Stationary crack propagation in a two-dimensional visco-elastic network model

- A simple viscoelastic model numerically reproduces stationary crack propagation.
- We examined the relation between the constant velocity V and the fracture energy G.
- The results for V vs. G at different parameters collapse well onto a master curve.
- The master curve exhibit a clear scaling regime with lower and upper bounds.
- We elucidate the physical mechanism for the propagation with the bounds.

We investigate crack propagation in a simple two-dimensional visco-elastic model and find a scaling regime in the relation between the propagation velocity and energy release rate or fracture energy, together with lower and upper bounds of the scaling regime. On the basis of our result, the existence of the lower and upper bounds is expected to be universal or model-independent: the present simple simulation model provides generic insight into the physics of crack propagation, and the model will be a first step towards the development of a more refined coarse-grained model. Relatively abrupt changes of velocity are predicted near the lower and upper bounds for the scaling regime and the positions of the bounds could be good markers for the development of tough polymers, for which we provide simple views that could be useful as guiding principles for toughening polymer-based materials.

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