Available online at www.sciencedirect.com

Composite Structures 85 (2008) 20–28 www.elsevier.com/locate/compstruct

Low-velocity impact failure of aluminium honeycomb sandwich panels C.C. Foo *, L.K. Seah, G.B. Chai School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore Available online 17 October 2007

Abstract In this paper, the failure response of aluminium sandwich panels subjected to low-velocity impact is discussed. A three-dimensional geometrically correct finite element model of the honeycomb sandwich plate and a rigid impactor was developed using the commercial software, ABAQUS. This discrete modelling approach enabled further understanding of the parameters affecting the initiation and propagation of impact damage. Strain-hardening behaviour of the aluminium alloys and the honeycomb core density were shown to affect the impact response. In addition, the impulse–momentum equation was incorporated into the energy-balance model, so that the impact force and deflection histories could be determined as well. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Aluminium honeycomb sandwich structures; Energy-balance model; Impact damage; Finite element analysis (FEA)

1. Introduction Sandwich panels are widely used in lightweight construction especially in aerospace industries because of their high specific strengths and stiffnesses. In the service life of a sandwich panel, impacts are expected to arise from a variety of causes. Debris may be propelled at high velocities from the runway during aircraft takeoffs and landings. Other examples include tools dropping on the structure during maintenance or even collisions by birds. Visual inspection may reveal little damage on the sandwich panel, but significant damage may occur between the impacted facesheet and the core. Reduction of structural stiffness and strength can occur, and consequently, propagate under further loading [1]. Thus, their behaviour under impact has received increasing attention. Finite element modelling is one popular and cost-effective approach involved in the study of sandwich structures. 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 *

Corresponding author. E-mail address: [email protected] (C.C. Foo).

0263-8223/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2007.10.016

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. Gibson and Ashby [2] developed analytical formulations for the in-plane moduli and yield strengths for regular hexagonal honeycomb core. Their material models were investigated by Triplett and Schonberg [3]. They conducted a numerical analysis for circular honeycomb sandwich plates subjected to low-velocity impact, and found that comparison with experimental results was inaccurate when honeycomb crushing was ignored for the finite element model. Meraghni et al. [4] modified the classical laminate theory and applied it on a unit cell to derive the equivalent elastic rigidities for the honeycomb core. However, theoretical formulation of the effective elastic constants for the core could be tedious or almost impossible if the sandwich construction is too complicated. Even if it is possible, the mathematical derivations for one type of sandwich core might not be applicable to other types. An equivalent 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 in impact problems [5]. One possible reason is that it may be difficult to simulate exact

C.C. Foo et al. / Composite Structures 85 (2008) 20–28

damage progression since the honeycomb is made up of discrete cells. The onset of damage progression and failure in honeycomb core may be sensitive to detailed 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. A great deal of research work has been carried out in experimental and numerical studies, but relatively fewer analytical solutions have been proposed for sandwich structures because of the complex interaction between the composite facesheet and core during deformation and failure. Such solutions highlight important impact parameters, and provide benchmark solutions for more refined finite element analysis. The spring-mass and energy-balance models are two popular mathematical models used to study the impact dynamics of foreign objects on composite structures. In the spring-mass model, there is a combination of bending, shear, membrane and contact springs to represent the transverse load-deformation behaviour. The complete force history is then predicted by solving the equations of motion for the system [6]. Most analytical models assume elastic behaviour and they are unable to model damage growth. In addition, they neglect core crushing and large facesheet deflections [7]. Olsson and McManus [8] showed that by taking into account large deflection plate theory and core yielding, analytical predictions of local load-indentation response of sandwich panels are significantly better than those using purely elastic indentation models. Thus, for analytical models to be successful in predicting the impact response of sandwich panels, large facesheet deflections and core crushing have to be considered as well. Fatt and Park [9] derived approximate solutions for the dashpot and spring resistances from the static load-indentation response using the principle of minimum potential energy, and then adjusted these properties with the dynamic material properties of the facesheet and core. They incorporated a constant force dashpot in the spring-mass model to represent the dynamic crushing resistance of the core. Anderson [10] also developed a single degree-of-freedom model that included a Maxwell damper as a mechanism to account for material damage on sandwich structures subjected to low-velocity impact. The energy-balance model [11] assumes that, when the structure reaches its maximum deflection under quasi-static behaviour, the projectile comes to a halt and all the initial kinetic energy has been used to deform the structure. The kinetic energy of the projectile is equated to the sum of energies due to contact, bending, shear and membrane deformations. The impact response for aluminium honeycomb sandwich structures was investigated using this energy-balance approach [12]. From load-indentation responses attained from static tests, it was observed that the aluminium sandwich structures displayed no ratedependency. Thus this suggested that the quasi-static assumption is viable at low impact velocities, and the energy-balance model is capable of modelling the impact

21

response of the sandwich structures. The analytical results agreed well with experimental ones for very low impact energies. Another benefit of this simple model is that it allows the identification of energy partitioning during impact; energies pertaining to bending, contact deformations or shear can be quantified separately. However, because the energy-balance model assumes an elastic response, and does not account for energy dissipation, it breaks down when core damage such as cell buckling or core crushing occurs at higher impact velocities. It was also pointed out that this model only yields the maximum impact force, but not the load-time history. Kasano [13] also introduced an analytical model, which was based on the conservation laws of energy and momentum, to consider impact perforation of carbon fibre composite laminates. By using the analytical model in conjunction with experimental test results, simple semi-empirical expressions for the ballistic and residual velocities of the projectile were derived. However, the load-time histories for the impact event were not considered. The work presented here seeks to predict damage and failure in aluminium honeycomb sandwich panels subjected to low-velocity impact. A three-dimensional geometrically correct finite element model of the honeycomb sandwich plate and a rigid impactor is developed using the commercial software, ABAQUS. By adopting a discrete modelling approach where the cellular walls and the facesheets are explicitly modelled using shell elements, accurate prediction of the damage mechanisms and failure are possible. In addition, the energy-balance model is used in conjunction with the law of conservation of momentum to solve for the impact load and deflection histories under low-velocity impacts. The local and global stiffnesses for the sandwich plate are derived using a quasi-static FE analysis. Numerical results are compared with experimental results. 2. Experimental investigation An experimental investigation on aluminium sandwich plates subjected to low-velocity impact loadings was conducted. These test specimens consisted of aluminium alloy 3003-H19 foil for the honeycomb core with aluminium alloy 1100-H14 for the facesheets. Each plate measured 100 mm  100 mm, with a core thickness of 20 mm and a thickness of 0.75 mm for each top and bottom facesheet. The density of the aluminium honeycomb was 72.0 kg/ m3, and the cell size was 6.35 mm. The Instron Dynatup 8250 impact testing machine, which was used for the drop weight impact tests, is shown in Fig. 1. Its principal features are: (1) a stiff, guided nearfree-falling mass; (2) a force transducer mounted in the falling tup, which has a capacity of 15.56 kN; (3) a hemispherical 13.1 mm diameter steel tup tip; (4) a velocity detector to measure the tup velocity prior to impact, and to trigger data collection; (5) a set of pneumatic clamps to hold the specimen in place; (6) a rebound brake assembly to prevent multiple impacts; and (7) a digital acquisition system.

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C.C. Foo et al. / Composite Structures 85 (2008) 20–28

Fig. 1. The Dynatup 8250 impact testing machine used in the 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. Impact force is measured discretely over time with the force transducer during impact. The velocity during impact is calculated by the integration of acceleration over time, where the acceleration is measured by the impact force divided by the mass of the dropweight. This calculated velocity is then used to derive the displacement of the impactor via integration. Graphical plots for the impact load and the displacement of the impactor as a function of time were then generated using these data. A range of impact energies that varied from 0.85 J to 13.0 J was achieved by varying the drop height of the impactor from 0.033 m to 0.50 m, respectively. The impactor mass used in all tests was 2.65 kg. All tests were performed at room temperature. 3. Finite element modelling In the numerical analysis, the explicit finite element computer software, ABAQUS/Explicit, was employed for both quasi-static and impact analyses. For the 100 mm  100 mm aluminium sandwich plates, the aluminium honeycomb core had a cell size of 6.35 mm, foil

thickness of 0.0635 mm and a core height of 20 mm. Each aluminium facesheet measured 0.75 mm thick. The top and bottom facesheets, as well as the honeycomb sandwich core, were meshed with shell elements. The adhesive bonding between the facesheet and the core was assumed to be perfect, and surface-based tie constraint was adopted at the facesheet-core interfaces. By doing so, each node of the honeycomb core at the interface was constrained to have the same translational and rotational motion as the node on the facesheet to which it was ‘‘tied”. The tie constraint then disallowed surfaces initially in contact from penetrating, separating, or sliding relative to one another. In ABAQUS, a general contact algorithm was introduced to simulate contact between the impactor and the top facesheet. This general contact algorithm enforces contact constraints using a penalty contact method [14]. The mesh on the top facesheet had to be refined adequately enough to interact with the rigid impactor, so that the impactor did not penetrate the facesheet. In addition, the rigorous mesh in the central region of the honeycomb core was required to capture the buckling of the cellular walls as core crushing occurred. Since it may not be possible to predict in advance which specific regions in the core 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/indentation point was also included. Since the thickness-to-span ratio for the sandwich plate was high, transverse shear deformation was expected to be significant. Therefore, elements in the core included the effect of transverse shear deformation. In addition, membrane strains and large rotations were accounted for, as large deformation effects were expected. To further simplify the problem, frictional response during contact between the impactor and the structure was neglected. Friction between the clamp plates and the facesheets was also ignored. 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-ofplane 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. In a quasi-static analysis, the response of the structure is usually dominated by its lowest mode [14]. By determining the natural mode (fundamental) frequency and its corresponding period, one can estimate the loading rate for the explicit quasi-static analysis such that inertia effects do not become important. Therefore, a frequency extrac-

C.C. Foo et al. / Composite Structures 85 (2008) 20–28

tion analysis was first carried out to determine the fundamental frequency for the sandwich model. Quasi-static analyses were then carried out with decreasing loading rates in order to converge on a quasi-static solution. Kinetic and internal energies results were checked during post-processing to ensure that dynamic effects were at a minimum – the kinetic energy of the system should be small. It was found that a step time that was a factor of 10 slower than that corresponding to the fundamental frequency was adequate for convergence in this case. Fig. 2 shows two finite element models of the sandwich plate in the impact simulation. 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. The square model in Fig. 2a is used to study the effect of membrane reaction of the facesheets on the overall response of the sandwich panel during impact. 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. The facesheets and the core for the aluminium sandwich plates were defined in ABAQUS as non-linear, isotropic, plastic materials, the properties of which are presented in Table 1. The symbols q, ry, ru and m denote density, yield strength, tensile strength and Poisson’s ratio, respectively. Three material models for the aluminium alloy were considered for the parametric study: (1) elastic perfectly plastic (herein defined as elastoplastic); (2) bilinear; and (3) Ramberg–Osgood strain-hardening. The models are

Fig. 2. The (a) square and (b) circular aluminium sandwich plates (not to scale).

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Table 1 Material properties for aluminium panels Property

Facesheets (1100-H14 aluminium alloy)

Core (3003-H19 foil aluminium alloy)

q (kg/m3) E (GPa) ry (MPa) ru (MPa) v

2700 70.0 117 124 0.33

2700 70.0 220 250 0.33

illustrated in Fig. 3. The elastoplastic model described a plastic material with an elastic regime when r < rY. The bilinear model, with linear strain-hardening, assumed a tangent modulus, Et, which is 0.7  the Young’s modulus, E, This is cited to be typical for aluminium alloys [15]. The strain-hardening model was described by the Ramberg–Osgood equation which can be found in many textbooks on mechanics:  m r rY r e¼ þa ð1Þ E E rY where a = 3/7 and m = 10 for typical aluminium alloy. 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 converged the maximum stress results to within 2%. 4. Analytical model During low-velocity impact, the aluminium sandwich plate essentially deforms under static loading, and it can be represented by a discrete dynamic system with equivalent masses and springs. One example is the two degreesof-freedom spring-mass (S-M) model proposed by Shivakumar et al. [11] as shown in Fig. 4. It has been suggested that the mass of the plate, M2, could be neglected if the impactor mass is greater than 3.5 times the plate mass. Kc, Kb, Ks and Km are springs representing the contact, bending, shear and membrane stiffnesses, respectively. As the plate is thick and membrane effects are not likely, it is assumed that the contribution of the membrane forces, and consequently Km, can be neglected. For simplicity, only a normal impact of the impactor on the sandwich plate is considered here. The next step would be to determine the local and global stiffnesses, Kc and Kbs, respectively. One approach is to decouple the local and global responses of the plate so that the stiffnesses can be determined separately, while ignoring the interaction between these two. When the sandwich plate is clamped around its edges, it experiences both local and global deformation. Local deformation, a, consists of the indentation of the top facesheet as the core crushes underneath, while global deformation, w, refers to the bending and shearing of the entire plate. A rigidly supported sandwich plate undergoes only local deformation of the top facesheet. The use of Hertzian

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C.C. Foo et al. / Composite Structures 85 (2008) 20–28

Fig. 3. Material models for aluminium alloys: (a) elastoplastic; (b) bilinear; and (c) Ramberg–Osgood model.

clamped this time. The contact load, P, is related to the mid-plane deflection of the sandwich plate, w, by the equation ð3Þ

P ¼ K bs w

Various energy terms can then be presented as follows [16]. The energy due to local indentation is given by Z a 1 P 1þn Ec ¼ P da ¼ ð4Þ 1 0 ðn þ 1ÞK nc The energy due to bending and shearing of the plate is Z w P2 P dw ¼ ð5Þ Ebs ¼ 2K bs 0

Fig. 4. Two degrees-of-freedom spring-mass model.

contact law is well-established for isotropic homogenous linear elastic bodies when the indentation is much smaller than the thickness of the plate [1]. However, for a sandwich plate, where the facesheets are stiff and the core is flexible, the local deformation consists of both transverse deflection of the top facesheet and core crushing. Hence, the Hertzian contact law may not be appropriate here. Fatt and Park [9] derived approximate solutions for the local stiffness using the principle of minimum potential energy. They considered three possible regimes for local deformation of the plate during the entire indentation process: (1) plate on an elastic foundation; (2) plate on a rigid-plastic foundation; and (3) membrane on a rigid-plastic foundation. Here, the local stiffness (Kc) is determined by performing a quasi-static explicit FE analysis for the sandwich plate which is rigidly supported. The quasi-static contact load, P, is related to the local indentation of the top facesheet, a, by the power law where n is some constant P ¼ K c an

ð2Þ

In reality, there exists an interaction between the local and global deformations [9]. As the core crushes during local deformation, its height reduces and the global bending and shearing stiffness of the sandwich plate becomes smaller. However, it is thought that this effect can be ignored since the impact damage is small and localized around the impactor for low-velocity impacts. Therefore, to obtain the global stiffness (Kbs), another quasi-static explicit FE analysis is carried out for the plate which is

For low-velocity impacts which result in small amounts of damage, the energy required to create damage can be neglected [6]. By the law of conservation of energy, the total work done by the contact load on the plate is equal to the change in kinetic energy of the impactor at time, t, 1 Ec þ Ebs ¼ M imp ðV 2imp  V ðtÞ2 Þ 2

ð6Þ

where Mimp denotes the mass of the impactor, Vimp is the impact velocity and V(t) refers to the velocity of the impactor at time t. The contact load is also a function of time, i.e. P = P(t). By the conservation of impulse–momentum, Z t M imp ðV imp  V ðtÞÞ ¼ P dt ð7Þ 0

Using Eqs. (6) and (7), the load and velocity histories can be solved. The integral on the right-hand side of Eq. (7) can be approximated by the area under the load-time curve using the trapezoidal rule. The deflection of the impactor, which is the sum of the local and global deformation, is the integration of the velocity history. 5. Results As a first step, an attempt was made to validate the numerical model with experimental results. A comparison of the predicted and experimental maximum deflections of the impacted facesheet and peak impact loads for a

C.C. Foo et al. / Composite Structures 85 (2008) 20–28

range of impact energies from 0.85 J to 13.0 J is shown in Fig. 5. The two sets of results demonstrate a good agreement, and this illustrates the capability of the numerical model to predict the impact event adequately. The largest error recorded was 15% for the predicted peak load for the case of 0.85 J impact energy. A parametric study was carried out to investigate the influence of metal plasticity models on the impact response of the aluminium sandwich plates. Three material models for the aluminium alloy were considered: (1) elastic perfectly plastic; (2) bilinear; and (3) Ramberg–Osgood strain-hardening. The impact force histories for these three material models are shown in Fig. 6a. The difference for the load-time history between the two strain-hardening models (bilinear and Ramberg–Osgood) is negligible. This also implies that a bilinear strain-hardening model may be used in place of a Ramberg–Osgood fit as a good approximation to predict the nonlinear response for the aluminium sandwich plates. As compared to the other two models, the elastoplastic model predicts a slightly lower maximum load (with a 12% difference when compared to 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 strainhardening models, the yield stress increases with plastic

strains. 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. Since 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. A square model of 100  100 mm2 was compared with an idealized circular model of diameter 76.4 mm to study the effect of membrane reaction of the facesheets on the impact response of the sandwich panel under clamped conditions. The load histories for the two plates are presented in Fig. 6b. 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% of that for the square one. This implies that the circular plate would be preferable because it is computationally more efficient. An effort was also made 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. Assuming that each core cell of the model is a perfect regular hexagonal cell unit of Fig. 7, the honey3.5

8

6

Peak Impact Load (kN)

FEM Expt

7 Max Deflection (mm)

25

5 4 3 2 1 0

FEM

3.0

Expt

2.5 2.0 1.5 1.0 0.5 0.0

0

5 10 Impact Energy (J)

15

0

5 10 Impact Energy (J)

15

Fig. 5. Comparison of experimental and numerical results for (a) maximum deflection, and (b) peak load over a range of impact energies.

Fig. 6. Comparison of load-time histories for the different models for impact at 7 J.

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C.C. Foo et al. / Composite Structures 85 (2008) 20–28

Fig. 7. The basic honeycomb element [17].

comb density, HD, can be derived [17], where q is the density of the foil material: HD ¼

2ðb þ lÞtq tq ¼ 1:54 kg=m3 ðb þ l cos hÞð2l sin hÞ b

ð8Þ

The density of the honeycomb core was gradually increased by adjusting the cell wall thickness, t, and the node width, b. 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. 8. 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. The coloured regions represent the yielded regions in the facesheet and core. It can be seen that as the core density was 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 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. Fig. 9 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. The amount of energy absorbed is almost identical for all core densities as shown in Fig. 9a. 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. On the other hand, denser cores experience higher peak impact loads, as seen

Fig. 8. Predicted damage areas for various core densities.

C.C. Foo et al. / Composite Structures 85 (2008) 20–28

in Fig. 9b. 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 analytical model was used to derive the impact response of the aluminium sandwich plate. Fig. 10 depicts the load-time history and load-deflection history for two impact velocities of 1.27 m/s and 2.3 m/s. Results were compared with test data, as well as simulation results. The comparisons indicate that a good agreement existed between the experimental and predicted results, in terms of peak load and overall profile. The analytical model was able to predict the impact response reasonably well up to the point of maximum load – the behaviour of the plate during unloading was not considered here. In addition, the stiffness of the plate (slope of the load-deflection curve) was represented well by both numerical and analytical models. This implies that the quasi-static assumption

Fig. 9. Variation of (a) percentage of absorbed energy with respect to impact energy, and (b) peak load, over a range of core densities.

27

adopted for the energy-balance model is valid. By determining the local and global stiffnesses of the aluminium sandwich plate under quasi-static indentation, the lowvelocity impact response of the same plate can then be predicted using the approach detailed in the previous section. 6. Conclusion The numerical investigation of aluminium sandwich panels subjected to low-velocity impact has enabled us to further understand the parameters affecting the initiation and propagation of impact damage. The strain-hardening material models for the aluminium alloys resulted in a stiffer impact response for the aluminium sandwich plate. However, between the bilinear and Ramberg–Osgood strain-hardening models, the impact response was similar. It appears that the bilinear strain-hardening model could replace the nonlinear Ramberg–Osgood model for predicting the nonlinear response for the aluminium sandwich plate. The membrane reaction of the facesheets was also found to have negligible effect on the impact response of the sandwich panel under clamped conditions. Hence the simulation runtime could be reduced by 25% if the circular plate, which is computationally more efficient, is used. In addition, 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 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. Thus, it implies that 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. Finally, the energy-balance approach, together with the impulse–momentum equation, had been used to provide accurate prediction of the load-time history and loaddeflection history up to the point of maximum load.

Fig. 10. Impact response for aluminium sandwich plates impacted at 1.27 and 2.30 m/s.

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References [1] Abrate S. Impact on composite structures. Cambridge: Cambridge University Press; 1998. [2] Gibson LJ, Ashby MF. Cellular solids: structures & properties. Oxford: Pergamon Press; 1988. p. 69–119. [3] Triplett MH, Schonberg WP. Static and dynamic finite element analysis of honeycomb sandwich structures. Struct Eng Mech 1998;6:95–113. [4] Meraghni F, Desrumaux F, Benzeggagh ML. Mechanical behaviour of cellular core for structural sandwich panels. Composites: Part A 1999;30:767–79. [5] Horrigan DPW, Aitken R. Finite element analysis of impact damaged honeycomb sandwich. Surrey, UK: FEA Ltd.; 1998. Available from: . [6] Abrate S. Modeling of impacts on composite structures. Compos Struct 2001;51:129–38. [7] Olsson R. Engineering method for prediction of impact response and damage in sandwich panels. J Sandwich Struct Mater 2002;4:3–29. [8] Olsson R, McManus HL. Improved theory for contact indentation of sandwich panels. Am Inst Aeronaut Astronaut J 1996;34(6): 1238–44.

[9] Fatt MSH, Park KS. Dynamic models for low-velocity impact damage of composite sandwich panels – Part A: Deformation. Compos Struct 2001;52:335–51. [10] Anderson TA. An investigation of SDOF models for large mass impact on sandwich composites. Composites: Part B 2005;36(2): 135–42. [11] Shivakumar KN, Elber W, Illg W. Prediction of impact force and duration due to low-velocity impact on circular composite laminates. J Appl Mech 1985;52:674–80. [12] Hassan MA, Cantwell WJ. The low velocity impact response of an aluminium honeycomb sandwich structure. Composites: Part B 2003;34:679–87. [13] Kasano H. Impact perforation of orthotropic and quasi-isotropic CFRP laminates by a steel ball projectile. Adv Compos Mater 2001;10(4):309–18. [14] ABAQUS Inc. Hibbitt, Karlsson, and Sorensen. Rhode Island, 2004. [15] Nguyen MQ, Jacombs SS, Thomson RS, Hachenberg D, Scott ML. Simulation of impact on sandwich structures. Compos Struct 2004;67:217–27. [16] Wen HM, Reddy TY, Reid SR, Soden PD. Indentation, penetration and perforation of composite laminates and sandwich panels under quasi-static and projectile loading. Key Eng Mater 1998;141–143: 501–2. [17] Bitzer T. Honeycomb technology. London: Chapman & Hall; 1997. p. 21–2.

Low-velocity impact failure of aluminium honeycomb ...

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