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In order to discern how preexisting defects such as single or multiple debondingsdelaminations in a curved armor system may affect its ballistic protection performance, twodimensional axial finite ele ment models were generated using the commercial software ANSYSAutodyn. The armor systems consid ered in this investigation are composed of boron carbide front component and Kevlarepoxy backing component. They are assumed to be perfectly bonded at the interface without defects. The parametric study shows that for the cases considered, the maximum back face deformation of a curved armor system with or without defects is more sensitive to its curvature, material properties of the ceramic front com ponent, and preexisting defect size and location than the ballistic limit velocity. Additionally, both the ballistic limit velocity andmaximum back face deformation are significantly affected by the backing com ponent thickness, frontbacking component thickness ratio and the number of delaminations
Materials and Design 64 (2014) 25–34 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes Ballistic protection performance of curved armor systems with or without debondings/delaminations Ping Tan ⇑ Land Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Melbourne, Victoria 3207, Australia a r t i c l e i n f o Article history: Received 14 February 2014 Accepted 14 July 2014 Available online 24 July 2014 Keywords: Finite element Projectile impact Ballistic protection Curved armor Debonding/delamination a b s t r a c t In order to discern how pre-existing defects such as single or multiple debondings/delaminations in a curved armor system may affect its ballistic protection performance, two-dimensional axial finite element models were generated using the commercial software ANSYS/Autodyn The armor systems considered in this investigation are composed of boron carbide front component and Kevlar/epoxy backing component They are assumed to be perfectly bonded at the interface without defects The parametric study shows that for the cases considered, the maximum back face deformation of a curved armor system with or without defects is more sensitive to its curvature, material properties of the ceramic front component, and pre-existing defect size and location than the ballistic limit velocity Additionally, both the ballistic limit velocity and maximum back face deformation are significantly affected by the backing component thickness, front/backing component thickness ratio and the number of delaminations Crown Copyright Ó 2014 Published by Elsevier Ltd All rights reserved Introduction Boron carbide (B4C) is one of the most attractive ceramics for lightweight armor systems against ballistic/projectile threats It has become more commonly used in military body armors over the past decades This is due to its attractive characteristics including low density, high hardness and high compressive strength [1–7] However, owing to its brittleness, which makes it susceptible to tensile failure, ceramic armor systems such as B4C generally contain some sort of backing materials such as composite materials This will prevent the ceramic strike face from suffering large deflection which can cause tensile failures Also, the composite backing layer absorbs the kinetic energy of the decelerated bullet/projectile and catches the ceramic and bullet/projectile fragments, preventing them from doing further harm To better understand the responses of B4C and its composite armor systems subjected to high velocity projectile/bullet impacts, various numerical and experimental studies have been conducted For example, Brantley [8] conducted microstructural and fractographic studies of the response of hot-pressed boron carbide ceramic subjected to projectile impact Shockey et al [9] experimentally investigated the failure phenomenology of various ceramics, including B4C, struck by a long rod penetrator Orphal et al [10] carried out ballistic tests for measuring the penetration ⇑ Tel.: +61 96268500; fax: +61 96267820 E-mail address: Ping.tan@dsto.defence.gov.au http://dx.doi.org/10.1016/j.matdes.2014.07.028 0261-3069/Crown Copyright Ó 2014 Published by Elsevier Ltd All rights reserved of confined boron carbide targets subjected to long tungsten rod impact Westerling et al [11] performed an experiment to investigate the influence of impact velocity and confinement on the resistance of boron carbide targets to the penetration of tungsten long-rod projectiles Also, finite element (FE) simulations were conducted using the commercial finite element software ANSYS/ Autodyn, in which the Johnson–Holmquist model (JH-2) [12] was used for modeling the response of boron carbide subjected to dynamic impacts It was reported that the simulated results for penetration velocity vs impact velocity agreed fairly well with the experimental results provided damage evolution was suspended below the transition region Holmquist and Johnson [13] carried out an investigation for the responses of boron carbide subjected to plate or projectile impact, in which the Johnson– Holmquist–Beissel (JHB) constitutive model developed previously by Johnson et al [14] was used Shokrieh and Javadpour [4] developed FE model using ANSYS/Lsdyna software for investigating the response of ceramic composite armor system subjected to a projectile impact, in which the ceramic composite armor was composed of boron carbide ceramic-faced panel and Kevlar 49 fiber composite backup panel It was shown that when the ratio of the plate thicknesses is different from the optimum magnitude evaluated according to Hetherington method [15], the armor performance is lower than the optimum case Chocron-Benloulo and Sánchez-Gálvez [16] developed an analytical model for simulating projectile impact onto ceramic/composite armors A good agreement between the numerical and analytical results was noted, 26 P Tan / Materials and Design 64 (2014) 25–34 especially for the high velocity cases Savio et al [5] conducted an experimental study for the ballistic performance of boron carbide tiles subjected to 7.62 mm armor piercing projectile impact It was reported that an insignificant or marginal increase in efficiency was observed for an increase in tile thickness from 5.2 mm up to 7.3 mm Zhang et al [17] developed a FE model using MSC.DYTRAN software for optimum design of a flat panel made of boron carbide ceramic strike face and Kevlar/epoxy backing plate under the impact of a projectile Fountzoulas and LaSalvia [6,7] developed two-dimensional (2D) and three-dimensional (3D) FE models using ANSYS/Autodyn for simulating the responses of the confined hot-pressed boron carbide targets subjected to tungsten-based penetrator impact, in which the boron carbide was modeled using the Polynomial equation of state (EOS) and Johnson–Holmquist strength and failure models (JH-2) available in Autodyn material library [18] It was noted from literature that the majority of research on ballistic performance of B4C and its composite armor systems has been conducted on flat panels, and investigation of the performance of curved B4C composite armor systems is very limited The ballistic protection behavior of curved armor system can be different from that of flat body armor, due to the curvature given to the curved body armor during its manufacturing from flat laminates This leads to stretching and shortening of fibers [19] Recently, optimal design of curved body armor systems is attracting military’s attention This is because body armor designed for men does not fit female soldiers well, and thus the armor is uncomfortable for female soldiers Also, if modern body armor is to become more ergonomic, it should be designed with a curvature for a comfortable body fit without undue bulk [20] It is a concern that undesirable pre-existing defects such as debondings/delaminations, which can occur in the armor system during the manufacturing process and/or in service, may significantly degrade the ballistic protection performance of a curved armor system It is therefore essential to understand the effect of pre-existing debondings/delaminations on the ballistic protection performance of curved armor systems to improve their defect/damage-survivability and defect/damage-tolerance In order to investigate the ballistic protection performance of various curved B4C/Kevlar armor systems subjected to flat-faced cylindrical projectile impact, 2D axial FE models with or without single or multiple pre-existing debondings/delaminations were developed using the commercial FE software ANSYS/Autodyn and following the similar procedure used previously [21,22] Subsequently, a parametric study was conducted to investigate the effects of key parameters such as the shape and thickness of the armor system components, the size, location and number of the pre-existing debondings/delaminations on the ballistic protection performance of the armor systems, including the ballistic limit velocity (Vbl) and maximum back face deformation (MAXBFD) Also, the influences of erosion strain of B4C and Kevlar/epoxy composite on the ballistic protection performance of the curved armor system were discussed, respectively Development of the finite element models To simulate the ballistic protection performances of curved B4C/ Kevlar armor systems with or without pre-existing debondings/ delaminations, corresponding 2D axial FE models were generated using the commercial FE software ANSYS/Autodyn, which is a special hydrocode for non-linear transient dynamic events such as ballistic impact, penetration and blast problems [23] Fig 1(a) and (b) illustrates two typical curved B4C/Kevlar armor systems with a pre-existing debonding or delamination, in which only half of the panel above the central line is shown due to the symmetry of the FE model In Fig 1, Rv and Lv stand for the size of the debonding/delamination and the distance between the debonding/delamination and the front surface of the Kevlar/epoxy component Gauge located at the center of the projectile is used for predicting the value of Vbl while gauge located at the back face of the Kevlar/epoxy composite component is used for obtaining the value of MAXBFD The baseline case considered in this investigation was composed of mm thick B4C front layer, 0.5 mm thick epoxy resin middle layer (i.e., adhesive layer), and 20 mm thick Kevlar/epoxy composite backing layer The thicknesses of the B4C and Kevlar/ epoxy composites were selected based on those of generic ballistic hard armor plates The armor system components were assumed to be perfectly bonded together at the interface without defects The length and diameter of the flat-faced cylindrical projectile were chosen to be 13.8 mm and 12.58 mm, which were determined based on those of a fragment-simulating caliber 50 [24] The Lagrange solver [25] was used for all armor material components and projectiles The interaction between each component in the present FE model was achieved using the Lagrange/Lagrange interaction logic An erosion algorithm was used for enhancing the ability of the Lagrange processor to simulate impact problems involving large deformation [11,21,25,26] This erosion option allows removal of elements when the local element geometric strain exceeds the specified value The geometric strain is calculated from the principal strain components (ei, eij, i = 1–3, j = 1–3) as [23]: eeff ẳ 1=2 2 je1 ỵ e22 ỵ e23 ị e1 e2 ỵ e2 e3 ỵ e3 e1 ị þ 3ðe212 þ e223 þ e231 Þj ð1Þ In this investigation, the geometric strain for erosion was selected to be 2.0 The type of geometric strain was chosen to be instantaneous The inertia of the eroded nodes was not retained Zero x-velocity and y-velocity boundary conditions were applied to the top surfaces of all composite components Gravity and friction from air resistance were ignored [22] 2.1 Material models The ability of a numerical model to realistically predict the response of an armor system to the projectile impact depends largely on the selection of appropriate material models and availability of associated input data In this investigation, the B4C was modeled by the Polynomial equation of state (EOS) and Johnson–Holmquist strength and failure model (JH-2) [12] The Polynomial EOS is expressed as: P ẳ A1 l ỵ A2 l2 ỵ A3 l3 ỵ B0 ỵ B1 lịq0 e q q0 2ị where P is pressure, l ¼ À 1; q and q0 stand for the density and zero pressure density, and e is the internal energy per unit mass (or specific internal energy) A1, A2, A3, B0 and B1 are material constants, and their corresponding data are listed in Table A-1 in Appendix A [23,27] The Johnson–Holmquist strength model (JH-2) for boron carbide was described in Fig [12] This model has been commonly used to simulate the dynamic response of boron carbide subjected to high velocity impact [6,11,28] The required input data for the JH-2 strength model, including shear modulus (G), Hugoniot elastic limit (HEL), intact strength constant (A), intact strength exponent (N), strain rate constant (C), fracture strength constant (B), maximum fracture strength ratio, fracture strength exponent (M), and those for Johnson–Holmquist failure model, including damage constant (D1), Damage constant (D2), Hydro tensile limit, Bulking constant (b), are listed in Table A-1 in Appendix A [23,27] In this investigation, the BORONCARBI material model available in the 27 P Tan / Materials and Design 64 (2014) 25–34 Kevlar/epoxy composite B4C R=170mm Epoxy resin Gauges 85mm Steel 4340 projectile Rv Central line Lv (a) Curved armor with debonding (b) Curved armor with delamination (c) Flat armor with debonding Fig Schematics of typical curved and flat B4C/Kevlar armor systems with pre-existing debonding/delamination ANSYS/Autodyn material library was used to model the B4C armor component subjected to projectile impact The epoxy resin was modeled using the Mie–Gruneisen EOS and Von Mises strength model The Mie–Gruneisen EOS [29] is generally written as: P ¼ PH ỵ Cqẵe eH 3ị Y ẳ ẵA þ Benp ½1 þ C ln eÃp ½1 À T m H ð9Þ where ep is the effective plastic strain, eÃp is the normalized effective plastic strain rate, A is the basic yield stress at low strains, B is the hardening constant, C is the strain rate constant, n is the hardening exponent, m is the thermal softening exponent and TH is the homologous temperature, which can be obtained by: where P is pressure and C is the Gruneisen coefficient The functions PH and eH are expressed as [30]: T H ẳ T T room ị=T melt T room ị q c2 l1 ỵ lị PH ẳ ẵ1 ỵ s1 1ịl2 in which T stands for temperature of a material, Troom is the room temperature and Tmelt is the melting temperature The required material properties for epoxy resin, Kevlar/epoxy composite and steel 4340 are listed in Table A-1 in Appendix A [23,27] EH ẳ 4ị PH l 2q0 ỵ l 5ị in which the parameters c1 and s1 for epoxy resin were obtained from the corresponding shock Hugoniot curve in the shock particle velocity plane The Von Mises strength model is given by: r1 r2 ị2 ỵ r2 r3 ị2 ỵ r3 r1 ị2 ẳ 2Y 21 6ị where r1, r2 and r3 are the principal stresses and Y1 is the yield strength in simple tension The Kevlar/epoxy composite was modeled using the orthotropic EOS (also known as the AMMHIS material model in [31]) and elastic strength model The incremental constitutive relation for this orthotropic material can be expressed as Dr11 C 11 Dr C 22 6 12 6 Dr33 C 13 6 Dr ¼ 23 6 6 Dr31 0 Dr12 C 12 C 22 C 13 C 23 0 0 C 23 C 33 0 0 C 44 0 0 C 55 0 0 32 d De11 ỵ 13 Dev ol 76 Ded ỵ De 76 22 v ol 7 7 76 Ded33 ỵ 13 Dev ol 76 7 76 De23 76 54 De31 C 66 De12 0 ð7Þ d ij where Cij, Drij, De and Devol stand for the stiffness constant, deviatoric stress component, deviatoric strain component, and volumetric strain increment, respectively The volumetric strain increment can be evaluated by Eq (8) as follows [32]: Dev ol % e11 ỵ e22 ỵ e33 ð8Þ The above material model has been used by other authors for simulating the non-linear stress–strain relationships for Kevlar/ epoxy composites [33–35] The steel 4340 material used for the projectile was modeled using linear EOS and the Johnson–Cook strength model In the Johnson–Cook strength model [30], the yield stress Y is defined as: ð10Þ 2.2 Convergence and validation of the present finite element model For assessing the convergence of the present FE model, a mesh sensitivity analysis was conducted by varying the mesh size of the components, such as the mesh size for the Kevlar/epoxy was chosen to be 0.2, 0.5, and 1.5 mm, respectively The differences of the ballistic limit velocity between the models having mesh size of 0.2 mm and 0.5 mm, 0.2 mm and mm, 0.2 mm and 1.5 mm are 0.9%, 1.7% and 12.1% respectively, thus demonstrating convergence of the FE model All subsequent investigations used the mesh size equal to or less than mm Validations of the modeling approach, which was used for developing the previous and present FE models, were conducted in [21–22] Fig shows the dynamic response of a curved B4C/Kevlar armor system with a pre-existing debonding (Fig 1(a)) and subjected to a projectile impact at t = 0, 0.01, 0.03 and 0.05 ms, respectively As the projectile moves forwards, the projectile length is diminished and the armor system plug occurs These findings are similar to those shown in Fig 25 in [36] for demonstrating blunt ballistic penetrator erosion and plate plugging when a ballistic plate is subjected to a blunt ballistic penetrator impact This suggests that the FE model used here has the capability to simulate the dynamic response of a curved B4C/Kevlar armor system subjected to a projectile impact Results and discussion The effects of key parameters on the predicted values of Vbl and MAXBFD for a curved B4C/Kevlar composite armor system, which was subjected to a flat-faced cylindrical projectile impact, were evaluated using the present FE model These key parameters include: erosion strain; curvature of the armor system; ceramic material properties; size, location and number of the pre-existing or artificially introduced debondings/delaminations; ratio of B4C to Kevlar/epoxy backing plate thickness (Rcd = hc/hb); Kevlar/epoxy 28 P Tan / Materials and Design 64 (2014) 25–34 Epoxy resin Kevlar/Epoxy composite B4C Projectile (a) t = (b) t = 0.01 ms (c) t = 0.03 ms (d) t = 0.05 ms Fig Dynamic response of a curved B4C/Kevlar armor system having pre-existing debonding of Rv = mm and subjected to a projectile impact backing plate thickness (hb) They are varied in individual simulation: erosion strain of 0.5, 1, 1.5, and [23]; radius of curved armor of 120, 170 and 220 mm; ceramic material properties of B4C in Table A-1 and SiC in Table in [22]; size of the pre-existing debonding/delamination of 0, and 15 mm; location of the preexisting debonding/delamination of 0, 11 and 18 mm; the B4C and Kevlar/epoxy component thickness ratio of 1/9, 0.2, 1/3, 0.5, 0.7 and 1; Kevlar/epoxy thickness of 10, 20 and 30 mm and delamination number of 1, and were used The predicted value of Vbl was obtained by averaging the initial velocity V p0 that led to a partial penetration and the velocity V c0 that led a complete penetration The difference between V p0 and V c0 was chosen to be 10 m/s To evaluate the MAXBFD, an initial velocity of 700 m/s was applied to the projectile, which was determined based on the results from a preliminary study to avoid removal of the element on which the gauge is located The predicted values of Vbl and MAXBFD as a function of the erosion strain are presented in Fig for the B4C component and Fig for the Kevlar/epoxy component For the cases considered, the predicted values of Vbl and MAXBFD are not sensitive to variation of the erosion strain except for the case in Fig 4(b), in which the predicted value of MAXBFD reduces significantly when the erosion strain of the Kevlar/epoxy component increases from 0.5 to 1, beyond that the MAXBFD decreases slightly up to erosion strain = In the following discussion, the erosion strain is chosen to be for both B4C and Kevlar/epoxy composite The variations of the predicted Vbl and MAXBFD with the radii of curved armor systems (Rp) with and without debonding were plotted in Fig 5(a) and (b), respectively Fig 5(a) illustrates that for both cases with and without debonding, an increase in the panel’s radius results in a slight reduction in Vbl This is consistent with the experimental results shown in Figure 4.3 in [37] (i.e., the ballistic limit for graphite epoxy composite panels increased monotonically as the curvature of the panel was increased) Fig 5(b) shows that the predicted value of the MAXBFD increases with the radius of the panel with or without debonding It is consistent with the finding in [38] (i.e., for the same indentation force, the indentation depth increases with increasing radii of curvature) A comparison of the ballistic protection performance between the curved and flat panels is illustrated in Fig for the cases with and without debonding of Rv = mm As expected, the predicted value of Vbl for the curved panel is higher than the flat panel This is consistent with the findings in [33] (i.e., the helmet has a higher Table The selected values of Rcb, hc, hb and hcb for the case of AD = 4.0357 g/cm2 Rcb (=hc/hb) 1/9 1/5 1/3 1/2 7/10 hc (mm) hb (mm) hcb (=hc + hb) (mm) 2.3 21 23.3 3.7 18.5 22.2 5.3 16 21.3 6.84 13.67 20.51 8.16 11.66 19.82 9.5 9.5 19 ballistic resistance than that of a Kevlar laminate), [39] (i.e., the convex panel has higher ballistic resistance than the corresponding flat panel made of the same material), and [40] (i.e., normalized ballistic limits for the KevlarÒ KM2 helmets are higher than those for the KevlarÒ KM2 flat panels) In contrast, the predicted value of MAXBFD for the curved panel is significantly lower than the flat panel Also, it is noted from Fig that a pre-existing debonding of Rv = mm results in slight reduction in the predicted Vbl, which is similar to the finding in [22] However, it is interesting to note that for both curved and flat panels, the predicted value of MAXBFD for the case with debonding of Rv = mm is the same as that without debonding, which is different from that reported in [22] (i.e., a pre-existing debonding of Rv = mm within a SiC/Kevlar composite flat panel results in significant increase in the predicted value of MAXBFD) This implies that the B4C/Kevlar flat panel considered in this investigation could be less sensitive to the preexisting debonding than the SiC/Kevlar composite panel in [22], and thus have better defect/damage-survivability and defect/damage-tolerance Fig shows a comparison of the predicted Vbl and MAXBFD between the B4C/Kevlar and SiC/Kevlar curved armor systems having a radius of 170 mm and debonding of Rv = mm It indicates that for the cases considered, replacing the B4C with SiC slightly reduces the predicted value of Vbl, but significantly increases the predicted value of the MAXBFD for both cases with and without debonding Also, it is interesting to note that a pre-existing debonding of Rv = mm results in slight reduction in predicted Vbl for both SiC/Kevlar and B4C/Kevlar curved armors However, it does not affect the predicted MAXBFD for the B4C/Kevlar armor system but results in a slight increase in the MAXBFD for the SiC/Kevlar armor system This implies that for the cases considered, the B4C/Kevlar armor system has better ballistic performance than the SiC/Kevlar armor system, which is consistent with the outcome for the flat panel mentioned previously The variations of the predicted Vbl and MAXBFD with Rv and Lv are plotted in Figs and 9, respectively Fig shows an increase in Rv results in an increase in the predicted MAXBFD but slight reduction in the predicted Vbl These are similar to the findings for the SiC/Kevlar flat panel in [22], and the testing results in [41] (i.e., for hard armor plates made of B4C strike plates backed with ultra-high-molecular-weight polyethylene (UHMWPE) backing plates and subjected to 7.62 Â 39 M43 FMJ projectile impact, the size of an artificially introduced debonding/delamination does not significantly affect the ballistic limit of the hard armor plates) Also, it is similar to that reported in [42] (i.e., the existence of deliberately introduced delamination did not significantly influence impact resistance This may be caused by the fact that delamination did not seem to dissipate a major amount of energy) Fig illustrates that effect of Lv on the predicted Vbl or MAXBFD is insignificant This is similar to the finding in [41] (i.e., the location 29 1500 20 1200 16 MAXBFD (mm) Vbl (m/s) P Tan / Materials and Design 64 (2014) 25–34 900 600 12 300 0 0.5 1.5 2.5 Erosion strain Erosion strain (b) Variation of MAXBFD vs erosion strain (a) Variation of Vbl vs erosion strain 1500 20 1200 16 MAXBFD (mm) Vbl (m/s) Fig Variations of the predicted Vbl and MAXBFD vs erosion strain for B4C 900 600 12 300 0 0.5 1.5 2.5 0.5 1.5 2.5 Erosion strain Erosion strain (a) Variation of Vbl vs erosion strain (b) Variation of MAXBFD vs erosion strain 2000 20 1600 16 MAXBFD (mm) V bl (m/s) Fig Variations of the predicted Vbl and MAXBFD vs erosion strain for Kevlar/epoxy composite 1200 800 perfect panel 400 perfect panel panel having Rv = mm 12 panel having Rv = mm 0 50 100 150 200 250 Rp (mm) (a) Variation of Vbl vs Rp 50 100 150 200 250 Rp (mm) (b) Variation of MAXBFD vs Rp Fig Effect of Rp on the predicted Vbl and MAXBFD for the cases with and without debonding of Rv = mm of an artificially introduced debonding/delamination does not significantly affect the ballistic limit of the hard armor plates) Fig 10 shows the schematics of six armor system having the same areal density (AD) of 4.0357 g/cm2 but different value of the B4C and Kevlar/epoxy component thickness ratio (Rcb) The thicknesses for these armor systems (hcb) and their corresponding components (hb, hc) were listed in Table The variations of the predicted Vbl and MAXBFD vs Rcb are plotted in Fig 11 It indicates that the predicted Vbl increases significantly with Rcb This finding is similar to that shown in Fig in [15] for the armor systems without any defect (i.e., for the case of Rcb 1, the theoretical and experimental results of the Vbl for ceramic/aluminum armor systems increases significantly as the Rcb increases) Also, the figure shows the predicted 30 P Tan / Materials and Design 64 (2014) 25–34 20 2000 perfect having Rv = mm perfect 16 MAXBFD (mm) 1600 Vbl (m/s) having Rv = mm 1200 800 400 12 Flat panel Curved panel Flat panel Curved panel Type of panel Type of panel (a) Effect of panel type on Vbl (b) Effect of panel type on MAXBFD Fig Comparisons of the predicted Vbl and MAXBFD between the curved and flat armor systems 20 1500 perfect perfect having Rv = mm 16 MAXBFD (mm) 1200 V bl (m/s) having Rv = mm 900 600 12 300 0 B4C/Kevlar B4C/Ke vlar SiC/Kevlar Type of ceramic SiC/Kevlar Type of ceramic (a) Effect of ceramic type on Vbl (b) Effect of ceramic type on MAXBFD 2000 20 1600 16 MAXBFD (mm) Vbl (m/s) Fig Comparison of the predicted Vbl and MAXBFD between the SiC/Kevlar and B4C/Kevlar curved armor systems with and without debonding of Rv = mm 1200 800 400 12 0 12 16 20 10 15 Rv (mm) Rv (mm) (a) Effect of Rv on Vbl (b) Effect of Rv on MAXBFD 20 Fig Effect of Rv on the predicted Vbl and MAXBFD for the curved armor system having radius of 170 mm (for the case of Lv = 0) MAXBFD significantly decreases with an increase in Rcb until Rcb = 1/3, up to Rcb = the predicted MAXBFD changes slightly Fig 12 shows the variations of the predicted Vbl and MAXBFD with the thickness of Kevlar/epoxy backing component (hb) It is noted that for the curved armor systems with and without debonding of Rv = mm, an increase in hb results in an obvious decrease in the predicted MAXBFD and a significant increase in the predicted Vbl This is due to that for the panel having higher value of hb, more 31 P Tan / Materials and Design 64 (2014) 25–34 20 1600 16 MAXBFD (mm) 2000 Vbl (m/s) 1200 800 12 400 0 10 15 20 10 Lv (mm) 15 20 Lv (mm) (b) Effect of Lv on MAXBFD (a) Effect of Lv on Vbl Fig Effect of Lv on the predicted Vbl and MAXBFD for the curved armor system having radius of 170 mm (for the case of Rv = mm) Epoxy resin B4C Kevlar/epoxy composite Projectile (a) Rcb = 1/9 (b) Rcb = 1/5 (c) Rcb = 1/3 (d) Rcb = 1/2 (e) Rcb = 7/10 (f) Rcb = Fig 10 Schematics of the B4C/Kevlar curved armor systems having different value of Rcb (for the case of having Rv = mm and AD = 4.0357 g/cm2) 4000 10 MAXBFD (mm) Vbl (m/s) 3000 2000 1000 0 0.2 0.4 0.6 0.8 Rcb (a) Effect of Rcb on Vbl 0.2 0.4 0.6 0.8 Rcb (b) Effect of R cb on MAXBFD Fig 11 Variations of the predicted Vbl and MAXBFD vs Rcb for the case of R = mm and AD = 4.0357 g/cm2 work is done to cause failure of the panel and more energy is spent in overcoming the friction between the panel and projectile, and thus result in that the Vbl for a panel having higher value of hb is greater than that having a smaller value of hb The schematics of the curved armor systems having different number of pre-existing or artificially introduced delamination (Ndel) are shown in Fig 13 The variations of the predicted Vbl and MAXBFD with Ndel are plotted in Fig 14 It indicates that an increase in Ndel results in a reduction in the predicted Vbl This is expected since the Vbl decreases with a reduction of the areal mass of the armor system around the projectile impact point [15], which is reduced as Ndel increases However, it is interesting that for the cases considered, the predicted MAXBFD for the case of Ndel = is less than that for Ndel = or Ndel = It is hard to interpret the predicted MAXBFD results since the dynamic fracture mechanics for the composite armor system is extremely complex as mentioned in [43] The inertia effects, vibrations and stress wave interactions can all be present and can cause unexpected results P Tan / Materials and Design 64 (2014) 25–34 2000 20 1600 16 MAXBFD (mm) Vbl (m/s) 32 1200 800 12 Debond with Rv=5 400 Perfect Debond with Rv=5 Perfect 0 10 20 30 40 10 20 30 40 hb (mm) hb (mm) (b) Effect of hb on MAXBFD (a) Effect of hb on Vbl Fig 12 Effect of hb on the predicted Vbl and MAXBFD for the curved B4C/Kevlar armor systems with and without debonding of Rv = mm B4C Kevlar/epoxy composite Epoxy resin Projectile (a) Ndel = (b) Ndel = (c) Ndel = Fig 13 Schematics of the B4C/Kevlar curved armor systems having Ndel = 1, 3, 5, respectively (for the case of Rv = 15 mm) Conclusions 1500 12 1200 10 MAXBFD (mm) Vbl (m/s) Optimal design of curved body armor systems is attracting the attention of military users This work aims at investigating the ballistic protection performance of curved B4C/Kevlar composite armor systems with or without debondings/delaminations, including the maximum back face deformation and ballistic limit velocity A parametric study has been conducted using the present 2D axial FE model, which was developed using the commercial finite element analysis software ANSYS/Autodyn and following a procedure similar to that used previously for investigating the protection behaviors of selected flat panels against projectile impacts The parametric study shows that for the considered curved armors subjected to flat-faced cylindrical projectile impact, the predicted maximum back face deformation is more sensitive to its curvature and the material properties of the ceramic front component than the predicted ballistic limit velocity The effects of the size and location for a single pre-existing debonding/delamination on the predicted maximum back face deformations are more significant than those on the predicted ballistic limit velocity For considered curved body armors having the same areal density but different front/backing component thickness radio, an increase in the ratio results in a significant increase in the predicted ballistic limit velocity However, it is interesting to note that the predicted maximum back face deformation significantly decreases with an increase in front/backing component thickness ratio Rcb until Rcb = 1/3, up to the predicted maximum back face deformation changes slightly As expected, an increase in the backing component thickness causes an increase in the predicted ballistic limit velocity and a reduction in the predicted maximum back face deformation An increase in the number of pre-existing delaminations within the Kevlar/epoxy backing component results in a reduction in the predicted ballistic limit velocity, whereas the predicted maximum back face deformation for the case having three pre-existing delaminations is less than that having one or five pre-existing delaminations Replacing SiC with B4C for the front component does not result in a significant increase in the predicted ballistic limit velocity but significant reduction in the predicted maximum back face deformation Also, the predicted maximum back face deformation for the case having B4C front face is less 900 600 300 0 Ndel 6 Ndel Fig 14 Effect of Ndel on the predicted Vbl and MAXBFD for the curved armor systems with delamination of Rv = 15 mm 33 P Tan / Materials and Design 64 (2014) 25–34 Table A-1 Material properties [23,27] Epoxy resin C0 q0 (kg/m3) 1.13 1186 c1 (m/s) 2730 s1 1.493 Shear modulus (kPa) 1.45 Â 106 Steel 4340 q0 (kg/m3) 7830 Hardening exponent 0.26 Bulk modulus (kPa) 1.59 Â 108 Strain rate constant 0.014 Shear modulus G (kPa) 7.7 Â 107 Thermal softening exponent 1.03 Yield stress (kPa) 7.92 Â 105 Melting temperature (K) 1.793 Â 103 Hardening constant (kPa) 5.1 Â 105 Ref strain rate Bulk modulus A1 (kPa) 2.33 Â 108 G (kPa) 1.99 Â 108 B 0.5 D2 A2 (kPa) Â 107 HEL (kPa) 1.25 Â 107 Max fracture strength ratio 0.15 Hydro tensile limit (kPa) À7.3 Â 106 A3 (kPa) A 0.987 M b B0 N 0.77 C22 (kPa) 1.35 Â 107 G12 (kPa) Â 106 Tensile failure strain 22 0.08 C33 (kPa) 1.35 Â 107 G13 (kPa) Â 106 C12 1.14 Â 106 G23 (kPa) Â 106 Tensile failure strain 33 0.08 Yield stress (kPa) 2.76 Â 104 Boron carbide q0 (kg/m3) 2516 B1 C 0.027 D1 0.1 Kevlar/epoxy q0 (kg/m3) C11 (kPa) 1650 3.425 Â 106 C23 C13 1.2 Â 106 1.14 Â 106 Tensile failure strain 11 0.01 sensitive to pre-existing debonding than that having SiC front face This implies that the B4C/Kevlar armor systems may have better defect/damage-survivability and defect/damage-tolerance Acknowledgements This research work was motivated by the Defence Materials Technology Centre Personnel Survivability program, Project 7.1.2 on Life of Type of Armor materials The author would like to thank Dr M Ling, Dr B Dixon, Dr R Gailis and Dr C Woodruff for assistance during the preparation of the manuscript Appendix A See Table A-1 References [1] Chheda M, Normandia J, Shih J Improving ceramic armor performance Special report, ceramic defence, January, 2006 [2] Campbell J, Klusewitz M, LaSalvia J, et al Novel processing of boron 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