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The main aim of this work is to study the flow, failure, and rupture dynamics of a benchmark low-density polyethylene (BASF Lupolen 1840H) in true tensile creep conditions in both the viscoelastic and elastic deformation regimes. For this, we used a novel extensional rheometer that for the first time allows real controlled-stress conditions to be applied to the materials (as opposed to nominally controlled-stress) until physical rupture occurs (as opposed to being limited by maximum Hencky strain). We observed that constant strain rate was achieved for all flow conditions, and depending on the level of applied tensile stress, one or two states were obtained. In the former case, the observed mode of rupture was ductile, or liquid-like, and in the latter was cohesive, or elastic-like. The coupling at the molecular level between these flow and rupture mechanisms is not yet fully understood, although some recent studies in the literature may be able to offer at least partial explanations. [ABSTRACT FROM AUTHOR]