A design protocol for failure resilient architected metamaterials
There has been a recent explosion in the development of light and strong mechanical metamaterials reporting extreme effective and functional properties. As additive manufacturing progresses to proliferate these metamaterials, their application as structural materials is ultimately limited by their tolerance to damage and defects. While significant advances have been made in reporting their stiffness and strength, material properties that enable us to define the tolerance to defects as yet remain unclear. All work to-date has a-priori assumed that a material property known as fracture toughness exists for these materials akin to usual continuum solids, without a-posteriori experimental validation. In fact, all existing experimental measurements are based on metamaterial specimens comprising only dozens to at most a few hundred unit cells where the so called “K-field” required to define an effective toughness is not established. Thus, an understanding of defect sensitivity in these metamaterials has remained unknown.
In this work, we perform a series of fracture toughness measurements (uniaxial to multiaxial loadings) coupled with in-situ X-ray CT visualization on a range of octet-truss specimens comprising up to millions of unit cells. This was combined with large-scale numerical calculations and a theoretical analysis to decipher the elusive fracture behaviour of 3D metamaterials. It is demonstrated that (i) stress intensity factor K_I is insufficient to characterize fracture and (ii) standard fracture testing protocols, established over the last 50 years, are inappropriate for such materials. We uncover the significance of T-stress (T) effects in elastic-brittle fracture of open-cell architected metamaterials. Using asymptotic analysis we extend the findings to construct fracture mechanism maps (with K_I & T) that can characterize the failure of slender-beam (relative densities less than 20%) periodic truss 3D metamaterials under arbitrary loadings. These findings led to a revision of elastic fracture mechanics and thereby the development of a general design methodology and testing protocol for mechanical metamaterials. The framework is envisioned to form the basis for fracture characterization in other discrete elastic-brittle solids where the notion of fracture toughness is known to breakdown.