The Young’s modulus values and strength values are listed in Table. 2.
The monotonic Young’s modulus and strength values are calculated from
the linear region of the curves shown in Fig.5a. The cyclic Youngs’
modulus is calculated from the slope of the unloading part of the curve
shown Fig. 5b. The cyclic modulus values are higher than the monotonic
values indicating that the samples reach stabilization after the first
loading cycle. Comparing the values with respect to the topology, the
effect of the presence of vertical struts is clearly evident: cubic
regular samples had the highest Young’s modulus followed by cubic
irregular, trabecular and star-based structures. Cross-based structures
with only oblique struts had the lowest stiffness. Similar conclusions
can be made on the yield strength and maximum compressive strength
values.
Further considerations can be made by observing how the irregularity
affects the outcomes. The irregularity decreases the stiffness and
strength by introducing bending dominated behavior in the structure.
This effect is highly pronounced in structures having vertical struts.
In cube-based structures, a decreases of 38% in cyclic modulus, 36% in
yield stress and 24% in maximum stress was observed. In star-based
structures, a decreases of 28% in cyclic modulus, 25% in yield stress
and 21% in maximum stress was observed. In cross based structures, the
irregularity had least effect with only 4-6% decrease in cyclic modulus
and stress values. The modulus and the stress values of trabecular
structures were similar to those of cubic irregular and star regular
samples. The random orientation of the struts seems to help in terms of
an isotropic distribution of load among struts.
Fatigue
test
The S-N curves obtained from the fatigue tests for all the specimens are
compared in Fig.7. The curve fitting parameters and the scatter in the
fatigue data are as indicated in Table 3. The S-N curves clearly
indicate the effect of cell topology on the fatigue behavior. As shown
in Fig. 7a, cubic regular specimens represented exceptional fatigue
properties and maintained their structural integrity up to
107 cycles under any applied load below
0.8σy. During the experimental tests, buckling mechanism
dominated the failure of cubic regular structures under compression. In
this case, the absence of any sort of bending mechanism retards the
fatigue crack growth36. As a consequence, an expected
curve is obtained by increasing the load slightly above
0.8σy. Similar behavior that none of the specimens
failed for all ranges of porosity31, was also reported
by Yavari et al. for cubic cellular structures . By contrast, the S-N
curve of cubic irregular specimens in Fig.7a indicates significantly
lower fatigue strength. The effect of displacement of the nodes to
induce irregularity was clearly seen and it was much more significant
than the effect seen in the quasi-static compression test, where a
decrease of only 24-36% of strength values was observed. The fatigue
crack starts to grow at a relatively early stage because the randomly
displaced nodes and the inclined struts introduce bending moments in the
structure. Similar to the cubic specimens, star shaped and cross shaped
specimens show lower fatigue strengths due to the irregularity, as shown
in Fig. 7b and 7c. Despite the presence of vertical struts in star
regular specimen, an early fatigue failure was observed when compared to
the cubic specimens due to the oblique struts which induce bending
moment in the specimen. Generally, a clear reduction of fatigue strength
can be seen for all irregular topologies. Even though the irregularity
caused a decrease of only 21-25% in the static strength values as
previously evidenced in the compression test, the decrease of the S-N
data points is much higher, increasing up to 80% in the the high-cycle
part of the plot. However, a smaller difference between the regular and
irregular topologies was observed for cross structures. Interstingly,
also in static compression test the differences between regular and
irregular cross-based structures were quite low. The fatigue behavior of
trabecular structure Fig.7d was inferior to the regular cubic and star
structures, but it was superior to the irregular cubic and star
structures. The advantages of the quasi-isotropic structure induced by
the randomization are more evident in this fatigue test configuration
rather than in the static compression test . The S-N curves of cross
based specimens show that the specimens were not able to sustain more
than 106 cycles even at the lower range of the applied
load. Therefore, the fatigue strength of all the structures were
calculated at 106 cycles and is reported in Table. 4