Fracture toughness and crack propagation in anisotropic triangular lattices

This study investigates the fracture toughness, critical energy release rate, and crack growth resistance (R-curve) of anisotropic triangular lattices. Anisotropy is introduced by tailoring the lattice microstructure through variations in the thickness ratio $\bar{t}$ of struts, while maintaining a constant relative density. The mode I fracture response is analyzed using the finite element method, based on a boundary layer technique. The simulations demonstrate a non-monotonic dependence of the fracture toughness on $\bar{t}$, with peak values occurring at distinct thickness ratios depending on the crack orientation relative to the lattice topology. The corresponding critical energy release rate exhibits the same non-monotonic trend, but with a distinct dependence on $\bar{t}$. The crack propagation analysis reveals that anisotropy strongly affects both the crack growth resistance and the corresponding crack growth path. Specifically, when the initial crack line is perpendicular to the vertical struts, increasing $\bar{t}$ enhances resistance, and the crack tends to propagate along the initial crack line. On the other hand, when the initial crack line is parallel to the vertical struts, increasing $\bar{t}$ first leads to a reduction in both fracture toughness and crack growth resistance, accompanied by a transition from slanted propagation to penetration along the initial crack line. However, beyond a critical thickness ratio ($\bar{t}\approx 1.50$), the penetration growth persists only up to a limited distance from the initial crack tip, after which crack propagation resumes along a slanted path. This variation in the crack propagation process significantly enhances the crack growth resistance. Altogether, the results provide key insights into the fracture response of anisotropic lattices, offering practical guidelines for designing architected materials with improved toughness and controlled crack propagation.