Quasi-static and low-velocity impact failure of aluminium honeycomb sandwich panels C C Foo, G B Chai , and L K Seah School of Mechanical and Aerospace Engineering, Division of Engineering Mechanics, Nanyang Technological University, Singapore The manuscript was received on 16 March 2006 and was accepted after revision for publication on 9 May 2006. DOI: 10.1243/14644207JMDA98

Abstract: This article presents an extensive experimental and numerical investigation of aluminium sandwich plates subjected to quasi-static loading and low-velocity impact. The objective of this research is to understand and, ultimately, predict the initiation and progression of damage in an aluminium sandwich plate subjected to low-velocity impact. The static indentation and impact problems were analysed using the commercial finite-element software, ABAQUS. Quasi-static indentation tests and low-velocity drop weight tests were conducted to characterize the failure and to determine the extent of damage observed in aluminium sandwich plates. Comparison of the numerical load history, specimen damage area, and residual indentation with experimental results demonstrated the ability of the modelling methodology to capture the impact characteristics. Experimental results also indicated that the damage mode experienced on the impacted facesheet may be correlated to the energy absorbed by the plate during the impact event and the static failure energy. A numerical parametric study was conducted to determine the effect of various geometric parameters, such as foil thickness and cell size, on the damage resistance of the core and impacted facesheet. Findings showed that the energy absorbed during impact is independent of the core density. However, denser cores exhibited greater peak loads but experienced smaller damage profiles in the core and impacted facesheet. Keywords: aluminium honeycomb sandwich structures, explicit finite-element analysis, impact damage

1

INTRODUCTION

Sandwich structures are extensively used in modern aircraft, vehicles, and lightweight structures. In aircraft, honeycomb sandwich is used primarily for the fuselage cylindrical shell; the floors, side panels, and ceiling in the aircraft are also constructed using sandwich structures [1]. Other examples of structures composed of sandwich panels include helicopter rotor blades, ship hulls, and skis. They are particularly preferred for their high-specific strength and stiffness, and fatigue resistance. In

Corresponding author: School of Mechanical and Aerospace

Engineering, Division of Engineering Mechanics, Nanyang Technological

University,

50

Nanyang

Singapore. email: [email protected]

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Avenue,

639798,

addition, they have the potential for improved structural efficiency and reduced manufacturing costs. In the service life of a sandwich structure, impacts are expected to arise from a variety of causes. Typical in-service impacts include debris propelled by the landing wheels on the runway during aircraft takeoffs and landings. Others include tools dropping on the structure during maintenance or even collisions by birds. In some instances, damage may occur on the top facesheet with insignificant damage on the bottom one. Penetration may be incomplete, resulting in a redistribution of stresses along the damaged facesheet. Visual inspection may reveal little damage, but significant damage may occur between the impacted facesheet and the core [2]. Reduction of structural stiffness and strength can occur and, consequently, propagate under further loading. This relatively poor resistance to localized impact loading Proc. IMechE Vol. 220 Part L: J. Materials: Design and Applications

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C C Foo, G B Chai, and L K Seah

has become a concern for both manufacturers and end-users who need to locate damages for repair of structural members. Widespread application of sandwich structures in aircraft industries has thus been inhibited due to the lack of understanding of the impact damage mechanisms, and the effect of such damage on structural performance.

2

LITERATURE REVIEW

Honeycombs are usually made out of either metallic or composite materials. The cell walls are thicker in the composite honeycombs and they tend to fail by the fracture of cell walls, whereas metallic honeycombs fail by plastic buckling of the cell walls. Horrigan and Aitken [3] postulated that the most notable difference between a non-metallic and a metallic honeycomb structure under quasi-static compression loading is the post-buckling load carrying capacity. Metallic honeycombs (e.g. aluminium) that undergo plastic buckling form plastic hinges upon impact and additional plastic work has to be done for further deformation, thus they retain much of their load carrying capacity. The behaviour of metallic honeycombs under compressive failure is also similar to that of an elastic perfectly plastic material [3]. Metallic sandwich panels are often used as energy absorbers for compressive crushing in the outof-plane direction. Hence, there exists strong interest in the strength characteristics and behaviour of metallic sandwich panels in such applications. Wierzbicki [4] formulated a closed-form solution for the crushing strength of hexagonal metallic honeycombs subjected to out-of-plane loading, and Cote et al. [5] derived an analytical model for the buckling strength of square stainless steel honeycombs. The effects of cell shape and foil thickness on the crushing behaviour of bare aluminium honeycombs were numerically investigated by Yamashita and Gotoh [6], and they showed that experimental honeycomb samples exhibited cyclic buckling patterns that were comparable to those observed in the computational results. Paik et al. [7] carried out out-of-plane crushing tests on aluminium sandwich panels, and reported that the core height does not influence their crushing strength. The foil thickness of the honeycomb cell appeared to be a more important parameter for this particular type of loading. The study on impact damage resistance involves the implementation of impact tests experimentally with a set of parameters, followed by the identification of dominant damage mechanisms and finally, the establishment of relationships between critical parameters and these mechanisms. A variety of test procedures had been proposed to simulate the actual impact by foreign objects on sandwich Proc. IMechE Vol. 220 Part L: J. Materials: Design and Applications

panels [8– 12]. Abrate [2] provided an exhaustive list of references associated with these efforts. However, he pointed out that most experimental studies considered a single sandwich configuration and investigated the effect of governing parameters. Thus, results from each study may seem to contradict each other. Furthermore, test programmes are destructive, time consuming and, consequently, expensive for the the industry [13]. Finite-element (FE) software, such as ANSYS/ LS-Dyna and ABAQUS, are popular commercial tools employed within various engineering industries, such as aerospace and automotive industries. FE modelling has provided researchers a cost-effective approach to obtain the sandwich behaviour in largescale structure simulations as well as detailed local deformation analysis. The flexibility of modelling either a localized region through the thickness or the entire sandwich panel is one attractive aspect of the modelling approach. In addition, geometric and material parameters can be easily varied in numerical models. Apart from prototyping and testing, numerical simulation can further augment the design process by minimizing design costs, which would result in greater efficiency. Hence, the development of a software tool that can be used to predict the impact damage in sandwich structures would be useful. To attain efficiency in numerical analysis, the core in sandwich structures, which has a large number of cells, is usually replaced with an equivalent continuum model. The sandwich panels are analysed in terms of their effective properties rather than by consideration of their real cellular structure. A number of experimental and analytical techniques have been proposed to predict the effective continuum properties of the core in terms of its geometric and material characteristics [14 –16]. Gibson and Ashby [17] published analytical formulations for the upper and lower limits of the transverse shear moduli for regular hexagonal honeycomb core. Their material models were investigated by Triplett and Schonberg [18], who conducted a numerical analysis for circular honeycomb sandwich plates subjected to lowvelocity impact. They found that comparison with experimental results was inaccurate when honeycomb crushing was ignored for the FE model. In order to derive an elasticity solution for the effective continuum properties, simplifying assumptions are often undertaken. A continuum model may seem a convenient way to represent the real core geometrically, but errors have also been attributed to the continuum model when it is used to model damage [3] in impact problems. One possible reason is that it may be difficult to simulate the exact damage progression as the honeycomb is made up of discrete cells. The onset of damage progression and failure in honeycomb core may be sensitive to detailed JMDA98 # IMechE 2006

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local damage distribution along the cells. This limitation can be overcome by adopting discrete-element modelling approaches, so that more realistic distributions of stresses and strains can be obtained in the detailed core structure. The work presented here seeks to predict the damage and failure in aluminium honeycomb sandwich panels subjected to low-velocity impact using a thorough numerical analysis and an extensive experimental investigation. By adopting a discretemodelling approach where the cellular walls and the facesheets are explicitly modelled using shell elements, accurate predictions of the damage mechanisms and, ultimately, failure are possible. 3

NUMERICAL INVESTIGATION

In the numerical analysis, the static indentation test and drop weight impact test are replicated as close as possible in the virtual domain but without incurring high computational expenses. The commercial FE computer software called ABAQUS [19] was employed for this purpose. The following points are valid for both static and impact analyses. 1. As the thickness-to-span ratio for the sandwich plate is high, transverse shear deformation is expected to be significant. Elements in the core must include the effect of transverse shear deformation. In addition, membrane strains and large rotations must be accounted for, as large deformation effects are expected. 2. The adhesive bonding between the facesheet and the core was assumed to be perfect, and surfacebased tie constraint was adopted at the facesheet-core interfaces. In doing so, each node of the honeycomb core at the interface is constrained to have the same translational and rotational motion as the node on the facesheet

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to which it is ‘tied’. The tie constraint then prevents surfaces initially in contact from penetrating, separating, or sliding relative to one another. 3. The impactor/indentor was modelled as a rigid body using four-noded linear tetrahedron continuum elements, and its motion was governed by the rigid body reference node. The impactor/ indentor had a Young’s modulus of 200 GPa, with a Poisson’s ratio of 0.3. In the impact analysis, the 13.1 mm diameter steel spherical impactor had a density of 2.25 106 kg/m3 to reflect its actual mass in the experiment, which was 2.65 kg in all impact simulations. In addition, gravitational load and an initial velocity, v0, were assigned to the impactor at its reference node. The impactor was also constrained to move only in the out-of-plane direction (i.e. Z-direction) of the plate. To reduce the runtime, all simulations commenced with the impactor situated just 0.1 mm above the sandwich plate. However, for the static analysis, gravitational load and initial velocity were not assigned. Instead, only a download displacement load in the Z-direction was prescribed on the indentor’s reference node to simulate the static indentation test. 4. In the experiments, the support fixture facilitated as circular clamped boundary conditions. As such, the boundary conditions of the area beyond the 76.4 mm diameter hole on both facesheets were prescribed to be fixed, i.e. the six translational and rotational degrees of freedom were set to zero. Friction between the clamp plates and the facesheets was also ignored. Figure 1 shows two FE models of the sandwich plate in the impact simulation. The square model in Fig. 1(a) is used to study the effect of membrane reaction of the facesheets on the overall response of the sandwich panel during impact. The idealized model of Fig. 1(b) is preferred

Fig. 1 FE models of clamped sandwich plate with impactor: (a) a square plate model of actual size and geometry, (b) computationally efficient model

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Table 1 Material properties for aluminium panels

Property

Facesheets (1100-H14 aluminium alloy)

Core (3003-H19 foil aluminium alloy)

r (kg/m3) E (GPa) n sy (MPa) su (MPa)

2700 70 0.33 117 124

2700 70 0.33 220 250

as it is computationally more efficient. The circular aluminium sandwich plate is of diameter 76.4 mm, and the square plate measures 100 100 mm2. Details of their results will be discussed later. 5. A general contact algorithm was introduced to simulate the contact between the impactor and the top facesheet. In ABAQUS, this general contact algorithm enforces contact constraints using a penalty contact method. The penalty stiffness that relates the contact force to the penetration distance is chosen automatically by ABAQUS, so that the effect on the time increment is minimal with insignificant penetration. This is important for accuracy in the explicit dynamics method [19]. The mesh on the top facesheet has to be refined adequately enough to interact with the rigid impactor, so that the impactor does not penetrate the facesheet. The rigorous mesh in the central region of the honeycomb core is required to capture the buckling of the cellular walls during the impact as core crushing occurs. 6. As the core crushes during the impact, the cellular walls underneath the impact point buckle. As it may not be possible to predict in advance which specific regions will be in contact, contact has to be allowed to occur in a very general manner so that any regions can contact any other regions, on either side of the cellular walls. Thus, self-contact for the cellular walls of the honeycomb core in the vicinity of the impact point was also included.

Fig. 2

7. Frictional response during contact between the impactor and the structure can be chaotic, and has been neglected to simplify the problem. The facesheets and the core for the aluminium sandwich plates are defined in ABAQUS as nonlinear, isotropic, plastic materials, the properties of which are presented in Table 1. The symbols r, sy, su, and n denote density, yield strength, tensile strength, and Poisson’s ratio, respectively. Three material models for the aluminium alloy were considered for the parametric study: (a) elastic perfectly plastic (herein defined as elastoplastic); (b) bilinear; and (c) Ramberg – Osgood strain-hardening. The models are illustrated in Fig. 2. The elastoplastic model is described as a plastic material with an elastic regime when s , sy. The bilinear model, with linear strainhardening, assumed a tangent modulus, Et, which is 0.7 the Young’s modulus, E – this is cited as typical for aluminium alloys in reference [20]. The strain-hardening model was described by the Ramberg – Osgood equation, found in many textbooks on mechanics

1¼

s sY s m þa E E sy

(1)

where a ¼ 3/7 and m ¼ 10 for typical aluminium alloy. The rate-sensitivity of the properties of the aluminium alloys has been ignored here because it is assumed that during low-velocity impact, the aluminium sandwich plate essentially deforms in a quasi-static manner. A mesh convergence study was carried out to ensure the mesh refinement in the sandwich structure was sufficiently fine enough to capture the stresses and deformations with reasonable accuracy. The chosen mesh would have converged the maximum stress results to within 2 per cent. Figure 3 shows the comparison of the load – time history of two models of different mesh densities (one having 11 847 elements and

Material models for aluminium alloys: (a) elastoplastic, (b) bilinear, and (c) Ramberg– Osgood model

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Fig. 3

Load histories comparison of two models of different mesh density

the other having 23 755 elements). Keep in mind that the model is most dense around the region where the impact contact occurs.

4

EXPERIMENTAL INVESTIGATION

An experimental investigation on sandwich plates subjected to quasi-static indentation and low-velocity impact loadings is presented in this section. These test specimens consisted of aluminium alloy 3003-H19 foil for the honeycomb core with aluminium alloy 1100-H14 for the facesheets. Each plate is measured 100 100 mm, with a core thickness of 20 mm and a thickness of 0.75 mm for each top and bottom

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facesheet. The density of the aluminium honeycomb was 72.0 kg/m3 and the cell size was 6.35 mm. A range of impact energies that varied from 0.85 to 13.0 J was achieved by varying the drop height. The impactor mass used in all tests was 2.65 kg. All tests were performed at room temperature. The test systems for the static indentation and dynamic impact tests are shown in Figs 4(a) and (b), respectively. The static indentation tests were conducted using the Instron 5500R test system, shown in Fig. 4(a), operating under displacement control at a constant cross-head speed of 0.5 mm/min. The indentor used in the static tests and the impactor used in the impact tests had the same diameter for consistency. The restraint fixture simulated circular clamped conditions as same dimensions as that found in the impact test. The specimen was positioned between the top and bottom clamp plates, with the mid-point of the plate directly located underneath the indentor. The two clamped plates were then bolted in place manually. The Instron Dynatup 8250 impact testing machine of Fig. 4(b) was used for the drop weight impact tests. Upon release, the free-falling impactor would fall along two smooth guided columns, and through the centre hole of the clamp plate of diameter 76.4 mm to strike the specimen. The support fixture for the specimen facilitated circular clamped condition. The pneumatic clamp plates prevented any movement of the specimen, without causing any buckling of the honeycomb core prior to impact. After the first impact, the rebound brake was activated to support the crosshead, and thus the impactor was only allowed to strike the specimen once. Transient response of the samples included the velocity and deflection of the impactor, as well as load, as a function

Fig. 4 The test systems used in the quasi-static and impact tests: (a) Instron 5500R testing machine, (b) Dynatup 8250 impact testing machine

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experimental results might be attributed to the position of the indentor over the honeycomb core. Indentation above a cell wall would yield a slightly different response to that over an open cell. The results from the three test specimens were averaged to give P ¼ 2.73 kN, df ¼ 4.95 mm, and Es ¼ 7.37 J. 4.2

Fig. 5

Load –displacement curves for aluminium panels subjected to static indentation

of time. Graphical plots were then generated using the data collected from the data acquisition system.

4.1

Quasi-static test results

The static tests were stopped after reaching the failure load for each specimen, and the failure load, P, and the deflection of top facesheet at failure, df, were noted. The area under the curves up to P was calculated to give the static energy for failure, Es. The load –displacement curves for the samples are presented in Fig. 5. Good repeatability was observed for identical sandwich panels in terms of their load – displacement response. The scatter in the

Fig. 6

Impact test results

Force histories and load – displacement plots for four samples of aluminium sandwich panels impacted at 7.0 J by the 2.65 kg impactor are shown in Fig. 6. The plots are similar for identical samples, and this highlights the repeatability and consistency of the experiments. As shown in Fig. 6(a), the loading and unloading are relatively smooth for the force – time histories. The load –displacement curves in Fig. 6(b) depict a steep initial stiffness immediately upon impact up to 0.5 kN, and this stiffness reduced and remained relatively constant thereafter up to the maximum load of 2.6 kN. Then, the load started to decrease, which can be attributed to the damage. The damage is considered as a loss of stiffness, and this may explain why unloading occurred over a shorter period of time as compared with loading. The relatively higher loading rate at the beginning might be due to the global stiffening of the plate immediately upon impact, as stress waves propagate throughout the structure. Three different material models were each included separately in the analysis to study the influence of the metal plasticity models on the impact response of the aluminium sandwich plates. The impact force histories for these three material models are shown in Fig. 7(a). The difference for the load – time history between the two strain-hardening

Impact response at 7 J: (a) load –time histories response, (b) load –displacement histories response

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Fig. 7 Comparison of load – time histories for the different models for impact at 7 J: (a) three different non-linear material models, (b) two different geometrical models

models (bilinear and Ramberg – Osgood) is negligible. As compared with the other two models, the elastoplastic model predicts a slightly lower maximum load (with a 12 per cent difference when compared with the experimental result) and longer contact duration. This is expected because, for an elastoplastic material model, the yield stress is constant during plastic straining, whereas for the strain-hardening models, the yield stress increases with plastic strains. For example, at 3.4 ms when the load drop occurs for the elastoplastic model, the peak von Mises stress in the honeycomb core is 220 MPa. However for the strain-hardening model, the peak von Mises stress in the core at 3.0 ms is 250 MPa. Consequently, this implies that the impact load would be higher for the strain-hardening models. According to Newton’s third law, there is an equal but opposite load acting on the impactor. Thus the impactor would be brought to a halt faster, resulting in a shorter duration. As the same yield stress is defined for all three models, it is obvious that the strain-hardening behaviour of the aluminium alloys does affect the impact response for the sandwich plates. The load histories for the two plates shaped differently as mentioned earlier are presented in Fig. 7(b). The results for both cases are almost identical. The number of elements used for the circular plate was less than that for the square one. As a result, it was found that the runtime for the circular plate was 75 per cent of that for the square one. Therefore, the circular plate is more efficient computation-wise. Kinetic and internal energy plots are used to illustrate the energy absorption capability of sandwich plates. Figure 8(a) depicts the kinetic and internal energy histories for the aluminium sandwich plates for an impact energy of 7.0 J. The total energy for the whole system, which is the summation of the JMDA98 # IMechE 2006

kinetic energy and internal energy, is shown to be constant throughout the impact event. The internal energy comprises the energy dissipated by plastic dissipation and the recoverable strain energy. Energy dissipation due to damping mechanisms in the plate, as well as friction at the boundary edges and the impact zone, are assumed to be negligible in this study. When the impactor strikes the plate, there arises a contact pressure in the small area of contact between the two bodies. This pressure results in local deformation in the contact area and subsequently, indentation. Because of this contact pressure, there exists a resultant force that acts equally in opposite directions on both colliding bodies. This impact force initially increases with increasing indentation, and reduces the speed at which the impactor approaches the plate. As such, the impactor slows down and loses kinetic energy. This continues until it reaches a point where the work done by the impact force is able to bring the impactor to a halt. The kinetic energy of the impactor becomes zero at maximum displacement. Simultaneously, the equal but opposite impact force acting on the plate does work and increases the internal strain energy of the plate, as shown in Fig. 8(b). It is observed that the internal energy for the top facesheet is higher than that for the core, and it accounts for 54 per cent of the entire internal energy for the plate. However, the internal energy of the bottom facesheet is almost negligible. This is probably due to the highly localized impact damage, which is limited to the upper facesheet and the vicinity of the impact point in the core. As the sandwich plate is thick, bending of the plate would also be at a minimum. All of these imply that the global deformation of the plate is negligible, when compared to the local indentation. Proc. IMechE Vol. 220 Part L: J. Materials: Design and Applications

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Fig. 8

Energy plots for aluminium sandwich panel subjected to 7 J impact: (a) kinetic and internal energy plots, (b) strain energy plots

During the unloading phase, the recoverable strain energy which constitutes the elastic part of the internal energy for the plate is released, immediately after the impactor comes to a halt. This is illustrated in Fig. 8(b). The release of this energy stored earlier during loading generates the force to drive the two bodies apart, and they separate with some relative velocity. As the plate is clamped in position, only the impactor is expected to move. At the instant, the impactor separates from the plate and its kinetic energy is found to be 0.26 J, which equates to the release of strain energy for the sandwich plate. Therefore, 96 per cent of the impact energy has been transferred to the plate. Bearing in mind that the internal energy consists of both energy dissipated due to plasticity and the recoverable strain energy, this implies that a major portion of the plate’s internal energy has been dissipated due to plasticity. The energy dissipated through plasticity during the impact event is illustrated in Fig. 9. In an inelastic collision, the interaction forces between the colliding bodies are non-conservative, and kinetic energy is lost during loading and unloading. As the plate is modelled as a non-linear inelastic material with strain-hardening effects, plastic deformation would occur once yield stress is reached. Energy is then dissipated due to plasticity. Assuming that each core cell of the model is a perfect regular hexagonal cell unit of Fig. 10, the honeycomb density, HD, can be derived [21], where r is the density of the foil material

HD ¼

2(b þ l)t r tr ¼ 1:54 (b þ l cos u)(2l sin u) b

(2)

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The density of the honeycomb core was gradually increased by adjusting the cell wall thickness, t, and the node width, b. Table 2 summarizes the various density models used for this study. In this parametric study, the 100 mm2 aluminium sandwich plates with a constant core height of 20 mm were subjected to a 7.0 J impact, and the resulting damage to the impacted facesheet and core are compared in Fig. 11. The plots presented are the contour plots for the equivalent plastic strain at the end of the impact event. This strain is a scalar variable that is used to represent the inelastic deformation in a material [14]. The coloured regions represent the yielded regions in the facesheet and core. It can be seen that as the core density was

Fig. 9

Dissipated energy plots for aluminium sandwich panel subjected to 7 J impact

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Fig. 10 The basic honeycomb element Table 2 Aluminium sandwich plates with varying honeycomb core densities

Plate

Cell wall thickness, t (mm)

Node width, b (mm)

Core density, HD (kg/m3)

A B C D E

0.0635 0.0635 0.0508 0.0635 0.0762

7.51 4.62 3.67 3.67 3.67

35.2 57.2 57.6 72.0 86.4

increased, the damage resistance of the structure improved, and the size of the damaged areas decreased. The damage profile on the impacted facesheets were circular in shape, while the damaged

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areas in the honeycomb core were localized, and concentrated mainly in the vicinity of the impact point and in the upper half of the core. Figure 12 illustrates the variation of energy absorbed by the plate which is normalized by the impact energy, and peak impact loads for the range of honeycomb core densities listed in Table 2. The amount of energy absorbed is almost identical for all core densities as shown in Fig. 12(a). This could be expected because core crushing occurs in a region relatively small as compared to the size of the whole plate. The influence of the core density on the energy absorbed by this localized damage would be much smaller, as compared to, for example, global crushing of the entire plate. In contrast, denser cores experience higher peak impact loads, as seen in Fig. 12(b). One explanation is that as the core density increases, the number of cells packed within the core increases as well. Consequently, within the same impact zone, the impact load would be resisted by more cell walls. Hence, the plate becomes stiffer. The damage profiles for two sandwich plates, plate B and plate C (details of their honeycomb densities are given in Table 2) are shown in Fig. 13. Interestingly, even though both plates have a core density which is almost equivalent,

Fig. 11 Predicted damage areas for various core densities: (a) on top facesheet, (b) in the honeycomb core at mid-section

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Fig. 12

Variation of (a) percentage of absorbed energy with respect to impact energy, (b) peak load, over a range of core densities

the damage profiles for both plates in the impacted facesheet and core are different. According to equation (2), for a constant r, the honeycomb core density depends on the ratio t/b. It is noted that the core in sandwich plate C has a smaller foil thickness, as compared to plate B. In addition, as plate C has a smaller cell size, it will have more honeycomb cells packed in its core, and the space across each separate cell wall is closer. It is thought

Fig. 13

that the stress sustained by the impacted facesheet on plate C would be transferred onto this greater number of cell walls. As a result, this might result in a smaller yielded region on the facesheet. However, as the core in plate C has a smaller foil thickness, the cell walls would be more susceptible to buckling and crushing. This suggests that the yielded region in the core for plate C would be larger as compared to plate B.

Comparison of damage areas in sandwich plates of core densities of about 57 kg/m3 for (a) plate C, on top facesheet, (b) plate B, in the honeycomb core at mid-section

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5

COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS

The load –deflection response curves of the experiment compared with those of the FE analysis for both the quasi-static indentation and impact loads are presented in Fig. 14. The quasi-static curves in Fig. 14(a) show a close fit initially up to a deflection of 2.65 mm after which, the numerical model experienced lower reaction loads compared to the experimental case. One reason is that in ABAQUS/ Standard, the self-contact capability cannot be used. This becomes problematic when the deflection becomes large, as the core crushes and the cellular walls come into contact with each other. However, the numerical model still predicts an acceptable failure load at 2.49 kN. The impact load – deflection curves are plotted in Fig. 14(b).

Fig. 14

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The numerical result compares well with the experimental result. The numerical model also predicted the dent depth to be identical to that on the specimen. The load –time histories from the experiment and FE analysis for the 7.0 J impact case are presented in Fig. 15. The aluminium alloys assume a bilinear strain-hardening material model in the FE analysis. The comparisons indicate that a good agreement existed between the experimental and predicted results, in terms of peak load and overall profile. The impact duration for the FE case was about 0.5 ms shorter. This is probably due to the stiffer FE model. The oscillations observed during the loading part in the FE curve might be due to the fact that no structural damping was implemented in the FE model. The experimental curve does not show such oscillations because of signal filtering.

Load –deflection response curves: (a) quasi-static load, (b) impact load

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Fig. 17 Fig. 15

Load –time histories for impact on aluminium sandwich plate at 7 J

Figure 16 shows a comparison of the predicted and experimental maximum deflections of the impacted facesheet and peak impact loads for a range of impact energies. The two sets of results demonstrate a good agreement. The largest difference recorded was 15 per cent for the predicted peak load for the case of 0.85 J impact energy.

Fig. 16

Comparison of experimental and numerical results for (a) maximum deflection, (b) peak load over a range of impact energies

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Linear relationship between energy absorbed and the impact energy

The ratio of absorbed energy by the plate during impact (Eabs) to the static energy for failure (Es) are plotted against impact energy (Eimp) as shown in Fig. 17. The energy absorbed by the plate increases linearly as the impact energy increases. At an impact energy of 8 J, the ratio (Eabs/Es) is unity. When this ratio is greater than unity, i.e. at an impact energy of 8 J or more, fracture and tearing are evident on the impacted facesheet, as shown in Fig. 18. The damage mode bears a close resemblance to the one observed in the static test of Fig. 18(a). In contrast, when the ratio is less than unity, the only observed damage on the impact facesheet is a dent

Fig. 18

Damage sustained in (a) static test, (b) 7 J, (c) 10 J, (d) 13 J impact tests

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Fig. 19

Predicted impact damage on top facesheet for (a) numerical simulation compared with (b) experimental result for an impact energy of 7 J

Table 3 Diameter of damage area (mm) on top facesheet over a range of impact energies Eimp (J)

Experiment

Numerical

2.0 7.0 10.0 13.0

15.0 18.5 21.0 23.0

18.8 22.0 24.4 25.6

as seen in Fig. 18(b). This implies that the amount of absorbed energy could serve as an indicator to the extent of damage sustained in a low-velocity impact. Figure 19 shows the predicted impact damage on the top facesheet compared with the experimental result for an impact energy of 7 J. The damage areas in both cases are circular, and the size of the predicted damage area agrees well with the experimental result. Table 3 compares the damage area on the top facesheet for a range of impact energies for both experimental and numerical studies. Good agreement is demonstrated, and this further illustrates the capability of the model to represent the damage on the impacted facesheet adequately.

6

CONCLUDING REMARKS

A thorough numerical and extensive experimental investigation of sandwich panels subjected to quasistatic loading and low-velocity impact is presented. A three-dimensional FE model for the honeycomb sandwich plate was developed using the commercial FE software, ABAQUS v6.4, and both quasi-static indentation and impact problems were analysed. Experimental static indentation and low-velocity impact tests were performed to validate the numerical model. The static indentation tests were performed on thick square aluminium sandwich plates to estimate static energy for failure. This energy was correlated to the energy absorbed by the plate JMDA98 # IMechE 2006

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during impact. Results seem to suggest that the type of damage mode experienced by the impacted facesheet during both static and impact loadings may be related to these two parameters. Impact tests also revealed that the absorbed energy increases linearly with impact energy. The numerical load history, specimen damage area, and residual indentation were compared with experimental results. It demonstrated the ability of the modelling methodology to capture the impact characteristics. A parametric study was also conducted to determine the effect of various geometric parameters, such as foil thickness and cell size, on the damage resistance of the core and impacted facesheet. Results showed that the energy absorbed during the impact is independent of the core density. However, denser cores exhibited greater peak loads and experienced smaller damage profiles in the core and impacted facesheet. The thickness and density of the foil, as well as the cell size of the honeycomb, are important design parameters for the honeycomb core. A foil with higher density and greater thickness will result in a more damage tolerant core. Smaller cell sizes will also improve the tolerance of the core to impact damage. The validation of the modelling methodology through the analysis of aluminium honeycomb sandwich panels has thus provided confidence to extend the analysis to composite sandwich plates that will form the bulk of our future work. ACKNOWLEDGEMENTS We are grateful for the funding received from Agency for Science, Technology and Research (A STAR) of Singapore and to the School of Mechanical and Aerospace Engineering, Nanyang Technological University of Singapore for the use of the computing and laboratory facilities.

REFERENCES 1 Vinson, J. R. The behaviour of sandwich structures of isotropic and composite materials, 1999 (Technomic Publishing Company, Lancaster, PA). 2 Abrate, S. Impact on composite structures, 1998 (Cambridge University Press, Cambridge) 3 Horrigan, D. and Aitken, R. Finite element analysis of impact damaged honeycomb sandwich, FEA Ltd., Surrey, UK, 1998, available from www.lusas.com 4 Wierzbicki, T. Crushing analysis of metal honeycombs. Int. J. Impact. Eng., 1983, 1(2), 157 –174. 5 Cote, F., Deshpande, V. S., Fleck, N. A., and Evans, A. G. The out-of-plane compressive behaviour of metallic honeycombs. Mater. Sci. Eng., A, 2004, 380, 272 – 280.

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6 Yamashita, M. and Gotoh, M. Impact behaviour of honeycomb structures with various cell specifications – numerical simulation and experiment. Int. J. Impact. Eng., 2005, 32, 618 – 630. 7 Paik, J. K., Thyamballi, A. K., and Kim, G. S. The strength characteristics of aluminium honeycomb sandwich panels. Thin-walled Struct., 1999, 35, 205 – 231. 8 Herup, E. J. and Palazotto, A. N. Low-velocity impact damage initiation in graphite/epoxy/nomex honeycomb sandwich plates. Compos. Sci. Technol., 1997, 57, 1581– 1598. 9 Wen, H. M., Reddy, T. Y., Reid, S. R., and Soden, P.D. Indentation, penetration and perforation of composite laminates and sandwich panels under quasi-static and projectile loading. Key Eng. Mater., 1998, 141 – 143, 501 – 502. 10 Hazizan, M. A. and Cantwell, W. J. The low velocity impact response of an aluminium honeycomb sandwich structure. Compos. B, 2003, 34, 679 – 687. 11 Roach, A. M., Evans, K. E., and Jones, N. The penetration energy of sandwich panel elements under static and dynamic loading: part I. Compos. Struct., 1998, 42, 119 – 134. 12 Zhao, H. and Gerard, G. Crushing behaviour of aluminium honeycombs under impact loading. Int. J. Impact. Eng., 1998, 21, 827 – 836. 13 Aktay, L., Johnson, A. F., and Holzapfel, M. Prediction of impact damage on sandwich composite panels. Comput. Mater. Sci., 2004, 32, 252 – 260. 14 Burton, W. S. and Noor, A. K. Assessment of continuum models for sandwich panel honeycomb cores. Comput. Methods Appl. Mech. Eng., 1997, 145, 341 – 360. 15 Meraghni, F., Desrumaux, F., and Benzeggagh, M. L. Mechanical behaviour of cellular core for structural sandwich panels. Compos. A, 1999, 30, 767 –779. 16 Hohe, J. and Becker, W. A mechanical model for two-dimensional cellular sandwich cores with general geometry. Comput. Mater. Sci., 2000, 19, 108 – 115.

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17 Gibson, L. J. and Ashby M. F. Cellular solids: structures & properties, 1988 (Pergamon Press, Oxford). 18 Triplett, M. H. and Schonberg, W. P. Static and dynamic finite element analysis of honeycomb sandwich structures. Struct. Eng. Mech., 1998, 6, 95– 113. 19 ABAQUS Inc. Hibbitt, Karlsson, and Sorensen, 2004, Rhode Island. 20 Nguyen, M. Q., Jacombs, S. S., Thomson, R. S., Hachenberg, D., and Scott M. L. Simulation of impact on sandwich structures. Compos. Struct., 2004, 67, 217 – 227. 21 Bitzer, T. Honeycomb technology, 1997 (Chapman & Hall, London).

APPENDIX Notation b E, Et Eabs Eimp Es HD P t a, m df 1 n v0 r s sy su

cell node width Young’s modulus, tangent modulus absorbed energy during impact impact energy static energy for failure honeycomb core density failure load cell wall thickness constants for Ramberg –Osgood equation deflection of top facesheet at failure strain Poisson’s ratio initial velocity density stress yield strength tensile strength

JMDA98 # IMechE 2006