The extended scaling laws of the mechanical properties of additively manufactured body-centered cubic lattice structures under large compressive strains

Additively manufactured lattice structures are porous light-weight structures with mechanical properties that are dictated both from the topology and the parent material properties. When printed from metals, these structures can withstand large continuous plastic deformation. In this paper, we focus on body-centered cubic (BCC) lattice structures under compression up to large deformation strains, and we propose relations between the slenderness ratio of struts and the following mechanical properties: Young's modulus, yield strength, hardening rate of the structure and the densification strain. We perform a systematic study using finite element modelling (FEM) to find how both material properties and lattice structures are affecting the effective mechanical properties of BCC lattice structures under compression. Based on this analysis we propose the scaling laws of the mechanical properties. The scaling laws can be explained as an extension of the Gibson-Ashby power law relations for benddominated structures with non-slender beams. We also discuss how rounding the connections between the struts using fillets affects the scaling laws. We demonstrate the scaling laws in the analysis of experimental results, showing the accuracy and limitations of the scaling laws in predicting the mechanical properties, with an emphasis on large deformations. In the analysis, we use experimental values published in literature, and we also present here experimental results of lattice structures printed from Inconel 718.