On brittle fracture of two-dimensional lattices with material anisotropies

For the first time, this paper proposes a multiscale computational approach to investigate mixed-mode I/II fracture in two-dimensional lattices containing material anisotropies which find their applications in additive manufacturing of cellular structures. The layer-by-layer fabrication of lattices produced by the additive manufacturing techniques causes material anisotropies corresponding to the build orientation. Such material anisotropies, together with the cell topology, affect the fracture behavior of lattice components under various mechanical loading. The effective macroscopic elastic properties of periodic lattices obtained via numerical homogenization are fed into a continuum-based fracture criterion to obtain crack path and onset of fracture under mixed-mode I/II conditions. Different cell topologies are considered, and the predictions are compared with the results obtained directly by the finite element analysis. The results of this work can pave the way toward further understanding, and eventually, optimizing fracture toughness of additively manufactured lattices against various loading profiles.