Armour is an essential feature of any military vehicle because it protects both weapons and personnel in a battlefield. In the current circumstances, civilian cars also need to be armoured from terrorist threats. The primary purpose of the armour is to withstand impact loads generated by fast-moving projectiles like bullets, shrapnel or missiles. Various materials such as ceramic composites( [1] ), metal composites( [2] [3] ) and ceramic tiles backed by metal or composite plates( [4] ) were used as armour. Also, some ceramics like Boron Carbide(BC) have proven effective at and above ordnance velocities( [5] ). Some unique composites such as glass fibre reinforced hybrid resins were effective in impact vibration damping( [6] ). The usage of grid stiffened composite panels were studied under three-point bending( [7] Analysis and testing of various types of impact loads, generated on these armour plates have to be taken as seriously. When
Armour is an essential feature of any military vehicle because it protects both weapons and personnel in a battlefield. In the current circumstances, civilian cars also need to be armoured from terrorist threats. The primary purpose of the armour is to withstand impact loads generated by fast-moving projectiles like bullets, shrapnel or missiles. Various materials such as ceramic composites( [1] ), metal composites( [2] [3] ) and ceramic tiles backed by metal or composite plates( [4] ) were used as armour. Also, some ceramics like Boron Carbide(BC) have proven effective at and above ordnance velocities( [5] ). Some unique composites such as glass fibre reinforced hybrid resins were effective in impact vibration damping( [6] ). The usage of grid stiffened composite panels were studied under three-point bending( [7] Analysis and testing of various types of impact loads, generated on these armour plates have to be taken as seriously. When the armour can withstand the loads that it is designed for, and at the same time, it has to be lightweight, then the idea can be revolutionary. So, protecting the personnel inside is of primordial importance; at the same time, manufacturing of these sophisticated vehicles with lesser weight has enabled agility, lower material costs resulted in less fuel consumption. The search for better performance armour which is lighter is never-ending. Various attempts have been made to reduce the weight of the armour by using high strength Aluminium alloys, tougher polymer matrix composites, stronger metal matrix composites, laminates made out of glass, ceramics or metals [8] . The study of impact involves various classical disciplines such as contact mechanics, wave propagation in solids, plastic deformation in materials, fracture mechanics and thermodynamics. The ballistic phenomenon is extremely complex and non-linear due to parameters such as high strain rates (greater than 10 3 s −1 ), high pressures (10 GPa), high temperature (locally can go beyond melting temperature). Non-linearity is also introduced due to large displacements and changes in boundary conditions with time. In order to perform numerical simulations, one has to work in simplifying the study to understand the phenomenon as one by one. Additive manufacturing(AM) has enabled physical visual- 
Armour is an essential feature of any military vehicle because it protects both weapons and personnel in a battlefield. In the current circumstances, civilian cars also need to be armoured from terrorist threats. The primary purpose of the armour is to withstand impact loads generated by fast-moving projectiles like bullets, shrapnel or missiles. Various materials such as ceramic composites( [1] ), metal composites([2] [3] ) and ceramic tiles backed by metal or composite plates( [4] ) were used as armour. Also, some ceramics like Boron Carbide(BC) have proven effective at and above ordnance velocities( [5] ). Some unique composites such as glass fibre reinforced hybrid resins were effective in impact vibration damping( [6] ). The usage of grid stiffened composite panels were studied under three-point bending( [7] Analysis and testing of various types of impact loads, generated on these armour plates have to be taken as seriously. When the armour can withstand the loads that it is designed for, and at the same time, it has to be lightweight, then the idea can be revolutionary. So, protecting the personnel inside is of primordial importance; at the same time, manufacturing of these sophisticated vehicles with lesser weight has enabled agility, lower material costs resulted in less fuel consumption. The search for better performance armour which is lighter is never-ending. Various attempts have been made to reduce the weight of the armour by using high strength Aluminium alloys, tougher polymer matrix composites, stronger metal matrix composites, laminates made out of glass, ceramics or metals [8] . The study of impact involves various classical disciplines such as contact mechanics, wave propagation in solids, plastic deformation in materials, fracture mechanics and thermodynamics. The ballistic phenomenon is extremely complex and non-linear due to parameters such as high strain rates (greater than 10 3 s −1 ), high pressures (10 GPa), high temperature (locally can go beyond melting temperature). Non-linearity is also introduced due to large displacements and changes in boundary conditions with time. In order to perform numerical simulations, one has to work in simplifying the study to understand the phenomenon as one by one. Additive manufacturing(AM) has enabled physical visual-
Armour is an essential feature of any military vehicle because it protects both weapons and personnel in a battlefield. In the current circumstances, civilian cars also need to be armoured from terrorist threats. The primary purpose of the armour is to withstand impact loads generated by fast-moving projectiles like bullets, shrapnel or missiles. Various materials such as ceramic composites([1]), metal composites([2] [3] ) and ceramic tiles backed by metal or composite plates( [4] ) were used as armour. Also, some ceramics like Boron Carbide(BC) have proven effective at and above ordnance velocities( [5] ). Some unique composites such as glass fibre reinforced hybrid resins were effective in impact vibration damping( [6] ). The usage of grid stiffened composite panels were studied under three-point bending( [7] Analysis and testing of various types of impact loads, generated on these armour plates have to be taken as seriously. When the armour can withstand the loads that it is designed for, and at the same time, it has to be lightweight, then the idea can be revolutionary. So, protecting the personnel inside is of primordial importance; at the same time, manufacturing of these sophisticated vehicles with lesser weight has enabled agility, lower material costs resulted in less fuel consumption. The search for better performance armour which is lighter is never-ending. Various attempts have been made to reduce the weight of the armour by using high strength Aluminium alloys, tougher polymer matrix composites, stronger metal matrix composites, laminates made out of glass, ceramics or metals [8] . The study of impact involves various classical disciplines such as contact mechanics, wave propagation in solids, plastic deformation in materials, fracture mechanics and thermodynamics. The ballistic phenomenon is extremely complex and non-linear due to parameters such as high strain rates (greater than 10 3 s −1 ), high pressures (10 GPa), high temperature (locally can go beyond melting temperature). Non-linearity is also introduced due to large displacements and changes in boundary conditions with time. In order to perform numerical simulations, one has to work in simplifying the study to understand the phenomenon as one by one. 
Armour is an essential feature of any military vehicle because it protects both weapons and personnel in a battlefield. In the current circumstances, civilian cars also need to be armoured from terrorist threats. The primary purpose of the armour is to withstand impact loads generated by fast-moving projectiles like bullets, shrapnel or missiles. Various materials such as ceramic composites([1]), metal composites([2] [3] ) and ceramic tiles backed by metal or composite plates( [4] ) were used as armour. Also, some ceramics like Boron Carbide(BC) have proven effective at and above ordnance velocities( [5] ). Some unique composites such as glass fibre reinforced hybrid resins were effective in impact vibration damping( [6] ). The usage of grid stiffened composite panels were studied under three-point bending( [7] Analysis and testing of various types of impact loads, generated on these armour plates have to be taken as seriously. When * Corresponding author. Tel.: +91-44-2257-4718 ; fax: +91-44-2257-4652.
E-mail address: sspandian@iitm.ac,in (Soundarapandian Santhanakrishnanan). the armour can withstand the loads that it is designed for, and at the same time, it has to be lightweight, then the idea can be revolutionary. So, protecting the personnel inside is of primordial importance; at the same time, manufacturing of these sophisticated vehicles with lesser weight has enabled agility, lower material costs resulted in less fuel consumption. The search for better performance armour which is lighter is never-ending. Various attempts have been made to reduce the weight of the armour by using high strength Aluminium alloys, tougher polymer matrix composites, stronger metal matrix composites, laminates made out of glass, ceramics or metals [8] . The study of impact involves various classical disciplines such as contact mechanics, wave propagation in solids, plastic deformation in materials, fracture mechanics and thermodynamics. The ballistic phenomenon is extremely complex and non-linear due to parameters such as high strain rates (greater than 10 3 s −1 ), high pressures (10 GPa), high temperature (locally can go beyond melting temperature). Non-linearity is also introduced due to large displacements and changes in boundary conditions with time. In order to perform numerical simulations, one has to work in simplifying the study to understand the phenomenon as one by one. Additive manufacturing(AM) has enabled physical visual-2351-9789 © 2019 The Authors. Published by Elsevier B.V. Peer review under the responsibility of the scientific committee of NAMRI/SME. 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to isation of any novel and complex design. Also, generating the prototypes with any available fused deposition modelling(FDM) machine is a highly cost-effective solution.
Various polymers, such as PLA, ABS, have been used in FDM for making the prototypes of lattice, honeycomb [9] and isogrid structures [10] . Nowadays, carbon fibre reinforced polymer(CFRP) is used in FDM for making lightweight structures.
Poly-Lactic Acid(PLA) is a biodegradable polymer [11] and excellent forming capabilities at room temperatures with very good mechanical properties [12] . Several studies have been performed with PLA with different carbon reinforcements such as continuous carbon fibre [13] , short carbon fibres [14] and both the methods show a substantial increase in tensile strength [13] and tensile modulus [14] .
In this study, a study on the effect of impact loading phenomenon on Isogrid lattice structure through projectile impact tests and validation with numerical simulations was attempted. Isogrid is a type of stiffening structure that is made up rectangular ribs arranged in a series of triangles. It derives its name from the isotropic properties that it exhibits because of the triangular ribs. The idea has been derived from the advantage provided by the highly efficient triangular trusses. The Isogrid structure is extensively researched and used in reducing the weight of the aircraft and spacecraft structures while holding the integrity of the hulls [15] .In order to validate the design with Isogrid stiffened plates, 10% carbon PLA has been used for generating the sample for impact testing.
For the convenience of understanding the behaviour of Isogrid under impact loading conditions, a simplified analysis was performed. The impacting body was assumed to be rigid. The projectile impact tests on the plate understudy with a velocity of 100ms −1 in the range of sub-ordnance (less than 500 ms −1 ) velocities for 10C-PLA were done. And also 600ms −1 for AISI steel 4340 simulations was also done. 
There were various material models developed over the years for modelling the behavior under impact and ballistic conditions, such as: Johnson-Cook plasticity material model [18] , Zerilli-Armstrong material model [16] , Combined J-C and Z-A, Steinberg-Guinan Model [19] (strain rates greater than 10 5 s −1 ). These high strain rate plasticity models(impact and ballistic deformations) were validated by Taylor's cylinder impact tests [20] [21] . Taylor's cylinder impact test has helped to experimentally determine the dynamic compressive yield strength of a material in the strain rate ranges of 10 2 s −1 to10 5 s −1 . The test and the theoretical procedure was initially invented by Sir Geoffrey Taylor in 1948 [20] and experimentally demonstrated by A.C Whiffin [21] in the same year.
Joshnson-Cook(JC) model [18] , an empirical constitutive model for metals, has gained wide acceptance in the scientific community. Since it has been developed from experimental studies on various metals, it has remained as valid for lower strain rates and even into quasi static regimes. For this reason JC model was chosen in this study for simulations.
where
in which A is the initial yield stress, B is the strain hardening coefficient, n in the strain hardening exponent, p is the effective plastic strain,˙ p is the effective plastic strain rate,˙ 0 is the user defined reference strain rate (normally taken as 1.0 s −1 ), C is the strain rate coefficient, T r is the room temperature taken as 22 o C, T m is the melting temperature is typically solidus temperature for an alloy, the thermal softening coefficient is given by m.
The JC Parameters for AISI 4340 Steel [18] are given in Table 1 [22] which was based on continuum mechanics. It was derived from void growth and fracture strain model [23] . In JC failure criterion, a damage parameter(D) was assumed. It was representing a continuous degree of damage in the element under considerations (4) .
Here, f =equivalent plastic strain at fracture; p =effective plastic strain;˙ p =effective plastic strain rate; D p = plastic deformation rate tensor; and D 1 ,...,D 5 are empirical material parameters. The damage constants for Johnson-Cook model [17] for AISI steel 4340 [18] [17] are given in the Table 2 
The mechanical properties of the chosen materials for bullet [24] and target AISI steel 4340 material [18] are given in Table  3 
The initial Isogrid parameters (Fig. 1 ) used in the model were: Skin thickness of the plate=t= 0.6 inches Rib width=b=0.3 inches Rib depth=d= 1.8 inches Height of the triangle=h= 4.1 inches. These parameters were obtained by using the formulations provided by NASA in Isogrid design handbook in 1973 [15] . The detailed procedure used in the study was given below. Material: Lead [24] Diameter: 0.8in. Density: ρ=11340 kgm −3 [24] Volume: V=0.268in 3 Travelling at velocity, v=600 ms −1 =23622 ins −1 mass, m=0.05 kg
The total kinetic energy of the ball was assumed equivalent to work done on the target body(8). 
Where F max = Impact load if the assumed total penetration, s=0.01m Upon substituting the known values in Eq. 8, F max =1800kN was calculated and then it was used in Eq. 9.
σ y =1145.76MPa=166.178ksi, has been obtained from Johnson-Cook material model [18] by assuming Effective plastic strain rate,˙ p =100 s −1 Effective plastic strain, p =0. 12 By using the available data and the Eq. 9, the area of cross section area of Isogrid ribs was arrived as 0.4594 in 2 . Then again by assuming Rib thickness, b= 0.3in, rib depth, d= 1.53in was arrived.To facilitate fillets of radii 0.25in d=1.8in was finalised for initial simulations. Using the derived initial Isogrid parameters, a 3D geometric model (Fig. 3) was developed on 0.6 inch thick plate.
The initial simulations performed in this work have served as a way to understand the role of Isogrid and its parameters in withstanding for various impact loads. In order to have a way of comparison, the simulations with the same set of parameters on two types of solid plates with 0.6inch thickness plate (Fig.  2b ) with 2.4inch thickness (Fig. 2a) Isogrid stiffened 0.6inch plate (Fig. 3) were performed. Two types of impactors were used such as-1. Lead sphere of 0.8inch diameter (Fig. 4a) . (Fig. 4b) .
The simulations were allowed to run for 2 milliseconds for all cases (2.4inch thick plate 2a, 0.6inch thick plate 2b, plate stiffened by isogrid without H-ribs 3a, plate stiffened with h-ribs 3b).
The simulations for 10C-PLA were also performed. The material properties considered for 10C-PLA were as per the datasheet provided by the vendor of the commercially available CFRP11 (Table 4 ). 
The mesh convergence sequence (Fig. 6) for 10C-PLA analysis was done from a coarse mesh of element size 0.01m in all coordinates and a minimum time step of 1xe −7 with a total time of simulation was 60ms. The spatial mesh size was reduced by a spatial step of 0.001m. It was observed that the sizes 0.004m and 0.005m had yielded the same maximum total deformations, and hence the size 0.005m was employed for all the simulations (Fig. 5) . Similarly, it was observed that the mesh size of 0.002m was used as the mesh size for AISI Steel 4340 simulations. To-4 tal deformations were converging to the same value as 0.001m mesh size.
The inbuilt ANYSYS adaptive meshing sequence was followed for all the cases (2.4inch thick plate 2a, 0.6inch thick plate 2b, plate stiffened by isogrid without H-ribs 3a, plate stiffened with h-ribs 3b). The impactors -the Ball (Lead sphere) and the bullet (Lead bullet) were used as rigid bodies, and the simulations were performed. The target plates were fixed on top and bottom faces.
The model was redesigned to meet the fixture specifications of the gas gun equipment (Fig. 8) . The rib area fraction (ratio of the area of ribs to the total area) was kept constant at 0.18. The rest of the parameters were adjusted to meet the fixture size of 150mm×150mm, keeping a minimum of 5mm skin thickness(t). A new set of simulations with 10C-PLA as the material was also performed at 100ms −1 . These new simulations were allowed to run for a period of 20µs. The mesh convergence tests were also performed on the new model, and it was found that the results were consistent at both 1.5mm and 1.3mm mesh sizes; hence the mesh size 1.5mm was chosen for these analyses.
The initial simulations have given enough insights into investigating the effect of H-ribs on Isogrid stiffened plates. Design of experiments was done in such a way that the design validation of Isogrid stiffened plates can be done in the most cost effective way. So, the samples were scaled down to facilitate proper seating in the fixtures provided on the gas gun equipment (Fig. 7 ) . The specimen was held in place with the help of four C-Clamps as shown in Fig. 8 . Before performing the projectile impact tests on the samples, Izod test on seven ASTM D256 standard Izod Samples (Fig. 10 ) was performed.
Izod test on seven samples were revealed that an average energy absorbed before failure of about 3.77J. The specimen dimensions were 75mm × 10mm × 10mm, with the notch placed at 28mm from the top. Notch angle was 45 • degrees and has a base radius of 2mm (Fig. 9) .
Each of the specimen were manufactured using 10% carbon Poly-Lactic Acid (PLA) which was commercially available. The notch was inbuilt in the CAD model. For uniformity and best possible strength 100% infill was used for all the specimen.
Area of cross section behind the notch was 84.0328 mm 2 . The average energy absorbed per unit area before fracture was 4.486 ×10 −3 J/mm 2 . The density of 10C-PLA as per the data provided by the supplier was 1.29 g/cm 3 (Fig. 11 ) and corresponding weight of the Izod specimen was 9.65g as theoretically, but the weight has varied. It was known that the filament was exposed to atmosphere has absorbed moisture thereby the mechanical properties of the material deteriorated [25] . It was observed from the Izod tests, the specimen 2 has exhibited brittle fracture, because the fractured surface was appearing to be smooth unlike the other sample which has shown lightly fibrous exposed surfaces (Fig. 12) .
From the results though, all of the specimens were printed using same printing parameters. The filament for specimen 2 has shown more crystalline behaviour than specimen 4 (Fig. 5) . 
Izod tests revealed that an average energy of 5.026×10 −5 Jmm −3 was absorbed by the Izod specimen. This was used to calculate the minimum velocity required for the 5mm thick trivial plate to withstand through energy balance for known volume of the trivial plate. The each trivial plate sample (Fig. 14) were held in place by four C-Clamps (Fig. 8) and were shot at by a projectile fired from the gas gun (Fig. 7) .The input for the gas gun (Fig. 7) setup was the air pressure in the air holding tank before the valve was open and the projectile was ejected out. 
The initial velocity of impact required for 13.36mm thick plate was estimated from the average energy absorbed per unit volume for the trivial case(5mm thick plate). The value 13.36mm was obtained by equating volumes of scaled down Isogrid stiffened plate and the sample plate. Some of the samples have indicated (Fig. 16c and Fig. 16d ) that the air trapped in between layers has expanded and air pocket has developed after the impact test.
Two types of grid stiffened plates have been tested and analyzed in this study, namely The Isogrid stiffened plates without H-ribs samples (Fig.  17a) and with H-ribs (Fig. 17b) were held in the gas gun fixture one after the other and impacted with a projectile at a velocity around 100ms −1 . These samples have been designed to have geometric volume. The tests were conducted on a single stage gas gun equipment (Fig. 7) .
Initially, when the ball or bullet was made as deformable but, both the ball and bullet have gotten completely disintegrated. Because lead based material(Pb) was not strong enough to penetrate AISI steel 4340. Also, the focus was more on optimising the Isogrid structure built on the plate. Therefore, the impactors such as the ball and the bullet were made as rigid bodies. From the results, it was observed that, the severity of the damage was more in the case of bullet impacting the bodies 2. The oscillating stress was observed in all the graphs (Figs. 18 -21) because, when the projectile impacted the target, a compressive wave was generated, at the same time, a small tensile wave was beginning at the wall, due of stress gradient. This primary compressive wave has reflected from the nearby wall and came back as a tensile wave. By the time, this has come back to the source, another lesser intensive compressive When two unlike waves (compressive and tensile travelling in same direction or compressive and compressive travelling in opposite direction) have interacted, the stress amplitude was reduced. Similarly, when like waves (compressive and compressive in same direction or compressive and tensile waves travelling in opposite directions) have interacted the stress amplitude was added up (Fig. 22) .
The Impact phenomenon of bullet on Isogrid stiffened plate without H-ribs was failed the part completely, because of complete penetration of the bullet. The spalling of the stiffened plate (Fig. 30b) was a dangerous phenomenon that should be avoided. Interestingly, this did not happen in unstiffened plate because the stress wave had time to travel to the edge of the plate and back to the source of impact. However, it has undergone plastic deformation but the bullet did not penetrate completely (Fig. 29) . This was happening because nearby triangular ribs kept on reflecting the compressive stress since the wave has no redundant load path to propagate (Fig. 31 ). This has kept the stresses at the impact point higher for longer duration until at 0.09ms (Fig. 31e) , the plate was fracturing and shrapnel were projected out. Once the plate has been fractured, 8 the stress wave now has started reflecting from the fracture point and travelled into the ribs (Fig. 31f) .
The increasing deformation values that were observed in (Fig.  21 ) was because the chipped out elements were travelling away from the target body with a huge amount of momentum due to impact. This phenomenon was clearly not seen in the Impact phenomenon of the bullet on Isogrid stiffened plate with H-ribs ( Fig. 22) The isogrid stiffened plate sample-1 (Fig. 23 ) with H-ribs was impacted twice in order to make sure that the projectile impacts at the node of the ribs. And it was observed that there was sufficient elastic recovery from the triangular rib after the bullet has penetrated through it. In the sample-2( Fig. 24) with H-ribs, the bullet impacted one of the ribs and disintegrated the layers of the ribs into visible fibres. The bullet had not impacted any of the rib features in the sample-3( Fig. 25) with H-ribs and went straight through and imparted only 13.45J of energy.
The Isogrid stiffened plate sample-1 (Fig. 26 ) without H-ribs was impacted with a bullet with an initial velocity of 116ms −1 and the bullet went through the skin without affecting the ribs. While in the samples(Figs. (Fig. 24 ), (Fig. 25) ), the impactor was obstructed by the ribs features. 
It was found that in the new models suitable for experiments, the isogrid stiffened plate with H-ribs was more stable with 6ribs were participating in distributing the maximum stress(41MPa) (Fig. 32a) . Whereas, the isogrid stiffened plate without H-ribs has only four ribs to distribute the maximum stress(45.2MPa) (Fig. 32b) . These results were obtained when the projectile impacts the plates at the centre of any node. Also, the maximum equivalent stress appearing on the plates stiffened by isogrid with H-ribs was stabilizing over time( Fig.  33 ) at 32MPa.
The experiments were carried out to achieve a projectile impact on one of the nodes, but the impact was an unpredictable phenomenon. The probability of bullet hitting the nodal areas in 2D was around 0.008, and that of hitting the rib area in 2D was 0.17. Therefore, the number of unit cells and the thickness of the ribs play a major role in deciding the strength of the plate. The number of unit cells was a trade off between the strength and the weight of the stiffened plate. This study was performed considering 20 unit cells. This work could be further extended to optimize the design for a specific application with a sufficient number of unit cells.
The Isogrid stiffened plates with H-ribs were performing good under the considered impact loading conditions (a rigid ball, a rigid bullet impacting the target bodies with initial velocity of 600ms −1 ). Though, there was considerable deformation(20mm) in plates stiffened by Isogrid, it was still less than (by 60%) that without H-ribs. without H-ribs.
The initial velocity for the trivial case (5mm thick plate) was obtained as 23.3ms −1 from Izod tests but from experiments, the trivial case plate could withstand much higher velocities (around 46m/s) indicating, strain hardening at higher strain rates of projectile impacts than Izod test. Average energy per unit volume of trivial plate specimen was 1.323 × 10 −4 Jmm −3 .
The initial velocity for the plate specimen (13.36mm thick plate) was obtained as 81ms −1 (from energy per unit volume of trivial case) while from experiments it was about 76ms −1 .
Isogrid stiffened plates with H-ribs were able to withstand a velocity of upto 95ms −1 while Isogrid stiffened plates without H-ribs could were withstanding a velocity of upto only 60ms −1 .
It was indicating that Isogrid stiffened plates with H-ribs were at least 37% more stronger than Isogrid stiffened plates without H-ribs from experiments.
Building Isogrid without H-ribs on any body subjected to impact loading cannot be advisable because it has completely weakened the body rather than helping the body to withstand the stresses.
Also, Isogrid stiffened plates with H-ribs were doing well in distributing the stresses across the ribs through multiple load paths. Therefore, it was found Isogrid stiffening has helped in designing structures for withstanding higher impact loads.