A Novel Lattice Structure for Enhanced Crush Energy Absorption

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

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, L_c = 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  before joining a corner prism (i.e., four prisms from neighboring unit cells make a cube of 4 mm X 4 mm X 4 mm). The crossing points between trusses were made into smooth bends (see Figure 2(c)) instead of sharp corners to reduce stress concentration.

        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 (210^oC), 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

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

Specific energy absorption (SEA) (in unit kJ/kg or J/g) and the dimensionless crush force efficiencies (CFE) are two metrics of particular interest in this study, as defined in Equations (1) and (2).

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), M_m is the crushed mass, F_m is the mean crush load (i.e., EA divided by crush length in unit N) and F_max 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