Page 63 - MSAM-2-1

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

Table 1. Wall thickness comparison between designs and as‑fabricated specimens
Wall thickness (mm) 1 order 2 order 3 order
rd
st
nd
Designed Fabricated Designed Fabricated Designed Fabricated
rd=20% 3.110 3.17–3.27 1.610 1.60–1.83 0.840 0.85–0.89
rd=30% 4.665 4.66–4.88 2.415 2.58–2.67 1.260 1.35–1.42
rd=40% 6.220 6.16–6.32 3.220 3.22–3.43 1.680 1.75–1.93
rd: Relative density. Measurements of fabricated specimens were made using a caliper with precision of two decimal places

printing process of each layer. The extruder is expected to equations were used to calculate the effective axial
*
generate a filament line with uniform width. However, a stress (σ * yx ) and effective axial strain (ε ) in the
yx
thin print line in the beginning may widen as the nozzle y-direction (compression direction):
pressure increases. This could be more distinct when R
printing curves, which is a characteristic feature in Moore σ * yx = y , (II)
curve-inspired structures. A y
δ (III)
2.2. Quasi-static and cyclic compression tests ε * yx = L y
Uniaxial compression tests were performed using Instron’s y
universal testing machine (5900R Series), with a 30 kN load Where R is the total reaction force from the structure,
y
cell. A loading rate of 2 mm/min was applied to all testings. while A is the cross-sectional area of the whole structure
y
Unit cells were compressed up to 70% strain (displacement that is perpendicular to the y-direction; L denotes the
y
of 35 mm) from two in-plane directions. Three specimens height of the structure (length along y-direction), while
were tested for each design to ensure the reliability of δ is the total displacement experienced by the structures
y
results. Force-displacement data and real-time videos were along the y-direction.
captured and recorded from the experiment to study the For cyclic testings, two parameters were used to evaluate
responses of different structures. To further investigate the performance of the structures. First, residual strain
the energy absorption performance of the metamaterials, was measured after the first and all six loading-unloading
loading and unloading compression tests were conducted. cycles to assess the amount of plastic deformation. Second,
Herein, cyclic experiments were adopted to obtain the dissipated energy, which is referred as plastic strain energy,
structural response of low cyclic-loading events, such as was calculated by subtracting the released energy during
earthquake ; however, fatigue was not considered. Six the reloading period from the stored energy during the
[44]
cycles were applied to each specimen. Force-displacement loading period (Figure 3B) .
[46]
curves were captured to estimate energy absorption and Based on the definition of dissipated energy ( E ),
dissipated
then converted to effective stress-strain curves to evaluate it was calculated from the force-displacement curve
the residual strain.
accordingly:
SEA, which is defined as the amount of energy absorbed n
by the material per unit mass, has been widely used as a x max n
parameter to indicate the energy absorption capacity of a E stored = ∫ F ( ) x loading dx (IV)
crushed material . SEA can be calculated by integrating 0
[45]
the force-displacement curve (Figure 3A) and then divided x max
n
=
by the total mass of materials : E released ∫ F x() n unloading dx , (V)
[43]
d Fx () 0
x
SEA = ∫ d, (I) E dissipated = E stored − E released , (VI)
0 m
Where F (x) is the reaction force captured by load Where E stored is the sum of energy stored in the structure
cell during experiment, x denotes the compression during all loading cycles, E released is the sum of energy
displacement, and m is the mass of the structure. released from the structure during all unloading cycles,
To compare the performance of different designs, and n is the total number of loading and unloading cycles.
effective stress-strain curves were derived from force- To evaluate the resilience of the proposed structures
displacement curves and compared. The following toward permanent deformation and potential damage

Volume 2 Issue 1 (2023) 4 https://doi.org/10.36922/msam.53