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 K_Ic of a snub-trihexagonal lattice scales linearly with relative density p. In contrast, the fracture toughness of snub-square and elongated-triangular lattices scale as p^1.5, 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 measure the asymptotic fracture toughness. This result may be useful to guide the design of future experiments.