Fig.4 (a) Normalized S-N curve with yield stress (b) Normalized S-N curve with Young’s modulus for all samples
Previous studies have shown that the normalized S-N curve for structures with the same topology and varying porosity fall into a single line. The effect of material is also a major factor while considering the normalized S-N curves as indicated by Ahmadi et al.37. In the current study, the normalized S-N curves were obtained by using the yield strength as shown in Fig. 9a and by using cyclic Young’s modulus as shown in Fig. 9b. The normalized curves of Fig.9a indicated that the three irregular configuration structures were grouped together with the trabecular structure and the purely bending dominated cross regular structure. The star regular curve was above the earlier mentioned bending dominated structures, and the cubic regular structures, purely stretching dominated, have the highest fatigue strength. Similar behavior in the normalized S-N curve was observed when comparing BCC, SC-BCC and FCC structures with simple cubic (SC) structure by Peng et al.55. The normalized S-N curve shown in Fig. 9b indicates that the fatigue curve of star regular and cross regular overlap with each other. While, the irregular and trabecular specimens except cross irregular have a certain overlap at the lower end of the graph. This clearly indicated the effect of irregularity in the structure leading to a decrease in the fatigue strength.

Fracture plane and Fracture surface

The fatigue fracture planes for all the topologies are shown in Fig. 10. The images have been captured from the video recorded during the compression-compression fatigue test carried out with increasing load. The fracture planes indicate the effect of topology on the failure mechanism. Cubic irregular structures were found to fail mostly due to the buckling of vertical struts in the first two layers. The failure mechanism in other topologies indicates shear bands. In star regular and cross irregular structures, the specimens failed in one plane. In cross regular structure, the failure initiated with a shear band at exactly +45°, followed by complete compression of all the struts forming a barrel shape. In case of star irregular structure, multiple shear bands were observed at both +30° and -30° planes. In trabecular structures, the fracture was initiated at multiple locations leading to failure bands along more than two planes. This kind of failure supports the idea that a random distribution of struts is able to decelerate the crack propagation as observed on the frequency plot. The images also seem to indicate that the failure initiated at the junctions. This matter was further analyzed by means of SEM observations.