Page 72 - MSAM-2-1

Materials Science in Additive Manufacturing Energy absorption of Moore’s thin-walled structures

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Table 3. Specific energy absorption for the 4 order for 4 order structures. However, the SEA in LD1 was more
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structures subjected to quasi‑static compressive loadings sensitive to increment in relative density compared to LD2.
By comparing the values in Table 3 and Figure 11, it could
SEA (J/kg) 4 order structure be extrapolated that SEA decreases with the increase in
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Loading direction 1 Loading direction 2 fractal hierarchy after the 2 order. The compliance feature
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rd=20% 67.05 64.77 and snap-in instability are more pronounced in higher
rd=30% 321.94 211.88 orders, and the strength of the structures is sacrificed.
rd=40% 491.68 339.08 Therefore, the energy absorption capacities are reduced for
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rd: relative density high order structures (higher than the 2 order).
4. Conclusions
3.5. Parametric study
A parametric study using FE simulation was conducted This paper presents a series of thin-walled structures
on 4 order structures with different relative densities inspired by Moore space-filling curves. Nine designs,
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to further explore the influences of fractal hierarchy and featuring three hierarchies with three relative densities, that
relative density on structural responses. To compare is, 20%, 30%, and 40%, were proposed and investigated.
the responses of the 4 order structures with the 1 , The FFF 3D printing technology was used to manufacture
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2 , and 3 order structures, the effective stress-strain the samples with carbon fiber-reinforced nylon. Both
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curves of the 3 order structures were used as references quasi-static and loading-unloading compression tests were
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(Figure 13A and B). As revealed in Figure 13A and B (left conducted to obtain and analyze the mechanical responses
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panels), the 4 order structures yielded more compliant and energy absorption capacity of the proposed structures.
behaviors than the 3 order structures at any given relative Simulations were also performed to further elaborate the
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density in both LD1 and LD2. The increase by one fractal mechanical behaviors that were not observed from the
order led to quadruple complexity and meandering features experiment, that is, stress distribution. Herein, several
in the cross-sectional configuration. The large number of conclusions were drawn.
curved segments gave rise to more snap-in instability and (i) The space-filling feature of Moore curves offered
structural compliance, which were also manifested in more great compliance to the thin-walled structures. All
serrated stress-strain curves of the 4 order structures. the fractal structures exhibited high level of flexibility,
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Figure 13A and B (right panels) shows clearer effective which could provide great potential for energy
stress-strain curves of the 4 order structures, while absorbing device with large strain endurance before
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Figure 13C and D displays the structural deformations failure. Fractal hierarchy was positively related to
of the 4 order structures under compression from compliance, while relative density was the opposite.
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LD1 (rd = 20%) and LD2 (rd = 30%), respectively. With (ii) The meandering pattern of Moore space-filling curves
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the increase in relative density, the 4 order structure and the smooth geometry design enabled the snap-in
experienced higher stress in both in-plane directions due of thin-walled structures. A certain degree of such
to its thicker wall-thickness. The drastic stress drops were instability reduced the stress within the structures,
created by the multiple simultaneous snap-ins (see 20% enhancing the energy absorption capacity. The
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strain in Figure 13C and D). A plateau phase (Figure 13B 2 order structures outperformed the 1 , 3 , and
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[right panel]) in the effective stress-strain curves at a 4 order structures in absorbing energy.
strain of 40% after the stress jump could be observed for (iii) During quasi-static compression test, the SEA
all 4 order structures in LD2. This could be explained by was relatively higher when subjected to LD2 than
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the structural deformation in Figure 13D. After the 30% when subjected to LD1 due to the cross-sectional
strain, both sides of the structure expanded outward in configuration and snap-in behavior.
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a transverse direction. The snap-ins along the side edges (iv) In cyclic loading tests, the 2 order structure exhibited
eventually unlocked and slid further outward, resulting better resilience. Smaller energy dissipation ratio and
in a long plateau phase. However, this was not observed less residual strain indicated the promising ability
in LD1 as only flat surface contacts, without snap-ins, of the 2 order structure to resist deformation and
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occurred along the longitudinal edges (Figure 13C). damage from external loadings.
Table 3 summarizes the corresponding SEA for the Overall, the proposed designs inspired by Moore space-
4 order structures under different loading directions. filling curves in the present study open a new avenue for
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Consistent with the results obtained from the first three further research into the field of lightweight structures
orders, SEA has a positive relationship with relative density for energy absorption. The combination of thin-walled

Volume 2 Issue 1 (2023) 13 https://doi.org/10.36922/msam.53