However, residual stress and distortion for injection molded part with metal-insert cannot be predicted well。 Because the thermal behave of inserted metal is always ignored。 In this paper, we developed a process chain analysis for the injection molding with metal-insert, which could predict the residual stress and distortion accurately。 Polymer injection analysis was carried out by Moldflow with thermal viscoelastic model, and then residual stress of plastic part was exported by the Abaqus Interface for Moldflow。 Meanwhile, residual stress of inserted metal part was calculated by elastic-plastic model by Deform 3D, a commercial FEM software。 Finally, assembling the plastic part and inserted metal part together, final distortion was predicted by Abaqus。 This developed approach was proved from numerical experiments to be effective method for residual stress and distortion analysis。 Through comparing with 3D scanning photograph that could show the distribution of  distortion  and  get  the  measured  its  values,  we  found  that the

simulation results were in accord with experiment results。 After finding

Fig。 1 Thermal conductivity and specific heat curves: (a) AZ91D, (b)SC-1004A

of temperature and solidification, as well as an accurate material model is the basis to simulate stress and distortion。 The thermal model, mechanical model and material model are not independent but strongly interacted。

Using the thermal model, thermal distribution could be calculated。 Thereby, thermal stress could be calculated as accurate as temperature distribution。 Temperature T as a function of time t was calculated by heat transfer equation (Eq。 (1)) in our simulation。10 Material properties are listed in Fig。 1 where metal is magnesium alloy named AZ91D and polymer is polycarbonate named Lupoy SC-1004A。

the reason of distortion, another task in our research was to minimize

∂ (ρC T) + ∇⋅ (ρC vT) = ∇⋅ (λ∇T)

(1)

the distortion。 Optimal design was carried out to achieve the goal。 Melt temperature, die temperature, packing pressure and packing time were taken into account as important parameters。 Through comparison, the results by optimal design showed that it could reduce the distortion of product effectively。

2。 Theory of Stress Prediction

2。1 Thermal model

Stress simulation in injection molding with metal insert process is a complex problem consisting of several tasks, so the correct prediction

--- p p

∂t

Where ρ is density, Cp is heat, λ is thermal conductivity, v is velocity of the melt, t is the  time。

2。2 Thermo-viscoelastic model for polymer part

By assuming that viscoelastic behavior exists over temperature and pressure in a molding cycle, the constitutive equation of polymer could be used from the molten state above the glass transition temperature Tg to solidified material below Tg。 Furthermore, the model as shown in Eq。

(2) could be described over a wide range of temperature and pressure by

a single master-curve at some reference state together with associated shift factor。11,12

L is relaxation modulus of polymer, ε is the total strain and θ is the thermal strain。 ξ is material time of which expression is as  follow:

where η(T) is the viscosity at temperature T, η(Tg) is the viscosity at the glass transition temperature Tg, which is equal to 1012 pa*s for the most polymer。 α is thermal expansion coefficient。 Relaxation modulus L(t) could be pided into two parts, shear relaxation modulus and bulk relaxation modulus。 The expression is shown as  follows: