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Statistical aspects in crack growth phenomena: how the fluctuations reveal the failure mechanisms

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Abstract

Material failure often gives rise to strong fluctuations that reflect on the rough trajectory followed by cracks and on their intermittent dynamics. Deciphering these fluctuations is a major challenge as they reveal how cracks interact with the material microstructure. Here, we illustrate through recent studies how the statistical properties of these fluctuations shed light on the elementary failure mechanisms taking place at the microstructure scale. The implications of these findings in terms of material characterization and failure analysis are discussed and some promising directions for future investigations are presented.

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Notes

  1. The principal value PV \(\int \) in Eq. (2) ensures the convergence of the integral.

  2. The constant \(\varOmega _\epsilon \) involved in Eq. (9) is chosen such that the average of \(\omega (\mathbf {x})\) over all \(\mathbf {x}\) is zero.

  3. The actual decomposition of the height variation computed as a scale \(\delta r\) into the sum of height variations computed at a finer scale \(\epsilon = \delta r/n\) where n is an integer writes as \(\delta h(\mathbf {x},\delta \mathbf {x}) = h(\mathbf {x} + \delta \mathbf {x}) - h(\mathbf {x}) = \sum \nolimits _{k=1}^{n} h(\mathbf {x} + \frac{k}{n} \delta \mathbf {x}) - h\left( \mathbf {x} + \frac{k-1}{n} \delta \mathbf {x}\right) = \sum \nolimits _{k=1}^{n} \delta h\left( \mathbf {x} + \frac{k-1}{n} \delta \mathbf {x}, \frac{\delta \mathbf {x}}{n}\right) \).

  4. Note however that the idea of Mandelbrot et al. (1984) was to establish a correlation of the material toughness with the roughness exponent, and not with a crossover length scale between two self-affine regimes as suggested by these recent studies.

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Acknowledgments

The author would like to acknowledge his colleagues Daniel Bonamy, Jean-Philippe Bouchaud, Julien Chopin, Angelo Simone and Stephane Vernède for their contributions to this work and thank Elisabeth Bouchaud and Jean-Baptiste Leblond for their invaluable support.

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

    Laurent Ponson

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  1. Laurent Ponson
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Correspondence to Laurent Ponson.

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Ponson, L. Statistical aspects in crack growth phenomena: how the fluctuations reveal the failure mechanisms. Int J Fract 201, 11–27 (2016). https://doi.org/10.1007/s10704-016-0117-7

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