### Abstract

We investigate by means of computer simulations the effect of structural disorder on the statistics of cracking for a thin layer of material under uniform and isotropic drying. For this purpose, the layer is discretized into a triangular lattice of springs with a slightly randomized arrangement. The drying process is captured by reducing the natural length of all springs by the same factor, and the amount of quenched disorder is controlled by varying the width ξ of the distribution of the random breaking thresholds for the springs. Once a spring breaks, the redistribution of the load may trigger an avalanche of breaks, not necessarily as part of the same crack. Our computer simulations revealed that the system exhibits a phase transition with the amount of disorder as control parameter: at low disorders, the breaking process is dominated by a macroscopic crack at the beginning, and the size distribution of the subsequent breaking avalanches shows an exponential form. At high disorders, the fracturing proceeds in small-sized avalanches with an exponential distribution, generating a large number of microcracks, which eventually merge and break the layer. Between both phases, a sharp transition occurs at a critical amount of disorder ξ_{c}=0.40±0.01, where the avalanche size distribution becomes a power law with exponent τ=2.6±0.08, in agreement with the mean-field value τ=5/2 of the fiber bundle model. Moreover, good quality data collapses from the finite-size scaling analysis show that the average value of the largest burst Δ_{max} can be identified as the order parameter, with β/ν=1.4 and 1/ν1.0, and that the average ratio m _{2}/m_{1} of the second m_{2} and first moments m _{1} of the avalanche size distribution shows similar behavior to the susceptibility of a continuous transition, with γ/ν=1, 1/ν0.9. These results suggest that the disorder-induced transition of the breakup of thin layers is analogous to a continuous phase transition.

Original language | English |
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Article number | 041114 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 84 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 11 2011 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*84*(4), [041114]. https://doi.org/10.1103/PhysRevE.84.041114