Impact penetration and perforation performance of square sandwich panels with EPS foam core

Abstract

This paper addresses the impact penetration and perforation behaviour of sandwich panels having a low density core expanded polystyrene foam (EPS) bonded to two aluminum (6061-T6) face-sheets. The effects of foam and plate thicknesses on the impact energy absorption of sandwich panels were also investigated. The dynamic response of panels was analyzed using the explicit finite element method. The foam core material was modeled as a crushable foam material with ductile damage, and the metal face-sheets as Johnson-Cook (JC) material. The cohesive response of the adhesive interface was considered using cohesive zone model. The analyses showed that the impact energy, face-sheet and foam core thickness affected significantly failure modes, contact force levels and histories. The low-speed impact tests of the sandwich panels with different face-sheet and foam core thicknesses showed similar contact force histories, energy absorption ability and deformation modes to those of finite element analyses.

1 Introduction

Sandwich structures, consisting of a low-density core, between two thin and stiff face-sheets have been increasingly used in the applications requiring high flexural rigidity, buckling resistance, and energy absorption and bending stiffness. The face-sheet materials are usually aluminium or fibre reinforced polymers whereas the core material is woods, expanded metals, polymer and metal foams, and polymers and metal honeycombs. The foam core holds together and stabilizes outer face-sheets against buckling under edgewise compression, torsion or bending loads. The face-sheets increase the effective moment of inertia of panels under in-plane loads while the core transfers shear loads between face-sheets. Loads are transferred via adhesive layer between the face-sheets and core. The static and dynamic behaviors of sandwich panels have been investigated extensively [1, 2]. Feng and Aymerich [3] investigated the structural and damage response of foam-based sandwich structures under low velocity impact using the finite element method. They implemented a three dimensional damage model to ABAQUS/Explicit and interfacial cohesive laws to model damage modes occurring in the composite face-sheets, such as fibre fracture, matrix cracking and delaminations, and a crushable foam plasticity model to foam core. Experimental and predicted force histories, force-displacement curves and dissipated energy levels were in good agreement. They also predicted reasonably accurate temporal sequence of primary damage events, and planar extension of the damage area. Manes et al [4] investigated the low velocity impact behaviour of sandwich panels with Al2024-T3 aluminum face-sheets and honeycomb Nomex$^{TM}$. They used a detailed finite element model at a micro mechanical level using the data obtained from flat-wise compressive test of honeycomb cores and considering a ductile failure for aluminum face-sheets. The experimental and predicted damage shapes and failure onset were in a good agreement. Wang et al [5] studied the low velocity impact behaviour of foam-core sandwich panels considering the effects of the impactor diameter, impact energy, face-sheet thickness and foam-core thickness. They modeled the polyurethane foam core as a crushable foam material, and applied a three-dimensional finite element model with progressive damage model to analyse the impact response of sandwich panels having the face-sheets made of plain weave carbon fabric laminated composite. They developed a progressive damage model based on the generalized Schapery theory to describe the nonlinear behavior of plain weave carbon laminates. Based on the experimental and finite element analysis they showed that the peak load, absorbed energy and contact duration increased with increasing impact energy, the absorbed energy and contact duration decreased with increasing impactor size, the absorbed energy and contact duration decreased with increasing face-sheet thickness, but the peak loads increased. Zhou et al [6] investigated the low velocity impact response, perforation resistance of foam based sandwich panels and the oblique loading effect experimentally and numerically. The perforation resistance of plain foam was strongly dependent on the properties of foam core. PVC foams with higher densities exhibited superior perforation resistance in their associated sandwich structures. The results of impact tests such as the impact load-displacement responses and the perforation energies of both plain foams and sandwich panels were in good agreement with the finite element results. Hosur et al [7] studied the impact performance of neat and nanophased foam core sandwich composites with three-layered plain weave carbon fabric/Sc-15 epoxy composite face sheets, which were fabricated using the co-injection resin transfer molding process. They determined peak load level, absorbed energy, the time and deflection at peak load level. They used a scanner, optical and scanning electron microscopes to understand the failure patterns. Sandwich panels with nanophased foam sustained higher loads and exhibited smaller damage areas as compared with those of the neat counterparts but yielded a foam cores exhibited more brittle fracture. Zhou et al [8] investigated the low velocity impact behaviour of sandwich structures having carbon fibre skins and cores fabricated by bonding foams of different densities; thus, the linear PVC, crosslinked PVC (Polyvinyl chloride) and PEI (Polyetherimide) foams were bonded together to produce a three-layer core. They modeled the impact response of foam core sandwich panels with the finite element method and compared the load-displacement responses and failure modes with the experimental ones. They observed that the panels failed in a through-thickness shearing mode, leaving a clear cylindrical hole in the multi-layered core and placing the high density foam core against the top surface skin could result in an improved perforation resistance relative to the sandwich panels that the higher density foam contacts with the distal surface, and that the graded structures could out-perform their monolithic counterparts in terms of their perforation resistance.

Hachemane et al [9] investigated the impact and indentation behaviours of composite sandwich structures made of jute/epoxy-cork sandwich material. They evaluated the impact energy and cork density influence over the sandwich plate damage behaviour by instrumented static and dynamic tests, and showed that both cork density and impact energy affected onset damage force, maximum force and damage size. The sandwich laminates dissipated more energy by 11% under impact loading. Tan et al [10] investigated the dynamic response of clamped sandwich beams with aluminum alloy open-cell foam core and the effects of face-sheet and core thickness on the impact behaviour for different impact energies. They observed that tensile crack and core shear were dominant failure modes, and the thickness of foam core played an important role on the failure mechanism of the sandwich beams. Yang et al [11] investigated the low velocity impact response of closed cell polymeric foam core sandwich panels made of woven carbon/epoxy laminate face-sheets under two different impact energies of 10 and 50 J at cold, room and high temperature conditions. They analysed the impact behaviour of sandwich structures using the finite element method, and implemented a crushable foam material model for foam core, continuum damage model for face-sheets and a cohesive model for bonding layers. They also determined the damage and delamination characteristics via ultrasonic testing and high speed cameras, and observed that the larger damage zone occurred at high exposure temperatures for both low and high impact energies. Chen and Li [12] investigated experimentally and numerically the performance of composite lightweight structural insulated panels with expanded polystyrene core against windborne debris impacts. They examined the failure modes of Structural Insulated Panel (SIP) with Expanded Polystyrene Sandwich (EPS) by flat metal skins under various impact velocities by means of two high speed cameras. They analysed these sandwich panels via LS-DYNA and used their test data to calibrate the accuracy of numerical model. Elnasri and Zhao [13] aimed to determine the piercing force of sandwich panels with foam cores under an impact loading. They predicted that the piercing force versus displacement curves of sandwich panels were in good agreement with experimental results. Their validated model was successful for a large range of impact velocities. Gunes and Arslan [14] investigated the low velocity impact behaviour of sandwich structures with aluminum honeycomb core. Their finite element model for sandwich structures predicted contact forces and deformations in good agreement with experimental ones. They found that the stiffness and stability of sandwich structures were increased with decreasing cell size of aluminum honeycomb, but the core height of aluminum honeycomb had a minor effect on the impact response of sandwich plates. Yang et al [15] investigated the low velocity impact response and compression after impact (CAI) behaviour of foam-filled sandwich panels with hybrid face-sheets. They manufactured foam-filled sandwich panels with six types of face-sheets by vacuum-assisted resin injection (VARI) process. The micro-structure analysis of impacted specimens using scanning electron microscope (SEM) showed that the damage modes, such as matrix cracking, fiber breaking, foam cracking, occurred in sandwich panels with pure carbon face-sheets, and that the panels with pure carbon face-sheet had poor impact resistance properties whereas the hybrid panels with different plies could provide higher maximum contact force and absorb more impact energy due to carbon fiber breaking on/near the contact surface. Jing et al. [16] investigated the deformation/failure modes and dynamic response of peripherally clamped square monolithic and sandwich panels with metallic foam, three types of cores: closed-cell aluminum foam core, open-cell aluminum foam core and aluminum honeycomb core under an impulsive loading. In all sandwich panels a large global inelastic deformation, and an obvious local compressive failure in the central area was occurred. Hundley et al [17] investigated the low velocity impact response of sandwich panels reinforced with lattice core structure. They used two different core materials as an UV (Ultraviolet)-cured photopolymer lattice, and an aluminum alloy lattice cast. They studied both quantitative and qualitative measurements and used for model validation including; impactor force-time history, impact and post-rebound velocity and damage zone. Their force-time predictions were in good agreement with the experimental measurements. Each sandwich panel was capable of absorbing the kinetic energy of impactor with minimal damage to the back (non-impacted) face of the panel and lattice core sandwich panels absorbed all of the incident kinetic energy. Zhang et al [18] investigated the low velocity impact and indentataion behaviour on the energy absorption of sandwich panels using a high-speed camera system so as to obtain the surface profiles of panels and the depth of ultimate indentation. Their three dimensional finite element and experimental results showed that the adhesive layers on energy absorption had a non-ignorable effect and the honeycomb played a dominant role in energy absorption. Manes et al [19] investigated the strain rate behaviour and material model identification of an Al 6061 T6 alloy which finds widely applications in ballistic impact scenario. They concluded that the strain rate had insignificant effect until $10^{3}\,\text{s}^{-1}$ on the flow stress while over $10^3\,\text{s}^{-1}$ there was an appreciable increase in the strain rate sensitivity. They obtained the model parameters on the basis of the experimental tests performed in the strain rate range between $10^{-4}$ and $10^{4}\,\text{s}^{-1}$.

There are numerous studies on the impact behaviour of sandwich panels with various kinds of foam core. Polymeric foams, such as expanded polystyrene (EPS) foam, are preferred in various industries because they can dissipate large amount of impact energy causing low reaction forces. EPS foam is also low cost, light and suitable for mass production. Sandwich panels with EPS foam core requires to investigated in terms of the capability of energy absorbing, both penetration and perforation damage resistance etc. This study investigates the penetration and perforation resistance of sandwich panels with low density foam core bonded to metal face-sheets. The low velocity impact response of the sandwich panels was studied using the three dimensional non-linear finite (explicit) element model in order to determine the influence of the foam core and face-sheet thicknesses on the penetration and perforation resistance of sandwich structures. The numerical model was calibrated using experimental results based on the low velocity impact tests performed via the drop weight test system. The calibrated model predicted that the contact force histories, kinetic energy histories and deformation modes were in good agreement with experimental results. Special attention was paid to the damage behaviors of the face-sheets, foam core and bonding regions between the face-sheet and core around the impacted region as well as the failure modes of the face-sheets, foam core and adhesive layer. The study also considers the coupling effect of face-sheet and core thickness on the penetration and perforation responses of foam core sandwich panel under a low velocity impact.

2 Experimental procedure

The low velocity impact tests of sandwich panels were performed via Fractovis Plus low-velocity impact test equipment (figure 1). This device works according to the drop weight impact test principle. The impactor goes up a calculated height to achieve a desired impact energy. Specimens are mounted to the bottom part of impact device according to the datum position of impactor. There is a velocity sensor at the datum position of impactor so that, the velocity of impactor could be measure a before the impactor contacts to specimen. After the impactor contacted specimen, the anti-rebound system is triggered and the impactor is allowed to jump once. The penetration and perforation performances of the foam core sandwich panels was investigated for two different face-sheets (0.5, 1.0 mm) and foam thicknesses (10, 20 mm). Types (I, II, III and IV) describe each configurations in terms of different thicknesses of sandwich panels (Table 1). An apparatus was designed and manufactured to mount the sandwich panels on the impact test equipment. The specimens were fastened to this apparatus by bolts so that a fixed edge boundary condition along all edges can be achieved (figure 2). The specimens having unsatisfactory bonding quality were used in a series of preliminary tests to provide the optimal impact conditions considering the temporal variations of contact force. Low velocity impact tests were repeated at least twice for each of all sandwich configurations for each impact energy of 50, 100 and 150 J (Table 2). In case the contact force histories of the first two impact tests for each panel configuration were dissimilar, the tests were repeated for that panel configuration until a similar contact force variation is obtained. The impactor has a diameter of 20 mm, a mass of 10.045 kg and hemispherical tip geometry was used.

Fig. 1

Low velocity impact test system.

Fig. 2

Sandwich panel components and bonding apparatus.

Table 1 The sandwich panel specimen configurations.

Table 2 Impact energy levels

2.1 Specimen preparation

The sandwich panel specimens consist of two face-sheets, foam core and adhesive layers to bond face-sheets with foam core. The face-sheets were manufactured from aluminium Al-6061-T6 plates in two thicknesses of 0.5 and 1 mm, length and wide of 2000 $\times$ 1000 mm. The face-sheets were cut in dimensions of $170\times 170\,\text{mm}$ by guillotine and twelve screw holes were drilled in a diameter of 8 mm by CNC machines in order to mount the sandwich panels firmly to the impact test equipment. The foam core material was selected as expanded polystyrene (EPS) foam in the thickness of 10 and 20 mm, and in a density of $20\,\text{kg/m}^3$. The foam core materials were cut in size of $170\times 170$ mm by using a portable saw. Aluminum 6061-T6 was selected for the face-sheets material and EPS foam core for the core material. Aluminum 6061-T6 has a wide use in various industrial applications. Similarly, EPS foam core is widely preferred due to its good absorbing capability of impact energy. Therefore, sandwich panels having low density foam and high strength face-sheets was considered in this study. In comparison to other sandwich panels in literature the present structure offers high strength, lower weight and production cost. The face-sheets and foam core material were bonded using two components adhesive (ARALDITE 2015). Before applying adhesive, the bonding surfaces were cleaned by using ethanol ($\hbox {C}_2\hbox {H}_6\hbox {O}$) which is very effective in the cleaning of impurities and dirt affecting adversely the bonding quality of two plates. In order to get a uniform adhesive layer between face-sheets and core material without air bubbles as possible, a uniform pressure was applied to adhesive layer between two face-sheets. A bonding apparatus was designed and manufactured in dimensions of $220\times 220\times 5\,\text{mm}$. The apparatus surfaces contacting with the face-sheet surfaces were machined precisely. The upper and lower parts of bonding apparatus were manufactured so as to be joined by bolts. This apparatus also provides gentle pressure to be distributed uniformly over the sandwich structure necessary for an effective bonding. The thickness-jigs were also produced to achieve a constant adhesive thickness of 0.25 mm (figure 2) . For this purpose, four similar thickness-jigs in the total thickness of specimen including the adhesive thicknesses were placed between the upper and lower parts of the bonding apparatus. A set of ten apparatus was manufactured so that ten specimens could be produced simultaneously. The two-components adhesive, Araldite 2015, needs an average curing time of 48-72 hours at room temperature. Therefore, all bonded specimens were left to a curing time of 72 hours at room temperature. During the bonding process the adhesive was first rolled up by a hoe on to the face-sheet bonding surface, and then the sandwich structure was compressed between the upper and lower parts of apparatus so that the air bubbles could be removed as possible and to achieve a better bonding. Some amount of adhesive may be squeezed due to the applied pressure and this may cause the specimens to bond to both the lower and upper parts of apparatus. Therefore, the surfaces of both face-sheets were cleaned and some amount of liquid paraffin was applied on to the contacting surfaces of the upper and lower parts of bonding apparatus. After a curing time of 72 h the bonding apparatus was demounted, and the specimen was removed, and the excessive adhesives were cleaned from both the specimens and lower and upper parts of apparatus.

Table 3 Constants for Johnson-Cook dynamic failure model of Aluminum Al6061 T6 [21].

3 Numerical model

The numerical model in order to analyse the perforation of sandwich panels was developed using ABAQUS/Explicit [20]. The effects of geometric parameters were investigated to improve the impact energy absorption capability of sandwich panels. The non-linear behaviour of face-sheets materials was modeled using Johnson-Cook material model. The Johnson-Cook dynamic failure model is used as a specific case of the ductile damage initiation criterion for metals in ABAQUS/Explicit. The important parameters used in Johnson-Cook dynamic failure model are given in Table 3 for aluminum 6061 T6 [21]. The Johnson-Cook material model represents empirically the flow stress as follows [21],

$$\begin{aligned} \sigma = \left[ A+B(\epsilon _p)^n\right] \left[ 1+C ln\left( \frac{\dot{\epsilon _p}}{\dot{\epsilon _0}}\right) \right] \left[ 1-\left( \frac{T-T_a}{T_f-T_a}\right) ^m\right] \end{aligned}$$

(1)

where $\sigma$ is effective stress, A is elastic limit, B and n are the characteristic constants of plastic behaviour, C represents the sensitivity to the strain rate, $\dot{\epsilon _0}$ is the reference strain rate (typically set to $1\,\text{s}^{-1}$) $\epsilon _p$, and $\dot{\epsilon _p}$ are the plastic strain and the plastic strain rate, respectively, T ise the material temperature, $T_a$ is the room temperature, $T_f$ is the material melting temperature respectively, m is a material constant including the temperature dependency [21]. Abaqus/Explicit [20] provides a dynamic failure model specifically for the Johnson-Cook plasticity model, which is suitable for only high-strain-rate deformation of metals. The Johnson-Cook dynamic failure model is based on the value of the equivalent plastic strain at element integration points; failure is assumed to occur when the damage parameter exceeds 1. The damage parameter is defined as

$$\begin{aligned} w=\sum \left( \frac{\Delta \varepsilon _p}{\varepsilon _{p,f}}\right) \end{aligned}$$

(2)

where $\Delta \varepsilon _p$ is an increment of the equivalent plastic strain, $\varepsilon _{p,f}$ is the strain at failure, and the summation is performed over all increments in the analysis. The strain at failure, $\varepsilon _{p,f}$ , is assumed to be dependent on a non-dimensional plastic strain rate, $\dot{\epsilon _p} / \dot{\epsilon _0}$ ; a dimensionless pressure-deviatoric stress ratio, p / q (where p is the pressure stress and q is the Mises stress). The dependencies are assumed to be separable and are of the form

$$\begin{aligned} \epsilon _{p,f}= \left[ d_1+d_2\ exp\left( d_3\frac{p}{q}\right) \right] \left[ 1+d_4ln \left( \frac{\dot{\varepsilon _p}}{\dot{\varepsilon _0}} \right) \right] \left( 1+d_5\left( \frac{T-T_a}{T_f-T_a}\right) \right) \end{aligned}$$

(3)

where $d_1-d_5$ are failure parameters. In case this failure criterion is met, the deviatoric stress components are set to zero and remain zero for the rest of the analysis [20].

The inelastic nonlinear behaviour of foam was simulated using the crushable foam model with the isotropic hardening which is avalible in ABAQUS (crushable foam and crushable foam hardening option), in which the hardening behaviour may be represented in terms of uni-axial compressive stress and plastic strain. The yield surface for the isotropic hardening model is defined as [20],

$$\begin{aligned} F=\sqrt{q^2+\alpha ^2p^2}-B=0 \end{aligned}$$

(4)

where p is pressure stress, ($p=(-1/3)\text { trace }\sigma$), q is Mises stress, ($q=\sqrt{(3/2)S:S}$), S is the deviatoric stress, ($S=\sigma +pI$), B is the size of the vertical axis of the yield ellipse, ($B=\alpha p_c=\sigma _c\sqrt{1+(\alpha /3)^2}$), $\alpha$ is the shape factor of the yield ellipse that defines the relative magnitude of the axes, $p_c$ is the the yield stress in hydrostatic compression, and $\sigma _c$ is the absolute value of the yield stress in uniaxial compression. The yield surface represents the Mises circle in the deviatoric stress plane. The shape factor, $\alpha$, can be computed using the initial yield stress in uniaxial compression, $\sigma _c^0$, and the initial yield stress in hydrostatic compression, $P_c^0$ (the initial value of $P_c$ ), using the relation [20]:

$$\begin{aligned} \alpha =\frac{3k}{\sqrt{9-k^2}} \qquad \text {where} \qquad k=\frac{\sigma _c^0}{p_c^0} \end{aligned}$$

(5)

Ductile Damage Criterion as the damage criteria was used. As the strain rate increases, an increase in the yield stress of some materials is observed. For many foam materials, this increase in yield stress becomes more important when the stain rates are in the range of 0.1 to 1 per second, and this importance increases much more when the strain rates increase by 10-100 per second. Cowper-Symonds Power Law rule is defined as the strain rate rule, and it is in the following form [20];

$$\begin{aligned}&\dot{\bar{\varepsilon }}^{pl}=D(R-1)^n \qquad R\ge 1 \end{aligned}$$

(6)

$$\begin{aligned}&R\equiv \frac{\bar{B}}{B} \end{aligned}$$

(7)

where B is the size of the static yield surface and $\bar{B}$ is the size of the yield surface at a nonzero strain rate. The ratio R can be written as:

$$\begin{aligned} R-1=\left( r-1\right) \frac{3k_t+r\left[ k+k_t \left( 3-k\right) \right] }{\left( 1+k_t\right) \left( 3k_t+r k\right) } \end{aligned}$$

(8)

where r is the uniaxial compression yield stress ratio defined by:

$$\begin{aligned} r\equiv \frac{\bar{\sigma }_c}{\sigma _c} \end{aligned}$$

(9)

where $\sigma _c$ is the uniaxial compression yield stress at a given value of $\varepsilon _{axial}^{pl}$ axial for the experiment with the lowest strain rate and can depend on temperature and predefined field variables; D and n are material parameters that can be functions of temperature and, possibly, of other predefined field variables.

Fig. 3

Stress-strain curve of EPS foam core.

The compression yield-stress ratio and fracture energy were calculated in order to define the crushable foam behaviour. The stress-strain curve was obtained from the uni-axial compression test of EPS core material (figure 3). Isotropic hardening option needs two parameters as compression yield stress ratio and plastic Poisson’s ratio. Plastic Poisson’s ratio, which is defined as the ratio of the transverse strain to the longitudinal plastic strain under uniaxial compression, should be in the range of −1 and 0.5 [20]. Plastic Poisson ratio’s was taken zero in this study and the compression yield stress ratio (k) was calculated from the following equation (Plastic Poisson’s ratio, $v_p$) [20];

$$\begin{aligned} k= \sqrt{3(1-2v_p)} \end{aligned}$$

(10)

The ductile damage criterion needs fracture strain and energy. The fracture strain and energy of EPS foam core material was obtained from compression test by calculating the area under the experimental force-displacement curve in Matlab [22].

The cohesive zone model (CZM) was implemented to model the interfacial failure of adhesive layers. The adhesive layers are simulated by means of 3D cohesive elements (COH3D8) placed between face-sheets and core. In the cohesive zone model, the fracture process zone is lumped into one cohesive layer and the fracture behaviour is characterized by a traction–separation law. The fracture toughness related with cohesive parameters in mode I and mode II can be obtained by using Double Cantilever Beam (DCB) test and the End Notched Flexure (ENF), respectively The cohesive zone model relies on relationships between cohesive tractions and relative displacements (in tension or shear). The nominal traction stress vector $\tilde{t}$, with the components: $t_n$, $t_s$ and $t_t$ (in three dimensional problems), are normal and two shear tractions, respectively. The corresponding separation displacements are denoted by $\delta _n$ , $\delta _s$ and $\delta _t$, respectively. The elastic behavior can be written as

$$\begin{aligned}{}[t]= [K][\delta ] \end{aligned}$$

(11)

$$\begin{aligned} \begin{bmatrix} t_n \\t_s \\ t_t \end{bmatrix}= \begin{bmatrix} K_{nn}&0&0 \\ 0&K_{ss}&0 \\0&0&K_{tt} \end{bmatrix}\begin{bmatrix} \delta _n \\ \delta _s \\ \delta _t \end{bmatrix} \end{aligned}$$

(12)

The stiffness matrix [K] includes the stiffness parameters epoxy of adhesive. $G_n$ and $G_s$ are areas under CZM laws in tension or shear (figure 4). The cohesive parameters of the epoxy adhesive (Araldite 2015) are given in Table 4 [23]. The failure mechanism consists of a damage initiation criterion and a damage evolution law. The cohesive zone model assumes that the damage can propagate according to a specified damage evolution law after a damage initiation criterion is satisfied and the linear or non-linear traction-separation responses can be implemented to the damage evolution. In this study, the Quadratic Maximum Nominal Stress damage initiation criterion was used [20]. Damage is initiated when quadratic interaction function between traction and separation reaches 1, which is represented as,

$$\begin{aligned} \left\{ \frac{\langle t_n \rangle }{t^0_n}\right\} ^2+\left\{ \frac{t_s}{t^0_s}\right\} ^2+\left\{ \frac{t_t}{t^0_t}\right\} ^2=1 \end{aligned}$$

(13)

Fig. 4

Linear CZM law with triangular shape.

Table 4 Cohesive parameters of adhesive Araldite 2015 [23].

Once the damage initiation criteria is satisfied the delamination stiffness is degraded. A scaler damage variable, D which affects the contact stress component as,

$$\begin{aligned} t_n= \left( 1-D\right) t^{und}_n \end{aligned}$$

(14)

$$\begin{aligned} t_s= \left( 1-D\right) t^{und}_s \end{aligned}$$

(15)

$$\begin{aligned} t_t= \left( 1-D\right) t^{und}_t \end{aligned}$$

(16)

where $t^{und}_n$, $t^{und}_s$ and $t^{und}_t$, are damage free contact stresses in normal, shear in s-direction and shear in t-direction respectively. To describe the evolution of damage under a combination of normal and shear separations across the interface, an effective separation is defined as,

$$\begin{aligned} \delta _m=\sqrt{\langle \delta _n \rangle ^2+\delta _s^2+\delta _t^2} \end{aligned}$$

(17)

A three dimensional cohesive element (COH3D8) was used to model the cohesive response of adhesive layers. The artificial cohesive thickness was taken as 0.25 mm for the adhesive layers. The 3D finite element models of 170 $\times$ 170 mm sandwich panels were generated using solid elements (C3D8R) for metal face-sheets, core, adhesive layers, respectively (figure 5). The impactor was modeled as a rigid hemispherical body using rigid elements (R3D4). The impact energy was imposed by specifying an initial velocity to the impactor. The impactor can move only normal direction, since its movements in the other directions are prevented. The sandwich panels were fastened by bolts to create a fixed edge boundary condition, as possible. In general, specimens were fastened to impact device using compression forces with pneumatic system. However, the EPS foam core has low density and can deform very easily. Therefore, a boundary condition considering bolts is suitable to simulate the fastening specimens to impact device. Bolts were modeled with a rigid body behaviour. Both face-sheets and foam core were modeled using three dimensional solid finite elements (C3D8R) with three degrees of freedom at each node. Aspect ratio of 1.0 was used for the face-sheets elements. The characteristic element length for the cohesive elements and foam core elements was taken as 1 mm. Since significant element distortions, which may cause numerical instabilities at integration points, occurred in the deformed mesh geometry of the foam core during the analysis, an adaptive meshing algorithm (Arbitrary Lagrangian and Eulerian Algorithm) was implemented to improve excessively distorted element geometries. At the end of each time increment, highly deformed finite elements were determined and the load increments and the deformed element geometries were modified such that the element distortions can be negligible and the numerical integrations can be accurate reasonably. The hourglass control was also used for the finite elements of core material to avoid excessive element distortions and to carry out numerical integrations accurately. The mechanical contact between the impactor, sandwich panel and bolts was modeled by the GENERAL CONTACT ALGORITHM (contact domain-All with self) with tangential behaviour and penalty friction formulation with friction coefficient of 0.4 in Abaqus/Explicit. This contact formulation was also applied to the contact stage of face-sheets and core after the adhesive cohesive elements were fully damaged and a zero stiffness was attributed to these elements. The contact between the face-sheets and adhesive layer, and the core and adhesive layer was modeled using SURFACE TO SURFACE contact method based on TIE constraints.

Fig. 5

Finite element model

4 Results

The low velocity impact tests of foam core sandwich panels were performed for two different foam core (10, 20 mm) and plate thicknesses (0.5, 1 mm) at the impact energies of 50, 100 and 150 J, respectively. The effects of the geometric design parameters, such as foam core and plate thicknesses were investigated in order to improve the impact energy absorption capability of sandwich panels. The temporal variations of the contact force and kinetic energy were predicted numerically and measured experimentally for three impact energies of 50, 100 and 150 J, respectively. The theoretical and experimental results were compared in order to validate the use of cohesive zone model to predict the adhesive damage initiation and propagation.

4.1 Pre-study

First, the low velocity impact tests were performed to determine the applicability of Johnson-Cook material model for the dynamic behaviour of a single aluminum 6061-T6 plate. The explicit finite element analysis of a fixed single aluminum plate modeled with Johnson-Cook model presented the results in good agreement with experimental results. Figure 6(a) compares the experimental and predicted contact force histories of the single plate an Al 6061-T6 having a thickness of 1 mm under the impact energies of 25, 50 and 75 J, respectively. The contact force increases with increasing impact energy whereas the total contact duration decreases. The contact force levels and general trends of the contact force-time variations are similar. Figure 6(b) shows that the experimental and calculated temporal variations of kinetic energy of an Al 6061-T6 single plate are in good agreement. The single aluminum single plate was perforated at nearly an impact energy of 60 J. Both predicted and experimental kinetic energy histories are similar for an Al 6061-T6 single plate under impact energy levels of 25, 50 and 75 J. Figure 7 shows the after-impact deformed shape and area of damaged region in Al 6061-T6 single plate for an impact energy of 75 J. The perforation shape at the impact region is symmetrical for the numerical model, whereas, it is not symmetrical for the experimental test. The area of damaged region is about $503.60\,\text{mm}^2$ and perimeter of damage region is about 88.22 mm for the experimental test and numerical ones are about $452.39\,\text{mm}^2$ and 75.40 mm.

Fig. 6

(a) Contact force and (b) kinetic energy histories of a single Al 6061-T6 plate for different impact energies.

Fig. 7

The after-impact deformed shape and area of the damaged region in a single Al 6061-T6 plate for an impact energy of 75 J (A: area, P: perimeter).

4.2 Type I, 1/10/1 mm

In Type I (Table 2), the foam core is thin but the face-sheets are thick. Figure 8(a) compares the experimental and predicted contact force histories for the impact energies of 50, 100 and 150 J, respectively. The experimental and predicted contact force histories are in a good agreement in case their trends and levels are concerned. The predicted peak contact force values are 7.86, 11.75 and 13.89 kN, whereas the experimental ones are 8.88, 13.41 and 14.01 kN for present impact energies, respectively. The differences between the experimental and predicted peak contact forces as well as the contact durations are very small. Figure 8(b) shows both experimental and predicted kinetic energy histories for different impact energies, respectively. The numerical model of the sandwich panel (Type I) predicts that the kinetic energies of impactor reduced from 50, 100 and 150 J to 7.12, 7.65 and 0.08 J, respectively. Thus, Type I could dissipate the impact energies (50, 100 and 150 J) by 85.76, 92.35 and $99.95\%$, respectively. The experimental tests of Type I indicate the impactor energy from 50, 100 and 150 J to reduce to 10.72, 14.78 and 0.01 J, respectively. Thus, the present impact energies (50, 100 and 150 J) are dissipated by 78.56, 85.22 and $99.99\%$, respectively. The sandwich panel was perforated at an impact energy of 150 J. All sandwich panels (Type I) had a similar dissipation ability of the impact energy based on the predicted and experimental kinetic energy histories.

Fig. 8

(a) The contact force and (b) the kinetic energy histories of Type I (1/10/1 mm) for different impact energies.

Fig. 9

The after-impact deformed regions top and bottom surfaces of Type I (1/10/1mm) for different impact energies(A: area, P: perimeter).

Figure 9 shows the experimental and predicted after-impact deformed regions on the top and bottom surfaces and the shapes and areas of these regions in the sandwich panels (Type I) for impact energies of 50, 100 and 150 J, respectively. The predicted and experimental deformed shapes are almost similar for the present impact energies. As the impact energy is increased, the impactor penetrates more. An impact energy of 50 J is not enough for the perforation of the impactor into sandwich panels, and an impact energy of 100 J results in a partly perforation only in the top face-sheet of the sandwich panel. However, an impact energy of 150 J fully penetrates into the sandwich panel. The foam core provides geometrical continuity between top and bottom face-sheets. The top face-sheet meets with impactor firstly so, it deforms more than the bottom face-sheet. The effect of fixed edge condition is apparent in the top face-sheet. The areas and perimeters of the perforated and affected regions by the impactor were calculated using the image processing technique. The measured areas of the damaged regions (experimental) are about 66.55, 142.36 and $595.11\,\text{mm}^2$ and their perimeters are about 28.92, 66.22 and 89.41 mm, whereas the calculated areas are 65.53, 143.65 and $540.26\,\text{mm}^2$ and the calculated perimeters are 28.70, 49.31 and 82.70 mm for present impact energies, respectively (figure 9). The calculated and measured areas and perimeters of the damaged regions are similar. In order to determine the damage formation through the thickness of the sandwich panels in the central impacted region, the test specimens after impact tests were cut into four symmetric portions. Figure 10 explains the cross section views of specimens. Thus, the test specimens were cut into four symmetrical parts but the finite element models were cut into two equal parts symmetrically. Figure 11 shows the predicted (FEM) and experimental cross-section views and failure modes in Type I specimens for the impact energies of 50, 100 and 150 J, respectively. The central permanent deflections in the upper (U) and lower (L) faces of the sandwich panels increase with the increasing impact energy. The sandwich panels exhibited a good perforation resistance until an impact energy level of 150 J. Adhesive failures appeared only for the impact energies of 100 and 150 J and partly delaminations between face-sheets and foam core occurred. For the impact energy of 50 J, the top face-sheet does not contact to the bottom face-sheet and the experimental and predicted after-impact deformed shapes of the impact region are almost same. The impact energy of 100 J results in the top face-sheet contact to the bottom face-sheet while the top face-sheet is partly perforated. The experimental and predicted after-impact deformed shapes are also similar. An impact energy of 150 J is critical since the impactor fully penetrated into both top and bottom face-sheets.

Fig. 10

The cross-section views and arrangements of a test specimen.

Fig. 11

The cross-section views of Type I (1/10/1mm) for different impact energies (*:perforated).

Fig. 12

(a) The contact force and (b) the kinetic energy histories of Type II (1/20/1 mm) for different impact energies.

4.3 Type II, 1/20/1 mm

The sandwich panels (Type II) consist of two thick face-sheets (1 mm) and a thick foam core (20 mm). Figure 12(a) compares the predicted and experimental contact force histories for the impact energies of 50, 100 and 150 J, respectively. As the impact energy is increased, the contact force levels increased until the sandwich panel was perforated. After the damage perforation occurred in the top or bottom face-sheets, the predicted and experimental peak contact force levels were not affected. The predicted and experimental contact force levels and the general trend of contact force-time histories are similar for an impact energy of 50 J, whereas other higher impact energy levels exhibit a close trend. For the present impact energy levels, the predicted and experimental peak contact force values are 7.23(7.03), 8.69(9.26) and 9.08(9.84) kN, respectively. However, the differences between the predicted and experimental peak contact force levels are about 2.76, 6.16 and $7.72\%$, respectively. In case of the impact energies of 100 and 150 J, the contact force-time curves exhibit two stages; such as the first perforation stage into the top face-sheet and the second perforation stage into the bottom face-sheet. This occurs due to a thicker foam core thickness (20 mm). The penetration time for a thicker foam core (20 mm) gets longer than those of a thinner foam core (10 mm). Figure 12(b) shows the predicted and experimental kinetic energy histories for different impact energies. The predicted kinetic energies reduce from 50, 100 and 150 J to 7.07, 10.74 and 12.37 J, respectively. Thus, the present impact energies of 50, 100 and 150 J are dissipated by 85.86, 89.26 and $91.75\%$, respectively. The experimental kinetic energies reduce to 6.88, 32.97 and 29.7 J, and are dissipated by 86.24, 67.03 and $80.20\%$, respectively. The sandwich panels (Type II) do not exhibit a full perforation at these impact energy levels. The top face-sheet is perforated at an impact energy of 90 J whereas the bottom face-sheet is partly perforated at an impact energy of 150 J. The predicted and experimental contact durations are almost same. In comparison with Type I, increasing the foam core thickness decreased peak contact force levels and increased contact duration.

Fig. 13

The after-impact deformed regions on the top and bottom surfaces of Type II (1/20/1mm) for different impact energies (A: area, P: perimeter).

Figure 13 compares the experimental and predicted deformed shapes and areas of the damaged regions in Type II sandwich panels. Deformations on the bottom face-sheet are not apparent for an impact energy of 50 J. However, the plastic deformations on both top and bottom face-sheets become more significant with increasing impact energy. The finite element analysis indicates that an impact energy of 150 J results in partly tearings in the top and bottom face-sheets, especially in the central region contacting with the impactor, and this small cracks get larger in the bottom face-sheets. The measured areas of the after-impact damaged regions are about 192.34, 551.13 and $529.81\,\text{mm}^2$ and their perimeters are about 49.16, 90.80 and 127.11 mm, whereas the calculated areas are about 161.00, 543.48 and $546.25\,\text{mm}^2$ and perimeters are 44.98, 86.28 and 83.25 mm for the present impact energies, respectively. The calculated and experimental damaged areas are in good agreement. The damaged area increases with increasing impact energy. As the foam core thickness is increased, the penetration and perforation resistances and the damaged areas increase. In order to show the effect of the foam thickness on the perforation and penetration resistance of Type II sandwich specimens the cross-section views of the central impact regions of the present specimens are shown in Figure 14 based on the predicted and experimental and results. The deformation modes in the top and bottom face-sheets Type II is different from those of Type I. The deformation (permanent compression) through the foam core thickness is smaller than those of Type I (figure 11) and the foam thickness between the top and bottom face-sheets remains nearly same for Type II whereas a fully compressed foam layer and the top and bottom face-sheets contact each other for Type I (figure 11). The predicted and experimental cross-section views of the central deformed regions are similar; therefore, the finite element model of the sandwich panels are also successful to model the damage mechanism failure of impacted region and delaminations.

Fig. 14

The cross-section views of Type II (1/20/1mm) for different impact energies (*:perforated).

Fig. 15

(a) The contact force and (b) the kinetic energy histories of Type III (0.5/10/0.5 mm) for different impact energies.

4.4 Type III, 0.5/10/0.5 mm

The sandwich panels (Type III) consist of thinner face-sheets (0.5 mm) and foam cores (10 mm). Figure 15(a) shows the temporal predicted and experimental contact force variations of the sandwich panel Type III for different impact energies. The top face-sheet is perforated at an impact energy of 50 J. The peak contact force levels are not affected by the increased impact energy; thus it reaches about 6 kN for three impact energies. However, the contact durations decrease with increasing impact energies. The predicted and experimental contact force histories exhibit similar trend and the predicted and experimental total contact durations are very close. The perforation periods of the top and bottom face-sheets can be observed from the experimental temporal contact force curves, whereas the temporal predicted force variations are not suitable for this. The foam core material has low density and the face-sheets thickness is thin for Type III. The predicted contact force curves indicate very small reductions at force levels during the perforation period of the first (front) plate and the penetration period in the second (back) plate. Figure 15(b) compares the predicted and experimental kinetic energy histories of Type III for different impact energies. At an impact energy of 50 J, the finite element model predicts that the kinetic energy reduced to 5.75 J from 50 J; therefore, an impact energy of 50 J could be dissipated by $88.5\%$. The experimental study predicts a reduction in the kinetic energy to 12.29 J from 50 J and a dissipation by $75.42\%$. The impact energies of 100 and 150 J result in full perforation in both front and back plates, and the kinetic energy histories indicate that the impactor penetrated fully into both plates and the kinetic energy of the impactor remained nearly constant after full penetration. The kinetic energy histories show that an impact energy of 90 J is necessary for a full penetration of the impactor into both front and back plates. In case of a lower impact energy the impactor can perforate only the front plate and cause a partly penetration into the back plate. As the face-sheet thickness is decreased, the peak contact force levels and the capability of absorbing impact energy decreases.

Fig. 16

The after-impact deformed regions on the top and bottom surfaces of Type III (0.5/10/0.5mm) for different impact energies (A: area, P: perimeter).

Figure 16 compares the after-impact deformed shapes of the damaged regions on both front and back face-sheets of Type III based on the finite element analysis and experiments for different impact energies. The predicted and experimental areas and perimeters of the damaged regions are also compared. The experiments indicate partly or full perforation into both the front and back plates depending on the impact energy level. However, the finite element analysis predicts a full penetration with some tearings in the front face-sheet, and partly penetration in the back face-sheet for an impact energy of 50 J. However, both the finite element analysis and experiments indicate a good agreement as far as the deformed geometries of damaged regions in both and front plates are concerned. The experimental damaged areas were measured as 289.64, 483.29 and $411.62\,\text{mm}^2$ and their perimeters as 71.27, 86.30 and 75.21 mm, whereas the damaged areas were predicted as 255.20, 466.52 and $410.95\,\text{mm}^2$ and their perimeters as 53.47, 76.57 and 84.40 mm for present impact energies, respectively. As the impact energy is increased, the damage-region areas increase for the impact energies of 50 and 100 J. As Type I and Type III are compared, Type I has better penetration and perforation resistance than Type III. The sandwich panels (Type III) experience have larger damaged areas than Type I. Figure 17 also compares the experimental and predicted section views to show the delaminations and interfacial failures in the sandwich panels (Type III) for the present impact energy levels, respectively. Adhesive layers fail, and the top face-sheets contact permanently to the bottom face-sheets for all impact energies. It is obvious that the perforation and penetration resistance decreases with decreasing face-sheets thickness. The experimental and predicted after-impact deformed shapes of the damaged central regions are similar. The delaminations and adhesive failures become more apparent in the section views by means of the cohesive zone model. The sandwich panels (Type III) deform plastically more than Types I and II and its top and bottom face-sheets perforated fully for all impact energies, whereas the top and bottom face-sheets can be perforated only at an impact energy of 150 J for Types I and II sandwich panels.

Fig. 17

The cross-section views of Type III (0.5/10/0.5 mm) for different impact energies (*:perforated).

Fig. 18

(a) The contact force and (b) the kinetic energy histories of Type IV (0.5/20/0.5 mm) for different impact energies.

4.5 Type IV, 0.5/20/0.5 mm

The sandwich panels (Type IV) were manufactured from two thin face-sheets (0.5 mm) and a thick foam core (20 mm). In order to determine the effects of a thin skin face-sheet and thick foam core on the deformation and damage mechanism of the sandwich panels, the predicted and experimental contact force and impactor kinetic energy histories were determined for different impact energies (50, 100 and 150 J) as shown in Figure 18. The experimental and predicted temporal contact force variations exhibit almost similar trend for all impact energies (figure 18a). However, the experimental temporal contact force variations indicate clearly the full-penetration of the impactor into the (front) face-sheet (it is perforated). In case of the lowest impact energy (50 J) the penetration into the second (back) face-sheet becomes smooth. Increasing the impact energy (100 and 150 J) results in full penetration into the back face-sheet (it is perforated). This stage is still evident in the experimental contact force histories whereas the predicted histories show a smooth variation during the penetration of the impactor into the back face-sheet. The foam core absorbs kinetic energy until the impactor contacts with the back face-sheet. The total contact durations decrease by $63\%$ with an increasing impact energy to 150 J from 50 J. Especially, the impactor travels through the front face-sheet thickness in a shorter time (8 to 6 ms) with increasing impact energy to 150 J from 50 J. However, this duration through the back face-sheet reduces 17 ms to 8 ms. Accordingly, increasing the impact energy results in a fast penetration and deformation to take place faster through face-sheet and foam materials. Figure 18(b) compare the predicted and experimental temporal kinetic energy histories of the sandwich panels (Type IV) for different impact energies. For an impact energy of 50 J, the kinetic energy can be reduced to $\sim 20\,\text{J}$; thus, it can be dissipated by $60\%$ whereas the finite element method predicts a decrease to 8 J and a dissipation of $\sim 80\,\text{J}$. Increasing the impact energy (100 and 150 J) results in full penetration into the impactor; thus, both front and back face-sheets are perforated. The kinetic energy variations become similar for 100 and 150 J. An impact energy of $\sim 80\,\text{J}$ is a limit energy for the sandwich panels; thus, the face-sheets of the sandwich panels are fully perforated after an energy of 80 J was dissipated. Consequently, the sandwich panels (Type IV) can dissipate $\sim 80$ and $\sim 50\%$ of the impact energies 100 and 150 J, respectively. In addition, the front and back face-sheets (and foam core) can dissipate 52 and 30 J of the impact energies of 100 and 150 J. The sandwich panels (Type IV) result in lower peak contact force levels than other types of sandwich panels. Increasing foam core thickness also decreases peak contact force levels.

Fig. 19

The after-impact deformed regions on the top and bottom surfaces of Type IV (0.5/20/0.5 mm) for different impact energies (A: area, P: perimeter).

Fig. 20

The cross-section views of Type IV (0.5/20/0.5 mm) for different impact energies (*:perforated).

Figure 19 shows the experimental and predicted deformed shapes of both top and bottom faces and damaged areas in the top face-sheet of the sandwich panels (Type IV) for different impact energies. An impact energy of 50 J is not enough for the perforation into the top and bottom faces of the specimen. The predicted and experimental results indicate same behaviour. However, the top and bottom face-sheets of the specimens were perforated for 100 and 150 J. Increasing the impact energy makes the perforation more evident, the hole in the front plate induced by the impactor becomes more clear in a near-circle form. However, the predicted hole geometry is plus-shaped, which implies that the tearings in the front plates occurred along the major and minor principal axes. The back plates of sandwich panels experience perforation for 100 and 150 J whereas no tearing is observed for 50 J. The experimental hole geometries of the back plates (100 and 150 J) are near-circle with small tearing lines. However, the back plates were predicted to have plus-shaped tearings which were along the minor and major principal axes for 100 and 150 J. The sizes of the holes on the front and back faces are not identical, the back face-holes are slightly larger than the front face-holes. This indicates the effect of the front stress waves traveling faster than the impactor end. It is evident that a limit impact energy exists in order to perforate the front and back face-sheets; therefore, the impact energy absorbing capability of this sandwich panel (Type IV) is better than those of the sandwich panel (Type III, Figure 16). The size of the holes explains that a thicker foam can contribute to the energy absorption of the panel, since larger holes in both front and back face-sheets in Type III (figure 16) occur than those in Type IV having 20 mm-foam thickness (figure 19). The experimental damaged areas are 484.43, 544.72 and $628.48\,\text{mm}^2$ and their perimeters are 81.34, 90.12 and 93.35 mm, whereas the predicted areas are 451.97, 487.65 and $604.30\,\text{mm}^2$ and perimeters are 75.36, 89.47 and 97.83 mm for present impact energy levels, respectively. As the impact energy is increased, the damaged areas increase. In case Type III and IV are compared, the sandwich panels (Type IV) have larger damaged areas than Type III sandwich panels. In case Type II and IV are considered, decreasing face-sheet thickness increases damaged areas. Figure 20 shows the predicted and experimental section views and failure modes of Type IV sandwich panels for the present impact energies, respectively. The central permanent deflections in the sandwich panels increase with increasing impact energy. As the lowest impact energy of 50 J is considered, only the top face-sheet perforates, and the experimental and predicted after-impact deformed shapes are almost same. The impact energies of 100 and 150 J result in both top and bottom face-sheets to be fully perforated. The experimental and predicted after-impact deformed shapes are also almost same for these impact energies. Even though Type IV has better penetration and perforation resistance than Type III, Type II exhibits better penetration and perforation resistance than Type IV. It is evident that the face-sheet thickness is more effective on the penetration and perforation resistance than the foam core thickness. Table 5 shows the energy rates absorbed by each component of the sandwich panels for the present impact energies. In case of an impact energy of 50 J, the foam cores in all type sandwich panels can dissipate by $22\%$ of the impact energy. However, as the impact energy is increased, the energy rate absorbed by the foam core decreases. The adhesive layers can not absorb energy as much as other components since it is very thin, whereas the face-sheets can absorb by $35{-}87\%$ of the impact energy. As the impact energy is increased, the energy rate absorbed by the bottom face-sheet increases. The energy rate absorbed by the face-sheets was found to be higher in the specimens having better penetration and perforation resistance.

Table 5 The energy rates absorbed by each component of the sandwich panels for different impact energies.

5 Summary and conclusions

This study addresses the low-speed impact response of sandwich panels with expanded polystyrene foam core for different foam core thicknesses, face-sheet thicknesses and impact energies. The temporal variations of contact force, the kinetic energy histories and the deformed shapes of the after-impact central region were determined experimentally and numerically. The numerical model was successful and the calculated test results were in good agreement with experimental ones. The Johnson-Cook model was used to model the penetration and perforation behaviour of metal face-sheets and the cohesive zone model (CZM) was implemented for the failure of adhesive layer. First, a pre-study for a single aluminum plate was made to verify the Johnson Cook model for metal face-sheets based on the experiments. The effects of the foam core and face-sheet thicknesses were investigated in order to improve the capability of the impact energy absorption of the sandwich panels under three impact energy levels, as follows:

• Impact effects: Increasing impact energy increased peak contact force levels for all specimens until specimens are perforated. For the perforated specimens, the peak contact force levels remained same. The predicted and experimental contact force-time histories exhibited similar trends for all impact energies. The minimum peak contact force levels were observed for Type IV, whereas the maximum peak contact force levels occurred for Type I. As the foam core thickness was increased or the face-sheet thickness was increased, the peak contact force levels decreased. The central permanent deflections also increased with increasing impact energy for all specimens. Increasing face-sheet and foam core thicknesses increased both penetration and perforation resistances. Type II-sandwich panels offered better penetration and perforation resistances than other Types sandwich panels.

• Energy absorption: The specimens with thicker foam core absorbed more impact energy and a thicker foam core improved the energy absorption capability as well. Type I-sandwich panels were perforated at an impact energy of 150 J. Type II-sandwich panels did not exhibit a full perforation at test-impact energy levels. The impact energies of 100 and 150 J resulted in full perforation in both the top and bottom face-sheets of Type III-sandwich panels. An impact energy of 80 J was a limit energy for Type IV-panels; thus, both top and bottom face-sheets of the panels were fully perforated as soon as an energy of 80 J was dissipated.

• Foam core thickness: The contact force levels decreased with increasing foam core thickness. The sandwich panels with thicker foam core exhibited a better energy absorption capability than the sandwich panels with thinner foam core. The impact penetration and perforation resistance was also improved with increasing foam core thickness.

• Face-sheet thickness: The lower peak contact force levels occurred in the sandwich panels with thinner face-sheet. However, as the face-sheet thickness was decreased, the sandwich panels were fully perforated. An impact energy of 90 J was enough to perforate the face-sheets of the fully sandwich panels with thinner face-sheet. Based on the predicted results the sandwich panels with thinner face-sheet exhibited different behaviours in terms of deformation geometry, thus; the face-sheets had plus-shaped tearings which were along the minor and major principal axes. In the perforated sandwich panels the size of the damaged areas in impacted regions increased; therefore, the sandwich panels with thinner face-sheets had larger damaged areas than the sandwich panels with thicker face-sheets.