Abstract
Interest is growing in the wide variety of fractal objects1 found in nature; these include electric discharge patterns2, infinite percolation clusters3,4, branched polymers5,6 and surface irregularities7. The question of whether surface cracks, such as those that occur in protective coatings, also lead to fractal-like structures is another problem of great interest. Here we study this question theoretically, making use of a molecular model for material failure, introduced previously8, which is based on the kinetic theory of fracture9,10. The model is applied to a two-dimensional surface stretched in one direction, and our results show that the cracks developing in the material exhibit properties similar to each other, at least at the molecular level. For a wide range of values of the elastic constants of the material, the fractal dimensionality is found to have a universal value, D = 1.27 ± 0.02.
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Termonia, Y., Meakin, P. Formation of fractal cracks in a kinetic fracture model. Nature 320, 429–431 (1986). https://doi.org/10.1038/320429a0
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DOI: https://doi.org/10.1038/320429a0
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