G(β) is material constant and τ β is relaxation time。 K0 is constant value in bulk modulus

A(1)  and A(2)  are the form of constant matrices as below:

Fig。 2 Temperature dependent stress parameters: (a) Yield stress; (b) hardening exponent

In the plastic part, stress equation with hardening power law was applied:13

In the process chain analysis, the equations above were applied in Moldflow and Abaqus for stress calculation of polymer part during filling, packing and cooling stages, as well as distortion analysis。  All

material properties of polycarbonate (SC-1004A) could be obtained from Moldflow material database。

2。3 Elastic-plastic model for metal insert

The mechanical model is used to describe the evolution of thermal and mechanical strains caused by thermal and mechanical stresses。 In consequence, the stresses and distortion are closely related to the temperature history of metal and the contact forces with molds。

Elastic-plastic model with hardening power law was applied which consists of elastic part, thermal part and plastic part。 In the elastic and thermal part, the model was mainly characterized by the young’s modulus and the thermal expansion of which the expression was described as follow:

where σ0 is yield stress which corresponds to the stress at which plastic deformation starts, σ∞ is ultimate yield stress and a is hardening exponent。 These parameters are temperature dependent as shown in Fig。 2。

3。 Experiments

3。1 Injection  molding

The geometry of the mobile phone framework was shown in Fig。 3 where experimental casting sheets were performed using a commercial injection molding machine (LGH250D, 200ton closing force, LG Cable Co Ltd)。 The geometry included, besides the mold, the runner, the gate, metal insert part and plastic part。 In the series of experiments, Magnesium alloy AZ91D was used as metal-insert and polycarbonate

named Lupoy SC-1004A provided  by LG Electronics  was used    in

injecting。 Material and process parameters were listed in Table 1, which were used in manufacture and could be found in Moldflow  material

where σ is stress, E is Young’s modulus, ε is total strain, εT  is thermal

stain, εpl is plastic strain, α is thermal expansion coefficient, T is current temperature, Tref  is reference temperature which is 25oC normally。

database。

For the framework that we used in analysis, different position had different thickness because of the complex geometry that caters to the

Fig。 4 Design drawing of mobile phone framework

Fig。 3 Mobile phone framework produced by injection molding

Table 1 Process conditions and material properties

Fig。 5 3D scanning system: naviSCAN3D

requirement of actual smart phone design。 But the complex shape was conducive to our analysis for finding out the reason of distortion。 Two main regions consisted of two different thickness, 0。37 mm and 0。70 mm, which were used to verify the thermal stress difference。 The drawing of injection product used in the experimental procedure was shown in Fig。 4。 The center region was Mg alloy and the surrounding region was filled by polycarbonate。

3。2 Injection molding

Normally, the layer removal method is used to evaluate the magnitude of residual stress。 A small layer form the surface of product is removed through this method, leading to a measurable deformation。 Treuting and Read14 cut the layer by machining。 Jasen et al。15 improved the method by using an excimer laser for the layer removal to avoid the problem of the machining stress。 However, the layer removal method cannot be applied to injection molded products with complex  shape。