ceramic and the deformation of the back plate are obtained, and the anti-penetration performance of the ceramic joint position is studied.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e shows the process of steel core penetrating into 2mm aluminum alloy clapboard joints. Ceramic materials have the characteristics of high hardness, low density and high compressive strength. Aluminum alloy materials are softer and lower in strength than ceramics. The compressive strength of ceramic materials is much higher than the impact load generated by projectiles, while the compressive strength of aluminum alloy materials is less than the impact load generated by projectiles. In the pit-opening stage, the steel core is less resistant when it hits the aluminum alloy material, and the steel core head only undergoes small deformation without erosion. In the coarse stage of the pier, the areas on both sides of the steel core head are eroded by ceramics, but the overall kinetic energy is large. Due to the lack of anti-penetration ability at the joint, the residual velocity of the projectile is high, and the penetration of the projectile into the aluminum alloy sandwich plate and UHMWPE is mainly perforation damage.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab8\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparison of simulation results under different working conditions.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThickness of aluminum alloy partition\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eUHMWPE back convex\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eResidual speed of steel core\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eResidual mass of steel core\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epenetration\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e500m/s\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.72g\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.00g\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.2mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.98g\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eComparing the kinetic energy time history curves of steel core under three different working conditions in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e and the simulation results under different working conditions in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, the resistance and erosion of steel core under the working condition of 2mm aluminum alloy baffle are much smaller than those under the other two working conditions, so the kinetic energy attenuation of steel core is much smaller than that under the other two working conditions. The anti-single penetration ability of 1mm aluminum alloy clapboard and 0mm aluminum alloy clapboard is not much different, but the ceramic damage of 0mm aluminum alloy clapboard is more serious after being impacted by steel core, while the ceramic damage of 1mm aluminum alloy clapboard is weakened after the shock wave passes through different wave impedance media of ceramic-metal-ceramic, and the ceramic damage cloud diagram is shown in Fig. 11.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eBased on the experiment of 7.62 mm penetrator penetrating ceramic-metal composite structure, the numerical model of the joint position of 7.62 mm penetrator penetrating ceramic-metal composite structure is established and verified. The anti-penetration performance of the splicing ceramic-metal composite structure is studied, and the relationship between the composite structure and the anti-penetration performance is analyzed. The main conclusions are as follows.\u003c/p\u003e \u003cp\u003e(1) The aluminum alloy sandwich plate can provide effective support for the ceramic back. The projectile is more resistant to the ceramic panel during the penetration process. The contact time between the ceramic and the projectile increases, and the projectile is fully eroded. At the same time, the metal plate can absorb the energy of the projectile through compression, shear and bending, thereby improving the ballistic resistance of the overall structure.\u003c/p\u003e \u003cp\u003e(2) The anti-penetration performance of the composite structure increases gradually with the increase of the thickness of the UHMWPE backplane. When the thickness of the backplane reaches a certain threshold, the anti-penetration performance of the composite structure cannot be significantly improved by continuously increasing the thickness of the backplane.\u003c/p\u003e \u003cp\u003e(3) Adding a certain thickness of the metal partition at the joint can effectively reduce the damage of the ceramic, and there is an optimal range of the metal partition.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e This research was funded by National Defense Basic Research Program of China, grant number JCKY2019209C001\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated and analysed during the current study are not publicly available due \u0026nbsp; but are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eWuHao wrote the main manuscript text\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang D.Z.; Qin R M.Experimental and Numerical Simulation Study on Anti-Projectile Penetration Performance of Ceramic /Fiber Composite Armor. 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Ceramics International 2020, \u003cem\u003e46\u003c/em\u003e(\u003cem\u003e15\u003c/em\u003e), 23760\u0026ndash;23772\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBao K.Experimental and numerical simulation study of Projectile Impact on boron Carbide ceramic composite target. Explosion and Shock Waves 2019, \u003cem\u003e39\u003c/em\u003e(\u003cem\u003e12\u003c/em\u003e), 57\u0026ndash;68\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSun X.; Zhang L.H.Effect of panel on penetration resistance of ceramic composite protective structure. Armored forces journal 2023, \u003cem\u003e2\u003c/em\u003e(\u003cem\u003e02\u003c/em\u003e), 89\u0026ndash;94\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"ceramics, anti-penetration performance, aluminium alloy sandwich plate, UHMWPE","lastPublishedDoi":"10.21203/rs.3.rs-3872452/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3872452/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAiming at the problems of edge weakening effect and gap defects in ceramic metal composite structure, the anti-penetration performance of ceramic metal composite structure was studied. Based on the experimental study of ceramic metal composite structure against 7.62 mm armor-piercing incendiary projectile penetration, the numerical model of ceramic metal composite structure against penetration was established. According to the experimental results, the reliability of the numerical simulation method was verified, and the anti-penetration performance at the ceramic joint was analyzed. The results show that the aluminum alloy sandwich plate can provide effective support for the ceramic. With the increase of the thickness of the aluminum alloy sandwich plate, the anti-penetration performance of the composite structure is improved. The anti-penetration performance of the composite structure increases with the increase of the thickness of the UHMWPE backplane. When the backplane reaches a certain thickness threshold, increasing the thickness of the backplane cannot significantly improve the anti-penetration performance of the composite structure. Adding a certain thickness of metal separator at the joint can effectively reduce the damage of ceramics.\u003c/p\u003e","manuscriptTitle":"Penetration resistance of joint joints of constrained ceramic-metal composite structures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-07 12:00:54","doi":"10.21203/rs.3.rs-3872452/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8e00e767-23c9-4c7a-8687-5286cc8f3010","owner":[],"postedDate":"February 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":28568039,"name":"Physical sciences/Engineering"},{"id":28568040,"name":"Physical sciences/Engineering/Mechanical engineering"}],"tags":[],"updatedAt":"2024-03-05T09:19:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-07 12:00:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3872452","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3872452","identity":"rs-3872452","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}