Brittle fracture in materials with random defects

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Abstract
We study the failure properties of a defected square lattice of Born springs under uniaxial tensile strain. The springs fail completely and irreversibly once a critical strain energy is exceeded. The Born potential provides an effective bending force that yields realistic crack microstructures, which are analyzed in detail. As the defect density increases, the crack becomes increasingly ramified, even though fewer spring failures are required for complete breakdown. The failure stress and Young’s modulus approach zero as the system approaches the percolation threshold. Cumulative failure-stress distributions appear consistent with both Weibull and Duxbury-Leath forms. The size and composition of the crack (in terms of initial defects and broken springs) are analyzed as functions of defect density, lattice size, and bending constant.