Universality in the velocity jump in the crack propagation observed for food-wrapping films for daily use

TL;DR

This study demonstrates a clear, reproducible velocity jump in crack propagation through a everyday PVDC food-wrapping film under dynamic boundary conditions, with the jump occurring near a fixed strain $ε_c$ and speeds jumping from $V_B$ to $V_A$ by several orders of magnitude. By scaling the driving strain to the product $εL$, the authors uncover a universal master curve $V = F(εL)$ that collapses data across pulling speeds and sample heights, suggesting a small crack-tip length scale $l^*$ governs deformation. Rheology reveals a glass-transition timescale on the order of tens of milliseconds, hinting that multi-relaxation viscoelasticity and the glass transition are central to the velocity jump, extending the concept beyond single-relaxation elastomers. The findings provide a practical route to harness velocity-jump dynamics for designing tougher polymer films and offer guidance for theoretical models that incorporate multi-relaxation viscoelasticity, with potential relevance to separator materials in batteries. The work also shows that the jump and its universality persist despite real-world complexities such as edge effects and different blind painting protocols, making the phenomenon a robust tool for material design.

Abstract

The velocity jump found in the crack propagation for rubbers has been a powerful tool for developing tough rubber materials. Although it is suggested by a theory that the jump could be observed widely for viscoelastic materials, the report on a clear jump is very limited and, even in such a case, reproducibility is low, except for elastomers. Here, we use a mundane food-wrapping film as a sample and observe the crack propagation velocity with pulling the sample at a constant speed in the direction perpendicular to the crack. As a result, we find the jump occurs at a critical strain with high reproducibility. Remarkably, the plot of the crack-propagation velocity as a function of strain can be collapsed onto a master curve by an appropriate rescaling, where the master curve is found to be universal for change in the pulling speed and in the sample height. The result reveals a key parameter for the jump is the strain, suggesting the existence of a small length that governs the deformation along the crack. The present study sets limitations on future theories and opens an avenue for the velocity jump to become a tool for developing a wide variety of tough polymer-based materials.

Figures (5)

• Figure 1: (a) Experimental setup for the dynamic experiment. (b) Illustration for the long and thin tape-like area along the crack path.
• Figure 2: (a) Crack tip position $X$ vs. time $t$ before the jump at $X=X_{c}$ and $t=t_{c}$. (b) Crack tip position $\Delta X$ vs. time $\Delta T$ after the jump, where $\Delta X=X-X_{c}$ and $\Delta T=t-t_{c}$. The three sets of the data are obtained from different three samples for $U=1$ mm/s and $L=15$ mm.
• Figure 3: (a) Velocity $V$ vs. strain $\varepsilon$ for a fixed $L$, exhibiting a collapsed straight region on the log-log scale before the jump and a collapsed point just after the jump. (b) $V$ vs. $\varepsilon$ for a fixed $U$. (c) All the data in (a) and (b) on a rescaled horizontal axis $\varepsilon L$, showing $V$ is a function of $\varepsilon L$ in the straight region and at the points just before and after the jump. (d) $V$ vs. $\varepsilon L$ obtained for various parameters by a different way of painting to visualize the crack propagation: partial painting (see the text for the details).
• Figure 4: Stress vs. Strain. (a) Dependence on the stretching direction. (b) Dependence on the sample size. (c) Dependence on the stretching speed. (d) Magnified version of (c).
• Figure 5: Complex modulus and $\tan\delta$ as a function of temperature at $f=1$ and $30$ Hz.