Energy-based approach for failure assessment of 3D architectured materials

Abstract

3D architectured materials with features at the micro-/nano-scale can attain extreme mechanical properties, overcoming the tradeoff between lightness, strength and damage tolerance. The combination of the material size effect and the geometry (architecture) gives rise to peculiar mechanical behaviors, often found in biological systems. Despite stiffness and strength have been widely investigated for a large variety of geometries, fracture properties, such as fracture toughness, of 3D cellular materials have not been deeply studied yet. Here, we re-adapt an energy-based approach, called averaged strain energy density (ASED), to assess the failure of 3D nanolattices. An octet geometry characterizes the unit cell of the periodic cellular material adopted in this work, without loss of generality. By exploiting of preliminary experimental results on a compact tension (CT) specimen, with smallest features at the nano-scale, a finite element model is created to assess its failure (first beam to fracture) under mode 1, employing the energy criterion. The structural control volume, i.e. the volume around the notch where the strain energy is averaged, is assumed to be a portion of a square cuboid centered at the notch/crack tip, cut by the notch flanks, and with semi-length of the edge equal to the unit cell size, being the zone of highest and steepest strain energy density concentration and gradient, respectively. Based on this energy criterion, the fracture toughness is determined as a function of the relative density (ρ¯) and unit cell length (L), in agreement with the classical power-law behavior, i.e. √Lρ−d. Preliminary experimental and numerical results seem to be in agreement, however, further research is needed to face the problem of modeling the fracture of such materials.