This work focuses on the fracture mechanics of lightweight 2D lattices made of a brittle parent solid. In contrast to traditional fracture mechanics of monolithic solids, where the stress and displacement fields are described by the stress intensity factors, defining the corresponding fields in lattices remains an open challenge. In this regime, classical continuum approaches might not be valid due to inhomogeneous deformations that depend on the lattice topology and number of cells in the domain. The complexity of the microstructure can strongly alter the stress behavior ahead of an existing crack as well as its propagation path under external loads. Here we propose an energy-based method that combines experiments, modeling and theory in order to define and predict the fracture properties of lattice materials. Our framework involves establishing the crack profile under given macroscopic loads and calculating the associated strain energies for the cracked and intact lattice. The energy release rate for the lattice is then formulated as a function of loading condition, crack length and base material properties. The fracture energy is calculated experimentally using tensile tests to failure of cracked specimens with different crack lengths, in a similar manner to tearing experiments in polymers performed by Rivlin and Thomas. We then employ Griffith’s energy balance criterion to predict macroscopic failure stress and estimate the lattice toughness. Two typical in-plane isotropic lattices, triangular lattice and honeycomb, are employed to illustrate the framework. Under uniaxial tensile loading condition, the stretching dominated triangular lattice shows a horizontal crack propagation path similar to the monolithic solids, while the bending dominated honeycomb exhibits an inclined crack propagation path. The crack profile in the triangular lattice is fully contributed by crack opening, while the crack profile in the honeycomb is a combination of crack opening and crack sliding. The failure of the critical ligament ahead of the crack in the triangular lattice is mainly caused by tension, while the failure of the critical ligament ahead of the crack in the honeycomb is overwhelmingly generated by bending. The energy release rate and fracture energy in triangular lattice and honeycomb are connected by Griffith’s energy balance, and hence the fracture properties of the lattice materials are obtained. This energy-based methodology gives a favorable prediction of the macroscopic critical stress and remains accurate even for small cracks. The fracture toughness obtained by this framework shows a reasonable relationship with the relative density of the lattice as well.

Energy-Based Fracture Mechanics of 2d Lattices

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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