To calculate the thermal stresses and the thermal birefringence, the linear viscoelasticity and photoviscoelasticity earlier employed in quenching of single layer [33, 34] and multilayer  polymer slabs was used.
The residual thermal stresses and birefringence in CIM disks are treated as those for freely quenched polymer plates and are calculated based on the linear viscoelasticity and photoviscoelasticity with the volume relaxation effects included [33-35], Based on varying temperature fields, the changes in the relaxation modulus and stress-optical coefficient functions with temperature and time are determined and utilized to calculate the thermal stresses until the CIM disk cools down to the mold temperature.
Brcic, Photoviscoelasticity in Theory and Practice, Springer-Verlag, New York (1972).
The present modeling is based on the linear viscoelasticity and linear photoviscoelasticity accounting for the time and temperature dependence of mechanical and optical properties with the volume relaxation based on the first-order rate equation .
The photoviscoelasticity means that the stress-optical coefficient obtained from creep experiments and the strainoptical coefficient obtained from stress-relaxation experiments, similar to the relaxation modulus, vary with temperature and time.
The first basic mathematical approach of the photoviscoelasticity was given by Mindlin  who used a four-element mechanical model for the incompressible material and assumed that only the spring contributes to the birefringence.
The thermal birefringence is calculated from the thermal stresses using the linear photoviscoelasticity and free volume theory taking into account the density relaxation (44-46).
The residual thermal stresses and birefringence in ICM disks are treated as those for freely quenched polymer plates and are calculated based on the linear viscoelasticity and photoviscoelasticity with the volume relaxation effects included (45), (65).
The linear viscoelasticity and photoviscoelasticity with the volume relaxation effects are used to calculate the residual thermal stresses and birefringence (45).
Lee and Kwon (10), (11) have developed a refined physical modeling based on the free volume theory, viscoelasticity, and photoviscoelasticity and have predicted the residual stress and birefringence in injection and injection/compression molded center-gated disk in a systematic manner.
The most elaborate physical modeling of entire injection molding stages in the literature has included nonlinear viscoelasticity and photoelasticity for the liquid state and linear viscoelasticity, photoviscoelasticity and free volume theory for the solid state along with a Tait's state equation, and could successfully predict birefringence and residual stress profile especially when a pressure dependent lateral motion model (PLMM) was adopted (10-13).
In contrast, for the solidified state below the no-flow temperature, the linear viscoelastic solid model was employed as the constitutive equation, and a photoviscoelasticity
theory was used to calculate the birefringence.