This work investigates the effect of material dispersion on the tensile strength of brittle diamond lattice structure. In actual lattice structures fabricated by additive manufacturing, the dispersion of strength comes from microscale defect, geometric deviation and manufacture-induced anisotropy. The weakening of ultimate failure strength due to material dispersion cannot be predicted by most existing theoretical models, because they assume homogeneous and determinate mechanical properties of the lattice structure. In this paper, we employ diamond lattice structure made from brittle material as a typical example, and its tensile behavior is numerically investigated by incorporating the Gaussian distribution of strut strength. Inspired by the simulation results, a stochastic theoretical model is developed to predict the deformation and failure of diamond lattice structure with material dispersion. This model captures the fact that weaker struts break first even if the whole structure can still bear load. With the continuous increase of stress, these broken struts accumulate into continuous cracks, and ultimate failure occurs when the energy release rate of the initiated crack surpasses the intrinsic fracture toughness of the lattice structure. This research supplements stochastic feature into classical theories, and improves the understanding of potential strengthening and toughening designs for lattice structures.

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