The Anomalous Crack Growth Behaviour of an Elastic-Brittle Octet-Truss Architected Solid

Abstract

Strongly rising R-curves are observed for octet-truss architected material specimens comprising ~1 million unit cells and made from an elastic-brittle parent material. The measurements are supported by finite element (FE) calculations where the octet-truss is modelled discretely and show that the pseudo-ductility is not related to the usual toughening mechanisms such as crack bridging or crack-tip plasticity. Rather, the toughening is attributed to the three-dimensional (3D) structure of the octet-truss specimen: remarkably, no R-curve effect is observed in a quasi two-dimensional (2D) octet-truss specimen. This anomalous behaviour is clarified via FE calculations of the indentation stiffness of the octet-truss which reveal a strong indentation size effect in 3D with the stiffness decreasing with decreasing indenter size relative to the cell size of the octet-truss. In the 3D octet-truss, the size independent continuum stiffness is only attained for indenter sizes greater than about 20 unit cells while the size effect is almost absent in the quasi-2D octet-truss. The strong elastic softening in the 3D octet-truss in the presence of strain gradients gives rise to a large elastic crack-tip process zone. This in turn implies that a specimen geometry independent fracture toughness (i.e., a material property) can only be measured in specimens with large numbers of unit cells. We report a fracture mechanism map that reveals that measurements of specimen geometry independent fracture toughness can only be made in specimens with more than ~10 million unit cells. This map is also used to rationalise the measured rising R-curves in the 3D specimens with ~ 1 million unit cells. We end with a discussion on the implication of these findings for the laboratory measurement of the fracture toughness of both architected materials as well as biological cellular materials such as bone.

Keywords: architected materials, fracture toughness, Size effect, R-curves