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Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor
Accepted Manuscript Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor Dahai Zhang, Qingguo Fei, Peiwei Zhang PII: DOI: Reference:
S0263-8223(16)32008-6 http://dx.doi.org/10.1016/j.compstruct.2017.02.053 COST 8274
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
29 September 2016 30 December 2016 10 February 2017
Please cite this article as: Zhang, D., Fei, Q., Zhang, P., Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor, Composite Structures (2017), doi: http://dx.doi.org/10.1016/j.compstruct. 2017.02.053
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Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor
Dahai Zhang1,2,3 , Qingguo Fei 1, *, Peiwei Zhang1,3 (1 Department of Engineering Mechanics, Southeast University, Nanjing 210096, China) (2 Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, 3122, Australia) (3 Key Laborator y of Lightweight and Reliability Technology for Engineering Vehicle, College of Hunan Province, Changsha 410114, China)
* Corresponding author. E-mail address: [email protected] (Q. Fei) 1
Abstract Indentation response and energy absorption property of honeycomb sandwich panels subjected to drop-weight impact under a spherical impactor were investigated. Experiments were conducted using a pendulum-impact system. A three-dimensional finite element model with micro-structure considered was built and validated. In conjunction with experimental and numerical methods, analytical models of indentation response and energy balance specifically aimed to solve problems of low-velocity impact of a spherical indenter on sandwich panels were deduced. Results show that a hemispherical residual dent caused by bending of top face-sheet and core crushing is left on top face-sheet after impact. It also concludes that more than 80% of impact energy is absorbed mostly b y top face-sheet and honeycomb core. The main form of energy dissipation is plastic dissipation. In addition, parametric studies were carried out to explore effects of impact energy on impact behavior b y altering impact velocity or impactor mass. Different effects are observed for the two approaches and some useful semi-empirical formulations based on both experimental and numerical results are overfitted to estimate the residual dent depth and energy absorbed during a drop-weight impact event on a honeycomb sandwich panel under a spherical impactor.
Keywords: Honeycomb sandwich panel; Drop-weight impact; Indentation; Energy absorption; Spherical impactor;
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1. Introduction Due to their excellent crashworthiness performance and energy absorption ability [1, 2], sandwich structures have become attractive candidates in many engineering applications, including automotive industry [3], aeronautics [4], transportation engineering [5] and personal protective equipment [6]. During the period of their serves, sandwich structures are susceptible to low-energy/low-velocity impacts, such as runway debris, hailstones, tools dropped during maintenance and so on [7-9]. Unlike high-velocity impact, damages caused by low-velocit y impact are often internal and invisible but can significantly reduce stiffness and strength of the structures, which will result in shortening service life of the structures. Generally, for a metal sandwich panel subjected to low-energy/low-velocity impact, plastic deformation including face-sheets bending and core crushing [10-12] rather than penetrative damages [13, 14] occur. Most of the impact energy would be absorbed and dissipated during the process while the rest is retained in the impactor as rebound kinetic energy [15]. After impact, an undetectable or barely detectable by visual inspection residual plastic indentation may be left on top face-sheet of the sandwich panel. Indentation characteristics and energy absorption propert y are basically determined b y crashworthiness of the structure, which is extremel y sensitive to the mechanical property of matrix material [16], geometric parameters of face-sheets [17] and core especiall y [18-20]. A large number of experimental, analytical and numerical studies have been carried out to investigate the performance of sandwich structures subjected to low-energy/low-velocit y impact loadings. Research scope of the problem mainly contains [21-37]: 1) contact response between the impactor and sandwich panel; 2) residual property of the sandwich panel after impact; 3) failure mechanism of the sandwich panel by impact; 4) energy absorption property of the sandwich panel; 5) parametric study on geometry of the impactor and sandwich panel; 6) optimization analysis; A series of quasi-static and dynamic low-velocity tests using a hemispheric impactor on aluminum honeycombs and sandwich panels were conducted by Shitta-Bey et al. [22], which
3
indicated that sandwich panels provide higher crushing forces and better crashworthiness than corresponding bare honeycomb samples due to plastic yielding of the face-sheet. Comparison of structural responses in impact events were studied by Crupi et al. [23] using a drop test machine to determine the difference of energy absorption and failure modes for polymeric and aluminum sandwich panels. Effects of impact variables such as face-sheet thickness and core thickness on the impact behavior and resulting impact damage states subjected to low-velocity impact with hemispherical steel impactors of different diameters at various energy levels were studied by Wang et al. [24]. Parameters such as impact force histor y, energy absorbed and contact duration were tested and discussed. Those studies mainly focused on impactor with a spherical or hemispherical shape, there were also a lot of tests undertaken with other types of impactor, including conical [25], truncated [26] and flat [27]. Some analytical models were established to investigate indentation response of sandwich structures under low-velocity impact. Earlier analytical solutions mainly focused on elastic response of the whole structure or on elastic face-sheets and plastic core [28, 29]. The model was widely employed to determine the indentation response under a point or line loading. A large deformation model for a plastic string resting on a plastic foundation and undergoing localized mass impact was proposed by Wierzbicki et al. [30]. The model was adopted and improved by Xie et al. [31], they theoretically studied the localized indentation of sandwich panels with metallic foam core and derived the analytical models for a fat indenter and a spherical indenter. Mu et al. [32] further improved the model to predict indentation behavior of sandwich circular panel with gradient foam cores under a flat indenter. Besides, spring-mass model and energy-balance model [33] were also widely adopted to predict the peak impact force, impact duration, energy absorption and equivalent stiffness of sandwich structures. Compared with experimental and analytical method, numerical method provides a much more cost-effective and convenient approach. It has been widely employed to simulate the coupling analysis and whole process of impact. Wide areas of research have been simulated and discussed using numerical method, including impact force histor y, contact duration, characteristics of energy absorption, failure modes for face-sheet and core, and so on [14-16, 20, 24, 34-37]. The main purpose of this paper is to explore the indentation response and energy
4
absorption property as well as energy distribution of honeycomb sandwich panels subjected to low-energy drop-weight impact with a spherical indenter. In section 2, drop-weight impact tests of four groups of impact energy were conducted, during which a pendulum-impact installation, a high-speed video record system and an advanced optical measurement method were employed. In section 3, a three-dimensional FE (finite element) model of the sandwich panel was developed and employed in simulations of drop-weight impacts. Meanwhile, results predicted by the simulations were compared with experiments in order to validate the FE model. In section 4, an analytical load-indentation model was deduced in conjunction with a revised energy balance model to solve for impact response and energy absorption, both models were revised to be suitable for this investigation. In section 5, impact response of the sandwich panel such as impact force histor y, energy absorbing-dissipating process and energy distribution of different components during the impact were discussed and summarized. Moreover, parametric studies were performed to identify the effect of impact energies obtained by var ying impact velocity or mass of impactor on energy absorption efficiency as well as energy distribution characteristics.
2. Experimental procedure 2.1. Specimen description Experiments of honeycomb sandwich panels under drop-weight impact were carried out first in order to validate the numerical model. The specimens as shown in Fig.1 are made of aluminum alloy for both honeycomb core and face-sheets, which are cemented b y adhesive layers made of epoxy resin. The materials for the face-sheets and honeycomb core are A5083-H321 and A3003-H19 respectively. The cell shape of honeycomb core is regular hexagonal (the most common cell shape). Each panel measures L1 × L2 = 150 mm × 150 mm with a thickness t f = 0.5 mm for each top and bottom face-sheet, a thickness h = 15 mm for
hexagonal honeycomb core and a thickness
t a = 0.15 mm
for adhesive layers between
face-sheets and core. Wall thickness and wall length of the hexagonal honeycomb core are
t c = 0.07 mm and lc = 6 mm , respectively. Relative density of the honeycomb core can be calculated from [2],
5
ρc =
2 tc ρc 3 lc
(1)
where ρ c is the density of matrix material of the honeycomb core. The details of specification of the aluminum honeycomb sandwich panels tested are illustrated in Tab.1.
Honeycomb core
Fig.1. A honeycomb sandwich panel specimen Table 1. Specification of the aluminum honeycomb sandwich panels Properties Size of the panel
150 × 150 × 16 .3 mm
Weight of the panel
83.15 × 10 -3 kg
Density of the panel
226 .72 kg/m 3
Cell wall length of the core
6 .0 mm
Cell wall thickness of the core
0.07 mm
Height of the honeycomb core
15.0 mm
Thickness of the face-sheets
0 .5 mm
Thickness of the adhesive layers
0.15 mm
2.2. Arrangement and results As shown in Fig.2, three parts make up the experimental system, including a pendulum-impact part, a video camera part and a three-dimensional shape measurement part, respectively. To better explain the experimental methods, a sketch map of the pendulum-impact part and the video camera part are drawn in Fig.3. As shown in Fig.3, the pendulum-impact part is composed of a honeycomb sandwich panel, a pendulum impactor with a constant radius of D = 40 mm and mass of M = 0.3 kg hung on the supporting frame by rigid wire.
6
a
b
c
Fig.2. Experimental setup: a) the pendulum-impact part; b) the video camera part; c) the 3-D shape measurement part.
Front view
Side view
Fig.3. Sketch map of the pendulum-impacting part and the video camera part
The honeycomb sandwich panel was completely clamped fixed all sides and the bottom face-sheet was not fixed. Impact energy was obtained by converting gravitational potential energy into kinetic energy and a range of energy was achieved through changing the initial
7
height. Meanwhile, kinematic images of the process were recorded by a video camera part, a calibration background table was employed to help catch the initial height and rebound height of the impactor. The absorbed energy Ea is calculated from: E a = E KI − E KR = Mg ∆H = Mg ( H I − H R )
(2)
1 M V I2 = Mg H I 2 1 E KR = M V R2 = Mg H R 2 E KI =
(3) (4)
where E KI , E KR are impact and rebound kinetic energies of the impactor, respectively; VI , VR are impact and rebound velocities of the impactor, respectively; H I , H R are initial and rebound heights of the impactor, respectively; ∆H is gap height of the impactor. Note that the impactor would drop again after reached the largest rebound height, which is unconcerned here. Hence, the impactor was manually caught after it drops again before it impacted the panel in case of multiple impacts. In this paper, four impact energy groups were conducted and each tested three times: 1.47J, 2.94J, 3.81J and 4.41J, respectively. Generally, as shown in Fig.4, there are three distinct regimes during the impact process: a dropping regime, a contact regime and a rebound regime. Energy converting of the impactor is proceed in the dropping regime, required impact energy is obtained from converting of gravitational potential energy in the end of this regime. Interaction and energy absorbing occur in the contact regime. In the rebound regime, impactor will rebound with a much smaller velocity for impact energy hardly completely be absorbed by the target in a low-velocity drop-weight impact incident. A residual plastic indentation will be left on top face-sheet of the sandwich panel in the end.
Impact Process
VI
VR
Impactor
Fig.4. Impact process
8
Residual Dent
A three-dimensional shape measurement part was employed to measure the surface deformation and residual dent depth of the panel after tests. An optical geometry of fringe projection method was adopted in this paper, the method can be simply described as follows [38], a grating was projected onto the surface of an object through a focusing lens and a CCD (Charged Couple Device) camera was adopted to capture the deformed grating image on the object surface, which was followed by a subsequent analysis. Fig.5 shows the projected fringe pattern and three-dimensional topography plot of the specimens impacted at different impact energies. Residual dent depths obtained through analysis of the figures as well as energy absorbed are shown in Tab.2. a) b)
c)
d)
Fig.5. Projected fringe pattern and 3-D plot of specimens under different impact energies: a) 1.47J, b) 2.94J, c) 3.81J, d) 4.41J. Table 2. Experimental results. 1 1-1#
1-2#
2 1-3#
2-1#
2-2#
3 2-3#
3-1#
3-2#
4 3-3#
4-1#
4-2#
Initial height (m)
0.50
1.00
1.30
1.50
Impact energy (J)
1.47
2.94
3.81
4.41
Initial velocity (m/s)
3.13
4.43
5.05
5.42
4-3#
Rebound height (m)
0.105
0.092
0.108
0.146
0.157
0.157
0.180
0.195
0.207
0.184
0.191
0.136
Height gap (m)
0.395
0.408
0.392
0.854
0.843
0.843
1.120
1.105
1.093
1.316
1.309
1.364
Energy-absorbed (J)
1.161
1.199
1.152
2.510
2.478
2.478
3.293
3.249
3.213
3.872
3.851
4.017
Dent depth (mm)
1.80
1.89
1.77
2.63
2.56
2.51
2.98
2.92
3.03
3.20
3.07
3.27
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3. Numerical model 3.1. Finite element modeling FE model of the sandwich panel and impactor were built. The simulations were performed using an explicit dynamic finite element code (ABAQUS/Explicit). A micromechanical approach with actual discrete hexagonal microstructure of the honeycomb considered was adopted. As shown in Fig.6, a detailed honeycomb structure model was established using nominal dimensions by modeling each cellular explicitly. The fine micromechanical model of the core was established based on ideal geometry of the honeycomb cells instead of a continuous model with equivalent properties. A unit cell was firstly modelled and replicated in X-direction and Y-direction to create other individual cells. Then, the individual cells were merged together to assemble the honeycomb core. Adhesive layers between the face-sheets and honeycomb core usually be neglected in numerical models [37, 39, 40], by doing this, bonding between face-sheets and core was assumed to be perfect, each node of the honeycomb core at the interface is constrained to have the same translational and rotation motion as node on the face-sheet to which it was coupled. However, this assumption and simplification result in decrease of analysis accuracy more or less. In this paper, a more reasonable modelling approach was adopted, specifically, the face-sheet and adhesive layer were modelled as double layers [41] with respective properties, as shown in Fig.6.
Fig.6. Geometry model of the sandwich panel, impactor and double layers of adhesive layer and face-sheet
For computing efficiency, the impactor was placed just 1mm upon the top face-sheet and was modelling using four-node linear tetrahedron continuum elements. The impactor was
10
considered rigid and an initial velocity was assigned to the impactor at its reference node as motion of all nodes of the impactor is governed by the rigid body reference point. The face-sheets and honeycomb core were all meshed with shell elements. The face-sheets and honeycomb core as well as the adhesive were all defined as ideal elastic-plastic materials, the strain-rate effect was not considered. The mechanical properties of different components of the sandwich panel are listed in Tab.3. Table 3. Mechanical properties of different components
Face-sheets
Adhesive
(A5083-H321)
(Epoxy resin)
(A3003-H19)
Density ρ (kg/m )
2700
1500
2700
Young’s modulus E (GPa)
72.0
5.0
70.0
Poisson ratio ν
0.33
0.3
0.33
Yield stress σ 0 (MPa)
280
20
185
Property 3
Core
Data are provided by the manufacturer.
A general contact algorithm was introduced and was widely employed to simulate contact between the impactor and the sandwich panel [25, 40], and was also applied in this paper. This general contact algorithm enforces contact constrains using a penalty contact method in ABAQUS [25], the friction coefficient was chosen to be 0.3. Moreover, in order to achieve convergence, a reasonable fine mesh at vicinity of the contact area was carried out. The mesh generation was followed by a convergence study and all results presented in this paper are converged. Fig.7 shows the effect of mesh size on simulation results and computing time, 0.5mm (12 elements on each cell wall) was chosen as the size of smallest elements at vicinity of the contact area for both computing efficiency and results accuracy considering. FE model of the sandwich panel and impactor are drawn in Fig.8 as well as details of the contact area.
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Fig.7. Convergence analysis
Rigid Impactor
Boundary c o nd it i o n: fixed x,y,z
Fig.8. FE model of the sandwich panel and impactor
3.2. Numerical model validation Predicted results and experimental data were compared to validate the numerical model. Fig.9 shows comparison of the experimental and numerical deformation of top face-sheet as well as cross-section of the sandwich panel after impact at the case of 5.05 m/s, the other cases display the similar characteristic. As shown in the figure, a plastic residual dent was left after impact with bending of top face-sheet and fold of cell walls along axial direction. As it can be seen from the figures, no obvious penetrative damage and crack damage were observed and the face-sheets and honeycomb core were still boned very well. The honeycomb core and the top face-sheet at the contact area were compressed in the out-of-plane direction, which produced buckling (elastic or plastic buckling) of the cell walls, initiating from the top end. Due to the
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spherical impactor, the buckling of the cell walls was not uniform and was less and less from the center of the impactor area to the outside. It is also found diameter of the dent is larger than that of the impactor because of gradual deformation of the face-sheet, mechanism of the formation of indentation is also successfully predicted by the numerical simulation.
Expt.
FEM
a) top face-sheet
Expt.
FEM
b) cross-section Fig.9. Deformations of the top face-sheet and honeycomb cells
Specific data of the simulated and experimental residual dent depths and energies absorbed are illustrated in Tab.4. The hourglass energy produced during the simulations is generall y lower than 5% of the total energy, 0.074J for the case of 3.81J for instance. It demonstrates a good agreement in both sets of results, the largest error record is +4.51% for the predicted residual dent depths and -4.09% for the predicted energy absorbed for the case of 3.81J. The errors are mainly produced by ideall y process in establishing of the FE model. The validation implies that the modelling method adopted in this paper is correct and is able to predict impact response of the honeycomb sandwich panel subjected to drop-weight impact. Table 4. Comparison of experimental and numerical results Case-1
Energy absorbed (J) Error Dent depth (mm) Error
Case-2
Case-3
Case-4
Expt.
FEM
Expt.
FEM
Expt.
FEM
Expt.
FEM
1.171
1.125
2.489
2.424
3.252
3.119
3.913
3.762
-
-3.93%
-
-2.61%
-
-4.09%
-
-3.86%
1.82
1.90
2.57
2.66
2.96
3.10
3.19
3.33
-
+4.39%
-
+3.50%
-
+4.51%
-
+4.39%
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4. Analytical formulation 4.1. Load-indentation characteristics
As shown in Fig.10, considering a sandwich panel with honeycomb core dented by a rigid spherical impactor, local deformation occurs on the top face-sheet because of low strength of the honeycomb core and low bending stiffness of the face-sheet.
Fig.10. Schematic profiles of a honeycomb sandwich panel dented under a spherical impactor
The honeycomb core is assumed to be an ideally plastic foundation with a constant crushing resistance for the size of impactor is much larger than the cell size of honeycomb core. Generally, the localized indentation area is larger than the contact radius because the exist of face-sheet, a quadratic polynomial was proposed by Wierzbicki [30] and Xie [31] to describe the local indentation field of the top face-sheet, which could be represented as,
δ − ( R − R2 − r 2 ) δ − τ 2 / 2 R ⋅ [1 − (r − τ ) /(ξ − τ )]2
α (r) =
(
)
r ≤τ
τ < r ≤ξ
(5)
where δ and ξ are indentation depth and radius of the local indentation region on the top face-sheet, respectively; radius of the spherical impactor is R ; the contact radius is τ . As the shape of indentation profile is symmetrical about its center, boundary conditions: α (r = 0) = δ dα ( r ) =0 dr (r = 0 ) α (r = ξ ) = 0 dα ( r ) =0 dr (r =ξ )
at r = 0 (6) at r = ξ
are satisfied.
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Solutions for the indentation response can be derived based on the principle of minimum potential energy [30-33, 42]. Total potential energy of the system is
Π = Uf + Uc − W
(7)
where U f is the plastic strain energy of top face-sheet, U c is the plastic work due to compressive deformation of the honeycomb core, the external work is δ
∫
W = F dδ
(8)
0
where F is the indentation force. Moreover, the plastic strain energy of top face-sheet can be calculated b y
Uf =
∫N
0
ε r dA
(9)
A
1 ∂α (r) 2 ∂r
where A is deformation area of the top face-sheet, N0 = σ f t f and ε r =
2
are the
fully plastic membrane force and radial tensile strain, σ f is the flow stress of the top face-sheet. Hence, the expression of U f can be rewritten as. 2
π τ4 π τ 2 ξ + 3τ Uf = σ f t f 2 + σ f t f δ − 4 3 2R ξ − τ R
(10)
The plastic work due to compressive deformation of honeycomb core is ξ
∫
∫
V
0
Uc = σ pl dV = σ pl α (r) ⋅ 2π r dr
(11)
where V is volume of the honeycomb core crushed, σ pl is the plateau stress of the single length regular hexagonal honeycomb in the out-of-plane direction, which can be calculated from [2]
σ pl
t = 5.6 c lc
5/3
σc
(12)
where σ c is flow stress of matrix material of the honeycomb core. The expression of U c can be rewritten b y substituting Eqs. (5) and (11) as
Uc =
π 6
[
(
)(
σ pl 3δτ 2 + δ − τ 2 / 2 R ξ 2 + 2τξ
)]
(13)
Substitute Eqs. (8), (10) and (13) into (7), the total potential energy is determined as 2
δ τ 2 ξ + 3τ π Π = σ f t f 2 + σ f t f δ − + σ pl 3δτ 2 + δ − τ 2 / 2R ξ 2 + 2τξ − Fδ 0 4 3 2R ξ − τ 6 R
π
τ4
π
[
15
(
)(
)] ∫
(14)
By minimizing Π respect to δ [32], the indentation force is obtained as
F=
∂ Uf ∂ Uc 2π τ 2 ξ + 3τ π + = σ f t f δ − + σ pl 3τ 2 + ξ 2 + 2τξ ξ τ ∂δ ∂δ 3 2 R − 6
(
)
(15)
Using the condition that partial derivatives of indentation force with respect to ξ and τ [31], i.e.
∂F / ∂ξ = 0 ∂F / ∂τ = 0
(16)
The relationship of indentation depth, contact radius and maximum plastic deformation region can be obtained as follows:
τ 2 1 σ pl τ− (ξ + τ )(ξ − τ )2 = 0 δ − 2R 8σ ftf 2 σ τ 2 pl (ξ − τ ) ξ 2 + 2ξτ + 3τ 2 = 0 (ξ + 3τ ) − R σ t f f
(
)
(17)
Hence, the indentation force can be determined by substituting Eq. (17) into (15). It should be noted that adhesive layers are neglect in the above formulations, the fully plastic membrane force N 0 should be revised in considering effect of the adhesive layers by
σ t N0 = 1 + a a σ f tf
N0
(18)
where σa is flow stress of the adhesive layers.
4.2. Revised energy balance model The energy balance model [33, 43] is widely adopted to predict the impact response of sandwich structures. It is assumed that the target responds quasi-statically during the impact event and that kinetic energy of the target is absorbed in bending, shear and contact effect deformations,
1 MV I2 = E b + E s + E c 2
(19)
Where E b , E s , E c refer to energy dissipation in bending, shear and contact effects, respectively. As shown in Eq. (15), the contact force is determined b y local indentation, contact radius and deformation region, which is related to each other as Eq. (17). The contact force can be simplified as a function relationship with local indentation [43],
F = f (δ ) = Kcδ n
16
(20)
where K c is local stiffness of the sandwich structure and n is some constant. It is assumed that kinetic energy of the impactor is totally absorbed and dissipated in the impact incident. However, the impactor may rebound after the contact in a drop-weight impact event. Moreover, global deflection of the panel is negligible and no deformation happens on the bottom face-sheet
considering
low-velocity/low-energy.
The
energy
balance
model
for
a
low-velocity/low-energy drop-weight impact event could be revised and simplified as, δ 1 1 M VI2 −V (t) 2 = Ec = Fdδ = Kcδ n+1 0 2 n +1
(
)
∫
(21)
5. Results and discussion 5.1. Impact response description As stated above, there are three distinct regimes in the impact process. During which, contact regime is the most important one as interaction and energy absorbing all occur in this regime. The contact regime can be further divided into three stages according to motion state of the impactor (see Fig.11): I) velocity-decreasing stage; II) velocity-zero stage; III) velocity-rebounding stage. Fig.12 gives the contact force versus time and indentation depth on the top face-sheet for impact energy of 3.81J, the other cases display a similar characteristic, the constants in Eq. (20) could be estimated using least-squares method based on the numerical impact force and local indentation as shown in Fig.12. The local stiffness K c = 0.530 kN/mm and the constant n = 1.012 for the investigated sandwich panels in this paper. Three obvious different stages can also be distinguished from the figure. In stage (I), velocity of the impactor is decreasing from V I to zero while indentation depth of the sandwich is increasing from zero to a biggest value. Stage (II) is actually a moment, at which impactor reaches the lowest position and the velocity becomes zero, peak of the impact force also appears at this moment. In stage (III), velocity of the impactor is reincreasing from zero to V R , but in the opposite direction. Meanwhile, a little amount of indentation rebound is generated and the impact force deceasing ver y quickly. In the end, the impactor is separate from the sandwich panel with a constant rebound velocity and a residual dent is left on top face-sheet of the sandwich panel.
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Contact Regime
I
II
III
Fig.11. Three stages of the contact regime: I) velocity-decreasing stage; II) velocity-zero stage; III) velocity-rebounding stage.
II
I III
Fig.12. Impact load vs. time & dent depth for the impact energy of 3.81J
5.2. Energy absorbing and dissipating By the law of conservation of energy, total energy of the system is constant throughout the impact event, which is the initial kinetic impact of the impactor. As impact processes, kinetic energy of the impactor is decreasing and absorbed. Ignore kinetic energy of the sandwich panel, damage dissipation such as friction dissipation, heat effect and gas compression effect, the total energy of the system can be simplified as a summation of kinetic energy of the impactor and internal energy of the sandwich panel,
Etotal = E KI = Ek (t ) + E IS (t )
18
(22)
where E k (t ) , E IS (t ) are kinetic energy of the impactor and internal energy of the sandwich panel at time t , respectively. Internal energy of the sandwich panel consists three part, E IS (t ) = E It (t ) + E Ic (t ) + E Ib (t )
(23)
where E It (t ) , E Ic (t ) , E Ib (t ) refer to internal energy of top face-sheet, honeycomb core and bottom face-sheet at time t , respectively. Using Eqs. (2), (21), (22), energy absorbed in the end is the difference value of initial and rebound kinetic energy of impactor and all transformed into internal energy of the sandwich panel, which is the area between the impact force curve and indentation axis, Ea =
(
)
1 M V I2 − VR2 = E IS = 2
δ0
∫
0
F dδ
(24)
where δ 0 is the residual dent depth on the top face-sheet. E KI =
1 MV I2 2 Kinetic energy of impactor
II
III
Ea = E KI − E KR
I 1 E KR = MVR2 2 Fig.13. Energy converting history for the impact energy of 3.81J
Fig.13 illustrates kinetic energy of the impactor, internal energy of the sandwich panel as well as ever y components of the sandwich for the impact energy of 3.81J case. In stage (I), kinetic energy of the impactor is dropping rapidly after contact with sandwich panel, which is transformed into internal energy of the sandwich panel. Kinetic energy of the impactor becomes zero at the lowest position, i.e. stage (II), at the same time, internal energy of the sandwich panel reaches the largest. As impact continues, kinetic energy of the impactor reincreases again with rebound of the impactor, where is stage (III). In the end of the impact event, the impactor is separate from the sandwich panel with a constant rebound kinetic energy E KR . Moreover, specific data of energy absorbed and dissipated in different terms for different components are illustrated in Tab.5. Here, a symbol η is defined to evaluate the energy
19
absorption efficiency, as
η=
Ea E total
(25)
As shown in Tab.5, η = 81.6% is observed for the case of impact energy of 3.81J, which means about 81.6% of the total energy is absorbed by the sandwich panel, among which 42.3% is absorbed by the top face-sheet and 39.2% is absorbed by the honeycomb core. It also can be seen that energy absorbed b y the bottom face-sheet is very small (0.1%), which indicates that global deformation is negligible compared to local indentation. It should be noted that energy absorbed by face-sheet here contains both absorbed by face-sheet and its bonded adhesive layer. Besides, internal energy is composed of various terms, including elastic strain energy, plastic dissipation, artificial strain energy and energy dissipated b y viscoelasticity. Among which plastic dissipation is the major factor, about 91.9% of the energy absorbed (75.0% of the total energy) is expended as plastic dissipation. Table 5. Percentage of energy absorbed by differnet components for the impact energy of 3.81J Component
Type
Energy(J)
Percentage
3.81
100%
Internal energy
3.119
81.6%
Plastic dissipation
2.866
75.0%
Strain energy
0.167
4.37%
Others
0.086
2.25%
Internal energy
1.616
42.3%
Plastic dissipation
1.484
38.8%
Strain energy
0.126
3.30%
Internal energy
1.498
39.2%
Plastic dissipation
1.382
36.2%
Strain energy
0.037
0.97%
Internal energy
0.004
0.10%
Plastic dissipation
-
-
Strain energy
0.004
0.10%
Imapct energy
Sandwich panel
Top Facesheet
Honeycomb Core
Bottom Facesheet
5.3. Effect of impact energy During an impact incident, impact energy is a key parameter widely used to characterize the event. In order to investigate the influence of impact energy on indentation response of sandwich panel, residual dent depth and energy absorption of the sandwich panel under different impact energies are simulated. As stated above, different impact energies in the
20
experiments are obtained b y var ying impact velocity V I through changing initial height H I of the impactor. Besides, different impact energies can also be obtained b y changing the impactor mass M . A same impact energy can be obtained by both approaches, but a different influence on the indentation and energy absorbed is foreseeable. In this section, simulations of sandwich panel impacted by different impact energies through the two approaches are conducted and the difference of influence are discussed. Table 6. Different impact energies obtained through varying impactor mass and impact velocity Honeycomb cell: wall length 6 mm, thickness 0.07 mm;
Parameters Impact energy(J) Approach 1. Approach 2.
0.76
1.90
2.86
3.81
7.62
11.43
15.24
2.26
3.57
4.37
5.05
7.14
8.75
10.10
0.06
0.15
0.225
0.3
0.6
0.9
1.2
Impact velocity(m/s) (Constant impactor mass: 0.3kg.)
Mass(kg) (Constant impact velocity: 5.05m/s.)
As illustrated in Tab.6, seven different impact energies are obtained through two approaches: 1) varying impact velocity under remaining impactor mass; 2) varying impactor mass under remaining impact velocity. 5.3.1. Residual dent depth
Fig.14 plots effect of impact energy on residual dent depth on top face-sheet on a Cartesian coordinate as well as a double-logarithmic coordinate. As shown in the figure, the dent depth non-linearly increases with increase of impact energy for both approaches as well as the experimental results. However, a little difference of the two approaches can be observed, the dent depth is much sensitive to the variation of velocity compared to impactor mass. This is expected and can be explained as follow. Generally, as presented in Eq. (21), a larger impact energy will lead to a deeper dent. However, for the same impact energy, a larger mass of the impactor will create a larger radius of local indentation area on the top face-sheet ξ as well as a larger contact radius τ , which will further lead to a smaller dent depth δ , see Fig.10. It is embodied in the figure that for impact energy between 0.76J to 3.81J, smaller δ 0 is observed for the curve of effect of mass while larger δ 0 is observed for impact energy between 3.81 J to 15.24J. Hence, a smaller slope of the curve for effect of mass is illustrated in Fig. 14-b.
21
a)
b)
Fig.14. Effect of impact energy on indentation
Regression model by using ordinary least-squares method is made and the semi-empirical models to estimate the residual dent depth for both approaches are acquired based on the experimental results as well as the numerical results. The semi-empirical model established based on the experimental results is,
( )
log (δ 0 ) = 0.5492 log E KI + 0.1638
(26)
The semi-empirical models established based on the numerical results are, By varying the impact velocity,
( )
(27)
( )
(28)
log (δ 0 ) = 0.5674 log E KI + 0.1569
By varying the mass of impactor, log (δ 0 ) = 0.4963 log E KI + 0.2019 5.3.2. Energy absorption
Experimental and numerical results of energy absorbed by sandwich panel for different impact energies is drawn in Fig.15. Besides, energy distribution in different components are plotted in Fig.16. It should be noted that energy absorbed by different components could not be obtained experimentally, so all data illustrated in Fig.16 are the results of FEA. As stated in section 3.1, the face-sheet and its bonded adhesive layer were modeled as double layers, so the energy absorbed by top face-sheet here contains both face-sheet and its bonded adhesive layer. It can be seen that for low-energy drop-weight impact on honeycomb sandwich panels, energy absorbed by sandwich panel increases almost linearly with increase of impact energy and no
22
obvious difference is observed for the two approaches. Moreover, energy absorption efficiency
η also increases with increase of impact energy, i.e. higher percentage energy is absorbed for a larger impact energy.
a)
b)
Fig.15. Effect of impact energy on energy absorption
Fig.16. Energy absorbed by different components
As stated in section 5.1.2, energy absorbed by bottom face-sheet is negligible, based on which Eq. (23) can be simplified and substituted into Eq. (24),
(
)
1 Ea = M VI2 − VR2 ≈ EIt + EIc 2
(29)
Hence, only energy absorbed b y top face-sheet E It and honeycomb core E Ic are plotted and discussed here. It can be seen that almost same energy is absorbed for the two approaches
23
under a same impact energy, but big difference is observed in energy distribution. Specifically, under a lower impact energy (0.76 J for instance), E It is smaller and E Ic is larger for approach of varying velocity. While it’s totally opposite under a larger impact energy (15.24 J for instance), where E It is larger and E Ic is smaller. But, they can be universally described as follow: E It is smaller and E Ic is larger for impactor with a larger radius under a same impact energy. Considering most of the energy absorbed is plastic dissipation, which is U f for top face-sheet and U c for honeycomb core. Using Eqs. (9) and (11), ratio of energy absorbed due to the plastic deformation of honeycomb core to that due to top face-sheet is,
∫
σ pl dV Uc V β= = Uf N0 ε r dA
(30)
∫
A
As the top face-sheet and adhesive layer were modeled as a doube-layers sheet, the revised fully plastic membrance force N0 in Eq. (18) is employed here. A dimensionless paramerter
ϕ is intorduced [32],
ϕ=
σ pl R σ ftf
(31)
Considering the plasteau stress of honeycomb core σ pl is much lower than flow stress of the top face-sheet as shown in Eq. (12), the parameter ϕ is ver y small. Hence, an asymptotic solution for the parameter β is obtained [31],
(
)
β ≈ 2 2ϕ 1 − 2ϕ + ο (ϕ )
(32)
It can be seen from Eq. (31) and (32) that β is in proportion to radius of the impactor R under same σ pl , σ f , t f . Hence, under the same impact energy, energy absorbed b y top face-sheet is smaller and energy absorbed by core is larger for an impactor with a larger mass and lower velocity. Regression model by using ordinary least-squares method is made and the semi-empirical models to estimate the energy absorbed for both approaches are acquired based on the experimental results as well as the numerical results. The semi-empirical model established based on the experimental results is, E a = 0.9201 E KI − 0.2013
24
(33)
The semi-empirical models established based on the numerical results are, By var ying the impact velocity, E a = 0.9104 E KI − 0.2529
(34)
E a = 0.8959 E KI − 0.2010
(35)
By var ying the mass of impactor,
It can be seen from the equations that the semi-empirical model compared very well for experimental and numerical results. Moreover, a general formula can be further established for energy absorbed b y sandwich panel during a low energy/low velocity impact event under a spherical impactor based on Eqs. (33) - (35), E a = λ E KI − C
(36)
Hence, energy absorption efficiency is
η=
Ea C =λ − I E KI EK
(37)
where λ , C are some constant. It is noticed that E KI ≠ 0 when Ea = 0 , which means there is
~ a threshold for impact energy E KI = C / λ , where plastic deformation starts occurrence. And it can also be explained why higher energy absorption efficiency is observed for larger impact energy.
6. Conclusion An investigation on indentation response and energy absorption property of honeycomb sandwich panels subjected to low-energy drop-weight impact under a spherical impactor was proposed. Experiments based on a pendulum-impact system were first undertaken, during which energy absorbed and residual dent on the top-face sheet were measured. A three-dimensional numerical model considering the micro-structure of honeycomb core was further established and validated by experimental results. Analytical formulations including a load-indentation response model based on the principle of minimum potential energy and an energy balance model were deduced and revised. Moreover, impact response of the sandwich panel, energy absorption property and effect of impact energy were specifically analyzed and discussed. The major contribution and conclusions can be summarized. •
For a low-energy impact, no obvious penetrative damage, crack damage or debonding between face-sheets and core were observed, the honeycomb core at the contact area was
25
compressed and produced cell walls buckling, which was initiating from the top end. The buckling was less and less from the center of the impactor area to the outside due to the spherical impactor. •
A plastic analytical model of indentation response for low-energy impact under a spherical indenter on honeycomb sandwich panel were established, during which the effect of the adhesive layers was fully considered. A revised and simplified energy balance analytical model specifically suitable for low-energy impact under a spherical indenter on honeycomb sandwich panel was also established based on the observation of experimental results.
•
Honeycomb sandwich panels perform satisfied in energy absorption. Generally, more than 80% of the impact energy is absorbed and dissipated, among which almost all (99.9%) is absorbed b y the top face-sheet and honeycomb core. Plastic dissipation is the major term in the energy absorbed, more than 90% of the energy absorbed is expended as plastic dissipation.
•
For a low-energy drop-weight impact, impact energy has a great and different influence on dent depth and energy absorption. Specifically, dent depth non-linearly increases while energy absorbed increases almost linearly with increase of impact energy. Besides, different approach b y var ying impact velocity or mass of impact also make difference.
•
Energy absorption efficiency increased with increase of impact energy due to exist of a threshold where plastic deformation starts occurrence. Ratio of energy absorbed by top face-sheet to honeycomb core was in proportion to radius of the impactor.
•
Semi-empirical formulations to estimate the residual dent depth and energy absorbed for different impact energies and different approaches are given.
Acknowledgements This work was supported by a research grant by the National Natural Science Foundation of China (No.11572086), a research grant by Jiangsu Natural Science Foundation of China (No. BK2012318) and a research grant by Key Laborator y of Lightweight and Reliabilit y Technology for Engineering Vehicle, College of Hunan Province (No.2016kfjj08).
26
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S0263-8223(16)32008-6 http://dx.doi.org/10.1016/j.compstruct.2017.02.053 COST 8274
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
29 September 2016 30 December 2016 10 February 2017
Please cite this article as: Zhang, D., Fei, Q., Zhang, P., Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor, Composite Structures (2017), doi: http://dx.doi.org/10.1016/j.compstruct. 2017.02.053
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Drop-weight impact behavior of honeycomb sandwich panels under a spherical impactor
Dahai Zhang1,2,3 , Qingguo Fei 1, *, Peiwei Zhang1,3 (1 Department of Engineering Mechanics, Southeast University, Nanjing 210096, China) (2 Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, 3122, Australia) (3 Key Laborator y of Lightweight and Reliability Technology for Engineering Vehicle, College of Hunan Province, Changsha 410114, China)
* Corresponding author. E-mail address: [email protected] (Q. Fei) 1
Abstract Indentation response and energy absorption property of honeycomb sandwich panels subjected to drop-weight impact under a spherical impactor were investigated. Experiments were conducted using a pendulum-impact system. A three-dimensional finite element model with micro-structure considered was built and validated. In conjunction with experimental and numerical methods, analytical models of indentation response and energy balance specifically aimed to solve problems of low-velocity impact of a spherical indenter on sandwich panels were deduced. Results show that a hemispherical residual dent caused by bending of top face-sheet and core crushing is left on top face-sheet after impact. It also concludes that more than 80% of impact energy is absorbed mostly b y top face-sheet and honeycomb core. The main form of energy dissipation is plastic dissipation. In addition, parametric studies were carried out to explore effects of impact energy on impact behavior b y altering impact velocity or impactor mass. Different effects are observed for the two approaches and some useful semi-empirical formulations based on both experimental and numerical results are overfitted to estimate the residual dent depth and energy absorbed during a drop-weight impact event on a honeycomb sandwich panel under a spherical impactor.
Keywords: Honeycomb sandwich panel; Drop-weight impact; Indentation; Energy absorption; Spherical impactor;
2
1. Introduction Due to their excellent crashworthiness performance and energy absorption ability [1, 2], sandwich structures have become attractive candidates in many engineering applications, including automotive industry [3], aeronautics [4], transportation engineering [5] and personal protective equipment [6]. During the period of their serves, sandwich structures are susceptible to low-energy/low-velocity impacts, such as runway debris, hailstones, tools dropped during maintenance and so on [7-9]. Unlike high-velocity impact, damages caused by low-velocit y impact are often internal and invisible but can significantly reduce stiffness and strength of the structures, which will result in shortening service life of the structures. Generally, for a metal sandwich panel subjected to low-energy/low-velocity impact, plastic deformation including face-sheets bending and core crushing [10-12] rather than penetrative damages [13, 14] occur. Most of the impact energy would be absorbed and dissipated during the process while the rest is retained in the impactor as rebound kinetic energy [15]. After impact, an undetectable or barely detectable by visual inspection residual plastic indentation may be left on top face-sheet of the sandwich panel. Indentation characteristics and energy absorption propert y are basically determined b y crashworthiness of the structure, which is extremel y sensitive to the mechanical property of matrix material [16], geometric parameters of face-sheets [17] and core especiall y [18-20]. A large number of experimental, analytical and numerical studies have been carried out to investigate the performance of sandwich structures subjected to low-energy/low-velocit y impact loadings. Research scope of the problem mainly contains [21-37]: 1) contact response between the impactor and sandwich panel; 2) residual property of the sandwich panel after impact; 3) failure mechanism of the sandwich panel by impact; 4) energy absorption property of the sandwich panel; 5) parametric study on geometry of the impactor and sandwich panel; 6) optimization analysis; A series of quasi-static and dynamic low-velocity tests using a hemispheric impactor on aluminum honeycombs and sandwich panels were conducted by Shitta-Bey et al. [22], which
3
indicated that sandwich panels provide higher crushing forces and better crashworthiness than corresponding bare honeycomb samples due to plastic yielding of the face-sheet. Comparison of structural responses in impact events were studied by Crupi et al. [23] using a drop test machine to determine the difference of energy absorption and failure modes for polymeric and aluminum sandwich panels. Effects of impact variables such as face-sheet thickness and core thickness on the impact behavior and resulting impact damage states subjected to low-velocity impact with hemispherical steel impactors of different diameters at various energy levels were studied by Wang et al. [24]. Parameters such as impact force histor y, energy absorbed and contact duration were tested and discussed. Those studies mainly focused on impactor with a spherical or hemispherical shape, there were also a lot of tests undertaken with other types of impactor, including conical [25], truncated [26] and flat [27]. Some analytical models were established to investigate indentation response of sandwich structures under low-velocity impact. Earlier analytical solutions mainly focused on elastic response of the whole structure or on elastic face-sheets and plastic core [28, 29]. The model was widely employed to determine the indentation response under a point or line loading. A large deformation model for a plastic string resting on a plastic foundation and undergoing localized mass impact was proposed by Wierzbicki et al. [30]. The model was adopted and improved by Xie et al. [31], they theoretically studied the localized indentation of sandwich panels with metallic foam core and derived the analytical models for a fat indenter and a spherical indenter. Mu et al. [32] further improved the model to predict indentation behavior of sandwich circular panel with gradient foam cores under a flat indenter. Besides, spring-mass model and energy-balance model [33] were also widely adopted to predict the peak impact force, impact duration, energy absorption and equivalent stiffness of sandwich structures. Compared with experimental and analytical method, numerical method provides a much more cost-effective and convenient approach. It has been widely employed to simulate the coupling analysis and whole process of impact. Wide areas of research have been simulated and discussed using numerical method, including impact force histor y, contact duration, characteristics of energy absorption, failure modes for face-sheet and core, and so on [14-16, 20, 24, 34-37]. The main purpose of this paper is to explore the indentation response and energy
4
absorption property as well as energy distribution of honeycomb sandwich panels subjected to low-energy drop-weight impact with a spherical indenter. In section 2, drop-weight impact tests of four groups of impact energy were conducted, during which a pendulum-impact installation, a high-speed video record system and an advanced optical measurement method were employed. In section 3, a three-dimensional FE (finite element) model of the sandwich panel was developed and employed in simulations of drop-weight impacts. Meanwhile, results predicted by the simulations were compared with experiments in order to validate the FE model. In section 4, an analytical load-indentation model was deduced in conjunction with a revised energy balance model to solve for impact response and energy absorption, both models were revised to be suitable for this investigation. In section 5, impact response of the sandwich panel such as impact force histor y, energy absorbing-dissipating process and energy distribution of different components during the impact were discussed and summarized. Moreover, parametric studies were performed to identify the effect of impact energies obtained by var ying impact velocity or mass of impactor on energy absorption efficiency as well as energy distribution characteristics.
2. Experimental procedure 2.1. Specimen description Experiments of honeycomb sandwich panels under drop-weight impact were carried out first in order to validate the numerical model. The specimens as shown in Fig.1 are made of aluminum alloy for both honeycomb core and face-sheets, which are cemented b y adhesive layers made of epoxy resin. The materials for the face-sheets and honeycomb core are A5083-H321 and A3003-H19 respectively. The cell shape of honeycomb core is regular hexagonal (the most common cell shape). Each panel measures L1 × L2 = 150 mm × 150 mm with a thickness t f = 0.5 mm for each top and bottom face-sheet, a thickness h = 15 mm for
hexagonal honeycomb core and a thickness
t a = 0.15 mm
for adhesive layers between
face-sheets and core. Wall thickness and wall length of the hexagonal honeycomb core are
t c = 0.07 mm and lc = 6 mm , respectively. Relative density of the honeycomb core can be calculated from [2],
5
ρc =
2 tc ρc 3 lc
(1)
where ρ c is the density of matrix material of the honeycomb core. The details of specification of the aluminum honeycomb sandwich panels tested are illustrated in Tab.1.
Honeycomb core
Fig.1. A honeycomb sandwich panel specimen Table 1. Specification of the aluminum honeycomb sandwich panels Properties Size of the panel
150 × 150 × 16 .3 mm
Weight of the panel
83.15 × 10 -3 kg
Density of the panel
226 .72 kg/m 3
Cell wall length of the core
6 .0 mm
Cell wall thickness of the core
0.07 mm
Height of the honeycomb core
15.0 mm
Thickness of the face-sheets
0 .5 mm
Thickness of the adhesive layers
0.15 mm
2.2. Arrangement and results As shown in Fig.2, three parts make up the experimental system, including a pendulum-impact part, a video camera part and a three-dimensional shape measurement part, respectively. To better explain the experimental methods, a sketch map of the pendulum-impact part and the video camera part are drawn in Fig.3. As shown in Fig.3, the pendulum-impact part is composed of a honeycomb sandwich panel, a pendulum impactor with a constant radius of D = 40 mm and mass of M = 0.3 kg hung on the supporting frame by rigid wire.
6
a
b
c
Fig.2. Experimental setup: a) the pendulum-impact part; b) the video camera part; c) the 3-D shape measurement part.
Front view
Side view
Fig.3. Sketch map of the pendulum-impacting part and the video camera part
The honeycomb sandwich panel was completely clamped fixed all sides and the bottom face-sheet was not fixed. Impact energy was obtained by converting gravitational potential energy into kinetic energy and a range of energy was achieved through changing the initial
7
height. Meanwhile, kinematic images of the process were recorded by a video camera part, a calibration background table was employed to help catch the initial height and rebound height of the impactor. The absorbed energy Ea is calculated from: E a = E KI − E KR = Mg ∆H = Mg ( H I − H R )
(2)
1 M V I2 = Mg H I 2 1 E KR = M V R2 = Mg H R 2 E KI =
(3) (4)
where E KI , E KR are impact and rebound kinetic energies of the impactor, respectively; VI , VR are impact and rebound velocities of the impactor, respectively; H I , H R are initial and rebound heights of the impactor, respectively; ∆H is gap height of the impactor. Note that the impactor would drop again after reached the largest rebound height, which is unconcerned here. Hence, the impactor was manually caught after it drops again before it impacted the panel in case of multiple impacts. In this paper, four impact energy groups were conducted and each tested three times: 1.47J, 2.94J, 3.81J and 4.41J, respectively. Generally, as shown in Fig.4, there are three distinct regimes during the impact process: a dropping regime, a contact regime and a rebound regime. Energy converting of the impactor is proceed in the dropping regime, required impact energy is obtained from converting of gravitational potential energy in the end of this regime. Interaction and energy absorbing occur in the contact regime. In the rebound regime, impactor will rebound with a much smaller velocity for impact energy hardly completely be absorbed by the target in a low-velocity drop-weight impact incident. A residual plastic indentation will be left on top face-sheet of the sandwich panel in the end.
Impact Process
VI
VR
Impactor
Fig.4. Impact process
8
Residual Dent
A three-dimensional shape measurement part was employed to measure the surface deformation and residual dent depth of the panel after tests. An optical geometry of fringe projection method was adopted in this paper, the method can be simply described as follows [38], a grating was projected onto the surface of an object through a focusing lens and a CCD (Charged Couple Device) camera was adopted to capture the deformed grating image on the object surface, which was followed by a subsequent analysis. Fig.5 shows the projected fringe pattern and three-dimensional topography plot of the specimens impacted at different impact energies. Residual dent depths obtained through analysis of the figures as well as energy absorbed are shown in Tab.2. a) b)
c)
d)
Fig.5. Projected fringe pattern and 3-D plot of specimens under different impact energies: a) 1.47J, b) 2.94J, c) 3.81J, d) 4.41J. Table 2. Experimental results. 1 1-1#
1-2#
2 1-3#
2-1#
2-2#
3 2-3#
3-1#
3-2#
4 3-3#
4-1#
4-2#
Initial height (m)
0.50
1.00
1.30
1.50
Impact energy (J)
1.47
2.94
3.81
4.41
Initial velocity (m/s)
3.13
4.43
5.05
5.42
4-3#
Rebound height (m)
0.105
0.092
0.108
0.146
0.157
0.157
0.180
0.195
0.207
0.184
0.191
0.136
Height gap (m)
0.395
0.408
0.392
0.854
0.843
0.843
1.120
1.105
1.093
1.316
1.309
1.364
Energy-absorbed (J)
1.161
1.199
1.152
2.510
2.478
2.478
3.293
3.249
3.213
3.872
3.851
4.017
Dent depth (mm)
1.80
1.89
1.77
2.63
2.56
2.51
2.98
2.92
3.03
3.20
3.07
3.27
9
3. Numerical model 3.1. Finite element modeling FE model of the sandwich panel and impactor were built. The simulations were performed using an explicit dynamic finite element code (ABAQUS/Explicit). A micromechanical approach with actual discrete hexagonal microstructure of the honeycomb considered was adopted. As shown in Fig.6, a detailed honeycomb structure model was established using nominal dimensions by modeling each cellular explicitly. The fine micromechanical model of the core was established based on ideal geometry of the honeycomb cells instead of a continuous model with equivalent properties. A unit cell was firstly modelled and replicated in X-direction and Y-direction to create other individual cells. Then, the individual cells were merged together to assemble the honeycomb core. Adhesive layers between the face-sheets and honeycomb core usually be neglected in numerical models [37, 39, 40], by doing this, bonding between face-sheets and core was assumed to be perfect, each node of the honeycomb core at the interface is constrained to have the same translational and rotation motion as node on the face-sheet to which it was coupled. However, this assumption and simplification result in decrease of analysis accuracy more or less. In this paper, a more reasonable modelling approach was adopted, specifically, the face-sheet and adhesive layer were modelled as double layers [41] with respective properties, as shown in Fig.6.
Fig.6. Geometry model of the sandwich panel, impactor and double layers of adhesive layer and face-sheet
For computing efficiency, the impactor was placed just 1mm upon the top face-sheet and was modelling using four-node linear tetrahedron continuum elements. The impactor was
10
considered rigid and an initial velocity was assigned to the impactor at its reference node as motion of all nodes of the impactor is governed by the rigid body reference point. The face-sheets and honeycomb core were all meshed with shell elements. The face-sheets and honeycomb core as well as the adhesive were all defined as ideal elastic-plastic materials, the strain-rate effect was not considered. The mechanical properties of different components of the sandwich panel are listed in Tab.3. Table 3. Mechanical properties of different components
Face-sheets
Adhesive
(A5083-H321)
(Epoxy resin)
(A3003-H19)
Density ρ (kg/m )
2700
1500
2700
Young’s modulus E (GPa)
72.0
5.0
70.0
Poisson ratio ν
0.33
0.3
0.33
Yield stress σ 0 (MPa)
280
20
185
Property 3
Core
Data are provided by the manufacturer.
A general contact algorithm was introduced and was widely employed to simulate contact between the impactor and the sandwich panel [25, 40], and was also applied in this paper. This general contact algorithm enforces contact constrains using a penalty contact method in ABAQUS [25], the friction coefficient was chosen to be 0.3. Moreover, in order to achieve convergence, a reasonable fine mesh at vicinity of the contact area was carried out. The mesh generation was followed by a convergence study and all results presented in this paper are converged. Fig.7 shows the effect of mesh size on simulation results and computing time, 0.5mm (12 elements on each cell wall) was chosen as the size of smallest elements at vicinity of the contact area for both computing efficiency and results accuracy considering. FE model of the sandwich panel and impactor are drawn in Fig.8 as well as details of the contact area.
11
Fig.7. Convergence analysis
Rigid Impactor
Boundary c o nd it i o n: fixed x,y,z
Fig.8. FE model of the sandwich panel and impactor
3.2. Numerical model validation Predicted results and experimental data were compared to validate the numerical model. Fig.9 shows comparison of the experimental and numerical deformation of top face-sheet as well as cross-section of the sandwich panel after impact at the case of 5.05 m/s, the other cases display the similar characteristic. As shown in the figure, a plastic residual dent was left after impact with bending of top face-sheet and fold of cell walls along axial direction. As it can be seen from the figures, no obvious penetrative damage and crack damage were observed and the face-sheets and honeycomb core were still boned very well. The honeycomb core and the top face-sheet at the contact area were compressed in the out-of-plane direction, which produced buckling (elastic or plastic buckling) of the cell walls, initiating from the top end. Due to the
12
spherical impactor, the buckling of the cell walls was not uniform and was less and less from the center of the impactor area to the outside. It is also found diameter of the dent is larger than that of the impactor because of gradual deformation of the face-sheet, mechanism of the formation of indentation is also successfully predicted by the numerical simulation.
Expt.
FEM
a) top face-sheet
Expt.
FEM
b) cross-section Fig.9. Deformations of the top face-sheet and honeycomb cells
Specific data of the simulated and experimental residual dent depths and energies absorbed are illustrated in Tab.4. The hourglass energy produced during the simulations is generall y lower than 5% of the total energy, 0.074J for the case of 3.81J for instance. It demonstrates a good agreement in both sets of results, the largest error record is +4.51% for the predicted residual dent depths and -4.09% for the predicted energy absorbed for the case of 3.81J. The errors are mainly produced by ideall y process in establishing of the FE model. The validation implies that the modelling method adopted in this paper is correct and is able to predict impact response of the honeycomb sandwich panel subjected to drop-weight impact. Table 4. Comparison of experimental and numerical results Case-1
Energy absorbed (J) Error Dent depth (mm) Error
Case-2
Case-3
Case-4
Expt.
FEM
Expt.
FEM
Expt.
FEM
Expt.
FEM
1.171
1.125
2.489
2.424
3.252
3.119
3.913
3.762
-
-3.93%
-
-2.61%
-
-4.09%
-
-3.86%
1.82
1.90
2.57
2.66
2.96
3.10
3.19
3.33
-
+4.39%
-
+3.50%
-
+4.51%
-
+4.39%
13
4. Analytical formulation 4.1. Load-indentation characteristics
As shown in Fig.10, considering a sandwich panel with honeycomb core dented by a rigid spherical impactor, local deformation occurs on the top face-sheet because of low strength of the honeycomb core and low bending stiffness of the face-sheet.
Fig.10. Schematic profiles of a honeycomb sandwich panel dented under a spherical impactor
The honeycomb core is assumed to be an ideally plastic foundation with a constant crushing resistance for the size of impactor is much larger than the cell size of honeycomb core. Generally, the localized indentation area is larger than the contact radius because the exist of face-sheet, a quadratic polynomial was proposed by Wierzbicki [30] and Xie [31] to describe the local indentation field of the top face-sheet, which could be represented as,
δ − ( R − R2 − r 2 ) δ − τ 2 / 2 R ⋅ [1 − (r − τ ) /(ξ − τ )]2
α (r) =
(
)
r ≤τ
τ < r ≤ξ
(5)
where δ and ξ are indentation depth and radius of the local indentation region on the top face-sheet, respectively; radius of the spherical impactor is R ; the contact radius is τ . As the shape of indentation profile is symmetrical about its center, boundary conditions: α (r = 0) = δ dα ( r ) =0 dr (r = 0 ) α (r = ξ ) = 0 dα ( r ) =0 dr (r =ξ )
at r = 0 (6) at r = ξ
are satisfied.
14
Solutions for the indentation response can be derived based on the principle of minimum potential energy [30-33, 42]. Total potential energy of the system is
Π = Uf + Uc − W
(7)
where U f is the plastic strain energy of top face-sheet, U c is the plastic work due to compressive deformation of the honeycomb core, the external work is δ
∫
W = F dδ
(8)
0
where F is the indentation force. Moreover, the plastic strain energy of top face-sheet can be calculated b y
Uf =
∫N
0
ε r dA
(9)
A
1 ∂α (r) 2 ∂r
where A is deformation area of the top face-sheet, N0 = σ f t f and ε r =
2
are the
fully plastic membrane force and radial tensile strain, σ f is the flow stress of the top face-sheet. Hence, the expression of U f can be rewritten as. 2
π τ4 π τ 2 ξ + 3τ Uf = σ f t f 2 + σ f t f δ − 4 3 2R ξ − τ R
(10)
The plastic work due to compressive deformation of honeycomb core is ξ
∫
∫
V
0
Uc = σ pl dV = σ pl α (r) ⋅ 2π r dr
(11)
where V is volume of the honeycomb core crushed, σ pl is the plateau stress of the single length regular hexagonal honeycomb in the out-of-plane direction, which can be calculated from [2]
σ pl
t = 5.6 c lc
5/3
σc
(12)
where σ c is flow stress of matrix material of the honeycomb core. The expression of U c can be rewritten b y substituting Eqs. (5) and (11) as
Uc =
π 6
[
(
)(
σ pl 3δτ 2 + δ − τ 2 / 2 R ξ 2 + 2τξ
)]
(13)
Substitute Eqs. (8), (10) and (13) into (7), the total potential energy is determined as 2
δ τ 2 ξ + 3τ π Π = σ f t f 2 + σ f t f δ − + σ pl 3δτ 2 + δ − τ 2 / 2R ξ 2 + 2τξ − Fδ 0 4 3 2R ξ − τ 6 R
π
τ4
π
[
15
(
)(
)] ∫
(14)
By minimizing Π respect to δ [32], the indentation force is obtained as
F=
∂ Uf ∂ Uc 2π τ 2 ξ + 3τ π + = σ f t f δ − + σ pl 3τ 2 + ξ 2 + 2τξ ξ τ ∂δ ∂δ 3 2 R − 6
(
)
(15)
Using the condition that partial derivatives of indentation force with respect to ξ and τ [31], i.e.
∂F / ∂ξ = 0 ∂F / ∂τ = 0
(16)
The relationship of indentation depth, contact radius and maximum plastic deformation region can be obtained as follows:
τ 2 1 σ pl τ− (ξ + τ )(ξ − τ )2 = 0 δ − 2R 8σ ftf 2 σ τ 2 pl (ξ − τ ) ξ 2 + 2ξτ + 3τ 2 = 0 (ξ + 3τ ) − R σ t f f
(
)
(17)
Hence, the indentation force can be determined by substituting Eq. (17) into (15). It should be noted that adhesive layers are neglect in the above formulations, the fully plastic membrane force N 0 should be revised in considering effect of the adhesive layers by
σ t N0 = 1 + a a σ f tf
N0
(18)
where σa is flow stress of the adhesive layers.
4.2. Revised energy balance model The energy balance model [33, 43] is widely adopted to predict the impact response of sandwich structures. It is assumed that the target responds quasi-statically during the impact event and that kinetic energy of the target is absorbed in bending, shear and contact effect deformations,
1 MV I2 = E b + E s + E c 2
(19)
Where E b , E s , E c refer to energy dissipation in bending, shear and contact effects, respectively. As shown in Eq. (15), the contact force is determined b y local indentation, contact radius and deformation region, which is related to each other as Eq. (17). The contact force can be simplified as a function relationship with local indentation [43],
F = f (δ ) = Kcδ n
16
(20)
where K c is local stiffness of the sandwich structure and n is some constant. It is assumed that kinetic energy of the impactor is totally absorbed and dissipated in the impact incident. However, the impactor may rebound after the contact in a drop-weight impact event. Moreover, global deflection of the panel is negligible and no deformation happens on the bottom face-sheet
considering
low-velocity/low-energy.
The
energy
balance
model
for
a
low-velocity/low-energy drop-weight impact event could be revised and simplified as, δ 1 1 M VI2 −V (t) 2 = Ec = Fdδ = Kcδ n+1 0 2 n +1
(
)
∫
(21)
5. Results and discussion 5.1. Impact response description As stated above, there are three distinct regimes in the impact process. During which, contact regime is the most important one as interaction and energy absorbing all occur in this regime. The contact regime can be further divided into three stages according to motion state of the impactor (see Fig.11): I) velocity-decreasing stage; II) velocity-zero stage; III) velocity-rebounding stage. Fig.12 gives the contact force versus time and indentation depth on the top face-sheet for impact energy of 3.81J, the other cases display a similar characteristic, the constants in Eq. (20) could be estimated using least-squares method based on the numerical impact force and local indentation as shown in Fig.12. The local stiffness K c = 0.530 kN/mm and the constant n = 1.012 for the investigated sandwich panels in this paper. Three obvious different stages can also be distinguished from the figure. In stage (I), velocity of the impactor is decreasing from V I to zero while indentation depth of the sandwich is increasing from zero to a biggest value. Stage (II) is actually a moment, at which impactor reaches the lowest position and the velocity becomes zero, peak of the impact force also appears at this moment. In stage (III), velocity of the impactor is reincreasing from zero to V R , but in the opposite direction. Meanwhile, a little amount of indentation rebound is generated and the impact force deceasing ver y quickly. In the end, the impactor is separate from the sandwich panel with a constant rebound velocity and a residual dent is left on top face-sheet of the sandwich panel.
17
Contact Regime
I
II
III
Fig.11. Three stages of the contact regime: I) velocity-decreasing stage; II) velocity-zero stage; III) velocity-rebounding stage.
II
I III
Fig.12. Impact load vs. time & dent depth for the impact energy of 3.81J
5.2. Energy absorbing and dissipating By the law of conservation of energy, total energy of the system is constant throughout the impact event, which is the initial kinetic impact of the impactor. As impact processes, kinetic energy of the impactor is decreasing and absorbed. Ignore kinetic energy of the sandwich panel, damage dissipation such as friction dissipation, heat effect and gas compression effect, the total energy of the system can be simplified as a summation of kinetic energy of the impactor and internal energy of the sandwich panel,
Etotal = E KI = Ek (t ) + E IS (t )
18
(22)
where E k (t ) , E IS (t ) are kinetic energy of the impactor and internal energy of the sandwich panel at time t , respectively. Internal energy of the sandwich panel consists three part, E IS (t ) = E It (t ) + E Ic (t ) + E Ib (t )
(23)
where E It (t ) , E Ic (t ) , E Ib (t ) refer to internal energy of top face-sheet, honeycomb core and bottom face-sheet at time t , respectively. Using Eqs. (2), (21), (22), energy absorbed in the end is the difference value of initial and rebound kinetic energy of impactor and all transformed into internal energy of the sandwich panel, which is the area between the impact force curve and indentation axis, Ea =
(
)
1 M V I2 − VR2 = E IS = 2
δ0
∫
0
F dδ
(24)
where δ 0 is the residual dent depth on the top face-sheet. E KI =
1 MV I2 2 Kinetic energy of impactor
II
III
Ea = E KI − E KR
I 1 E KR = MVR2 2 Fig.13. Energy converting history for the impact energy of 3.81J
Fig.13 illustrates kinetic energy of the impactor, internal energy of the sandwich panel as well as ever y components of the sandwich for the impact energy of 3.81J case. In stage (I), kinetic energy of the impactor is dropping rapidly after contact with sandwich panel, which is transformed into internal energy of the sandwich panel. Kinetic energy of the impactor becomes zero at the lowest position, i.e. stage (II), at the same time, internal energy of the sandwich panel reaches the largest. As impact continues, kinetic energy of the impactor reincreases again with rebound of the impactor, where is stage (III). In the end of the impact event, the impactor is separate from the sandwich panel with a constant rebound kinetic energy E KR . Moreover, specific data of energy absorbed and dissipated in different terms for different components are illustrated in Tab.5. Here, a symbol η is defined to evaluate the energy
19
absorption efficiency, as
η=
Ea E total
(25)
As shown in Tab.5, η = 81.6% is observed for the case of impact energy of 3.81J, which means about 81.6% of the total energy is absorbed by the sandwich panel, among which 42.3% is absorbed by the top face-sheet and 39.2% is absorbed by the honeycomb core. It also can be seen that energy absorbed b y the bottom face-sheet is very small (0.1%), which indicates that global deformation is negligible compared to local indentation. It should be noted that energy absorbed by face-sheet here contains both absorbed by face-sheet and its bonded adhesive layer. Besides, internal energy is composed of various terms, including elastic strain energy, plastic dissipation, artificial strain energy and energy dissipated b y viscoelasticity. Among which plastic dissipation is the major factor, about 91.9% of the energy absorbed (75.0% of the total energy) is expended as plastic dissipation. Table 5. Percentage of energy absorbed by differnet components for the impact energy of 3.81J Component
Type
Energy(J)
Percentage
3.81
100%
Internal energy
3.119
81.6%
Plastic dissipation
2.866
75.0%
Strain energy
0.167
4.37%
Others
0.086
2.25%
Internal energy
1.616
42.3%
Plastic dissipation
1.484
38.8%
Strain energy
0.126
3.30%
Internal energy
1.498
39.2%
Plastic dissipation
1.382
36.2%
Strain energy
0.037
0.97%
Internal energy
0.004
0.10%
Plastic dissipation
-
-
Strain energy
0.004
0.10%
Imapct energy
Sandwich panel
Top Facesheet
Honeycomb Core
Bottom Facesheet
5.3. Effect of impact energy During an impact incident, impact energy is a key parameter widely used to characterize the event. In order to investigate the influence of impact energy on indentation response of sandwich panel, residual dent depth and energy absorption of the sandwich panel under different impact energies are simulated. As stated above, different impact energies in the
20
experiments are obtained b y var ying impact velocity V I through changing initial height H I of the impactor. Besides, different impact energies can also be obtained b y changing the impactor mass M . A same impact energy can be obtained by both approaches, but a different influence on the indentation and energy absorbed is foreseeable. In this section, simulations of sandwich panel impacted by different impact energies through the two approaches are conducted and the difference of influence are discussed. Table 6. Different impact energies obtained through varying impactor mass and impact velocity Honeycomb cell: wall length 6 mm, thickness 0.07 mm;
Parameters Impact energy(J) Approach 1. Approach 2.
0.76
1.90
2.86
3.81
7.62
11.43
15.24
2.26
3.57
4.37
5.05
7.14
8.75
10.10
0.06
0.15
0.225
0.3
0.6
0.9
1.2
Impact velocity(m/s) (Constant impactor mass: 0.3kg.)
Mass(kg) (Constant impact velocity: 5.05m/s.)
As illustrated in Tab.6, seven different impact energies are obtained through two approaches: 1) varying impact velocity under remaining impactor mass; 2) varying impactor mass under remaining impact velocity. 5.3.1. Residual dent depth
Fig.14 plots effect of impact energy on residual dent depth on top face-sheet on a Cartesian coordinate as well as a double-logarithmic coordinate. As shown in the figure, the dent depth non-linearly increases with increase of impact energy for both approaches as well as the experimental results. However, a little difference of the two approaches can be observed, the dent depth is much sensitive to the variation of velocity compared to impactor mass. This is expected and can be explained as follow. Generally, as presented in Eq. (21), a larger impact energy will lead to a deeper dent. However, for the same impact energy, a larger mass of the impactor will create a larger radius of local indentation area on the top face-sheet ξ as well as a larger contact radius τ , which will further lead to a smaller dent depth δ , see Fig.10. It is embodied in the figure that for impact energy between 0.76J to 3.81J, smaller δ 0 is observed for the curve of effect of mass while larger δ 0 is observed for impact energy between 3.81 J to 15.24J. Hence, a smaller slope of the curve for effect of mass is illustrated in Fig. 14-b.
21
a)
b)
Fig.14. Effect of impact energy on indentation
Regression model by using ordinary least-squares method is made and the semi-empirical models to estimate the residual dent depth for both approaches are acquired based on the experimental results as well as the numerical results. The semi-empirical model established based on the experimental results is,
( )
log (δ 0 ) = 0.5492 log E KI + 0.1638
(26)
The semi-empirical models established based on the numerical results are, By varying the impact velocity,
( )
(27)
( )
(28)
log (δ 0 ) = 0.5674 log E KI + 0.1569
By varying the mass of impactor, log (δ 0 ) = 0.4963 log E KI + 0.2019 5.3.2. Energy absorption
Experimental and numerical results of energy absorbed by sandwich panel for different impact energies is drawn in Fig.15. Besides, energy distribution in different components are plotted in Fig.16. It should be noted that energy absorbed by different components could not be obtained experimentally, so all data illustrated in Fig.16 are the results of FEA. As stated in section 3.1, the face-sheet and its bonded adhesive layer were modeled as double layers, so the energy absorbed by top face-sheet here contains both face-sheet and its bonded adhesive layer. It can be seen that for low-energy drop-weight impact on honeycomb sandwich panels, energy absorbed by sandwich panel increases almost linearly with increase of impact energy and no
22
obvious difference is observed for the two approaches. Moreover, energy absorption efficiency
η also increases with increase of impact energy, i.e. higher percentage energy is absorbed for a larger impact energy.
a)
b)
Fig.15. Effect of impact energy on energy absorption
Fig.16. Energy absorbed by different components
As stated in section 5.1.2, energy absorbed by bottom face-sheet is negligible, based on which Eq. (23) can be simplified and substituted into Eq. (24),
(
)
1 Ea = M VI2 − VR2 ≈ EIt + EIc 2
(29)
Hence, only energy absorbed b y top face-sheet E It and honeycomb core E Ic are plotted and discussed here. It can be seen that almost same energy is absorbed for the two approaches
23
under a same impact energy, but big difference is observed in energy distribution. Specifically, under a lower impact energy (0.76 J for instance), E It is smaller and E Ic is larger for approach of varying velocity. While it’s totally opposite under a larger impact energy (15.24 J for instance), where E It is larger and E Ic is smaller. But, they can be universally described as follow: E It is smaller and E Ic is larger for impactor with a larger radius under a same impact energy. Considering most of the energy absorbed is plastic dissipation, which is U f for top face-sheet and U c for honeycomb core. Using Eqs. (9) and (11), ratio of energy absorbed due to the plastic deformation of honeycomb core to that due to top face-sheet is,
∫
σ pl dV Uc V β= = Uf N0 ε r dA
(30)
∫
A
As the top face-sheet and adhesive layer were modeled as a doube-layers sheet, the revised fully plastic membrance force N0 in Eq. (18) is employed here. A dimensionless paramerter
ϕ is intorduced [32],
ϕ=
σ pl R σ ftf
(31)
Considering the plasteau stress of honeycomb core σ pl is much lower than flow stress of the top face-sheet as shown in Eq. (12), the parameter ϕ is ver y small. Hence, an asymptotic solution for the parameter β is obtained [31],
(
)
β ≈ 2 2ϕ 1 − 2ϕ + ο (ϕ )
(32)
It can be seen from Eq. (31) and (32) that β is in proportion to radius of the impactor R under same σ pl , σ f , t f . Hence, under the same impact energy, energy absorbed b y top face-sheet is smaller and energy absorbed by core is larger for an impactor with a larger mass and lower velocity. Regression model by using ordinary least-squares method is made and the semi-empirical models to estimate the energy absorbed for both approaches are acquired based on the experimental results as well as the numerical results. The semi-empirical model established based on the experimental results is, E a = 0.9201 E KI − 0.2013
24
(33)
The semi-empirical models established based on the numerical results are, By var ying the impact velocity, E a = 0.9104 E KI − 0.2529
(34)
E a = 0.8959 E KI − 0.2010
(35)
By var ying the mass of impactor,
It can be seen from the equations that the semi-empirical model compared very well for experimental and numerical results. Moreover, a general formula can be further established for energy absorbed b y sandwich panel during a low energy/low velocity impact event under a spherical impactor based on Eqs. (33) - (35), E a = λ E KI − C
(36)
Hence, energy absorption efficiency is
η=
Ea C =λ − I E KI EK
(37)
where λ , C are some constant. It is noticed that E KI ≠ 0 when Ea = 0 , which means there is
~ a threshold for impact energy E KI = C / λ , where plastic deformation starts occurrence. And it can also be explained why higher energy absorption efficiency is observed for larger impact energy.
6. Conclusion An investigation on indentation response and energy absorption property of honeycomb sandwich panels subjected to low-energy drop-weight impact under a spherical impactor was proposed. Experiments based on a pendulum-impact system were first undertaken, during which energy absorbed and residual dent on the top-face sheet were measured. A three-dimensional numerical model considering the micro-structure of honeycomb core was further established and validated by experimental results. Analytical formulations including a load-indentation response model based on the principle of minimum potential energy and an energy balance model were deduced and revised. Moreover, impact response of the sandwich panel, energy absorption property and effect of impact energy were specifically analyzed and discussed. The major contribution and conclusions can be summarized. •
For a low-energy impact, no obvious penetrative damage, crack damage or debonding between face-sheets and core were observed, the honeycomb core at the contact area was
25
compressed and produced cell walls buckling, which was initiating from the top end. The buckling was less and less from the center of the impactor area to the outside due to the spherical impactor. •
A plastic analytical model of indentation response for low-energy impact under a spherical indenter on honeycomb sandwich panel were established, during which the effect of the adhesive layers was fully considered. A revised and simplified energy balance analytical model specifically suitable for low-energy impact under a spherical indenter on honeycomb sandwich panel was also established based on the observation of experimental results.
•
Honeycomb sandwich panels perform satisfied in energy absorption. Generally, more than 80% of the impact energy is absorbed and dissipated, among which almost all (99.9%) is absorbed b y the top face-sheet and honeycomb core. Plastic dissipation is the major term in the energy absorbed, more than 90% of the energy absorbed is expended as plastic dissipation.
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For a low-energy drop-weight impact, impact energy has a great and different influence on dent depth and energy absorption. Specifically, dent depth non-linearly increases while energy absorbed increases almost linearly with increase of impact energy. Besides, different approach b y var ying impact velocity or mass of impact also make difference.
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Energy absorption efficiency increased with increase of impact energy due to exist of a threshold where plastic deformation starts occurrence. Ratio of energy absorbed by top face-sheet to honeycomb core was in proportion to radius of the impactor.
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Semi-empirical formulations to estimate the residual dent depth and energy absorbed for different impact energies and different approaches are given.
Acknowledgements This work was supported by a research grant by the National Natural Science Foundation of China (No.11572086), a research grant by Jiangsu Natural Science Foundation of China (No. BK2012318) and a research grant by Key Laborator y of Lightweight and Reliabilit y Technology for Engineering Vehicle, College of Hunan Province (No.2016kfjj08).
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