Crack Front Dynamics across a Single Heterogeneity

J. Chopin, A. Prevost, A. Boudaoud, and M. Adda-Bedia

Phys. Rev. Lett. 107, 144301 – Published 26 September 2011

Abstract

We study the spatiotemporal dynamics of a crack front propagating at the interface between a rigid substrate and an elastomer. We first characterize the kinematics of the front when the substrate is homogeneous and find that the equation of motion is intrinsically nonlinear. We then pattern the substrate with a single defect. Steady profiles of the front are well described by a standard linear theory with nonlocal elasticity, except for large slopes of the front. In contrast, this theory seems to fail in dynamical situations, i.e., when the front relaxes to its steady shape, or when the front pinches off after detachment from a defect. More generally, these results may impact the current understanding of crack fronts in heterogeneous media.

Received 25 January 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.144301

Authors & Affiliations

J. Chopin, A. Prevost, A. Boudaoud, and M. Adda-Bedia

Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France

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Vol. 107, Iss. 14 — 30 September 2011

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Images

Figure 1
Sketch of the experiment. (a) Side view. A silicon elastomer block is peeled from a patterned glass substrate by means of a translation stage imposing a deflection, $d$ . (b) Top view. The substrate can be made chemically heterogeneous. Here, a glass strip of width $2 a$ is surrounded by chromium.Reuse & Permissions
Figure 2
Creep tests for homogeneous PDMS-glass and PDMS-chromium interfaces. At $t = 0 s$ , a deflection of 7 mm is applied for the glass interface and 0.180 mm for the chromium one. (a) and (b) Crack front velocities versus time. Insets: position of the crack $l$ versus time (insets). For the glass interface (a), the velocity exhibits a well-defined power-law tail of the form $t^{- 1.3}$ . In dashed lines are shown power-law curves $t^{- 1}$ and $t^{- 1.5}$ as a guide for the eyes. For the chromium interface (b), a power-law $t^{- 1.8}$ is shown as a guide for the eye. (c) Energy release rates $G$ versus time (left $y$ axis for glass and right $y$ axis for chromium). Note the difference in scale between the two $y$ axes.Reuse & Permissions
Figure 3
The steady profile of a crack front (appearing as the bright line) in the presence of a single or a double glass strip (lighter gray areas) of width $2 a = 20 μ m$ . (a) The crack front has an infinite slope at the edge of the strip (nonlinear regime), but the tails are well fitted by Eq. (3) (dashed line). Inset: zoom on the tip of the front. (b) Interaction of the front with two parallel strips. The distance between the strips midlines is $30 μ m$ . The predicted shape of the crack front position with two strips assuming a linear superposition of the solutions of Eq. (3) (dashed line) differs significantly from the real profile.Reuse & Permissions
Figure 4
(a) Relaxation of the crack front during the first 100 s following its detachment from the glass strip. Experimental data (○) are fitted by Eq. (4) (dashed line). For clarity, fronts are shown at intervals of 20 s. (b) and (c) Fitting parameters $W$ (●), $H$ (▪), and $L$ (▴) of Eq. (4) as a function of time. $H_{m}$ and $L = 2.2$ are roughly constant whereas $W$ increases nonlinearly with time. Inset: Log-Log plot of $W$ versus $t$ .Reuse & Permissions
Figure 5
Pinch-off from a strong defect. Evolution of the size of the neck $Δ X$ as a function of $Δ t = t_{r} - t$ for different widths $2 a$ of the glass strip : 31 (●), 63 (□), 256 (▽), 511 (▵), $1020 μ m$ (⋄). $t$ is time and $t_{r}$ the instant of topological change. Insets: picture of the crack front near the end of the glass strip; all data collapse on a master curve: $Δ X / 2 a = 1.17 (Δ t / τ)^{0.47}$ , where $τ = 2 a / v$ with $v$ the mean velocity of the front evaluated from the tails.Reuse & Permissions

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