聚合物熔体三维挤出胀大的数值模拟

THE NUMERICAL SIMULATION OF THREE-DIMENSIONAL EXTRUDATE SWELL OF POLYMER MELTS WITH K-BKZ INTEGRAL CONSTITUTIVE EQUATION

采用有限元方法分析K-BKZ本构方程描述的聚合物熔体的三维挤出胀大.对于本构方程中偏应力张量的计算,首先给出质点的运动轨迹,分段求出局部的变形梯度张量,再求出整体的变形梯度、Cauchy-Green应变张量和 Finger应变张量,沿轨迹采用分段高斯积分计算应力.把应力作为方程的右端项,给出迭代方法,求解非线性方程组.并根据自由面处的边界条件,迭代得出出口处自由面的最终位置.对轴对称流道和矩形流道进行分析计算,并把结果与二维分析和实验结果进行了比较,显示方法是可行的.

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.