Figure 1

Crack in an elastic solid. The crack edge is along the $z$ axis.Reuse & Permissions

Figure 2

The dependence of the effective surface energy ${\gamma }_{\mathrm{eff}}$ on the crack velocity $v$ for a rubber characterized by the spectral density $H\left(\tau \right)\sim {\tau }^{-1∕2}$ for ${\tau }_1<\tau <{\tau }_0$ and zero otherwise. The solid line is the result of the full theory, Eq. (25), while the dashed line is the approximation (29). We have assumed ${\tau }_0∕{\tau }_1={10}^6$ and $E_{\infty }∕E_0={10}^3$. The reference velocity $v_0=a_0∕\left(2\pi {\tau }_0\right)$, where $a_0$ is the cutoff distance in the limit of arbitrary slowly moving crack. The logarithm is with 10 as the basis.Reuse & Permissions

Figure 3

The logarithm of the Fourier transform of the viscoelastic modulus as a function of the logarithm of time for a styrene-butadiene rubber compound.Reuse & Permissions

Figure 4

Fracture energy $G$ for styrene-butadiene rubber at various cutting or tearing speeds at $T=25°\mathrm{C}$. Adopted from Ref. 5.Reuse & Permissions

Figure 5

The singular stress region at a crack tip in continuum mechanics can be removed either by (a) tip blunting (tip diameter $a$) or (b) by introducing a lateral region (linear size $a$) over which the bond breaking occurs. The latter is the so-called Barenblatt process zone.Reuse & Permissions

Figure 6

The crack-tip process zone in most materials is very complex, involving cavity formation, stringing, chain pull-out (for polymers), and bond breaking.Reuse & Permissions

Figure 7

When a crack propagates fast in a viscoelastic solid, one can distinguish between three separate spatial regions: (a) an inner region where the perturbing frequencies $\omega =v∕r$ (where $r$ is the distance from the crack tip) are so high that the rubber response corresponds to the hard glassy region characterized by the (high-frequency) elastic modulus $E_{\infty }$, (b) an outer region where the perturbing frequencies are so small that the rubber responds with its zero-frequency modulus $E_0$, and (c) an intermediate region where the full complex viscoelastic modulus $E\left(\omega \right)$ enters and where the bulk viscoelastic energy dissipation occur (schematic).Reuse & Permissions

Figure 8

The dependence of the effective surface energy ${\gamma }_{\mathrm{eff}}$ on the crack velocity $v$ for a case where the rubber is characterized by a single relaxation time $\tau ={\tau }_0$. The reference velocity $v_0=a_0∕\left(2\pi {\tau }_0\right)$, where $a_0$ is the cutoff distance in the limit of an arbitrary slowly moving crack.Reuse & Permissions