Simulation and analysis of birefringence in magneto-optical discs .A. Formulation

A numerical simulation tool is presented for the analysis of birefringence in substrates for Magneto-Optical (MO) Discs, typically manufactured using injection-compression molding type processes. The simulation comprises the entire manufacturing process covering the filling, the holding, and the cooling stage, as well as mold opening and further cooling in air. The flow-induced birefringence is modeled using a non-isothermal Hele-Shaw formulation for the flow kinematics and the incompressible Leonov model for the computation of the three-dimensional viscoelastic stresses. Heat transfer between the mold and the resin is accurately accounted for by solving the energy equation not only for the resin, but also for the mold, with full coupling between them. The cooling-induced birefringence is computed throughout the entire process using an incremental displacement formulation and assuming linear-viscoelastic material behavior. To properly account for the viscoelastic nature of the stress-optical coefficient, Osaki's approach has been adopted, where the viscoelastic shear-modulus is split into its glass and rubber component, each associated with a different, but constant stress-optical coefficient. All material parameters are a function of temperature and of time, and/or pressure where applicable. The governing equations are solved using a Boundary-Fitted Coordinate System (BFCS) approach. Due to symmetry, only a gapwise analysis is necessary. However, the stress-field is fully three-dimensional. The analysis is also applicable to parallel-plate flows. Part A of this paper covers the basic formulation, while Part B presents physical insight into the complicated birefringence generation process using results from numerical parameter studies and comparisons with experimental results.