  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.
