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Numerical fracture mechanics based prediction for the roughening of brittle cracks in 2D disordered solids

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Abstract

The behavior of fractures in 2D brittle disordered materials results from the competition between the microstructural disorder that roughens cracks and the material elasticity that straightens them. The experimental fracture surfaces left behind are generally scale invariant and their complex geometry are still largely unexplained. Here, this issue is addressed numerically using the boundary element method that predicts incrementally the trajectory followed by cracks in an infinite elastic medium with a heterogeneous field of fracture energy. The predicted fracture profiles are characterized using their height-height correlation function and show scale invariant properties. In particular, simulated cracks are shown to follow a random walk with roughness exponent \(\zeta = 0.5\), irrespective of the level of microstructural disorder, indicating that the crack behavior is neither persistent nor anti-persistent, but instead, that the orientation of the next propagation increment is chosen randomly, independently of the past trajectory. This behavior is then interpreted from fracture mechanics calculations that show that the restoring force emerging from elasticity that generally straightens cracks vanishes in the limit of large specimens with respect to the characteristic size of the material heterogeneity. Our findings shed light on some experimental fracture patterns recently reported and suggests an explanation for the observation of two different types of fracture morphologies in 2D disordered brittle solids.

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Notes

  1. The development of \(G(\theta )/G_\mathrm {c}(\theta ) \simeq 1 - \cos ^2(\theta ) + \varDelta a/d \, f(\theta )\) around small angles \(\theta \ll 1\) for a continuous variation of \(G_\mathrm {c}\) shows that the limit \(\varDelta a/d \rightarrow 0\) corresponds to a straight path as the crack propagation direction along which this ratio is maximal converges then to \(\theta _\mathrm {max} \rightarrow 0\).

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Authors and Affiliations

  1. Institut Jean le Rond d’Alembert (UMR 7190), CNRS - Sorbonne Université, 75005, Paris, France

    Lamine Konate, Djimédo Kondo & Laurent Ponson

  2. Institut de Technologie Nuclèaire Appliquèe Universitè Cheikh Anta Diop, 10700, Dakar, Senegal

    Lamine Konate

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  1. Lamine Konate
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  2. Djimédo Kondo
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  3. Laurent Ponson
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Correspondence to Laurent Ponson.

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Konate, L., Kondo, D. & Ponson, L. Numerical fracture mechanics based prediction for the roughening of brittle cracks in 2D disordered solids. Int J Fract 230, 225–240 (2021). https://doi.org/10.1007/s10704-021-00576-1

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