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Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs
Accepted Manuscript Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs
Amer Beharic, Rafael Rodriguez Egui, Li Yang PII: DOI: Reference:
S0264-1275(18)30156-4 doi:10.1016/j.matdes.2018.02.066 JMADE 3733
To appear in:
Materials & Design
Received date: Revised date: Accepted date:
4 October 2017 23 February 2018 24 February 2018
Please cite this article as: Amer Beharic, Rafael Rodriguez Egui, Li Yang , Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Jmade(2017), doi:10.1016/j.matdes.2018.02.066
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ACCEPTED MANUSCRIPT
Drop-weight impact characteristics of
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additively manufactured sandwich
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Amer Beharic
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structures with different cellular designs
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Department of Industrial Engineering, University of Louisville, Louisville, 40292
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Rafael Rodriguez Egui
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Department of Industrial Engineering, University of Louisville, Louisville, 40292 *Li Yang
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Department of Industrial Engineering, University of Louisville, Louisville, 40292 *Corresponding author [email protected] Address: J.B. Speed Building, Room 311 Department of Industrial Engineering University of Louisville, Louisville, KY 40292 1-502-852-2197
ACCEPTED MANUSCRIPT Abstract In the design of sandwich panels with cellular cores for energy absorption, the geometrical effect of the cellular core design has not been investigated in details previously. In this work three cellular core designs, including re-entrant auxetic, octet-truss, and BCC lattice, were experimentally investigated for
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their performance under low-energy impact as sandwich structures. Samples with different cellular core designs were fabricated by laser sintering additive manufacturing process using Nylon 12 as material,
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and evaluated by drop weight testing under multiple strikes and at two levels of elevated temperatures
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(93°C and 121°C). It was found that beside relative densities, the geometrical design of the cellular cores could also significantly influence the impact energy absorption performance of the sandwich structures.
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It was also found that the impact energy absorption of the cellular structures investigated in this study does not have a significant correlation with either the quasi-static mechanical properties or the
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temperature. In addition, the auxetic cellular structure exhibits optimal overall energy absorption
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performance compared to both the octet-truss and the BCC lattice.
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Keywords: energy absorption, cellular structure, sandwich panel, additive manufacturing, drop-weight
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impact
ACCEPTED MANUSCRIPT 1. Introduction Sandwich structure designs are broadly used in lightweight applications for structural components in various industries such as aerospace, automobile transportation and construction [1-3]. These structures consist of a relatively low-stiffness core sandwiched between two rigid skins. The core structures usually
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provide space-filling and shear rigidity, while the skins are primarily responsible for bending rigidity. Porous structures are often adopted for the sandwich core in order to achieve lighweighting
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requirements, which can be either stochastic foam or cellular structures with pre-determined
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geometries such as honeycomb and truss lattices [4-6]. An abundance of literatures exist on the investigation of various properties of sandwich structures, including bending and shearing stiffness,
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energy absorption, vibration dampening, thermal insulation and lightweighting [7-10]. One particular area of interest to this study is the impact energy absorption, which is of critical importance in many
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applications where the intended designed functions of the sandwich structures is to protect of the
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backing structure from unwanted impact and to ensure structural integrity. Unlike the designs with quasi-static mechanical properties (e.g. bending stiffness, shear stiffness, bending strength, etc.), which
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could be assisted by well-established analytical models [8-10], the design of impact energy absorption
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for the sandwich structures largely relies on empirical approach [11-15]. The quasi-static stress-strain characteristics of cellular structures are sometimes employed to provide rough estimation for their
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impact energy absorption performance via finite element analysis [16-18]. Experimental studies reported conflicting results regarding the correlation between quasi-static and impact responses of cellular structures and sandwich structures, with some suggesting good correlation [17, 19, 20], while others observed a lack of obvious correlation [21-23]. Various design factors, including skin thickness, cellular core relative density, skin-core bonding and overall structural thickness have been reported to influence the impact properties of the sandwich structures. On the other hand, the investigation about geometrical design of the cellular core has been limited.
ACCEPTED MANUSCRIPT The design fundamentals for cellular structures has been well-established via various previous studies, which discussed the effect of geometrical designs to the mechanical properties of cellular structures [24, 25]. On the other hand, such design freedom was not explored adequately with the design of sandwich structures, and only a few geometries such as regular honeycomb [3, 13-15, 20, 26], square honeycomb
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[4, 23], BCC lattice [22], tetrahedral lattice [4, 27], pyramidal lattice [4], 3D Kagome lattice [4], tilted
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square honeycomb [4], Kagome honeycomb [28], square supercell [28], diamond honeycomb [28] and
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hexagonal honeycomb [28] have been investigated. Although these structures exhibit a range of design variations, the design protocol for the selection of these structures were not clarified. With regard to the
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impact characteristics, even fewer cellular designs have been investigated. On the other hand, from
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limited literatures it is clear that the geometry design of the cellular cores could significantly alter the impact energy absorption performance of sandwich structures [20, 29]. This calls for further studies in
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this area in order to establish a more comprehensive design theory for sandwich structures. In this work,
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experimental based studies were carried out with three cellular designs, namely the re-entrant auxetic, octet-truss, and BCC lattice, that represent three different types of cellular characteristics, in order to
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evaluate their drop weight impact characteristics as well as their correlations with quasi-static
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properties. In addition, as the mechanical properties of the nylon polymers exhibit significant temperature dependency at low-to-medium temperature ranges, it was also of interest to this study to
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evaluate the temperature effect of energy absorption of the nylon sandwich structures.
2. Design of sandwich structures It was hypothesized that the quasi-static mechanical characteristics of the cellular structures, including elastic modulus, yield strength, maximum strength and deformation mechanism, are correlated to their dynamic impact characteristics. Under quasi-static compressive stress, cellular structures that exhibit both higher elastic modulus and higher strength might exhibit lower overall energy absorption due to
ACCEPTED MANUSCRIPT the deformation mechanism. For example, as demonstrated in Fig.1, the cellular structure that exhibit higher modulus and higher strength might also exhibit significant layer-wise failure characteristics, which leads to catastrophic failure within a single layer and the drastic reduction of stress levels (Fig.1b). As a result, the total energy absorption during the compression under this type of mechanism could
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become lower than that from a more gradual failure mechanism exhibited by the cellular structure with
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lower strength and modulus (Fig.1a) [30]. From classic cellular design theory it is known that there exist
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two basic types of cellular elastic deformation modes, namely stretch-dominated deformation and bending-dominated deformation [31]. Stretch-dominated structures tend to exhibit higher elastic
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modulus and higher ultimate strength, while bending-dominated structures generally exhibit higher
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compliance, which might be favorable in energy absorption through elastic and plastic deformation. 60
50
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30 20 10 0 5
10
15 Strain (%)
20
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0
25
a. Lower modulus and lower strength
Stress (Mpa)
40
40
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Stress (Mpa)
50
30 20 10 0
30
0
5
10
15
20
25
30
35
Strain (%)
b. Higher modulus and higher strength
beam melting AM [30]
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Fig.1 Compressive stress-strain curve of two Ti6Al4V auxetic cellular structures fabricated via electron
As mentioned previously, three cellular designs were adopted for this study, which are the re-entrant auxetic structure, the octet-truss structure and the BCC lattice structure. Fig.2 shows the unit cells of the three cellular structures, along with the geometrical design parameters associated with each type. Note that in Fig.2 the strut thickness (t) is not shown, which is also a geometrical design parameter. Both reentrant auxetic and BCC lattice structures are bending-dominated structures, while the octet-truss structure is a stretch-dominated structure. On the other hand, the re-entrant auxetic structure exhibits
ACCEPTED MANUSCRIPT negative Poisson’s ratio, while the other two exhibits positive Poisson’s ratios. Octet-truss and BCC lattice structures have been studied extensively and are representative to the two types of deformation mechanisms [22, 32-34]. On the other hand, the auxetic structure has been suggested to exhibit good energy absorption abilities and is therefore also investigated [35, 36]. The detailed parameter design is
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shown in Table 1. In addition, with all the unit cell designs the cross section of the struts was designed to
L3 L H θ
Y
X
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X
L2
a. Re-entrant auxetic
L
Z
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Z L1
Z
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be a square with 1mm dimension.
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b. BCC lattice
X
Y
c. Octet-truss
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Fig.2 Unit cell design for cellular structure
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Three variations were designed for auxetic structures. Aux1 and Aux2 have the same H/L ratio and θ, therefore exhibits the same Poisson’s ratio [37]. On the other hand, Aux3 has similar relative densities as
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Aux2 but exhibits more significant auxetic effect (i.e. greater negative Poisson’s ratio) [37]. Three
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variations were designed for the BCC lattice. BCC1 and BCC2 have the same unit cell aspect ratio and different relative densities, while BCC2 and BCC3 have similar relative densities and different unit cell
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aspect ratios. Since there exist only one design parameter for the octet-truss structure, only two variations were designed with two levels of relative densities. The two levels of relative densities for all three cellular structures were set to be similar, with the lower one at ~0.12 and higher one at ~0.19 in order to allow for direct comparison between structures at same relative density levels. The sandwich structures were designed with constant skin thickness of 1mm. This dimension is considerably smaller than the overall thickness of the sandwich panel in order to reduce the energy absorption effect by the skins, which could become significant when the core density is low [38]. The
ACCEPTED MANUSCRIPT overall dimensions of the sandwich panels were determined by considering multiple factors. The first factor is the impactor head size, and the second factor is the size effect of the cellular structures. The impactor head size used for this study is 19.11mm, therefore the lateral dimensions of the sandwich structures must be significantly larger. Also, in order to account for the size effects of the cellular
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structures, which often causes stress concentration and boundary effects in the structure [39, 40], the
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numbers of unit cells in the sandwich structures in the lateral directions were set to be at least 8. Lastly,
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it was desired that the sample sizes are limited so that all the samples could be fabricated in the same batch of build. As illustrated in Fig.3, the sandwich designs have lateral dimensions of 70-80mm and 4
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layers of unit cells in the thickness direction.
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Re-entrant auxetic H (mm)
L (mm)
θ (deg)
Relative density
Aux1
6.5
4.7
70
0.122
Aux2
5
3.6
70
0.194
Aux3
7.7
4
50
0.203
L2 (mm)
L3 (mm)
Relative density
6.5
6.5
6.1
0.120
5
5
4.8
0.188
6
6
4.7
0.190
BCC3
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BCC2
L1 (mm)
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Design BCC1
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Design
BCC Lattice
Octet-truss Design
L (mm)
Relative density
Octet1
8
0.119
Octet2
6.2
0.187
Table 1 Geometrical design parameters for cellular structures
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4 layers
7080m m
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mm 70-80
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Fig.3 Design of sandwich structures
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3. Experimental procedures
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The final sandwich designs with the three cellular structures are shown in Fig.4. The designs were fabricated by the DTM Sinterstation 2500 laser sintering system using nylon 12 (ALM PA650) as material.
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The powder particle morphology is spherical, and the powder properties provided by the manufacturer
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are D50=55μm, D10=30μm and D90=100um. The reference mechanical properties of the nylon 12 material is listed in Table 2 [41], which should only be used as a benchmark as the material properties of AM
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nylon 12 is highly sensitive to the process parameters and orientations, which was not intended to be
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investigated in the current study [42]. As the focus of this study does not involve process optimization, the default process themes used for this type of processes was employed. Additional details about the
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process setup for the laser sintering systems can be found elsewhere [42, 43]. Although the temperature effect for additively manufactured nylon 12 was not readily available, from generic material information
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it was expected that the material would exhibit lower mechanical properties at elevated temperatures [44]. Without further available temperature-property information, it was also of interest to this study to evaluate whether the temperature variation (93°C versus 121°C in this study) introduces any significant effect to the impact performance of the structures. Each sample design was fabricated in both horizontal (i.e. sandwich thickness along the build direction) and vertical (i.e. sandwich thickness perpendicular to the build direction) orientations. Some of the fabricated samples are shown in Fig.4d. It is noted that due to the manufacturing schedule limitations, no BCC3 vertical samples were fabricated.
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Aux1
Aux2
BCC1
Aux3
BCC3
b. BCC sandwich
Octet2
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Octet1
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a. Auxetic sandwich
BCC2
d. Sandwich sample fabricated by laser sintering
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c. Octet-truss sandwich
Fig.4 Sandwich panel with cellular structures Modulus (MPa)
Tensile strength (MPa)
Density (g/cm3)
Elongation (%)
Nylon 12 (XY)
1700
46
0.95
4-15
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Name
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Table 2 Reference specifications of nylon 12 [41] After fabrication, the dimensions and total weight of each samples were measured. The results were
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used to calculate the relative densities of the samples and to provide dimensional information to the testing. In order to establish the quasi-static baseline properties, for each type of sandwich panel
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fabricated with either vertical or horizontal orientation, one sample was tested under compressive testing using the Instron 5569A tensile testing system at constant strain rate of 0.2/min. During the testing, the samples were placed between two platens and preloaded to approximately 10-20N prior to the actual compressive testing. All the samples were compressed to the strain value of 0.5. The elastic modulus, ultimate strength and total energy absorption at strain value of 0.5 of each sample were calculated from the stress-strain curves.
ACCEPTED MANUSCRIPT The drop-weight impact testing was performed on an instrumented Instron/Dynatup 8250. The system was equipped with accelerometer (PCM 350B04) and dynamic force transducer (PCM 200C20), which were located on the impactor assembly as shown in Fig.5a. Weight plates can be added to the impactor assembly to adjust the impact energy, and a winch was used to lift the impactor to designated height.
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The impactor head has a hemispherical shape with diameter of 19.11mm, and the total weight of the
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impactor assembly was 3.969kg. The samples were fixed on the sample platform by a pair of plates
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(Fig.5b). The upper plate has a circular opening of 76.2mm, and the bottom plate has a circular opening of 50.4mm. The fixture assembly was placed inside a temperature-controlled oven under the impactor
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assembly (Fig.5a), which was heated up to 93°C (200F) and 121°C (250F) during the impact testing. For
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each type of sample, the impact energy was determined by gradually increasing the total incident energy until damage occurs on the top skin. After the impact energy was determined, each sample was
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subjected to up to 5 strikes or until the bottom skin was perforated. 3-5 samples for each type were
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tested. The real-time acceleration and response force were recorded at 10kHz frequency and used to calculate the energy absorption of the samples. The energy absorption was taken as the difference
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between the incident energy and the rebound energy on the impactor assembly. Also noted that beside
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the BCC3 vertical samples which were not fabricated, the Octet2 vertical samples were not drop-weight
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impact tested due to the use of most samples during the initial setup trial.
ACCEPTED MANUSCRIPT a. Overall setup
b. Fixture for samples
Fig.5 Drop-weight impact testing system
4. Results and discussions
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It was previously established that the nylon 12 cellular sandwich structures fabricated via laser sintering
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exhibit relatively consistent qualities [45], which was also verified by this study by dimensional
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measurement of a randomly chosen sample for each design variant as shown in Table 3. The dimensional variability of all the samples was smaller than 0.5mm, which correspond to less than 0.1%
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and 0.2% dimensional errors in the x/y directions (i.e. directions normal to the build direction) and the z
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directions (i.e. the build direction). Therefore, for the consequent analysis, the nominal dimensions of the designs were used without affecting the discussions. Actual L1/L2
Designed L3
Actual L3
L1/L2 (mm)
(mm)
(mm)
(mm)
Aux1
78.806
79.1494
41.414
Aux2
79.937
79.499
Aux3
74.540
BCC1 BCC2
ΔL1/L2 (%)
ΔL3 (%)
40.900
0.4
1.2
32.423
32.50
0.5
0.2
74.199
43.031
43.003
0.5
0.1
78.000
77.596
35.822
35.900
0.5
0.2
70.000
69.545
29.375
29.400
0.7
0.1
72.000
72.049
20.537
20.014
0.1
2.5
Octet1
69.430
69.599
49.150
49.200
0.2
0.1
Octet2
72.494
72.600
38.967
39.000
0.1
0.1
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BCC3
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Design
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Designed
Table 3 Dimensional characteristics of randomly selected samples
ACCEPTED MANUSCRIPT The quasi-static compressive stress-strain curves for each types of cellular structures are shown in Fig.6. Fig.7 shows the typical characteristics of each of the cellular structure types after the completion of the quasi-static testing. During the quasi-static compressive testing, none of the samples exhibit strut fracture due to the high ductility of the nylon material, and upon unloading the structures also exhibit
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some elastic recoveries. Both the auxetic and the octet-truss designs exhibit “layerwise” deformation
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patterns, while the BCC designs exhibit diagonal deformation patterns and significant skin warping.
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Further discussions regarding the deformation characteristics of these cellular structures under quasi-
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static compressive stress can be found elsewhere from previous studies [30, 32, 34, 46]. The compressive behaviors of the sandwich structures were expected to be dominated by the cellular
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cores. Auxetic sandwich showed a typical cyclic pattern observed previously with this type of structures, which is caused by the layerwise failure pattern of the structure [30, 47]. The BCC sandwich and octet-
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truss sandwich exhibited typical stress-strain curves representative to bending-dominated and stretch-
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dominated cellular structures, respectively. With the BCC sandwich samples, there exist a significant plateau stage following the initial failure, which is expected to be favorable for energy absorption. In
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comparison, the octet-truss sandwich samples also exhibited plateau stages, although there also exist a
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“softening” stage immediately after the initial failure, which results in a significant reduction of stress levels. Overall the effect of fabrication orientation was not very significant, which should be related to
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the their cellular geometry designs and will be explained in the following discussions.
ACCEPTED MANUSCRIPT b. BCC sandwich
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c. Octet-truss
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a. Auxetic sandwich
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Fig.6 Quasi-static compressive stress-strain curves of sandwiches
b. BCC
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a. Auxetic
c. Octet-truss Fig.7 Typical samples tested by quasi-static compressive testing
ACCEPTED MANUSCRIPT
The elastic modulus, ultimate strength and total energy absorption of each type of sandwich are listed in Table 4. In addition, Fig.8 shows the comparisons of total energy absorption (J) and the volumetric energy absorption (J/mm3) of different sandwich designs.
(MPa)
Avg.
absorption
(MPa)
9.62
0.64 10.485
11.35
Aux2-Hori.
33.12
0.66 2.24 35.86
38.60
2.40
Aux3-Hori.
34.27
1.43
Aux3-Ver.
53.06
BCC1-Hori.
23.98
BCC1-Ver.
27.41
BCC2-Hori.
42.95
43.665
0.916 0.594 0.967
1.29
105.86
0.507
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0.8945
220.56
180.02
1.42
1.55
46.47
BCC3-Hori.
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3.11
13.20
Oct1-Hori.
25.46
1.28
Oct1-Ver.
32.95
Oct2-Hori.
45.14
1.54
29.205
75.38
1.415
0.695
0.4315 0.494
202.48
0.991 219.01
235.54
0.695
0.369 127.92
2.935 3.16
75.38
118.06
2.81
1.164 1.152
87.78
1.55
50.645
1.176 163.38
163.63 1.54
0.558 0.609
163.13 3.00
BCC2-Ver.
0.7805
129.35 132.84
2.89
44.71
56.15
0.873 183.225
189.69
1.63
25.695
Oct2-Ver.
0.203
139.48
1.83
13.20
0.1955
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Aux2-Ver.
(J/mm3) 0.188
176.76
2.32
Avg.
absorption
49.97
51.51
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Aux1-Ver.
energy
Avg.
48.43
0.65
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Aux1-Hori.
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(J)
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Strength Avg.
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Modulus Design
T
Volumetric
Energy
1.0645 1.138
ACCEPTED MANUSCRIPT
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Table 4 Quasi-static properties of different sandwich structures
b. Volumetric energy absorption
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a. Total energy absorption
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Fig.8 Comparison of quasi-static compressive energy absorption for sandwich structures From the results it is clear that the quasi-static energy absorption performance of the sandwich
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structures with each types of cellular core could be tailored at a broad range. The Octet2 design exhibits both highest modulus and strength, and due to its characteristic stress-strain pattern, it also achieved
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the highest amount of total energy absorption (at high relative density). However, the volumetric energy
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absorption of the Octet2 design is less outstanding compared to the other structures. This is due to the comparatively larger volume of the octet-truss structure compared to the other structures at the same
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relative density. At lower relative density level the BCC lattice design exhibits the highest overall energy
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absorption as well as volumetric energy absorption. However, at higher relative density level such advantage appears to diminish. When the relative density increases from 0.12 to 0.19, the total energy
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absorption capabilities of the re-entrant auxetic, the BCC lattice and the octet-truss structures increased by 267.8%, 36.9% and 71.21%, respectively, and volumetric energy absorption capabilities of the three structures increased by 357.5%, 108.6% and 146.7% respectively. It is therefore inferred that given sufficient relative density design windows, the re-entrant auxetic cellular structure would exhibit the highest quasi-static compressive energy absorption as well as volumetric energy absorption efficiency. On the other hand, if the relative density is restricted at lower levels, then the BCC lattice design appears to be advantageous.
ACCEPTED MANUSCRIPT The effect of fabrication orientation is closely related to the specific geometries of each unit cell designs. For re-entrant auxetic structure both vertical strut (H in Fig.2a) and re-entrant strut (L in Fig.2a) contribute to the mechanical strength of the structures. From the analytical property model it is known that with smaller re-entrant angle the re-entrant strut contribute more significantly to both the modulus
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and the strength of the structures [37, 48]. Furthermore, with laser sintering powder bed fusion process
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both the elastic modulus and the ultimate strength are the lowest along the build direction (z direction)
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and increase as the orientation angle relative to the z direction increases [49, 50]. Therefore, with Aux1 and Aux2 designs, although for the vertically built samples the re-entrant struts were more aligned to
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the z direction (20° as opposed to 70° in horizontally built samples) and are therefore considerably
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weaker, such effect was partly compensated by the strengthening of the vertical struts (oriented at 90° in relation to the z direction). On the other hand, with Aux3 due to the relatively small difference of
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build orientation for the re-entrant struts under both situations (50° versus 40°), the strengthening of
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the vertical struts becomes dominant, and the overall properties of the structure are therefore higher with the vertically built samples. For the BCC designs, due to the consistent strut orientation, the build
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orientation effect is also expected to be more consistent. For BCC1 and BCC2, due to the fact that the
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struts tilt at near 45° angle (41.1° to be more exact), the mechanical properties of the vertically built samples is expected to be similar to those of horizontally built samples. For BCC3, although no vertically
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built samples were fabricated, it could be expected that due to the relatively large strut tilt angle (~64.5°) the mechanical properties of the horizontally built samples would be significantly higher compared to vertically built samples. For octet-truss structures, due to the identical unit cell topology under both build orientations, the mechanical properties of samples under both build orientations are also similar, and the main contributor of the property enhancement for the vertically built samples is likely the horizontally fabricated vertical struts that align to the load direction.
ACCEPTED MANUSCRIPT Table 5 shows the impact energy levels that were used for each types of sandwich structures after the preliminary strike testing, along with the corresponding drop heights. For some designs multiple strikes were taken with gradually increasing impact levels before the top skin damage was visually observable. After the preliminary testing, the impactor was manually lifted to the desired height during the testing,
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which was expected to introduce minor variability with incident energy level. The response force curves
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for each type of sandwich structures upon the initial impact at 93°C are shown in Fig.9. For each sample,
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the occurrence of high response force was expected to correspond to the impact damage of the samples, since the impact energy levels were selected to induce damages to the samples. For horizontally
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fabricated samples, the maximum response forces for the designs that exhibit higher quasi-static
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strengths are also generally higher. The effect of build orientation was most significant for Aux2 design. The response forces of the vertically built Aux2 samples achieved exceptionally high levels (>20000N in
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Fig.8b), whereas the response forces of the horizontally built Aux2 samples were at the levels of 1400-
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1600N. This might be resulted from the signified contribution of the vertical struts during the impact process due to both the orientation enhancement effect and the increased density (compared to Aux1).
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On the other hand, for Aux3 samples, unlike the results from quasi-static testing, the response forces did
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not exhibit significant build orientation dependency. Such results suggest that for this design the reentrant struts are likely to contribute more significantly to the energy absorption responses during the
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impact deformation. Since for Aux3 designs the re-entrant struts are oriented near 45°, the orientation effect becomes less significant.
ACCEPTED MANUSCRIPT Samples Energy
Height
Temp. (m)
level (J)
(m)
93
24.70
0.635
121
24.70
0.635
93
19.76
0.508
121
19.76
0.508
93
17.78
0.457
121
17.78
0.457
93
-
-
Design Orientation
(°C) 93
Height
Temp. level (J)
Design Orientation
Energy
T
Samples
(°C) 17.78
0.457
Hori.
Hori. 121
-
-
93
19.76
0.508
121
19.76
0.508
93
15.81
0.406
BCC2 Ver.
CR
Ver.
IP
Aux1
Hori.
121
15.81
0.406
Aux2
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Hori. BCC3 93
19.76
0.508 0.508
121
-
-
93
18.77
0.483
93
7.90
0.203
121
18.77
0.483
121
7.90
0.203
93
19.76
93
19.76
0.508
121
19.76
0.508
93
24.70
0.635
121
24.70
0.635
93
-
-
121
-
-
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Ver.
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19.76
Aux3
0.508
93
7.90
0.203
93
19.76
0.508
121
19.76
0.508
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Octet1 Ver.
Hori.
CE
PT
19.76
7.90
Hori.
0.508
121
121
BCC1
Ver.
121
Hori.
Hori.
AN
Ver.
0.203 Octet2
Ver.
Ver.
Table 5 Average impact energy levels for each types of sandwich designs
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AN
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a. Horizontally built samples
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ACCEPTED MANUSCRIPT
c. Vertically built samples (Aux2 not shown)
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b. Vertically built samples
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Fig.9 Response forces of different sandwich designs upon initial impact at 93°C The response force curves for each type of sandwich structures upon the initial impact at 121°C are
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shown in Fig.10. Compared to Fig.9, similar correlations between quasi-static strengths and response
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forces were also observed for samples tested at 121°C. However, the response force levels for each type of structures exhibit no consistent trend over different temperature levels. It was expected that the
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reduced mechanical properties of nylon 12 exhibited at elevated temperature might introduce “softening” effect into the impact response of the cellular structures. However only Aux2 designs exhibited significant decrease of peak response force levels at higher temperature levels, which might be partly related to the more “dense” topology of this cellular design as well as the high degree of crystallinity of the nylon material used for laser sintering powder bed fusion, which potentially exhibits less pronounced softening effect.
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b. Vertically built samples
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a. Horizontally built samples
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Fig.10 Response forces of different sandwich designs upon initial impact at 121°C The average peak response forces and the maximum peak response forces under multiple impacts for all
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the sandwich designs built under both horizontal and vertical orientations are shown in Fig.11 and Fig.12,
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respectively. It was noticed that for all the cellular designs the average maximum peak force values are either about the same or larger than the initial peak force values, which indicates that all the structures
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exhibit consistent or even enhanced damage tolerance under continuously accumulating damage. This is
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further illustrated by the multi-impact response force curves of different sandwich designs as shown in Fig.13. The effect of quasi-static mechanical properties on the average peak force and maximum peak
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force does not appear to be significant for the designs investigated. It should also be noted that higher
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peak response force could also imply higher risk of damage for the structure intended to be protected if they are placed underneath the sandwich structures, since such high forces could potentially be
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transmitted through. Since in the current study the force sensor was placed on the impactor, the effectiveness of these cellular designs as protective barriers is beyond the scope of this study and will not be further discussed.
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Fig.12 Max. peak force under multiple impacts
b. Aux1-Ver.
e. Aux3-Hori.
f. Aux3-Ver.
c. Aux2-Hori.
d. Aux2-Ver.
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a. Aux1-Hori.
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Fig.11 Average peak force under multiple impacts
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h. BCC1-Ver.
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g. BCC1-Hori.
i. BCC2-Hori.
j. BCC2-Ver.
k. BCC3-Hori.
l. Octet1-Hori.
m. Octet1-Ver.
n. Octet2-Hori.
Fig.13 Multi-impact force curves for different cellular designs
ACCEPTED MANUSCRIPT The damage characteristics for the horizontally built re-entrant auxetic structures are shown in Fig.14. The temperature information is not shown as it does not appear to have significant effect, and the samples shown in Fig.14 were also randomly chosen with regard to the testing temperature. Aux1 and Aux2 designs exhibit similar characteristics with top and bottom perforation with sandwich skins. While
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the top perforation is localized, the bottom perforation occurs over larger areas. For both types of
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structures, the top skins and the core cellular structures both exhibit clear shearing fracture in the
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impacted areas, and there also exist obvious bending of top skins in the vicinity areas. On the other hand, the bottom skins for both type of structures exhibit clear skin delamination. Previous studies have
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shown that the re-entrant auxetic structures exhibit very small size effect and are able to distribute
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stress more evenly throughout the structures [51]. Therefore, the large area of damage for the bottom skins might be partly attributed to such stress distribution effect. The overall damage characteristic is
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also similar to the other additively manufactured cellular structures [22, 52]. For the Aux3 sandwich, the
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top skin exhibits significant skin wrinkling and delamination, and the bottom perforation damage also appears more significant compared to Aux2. This might be attributed to the more significant negative
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Poisson’s ratio effect, which introduces more significant shearing stress on the bottom skin panels
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through skin-core bonding constraint. It should be noted that the delamination damage with these sandwich panels is likely contributed by the local stress distribution effects upon the impact loading,
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which is significantly influenced by the type of core unit cell designs as previously reported [46]. The additively manufactured sandwich panels appear to exhibit stronger core-skin bonding since the entire structures were fabricated in one process using the same material, which differs from many traditional sandwich structures that are fabricated by bonding the core and skins and therefore tend to exhibit more bonding interfacial strength issues.
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a. Aux1
b. Aux2
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c. Aux3
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Fig.14 Damage characteristics of auxetic sandwich structures built horizontally The damage characteristics of the horizontally built BCC lattice sandwich structures are shown in Fig.15.
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For all the BCC lattice designs the top skins exhibit significant bending in the vicinity of the impact area,
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which indicates significant local stress concentration effect upon impact. The bottom skin perforations exhibit not only extensive areas accompanied by skin-core delamination, but also large skin cracks
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throughout the entire sandwich structures. The large area of damage spread might be attributed to the
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significant stress concentration effects of this type of cellular structures caused by the size effects [34], which appears to be detrimental for the energy absorbing protection applications.
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The sample designs for both the auxetic and the BCC sandwich structures also shed some lights to the occurrence of delamination. As in this study both cellular structures were bonded to the skin panels only at the end of the boundary struts. Therefore, the skin-core bonding was not as strong as the octet-truss sandwich structures, which have significantly larger cellular core-skin “contact” areas.
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b. BCC2
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c. BCC3
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Fig.15 Damage characteristics of BCC sandwich structures built horizontally
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The damage characteristics of the horizontally built octet-truss sandwich structures are shown in Fig.16. The top skins exhibit relatively well-defined perforation profile with small amount of extended damage
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around the impact area. The bottom skins of the octet-truss sandwich also exhibit both skin shearing
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and delamination, and for most samples the core residue that was sheared off from the structure extruded out from the bottom side more significantly compared to the other designs. This indicates that
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the “tangling”/retaining effect of the core cellular structure to the sheared residue is not as significant
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for the octet-truss structure, which might be attributed by the relatively sparse topology of this type of design. This could also negatively impact the energy absorption ability of these structures.
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Top
b. Octet2
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a. Octet1
Fig.16 Damage characteristics of octet-truss sandwich structures built horizontally
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For the vertically built samples, the damage characteristics are similar to the horizontal ones except for
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the Aux2 design, which are shown in Fig.17. For these samples, the bottom skins exhibit extended cracks
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similar to that observed with the BCC sandwich structures, which indicates strong stress concentration at the bottom skins that is unusual for the auxetic structures. This unique damage characteristic might
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contributed to the large peak response forces exhibit by these samples. Considering that the auxetic structures with large H/L ratio and small re-entrant angle θ exhibits rather significant layerwise failure
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mode under quasi-static compressive loading [33], it is speculated that such failure mode might be
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partly responsible for the occurrence of stress concentration due to significant internal compression of the cellular core structures, although additional studies will be needed to verify this theory.
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a. Sample 1
b. Sample 2
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Fig.17 Damage characteristics of Aux2 sandwich built vertically
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The average total energy absorptions for each type of cellular sandwich structure are shown in Fig.18, which show the comparisons of build orientations and testing temperatures, respectively. For auxetic
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sandwich structures, the vertically built samples absorb higher total energy under multiple impacts.
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Combining this observation with the previous observation with the peak response forces, it was speculated that while the vertical struts do not contribute to the initial damage of the structures, they
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do absorb significant amount of energies in consequent deformations and impact perforations, and therefore enhance the total energy absorption of the structures. On the other hand, the effects of
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temperature on the total energy absorption of the sandwich structures do not appear to be consistent.
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b. By temperature
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a. By build orientation
Fig.18 Average total energy absorption for cellular sandwich structures
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As some of the sandwich structures only sustained fewer than 5 impact strikes and consequently, might
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not have exhibit comparative total energy absorption abilities compared to the ones that sustained 5 strikes, the average energy absorptions per impact strike were investigated as shown in Fig.19. From the
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results, the BCC lattice structures exhibit more comparative energy absorption ability compared to the
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auxetic structures, while the octet-truss structures exhibit slightly lower energy absorption abilities. Comparing Fig.18 and Fig.19, the results suggest that for single strike impact the energy absorption
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abilities among the different cellular designs with different geometry designs do not exhibit significant differences, and the relative density appears to be the most significant factor. However, when multiple
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impacts are introduced, different cellular structures exhibit different ability in sustaining energy
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absorption functionality. The auxetic cellular structures appear to exhibit the highest performance as well as the highest performance tailorability, whereas the BCC lattice structures exhibit the lowest overall performance due to their low cumulative damage tolerance. On the other hand, despite the desirable quasi-static mechanical properties, the octet-truss structures do not exhibit outstanding energy absorption ability compared to the auxetic structures. Again from Fig.19 the energy absorption per impact strike does not exhibit consistent dependence on temperature.
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b. By temperature
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a. By build orientation
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Fig.19 Energy absorption per impact strike for cellular sandwich structures
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The performance advantage of the re-entrant auxetic structures is further demonstrated by the incident energy absorption ratio, which is defined as the ratio between the absorbed energy and the total
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incident energy. As shown in Fig.20, the Aux2 design exhibits incident energy absorption ratio as high as 0.93 for vertically built samples. For most other cellular structures, the incident energy absorption ratio
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is 0.6-0.7. The BCC1 design also exhibit high energy absorption ratio, although considering that this
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structure has rather low overall mechanical strength, it might still not be as efficient compared to the
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auxetic structures for the energy absorption applications.
a. By build orientation
b. By temperature
Fig.20 Incident energy absorption ratio for different cellular sandwich structures
ACCEPTED MANUSCRIPT 5. Conclusions In this study, sandwich structures with multiple cellular core designs including the re-entrant auxetic structure, the BCC lattice structure and the octet-truss structure were studied for their drop-weight impact energy absorption characteristics. The samples were fabricated by laser sintering system using
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nylon 12 as material. It was found that the quasi-static mechanical properties of these structures do not exhibit apparent correlations to their drop-weight impact energy absorption ability. On the other hand,
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the boundary stress concentration characteristics of each type of cellular structures appear to play a role
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in their drop-weight impact characteristics. For auxetic cellular sandwich, the minimized boundary stress concentration appears to contribute to the reduced damage on the backing side of the structures,
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although such benefit is also affected by the characteristic “catastrophic” failure exhibited by the high aspect ratio-low re-entrant angle designs (Aux3). In addition, for the re-entrant auxetic structures the
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buckling of the vertical struts might act as the most significant contributor to the enhancement of the
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energy absorption abilities of this structure. In general, the auxetic cellular designs exhibit the best total energy absorption and per-strike energy absorption abilities, as well as the highest structural
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performance efficiency for such applications, although the peak response forces of some of these
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designs might need to be subjected to additional scrutiny for shock impact protection applications. The BCC lattice structures exhibit good single-impact energy absorption abilities, which might be partly
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contributed by its relatively low mechanical strength and large damage area that helps absorbing energies. The octet-truss structure exhibits good overall energy absorption ability, although its performance efficiency is comparatively low due to the large cellular dimensions under the same relative densities. In addition, the octet-truss structure also exhibits relatively low residue retaining ability. The non-isotropic material properties of the laser sintering powder bed fusion additive manufacturing process introduces additional factors that complicates the design analysis of the sandwich structures for drop-weight impact performance, and additional works are likely needed to
ACCEPTED MANUSCRIPT systematically analyze the coupling effect of local material property variability and cellular geometry designs to the overall performance of the structures. Another piece of future work would be the roomtemperature drop-weight impact performance evaluation for the same designs, which will provide additional basis for comparison.
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6. Data availability
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The raw data required to reproduce these findings are available to download from http://dx.doi.org/10.17632/sh3wfgxypj.2. The processed data required to reproduce these findings is
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provided in this publication.
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7. Acknowledgement
The authors are grateful of the help of the Rapid Prototyping Center (RPC) at University of Louisville.
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This research was supported by the Intramural Research Initiation Grant (IRIG) at University of Louisville
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and partially supported by the Office of Naval Research (ONR) grant #N00014-16-1-2394.
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Graphical abstract
ACCEPTED MANUSCRIPT Highlights
The quasi-static mechanical properties of the sandwich structures with different cellular core designs have no significant correlations with impact properties
The drop-weight impact performance of sandwich structures is dependent on the type of core unit cell
Re-entrant auxetic core designs can be tailored to exhibit high energy absorption, but also exhibits
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and its geometry parameters
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high response forces
The BCC core designs exhibit good one-time impact performance due to low mechanical strength and
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The octet-truss core designs exhibit low volumetric impact performance and low residue retaining
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ability
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large energy dissipation area
Amer Beharic, Rafael Rodriguez Egui, Li Yang PII: DOI: Reference:
S0264-1275(18)30156-4 doi:10.1016/j.matdes.2018.02.066 JMADE 3733
To appear in:
Materials & Design
Received date: Revised date: Accepted date:
4 October 2017 23 February 2018 24 February 2018
Please cite this article as: Amer Beharic, Rafael Rodriguez Egui, Li Yang , Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Jmade(2017), doi:10.1016/j.matdes.2018.02.066
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ACCEPTED MANUSCRIPT
Drop-weight impact characteristics of
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additively manufactured sandwich
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Amer Beharic
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structures with different cellular designs
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Department of Industrial Engineering, University of Louisville, Louisville, 40292
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Rafael Rodriguez Egui
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Department of Industrial Engineering, University of Louisville, Louisville, 40292 *Li Yang
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Department of Industrial Engineering, University of Louisville, Louisville, 40292 *Corresponding author [email protected] Address: J.B. Speed Building, Room 311 Department of Industrial Engineering University of Louisville, Louisville, KY 40292 1-502-852-2197
ACCEPTED MANUSCRIPT Abstract In the design of sandwich panels with cellular cores for energy absorption, the geometrical effect of the cellular core design has not been investigated in details previously. In this work three cellular core designs, including re-entrant auxetic, octet-truss, and BCC lattice, were experimentally investigated for
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their performance under low-energy impact as sandwich structures. Samples with different cellular core designs were fabricated by laser sintering additive manufacturing process using Nylon 12 as material,
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and evaluated by drop weight testing under multiple strikes and at two levels of elevated temperatures
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(93°C and 121°C). It was found that beside relative densities, the geometrical design of the cellular cores could also significantly influence the impact energy absorption performance of the sandwich structures.
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It was also found that the impact energy absorption of the cellular structures investigated in this study does not have a significant correlation with either the quasi-static mechanical properties or the
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temperature. In addition, the auxetic cellular structure exhibits optimal overall energy absorption
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performance compared to both the octet-truss and the BCC lattice.
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Keywords: energy absorption, cellular structure, sandwich panel, additive manufacturing, drop-weight
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impact
ACCEPTED MANUSCRIPT 1. Introduction Sandwich structure designs are broadly used in lightweight applications for structural components in various industries such as aerospace, automobile transportation and construction [1-3]. These structures consist of a relatively low-stiffness core sandwiched between two rigid skins. The core structures usually
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provide space-filling and shear rigidity, while the skins are primarily responsible for bending rigidity. Porous structures are often adopted for the sandwich core in order to achieve lighweighting
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requirements, which can be either stochastic foam or cellular structures with pre-determined
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geometries such as honeycomb and truss lattices [4-6]. An abundance of literatures exist on the investigation of various properties of sandwich structures, including bending and shearing stiffness,
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energy absorption, vibration dampening, thermal insulation and lightweighting [7-10]. One particular area of interest to this study is the impact energy absorption, which is of critical importance in many
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applications where the intended designed functions of the sandwich structures is to protect of the
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backing structure from unwanted impact and to ensure structural integrity. Unlike the designs with quasi-static mechanical properties (e.g. bending stiffness, shear stiffness, bending strength, etc.), which
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could be assisted by well-established analytical models [8-10], the design of impact energy absorption
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for the sandwich structures largely relies on empirical approach [11-15]. The quasi-static stress-strain characteristics of cellular structures are sometimes employed to provide rough estimation for their
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impact energy absorption performance via finite element analysis [16-18]. Experimental studies reported conflicting results regarding the correlation between quasi-static and impact responses of cellular structures and sandwich structures, with some suggesting good correlation [17, 19, 20], while others observed a lack of obvious correlation [21-23]. Various design factors, including skin thickness, cellular core relative density, skin-core bonding and overall structural thickness have been reported to influence the impact properties of the sandwich structures. On the other hand, the investigation about geometrical design of the cellular core has been limited.
ACCEPTED MANUSCRIPT The design fundamentals for cellular structures has been well-established via various previous studies, which discussed the effect of geometrical designs to the mechanical properties of cellular structures [24, 25]. On the other hand, such design freedom was not explored adequately with the design of sandwich structures, and only a few geometries such as regular honeycomb [3, 13-15, 20, 26], square honeycomb
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[4, 23], BCC lattice [22], tetrahedral lattice [4, 27], pyramidal lattice [4], 3D Kagome lattice [4], tilted
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square honeycomb [4], Kagome honeycomb [28], square supercell [28], diamond honeycomb [28] and
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hexagonal honeycomb [28] have been investigated. Although these structures exhibit a range of design variations, the design protocol for the selection of these structures were not clarified. With regard to the
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impact characteristics, even fewer cellular designs have been investigated. On the other hand, from
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limited literatures it is clear that the geometry design of the cellular cores could significantly alter the impact energy absorption performance of sandwich structures [20, 29]. This calls for further studies in
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this area in order to establish a more comprehensive design theory for sandwich structures. In this work,
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experimental based studies were carried out with three cellular designs, namely the re-entrant auxetic, octet-truss, and BCC lattice, that represent three different types of cellular characteristics, in order to
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evaluate their drop weight impact characteristics as well as their correlations with quasi-static
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properties. In addition, as the mechanical properties of the nylon polymers exhibit significant temperature dependency at low-to-medium temperature ranges, it was also of interest to this study to
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evaluate the temperature effect of energy absorption of the nylon sandwich structures.
2. Design of sandwich structures It was hypothesized that the quasi-static mechanical characteristics of the cellular structures, including elastic modulus, yield strength, maximum strength and deformation mechanism, are correlated to their dynamic impact characteristics. Under quasi-static compressive stress, cellular structures that exhibit both higher elastic modulus and higher strength might exhibit lower overall energy absorption due to
ACCEPTED MANUSCRIPT the deformation mechanism. For example, as demonstrated in Fig.1, the cellular structure that exhibit higher modulus and higher strength might also exhibit significant layer-wise failure characteristics, which leads to catastrophic failure within a single layer and the drastic reduction of stress levels (Fig.1b). As a result, the total energy absorption during the compression under this type of mechanism could
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become lower than that from a more gradual failure mechanism exhibited by the cellular structure with
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lower strength and modulus (Fig.1a) [30]. From classic cellular design theory it is known that there exist
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two basic types of cellular elastic deformation modes, namely stretch-dominated deformation and bending-dominated deformation [31]. Stretch-dominated structures tend to exhibit higher elastic
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modulus and higher ultimate strength, while bending-dominated structures generally exhibit higher
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compliance, which might be favorable in energy absorption through elastic and plastic deformation. 60
50
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30 20 10 0 5
10
15 Strain (%)
20
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0
25
a. Lower modulus and lower strength
Stress (Mpa)
40
40
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Stress (Mpa)
50
30 20 10 0
30
0
5
10
15
20
25
30
35
Strain (%)
b. Higher modulus and higher strength
beam melting AM [30]
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Fig.1 Compressive stress-strain curve of two Ti6Al4V auxetic cellular structures fabricated via electron
As mentioned previously, three cellular designs were adopted for this study, which are the re-entrant auxetic structure, the octet-truss structure and the BCC lattice structure. Fig.2 shows the unit cells of the three cellular structures, along with the geometrical design parameters associated with each type. Note that in Fig.2 the strut thickness (t) is not shown, which is also a geometrical design parameter. Both reentrant auxetic and BCC lattice structures are bending-dominated structures, while the octet-truss structure is a stretch-dominated structure. On the other hand, the re-entrant auxetic structure exhibits
ACCEPTED MANUSCRIPT negative Poisson’s ratio, while the other two exhibits positive Poisson’s ratios. Octet-truss and BCC lattice structures have been studied extensively and are representative to the two types of deformation mechanisms [22, 32-34]. On the other hand, the auxetic structure has been suggested to exhibit good energy absorption abilities and is therefore also investigated [35, 36]. The detailed parameter design is
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shown in Table 1. In addition, with all the unit cell designs the cross section of the struts was designed to
L3 L H θ
Y
X
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X
L2
a. Re-entrant auxetic
L
Z
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Z L1
Z
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be a square with 1mm dimension.
Y
b. BCC lattice
X
Y
c. Octet-truss
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Fig.2 Unit cell design for cellular structure
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Three variations were designed for auxetic structures. Aux1 and Aux2 have the same H/L ratio and θ, therefore exhibits the same Poisson’s ratio [37]. On the other hand, Aux3 has similar relative densities as
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Aux2 but exhibits more significant auxetic effect (i.e. greater negative Poisson’s ratio) [37]. Three
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variations were designed for the BCC lattice. BCC1 and BCC2 have the same unit cell aspect ratio and different relative densities, while BCC2 and BCC3 have similar relative densities and different unit cell
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aspect ratios. Since there exist only one design parameter for the octet-truss structure, only two variations were designed with two levels of relative densities. The two levels of relative densities for all three cellular structures were set to be similar, with the lower one at ~0.12 and higher one at ~0.19 in order to allow for direct comparison between structures at same relative density levels. The sandwich structures were designed with constant skin thickness of 1mm. This dimension is considerably smaller than the overall thickness of the sandwich panel in order to reduce the energy absorption effect by the skins, which could become significant when the core density is low [38]. The
ACCEPTED MANUSCRIPT overall dimensions of the sandwich panels were determined by considering multiple factors. The first factor is the impactor head size, and the second factor is the size effect of the cellular structures. The impactor head size used for this study is 19.11mm, therefore the lateral dimensions of the sandwich structures must be significantly larger. Also, in order to account for the size effects of the cellular
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structures, which often causes stress concentration and boundary effects in the structure [39, 40], the
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numbers of unit cells in the sandwich structures in the lateral directions were set to be at least 8. Lastly,
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it was desired that the sample sizes are limited so that all the samples could be fabricated in the same batch of build. As illustrated in Fig.3, the sandwich designs have lateral dimensions of 70-80mm and 4
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layers of unit cells in the thickness direction.
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Re-entrant auxetic H (mm)
L (mm)
θ (deg)
Relative density
Aux1
6.5
4.7
70
0.122
Aux2
5
3.6
70
0.194
Aux3
7.7
4
50
0.203
L2 (mm)
L3 (mm)
Relative density
6.5
6.5
6.1
0.120
5
5
4.8
0.188
6
6
4.7
0.190
BCC3
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BCC2
L1 (mm)
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Design BCC1
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Design
BCC Lattice
Octet-truss Design
L (mm)
Relative density
Octet1
8
0.119
Octet2
6.2
0.187
Table 1 Geometrical design parameters for cellular structures
ACCEPTED MANUSCRIPT 1mm skin thickness
4 layers
7080m m
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mm 70-80
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Fig.3 Design of sandwich structures
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3. Experimental procedures
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The final sandwich designs with the three cellular structures are shown in Fig.4. The designs were fabricated by the DTM Sinterstation 2500 laser sintering system using nylon 12 (ALM PA650) as material.
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The powder particle morphology is spherical, and the powder properties provided by the manufacturer
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are D50=55μm, D10=30μm and D90=100um. The reference mechanical properties of the nylon 12 material is listed in Table 2 [41], which should only be used as a benchmark as the material properties of AM
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nylon 12 is highly sensitive to the process parameters and orientations, which was not intended to be
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investigated in the current study [42]. As the focus of this study does not involve process optimization, the default process themes used for this type of processes was employed. Additional details about the
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process setup for the laser sintering systems can be found elsewhere [42, 43]. Although the temperature effect for additively manufactured nylon 12 was not readily available, from generic material information
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it was expected that the material would exhibit lower mechanical properties at elevated temperatures [44]. Without further available temperature-property information, it was also of interest to this study to evaluate whether the temperature variation (93°C versus 121°C in this study) introduces any significant effect to the impact performance of the structures. Each sample design was fabricated in both horizontal (i.e. sandwich thickness along the build direction) and vertical (i.e. sandwich thickness perpendicular to the build direction) orientations. Some of the fabricated samples are shown in Fig.4d. It is noted that due to the manufacturing schedule limitations, no BCC3 vertical samples were fabricated.
ACCEPTED MANUSCRIPT
Aux1
Aux2
BCC1
Aux3
BCC3
b. BCC sandwich
Octet2
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Octet1
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a. Auxetic sandwich
BCC2
d. Sandwich sample fabricated by laser sintering
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c. Octet-truss sandwich
Fig.4 Sandwich panel with cellular structures Modulus (MPa)
Tensile strength (MPa)
Density (g/cm3)
Elongation (%)
Nylon 12 (XY)
1700
46
0.95
4-15
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Name
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Table 2 Reference specifications of nylon 12 [41] After fabrication, the dimensions and total weight of each samples were measured. The results were
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used to calculate the relative densities of the samples and to provide dimensional information to the testing. In order to establish the quasi-static baseline properties, for each type of sandwich panel
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fabricated with either vertical or horizontal orientation, one sample was tested under compressive testing using the Instron 5569A tensile testing system at constant strain rate of 0.2/min. During the testing, the samples were placed between two platens and preloaded to approximately 10-20N prior to the actual compressive testing. All the samples were compressed to the strain value of 0.5. The elastic modulus, ultimate strength and total energy absorption at strain value of 0.5 of each sample were calculated from the stress-strain curves.
ACCEPTED MANUSCRIPT The drop-weight impact testing was performed on an instrumented Instron/Dynatup 8250. The system was equipped with accelerometer (PCM 350B04) and dynamic force transducer (PCM 200C20), which were located on the impactor assembly as shown in Fig.5a. Weight plates can be added to the impactor assembly to adjust the impact energy, and a winch was used to lift the impactor to designated height.
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The impactor head has a hemispherical shape with diameter of 19.11mm, and the total weight of the
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impactor assembly was 3.969kg. The samples were fixed on the sample platform by a pair of plates
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(Fig.5b). The upper plate has a circular opening of 76.2mm, and the bottom plate has a circular opening of 50.4mm. The fixture assembly was placed inside a temperature-controlled oven under the impactor
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assembly (Fig.5a), which was heated up to 93°C (200F) and 121°C (250F) during the impact testing. For
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each type of sample, the impact energy was determined by gradually increasing the total incident energy until damage occurs on the top skin. After the impact energy was determined, each sample was
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subjected to up to 5 strikes or until the bottom skin was perforated. 3-5 samples for each type were
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tested. The real-time acceleration and response force were recorded at 10kHz frequency and used to calculate the energy absorption of the samples. The energy absorption was taken as the difference
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between the incident energy and the rebound energy on the impactor assembly. Also noted that beside
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the BCC3 vertical samples which were not fabricated, the Octet2 vertical samples were not drop-weight
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impact tested due to the use of most samples during the initial setup trial.
ACCEPTED MANUSCRIPT a. Overall setup
b. Fixture for samples
Fig.5 Drop-weight impact testing system
4. Results and discussions
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It was previously established that the nylon 12 cellular sandwich structures fabricated via laser sintering
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exhibit relatively consistent qualities [45], which was also verified by this study by dimensional
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measurement of a randomly chosen sample for each design variant as shown in Table 3. The dimensional variability of all the samples was smaller than 0.5mm, which correspond to less than 0.1%
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and 0.2% dimensional errors in the x/y directions (i.e. directions normal to the build direction) and the z
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directions (i.e. the build direction). Therefore, for the consequent analysis, the nominal dimensions of the designs were used without affecting the discussions. Actual L1/L2
Designed L3
Actual L3
L1/L2 (mm)
(mm)
(mm)
(mm)
Aux1
78.806
79.1494
41.414
Aux2
79.937
79.499
Aux3
74.540
BCC1 BCC2
ΔL1/L2 (%)
ΔL3 (%)
40.900
0.4
1.2
32.423
32.50
0.5
0.2
74.199
43.031
43.003
0.5
0.1
78.000
77.596
35.822
35.900
0.5
0.2
70.000
69.545
29.375
29.400
0.7
0.1
72.000
72.049
20.537
20.014
0.1
2.5
Octet1
69.430
69.599
49.150
49.200
0.2
0.1
Octet2
72.494
72.600
38.967
39.000
0.1
0.1
PT
CE
AC
BCC3
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Design
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Designed
Table 3 Dimensional characteristics of randomly selected samples
ACCEPTED MANUSCRIPT The quasi-static compressive stress-strain curves for each types of cellular structures are shown in Fig.6. Fig.7 shows the typical characteristics of each of the cellular structure types after the completion of the quasi-static testing. During the quasi-static compressive testing, none of the samples exhibit strut fracture due to the high ductility of the nylon material, and upon unloading the structures also exhibit
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some elastic recoveries. Both the auxetic and the octet-truss designs exhibit “layerwise” deformation
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patterns, while the BCC designs exhibit diagonal deformation patterns and significant skin warping.
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Further discussions regarding the deformation characteristics of these cellular structures under quasi-
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static compressive stress can be found elsewhere from previous studies [30, 32, 34, 46]. The compressive behaviors of the sandwich structures were expected to be dominated by the cellular
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cores. Auxetic sandwich showed a typical cyclic pattern observed previously with this type of structures, which is caused by the layerwise failure pattern of the structure [30, 47]. The BCC sandwich and octet-
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truss sandwich exhibited typical stress-strain curves representative to bending-dominated and stretch-
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dominated cellular structures, respectively. With the BCC sandwich samples, there exist a significant plateau stage following the initial failure, which is expected to be favorable for energy absorption. In
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comparison, the octet-truss sandwich samples also exhibited plateau stages, although there also exist a
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“softening” stage immediately after the initial failure, which results in a significant reduction of stress levels. Overall the effect of fabrication orientation was not very significant, which should be related to
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the their cellular geometry designs and will be explained in the following discussions.
ACCEPTED MANUSCRIPT b. BCC sandwich
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c. Octet-truss
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a. Auxetic sandwich
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AN
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Fig.6 Quasi-static compressive stress-strain curves of sandwiches
b. BCC
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a. Auxetic
c. Octet-truss Fig.7 Typical samples tested by quasi-static compressive testing
ACCEPTED MANUSCRIPT
The elastic modulus, ultimate strength and total energy absorption of each type of sandwich are listed in Table 4. In addition, Fig.8 shows the comparisons of total energy absorption (J) and the volumetric energy absorption (J/mm3) of different sandwich designs.
(MPa)
Avg.
absorption
(MPa)
9.62
0.64 10.485
11.35
Aux2-Hori.
33.12
0.66 2.24 35.86
38.60
2.40
Aux3-Hori.
34.27
1.43
Aux3-Ver.
53.06
BCC1-Hori.
23.98
BCC1-Ver.
27.41
BCC2-Hori.
42.95
43.665
0.916 0.594 0.967
1.29
105.86
0.507
PT
CE
0.8945
220.56
180.02
1.42
1.55
46.47
BCC3-Hori.
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3.11
13.20
Oct1-Hori.
25.46
1.28
Oct1-Ver.
32.95
Oct2-Hori.
45.14
1.54
29.205
75.38
1.415
0.695
0.4315 0.494
202.48
0.991 219.01
235.54
0.695
0.369 127.92
2.935 3.16
75.38
118.06
2.81
1.164 1.152
87.78
1.55
50.645
1.176 163.38
163.63 1.54
0.558 0.609
163.13 3.00
BCC2-Ver.
0.7805
129.35 132.84
2.89
44.71
56.15
0.873 183.225
189.69
1.63
25.695
Oct2-Ver.
0.203
139.48
1.83
13.20
0.1955
ED
Aux2-Ver.
(J/mm3) 0.188
176.76
2.32
Avg.
absorption
49.97
51.51
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Aux1-Ver.
energy
Avg.
48.43
0.65
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Aux1-Hori.
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(J)
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Strength Avg.
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Modulus Design
T
Volumetric
Energy
1.0645 1.138
ACCEPTED MANUSCRIPT
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Table 4 Quasi-static properties of different sandwich structures
b. Volumetric energy absorption
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a. Total energy absorption
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Fig.8 Comparison of quasi-static compressive energy absorption for sandwich structures From the results it is clear that the quasi-static energy absorption performance of the sandwich
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structures with each types of cellular core could be tailored at a broad range. The Octet2 design exhibits both highest modulus and strength, and due to its characteristic stress-strain pattern, it also achieved
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the highest amount of total energy absorption (at high relative density). However, the volumetric energy
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absorption of the Octet2 design is less outstanding compared to the other structures. This is due to the comparatively larger volume of the octet-truss structure compared to the other structures at the same
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relative density. At lower relative density level the BCC lattice design exhibits the highest overall energy
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absorption as well as volumetric energy absorption. However, at higher relative density level such advantage appears to diminish. When the relative density increases from 0.12 to 0.19, the total energy
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absorption capabilities of the re-entrant auxetic, the BCC lattice and the octet-truss structures increased by 267.8%, 36.9% and 71.21%, respectively, and volumetric energy absorption capabilities of the three structures increased by 357.5%, 108.6% and 146.7% respectively. It is therefore inferred that given sufficient relative density design windows, the re-entrant auxetic cellular structure would exhibit the highest quasi-static compressive energy absorption as well as volumetric energy absorption efficiency. On the other hand, if the relative density is restricted at lower levels, then the BCC lattice design appears to be advantageous.
ACCEPTED MANUSCRIPT The effect of fabrication orientation is closely related to the specific geometries of each unit cell designs. For re-entrant auxetic structure both vertical strut (H in Fig.2a) and re-entrant strut (L in Fig.2a) contribute to the mechanical strength of the structures. From the analytical property model it is known that with smaller re-entrant angle the re-entrant strut contribute more significantly to both the modulus
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and the strength of the structures [37, 48]. Furthermore, with laser sintering powder bed fusion process
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both the elastic modulus and the ultimate strength are the lowest along the build direction (z direction)
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and increase as the orientation angle relative to the z direction increases [49, 50]. Therefore, with Aux1 and Aux2 designs, although for the vertically built samples the re-entrant struts were more aligned to
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the z direction (20° as opposed to 70° in horizontally built samples) and are therefore considerably
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weaker, such effect was partly compensated by the strengthening of the vertical struts (oriented at 90° in relation to the z direction). On the other hand, with Aux3 due to the relatively small difference of
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build orientation for the re-entrant struts under both situations (50° versus 40°), the strengthening of
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the vertical struts becomes dominant, and the overall properties of the structure are therefore higher with the vertically built samples. For the BCC designs, due to the consistent strut orientation, the build
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orientation effect is also expected to be more consistent. For BCC1 and BCC2, due to the fact that the
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struts tilt at near 45° angle (41.1° to be more exact), the mechanical properties of the vertically built samples is expected to be similar to those of horizontally built samples. For BCC3, although no vertically
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built samples were fabricated, it could be expected that due to the relatively large strut tilt angle (~64.5°) the mechanical properties of the horizontally built samples would be significantly higher compared to vertically built samples. For octet-truss structures, due to the identical unit cell topology under both build orientations, the mechanical properties of samples under both build orientations are also similar, and the main contributor of the property enhancement for the vertically built samples is likely the horizontally fabricated vertical struts that align to the load direction.
ACCEPTED MANUSCRIPT Table 5 shows the impact energy levels that were used for each types of sandwich structures after the preliminary strike testing, along with the corresponding drop heights. For some designs multiple strikes were taken with gradually increasing impact levels before the top skin damage was visually observable. After the preliminary testing, the impactor was manually lifted to the desired height during the testing,
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which was expected to introduce minor variability with incident energy level. The response force curves
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for each type of sandwich structures upon the initial impact at 93°C are shown in Fig.9. For each sample,
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the occurrence of high response force was expected to correspond to the impact damage of the samples, since the impact energy levels were selected to induce damages to the samples. For horizontally
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fabricated samples, the maximum response forces for the designs that exhibit higher quasi-static
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strengths are also generally higher. The effect of build orientation was most significant for Aux2 design. The response forces of the vertically built Aux2 samples achieved exceptionally high levels (>20000N in
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Fig.8b), whereas the response forces of the horizontally built Aux2 samples were at the levels of 1400-
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1600N. This might be resulted from the signified contribution of the vertical struts during the impact process due to both the orientation enhancement effect and the increased density (compared to Aux1).
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On the other hand, for Aux3 samples, unlike the results from quasi-static testing, the response forces did
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not exhibit significant build orientation dependency. Such results suggest that for this design the reentrant struts are likely to contribute more significantly to the energy absorption responses during the
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impact deformation. Since for Aux3 designs the re-entrant struts are oriented near 45°, the orientation effect becomes less significant.
ACCEPTED MANUSCRIPT Samples Energy
Height
Temp. (m)
level (J)
(m)
93
24.70
0.635
121
24.70
0.635
93
19.76
0.508
121
19.76
0.508
93
17.78
0.457
121
17.78
0.457
93
-
-
Design Orientation
(°C) 93
Height
Temp. level (J)
Design Orientation
Energy
T
Samples
(°C) 17.78
0.457
Hori.
Hori. 121
-
-
93
19.76
0.508
121
19.76
0.508
93
15.81
0.406
BCC2 Ver.
CR
Ver.
IP
Aux1
Hori.
121
15.81
0.406
Aux2
US
Hori. BCC3 93
19.76
0.508 0.508
121
-
-
93
18.77
0.483
93
7.90
0.203
121
18.77
0.483
121
7.90
0.203
93
19.76
93
19.76
0.508
121
19.76
0.508
93
24.70
0.635
121
24.70
0.635
93
-
-
121
-
-
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Ver.
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19.76
Aux3
0.508
93
7.90
0.203
93
19.76
0.508
121
19.76
0.508
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Octet1 Ver.
Hori.
CE
PT
19.76
7.90
Hori.
0.508
121
121
BCC1
Ver.
121
Hori.
Hori.
AN
Ver.
0.203 Octet2
Ver.
Ver.
Table 5 Average impact energy levels for each types of sandwich designs
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a. Horizontally built samples
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ACCEPTED MANUSCRIPT
c. Vertically built samples (Aux2 not shown)
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b. Vertically built samples
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Fig.9 Response forces of different sandwich designs upon initial impact at 93°C The response force curves for each type of sandwich structures upon the initial impact at 121°C are
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shown in Fig.10. Compared to Fig.9, similar correlations between quasi-static strengths and response
CE
forces were also observed for samples tested at 121°C. However, the response force levels for each type of structures exhibit no consistent trend over different temperature levels. It was expected that the
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reduced mechanical properties of nylon 12 exhibited at elevated temperature might introduce “softening” effect into the impact response of the cellular structures. However only Aux2 designs exhibited significant decrease of peak response force levels at higher temperature levels, which might be partly related to the more “dense” topology of this cellular design as well as the high degree of crystallinity of the nylon material used for laser sintering powder bed fusion, which potentially exhibits less pronounced softening effect.
T
ACCEPTED MANUSCRIPT
b. Vertically built samples
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a. Horizontally built samples
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Fig.10 Response forces of different sandwich designs upon initial impact at 121°C The average peak response forces and the maximum peak response forces under multiple impacts for all
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the sandwich designs built under both horizontal and vertical orientations are shown in Fig.11 and Fig.12,
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respectively. It was noticed that for all the cellular designs the average maximum peak force values are either about the same or larger than the initial peak force values, which indicates that all the structures
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exhibit consistent or even enhanced damage tolerance under continuously accumulating damage. This is
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further illustrated by the multi-impact response force curves of different sandwich designs as shown in Fig.13. The effect of quasi-static mechanical properties on the average peak force and maximum peak
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force does not appear to be significant for the designs investigated. It should also be noted that higher
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peak response force could also imply higher risk of damage for the structure intended to be protected if they are placed underneath the sandwich structures, since such high forces could potentially be
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transmitted through. Since in the current study the force sensor was placed on the impactor, the effectiveness of these cellular designs as protective barriers is beyond the scope of this study and will not be further discussed.
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Fig.12 Max. peak force under multiple impacts
b. Aux1-Ver.
e. Aux3-Hori.
f. Aux3-Ver.
c. Aux2-Hori.
d. Aux2-Ver.
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M
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a. Aux1-Hori.
US
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Fig.11 Average peak force under multiple impacts
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ACCEPTED MANUSCRIPT
h. BCC1-Ver.
AC
CE
PT
g. BCC1-Hori.
i. BCC2-Hori.
j. BCC2-Ver.
k. BCC3-Hori.
l. Octet1-Hori.
m. Octet1-Ver.
n. Octet2-Hori.
Fig.13 Multi-impact force curves for different cellular designs
ACCEPTED MANUSCRIPT The damage characteristics for the horizontally built re-entrant auxetic structures are shown in Fig.14. The temperature information is not shown as it does not appear to have significant effect, and the samples shown in Fig.14 were also randomly chosen with regard to the testing temperature. Aux1 and Aux2 designs exhibit similar characteristics with top and bottom perforation with sandwich skins. While
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the top perforation is localized, the bottom perforation occurs over larger areas. For both types of
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structures, the top skins and the core cellular structures both exhibit clear shearing fracture in the
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impacted areas, and there also exist obvious bending of top skins in the vicinity areas. On the other hand, the bottom skins for both type of structures exhibit clear skin delamination. Previous studies have
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shown that the re-entrant auxetic structures exhibit very small size effect and are able to distribute
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stress more evenly throughout the structures [51]. Therefore, the large area of damage for the bottom skins might be partly attributed to such stress distribution effect. The overall damage characteristic is
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also similar to the other additively manufactured cellular structures [22, 52]. For the Aux3 sandwich, the
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top skin exhibits significant skin wrinkling and delamination, and the bottom perforation damage also appears more significant compared to Aux2. This might be attributed to the more significant negative
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Poisson’s ratio effect, which introduces more significant shearing stress on the bottom skin panels
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through skin-core bonding constraint. It should be noted that the delamination damage with these sandwich panels is likely contributed by the local stress distribution effects upon the impact loading,
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which is significantly influenced by the type of core unit cell designs as previously reported [46]. The additively manufactured sandwich panels appear to exhibit stronger core-skin bonding since the entire structures were fabricated in one process using the same material, which differs from many traditional sandwich structures that are fabricated by bonding the core and skins and therefore tend to exhibit more bonding interfacial strength issues.
ACCEPTED MANUSCRIPT Top
Top
Bottom
Bottom
a. Aux1
b. Aux2
Top
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IP
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Bottom
c. Aux3
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Fig.14 Damage characteristics of auxetic sandwich structures built horizontally The damage characteristics of the horizontally built BCC lattice sandwich structures are shown in Fig.15.
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For all the BCC lattice designs the top skins exhibit significant bending in the vicinity of the impact area,
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which indicates significant local stress concentration effect upon impact. The bottom skin perforations exhibit not only extensive areas accompanied by skin-core delamination, but also large skin cracks
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throughout the entire sandwich structures. The large area of damage spread might be attributed to the
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significant stress concentration effects of this type of cellular structures caused by the size effects [34], which appears to be detrimental for the energy absorbing protection applications.
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The sample designs for both the auxetic and the BCC sandwich structures also shed some lights to the occurrence of delamination. As in this study both cellular structures were bonded to the skin panels only at the end of the boundary struts. Therefore, the skin-core bonding was not as strong as the octet-truss sandwich structures, which have significantly larger cellular core-skin “contact” areas.
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Bottom
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a. BCC1
b. BCC2
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c. BCC3
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Fig.15 Damage characteristics of BCC sandwich structures built horizontally
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The damage characteristics of the horizontally built octet-truss sandwich structures are shown in Fig.16. The top skins exhibit relatively well-defined perforation profile with small amount of extended damage
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around the impact area. The bottom skins of the octet-truss sandwich also exhibit both skin shearing
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and delamination, and for most samples the core residue that was sheared off from the structure extruded out from the bottom side more significantly compared to the other designs. This indicates that
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the “tangling”/retaining effect of the core cellular structure to the sheared residue is not as significant
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for the octet-truss structure, which might be attributed by the relatively sparse topology of this type of design. This could also negatively impact the energy absorption ability of these structures.
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b. Octet2
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a. Octet1
Fig.16 Damage characteristics of octet-truss sandwich structures built horizontally
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For the vertically built samples, the damage characteristics are similar to the horizontal ones except for
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the Aux2 design, which are shown in Fig.17. For these samples, the bottom skins exhibit extended cracks
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similar to that observed with the BCC sandwich structures, which indicates strong stress concentration at the bottom skins that is unusual for the auxetic structures. This unique damage characteristic might
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contributed to the large peak response forces exhibit by these samples. Considering that the auxetic structures with large H/L ratio and small re-entrant angle θ exhibits rather significant layerwise failure
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mode under quasi-static compressive loading [33], it is speculated that such failure mode might be
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partly responsible for the occurrence of stress concentration due to significant internal compression of the cellular core structures, although additional studies will be needed to verify this theory.
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a. Sample 1
b. Sample 2
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Fig.17 Damage characteristics of Aux2 sandwich built vertically
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The average total energy absorptions for each type of cellular sandwich structure are shown in Fig.18, which show the comparisons of build orientations and testing temperatures, respectively. For auxetic
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sandwich structures, the vertically built samples absorb higher total energy under multiple impacts.
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Combining this observation with the previous observation with the peak response forces, it was speculated that while the vertical struts do not contribute to the initial damage of the structures, they
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do absorb significant amount of energies in consequent deformations and impact perforations, and therefore enhance the total energy absorption of the structures. On the other hand, the effects of
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temperature on the total energy absorption of the sandwich structures do not appear to be consistent.
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b. By temperature
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a. By build orientation
Fig.18 Average total energy absorption for cellular sandwich structures
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As some of the sandwich structures only sustained fewer than 5 impact strikes and consequently, might
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not have exhibit comparative total energy absorption abilities compared to the ones that sustained 5 strikes, the average energy absorptions per impact strike were investigated as shown in Fig.19. From the
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results, the BCC lattice structures exhibit more comparative energy absorption ability compared to the
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auxetic structures, while the octet-truss structures exhibit slightly lower energy absorption abilities. Comparing Fig.18 and Fig.19, the results suggest that for single strike impact the energy absorption
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abilities among the different cellular designs with different geometry designs do not exhibit significant differences, and the relative density appears to be the most significant factor. However, when multiple
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impacts are introduced, different cellular structures exhibit different ability in sustaining energy
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absorption functionality. The auxetic cellular structures appear to exhibit the highest performance as well as the highest performance tailorability, whereas the BCC lattice structures exhibit the lowest overall performance due to their low cumulative damage tolerance. On the other hand, despite the desirable quasi-static mechanical properties, the octet-truss structures do not exhibit outstanding energy absorption ability compared to the auxetic structures. Again from Fig.19 the energy absorption per impact strike does not exhibit consistent dependence on temperature.
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b. By temperature
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a. By build orientation
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Fig.19 Energy absorption per impact strike for cellular sandwich structures
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The performance advantage of the re-entrant auxetic structures is further demonstrated by the incident energy absorption ratio, which is defined as the ratio between the absorbed energy and the total
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incident energy. As shown in Fig.20, the Aux2 design exhibits incident energy absorption ratio as high as 0.93 for vertically built samples. For most other cellular structures, the incident energy absorption ratio
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is 0.6-0.7. The BCC1 design also exhibit high energy absorption ratio, although considering that this
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structure has rather low overall mechanical strength, it might still not be as efficient compared to the
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auxetic structures for the energy absorption applications.
a. By build orientation
b. By temperature
Fig.20 Incident energy absorption ratio for different cellular sandwich structures
ACCEPTED MANUSCRIPT 5. Conclusions In this study, sandwich structures with multiple cellular core designs including the re-entrant auxetic structure, the BCC lattice structure and the octet-truss structure were studied for their drop-weight impact energy absorption characteristics. The samples were fabricated by laser sintering system using
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nylon 12 as material. It was found that the quasi-static mechanical properties of these structures do not exhibit apparent correlations to their drop-weight impact energy absorption ability. On the other hand,
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the boundary stress concentration characteristics of each type of cellular structures appear to play a role
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in their drop-weight impact characteristics. For auxetic cellular sandwich, the minimized boundary stress concentration appears to contribute to the reduced damage on the backing side of the structures,
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although such benefit is also affected by the characteristic “catastrophic” failure exhibited by the high aspect ratio-low re-entrant angle designs (Aux3). In addition, for the re-entrant auxetic structures the
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buckling of the vertical struts might act as the most significant contributor to the enhancement of the
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energy absorption abilities of this structure. In general, the auxetic cellular designs exhibit the best total energy absorption and per-strike energy absorption abilities, as well as the highest structural
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performance efficiency for such applications, although the peak response forces of some of these
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designs might need to be subjected to additional scrutiny for shock impact protection applications. The BCC lattice structures exhibit good single-impact energy absorption abilities, which might be partly
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contributed by its relatively low mechanical strength and large damage area that helps absorbing energies. The octet-truss structure exhibits good overall energy absorption ability, although its performance efficiency is comparatively low due to the large cellular dimensions under the same relative densities. In addition, the octet-truss structure also exhibits relatively low residue retaining ability. The non-isotropic material properties of the laser sintering powder bed fusion additive manufacturing process introduces additional factors that complicates the design analysis of the sandwich structures for drop-weight impact performance, and additional works are likely needed to
ACCEPTED MANUSCRIPT systematically analyze the coupling effect of local material property variability and cellular geometry designs to the overall performance of the structures. Another piece of future work would be the roomtemperature drop-weight impact performance evaluation for the same designs, which will provide additional basis for comparison.
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6. Data availability
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The raw data required to reproduce these findings are available to download from http://dx.doi.org/10.17632/sh3wfgxypj.2. The processed data required to reproduce these findings is
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provided in this publication.
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7. Acknowledgement
The authors are grateful of the help of the Rapid Prototyping Center (RPC) at University of Louisville.
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This research was supported by the Intramural Research Initiation Grant (IRIG) at University of Louisville
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and partially supported by the Office of Naval Research (ONR) grant #N00014-16-1-2394.
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Graphical abstract
ACCEPTED MANUSCRIPT Highlights
The quasi-static mechanical properties of the sandwich structures with different cellular core designs have no significant correlations with impact properties
The drop-weight impact performance of sandwich structures is dependent on the type of core unit cell
Re-entrant auxetic core designs can be tailored to exhibit high energy absorption, but also exhibits
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and its geometry parameters
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high response forces
The BCC core designs exhibit good one-time impact performance due to low mechanical strength and
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The octet-truss core designs exhibit low volumetric impact performance and low residue retaining
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ability
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large energy dissipation area