Shock-wave theory for rupture of rubber

Crack-Tip Strain Field in Supershear Crack of Elastomers

We characterize the crack-tip strain field in the high-speed (supershear) crack in the elastomers propagating faster than the shear wave speed of sound (C_s). The dependence of steady-state crack velocity (V) on input tearing energy exhibits a crossover at V ≈ C_s between the subsonic (V < C_s) and supershear cracks (V > C_s). Several features of the crack-tip strain field such as strain-magnitude, extent boundary, and singularity exponent also change substantially accompanying the transition from subsonic to supershear cracks. The definite crossover of these characteristics at V ≈ C_s reflects the variations in the crack-growth mechanism: The inertia effect comes into play in the supershear crack. We also demonstrate that the azimuthal distribution of the local crack-tip strain has a close correlation with the macroscopic crack-tip shape, regardless of the regime of V.

Velocity mode transition of dynamic crack propagation in hyperviscoelastic materials: A continuum model study

Experiments of crack propagation in rubbers have shown that a discontinuous jump of crack propagation velocity can occur as energy release rate increases, which is known as the “mode transition” phenomenon. Although it is believed that the mode transition is strongly related to the mechanical properties, the nature of the mode transition had not been revealed. In this study, dynamic crack propagation on an elastomer was investigated using the finite element method (FEM) with a hyperviscoelastic material model. A series of pure shear test was carried out numerically with FEM simulations and crack velocities were measured under various values of tensile strain. As a result, our FEM simulations successfully reproduced the mode transition. The success of realising the mode transition phenomenon by a simple FEM model, which was achieved for the first time ever, helped to explain that the phenomenon occurs owing to a characteristic non-monotonic temporal development of principal stress near the crack tip.

The transition from subsonic to supersonic cracks

We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice. This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Subsonic cracks feature displacement fields consistent with a stress intensity factor. For supersonic cracks, the stress intensity factor disappears. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. This is one reason supersonic cracks in tension had been thought not to exist.

Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.

Supersonic crack propagation in a class of lattice models of mode III brittle fracture

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well-developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.

Hyperelasticity, viscoelasticity, and nonlocal elasticity govern dynamic fracture in rubber

Dynamic cracks in rubber can spontaneously oscillate under certain biaxial strain conditions [R. D. Deegan et al., Phys. Rev. Lett. 88, 014304 (2002)]. We have found that this unusual phenomenon can be understood from the unique mechanical properties of rubber: hyperelasticity, viscoelasticity, and nonlocal elasticity. While all these are important, the decisive role of nonlocality needs to be particularly emphasized. Through numerical simulations with a lattice model, we have quantitatively reproduced the experimental results.

Hot cracks in rubber: origin of the giant toughness of rubberlike materials

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy G(v) for high crack velocities v. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.

Crack motion in viscoelastic solids: the role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this "low-speed" regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.

Universality and hysteretic dynamics in rapid fracture

Experiments in the dynamic fracture of brittle polyacrylamide gels show that a single-crack state undergoes a hysteretic transition to the microbranching instability with a characteristic activation time. Quantitative measurements also indicate that features such as crack front inertia, self-focusing of microbranches, and the appearance of front waves are universal attributes of dynamic fracture.