The role played by viscoelasticity in the bulk material during the propagation of a dynamic crack in elastomers

Abstract

Investigation of dynamic fracture of elastomers can still be considered to be a relatively open area. When a sheet of elastomer is stretched in a tensile machine and a crack is introduced, the crack propagates at a speed that depends on the initial stretch level. There are instances where this speed is noted to exceed the shear wave speed based on the elastic modulus under high imposed stretches. Such cracks are called transonic cracks. It was usually hypothesized that either the hyperelastic or viscoelastic stiffening of the bulk material raises the wave speeds resulting in crack speeds entering the transonic regime. This article revisits the experiments performed on Polyurethane elastomers in Corre et al. (Int J Fract 224(1):83–100, 2020) to study the implications of both these hypotheses. Crack propagation has not been explicitly modeled, but the crack speeds are implicitly imposed on the geometry using the boundary conditions extracted from the experimental data. It has been determined that the viscoelasticity in the bulk is needed to describe and understand the transonic cracks in polyurethane elastomer. The inclusion of viscoelasticity results in the notions of ‘rubbery’ and ‘glassy’ wave speeds and hence, the transonic regime is defined considering the rubbery wave speed.

Appendix A: FE simulations for a different data extraction location

For the results of FE simulations presented in earlier sections, the boundary conditions were extracted along a line just above the crack path (green line in Fig. 5). To examine the effect of the location of data extraction line on the observed results, some more analyses have been performed where the data is extracted from the middle of the top half of the specimen instead of just above the crack path (purple line in Fig. 5). The new data extraction location is about 10 mm from the crack path in the undeformed configuration.

The analyses in the previous sections are then repeated with new data as boundary conditions. The results can be seen in Figs. 21 and 22.

Even in this case, the results of FE simulations with viscoelastic model can be seen to be closer to the experiments. In the case of horizontal displacements from Fig. 21, a bean shaped profile can be seen in the experimental result and the FE simulation with viscoelasticity. The case with just hyperelastic model does not exhibit this distinct profile. It shall be noted that the experimental result does not include the data near the top edge of the specimen.

Similarly, the velocity magnitudes from experiment and viscoelastic FE simulation are closer while hyperelastic result is not. This demonstrates the robustness of the viscoelastic model used and also indicates the presence of viscoelastic effects in regions far from the crack tip.