Fracture toughness of semi-regular lattices

Abstract

Previous studies have shown that the kagome lattice has a remarkably high fracture toughness. This architecture is one of eight semi-regular tessellations, and this work aims to quantify the toughness of three other unexplored semi-regular lattices: the snub-trihexagonal, snub-square and elongated-triangular lattices. Their mode I fracture toughness was obtained with finite element simulations, using the boundary layer technique. These simulations showed that the fracture toughness KIc of a snub-trihexagonal lattice scales linearly with relative density ρ̄. In contrast, the fracture toughness of snub-square and elongated-triangular lattices scale as ρ̄1.5, an exponent different from other prismatic lattices reported in the literature. These numerical results were then compared with fracture toughness tests performed on Compact Tension specimens made from a ductile polymer and produced by additive manufacturing. The numerical and experimental results were in excellent agreement, indicating that our samples had a sufficiently large number of unit cells to accurately measure the fracture toughness. This result may be useful to guide the design of future experiments.