Discrepancy between Subcritical and Fast Rupture Roughness: A Cumulant Analysis

Rough crack fronts in a sheet of paper, obtained during a creep experiment, do not follow true scaling laws. Local roughness exponents are estimated using the first order cumulant, a quantity recently introduced in the turbulence literature [J. Delour, J. F. Muzy, and A. Arneodo, Eur. Phys. J. B 23, 243 (2001)]. Using a large data set (102 fronts), we find a significant difference in local roughness between the slow (subcritical) and the fast growth regime.

Figure 1

Digitized post mortem sample and corresponding extracted front showing three stages: (a) initial crack ($L_i=2\mathrm{cm}$), (b) subcritical growth, (c) fast growth.

Figure 2

(a) ${log}_{10}{M}_1$ and (b) $C_1/\ln (10)$ versus scale calculated by the increments method for five different couples ($F$, $L_i$) during fast (slow in inset) crack growth.

Figure 3

(a),(b): $M_1$ and $M_2$ for slow (circles) and fast (squares) crack growth; (c),(d): Corresponding local slope. The error bars are determined as statistical errors of the mean ($\equiv$ standard deviation $/\sqrt{N}$ with $N=102$).

Figure 4

(a),(b): $C_1$ and $C_2$ versus scale with statistical error bars. In (b), the horizontal solid line corresponds to a signal with Gaussian statistics. (c),(d): Corresponding local slope of cumulants. Error bars give the statistical error of the mean.