The physics of fracture in an unstable polymeric liquid

Entangled polymer solutions and melts show a variety of behaviours under different
flow conditions. Recent step strain experiments [Macromolecules 42, 6261 (2009)]
demonstrated a fracture-like behaviour that was interpreted in terms of a massive loss of entanglements after yielding. This was taken to violate the Doi-Edwards tube model [The Theory of Polymer Dynamics (Oxford University Press, New York, United States, 1986)]. Here this phenomenon is investigated using the Rolie-Poly model, which approximates a successful version of the DE theory. The results give close quantitative agreement with the experiments, as well as with the proposal by Marrucci and Grizzuti in 1983 that entangled polymer liquids possess an elastic instability. The `fracture' is a transient manifestation of this elastic instability that relies on the amplification of spatially inhomogeneous fluctuations. Linear stability analysis of the fluid shows that there is also a viscous contribution to this instability so that this fracture-like behaviour is possible before the elastic limit is reached.