A Novel Lattice Structure for Enhanced Crush Energy Absorption
Published at : 19 Oct 2022
Volume : IJtech
Vol 13, No 5 (2022)
DOI : https://doi.org/10.14716/ijtech.v13i5.5829
Seek, C.Y., Kok, C.K., Lim, C.H., Liew, K.W., 2022. A Novel Lattice Structure for Enhanced Crush Energy Absorption. International Journal of Technology. Volume 13(5), pp. 1139-1148
| Chang Yuan Seek | STMicroelectronics Sdn. Bhd., Kawasan Perindustrian Tanjung Agas, 84007 Muar, Johor, Malaysia |
| Chee Kuang Kok | Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia |
| Chong Hooi Lim | Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia |
| Kia Wai Liew | Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia |
Lightweight and stiff lattice structures are good energy
absorbers. This study evaluates the energy absorption
capacity of a few common lattice structures printed out of PLA using fused
deposition modeling and proposes an
improved lattice structure. Simple cubic (SC), honeycomb (HC), body-centered cubic (BCC), and novel PeckGy80 (PG80) lattice structures were
subjected to compressive tests. The quasi-static load-displacement behavior of lattice specimens was
characterized in terms of specific energy absorption and crush load efficiency.
The damage mechanisms were then related to energy absorption. Cracks and
brittle fractures occurred in all lattice structures during the crush test.
Different lattice structures induced different damage mechanisms, significantly affecting their energy
absorption. SC lattice structure showed structural separation at a small
displacement, rendering it an ineffective energy absorber. BCC and HC lattice
structures demonstrated almost identical shear band failure modes. The PG80
lattice structure, although made of brittle PLA, displayed progressive failure
from the bottom layer to the upper layers, exhibiting both a high peak load
and stable post-yield behaviour. This
damage mode enabled the PG80 lattice to be far superior in terms of specific
energy absorption to HC, SC, and BCC lattice structures.
3D Printing; Energy absorption; Lattice structures; PLA; Quasi-static crush
Three-dimensional lattices, having replicated structures like those of cellular
solids, draw much attention owing to their high stiffness, strength and
ultra-lightweight (Dong et al.,
2020). Besides,
the capability of lattice structures to undergo considerable deformation at a
relatively low transmitted stress makes them good energy absorbers. Lightweight
and large energy absorption capacity are currently the main design priorities
in the automobile and aerospace sectors to minimize the amount of material and
hence fuel consumption (Helou & Kara, 2017; Ye et al., 2020). Traditionally, the role of energy absorption
has been filled by thin-walled tubes (Malawat et al., 2019). Recent findings indicated that polylactic acid
(PLA) lattice structures might be used as sacrificial claddings as material and
structure protection gear (Santos et al., 2021; Sun et al.,
2021).
The advancement in additive manufacturing provides design freedom in printing lattices, yet the effective design strategies of complex lattices suitable for various applications are still under research (Panesar et al., 2018). Three types of lattices are common, namely strut-based lattices, planar lattices, and surface-based lattices. The typical strut-based (a.k.a. bending dominated) lattices suffer from low structural stiffness, whereas the typical surface-based (a.k.a. stretch-based) lattices demonstrate low energy absorption (Riva et al., 2021). Common strut-based lattices include simple cubic (SC) and body-centered cubic (BCC), whereas honeycomb (HC) is a common planar lattice. These common latices had been printed using different materials (Obadimu & Kourousis, 2021). In a similar study, Park and Park (2020) made functionally graded lattices, including BCC and hexagonal HC structures, with photo-curable polyurethane resin. They found that the compressive stiffness of the lattice structures varied greatly, up to five orders of magnitude depending on design parameters. And all the structures displayed predominantly bending mode in compression. Santos et al. (2021) fabricated PLA and polyethylene terephthalate glycol-modified (PETg) lattice structures out of honeycomb and auxetic?type hexagonal unit cells to investigate their low-velocity impact response. They found that PETg was superior to PLA in terms of energy absorption. A hybrid design combining an octet and a bending-dominated structure printed in PLA showed a desirable stable post-yield stress plateau, which could hardly be achieved by the octet structure alone. The latest trend also included the use of cell topology and its modification (Sun et al., 2021).
Previous work demonstrated the feasibility of
SC, HC, and BCC lattices for energy absorption. Liu et al. (2021b) explored the mechanical performance of an SC
lattice structure fabricated using titanium alloys through selective laser
melting (SLM) technology. They found that the SC lattice structure showed
manageable plateau stress and excellent energy-absorption capability, and it
can be utilized in vibration damping machines and biomedical transplants (Liu et al., 2021b). It has been long observed that the HC lattice
possesses a superior energy absorption ability. When loaded uniaxially, the
honeycomb cells would bend and fold over steadily as demonstrated in (Ashby, 2006). On the other hand, BCC is a traditional form
of bending-dominated strut-based structure, which has gained significant
attention and has been experimentally and scientifically studied for its unique
mechanical and energy-absorbing properties (Mines et al., 2013; Ushijima et al., 2010; Gümrük
et al., 2013; Tancogne-Dejean & Mohr, 2018). The mechanical performance of the BCC lattice
structure was examined under numerous loading conditions (Gümrük et al., 2013; Tancogne-Dejean & Mohr, 2018), and the classical beam hypothesis approach was used
to forecast its mechanical performance (Ushijima et al.,
2010; Ushijima et al., 2013). In addition, drop-weight impact tests revealed that the BCC lattice
structure made of Ti–6Al–4V demonstrated superiority over the honeycomb (Mines et al., 2013), and compression tests indicated that the BCC
lattice structure made of Ti–6Al–4V seemed to be suitable for energy absorption
systems owing to the extended plateau region and low hardening period before
densification (Tancogne-Dejean
& Mohr, 2018).
Compared
to other printable materials such as ABS, nylon and (PETg), PLA possesses the
advantages of being biodegradable and cost-effective (Lololau et
al. 2021, Santos et al. 2021). Yet,
there appears to be a lack of a comprehensive evaluation of the performance of
PLA-printed lattices for energy absorption, which prompted this study. There are two objectives in this study. First,
the energy absorption capability of different lattice structures, namely SC,
HC, BCC, and a novel PG80, was characterized experimentally to establish the
basis for comparison. PG80 was not a pre-existing lattice structure but was the
result of trial-and-error in the course of this work. Secondly, the structural
failures of the lattice structures were related to energy absorption to
elucidate the superiority of the novel lattice structure.
2.1. Lattice Structures and Specimen Design
The SC, BCC, and PG80 lattice structures have proper strut placement in a unit cell of 10 mm X 10 mm x 10 mm. These lattice structures, together with the HC lattice structure, have equal overall sizes of 40 mm X 40 mm X 40 mm, as shown in Fig 1. The theoretical relative density of the SC, HC, BCC, and PG80 are 0.16, 0.36, 0.26, and 0.38, respectively. The actual relative density of the printed specimens turned out to be 0.17, 0.28, 0.20, and 0.34, respectively, for the same lattice structures. The relative density is the density of the lattice structure (i.e., the mass of the lattice over its apparent volume, namely 6.4X104 mm3) over the theoretical density of the PLA, 1240 kg/m3. To measure the actual relative density of the lattice structures, only the masses of the printed lattice structures need to be measured. The deviations in relative density may have resulted from imperfect support material removal and printing parameters. In as much as humanly possible, the printed specimens were all inspected for unintended sharp corners so that they were removed before crushing.
Figure 1 Printed lattice structures. (a) SC; (b) HC; (c) BCC; (d) PG80
Figure 2 shows
the unit cells of SC, HC, and BCC. The SC lattice is lined with square struts
having a cross-section of 2 mm X 2 mm (i.e., L = 9.5 mm and d = 1
mm in Figure 2(a)). The HC lattice was made of honeycombs in a hexagonal
arrangement. Each unit cell has a perimeter of 30 mm (i.e., L = 5 mm
each side, Lc = 10 mm, t = 1 mm in Figure 2(b)). When
one cell is laid hexagonally with another cell, the joining side forms a
honeycomb wall of 2 mm thick. The BCC lattice has eight struts per unit cell.
Every strut has a cross-section of 2 mm X 2 mm, whose corners are rounded by a
radius of 0.3 mm. The strut begins at the cell center and diverges to eight
corners. Its length is
While SC, HC, and BCC lattice structures were used in this study primarily for their prevalence in previous studies, the PG80 lattice structure was designed specifically in this study to retain the existing advantage of strut-based lattice architecture, namely outstanding energy absorption, with enhancement in strength or stiffness. The PG80 unit cell comprises nodes (n) and struts (S), as shown in Figure 3. The "X" configuration nodes are generated when four struts meet at the hollow cylinder. The "#" configuration nodes are located at the struts' intersection points. The hollow cylinder that exists at the middle of the unit cell serves as a connector that links three (3) of "X" configurations and two (2) "#" configurations in series. There are 20 struts and 20 nodes in total within a unit cell.
Figure 2 Unit cells of (a) SC, (b) HC, (c) BCC lattice
structures
|
|
Figure 3 PG80 lattice; (a) Unit cell, (b) “X” configuration, (c) “#” configuration
Based
on the number of nodes and struts, the Maxwell number (Maconachie, et al.,
2019)
turned out to be negative, making this structure exhibit a predominantly
bending mode. The solid struts on the "X" have a thickness of 1.4-1.7
mm (i.e., 2 mm diameter cylinders truncated by 0.3 mm on either side and by 0.6
mm when sandwiched in the unit cell, see Figure 3 (a) (right)), whereas those
hollow struts on the "#" have a mean diameter of 1.5 mm and thickness
of 0.5 mm. The hollow cylinder has a mean diameter of 4 mm and is 1 mm thick.
2.2. PLA materials and printing Parameters
The lattice structures were printed out of a PLA
filament with a diameter of 1.75±0.05 mm (produced by RoHS SGS (China), Brand
name: LanDu). The slicing program module was used to regulate the Makerbot
Replicator desktop 3D printer, which horizontally sliced the lattice structure
into thin layers. The lattice structures were printed in a flat orientation,
with each layer deposited in either a 0° or 90° direction, layer by layer from
the bottom up. In other words, the printing direction is perpendicular to the
compression direction. Printing parameters include feeding speed (3 mm/s),
printing temperature (210oC), printing orientation, support
building, and layer thickness. Quality was set to the default "Standard",
and the layer height was set at 0.2 mm with an infill of 10%. Table 1
summarizes the typical properties of the PLA as provided by Makerbot.
Table 1 Typical PLA properties
|
Value | |
|
Theoretical density ( |
1240 |
|
Flexural strength ( |
61.85 |
|
Tensile strength, printed ( |
46.77 |
|
Compressive strength, printed ( |
17.93 |
2.3. Quasi-static crush Test and Energy Metrics
Universal testing machine Instron model 3367 was used to conduct quasi-static crushing of the specimens. The test speed was set at 0.5 mm/min. The machine, specimen, and compression jigs are shown in Figure 4.
Figure 4 Photograph of compression machine, specimen, and jigs
where EA is the total energy absorbed (i.e., the area under the
curve of the force-displacement curve before the sign of densification, in unit
N-m or J), Mm is the crushed mass, Fm is
the mean crush load (i.e., EA divided by crush length in unit N) and Fmax
is the maximum crush load throughout the loading history (also in unit N).
Figure 5
Load-displacement curves of different lattice structures. Specimens are
designated by lattice type (e.g., SC) followed by sample number in the legend
Table 2 Energy
absorption of lattice specimens
|
|
Energy
Absorption ( |
Specific
Energy Absorption ( |
Average | |
|
SC |
S1 |
1.54 |
0.11 |
0.11 |
|
S2 |
1.48 |
0.11 | ||
|
|
S3 |
1.40 |
0.10 | |
|
HC |
S1 |
4.48 |
0.20 |
0.18 |
|
S2 |
3.39 |
0.15 | ||
|
|
S3 |
4.31 |
0.19 | |
|
BCC |
S1 |
0.90 |
0.06 |
0.08 |
|
S2 |
1.44 |
0.09 | ||
|
|
S3 |
1.17 |
0.08 | |
|
PG80 |
S1 |
23.47 |
0.87 |
0.87 |
|
S2 |
23.76 |
0.87 | ||
|
|
S3 |
23.87 |
0.88 | |
Table 2 summarizes the specific energy absorption
(SEA) of the samples tested for each lattice structure, where Table 3
presents the crush force efficiencies (CFE) of the same. Complying with
the load-displacement curves in Figure 5, PG80 lattice structure was at least
four times more efficient than the rest of the lattice structures in terms of
specific energy absorption. It also demonstrated superior crush force
efficiencies near 75%, while those of BCC, HC, and SC hovered around 40-55%.
Different
lattice structures induced different deformation modes, which readily explained
the specific energy absorption of the different lattice structures. The SC
lattices failed by elastic buckling along the vertical columns and brittle
fractures were visible in the forms of "straight" clean breaks
without noticeable area reduction through the cross-sections of the horizontal
columns. In all the samples, a quarter of the structure completely tore off, as
highlighted in the red oval in Figure 6(a) (left). The failure was
catastrophic, and the structure broke into pieces (Figure 6(a) (right)).
Elastic buckling and brittle failures do not favor energy absorption. Such
deformation patterns were absent in Liu et al.,
(2021b) as the titanium alloy material they used was ductile.
Table 3 Crush force efficiencies of
the lattice structures
|
|
Max load, |
Mean crush load, |
Crush force efficiency |
Average CFE | |
|
SC | |||||
|
S1 |
3487.50 |
1474.12 |
0.42 |
0.42 | |
|
S2 |
3395.50 |
1427.33 |
0.42 | ||
|
|
S3 |
3125.08 |
1348.99 |
0.43 | |
|
HC | |||||
|
S1 |
1479.45 |
699.59 |
0.47 |
0.45 | |
|
S2 |
1361.71 |
529.71 |
0.39 | ||
|
|
S3 |
1368.61 |
672.67 |
0.49 | |
|
BCC | |||||
|
S1 |
732.56 |
398.16 |
0.54 |
0.54 | |
|
S2 |
951.53 |
514.50 |
0.54 | ||
|
|
S3 |
862.61 |
472.67 |
0.55 | |
|
PG80 | |||||
|
S1 |
3938.81 |
2933.33 |
0.74 |
0.75 | |
|
S2 |
3930.73 |
2970.29 |
0.76 | ||
|
|
S3 |
3929.29 |
2983.29 |
0.76 | |
As the force
was applied beyond a threshold of around 1100 N – 1400 N in HC lattice
specimens, a crushing plane appeared at the cell walls' stationary end. It then
propagated along the green arrow in Figure 6(b) to the impacting end before the
interim densification set in. Wall bending and brittle fractures were two
common damage mechanisms. Consistent with the work of An
et al. (2017), which showed "X" failure mode originating from
the stationary end in their simulated aluminum honeycomb, the deflection of HC
specimens in this study exhibited the "\" mode (i.e., half of the
"X" mode) also originating from to the stationary end. Wall bending
enhanced energy absorption and prolonged the crush period, but the brittle
failure inhibited the growth of peak force.
Similar to the
HC lattice, the BCC lattice structures cracked along the global direction at
45°, equivalent to some shear band (colored in beige in Figure 6(c) (left)),
splitting it into two portions. The insert on the right (labeled 'x') shows a
squashed crack in the band-- a brittle fracture resulting in the strut of the
damaged unit cell breaking away and detaching from the node. The fracture band
implied that the node encountered the highest stress at a 45 ° inclined axis. Liu
et al. (2021a) observed this shear band formation in BCC and managed to
suppress its formations by enlarging their aluminum alloy BCC lattice nodes.
Such an approach, however, had been adopted in this study to some extent (see
Figure 2(c)) and did not suppress the shear band formation.
The
failure mechanism of PG80 lattice structures was totally different. The bottom
layer of the structure began to fold when the displacement reached 2 mm (see
Figure 6(d) (left), pink band). In particular, the hollow cylinders at the
bottommost layer deformed into an irregular shape, some vertical struts
buckled, and some "X" struts brittly fractured simultaneously. As the
lattice structure was further compressed, similar folding deformation
propagated to the immediately upper layer of the previous fold until multiple
layers failed and gradually piled up (See Figure 6(d) (right), pink band). 
Figure 6 Deformation
modes of different lattice structures. (a) SC; (b) HC; (c) BCC; (d) PG80
It is interesting to note that some ""#” configurations in a particular layer were not folded, indicating strong structural support (See Figure 6(d) (right), yellow circle). The horizontal columns of ""#” configuration were effective lacing to the vertical columns. Such ""#” configuration, when deployed in three dimensions, was shown to enhance energy absorption under compression (Ren et al., 2020). Progressive folding such as displayed in PG80 lattice, resulted in high energy absorption.
The
novel lattice structure PG80 demonstrated superior energy absorption
capability, at least four times greater than simple cubic, honeycomb, and
body-centered cubic lattice structures. Its crush force efficiency was at 75%,
which was higher than the other structures, indicating superior crush
stability. SC lattice structures gave high peak force with little compression
but buckled and failed catastrophically. Placing the struts diagonally towards
loading in BCC lattice induced shear. Using honeycomb instead of struts in HC
lattice structures induced progressive shearing. PG80's “#” configuration acted
like laced columns to inhibit buckling while inheriting the high peak force of
the SC lattice structure. The energy absorption of the lattice structure was closely
related to the deformation modes. Buckling in SC lattice yielded the lowest
energy absorption, and shear bands in BCC lattice and HC lattice absorbed crush
energy slightly better. Progressive folding of printed layers from the bottom
up, such as that in PG80, is much preferred for energy absorption. It is
recommended that the loading directions’ effect on these lattices’ energy
absorption be investigated to establish the superiority of PG80.
This
research work has not received any grant from any funding agency. The authors
are grateful to the University for granting them access to equipment to produce
this work.
An, L., Zhang, X., Wu, H., Jiang, W., 2017. In-Plane Dynamic
Crushing and Energy Absorption Capacity of Self-Similar Hierarchical Honeycombs.
Advances in Mechanical Engineering, Volume 9(6), pp. 1–15
Ashby, M., 2006. The Properties of Foams and Lattices. Philosophical
Transactions of the Royal Society A, Volume 364, pp. 15-30
Dong, G., Tang, Y., Li, D., Zhao, Y., 2020. Design and Optimization
of Solid Lattice Hybrid Structures Fabricated by Additive Manufacturing. Additive
Manufacturing, Volume 33, p. 101116
Gümrük, R., Mines, R., Karadeniz, S., 2013. Static Mechanical
Behaviours of Stainless Steel Micro-Lattice Structures under Different Loading
Conditions. Materials Science and Engineering: A, Volume 586, pp.
392–406
Helou, M., Kara, S., 2017. Design, Analysis and Manufacturing of
Lattice Structures: An Overview. International Journal of Computer
Integrated Manufacturing, Volume 31(3), pp. 243–261
Liu, X., Wada, T., Suzuki, A., Takata, N., Kobashi, M., Kato, M.,
2021a. Understanding and Suppressing Shear Band Formation in Strut-Based Lattice
Structures Manufactured by Laser Powder Bed Fusion. Materials and Design,
Volume 199, p.109416
Liu, Y., Zhang, J., Tan, Q., Yin, Y., Li, M., Zhang, M., 2021b.
Mechanical Performance of Simple Cubic Architected Titanium Alloys Fabricated
Via Selective Laser Melting. Optics & Laser Technology, Volume 134,
p. 106649
Lololau, A., Soemardi, T.P., Purnama, H., Polit, O., 2021.
Composite Multiaxial Mechanics: Laminate Design Optimization of Taper-Less Wind
Turbine Blades with Ramie Fiber-Reinforced Polylactic Acid. International
Journal of Technology, Volume 12(6), pp. 1273-1287
Ma, Q., Sahat, I., Mat Rejab, M., Hassan, S., Zhang, B., Merzuki,
M., 2019. The Energy-Absorbing Characteristics of Filament Wound Hybrid Carbon
Fiber-Reinforced Plastic/Polylactic Acid Tubes with Different Infill Pattern
Structures. Journal of Reinforced Plastics and Composites, Volume
38(23-24), pp. 1067–1088
Maconachie, T., Leary, M., Lozanovski, B., Zhang, X., Qian, M.,
Faruque, O., Brandt, M., 2019. SLM Lattice Structures: Properties, Performance,
Applications and Challenges. Materials & Design, Volume 183, p.
108137
Malawat, M., Sumarsono, D.A., Istiyanto, J., Prayogo, G.,
Dionisius, F., 2019. Theoretical Prediction of Dynamic Axial Crushing on a
Square Tube with Eight Holes Used as a Crush Initiator. International
Journal of Technology, Volume 10(5), pp. 1042–1055
Mines, R., Tsopanos, S., Shen, Y., Hasan, R., Mckown, S., 2013.
Drop Weight Impact Behaviour of Sandwich Panels with Metallic Micro Lattice
Cores. International Journal of Impact Engineering, Volume 60, pp.
120–132
Obadimu, S., Kourousis, K., 2021. Compressive Behaviour of
Additively Manufactured Lattice Structures: A Review. Aerospace, Volume
8(207), pp. 1–22
Panesar, A., Abdi, M., Hickman, D., Ashcroft, I., 2018. Strategies for
Functionally Graded Lattice Structures Derived using Topology Optimisation for Additive
Manufacturing. Additive Manufacturing, Volume 19, pp. 81–94
Park, J.-H., Park, K., 2020. Compressive Behaviour of Soft Lattice
Structures and Their Application to Functional Compliance Control. Additive
Manufacturing, Volume 33, p. 101148
Ren, H., Shen, H., Ning, J., 2020. Effect of Internal
Microstructure Distribution on Quasi-Static Compression Behaviour and Energy
Absorption of Hollow Truss Structures. Material, Volume 13(5094), pp.
1–14
Riva, L., Ginestra, P., Ceretti, E., 2021. Mechanical Characterization
and Properties of Laser-Based Powder Bed–Fused Lattice Structures: A Review. International
Journal of Advanced Manufacturing Technology, Volume 113, pp. 649–671
Santos, F., Rebelo, H., Coutinho, M., Sutherland, L., Cismasiu, C.,
Farina, I., Fraternali, F., 2021. Low Velocity Impact Response of 3D Printed
Structures Formed by Cellular. Composite Structures, Volume 256, p.
113128
Sun, Z.P., Guo, Y.B., Shim, V.P.W., 2021. Characterisation and Modeling
of Additively-Manufactured Polymeric Hybrid Lattice Structures for Energy
Absorption. International Journal of
Mechanical Sciences, Volume 191, p. 106101
Tancogne-Dejean, T., Mohr, D., 2018. Stiffness and Specific Energy
Absorption of Additively-Manufactured Metallic BCC Metamaterials Composed Of
Tapered Beams. International Journal of Mechanical Sciences, Volume 141,
pp. 101–116
Ushijima, K., Cantwell, W., Chen, D., 2013. Prediction of the
Mechanical Properties of Micro-Lattice Structures Subjected to Multi-Axial
Loading. International Journal of Mechanical Sciences, Volume 68, pp.
47–55
Ushijima, K., Cantwell, W., Mines, R., Tsopanos, S., Smith, M.,
2010. An Investigation into the Compressive Properties of Stainless Steel
Micro-Lattice Structures. Journal of Sandwich Structures & Materials,
Volume 13(3), pp. 303–329
Ye, G., Bi, H., Hu, Y., 2020. Compression behaviours of 3D printed
pyramidal lattice truss composite structures. Composite Structures,
Volume 233, p. 111706