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Injection molding is an important method in polymer molding processing. Numerical simulations have proven effective in studying viscoelastic injection molding problems. Traditional numerical simulations of injection molding typically rely on macroscale models. However, the performance of plastics is closely related to their micromolecular structure. Understanding the evolution of the micromolecular structure is essential for improving product quality. Therefore, the simulation study of coupling micro- and macroscales has important academic and practical value.
In this study, a multiscale smoothed particle hydrodynamic (SPH) method based on the bead-spring chain model is used to simulate viscoelastic injection molding. At the macroscale, the conservation equations of mass and momentum are solved using the SPH method, whereas at the microscale, the elastic stress is described using the Brownian configuration field method. The viscoelastic Couette flow is simulated using three types of bead-spring chain models. The effectiveness of the multiscale SPH method is verified by comparing simulation results with analytical solutions of the viscoelastic Couette flow of the Hookean dumbbell model and by comparing the numerical solutions of the viscoelastic Couette flow of the finitely extensible nonlinear elastic dumbbell model with the literature results. The bead-spring dumbbell model is extended to a bead-spring chain model, and the Couette flow is simulated. The influence of different numbers of beads on the viscoelastic flow is analyzed, and an appropriate number of beads is selected for numerical simulations. In addition, the multiscale SPH method is extended to simulate injection molding in C-shaped and N-shaped cavities. Micro- and macro-parameters in injection molding are investigated, including the first normal stress difference, molecular stretch, and mean conformation thickness. The convergence of the multiscale SPH method is evaluated by changing the total number of SPH fluid particles Nf at the macroscale and the total number of bead-spring chain models Nb in each particle at the microscale. The obtained numerical solutions for the velocity are consistent. Furthermore, the effects of different rheological parameters, such as the number of beads of the molecular chain M, the spring maximum extensibility bmax, the viscosity ratio β, the Reynolds number Re, and the Weissenberg number Wi, on the flow behavior of viscoelastic fluid are analyzed.
The results show that the multiscale SPH method can stably and effectively simulate viscoelastic injection molding. This method can obtain micromolecular information that is impossible to obtain using traditional macro closed-form constitutive equations. In addition, different rheological parameters significantly influence the viscoelastic flow behavior. Larger M and bmax values result in increased steady values of molecular stretch and mean conformation thickness. Larger β and Re values result in smaller peak values of the first normal stress difference and weaker overshoot phenomena. Furthermore, larger Wi values yield larger peak values of the first normal stress difference, more oscillating numerical values, smaller molecular stretch values, and greater mean conformational thickness values.
The multiscale method provides a new approach for simulating viscoelastic injection molding.
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