Computing flow-induced stresses of injection molding based on the Phan–Thien–Tanner model

A numerical approach is introduced to solve the viscoelastic flow problem of filling and post-filling in injection molding. The governing equations are in terms of compressible, non-isothermal fluid, and the constitutive equation is based on the Phan–Thien–Tanner model. By introducing some hypotheses according to the characteristics of injection molding, a quasi-Poisson type equation about pressure is derived with part integration. Besides, an analytical form of flow-induced stress is also generalized by using the undermined coefficient method. The conventional Galerkin approach is employed to solve the derived pressure equation, and the ‘upwind’ difference scheme is used to discrete the energy equation. Coupling is achieved between velocity and stress by super relax iteration method. The flow in the test mold is investigated by comparing the numerical results and photoelastic photos for polystyrene, showing flow-induced stresses are closely related to melt temperatures. The filling of a two-cavity box is also studied to investigate the viscoelastic effects on real injection molding.

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