Toughening Effect of Strain-Induced Crystallites in Natural Rubber

We study fracture propagation in stretched natural rubber sheets. Experimental results in specimens stretched less than 3.8 times show a monotonic increase in the crack speed with stretch and can be explained by a numerical model based on neo-Hookean theory and Kelvin dissipation. In specimens stretched more than 3.8 times, strain-induced crystallites act as reinforcing and toughening fillers and significantly increase fracture resistance, like nanostructures in other polymeric or biological materials. Consequently, as we increase the amount of stretch, fractures travel slower and slower, and eventually halt altogether.

Figure 1

Top panels: fracture speed as a function of the stored elastic energy $E$ (a); and of the stretch ratio ${\lambda }_y$ (b). In both panels, the symbols correspond to experimental data: △, ⋄, and ▽ represent $h=17.8$, 10.2, and 5.1 cm specimens, respectively. The dashed lines represent results from numerical simulations. Bottom panels: instantaneous particle velocity fields overlayed on images of three steadily propagating fractures in $h=17.8\mathrm{cm}$ specimens: (c) ${\lambda }_y=1.5$ and $V_c=8.3\mathrm{m}/\mathrm{s}$; (d) ${\lambda }_y=3.1$ and $V_c=25.6\mathrm{m}/\mathrm{s}$; (e) ${\lambda }_y=4.35$ and $V_c=8.7\mathrm{m}/\mathrm{s}$. Fractures propagate to the right, and the black regions are the actual opening. Random dots are marked on the rubber for particle velocity measurements. The translucent color layer is coded according to the vertical component of the particle velocity. Color scales are different in each panel. Arrows are velocity vectors. We note that the particle motions in regions very close to the fracture tip are not well resolved in our experiments, especially in the case of ${\lambda }_y=3.1$.

Figure 2

Photoelastic picture of a stationary crack (a) and a propagating crack (b). The stretch ratio in (a) is ${\lambda }_y=5.45$ and the orthogonal lines, drawn before cutting, are originally separated by 1 cm. In (b), crack propagates at $7.8\mathrm{m}/\mathrm{s}$ and the prestretch is ${\lambda }_y=4.25$. A regular fluorescent tube and a flash lamp are used in (a) and (b), respectively, as the light source. Colors in (a) and (b) correspond to local orientation of molecules, which is determined by the stress state. The dark corners in (b) on the right side are artifacts of illumination.

Figure 3

Normalized scattering intensity from the crystalline phase, estimated from x-ray diffraction experiments, as a function of stretch ratio ${\lambda }_y$ at $24°\mathrm{C}$. In the inset, x-ray diffraction data, measured by a Scintag diffractometer with a copper source, are shown for five stretch ratios, which are color coded according to the symbols in main frame. A broad amorphous halo exists in all specimen. The narrow peaks at 12.5° and 18.7° are due to talc mineral fillers in the rubber. A peak emerges at $2\theta =20.7$ at ${\lambda }_y=3$, which is the (210) diffraction peak from the crystallites. We represent the quantity of crystalline phase by the ratio between areas under (210) peak and the amorphous halo, which is plotted in the main frame. Our measurements under pure-shear load (${\lambda }_x=1$) are similar to previous x-ray diffraction studies under uniaxial elongation (${\lambda }_x={\lambda }_y^{-1/2}$) [6, 7, 8].

Figure 4

Stored elastic energy in specimen of critical height (see text) as a function of stretch ratio ${\lambda }_y$. A phase diagram is shown in the inset, in which the cross × and square □ correspond to propagating and stationary cracks in response to an initial cut, respectively. The blue line marks the phase boundary.