A systematic investigation of the deformation regimes, failure and physical ruptute of a low density polyethylene (LDPE) sample undergoing extension at a constant rate is presented. By combining integral measurements of the tensile forces and of the tensile stresses with the in-situ visualisation of the sample within a wide range of Weissenberg numbers Wi, three distinct deformation regimes are observed. At low Wi, Wi < 10, a viscous (flowing) deformation regime characterised by a single local maximum of the tensile force (engineering stress) related to the onset of a necking instability is observed. The rupture of the sample within this regime occurs via a ductile mechanism. For intermediate values of the Weissenberg number, 10 <= Wi <= 200, a transitional deformation regime characterised by a competition between the failure behaviour (primary necking) and the stabilising strain hardening (elastic) effects is observed. The physical rupture of the sample occurs via the emergence of secondary necks. As the Weissenberg number is further increased, Wi > 200, the strain hardening eventually wins over the necking instability which ultimately modifies the dynamics of the physical rupture of the sample. A quasi-thermodynamic picture of the extension process at various rates of deformation and temperatures is proposed. A detailed analysis of the experimentally observed scaling properties of the relevant physical quantities measured at the failure and the rupture points is provided. The paper closes with a discussion of the main findings and their possible impact onto the current understanding of failure and rupture of polymer melts in extensional flows. (C) 2015 Elsevier B.V. All rights reserved.