The dynamic extrusion process of a polymer melt through a capillary under a superimposed vibration has been was researched deeply, and a mathematical model for the primary normal stress difference of a polymer melt under the vibration force field was set up. Accordingly, the calculation steps of above primary normal stress difference were established based on a rheological measuring equipment which was disigned by the authors. The primary normal stress difference of polymer melt under a vibration force field can be calculated by measuring the instantaneous data of capillary die swell, capillary entry pressure, capillary volume flux, and their phase difference under vibration with different frequencies and amplitudes.
INTRODUCTIONThe elastic behavior of polymer melt in dynamic forming process results in the alteration of the rheological performance of polymer and the physical-mechanical properties of products [1][2][3][4][5][6] . To date, there have been no constitutive relations for polymer melts that can accurately describe their elastic behaviors under the vibration force field. The exploration of the response mechanism of polymer in dynamic forming process and its mathematical representation are extremely important questions in polymer engineering.In this paper, a mathematical model for the elastic behavior of polymer melts under a vibration force field has been established. This was done by taking a polymer melt that flows through a capillary under a superimposed vibration as the studied object, and using a Constant Velocity Dynamic Capillary Rheometer, which was designed by the authors [7][8][9][10] .