THE NUMERICAL SIMULATION OF THREE-DIMENSIONAL EXTRUDATE SWELL OF POLYMER MELTS WITH K-BKZ INTEGRAL CONSTITUTIVE EQUATION
聚合物熔体三维挤出胀大的数值模拟

Polymer Melts are a kind of non-Newtonian fluid. In this paper, a finite element tech-nique for three-dimensional extrudate swell of non-Newtonian fluids, say, polymer melts, employing K-BKZ integral constitutive model has been developed. In present method, the computation of the extra-stresses in the constitutive equation is as follow: give the moving particle tracking to find out the "local" deformation gradient tensor using step-by-step procedure. Therefore, the "global" deformation gradient, the Cauchy-Green strain tensor and Finger strain tensor can easily be cal-culated. At last, the stresses can be computed employing step-by-step Gauss integral along the particle tracking consequently, to solute the finite element non-liner equations by suitable "itera-tion" . Simultaneously, according to the boundary conditions of free surface, the final position and shape of exit free surface can be also found by iteration.Finally, based on the above technique, as an example, we simulated the 3D extrudate swell of HDPE melt in the square and rectangle dies. Result is in. good agreement with existing expermental swelling ratio. Obviously, it's efficient and successful that finite element method be used to simulate 3D-extrudate swell of non-Newtonian fluids with memory integral constitutive equations.