The defect sensitivity of brittle truss-based metamaterials

Abstract

Architected strut-based metamaterials fabricated via three-dimensional printing exhibit a wide range of geometric and material heterogeneity, including variations in strut size, surface roughness, embedded micro-cracks and disconnected struts. The locations and severity of these defects are highly variable; combined with the complexity of the structure itself, it is exceedingly difficult to identify critical defects that limit performance and inform qualification protocols. To address this challenge, we consider the impact of distributions of defects for various strut-based lattice topologies. The role of defects is analyzed using Weibull distributions of strut failure strains. We relate the statistical distributions of strut properties to macroscopic stress-strain performance, using high through-put finite element predictions in thousands of virtual tests. Increasing the prevalence of defects decreases macroscopic strength; however, this has the complementary effect of introducing apparent ductility, i.e. load capacity even after the onset of strut failures. Hence, there is a trade-off between achieving high strength and gradual loss of stiffness that is desirable for thermal loading or lattice cores. Predictions of average strength as a function of Weibull modulus provide knock-down factors relative to the defect-free strength. In turn, these clearly identify quantitative processing targets to mitigate the impact of defects.

Keywords

• Weibull statistics
• Truss lattice
• Brittle fracture
• Defect sensitivity