注塑成型流动诱导应力的数值计算

Numerical simulation of flow-induced stress in injection molding

根据注塑成型的特点引入合理的假设,简化了粘性、可压缩、非等温塑料熔体流动的控制方程及基于PTT(Phan Thien Tanner)模型的本构方程,用分部积分法推导了关于压力场的拟Poisson方程,用待定系数法导出了流动应力的解析表达式。用有限元法求解压力场,有限差分及"上风"法离散求解温度场,根据解析表达式计算速度场及应力场,再进行应力-速度迭代求出非线性问题的最终解。比较了PC材料的模拟结果与光弹实验结果,模拟结果与实验结果基本一致。

The governing equations are in terms of compressible, non-isothermal fluid, and the conservative equations are based on the PTT（Phan-Thien-Tanner） model. By introducing some assumptions according to the characteristics of injection molding and applying parts integration, a quasi-Poisson type equation about pressure is derived. Besides, an analytical form of stress is also generalized by employing Undermined Coefficient Method. After the pressure is discreted and calculated by Galerkin approach, the velocity and stress are determined by the analytical formula. The ＇upwind＇ difference scheme is employed to discrete the energy equation. Coupling is achieved by Relax Iteration Method between velocity and stress. The flow in the test mold is investigated by comparing the numerical results and photoelastie photos for polycarbonate. The good agreement indicates this method is valid for computing viscoelastic flow.