Fig。 9 Metal-insert model for thermal stress analysis

to model filling, packing, and cooling stages of the injection molding。 Numerical simulation was consisted of 3 modules: filling, packing and cooling。 A set of unified governing equations for flow field in the cavity, which is based upon the generalized Hele-Shaw model of a compressible viscous fluid under non-isothermal conditions, was used through the filling and post-filling stages。12 Convective heat transfer by the cooling liquid, viscous heating during both filling, packing and cooling stages, and heat conduction through the mold-polymer interface were accounted for in the thermal analysis。16 The coupled thermal and flow fields are solved with the control-volume approach to handle automatic melt-front advancement by using a hybrid FEM/FDM scheme。 Residual stresses were generated in the injection molded part due to non-uniform cooling and pressure distribution。 The constitutive equation for the linear viscoelastic material model was expressed as Eq。 (2) to Eq。 (8)。 Normalized shear relaxation modulus of the polymer melt measured by the MDTA and used for the viscoelastic stress analysis。17 For the thermal stress analysis of metal-insert part, the model was used as Fig。 9。 Analysis conditions were used as the same as Table 1。 Mold and polycarbonate were set as rigid body to simply the model and save unnecessary calculation time。 Mold temperature was a constant。 Temperature of polycarbonate part changed as stage changing。 The heat transfer coefficients between product and mold as well as between product and air were considered to be constants, 3000 W/m2*K and 25 W/m2*K。 The friction coefficient between product and mold may have some effect on the interaction and therefore on the stress history of the

Fig。  10  Analysis  result:  (a)  Distortion  pattern  of  simulation;    (b)

Comparison graph of distortion

product。 So the friction value of 0。1 was used in our model。 The ejection force was not taken into account。

After ejection, the analysis was taken by Abaqus, using the data listed in Table 1。 Data files were transported to Abaqus for 3D numerical stress analysis。 Thermo-viscoelastic model was used for polymer analysis and elastic-plastic model was used for metal analysis。 By tie constraint, polymer and metal were connected together that agreed with the actual conditions。 Because the product was exposed to the air after ejection, it cooled down from mold temperature 100oC to environmental temperature 25oC。 Coupled analysis was adopted in which thermal and mechanical analysis was performed together。

4。3 Analysis results and discussions

Residual stresses of the product were constrained by the mold。 After ejection, new stress equilibrium was achieved yielding residual stress distribution。 The molded polymeric part began viscoelastic deformation and the metal insert began elastic deformation as soon as they were ejected from the die。 Final distortion of simulation was shown as Fig。 10(a), which was compared with the actual distortion measured by 3D scanning as shown in Fig。 6。 9 measurement points were used to evaluate the distortion and the comparison results were listed in Fig。 10 (b)。 The actual maximum distortion was 0。263 mm and the simulated

Fig。 11 Temperature distribution at the beginning of packing

Fig。 12 Stress change curve during packing stage

Fig。 13 Stress change graph from the beginning of ejection to the end of complete cooling

Table 2 Process parameters with ranges and values

  Parameters Level 1 Level 2 Level 3