The development of multiphase liquid-liquid morphologies during mixing at small Reynolds numbers has been modeled. The mixing process is divided into i) stretching of dispersed drops, ii) breakup of the liquid threads formed, and iii) coalescence of the final droplets upon collision. Rules and criteria of the distinct processes are presented and combined to a general 2-zone mixing model simplifying the flow field into a sequence of alternating "strong and weak zones." In a "strong zone," dispersed drops and threads are stretched unless their radius is too small: meanwhile, the stretching threads might break up into droplets. In the subsequent "weak zone," the remaining threads may disintegrate while any drops present may coalesce. After passing a number of zones, stretching, breakup, and coalescence lead to a dynamic equilibrium that could be considered as the "final" morphology. Using the 2-zone mixing model, the influence of material parameters and processing conditions on the morphology has been studied. Interestingly, increasing either viscosity (dispersed or continuous phase) yields a finer morphology due to the delay of thread breakup (allowing for further stretching) and suppression of coalescence.
Long-term failure under constant or cyclic load is governed by the same process as short-term failure at constant rate of deformation. Failure proves to originate from the polymer's intrinsic deformation behavior, more particularly the true strain softening after yield, which inherently leads to the initiation of localized deformation zones. In a previous study we developed, and validated, a 3D constitutive model that is capable to predict the occurrence of these plastic instabilities, yielding quantitative predictions of the lifetime of polycarbonate under constant load. 1 Here we demonstrate that the same approach is also applicable to predict the life span of polycarbonate under cyclic loading conditions, over a large range of molecular weights and thermal histories, with a single parameter set only. The model incorporates the influence of physical aging, accelerated by the applied cyclic stress. For low cycle fatigue, at large stress amplitudes, where failure is thermally dominated, it is shown that the current constitutive model has to be extended to a multirelaxation time expression to properly describe the (evolution of the) energy dissipation.
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