Fig.2 Spectro microscopy images for strut thickness measurement (a) Cubic Irregular (b) Star Regular with thickness measurement in μm.

Quasi-static and fatigue testing

The mechanical tests were carried out under two loading conditions, monotonic quasi-static and cyclic. They were carried out according to the standard ISO 13314:2011 for metallic foams49. Both tests were carried out at room temperature using an INSTRON universal testing machine with a load capacity of 100kN. The displacement was measured using an Instron LVDT. A constant crosshead speed of 1mm/min and a data sampling frequency of 1kHz was employed. For each configuration, one specimen was tested under monotonic compression condition and four specimens under cyclic condition.
The stress-strain curve obtained from the monotonic testing condition is then used to acquire the monotonic Young’s modulus (Em), 0.2% offset yield strength (σy) and the maximum compressive strength (σmc). Cyclic tests were performed to obtain the cyclic Young’s modulus (Ec) after stabilization of the stress-strain response. The specimens were loaded between 20-70% of the yield load obtained from the monotonic testing condition using a triangular shape wave for five cycles.
High cycle compression-compression fatigue testing was carried out for a minimum of 12 specimens for each topology. RUMUL resonating fatigue test machine was used with an R-ratio of 0.1 in compression. The applied maximum load was chosen in the range 0.1-0.8 yield load to obtain the S-N curves36,50. It was verified that the contact surfaces of the specimens were flat with no irregularities. A frequency drop of 1 Hz during the test was considered as an indicator of fatigue failure in the specimens, and the number of cycles at that specific moment was recorded as fatigue life. The S-N curve was subsequently obtained by fitting the data points using a curve fitting expressed by equation 2, where σmax is the maximum stress, Nf is the number of cycles to failure, and C1, C2, m are the curve fitting parameters. The run-out condition for the specimens was set as 107 cycles and the fatigue strength of the specimens was calculated at 106 cycles using the S-N curves. The scatter of the fatigue data (S2) is calculated by equation 3, where σmax-i is the ithmaximum stress, σ’max-i is the ithestimated maximum stress, n is the number of data points and p is the number of parameters in equation 2 and the standard deviation of the fatigue strength was calculated as indicated in the reference18. Investigation of the fractured surface was carried out by using a JOEL JSM-IT300LV scanning electron microscope.
\(\sigma\max{=C1+}\frac{C2}{(Nf)m}\ \)………… (2)
\(S2=\ \frac{\sum_{i=1}^{n}{(\sigma max-i-\sigma^{{}^{\prime}}max-i)2}}{n-p}\)……………(3)
To obtain the deformation mechanism and the crack propagation planes characterizing any cellular structure considered herein, some dedicated fatigue tests were carried out at a frequency of 5Hz using an MTS 809 Axial/Torsional test system with a load capacity of 100 kN. To evaluate the failure sequence during the fatigue loading, a high speed camera with a capturing frequency of 30 Hz was used to record the whole duration of the fatigue tests. The frames from the captured video have been indicated in the results and discussion section.