Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet

We study the interaction of two collinear cracks in polymer sheets slowly growing towards each other, when submitted to uniaxial stress at a constant loading velocity. Depending on the sample’s geometry—specifically, the initial distances $d$ between the two cracks’ axes and $L$ between the cracks’ tips—we observe different crack paths with, in particular, a regime where the cracks repel each other prior to being attracted. We show that the angle $\theta$ characterizing the amplitude of the repulsion—and specifically its evolution with $d$—depends strongly on the microscopic behavior of the material. Our results highlight the crucial role of the fracture process zone. At interaction distances larger than the process zone size, crack repulsion is controlled by the microscopic shape of the process zone tip, while at shorter distances, the overall plastic process zone screens the repulsion interaction.

Figure 1

(a) Schematic representation of the experiments. A plastic sheet with two initial notches separated by vertical $d$ and horizontal $L$ distances is submitted to a mode I loading at a constant imposed velocity. We follow the slow interacting growth of the two cracks, with for instance (b) $d=2\mathrm{cm}$ and $L=4\mathrm{cm}$, in PC samples (close-up), with photoelasticity; or (c) PET Mylar® sheets (close-up) at two different times.

Figure 2

Crack pair trajectories for various experimental conditions obtained with PET Mylar®. We plot in (a) $\mathrm{\Delta }y-\mathrm{\Delta }{y}_t$ vs $\mathrm{\Delta }X-\mathrm{\Delta }{X}_t$ for $d=2\mathrm{cm}$, and various $L$. In (b), we represent $\mathrm{\Delta }Y-d$ vs $\mathrm{\Delta }X$ for $L=4\mathrm{cm}$ and various $d$, as well as for two different PET samples at $d=0\mathrm{cm}$ (inset).

Figure 3

Repulsion angle $\theta$ vs $d$ for a given $L=4\mathrm{cm}$ (PET) or $L=6\mathrm{cm}$ (PC), for different types of plastic sheets. Each point represents the estimated slope for one experiment, with its fitting residual as an error bar. Lines are guides for the eye.