Numerical study on the optimized thickness of layer configuration against the 7.62 APM2 projectile

Numerical study on the optimized thickness of layer configuration against the 7.62 APM2 projectile Divyanshu S. Morghode 1 , D. G. Thakur 1 *, Sachin Salunkhe 2 , 3 , Lenka Cepova 4 and Emad Abouel Nasr 5 1 Department of Mechanical Engineering, Defense Institute of Advanced Technology, Pune, India, 2 Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India, 3 Department of Mechanical Engineering, Gazi University Faculty of Engineering, Ankara, Türkiye, 4 Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB—Technical University of Ostrava, Ostrava, Czechia, 5 Department of Industrial Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia This study aimed to select suitable materials and optimize the thickness of these materials so that they could prevent the perforation of 7.62-mm AP bullets at 830 m/s impact velocity. A numerical method is used to analyze the impact on layered configurations of Al 2 O 3 and Al 7075-T651 to fulfill this aim. In order to optimize the thickness of the armor, normal impact and angular impact conditions were considered. Initially, a 20-mm Al 2 O 3 front plate with a 20mm Al 7075-T651 back plate is analyzed for layered configuration. Back plate thickness is reduced in steps to 10 mm such that no plastic deformation is observed on the rear side of the target. For further optimization of weight, the thickness of the Al 2 O 3 plate is reduced to 18 mm. The weight of this configuration is 1.77 kg, and the areal density is 97.22 kg/m2. This configuration is analyzed for target orientations such as 80°,70 °, and 60°. In this analysis, the projectile deformed in a mushroom shape for 90°and 80°target orientations, while for 70°and 60°target orientations, the projectile experienced more damage on the shank part. The most effective configuration with the highest degree of ballistic performance is a layered combination of the 18-mm Al 2 O 3 front plate and 10-mm Al 7075-T651 back plate at 70°target orientation. KEYWORDS 7.62 AP projectiles, Al 2 O 3 , Al 7075-T651, layered configuration, normal and oblique impact, thickness optimization 1 Introduction Security forces must operate in highly dangerous areas where terrorist attacks are always unavoidable. Ideally, security forces must have only bulletproof vehicles in such high-risk areas to provide necessary protection from such attacks. However, due to a lack of resources, it is not possible to have bulletproof vehicles in such large numbers. Hence, non-bulletproof vehicles are used for the routine movement of troops. However, such vehicles are vulnerable to attacks and cannot provide the required protection to the troops. So, the only solution available is to convert a non-bulletproof vehicle into a bulletproof vehicle using add-on armor. However, add-on armor increases the weight of the vehicle. Hence, materials used for the add-on armor need to be carefully selected, considering their density and optimizing their thickness to minimize the effect of their weight on the vehicle. So, the question that needs to be answered is “which materials and of what thickness, when fixed on ordinary OPEN ACCESS EDITED BY Mohamed A. Eltaher, King Abdulaziz University, Saudi Arabia REVIEWED BY Kadir Gunaydin, General Electric, United States Chang Yan, Xi’an University of Technology, China *CORRESPONDENCE D. G. Thakur, [email protected] RECEIVED 16 October 2023 ACCEPTED 18 March 2024 PUBLISHED 04 April 2024 CITATION Morghode DS, Thakur DG, Salunkhe S, Cepova L and Abouel Nasr E (2024), Numerical study on the optimized thickness of layer configuration against the 7.62 APM2 projectile. Front. Mech. Eng 10:1322640. doi: 10.3389/fmech.2024.1322640 COPYRIGHT © 2024 Morghode, Thakur, Salunkhe, Cepova and Abouel Nasr. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Mechanical Engineering frontiersin.org01 TYPE Original Research PUBLISHED 04 April 2024 DOI 10.3389/fmech.2024.1322640 vehicles, will provide protection against 7.62-mm APM2 bullets and make the vehicle bulletproof?”. Previous studies reveal that under the effect of high-velocity impact, materials show non-linear and dynamic behavior, including thermal softening, fracture, and strain rate hardening for metal (Forrestal et al., 1992;Forrestal and Warren, 2008;2009;Børvik et al., 2009;2010;Pedersen et al., 2011;Holmen et al., 2017), concrete (Rajput et al., 2017;2018;Rajput and Iqbal, 2017), and ceramic (Den, 1991;Fellows and Barton, 1999) targets. The finite element analysis of bullets’impact on various types of armor is done using explicit dynamic FE analysis. During such an analysis, different contact algorithms and material models are used. Flores-Johnson et al. (2011) performed numerical impact simulations on single-layer and multilayer configurations of steel and aluminum using a 7.62-mm AP bullet with an impact velocity of 770–950 m/s. LSDYNA software was used. The results show that multi-layered plates with different materials show greater resistance at the same area density. Rahman et al. (2016) conducted similar simulations using high-strength steel and Al 7075-T6 as targets, in which they studied the ballistic limit, the process of penetration, and deformation. The results showed that the triple-layered configuration achieves maximum weight reduction without compromising performance. Ceramic materials are widely used as armor materials because of their excellent ballistic resistance properties. Den (1991) studied that the projectile’s behavior during impact, identifying three phases: erosion of mass, mushrooming, and rigidity. Fellows and Barton (1999) developed impact models for semi-finite ceramic targets. Anderson and Walker (2005) presented the dwell phenomenon model for projectile impact on ceramic targets. An appropriate material model for steel core bullets, Al 2024-T351, and Al 2 O 3 was given by Turhan et al. (2008), in which the plastic kinematic hardening model was used for steel core projectiles and Al 2024T351, and the Johnson–Holmquist model was used for Al 2 O 3 . López-Puente et al. (2005) presented the optimum thickness of the toughened epoxy resin adhesive layer for alumina–aluminum armors. Mazaheri et al. (2017) studied the effect on ballistic limit velocity and energy absorption after wrapping Al foil on the impact face of Al 2 O 3 tiles. The study shows a 13% increase in ballistic limit velocity and an 11% increase in energy absorption with just a 2.4% increase in weight. Gálvez et al. (2005) Pranay and Panigrahi (2022a),Pranay and Panigrahi (2022b), and Pranay and Panigrahi (2022c) conducted a numerical study for the development of projectiles and attempted effective penetration of targets using ANSYS Explicit Dynamics/AUTODYN software. In Gálvez et al. (2005) , the effect of projectile tumbling has been studied for ceramic and aluminum armor. Wei and Zhang (2014) experimentally studied the projectile deformation modes for softcore and hard-core projectiles impacting ceramic targets at different impact velocities. In previous studies, different investigators have studied different parameters involved in the ballistic impact of the bullet on the target: residual velocity post-impact, the velocity of the ballistic limit, the pattern of perforation, mechanisms of fracture, etc. Furthermore, various materials that can be used as armor, along with different combinations and configurations of these materials, were highlighted in previous studies. From the literature review, it was observed that very few studies have been conducted on the optimization of armor plate thickness for proposing thickness for armor fabrication against 7.62-mm APM2 projectiles. Most of the work on ballistic impact in the open literature deals with metallic and non-metallic target materials with relatively low thicknesses and projectiles moving with sub-ordnance velocities. The penetration of multi-layered armor plates is a complex problem. In order to design protective structures, thickness and layer configurations are factors that must be considered carefully to ensure no penetration. It must also be ensured that no debris is projected to the rear of the armor and that there is no panel deflection. Thus, a systematic study remains needed to optimize the strength-to-weight ratio of armor materials while protecting against 7.62-mm APM2 bullets. The purpose of this study was to select suitable materials in the layered configuration with an optimized thickness of each layer such that they can be used as add-on armor on the body of a vehicle. The considered materials are Al 2 O 3 and Al 7075-T651. Al 2 O 3 material has characteristics of high strength and low density, while Al 7075T651 has characteristics of high strength and high ductility. Therefore, Al 2 O 3 is considered the front plate so that it can absorb the initial impact energy, undergo brittle fracture, and cause high projectile deformation. Al 7075-T651 is considered the back plate so that it can absorb the residual energy from the impact and fragments of Al 2 O 3 created due to its fracture. Most of the layered configuration studies do not consist of specific thicknesses of add-on armor for protection against projectiles. So, in this study, the optimum thickness is considered based on two criteria: first, the armor must successfully stop the projectile, and second, there must be no plastic deformation on the rear surface of the armor. This work presents a numerical study of the impact on the layered combination of Al 2 O 3 and Al 7075-T651 by a 7.62-mm APM2 bullet fired at 830 m/s. Furthermore, to optimize the thickness of the armor, normal impact and angular impact conditions were considered. The following sections explain in detail the numerical approach followed by the results observed. 2 Research methodology Initially, residual velocity is computed by numerical simulations while considering the normal impact at a given impact velocity on an Al 7075-T651 plate having a 20 mm thickness. The model is validated using the experiment results from the literature (Forrestal et al., 2010). A validated model is extended to study the layered armor consisting of Al 7075-T651 and Al 2 O 3 at normal and oblique impact conditions. Figure 1 represents a detailed research methodology flow chart. 2.1 Finite element modeling 2.1.1 Projectile Most researchers working with standard NATO ammunition use 7.62-mm steel-core bullets to analyze various target material impacts (Flores-Johnson et al., 2011). These bullets consist of an inner steel core and a protective outer jacket. This jacket is generally made of brass and is used to engage with the barrel’s lands so that Frontiers in Mechanical Engineering frontiersin.org02 Morghode et al. 10.3389/fmech.2024.1322640 spin can be provided to the bullet during its travel inside the barrel. However, this brass jacket does not affect the collision between the target material and bullet (Chen et al., 2013). Therefore, the jacket is not considered during the simulations to reduce the time required for computation. Senthil and Iqbal (2021) also used only the steel core, as shown in Figure 2, and compared the results with experimental data obtained using a projectile. The results matched the experiment results (Senthil and Iqbal, 2021). SolidWorks was used to design the bullet, and the design was imported into LS-DYNA for simulations. 2.1.2 Target LS-DYNA software was used for designing a model of the target. The target was designed as a circular plate with a diameter FIGURE 1 Research methodology flow chart. FIGURE 2 7.62-mm AP projectile (all dimensions are in mm) (Senthil and Iqbal, 2021). Frontiers in Mechanical Engineering frontiersin.org03 Morghode et al. 10.3389/fmech.2024.1322640 of 152 mm. This circular plate was further segregated into three regions. The impact region at the center of the circular target was designed as a square with each side measuring 10 mm. The second and third regions are circular and designed to have 30 mm and 50 mm diameters, respectively. Figure 3 shows the dimensions of the circular plate used as the target. FIGURE 3 Target discretizations. FIGURE 4 Mesh (A) projectile and (B) target. Frontiers in Mechanical Engineering frontiersin.org04 Morghode et al. 10.3389/fmech.2024.1322640 2.1.3 Meshing It is well-known that the most accurate results are obtained when two conditions are satisfied: first, when the density of the mesh and number of elements are higher, and second, when elements are closest to the system’s boundary. To cover the maximum volume and curvature of the bullet and target plate, hexahedral solid elements with eight nodes, reduced integration, and the Hourglass effect’s stiffness control are used for meshing. The meshing of the bullet was done in ABAQUS, and the meshing of the target plate was done in LS DYNA. The duplicate nodes were either removed or merged, depending on their dimensions. A comprehensive mesh convergence study was conducted to minimize the computation time and select the optimized element size for the projectile and impact region of the target. The results obtained by changing the element size were compared with results given in the literature (Forrestal et al., 2010). It was concluded that the size of elements in thesquareregionatthecenterofthetargetplatewouldbe 0.25 mm. Similarly, the size of the elements in the circular portion, having diameters of 30 and 50 mm, will be 0.5 and 1 mm, respectively. The size of an element beyond 50 mm in diameter will be 2 mm. Figure 4 represents the final mesh of the bullet and target plate. 2.2 Constitutive material models 2.2.1 Strength model by Johnson–Cook The strength model given by Johnson and Cook (1983) and Johnson and Cook (1985) defines the behavior of the strength of materials subjected to impact with high velocities. The model gives yield stress, i.e., Y, as a function of strain hardening, strain rate hardening, and temperature softening, and the equation for the same is shown below. YA+Bεn p  1+Clogε* p  1−Tm H  ,(1) where ε p is the effective plastic strain, ε p * is the normalized effective plastic strain rate, and T H is the homologous temperature [T H =(T–T room )/(T melt –T room )]. A, B, C, n, and m are material constants. The first bracket in Eq. 1 gives stress as the function of strain, which is determined by quasi-static tensile testing (ε p p =1.0sec −1 and T H =0).Aistheyieldstressatlower values of strains; B and n define strain hardening. The other two brackets represent the effects of hardening due to the strain rate and softening due to temperature. With softening due to thermal effects, yield strength is reduced to zero at melting temperatures T melt . The constants of materials are determined using the dynamic tensile test using a split Hopkinson Bar over a wide range of strain rates and temperatures. TABLE 1 Material property of Al 7075-T651 and bullet. Parameter Unit Al 7075-T651 (Jørgensen K. C. and Swan V., 2014) Bullet (Senthil and Iqbal, 2021) Young’s modulus E GPa 71.7 202 Poisson’s ratio υ0.33 0.32 Density ρkg m32810 7,850 Johnson–Cook strength model Yield strength A MPa 520 2,700 Strain hardening parameter B MPa 477 211 Strain hardening parameter n - 0.52 0.065 References strain rate _ ϵ0s−15e-4 1e-4 Strain rate constant C - 0.0025 0.005 References temperature K 293 293 Melting temperature K 893 1,800 Thermal softening parameter m - 1.61 1.17 Specific heat capacity CPJ kg.K910 452 Thermal expansion coefficient α1/K 2.3e-5 1.2e-5 Johnson Cook failure model Failure parameter D10.096 0.4 Failure parameter D20.049 0 Failure parameter D33.465 0 Failure parameter D40.016 0 Failure parameter D51.099 0 Frontiers in Mechanical Engineering frontiersin.org05 Morghode et al. 10.3389/fmech.2024.1322640 2.2.2 Johnson–Cook failure model The failure model given by Johnson–Cook was used to model material failures. Similarly, in the previous model, fracture strain, a material property, is given as an explicit function of temperature, strain rate, and pressure. The equation for the same is given as Eq. 2. εfD1+D2exp D3σ*  1+D4ln ε* () 1+D5TH  .(2) The dimensionless ratio of pressure and stress is represented as σ*= σ m /σ,whereσ m is primary stress, (σ 1 +σ 2 +σ 3 )/3, and σis effective stress or Von Mises stress (3J 2 ), where J 2 is the second invariant of the stress deviator. Dimensionless strain rate ε p is ε/ε 0 ,whereε 0 is the unit strain rate. T H is the homologous temperature, produced by internal heating. D 1 ,D 2 ,D 3 ,D 4 ,andD 5 are parameters of the model of fracture, and these can be obtained from experiments done in the laboratory. TABLE 2 Material properties for Al 2 O 3 (Zochowski et al., 2021). Parameter Unit Al 2 O 3 Density ρg/cm 3 3.84 Shear modulus G GPa 93 Intact strength coefficient A - 0.93 Fractured strength coefficient B - 0.31 Strain rate constant C - 0.007 Fracture strength exponent M - 0.6 Intact strength exponent N - 0.64 EPSI - 1 Max tensile hydrostatic pressure MPa 262 SFMAX - 1 Hugoniot elastic limit (HEL) MPa 8,000 Pressure at HEL MPa 1,460 Bulking factor β-1 Damage coefficient D 1 0.01 Damage coefficient D 2 0.7 Pressure constant K 1 GPa 131 Pressure constant K 2 GPa 0 Pressure constant K 3 GPa 0 *MAT_ADD_EROSION VOLEPS 0.05 FIGURE 5 Assembly and boundary conditions of the model. TABLE 3 Residual velocity with variation in the number of elements. No. of elements Residual velocity (m/s) 25 476.88 33 545.36 40 570.87 50 583 60 585.9 80 584.4 100 584.7 Frontiers in Mechanical Engineering frontiersin.org06 Morghode et al. 10.3389/fmech.2024.1322640 Changes occurring while loading are depicted in the Johnson–Cook model using the concept of linear summation. This model calculates changes in failure strain using the stress state, temperature, strain rate, and damage accumulated during loading. However, this model does not account for the degradation of the strength of the material or stiffness. When the critical value of damage is reached, the values of pressure and stress are abruptly reduced to zero. For this reason, it is said to be an instantaneous failure model. Damage is computed as the cumulative value, as given in Eq. 3, and failure is fixed at a critical value, which is generally taken as 1. Dε εf,(3) where εis the equivalent plastic strain increment that occurs during tensile loading and ε f is the equivalent strain to fracture corresponding to instantaneous conditions during the accumulation of the increment of strain. FIGURE 6 Depth of penetration for 50-mm Al 7075-T651 at an impact velocity of 830 m/s. FIGURE 7 Impact simulations on an independent Al 2 O 3 plate. Frontiers in Mechanical Engineering frontiersin.org07 Morghode et al. 10.3389/fmech.2024.1322640 2.2.3 Johnson–Holmquist model The Johnson–Holmquist model (Johnson and Holmquist, 1994), having an equation of state, model of strength, and model of damage, was used to define the behavior of Al 2 O 3. Polynomial equation-of-state (EOS) calculated the current value of pressure as a function of volumetric change, the model of strength gave equivalent strength for undamaged and damaged material, and the model of damage was used to show the transition of material from undamaged to damaged states. Normalized equivalent stress is defined as follows: σ*σi*−Dσi*−σf* () ,(4) where σ i * is the normalized intact equivalent stress, σ f * is the normalized fracture stress, and D is damage (0 ≤D≤1). FIGURE 8 Impact on the layered configuration of the 20-mm-thick Al 2 O 3 front plate and 20-mm-thick Al 7075-T651 back plate. FIGURE 9 Impact on the 20-mm-thick Al 2 O 3 front plate and 10-mm-thick Al 7075-T651 back plate. Frontiers in Mechanical Engineering frontiersin.org08 Morghode et al. 10.3389/fmech.2024.1322640 Normalized intact equivalent stress is shown in Eq. 5, and normalized fractured equivalent stress is shown in Eq. 6. σi*AP*+T* () N1+Clnε* () ,(5) σf*BP* () M1+Clnε* () ,(6) where A, B, C, M, and N are constants of material and normalized pressure. P* = P/P HEL , where P is the actual pressure and P HEL is the pressure at the Hugoniot elastic limit (HEL). The HEL is the net compressive stress corresponding to uniaxial strain (shock wave) exceeding the elastic limit of the material. Normalized maximum tensile hydrostatic pressure is represented as T* = T/P HEL , where T is the maximum tensile hydrostatic pressure that material can withstand, and the dimensionless strain rate is ε*=ε/ε 0 , where ε is the actual equivalent strain rate and ε 0 is the reference strain rate considered to be 1 s -1 . FIGURE 10 Impact on the 18-mm-thick Al 2 O 3 front plate and 10-mm-thick Al 7075-T651 back plate. FIGURE 11 Impact on 80°target orientation. Frontiers in Mechanical Engineering frontiersin.org09 Morghode et al. 10.3389/fmech.2024.1322640 Rajput, A., and Iqbal, M. A. (2017). Impact behavior of plain, reinforced and prestressed concrete targets. Mater. Des. 114, 459–474. doi:10.1016/j.matdes.2016. 10.073 Rajput, A., Iqbal, M. A., and Bhargava, P. (2017). Experimental and numerical study of concrete targets under high rate of loading. Procedia Eng. 173, 130–137. doi:10.1016/j. proeng.2016.12.049 Rajput, A., Iqbal, M. A., and Wu, C. (2018). 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