Brittle fracture of three-dimensional lattice structure

Abstract

This work aims to develop a greater understanding of fracture behaviour of a three-dimensional lattice structure. Octet-truss lattice was used in this study due to its high strength to density ratio and great potential in the advanced lightweight structure applications. The fracture toughness, K IC , was found to be almost isotropic while the modulus and strength were highly dependent on the model size and lattice orientation. The converged solution for the modulus and strength were obtained when model width is large compared to cell.The modulus can be varied by 20% and the strength can be doubled when lattice orientation was changed. The validity of linear elastic fracture mechanics(LEFM) was examined on dierent model geometries including single edge notch tension(SENT), compact tension(CT), single edge notch bending(SENB) and thumbnail crack model. It shows that the LEFM can be adequately used in the structures with linear crack fronts. In the thumbnail crack model, the curved crack front generates more complexity in the structure ahead of the crack tip which results in a signicant discrepancy in measured toughness compared to the models with linear crack fronts. Moreover, great fracture performance was exhibited in the lattices, where an increase in fracture load was observed during the crack growth.

Compressive behaviours of octet-truss lattices

“…In octet-truss lattice structures, applied load is generally carried by struts under tension and compression, while the bending struts have a second order effect on lattice strength. 17 The stress states of the unit cell under compressive load according to the analytical model in Gu et al. 17 is illustrated in Figure 9, in which red, blue and grey colours respectively represent struts under tension, compression and bending-dominated conditions.…”

“…17 The stress states of the unit cell under compressive load according to the analytical model in Gu et al. 17 is illustrated in Figure 9, in which red, blue and grey colours respectively represent struts under tension, compression and bending-dominated conditions. The analytical model is an individual cell derived from the infinite lattice structure.…”

“…The actual relative density ρ¯ac can be obtained through experimental measurement by where ρlattice is the density of the lattice structure and ρmaterial the density of the material of which the lattice is made. The tensile strength of the structure can be related to the relative density ρ¯ and material failure strength σf by 17 where I is equal to X, Y, or Z, and C I is a constant depending on the structure orientations and structure dimensions.

Figure 1.Definition of lattice orientations.

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“…Recently, Gu et al 17 The orientations were defined based on the loading direction and local coordinate of the unit cell. The theoretical relative density ̅ ℎ of the lattice can be calculated using the first-order approximation:…”

“…Recently, Gu et al. 17 performed a numerical analysis to study the mechanical properties of octet-truss lattices in three different orientations. The study revealed the influence of lattice orientations on the mechanical behaviour, including modulus, strength and fracture toughness.…”