Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation.

Figure 1

Storage modulus $G^{\prime }$ and loss modulus $G^{\prime \prime }$ as a function of angular frequency $\omega$ for $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}33$ at the reference temperature $120°\mathrm{C}$. The inset lists the values of the tube model parameters for both $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}33$ and $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}17$ at $120°\mathrm{C}$.

Figure 2

Results of filament stretching measurements. (a) Measured stress as a function of Hencky strain at different stretch rates at $120°\mathrm{C}$. For each rate the filament fractures at the end of the measurement. The inset shows the photos of one filament of $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}33$ at Hencky strain 0 and 1.5, respectively. (b) Critical stress for fracture as a function of Weissenberg number Wi. The inset shows the corresponding critical strain at fracture as a function of Wi.

Figure 3

Crack propagation in uniaxial extensional flow for $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}33$ stretched at $0.1{\mathrm{s}}^{-1}$ at $120°\mathrm{C}$. The time $t=0$ is set at the frame where the filament breaks. The minus sign in the time for other frames means it happens before the fracture. The white line in the middle is light shining through the filament. The breaking of the line around $-150\mathrm{ms}$ reveals the existence of crack 1, which is otherwise not visible before $-5.4\mathrm{ms}$ since it is on the front of the filament.

Figure 4

Crack profile and crack length at different times during crack propagation for $\mathrm{PS}\text{−}864\mathrm{k}/4\mathrm{k}\text{−}33$ stretched at $0.1{\mathrm{s}}^{-1}$ at $120°\mathrm{C}$. (a) Corresponding to crack 2 in Fig. 3. (b) Corresponding to crack 1 in Fig. 3. The black solid lines are $u(x)=a{x}^{1/2}$, and the black dashed lines are $u(x)=b{x}^{3/2}+c$, where $a$, $b$, and $c$ are constants and have been adjusted to fit the captured profiles. The gray solid lines are the local shear rates. (c) Crack length as a function of time obtained from two independent measurements. Depending on the angle of the facture facing the camera, the actual crack length may be longer than observed. Therefore, the plots in the figure are vertically shifted to get a master curve. The shift of measurements when compared to the dashed lines visible in (b) may also be due to the slight angle mismatch between the crack and the camera.