The fracture toughness of planar lattices: Imperfection sensitivity

The imperfection sensitivity of in-plane modulus and fracture toughness is explored for five morphologies of 2D lattice: the isotropic triangular, hexagonal and Kagome lattices, and the orthotropic 0/90∘0/90∘ and ±45∘±45∘ square lattices. The elastic lattices fail when the maximum local tensile stress at any point attains the tensile strength of the solid. The assumed imperfection comprises a random dispersion of the joint position from that of the perfect lattice. Finite element simulations reveal that the knockdown in stiffness and toughness are sensitive to the type of lattice: the Kagome and square lattices are the most imperfection sensitive. Analytical models are developed for the dependence of modes I and II fracture toughness of the 0/90∘0/90∘ and ±45∘±45∘ lattices upon relative density. These models explain why the mode II fracture toughness of the 0/90∘0/90∘ lattice has an unusual functional dependence upon relative density.