Residual stresses and birefringence in injection molding of amorphous polymers: Simulation and comparison with experiment

Abstract

A physical modeling and a two-dimensional numerical simulation of the injection-molding of a disk cavity by using a hybrid finite element method (FEM) and finite difference method (FDM) are presented. Three stages of the injection-molding cycle--filling, packing, and cooling--are included. The total residual stresses are taken to be a sum of the flow stresses calculated using a compressible nonlinear viscoelastic constitutive equation and the thermal stresses calculated using a linear viscoelastic constitutive equation. The total residual birefringence is taken to be the sum of the flow birefringence related to the flow stresses through the stress-optical rule, and the thermal birefringence related to the thermal stresses through the photoviscoelastic constitutive equation. The Tait equation is used to describe the P-V-T relationship. The simulation shows that without packing the birefringence in the surface layer of moldings, with its maximum near the surface, is caused by the frozen-in flow birefringence (flow stresses) and in the core region by the frozen-in thermal birefringence (thermal stresses). With packing, a second birefringence maximum appears between the center and the position of the first maximum due to flow in the packing stage. The predicted birefringence profiles and extinction angle profiles are found to be in fair agreement with corresponding measurements in literature for disk moldings. V V C 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 622-639, 2006

Birefringence in injection‐compression molding of amorphous polymers: Simulation and experiment

“…For numerical simulation in the filling, compression, packing and cooling stages, a nonlinear viscoelastic model is used [42]. The resulting set of nonlinear algebraic equations was solved with a globally convergent Newton's method [50, 51].…”

“…Mold filling during the ICM process is comprised of two stages: injection mold filling of a melt into a partially open mold and subsequent compression mold filling by closing the mold. Inelastic [52–54] and viscoelastic [46, 50, 54–57] simulations of the CIM have been already developed based on the control volume approach [54]. The governing equations for flow of the viscoelastic melt under nonisothermal conditions during the compression stage are presented earlier [57].…”

“…On the basis of the formulations described earlier [50, 55–58], a numerical scheme using CV/FE/FD for a two‐dimensional viscoelastic flow in a center‐gated disk is developed. To solve the equations, a set of appropriate boundary conditions is given first.…”

Thermal stresses and birefringence in quenched tubes and rods: Simulation and experiment

“…The thermal strain history was calculated using the volume relaxation theory developed by Rush [11] and implemented by Shyu and Isayev [23] and Isayev et al [18] for calculating thermal stresses in quenched plates, and Isayev et al [24] and Kwon and Lee [25] for calculating thermally induced stresses in injection molded parts. This theory states that when the polymer is quenched from an initial temperature higher than T g to temperature lower than T g , the polymer does not contract immediately.…”

Modelling Post-molding Warping

“…Reasonable agreement was seen, but it seems unlikely that warping of more complex parts can be handled this way. Isayev et al (2006) used a Hele-Shaw flow field, a Leonov non-linear viscoelastic model, and although the thermal expansion was assumed to be isotropic, they split the expansion behaviour into two ranges-above T m (or T g ) and below this. Kwon et al (2006) again used the Hele-Shaw flow field, with a Leonov model; they assumed no critical temperature for the thermal expansion coefficient and permitted anisotropic thermal expansion behaviour.…”