Abstract
The projectile impact resistance of sandwich panels with cellular cores with different layer numbers has been numerically investigated by perpendicular impact of rigid blunt projectile in ABAQUS/Explicit. These panels with corrugation, hexagonal honeycomb and pyramidal truss cores are impacted at velocities between 50 m/s and 202 m/s while the relative density ranges from 0.001 to 0.15 The effects of core configuration and layer number on projectile impact resistance of sandwich panels with cellular cores are studied. At low impact velocity, sandwich panels with cellular cores outperform the corresponding solid ones and nonmontonicity between relative density and projectile resistance of sandwich panels is found and analyzed. Multiplying layer can reduce the maximum central deflection of back face sheet of the above three sandwich panels except pyramidal truss ones in high relative density. Hexagonal honeycomb sandwich panel is beneficial to increasing layer numbers in lowering the contact force and prolonging the interaction time. At high impact velocity, though corrugation and honeycomb sandwich panels are inferior to the equalweighted solid panels, pyramidal truss ones with high relative density outperform the corresponding solid panels. Multiplying layer is not the desirable way to improve highvelocity projectile resistance.
Keywords:
numerical simulation; projectile impact; multilayer; sandwich panel; cellular core
1 INTRODUCTION
Cellular materials, due to their excellent properties, find wide use in many different fields such as aerospace, navigation, transport, military and so on. Cellular materials, especially cellular sandwich structures, can effectively lighten and strengthen structural component (Wadley, et al., 2003Wadley, H.N.G., Fleck, N.A. and Evans, A.G. (2003). Fabrication and structural performance of periodic cellular metal sandwich structures. Composites Science and Technology 63:23312341.) and also meet multifunctional requirements (Evans, et al., 2001Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F. and Wadley, H.N.G. (2001). The topological design of multifunctional cellular metals. Progress in Materials Science 46: 309327.) including energy absorption (Zhu, et al., 2010Zhu, F., Lu, G.X., Ruan, D. and Wang, Z.H. (2010). Plastic deformation, failure and energy absorption of sandwich structures with metallic cellular cores. International Journal of Protective Structures 1:507541.; Zhang, et al., 2014Zhang, X.C., An, L.Q. and Ding, H.M. (2014). Dynamic crushing behavior and energy absorption of honeycombs with density gradient. Journal of Sandwich Structures and Materials 16(2):125147.), shock cushioning (Xue and Hutchinson, 2004Xue, Z.Y. and Hutchinson J.W. (2004). A comparative study of impulseresistant metal sandwich plates. International Journal of Impact Engineering 30:12831305.), heat dissipation (Queheillalt, et al., 2008Queheillalt, D.T., Carbajal, G., Peterson, G.P. and Wadley, H.N.G. (2008). A multifunctional heat pipe sandwich panel structure. International Journal of Heat and Mass Transfer 51:312326.) and sound insulation (Xin and Lu, 2010Xin, F.X. and Lu, T.J. (2010). Analytical modelling of fluid loaded orthogonally ribstiffened sandwich structures: Sound transmission. Journal of the Mechanics and Physics of Solids 58:13741396.) due to their unique structure configuration. Being weightefficient components in aerospace applications, sandwich panels may undergo projectile impact in many situations. For example, fuselages are subjected to impact by hailstones, birds and debris. The resulting impact damage to the sandwich panels ranges from face sheet indentation to complete perforation, which can lead to severe consequence. It makes the study of the projectile impact resistance of sandwich components a significant task.
Much theoretical, numerical and experimental work in dynamic properties including projectile impact resistance of sandwich structures with cellular cores has been taken (Zhu, et al., 2008Zhu, F., Zhan, L.M., Lu, G.X. and Wang, Z.H. (2008). Deformation and failure of blastloaded metallic sandwich panelsExperimental investigations. International Journal of Impact Engineering 35:837951.; Jing, et al., 2011Jing, L., Wang, Z.H., Ning, J.G. and Zhao, L.M. (2011). The mechanical response of metallic sandwich beams under foam projectile impact loading. Latin American Journal of Solids and Structures 8:107120.; Yin, et al., 2013Yin, S., Wu, L.Z., Yang, J.S., Ma, L. and Nutt, S. (2013). Damping and lowvelocity impact behavior of filler composite pyramidal lattice structures. Journal of Composite Materials 48:17891800.; Ni, et al., 2013Ni, C.Y., Li, Y.C., Xin, F.X., Jin, F. and Lu, T.J. (2013). Ballistic resistance of hybridcored sandwich plates: Numerical and experimental assessment. Composites Part A: Applied Science and Manufacturing 46:6979.; Zhang, et al., 2013Zhang, G.Q., Wang, B., Ma, L., Xiong, J. and Wu, L.Z. (2013). Response of sandwich structures with pyramidal truss cores under compression and impact loading. Composite Structures 100:451463.; Su, et al., 2013Su, W., Xiang, Y., Jiang, Y.F., Huang, S.Q., Fan, H.L. and Liu, R.H. (2013). Quasistatic outofplane compression of hollow integrated woven textile sandwich composites. Applied Mechanics and Materials 423426:5862.; Fan, et al., 2014Fan, H.L., Zhao, L., Chen, H.L., Zheng. J.J., Jiang, Y.F., Huang, S.Q., Kuang, N. and Ye, C.X. (2014). Dynamic compression failure mechanisms and dynamic effects of integrated woven sandwich composites. Journal of Composite Materials 48:427437.; Jiang, et al., 2014Jiang, W.Z., Liu, Y., Gu, Y. and Lu, G.X. (2014). An analytical model of a clamped sandwich beam under lowimpulse mass impact. Latin American Journal of Solids and Structures 11:16511678.; Ebrahimi et al., 2016Ebrahimi, H., Ghosh, R., Mahdi, E., Hashemi, H.N. and Vaziri, A. (2016). Honeycomb sandwich panels subjected to combined shock and projectile impact. International Journal of Impact Engineering 95:111.). Liaghat et al. (2010Liaghat, G.H., Nia, A.A., Daghyani, H.R. and Sadighi, M. (2010). Ballistic limit evaluation for impact of cylindrical projectiles on honeycomb panels. ThinWalled Structures 48:5561.) introduced an analytical model based on energy method to predict the ballistic limit of metallic honeycombs. The results showed that increasing panel thickness and cell wall thickness helps improve the ballistic limit velocity and good agreement was reached with existing experimental data (Goldsmith and Louie, 1995Goldsmith, W. and Louie, D.L. (1995). Axial perforation of aluminum honeycombs by projectiles. International Journal of Solids and Structures 32:10171046.; Nia, et al., 2008Nia, A.A., Razavi, S.B. and Majzoobi, G.H. (2008). Ballistic limit determination of aluminum honeycombsExperimental study. Material Science and Engineering A 488:273280.). Moreover, configuration of the core will be of importance in determining the dynamic resistance of the sandwich panel (Xue and Hutchinson, 2004Xue, Z.Y. and Hutchinson J.W. (2004). A comparative study of impulseresistant metal sandwich plates. International Journal of Impact Engineering 30:12831305.; Dharmasena, et al., 2010Dharmasena, K.P., Queheillalt, D.T., Wadley, H.N.G., Dudt, P., Chen, Y., Knight, D., Evans, A.G. and Deshpande, V.S. (2010). Dynamic compression of metallic sandwich structures during planar impulsive loading in water. European Journal of Mechanics A/Solids 29:5667.). Compared with solid panel with the same mass, periodic cores such as honeycomb (Fleck and Deshpande, 2004Fleck, N.A. and Deshpande, V.S. (2004). The resistance of clamped sandwich beams to shock loading. Journal of Applied MechanicsTransactions of the ASME 71:386401.), corrugation (Rubino, et al., 2009Rubino, V., Deshpande, V.S. and Fleck, N.A. (2009). The dynamic response of clamped rectangular Yframe and corrugated core sandwich plates. European Journal of Mechanics A/Solids 28:1424.) and pyramidal truss (Yungwirth, et al., 2008Yungwirth, C.J., Wadley, H.N.G., O'Connor, J.H., Zakraysek, A.G. and Deshpande, V.S. (2008). Impact response of sandwich plates with a pyramidal lattice core. International Journal of Impact Engineering 35:920936.) sandwich panels show performance benefits in impact resistance and energy absorption. Furthermore, related to the corresponding empty core, hybrid cores (e.g., metallic latticepolymer (Yungwirth, et al., 2008Yungwirth, C.J., Wadley, H.N.G., O'Connor, J.H., Zakraysek, A.G. and Deshpande, V.S. (2008). Impact response of sandwich plates with a pyramidal lattice core. International Journal of Impact Engineering 35:920936.), metallic latticeceramic (Ni, et al., 2013Ni, C.Y., Li, Y.C., Xin, F.X., Jin, F. and Lu, T.J. (2013). Ballistic resistance of hybridcored sandwich plates: Numerical and experimental assessment. Composites Part A: Applied Science and Manufacturing 46:6979.; Wadley, et al., 2013Wadley, H.N.G., Dharmasena, K.P., O'Masta, M.R. and Wetzel, J.J. (2013). Impact response of aluminum corrugated core sandwich panels. International Journal of Impact Engineering 62:114128.) and metallic latticeconcrete (Ni, et al., 2015Ni, C.Y., Hou, R., Xia, H.Y., Zhang, Q.C., Wang, W.B., Cheng, Z.H. and Lu, T.J. (2015). Perforation resistance of corrugated metallic sandwich plates filled with reactive powder concrete: Experiment and simulation. Composite Structures 127:426435.) can offer large potential for enhancing the projectile properties of the sandwich panels.
The above studies are mainly about the impact resistance of singlelayer sandwich panels. Liang et al. (2007Liang, Y.M., Spuskanyuk, A.V., Flores, S.E., Hayhurst, D.R., Hutchinson, J.W., McMeeking, R.M. and Evans, A.G. (2007). The response of metallic sandwich panels to water blast. Journal of Applied MechanicsTransactions of the ASME 74:8199.) have found that the mass distribution between sheet and core significantly affects the performance of singlelayer sandwich panels with hexagonal honeycomb, Icore, and corrugated core during water blast loading and that "soft core" designs outperform those with "strong cores". Motivated by this finding in water blast, investigations about the multilayers which can provide appreciable softness due to layerbylayer crushing have be taken. Wadley et al. (2008Wadley, H.N.G., Dharmasena, K.P., Chen, Y.C., Dudt, P., Knight, D., Charette, R. and Kiddy, K. (2008). Compressive response of multilayered pyramidal lattices during underwater shock loading. International Journal of Impact Engineering 35:11021114.) and Dharmasena et al. (2009Dharmasena, K.P., Queheillalt, D., Wadley, H.N.G., Chen, Y.C., Dudt, P., Knight, D., Wei, Z.S. and Evans, A.G. (2009). Dynamic response of a multilayer prismatic structure to impulsive loads incident from water. International Journal of Impact Engineering 36:632643.) have investigated the response of multilayer sandwich panels, referred to pyramidal and prismatic sandwich panels respectively, to underwater shock loading and found that multilayer structures significantly reduce the transmitted pressures of an impulsive load and outperform the single core layer sandwich panels. Xiong et al. (2012Xiong, J., Vaziri, A., Ma, L., Papadopoulos, J. and Wu, L.Z. (2012). Compression and impact testing of twolayer composite pyramidalcore sandwich panels. Composite Structures 94:793801.) have conducted the quasistatic uniform compression and lowvelocity concentrated impact tests and found bilayer carbon fiber composite pyramidal truss cores have comparable specific energy absorption compared with glass fiber woven textile truss cores. Similar multilayer structures have been exploited to improve the energy absorption of sandwich panels (Fan, et al., 2013Fan, H.L., Yang, W. and Zhou, Q. (2013). Experimental research of compressive responses of multilayered woven textile sandwich panels under quasistatic loading. Composites: Part B: Engineering 42:11511156.; Kılıçaslan, et al., 2013Kılıçaslan, C., Güden, M., Odacı, İ, K. and Taşdemirci, A. (2013). The impact responses and the finite element modeling of layered trapezoidal corrugated aluminum core and aluminum sheet interlayer sandwich structures. Materials and Design 46:121133.; Li, et al., 2015Li, S.Q., Lu, G.X., Wang, Z.H., Zhao, L.M. and Wu, G.Y. (2015). Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading. International Journal of Mechanical Sciences 9697:112.). Li et al. (2016)Li, S.Q., Li, X., Wang, Z.H., Wu, G.Y., Lu, G.X. and Zhao, L.M. (2016). Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. Composites Part A: Applied Science and manufacturing 80:112. have investigated experimentally and numerically on the response of metallic sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. They found that for the graded panels with relative density descending core arrangement, the core plastic energy dissipation and the transmitted force attenuation were larger than that of the ungraded ones under the same loading condition.
However, so far relatively few studies directly compare the projectile impact resistance of multilayer sandwich panels with different cellular cores in different relative densities. In this paper, we numerically investigated the projectile impact resistance of sandwich panels with three typical core configurations named corrugation, hexagonal honeycomb and pyramidal truss, with the relatively wide range of relative density from 0.001 to 0.15 and impact velocity from 50 m/s to 202 m/s. Meanwhile, we also studied bilayer and trilayer sandwich panels under the above conditions. We analyzed the effects of core configuration and layer number on sandwich panels with the above cellular cores.
2 NUMERICAL SIMULATION
2.1 Finite Element Model and Geometry Parameter
Our finite element (FE) model is established referred to Zhang (2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.) in order to compare the FE results and experimental results. Sandwich panels with corrugation, hexagonal honeycomb and pyramidal truss cores are normally impacted by hard hemisphericalnosed projectiles of height h=27.5mm, radius r=3.75mm and mass m _{0}=10.4g. The schematic diagram of sandwich panel subjected to projectile impact is shown in Figure 1.
The cell schematic diagrams and relative density calculation equations of three kinds of sandwich panels are listed in Table 1. The t_{c} , b_{c} , h_{c} is respectively the thickness, length and height of corrugation cell; hexagonal honeycomb cell has the length l_{h} and two singlethickness t_{h} walls and one doublethickness 2t_{h} wall; t_{p} and l_{p} is respectively sectional side width and length of pyramidal truss. The angles between corrugation panel and xy plane is α_{xy} = 45º and the angles between pyramidal truss and x, y, z axis are α_{x} =60º, α_{y} =60º, α_{z} =45º. Relative density represents the volume fraction of cellular cell, i.e. corrugation wall, hexagonal honeycomb wall and pyramidal truss, taking up in the whole cell.
Moreover, we increase layer numbers of sandwich panels mentioned above but keep the same surface density ρ_{f} which is determined by
where N is the total number of sheets in sandwich structures and ρ is the parent material density which the cellular core uses, i.e. N=2 for singlelayer, N=3 for bilayer and N=4 for trilayer; H_{c} is the total height of core which is determined by H_{c} =kH_{ck} (k=1,2,3) and H_{ck} is the height of every single core; h_{f} is the total thickness of face sheet which is determined by h_{f} =kh_{fk} (k=1,2,3) and h_{fk} is the thickness of every single face sheet. The thickness of corresponding solid panel h_{s} is calculated by
Detailed geometry parameters of all three sandwich panels are given in Table 25.
2.2 Material
No.45 steel is used as parent material of projectile and Aluminum 2024T351 is used as parent material of sheet and cellular core, properties of which are listed in Table 6.
Material parameters for No.45 steel and Aluminum 2024T351 (Zukas, 1990Zukas, J.A. (1990). High velocity impact dynamics, John Wiley Sons (New York).).
The modified JohnsonCook constitution relation (Johnson and Cook, 1983Johnson, G.R. and Cook, W.H. (1983). A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 9th International Symposium on Ballistic (ISB9), Hague, p. 541547.) is applied to predict the flow and fracture behavior of the target and the equivalent von Mises stress includes as the effect of three material characteristics namely strain, strain rate, temperature, which reads
where A, B, C, m, n are material constants given in Table 6. The dimensionless plastic strain rate is defined by is effective plastic strain and
where ^{1}. The dimensionless temperature T^{*} (Johnson and Cook, 1983Johnson, G.R. and Cook, W.H. (1983). A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 9th International Symposium on Ballistic (ISB9), Hague, p. 541547.) is given by =1s is effective plastic strain rate at a reference strain rate
where T is actual temperature, T_{r} and T_{m} indicate room temperature and melting temperature, respectively. Material damage in the JohnsonCook model (Johnson and Cook, 1985Johnson, G.R. and Cook, W.H. (1985). Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering Fracture Mechanics 21:3148.) is predicted using the following law:
where ∆ε_{p} is the increment of equivalent plastic strain during an increment of loading and ε_{f} is the failure strain as function of three important material characteristics affecting the fracture of the ductile material i.e. stress triaxiality, strain rate and temperature (Johnson and Cook, 1985Johnson, G.R. and Cook, W.H. (1985). Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering Fracture Mechanics 21:3148.), which is determined by
wherein σ^{*} is the normalizd mean stress which is given by σ^{*} = σ_{m} /σ_{e} and σ_{m} is hydrostatic pressure and σ_{e} is equivalent von Mises stress. D _{1}, D _{2}, D _{3}, D _{4} and D _{5} are material constants referred to the experimental results of Zukas (1990Zukas, J.A. (1990). High velocity impact dynamics, John Wiley Sons (New York).), which are listed in Table 6.
2.3 Simulation
We used commercial FE software ABAQUS/Explicit (version 6.10) to carry out 3D FE simulation under projectile impact conditions. Rigid constraint was applied to the projectile. Symmetric boundary constraints about xz and yz planes were imposed. The other two sides of sandwich panel were fully clamped. The bonding between front and back face sheets and core was assumed to be perfect which lead to a relatively high evaluation of ballistic resistance of structure due to the ignorance of debonding between face sheets and core. General contact was imposed. In order to get the conservation result, friction was ignored in the contact between the components. Continuum shell elements S4R were assigned to solid panel, sheets, corrugation cores and hexagonal honeycomb cores while pyramidal trusses were meshed using beam elements B31 and bullet was assigned solid element C3D8R. At first mesh convergence test was conducted by comparing with the experimental results in Zhang (2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.) and the refined seed size 0.5 mm was chosen in the zone next to the projectile and coarser seed size 2 mm was used in other part of both face sheet and core as shown in Table 7. Then step time convergence test was also did as listed in Table 8 and 0.03 ms was chosen as the total time step for hexagonal honeycomb sandwich panel subjected to projectile impact V _{0}=202 m/s. The sandwich panel was just penetrated by projectile which was efficient in computing time. The mesh size was the same for other sandwich panels in the following and time step was chosen based on the identical guideline.
Mesh convergence test of singlelayer hexagonal honeycomb sandwich panel with = 0.037 based on the experimental result.
Step time convergence test of singlelayer hexagonal honeycomb sandwich panel with = 0.037.
The finite element model of sandwich panel was depicted in Figure 2. Whereas higher impact resistance of sandwich panel with cellular core can be obtained when the projectile impacts the interaction area of counterparts in cell, the sandwich panels were impacted within the gap of cell to get a conservation result, as illustrated in Figure 2. Zhang (2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.) stated that hexagonal honeycomb sandwich panel with V _{0} from 50 m/s to 202 m/s were imposed to projectile. = 0.037 has limited resistance to the projectile with the velocity greater than 250 m/s. Considering the comparison with Zhang's experimental result and meanwhile investigate the response in different impact velocities, range of projectile velocities
Finite element model of sandwich panel, taking bilayer sandwich panel for example: (a)corrugation, (b)hexagonal honeycomb and (c)pyramidal truss.
Present analysis was validated with the experimental results (Zhang, 2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.) as shown in Figure 3 and 4 and good agreement was reached.
Residual velocity in the normal impact of the singlelayer hexagonal square honeycomb sandwich panel: FE results compared with experimental results.
Hexagonal honeycomb sandwich panel after projectile impact: (a)front face sheet in experiment (Zhang, 2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.), (b)front face sheet in FE, (c)back face sheet in experiment (Zhang, 2014Zhang, Q.N. (2014). Study on the Ballistic Impact Effect of Sandwich Panels with Aluminum Honeycomb Cores, Master Thesis (in Chinese), Beijing Institute of Technology, China.) and (d) back face sheet in FE.
3 RESULT AND DISCUSSION
According to our FE simulation, results are qualitatively presented in two groups: (1) low velocity where the core and back face sheet cannot be perforated; (2) high velocity where sandwich panel can be totally perforated. Furthermore, the projectile impact resistance in low and high velocity can be characterized by ω central deflection of back face sheet and V _{r} residual velocity of projectile after perforation, respectively (see Figure 5). Effects of core configuration, relative density and layer number on projectile impact resistance are investigated and deformation and failure modes are observed and discussed. For readability, abbreviation are used in figures as the nomenclature that firstly corrug, honey and pyr are referred to corrugation, hexagonal honeycomb and pyramidal truss respectively, secondly number 1/2/3 is referred to layer number, thirdly comes the relative density and finally comes the impact velocity, i.e. corrug1002150 represents the singlelayer corrugation sandwich panel with the relative density 0.02 subjected to the projectile with the velocity 150 m/s.
Different phenomena after projectile impact: (a)deflection of back face sheet and (b) perforation with residual velocity.
3.1 Effect of Core Configuration
Fleck and Deshpande (2004Fleck, N.A. and Deshpande, V.S. (2004). The resistance of clamped sandwich beams to shock loading. Journal of Applied MechanicsTransactions of the ASME 71:386401.) have found that the sandwich beam outperforms the monolithic beam with the same mass resulting from the fact that thin front face sheet of the sandwich beam acquires a smaller fraction of the blast impulse compared to the relatively thick monolithic beam. We also compared the sandwich panels with the corresponding solid panels having the same surface density. The deflection versus relative density curves of three kinds of sandwich panels and corresponding solid panels when impact velocity is 50 m/s are shown in Figure 6. It is concluded that sandwich panels have superior resistance in lowvelocity projectile impact resistance compared with equalweighted corresponding solid panels. As depicted in Figure 7, unlike the structural response of solid panel subjected to impact, the core of sandwich panel is crushed after the impulse is transmitted to the front face sheet. Then the plastic bending of core unit cell and stretching of the thin front face sheet make much contribution to the dissipation of impact energy. Therefore, much more plastic dissipation energy can be absorbed by sandwich structures. Based on Table 9, plastic dissipation energy of sandwich structures is 20% to 50% higher than that in solid panels except the corrugated sandwich panel with ≤ 0.005. For these corrugated sandwich panel, core unit cells with the thickness lower than 0.044 mm are so weak that can hardly support the front face sheet during the impact that less energy is dissipated by plasticity though they makes the back face sheet suffer smaller deflection due to their severe deformation.
Deflection of three kinds of sandwich panels and corresponding solid panel when V _{0}=50 m/s.
Defomation of panel when reaching the maxium deflection during impact when V _{0}=50 m/s and ≤ 0.005:(a) solid panel, (b) corrugation sandwich panel, (c) hexagonal honeycomb sandwich panel and (d) pyramidal truss sandwich panel.
Plastic dissipation energy (unit:J) versus relative density of sandwich panels and corresponding solid panels when V _{0}=50m/s.
Generally speaking, the impact resistance of structures is beneficial to the high core energy absorption (Jing, et al., 2013Jing, L., Xi, C.Q., Wang, Z.H. and Zhao, L.M. (2013). Energy absorption and failure mechanism of metallic cylindrical sandwich shells under impact loading. Material & Design 52:470480.; Li, et al., 2014Li, X., Wang, Z.H., Zhu, F., Wu, G.Y. and Zhao, L.M. (2014). Response of aluminum corrugated sandwich panels under air blast loadings: Experiment and numerical simulation. International Journal of Impact Engineering 65:7988.).As depicted in Figure 8, among all three singlelayer sandwich panels, back face sheet hardly absorbs energy by plastic dissipation and most of plastic dissipation happen to front face sheet and core and moreover front face sheet dissipates more energy than core. Xue and Hutchinson (2003Xue, Z.Y. and Hutchinson, J.W. (2003). Preliminary assessment of sandwich plates subjected to blast loads. International Journal of Mechanical Sciences 45:687705.) concluded that the energy distribution is sensitive to the mass distribution caused by the increasing of relative density. When the core relative density is low i.e. Figure 6. = 0.001, the core is so weak compared with face sheet that it is not able to support the front face sheet such that large area of front face sheet contributes to the plastic dissipation and meanwhile the severe deformation happens to the core. Though the projectile approach forward, small deflection is found to the back face sheet. At higher core relative densities, the face sheet is so weak compared with the core that more energy is dissipated due to the plastic deformation of front face sheet and back face sheet is slightly affected. When it comes to medium core relative density, the face sheet and the core are competitive and the effect of sandwich panel is dominant, so a peak of deflection of bottom face sheet occurs as shown in
Percentage of plastic dissipation of face sheet and core as the function of relative density: (a) corrugation sandwich panel, (b) square honeycomb sandwich panel and (c) pyramidal truss sandwich panel.
When the impact velocity is between 105 m/s and 202 m/s, almost all the sandwich panel and solid panel are both perforated by the projectile. Shear failure and stretching happen to the face sheet but the core does not dissipate so much energy as that in low velocity. As shown in Figure 9, relatively thick solid panel outperforms the sandwich panel, however pyramidal truss sandwich panel with high relative density shows better projectile impact resistance than solid panel due to its stubby truss.
Residual velocity of three kinds of sandwich panels and corresponding solid panel when (a) V _{0}=188 m/s, and (b) V _{0}= 202 m/s.
So as to insight the enhancance in projectile resistance in pyramidal truss sandwich panels, plastic dissipation energy of sheets and core at 202 m/s in a lower and a higher relative density named Figure 10. Comparing Figure 10a and 10c, plastic dissipation energy of front and back face sheets of the pyramidal truss sandwich panel with Figure 10b and 10d, though front face sheets in relative density = 0.15 the central pyramidal truss are stronger to provide additional supporting against the impact instead of getting fractured before contacting projectile when = 0.15 during the perforation is nearly the same while core energyabsorption ability quite differs in two relative density. When = 0.02 and = 0.02. = 0.02 and = 0.15 are both sheared in the center, when = 0.02, coredissipated energy is about 5.2 J and only takes up the 15.4% of total plastic dissipation energy. When = 0.15 and corresponding deformation modes are shown in = 0.15, however, coredissipated energy is 188 J contributing up to 77.7% to total plastic dissipation energy. As shown in = 0.02 and
Plastic dissipation energy versus time of sheets and core of pyramidal truss sandwich panels in a lower and a higher relative density and corresponding solid panels when impact velocity V _{0}=202 m/s and deformation of pyramidal truss sandwich panels when t= 145μs: (a)(b) = 0.02 and (c)(d) = 0.15.
3.2 Effect of Layer Number
In order to investigate how layer number influences the impact resistance of sandwich panels, we have also simulated projectile impact to singlelayer, bilayer and trilayer sandwich panels in kinds of velocities. Surface density of each kind of sandwich panels are kept the same and detailed parameters are listed in Table 5. As deflectionrelative density curves when V _{0}=50 m/s are depicted in Figure 11, multilayer sandwich panels cannot certainly own better impact resistance ability and would even be inferior to singlelayer sandwich panels. For example, when Figure 11. It should be noted that for the corrugation sandwich panel with ≥ 0.04, multiplying layers can reduce the deflection of back face sheet of the sandwich panels except pyramidal truss ones with = 0.0001and = 0.02 the deflection of back face sheet of singlelayer corrugation sandwich panel is lower than those of the bilayer and trilayer ones and the deflection of front face sheet is also in that range i.e. 0.32 mm for singlelayer, 0.39 mm for bilayer and 0.54 mm for trilayer. When = 0.0005, the deflection of back face sheet is negtive due to the very weak core. = 0.15 as shown in
Deflectionrelative density curves when V _{0}=50 m/s (a) corrugation sandwich panels, (b) hexagonal honeycomb sandwich panels and (c) pyramidal truss sandwich panel.
The contact loadtime curves of singlelayer, bilayer and trilayer corrugation sandwich panels when V _{0}=50 m/s are depicted in Figure 12, respectively. The appearance of force indicates that the projectile contacts with the front face sheet. With the further impact, the projectile is resisted by corrugatioin cell wall or together with the back face sheet and the contact force increases with fluctuation. After the impact velocity of projectile reduces to zero, the projectile is rebounced due to the recovery of the compressed part and velocity increases until the projectile totally seperates itself from the sandwich panel. At that time, the contact force will reduce to zero. It is shown in Figure 12 that force values of multilayer corrugation sandwich panels are much lower than singlelayer ones in the former half but higher in the later half when Wadley, et al., 2008Wadley, H.N.G., Dharmasena, K.P., Chen, Y.C., Dudt, P., Knight, D., Charette, R. and Kiddy, K. (2008). Compressive response of multilayered pyramidal lattices during underwater shock loading. International Journal of Impact Engineering 35:11021114.)(Xiong, et al., 2012Xiong, J., Vaziri, A., Ma, L., Papadopoulos, J. and Wu, L.Z. (2012). Compression and impact testing of twolayer composite pyramidalcore sandwich panels. Composite Structures 94:793801.)( Kılıçaslan, et al., 2013Kılıçaslan, C., Güden, M., Odacı, İ, K. and Taşdemirci, A. (2013). The impact responses and the finite element modeling of layered trapezoidal corrugated aluminum core and aluminum sheet interlayer sandwich structures. Materials and Design 46:121133.)(Fan, et al., 2014Fan, H.L., Zhao, L., Chen, H.L., Zheng. J.J., Jiang, Y.F., Huang, S.Q., Kuang, N. and Ye, C.X. (2014). Dynamic compression failure mechanisms and dynamic effects of integrated woven sandwich composites. Journal of Composite Materials 48:427437.). Notably, the interaction time before that projectile is rebounded from corrugation sandwich panel is extended by increasing layer numbers in lower relative density Figure 12a) while the interaction time of multilayer corrugation sandwich panels are much shorter when Figure 12b and 12c). = 0.02 (see = 0.15 (see = 0.08 and = 0.02, = 0.08 and = 0.15 at = 0.02 and = 0.08. Load fluctuation is observed during the interaction and with the bending and progressive deformation of the cell sheets, the force keeps increasing. This phenomenon is also observed by (
Contact forcetime history of corrugation sandwich panels at V _{0}=50 m/s when (a) = 0.15. = 0.02 , (b) = 0.08 and (c)
As to hexagonal honeycomb sandwich panels, increasing layer numbers can not only noticeably lower force values of structures during impact but also prolong interaction time as shown in Figure 13. In pyramidal truss sandwich panel, force values of bilayer and trilayer is below the ones in singlelayer structure in the former half when Figure 14b and 14c), i.e. when = 0.02, but the force values of multilayer pyramidal truss during impact are higher and interaction times are much shorter(see = 0.15 it only takes about 0.169 ms to rebound the projectile in trilayer but the value is 2.81 ms in singlelayer. From the perspective of reducing force and prolonging the contact time, the hexagonal honeycomb sandwich panel is the best among the three sandwich panels. This finding will give certain instruction in designing antiimpact sandwich structures.
Contact forcetime history of hexagonal honeycomb sandwich panels at V _{0}=50m/s when (a) = 0.08 and (c) = 0.15 = 0.02 , (b)
Contact forcetime history of pyramidal truss sandwich panels at V _{0}=50 m/s when (a) = 0.02 , (b) = 0.08 and (c) = 0.15.
Concerning high velocity namely 105 m/s, 150 m/s and 202 m/s there, increasing layer number cannot enhance the projectile impact resistance of three kinds of sandwich panels as shown in Figure 1517, though there is a significant positive correlation between relative density and the projectile impact resistance of three kinds of sandwich panels with cellular cores. It is noted that the weaken by increasing layer number is more dramatical in pyramidal truss sandwich panel when V _{0}=202 m/s are listed in Table 10. = 0.15. For pyramidal truss sandwich panel when = 0.08 and = 0.15, the pyramidal truss do more contribution in plastic dissipation. When multiplying layer and keeping the same surface density, the thickness of pyramidal truss is reduced and thinner face sheet are more easily sheared by projectile so that multilayer ones underperform the singlelayer ones. Deformation modes after impact of three kinds of sandwich panels when
Residual velocity of corrugation sandwich panels with different layers when V _{0}=(a)105 m/s, (b)150 m/s and (c)202 m/s.
Residual velocity of hexagonal honeycomb sandwich panels with different layers when V _{0}=(a)105 m/s, (b)150 m/s and (c)202 m/s.
Residual velocity of pyramidal truss sandwich panels with different layers when V _{0}=(a)105 m/s, (b)150 m/s and (c)202 m/s.
4 CONCLUSIONS
The numerical simulation study of sandwich panels with cellular cores under projectile impact was performed using ABAQUS/Explicit finite element code. We investigated the effects of core configuration, relative density and layer number on projectile impact resistance in low and high velocity.
In low velocity (50 m/s)
Comparing with corresponding solid panel, sandwich panels with cellular cores have remarkable strength in projectile impact resistance due to their gradual deformation during impact. To get the relatively small deflection of bottom face sheet, either weak cellular core or strong one is admirable choice instead of choosing the cellular core with medium relative density. Considering the actual manufacturing condition, strong core of sandwich panel is preferred. Multiplying layer can reduce the maximum central deflection of back face sheet of the above three sandwich panels except pyramidal truss ones in high relative density. Moreover hexagonal honeycomb sandwich panel is beneficial to increasing layer numbers in lowering the contact force and prolonging the interaction time.
In high velocity (105 m/s to 202 m/s)
Though sandwich panels with cellular cores are inferior to the corresponding solid panels with the same surface density, pyramidal truss sandwich panel outperforms solid panel in high relative density due to the strong supporting of pyramidal truss. Increasing layer number has no help increasing the projectile impact resistance of above three kinds of sandwich panels except the hexagonal honeycomb sandwich panels in high relative density.
Acknowledgements
Supports of National Natural Science Foundation of China under Grant Nos. 11302270 and 11572059, Ph.D. Programs Foundation of Ministry of Education of China under Grant No. 20130191120015, Chongqing Natural Science Foundation under Grant No. cstc2013jcyjA00030 and State Key Lab for Strength and Vibration of Mechanical Structures of Xi׳an Jiaotong University under Grant No. SV2015KF12 are gratefully acknowledged.
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Publication Dates

Publication in this collection
Dec 2016
History

Received
20 Mar 2016 
Reviewed
03 Sept 2016 
Accepted
06 Sept 2016