Thermally activated crack fronts propagating in pinning disorder: simultaneous brittle/creep behavior depending on scale - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) Année : 2019

Thermally activated crack fronts propagating in pinning disorder: simultaneous brittle/creep behavior depending on scale

Résumé

We study theoretically the propagation of a crack front in mode I along an interface in a disordered elastic medium, with a numerical model considering a thermally activated rheology, toughness disorder, and long range elastic interactions. This model reproduces the large scale dynamics of the crack front position in fast or creep loading regimes, but also the small scale self-affine behavior of the front. Two different scaling laws are predicted for the front morphology, with a Hurst exponent of 0.5 at small scales, and a logarithmic scaling law at large scales, consistently with experiments. The prefactor of these scaling laws is expressed as function of the temperature, and of the quenched disorder characteristics. The cross-over between these regimes is expressed as function of the quenched disorder amplitude, is proportional to the average energy release rate, and to the inverse of temperature. This model captures as well the experimentally observed local velocity fluctuations probability distribution, with a high velocity tail $P(v) \sim v^{-2.6}$. This feature is shown to arise when the quenched disorder is sufficiently large, whereas smaller toughness fluctuations lead to a lognormal-like velocity distribution. Overall, the system is shown to obey a scaling determined by two distinct mechanisms as function of scale: namely, the large scales display fluctuations similar to an elastic line in an annealed noise excited as the average front travels through the pinning landscape, while small scales display a balance between thresholds in possible elastic forces and quenched disorder.
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Dates et versions

hal-01986645 , version 1 (18-01-2019)

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  • HAL Id : hal-01986645 , version 1

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Alain Cochard, Olivier Lengliné, Knut Jørgen Måløy, Renaud Toussaint. Thermally activated crack fronts propagating in pinning disorder: simultaneous brittle/creep behavior depending on scale. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990), 2019. ⟨hal-01986645⟩
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