Wave induced fracture of a sea ice analog

Abstract

We study at the laboratory scale the rupture of thin floating sheets made of a brittle material under a wave-induced mechanical forcing. We show that the rupture occurs where the curvature is maximum and the break-up threshold strongly depends on the wave properties. We observe that the critical stress for fracture depends on the forcing wavelength. Hence our observations are incompatible with a critical stress criterion for fracture. Instead, our measurements can be rationalized as an energy criterion: a fracture propagates when the material surface energy is lower than the released elastic energy, which depends on the forcing geometry. In light of these findings, it may be worthwhile to revisit current numerical models of sea ice fracture by ocean waves.

Figures (4)

• Figure 1: a) Sketch of the experimental set-up, showing the varnish layer and the one dimensional profilometry system. b) Experimental measurements of the dispersion relation of surface waves propagating under a varnish layer of thickness $h = 158 \pm 22~\mu$m (blue circles) obtained from a single experiment. The gravito-capillary dispersion relation (black dashed line)is superimposed. The experimental data points lie on the flexural branch, $\omega^2 \sim k^5$.
• Figure 2: a) 3 Photographies issued from the fracture of a single varnish sheet ($h \simeq 150~\mu$m) by propagative waves ($f = 3.33~$Hz, $A = 6.7~$mm and $\lambda = 14~$cm), after 12, 105 and 203 periods. 2)b) Photography of a varnish layer after $307$ periods with $\lambda = 27~$cm, $A = 5.9~$mm, $f=2.397~$Hz and $h = 90 \pm 13~\mu$m. The varnish has broken on the anti-nodes of the waves. c) Schematical representation of the sheet geometry near a fracture tip. A planar, non-linear wave locally induces a curvature on a characteristic length $L_{\kappa}$ in the transverse direction. For a large enough amplitude, a fracture of length $L_{crack}$ propagates along the wave crest/trough.
• Figure 3: a) Crack propagation in a varnish layer of thickness $h = 57\pm8~\mu$m for waves ($\lambda=43.12~$cm) of increasing amplitude (images 1,2 and 3), respectively $A=0.96/1.18/1.34~$cm. b) Crack length $L_{crack}$ as a function of the wave amplitude $A$ corresponding to the experiment of [Fig. \ref{['fig:3']}a)]. A linear fit of the experimental data (red line) gives the threshold amplitude for break-up $A_c = 1.01~$cm corresponding to $L_{crack}=0$. c) Wave amplitude threshold $A_c$ as a function of the wavelength $\lambda$ for different varnish layers, showing a linear relationship in a log-log scale. The varnish layer breaks in the non-linear wave regime of propagation, since $A_c k \simeq 0.16$.
• Figure 4: a) Wave profiles near the maximum of curvature for different wavelength. The normalized relative elevation $\eta-\eta_{min}/(A_{max}-\eta_{min})$ is plotted as a function of the position $x$ in unit of $\lambda$. The wavelength varies from $6.2$ to $54.1$cm. The average $L_{\kappa}$, the half width at maximum curvature, is showed with a blue circle, highlighting the auto-similarity of the wave profiles as well as their non linearity. b) Half width of max curvature $L_{\kappa}$ as a function of the wavelength $\lambda$ for the closest wave profile to the threshold. It shows a linear relationship $L_{\kappa} = \alpha \lambda$, with $\alpha = 0.079\pm 0.004$. c) Curvature threshold $\kappa_c$ for fracture as a function of the wavelength $\lambda$, compatible with $\kappa_c = \beta \lambda^{-1/2}$ with $\beta = 5.82\pm0.6$ m$^{-1/2}$.