Journal of Mechanical Science and Technology 29 (4) (2015) 1703~1713 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-015-0343-3

Process chain analysis of the dimensional integrity in a metal-insert polymer smart phone baseplate - from die casting to polymer injection molding† Kai Jin1, Taesan Kim1, Naksoo Kim1,* and Byeonggon Kim2 1

School of Mechanical Engineering, Sogang University, Seoul, 121-742, Korea Production Engineering Research Institute, LG Electronics, 222, LG-ro, Jinwi-myeon, Pyeongtaek-si, Gyeonggi-do, 451-713, Korea

2

(Manuscript Received May 18, 2014; Revised October 27, 2014; Accepted December 15, 2014) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Given the rapid development of die casting and polymer injection molding technologies, injection molding with metal-insert products, such as smart phone baseplate, can be widely produced and used. Injection molding usually has a complicated shape and high precision. Residual stress and related warping, local bending, and shrinkage are the key problems that affect the final product quality. These defects are generated because of temperature change, pressure, and cooling regime. In this research, finite element method was carried out to process chain analysis from die casting to polymer injection molding. This method predicted the residual stresses during the packing and cooling stages of die casting and polymer injection molding. The reason of distortion after ejection as well as the magnitude and distribution of distortion were also analyzed. To verify the calculated distortion after ejection, we compared the numerical analysis results with the experimental results that were measured by 3D scanning technology. The calculated deformation was consistent, and the residual stress was formed because of the different thicknesses of the sheets that resulted in different cooling rates, causing thermal stresses to become unevenly distributed. After the ejection, the uneven residual stress caused local distortion. Keywords: Die casting; Injection molding; Metal-insert; Residual stress; Local bending ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Computer-aided engineering has been developed and applied to design product shape and processing conditions and to predict product defects in all engineering fields. As the numerical analysis programs rapidly improve over the last decade, numerical analysis is widely used as a routine tool to determine product and mold cavity geometries and process conditions before actual manufacturing. Thus, it could be used in process chain analysis in a metal-insert polymer part of a smart phone. The production process of a metal-insert polymer part of a smart phone consists of two steps. The first step is die casting, which makes the metal-insert part, and the second step is injection molding, which makes the polymer. After die casting, the product needs cutting and sizing to match the design requirements and comply with dimensional tolerances. Die casting is a metal casting process that is characterized by forcing molten metal under high pressure into the mold cavity. The manufacturing process is relatively simple and involves only four main steps, namely, filling, packing, cooling, and ejecting. Die castings are characterized by a very *

Corresponding author. Tel.: +82 27058635, Fax.: +82 27120799 E-mail address: [email protected] † Recommended by Associate Editor Youngseog Lee © KSME & Springer 2015

good surface finish and dimensional consistency [1]. Given the thin-walled, complex structural metal-insert made of magnesium alloy, with the requirements of high precision and small dimensional tolerance, die casting process is applicable and successful in manufacturing and substituting numerous traditional technologies, such as turning and forging. In addition, the cast product combines superior strength and ductility, which suits to produce the framework of smart phone. The product is easily distorted after the ejection because of the residual stresses. Moreover, the product must meet the dimensional tolerances, which are confronted with complex geometry and very small section thickness in relation to the entire component size; thus, the straightening step, known as “sizing” is often used [2]. After straightening is completed, polymer injecting process is carried out to produce the polymer part, placing the cast sheet into the mold for injection molding. Injection molding is a manufacturing process for producing parts by injecting material into mold. Injection molding can be performed with a host of materials, such as glasses and common polymers. The hot polymer is injected into the mold where heat is removed from the polymer until it is rigid and stable enough to be ejected. After cooling to room temperature, the final product is finished. Although the process chain combined with die casting and

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injection molding has been developed maturely and applied widely, some defects still exist. Distortion caused by residual stress is the main defect. Residual stress is the stress left by the molding part under the condition of no external loads after ejection, which includes the flow-induced residual stress and thermal-induced residual stress. The flow-induced residual stress is caused by freeze-off packing pressure. During the non-isothermal transient flow of melt at the filling and packing stages, normal stress and shear stress are generated. If the cooling speed is very rapid, the macromolecular chain cannot completely relax, and the stress is then frozen in the cavity, turning into flow-induced residual stress. For the polymer, stress is related to the molecular orientation and the relaxation of flow stress during filling, packing, and cooling stages. In most cases, thermal-induced residual stress is the major residual stress, which is caused by non-uniform cooling of the molding part. Some areas with thin wall have a high temperature gradient, whereas other areas with thick wall have a low temperature gradient because of the complex geometry. Thus, the thin area cools down faster than the thick area. Consequently, the stress differences are developed during filling, packing, cooling, and ejecting stages [3]. After ejection, the residual stress redistributes and causes part distortion [4]. The residual stress in the injection molded part has been investigated in depth. Isayev and Hieber [5] analyzed the shear and normal stresses during the filling stage and calculated the stress relaxation at the cooling stage by using Leonov viscoelastic model. Kim et al. [6] applied incompressible Leonov constitutive equation to calculate the flow residual stress of center-gated disk during the injection and compression processes. Baaijens [7] calculated the flow residual stress in the thin-walled cavity. Meanwhile, thermal-induced residual stress is generated because of the non-uniformed cooling of polymer melt. Non-uniform thickness of product and nonuniform temperature distribution are the main reasons of the thermal residual stress. Non-uniformed temperature field is generated between the layer near the die surface and the central part. The temperature difference is generated between the thin and thick parts. The polymer in different locations is confronted with different thermal stresses. Bartnev [8] treated the material as pure elastomer and used thermoelastic theory, calculating the thermal residual stress. Lee and Rogers [9] showed that Laplace transforms can be effectively used for viscoelastic stress analysis only for a restricted class of problems. Isayev and Crouthamel [10] referred inorganic glass quenching thermal stress model to thermal residual stress calculation of polymer. Boitout [11] used the elastic model, considering the influences of thermal shrinkage and packing pressure. Commercial software, such as Moldflow, can calculate the residual stress of plastic part and accurately predict its distortion. The calculation and prediction for the injection molded part with metal-insert are accurate because the thermal behavior of inserted metal is always ignored. Commercial software, such as MAGMAsoft, can simulate the process of

die casting and predict the final distortion. However, such software always ignores the liquid flow stress during solidification. In the die casting process, solidification occurs at the solid-liquid mixed phase where liquid flow stress exists. In this research, we developed a process chain analysis for metalinsert polymer part from die casting to injection molding, overcoming all the aforementioned defects. Meanwhile, the residual stress and distortion of metal-insert polymer part of smart phone in each step were predicted using commercially available software, including AnyCasting, Deform 3D, Moldflow, and Abaqus.

2. Theory of stress prediction Stress simulation in the process chain is a highly complex problem; thus, the correct prediction of temperature, as well as an accurate material model, is the basis to simulate stress and distortion. The thermal, mechanical. and material models are not independent but strongly interacted. Thermal distribution can be calculated by using the thermal model. Thereby, thermal stress can be calculated as accurate as temperature distribution. Temperature T as a function of time t is calculated by the solution of heat transfer equation [12]. ¶ ( r C pT )+Ñ × ( r C p vT ) = Ñ × (lÑT ) ¶t

(1)

where ρ is the density, Cp is the heat capacity, λ is the thermal conductivity, v is the velocity of the melt, and t is the time. 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 mold. In the die casting process, phase change of metal occurs from liquid phase to solid-liquid mixed phase and ends by a solid phase. According to the study of Yoon et al. [13], the flow stress involves strain rate, solid fraction, and viscosity. The formula is shown in Eq. (2), where the solid fraction, fs, at equilibrium depends on the temperature and is given by the Scheil equation [14] as Eq. (4), where Ts is the solidus curve temperature, and Tm is the melt point temperature, and the power law exponent, n, has converge continuously to n = 1 for a Newtonian fluid when the solid fraction is zero [15, 16]. s = 3h ( 3e& ) n

( f s < 0.5)

s =s ¥ + (s 0 - s ¥ )e f s =1 - (

Ts - T ) Ts - Tm

1 1- k 0

- ae pl

( f s ³ 0.5)

(2) (3) (4)

where η(T) is the viscosity of material, σ0 is the yield stress, σ∞ is the ultimate yield stress, and a is the hardening exponent. When the solid fraction is more than 50%, the solid flow stress model plays a major role. To approximate the measure-

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ment of stress-strain curves, the elastic-plastic model with hardening power law was applied as shown in Eq. (3). If the stress is lower than yield stress, it follows the elastic model. In the injection molding process, the constitutive equation for polymer can be used from the molten state above the glass transition temperature Tg to the solidified material below Tg by assuming that viscoelastic behavior exists over temperatures and pressures in a polymer injecting cycle. Furthermore, the model as shown in Eq. (5) can be described over a wide range of temperature and pressure by a single master-curve at some reference states together with associated shift factor [17, 18]. ¶e ¶T )dt ' -a ¶t ' ¶t ' t t h[T (t ')] dt ' x (t ) = ò F[T (t ')]dt ' = ò 0 0 h [T (t ')] g t

s = ò L(x (t ) - x (t '))( 0

L(t ) = A(1)G (t ) + A(2) K (t ) m

G (t ) = å G ( b )e - t /t

(5)

Fig. 1. Metal-insert part of smart phone baseplate produced by HPDC.

(6) (7)

b

(8)

b =1

(9)

K (t ) = K 0

é 2 -1 -1ù 2 A(1) = êê -1 2 -1úú 3 êë -1 -1 2 úû

é1 1 1ù A(2) = êê1 1 1úú . êë1 1 1úû

(10)

L is the relaxation modulus of polymer, ε is the total strain, and θ is the thermal strain. ξ is a pseudo-time scale, which accounts for the temperature dependence of the material. η(T) is the viscosity at temperature T, and η(Tg) is the viscosity at the glass transition temperature Tg, which is equal to 1012 pa*s for the most polymer. α is the thermal expansion coefficient, which increases as a linear function as temperature increases. Relaxation modulus can be divided into two parts as shown in Eq. (7): the shear relaxation modulus G and the bulk relaxation modulus K. G ( b ) is the material constant, and t b is the relaxation time. K0 is the constant value in bulk modulus. A(1) and A(2) are the forms of constant matrices. In the process chain analysis, the aforementioned equations were applied in Moldflow for the residual stress calculation of plastic part during filling, packing, and cooling stages, and all the material data can be found in Moldflow database.

3. Experiments

(a)

(b) Fig. 2. AZ91D Material parameters showing: (a) thermal conductivity and specific heat [21]; (b) yield and tensile stress as a function of temperature dependence [12].

3.1 Die casting The process was carried out by high-pressure die casting (HPDC). The cast product of the smart phone is shown in Fig. 1, where experimental casting sheets were performed using a commercial HPDC-machine (SODICK, 125 ton closing force). In the series of experimental casting, magnesium alloy AZ91D was used, and all process parameters were measured and applied in process modeling. Some material parameters, such as heat transfer coefficient (HTC), are listed in Table 1. The parameters were used in manufacturing and simulation.

The mold was created using two hardened tool steel (SKD61). 3.2 Shape straightening - sizing The product generated warpage and local deformation because the section thickness was very small compared with the entire component size. Thus, meeting the dimensional tolerance is difficult. At this time, shape straightening technology, known as sizing, was necessary in manufacturing. Figs. 3(a) and (b) show the equipment, which was composed of top die,

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Table 1. Summary of HPDC process parameters. Name

Table 2. Process conditions used during the sizing process. Value

Material parameters

Name

Value

Top die speed

20 mm/s

HTC (Metal)

2500.0 W/(m2·°C)

Stroke

90.0 mm

HTC (Air)

25.0 W/(m2·°C)

Top die load

1000 N

Friction coefficient

0.1

Process conditions Filling speed

2.0 m/s

Packing pressure

12.0 MPa

Mold temperature

290.0°C

Molten material temperature

680.0°C

Packing time

2.0 s

Cooling time

4.0 s

Mold temperature

250.0°C

Cast product temperature

25.0°C

Loading time

5.0 s

(a)

(a)

(b) Fig. 4. Mobile phone baseplate produced by injection molding: (a) design drawing; (b) real product.

3.3 Injection molding (b) Fig. 3. Images of sizing process: (a) sizing machine; (b) FE model of the sizing process.

bottom die, heater, and hydraulic speed controller. In the sizing process, the cast product was placed into the bottom die, and then the top die moved down and reached a fixed position with a constant speed. When the top die, workpiece, and bottom die completely contacted, the top die provided a load and was maintained for several seconds, straightening the product shape. The detailed process conditions are listed in Table 2.

The geometry of smart phone baseplate is shown in Fig. 4, where experimental casting products were performed using an injection molding machine (LGH250D, 200 ton closing force, LG Cable Co. Ltd.). In addition to the mold, the geometry included the runner, gate, metal insert part, and plastic part. In the series of experiments, cast product (magnesium alloy, AZ91D) straightened by sizing was used as metal insert. Polycarbonate (Lupoy SC-1004A) provided by LG Electronics was employed in injection molding. Table 3 shows the list of material and process parameters, which were used in manufacturing and simulation. For the product, different positions had different thicknesses because of the complex geometry. However, two main regions

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Table 3. Summary of injection molding process parameters. Name

Value

Mold temperature

100°C

Melt temperature

320°C

Packing pressure

100 MPa

Packing time

2.5 s

Cooling time

10.0 s

Polymer

Lupoy SC-1004A

Elastic modulus

2280 MPa

Poisson ratio

0.417

Thermal expansion

7.3e-5/°C

Transition temperature

143.3°C

Density

1.1953 g/cm3

Metal

AZ91D

Elastic modulus

44800 MPa

Poisson ratio

0.35

Thermal expansion

2.6e-5/°C

Density

1.81 g/cm3

consisted of two different thicknesses, namely, 0.37 and 0.70 mm, which were used to verify the thermal stress difference. A schematic drawing of the injection baseplate used in the study is shown in Fig. 4 along with a picture of the as-molded part. Fig. 4 shows that the center region consisted of Mg alloy frame, and the surrounding region was filled with polycarbonate. The process was similar to die casting. As the plunger advanced, the melted polymer was forced to enter the mold cavity through a gate and runner system. The mold remained cold; thus, the polymer solidified almost as soon as the mold was filled. Once the cavity was filled, a holding pressure was maintained to compensate the material shrinkage. When the product was sufficiently cooled down to the mold temperature, the mold opened and the product was ejected.

(a)

(b)

(c)

(d)

3.4 3D scanning measurement In this paper, 3D scanning method was adopted. This simple and accurate method was used to measure the final distortion of each process. The measuring system is called “naviSCAN3D” [Fig. 5(a)], which is a combination of a coordinate measuring machine and a white light scanner system. The consolidation of the individual shots was seamlessly carried out. During the entire scanning sequence, the system monitored the position of both scanner and measuring objects and identified possible interfering movements. This technique ensured accurate and exact measurement results. After scanning, the displacement patterns of sample were obtained automatically as shown in Fig. 5, and the distortion at any position could be checked. If distortion is not observed in the work-piece, the displacement should be zero. If distortion occurs in some regions, the region will be described with

(e) Fig. 5. 3D scanning system: naviSCAN3D and displacement pattern of work-piece measured by 3D scanning: (a) 3D scanning system; (b) after die casting; (c) after sizing; (d) after injection molding; (e) distortion results of measure points at injection molding.

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Fig. 7. Temperature distribution of the casting of metal-insert part after filling in AnyCasting.

Fig. 6. Analysis process used to predict the distortion.

deeper color, and the displacement will be larger than those in other regions. Meanwhile, we selected nine measurement points in each process as shown in Fig. 5(d) and recorded their distortions. We examined eight samples, and the results are shown in Fig. 5(e).

4. Process chain analysis 4.1 Finite element analysis Residual stress was introduced into the product generated by non-uniform thermal transfer or solidification of the material or plastic deformation. This research aimed to simulate the distortion as close to the experiment as possible and analyze the reasons. To achieve these goals, three different kinds of finite element model were built, and four kinds of commercial software were employed (AnyCasting, Deform 3D, Moldflow, and Abaqus). The flow chart of the process chain analysis is presented in Fig. 6. The cavity filling stage is not usually considered because the filling is an instantaneous and complex process with a large number of fluid flow problems. In most studies, the temperature of melt after filling was assumed as a uniform temperature, and the yield stress in the mushy zone was set as a constant value. However, the temperature distribution is quite different as thickness changes in the real process, leading to yield stress difference. In this research, the procedure began with a filling simulation of die casting by using AnyCasting, which is based on finite volume method. Therefore, the element is hexahedron, and the geometry is approximately consistent. We could verify the temperature distribution as shown in Fig. 7.

After filling, the temperature data were mapped to the model, which used tetrahedron elements because the temperature distribution affected the stress calculation as shown in Eqs. (2)-(4). During the packing and cooling stages, a commercial numerical implicit finite element simulation tool named Deform3D [22] was utilized to calculate the residual stresses. The 3D element (C3D4) was employed for the full chain analysis. To maintain an accurate result, at least three elements with similar thickness direction were meshed as shown in Fig. 3(b). Coupled analysis between thermal and stress was used, and the flow stress was updated by user routine using Eqs. (2)(4). The temperature was calculated by Eq. (1), and the solid fraction fs was then updated by Eq. (4). When fs was smaller than 0.5, Eq. (2) was used, otherwise Eq. (3) was activated. To achieve consistency with the machine as close as possible, we determined the boundary and initial conditions in the simulation, such as melt temperature, die temperature, packing pressure, and cooling time, based on the industrial data shown in Table 1. The surfaces of die and work-piece cannot perfectly contact because they are not smooth. Therefore, some parameters cannot be clearly verified and defined, such as friction coefficient, heat transfer coefficient (HTC) between the casting and the die, and the instantaneous temperature of die contact surface. According to the research of Hofer et al. [23], the contact between the die and the casting was modeled as a small frictional contact, and the ejection forces were not considered. Thus, we obtained the study parameter for FE model, and the results are shown in Fig. 8. Nine measurement points were selected, which is the same as in Fig. 5(d), and the deviation between simulation and experiment was calculated. Smaller deviation value indicates that the experimental results are more consistent. Therefore, approximate HTC values and friction coefficient were determined and are listed in Table 1; thus, we could simulate the actual situation as close as possible. The material behavior was treated as isotropic and homogeneous over the entire casting process [24-27]. After ejection from the mold, distortion of cast product was generated as shown in Fig. 5(b), and the simulation result was

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(a)

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properties, geometry data, and the distribution of residual stress in the solidified part. Moldflow can accurately predict polymer distortion, but the deformation of molding injection with metal insert cannot be accurately predicted. Therefore, a detailed structural analysis that accounted for the residual stresses was conducted by Abaqus. The Abaqus Interface for Moldflow was used to translate these data into a format that can be used by Abaqus. Meanwhile, Moldflow cannot predict the thermal stress of metal-insert by thermal-viscoelastic model. Thus, transient temperature distribution and the thermal stress of metal-insert part were simulated by Deform 3D using the elastic-plastic model. The thermal stress simulated during the period of packing and cooling was approximate to the thermal stress generated. The calculated stress data were exported and converted to Abaqus format. After assembling the geometries of polymer and metal insert together and mapping the residual stresses of two parts, the Abaqus input file was obtained. Complete deformation from ejection to cooling down was obtained using tie constraint and two material models. Coupled analysis was adopted and thermal and mechanical implicit analyses were performed together. 4.2 Finite element analysis

(b) Fig. 8. Study parameter to determine: (a) HTC; (b) friction coefficient.

obtained [Fig. 12(a)]. The simulation was quite similar to the spring back analysis. As shown in Fig. 12(a), both X and Y directions of point A were fixed. Points B and C had a constraint in Y and X directions, respectively. Sizing simulation was then considered to correct the distortion, thereby finishing the cast product. After sizing, the metal insert part is finished. Thus, injection molding with metal insert should be conducted. In the injection molding, the model was used as shown in Fig. 4. The numerical simulation consisted of three parts, namely, filling, packing, and cooling. Convective heat transfer by the cooling liquid, viscous heating during filling, packing, and cooling stages, and heat conduction through the mold-polymer interface were accounted for in the thermal analysis [28]. Residual stresses were generated in the injection molded part because of the non-uniform cooling and pressure distribution. The constitutive equation for the linear viscoelastic material model was expressed as Eqs. (5)-(10). Normalized shear relaxation modulus of the polymer melt was measured by the MDTA and was used for the viscoelastic stress analysis [29]. Moldflow based on thermo-viscoelastic material model was used for the injection molding analysis. Boundary and initial conditions were obtained from the processed data required during the production as shown in Table 3. The same element and geometry data after sizing were used as metal insert part. The results of the analysis included descriptions of the material

In stress calculation of die casting, the calculated temperatures at the packing stage were taken as external loads acting on the cast sheet. At the beginning of packing, the thin part with higher cooling rate began to contract immediately in solidification. In such area, tensile stresses were formed in the tangential direction [30]. At the same time, the thick part cooled down slowly because of the low cooling rate. The stresses also increased because of the influence of the packing pressure, which maintained the metal filling up as shown in Fig. 9(a). As the packing advanced, when the thin part cooled down to the solid phase, the stress reached the peak. At this time, the stress in the thin part started to decline, and the direction changed from tensile to compressive because the cooling rate in the thin part was much lower than that in the thick part. The stress in the thick part kept increasing all the time, but the growth slowed down as the cooling rate decreased as shown in Figs. 9(b) and 10. Before ejection from the die, the almost complete cast product was subjected to stresses. After releasing the casting sheet from the die, no constrains from the mold were found, giving the sheet the freedom to distort. Thus, the stress changed, and the deformation could be obtained after ejection. The temperature of the cast product reduced from mold temperature to room temperature. The deformation distribution after ejection at room temperature is shown in Fig. 12(a). We chose nine measurement points as shown in Fig. 12(a) and compared with the 3D scanning displacement results. We conclude that the simulation results were quite close to the actual experimental results as shown in Fig. 11. During the sizing process, the structural organization

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(a)

Fig. 11. Displacement comparison at measuring points after die casting and sizing processes.

(b) Fig. 9. Effective stress distribution of FE model at packing stage of HPDC: (a) beginning; (b) ending.

(a)

(b) Fig. 10. Changes of effective stress in different thickness parts (Thin part and thick part).

rearranged because of the thermal motion of the atom. The internal residual stress was relieved, and the distortion disappeared through a big load. Through comparison, distortion before sizing and distortion after sizing were quite different as shown in Fig. 11. The effect of sizing process evidently reduced the distortion. Before sizing, the maximum value was 0.61 mm. After sizing, the value largely reduced up to 0.05 mm. The flatness also relatively improved as shown in Fig. 11, where distortions of all measurement points turned to be near zero. Therefore, the sizing process was quite a useful technology to the cast product.

Fig. 12. Deformation distribution of sizing process: (a) before sizing; (b) after sizing.

Similar to die casting, the residual stresses of the injection molded 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. The final distortion of simulation is shown in Fig. 13(a), which was compared with the actual distortion measured by 3D scanning as shown in Fig. 5(d). Nine measurement points were used to evaluate the distortion, and the comparison results are listed in Fig. 13(b). The

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(a)

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Fig. 14. Effective stress change at selected points during the packing stage of injection molding process.

creased (Fig. 13). The measured stresses in points 2, 7, and 9 are listed in Fig. 13(a). Before ejection from the mold, the almost complete product was subjected to stresses. After releasing from the mold, constrains were found from the mold, giving the product freedom to distort. The deformation distribution at room temperature is shown in Fig. 13(a). The simulation results were compared with the 3D scanning displacement results as shown in Fig. 13(b). (b) Fig. 13. Analysis result of injection molding: (a) distortion pattern of simulation; (b) distortion comparison curve.

actual maximum distortion was 0.263 mm, and the simulated maximum distortion of measurement points was 0.225 mm. A discrepancy existed between the measured and simulated values, which was caused by the slipping of polymer molecules at the mold surface, viscoelastic stress relaxation during cooling, the stress relaxation after ejection from mold, and the thermal stress simulation error. We conclude that the simulation and experimental results were basically consistent. Therefore, we can change the process conditions to optimal design. The reason for developing the distortion was the variation of residual stress between different sections. In stress calculation, the calculated temperatures in packing and cooling stages were considered as external loads acting on the metal insert and polymer part. At the beginning of packing, the thin part with higher temperature gradient began to contract immediately in solidification. In such area, tensile stresses were formed in the tangential direction [28], and stress was rapidly generated as shown in Fig. 14. Meanwhile, the thick part temperature slowly changed because of the lower temperature gradient, so the stress slowly increased. Meanwhile, the stress of polymer part also increased because of the influence of the packing pressure, which kept the melt filling up. As packing advanced, the stress in the thin part rapidly reached the peak, and the stress in the thick part kept increasing all the time, but the growth slowed down as the temperature gradient de-

5. Conclusions The capability of controlling the distortion of the process chain is a great challenge in manufacturing. This challenge can only be solved if the mechanisms of distortion development and its effects on the process are well understood. In our research, the following conclusions could be obtained: (1) The different thicknesses of metal part is the major reason for distortion. Different thicknesses lead to differences in the thin part, and the thick part slowly changed, thus causing a great temperature difference in the cross section. Hence, thermal stress is quite different between the thin and thick parts. After the ejection, this difference of residual stress leads to distortion. (2) An analysis method was proposed, which considered the influence of liquid flow at the beginning of the packing stage, and the temperature distribution of the melt after the filling stage. Other studies ignored the filling stage, and only treated the temperature as a uniform value at the beginning of packing. We employed the commercial software, AnyCasting, to predict the temperature distribution at the filling stage, using the data as initial conditions in packing analysis. Meanwhile, we employed the liquid flow stress model in our analysis, which the influence is always ignored. By using user routine of Deform 3D, the flow stress model could be easily made. (3) An analysis method was developed, which overcame the defect of Moldflow in metal-insert mold injection calculation. The influence of thermal stress of insert metal at the packing and cooling stages was considered, which used the elasticplastic model for the calculation. We also employed the com-

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mercial software, Abaqus, to predict the final distortion, by using the residual stress data mapped from Moldflow analysis. This analysis adopted the thermal-viscoelastic model to predict the stress and thermal stress data by Deform 3D. The distortion results between actual experiment and numerical analysis were compared and were quite similar. Thus, the method could be used to predict the distortion of other metalinsert injection-molded products. (4) The numerical analysis results were quite consistent with the experiments. The distortion after ejection was successfully predicted. Uniform temperature field should be considered during packing and cooling stages to minimize the distortion. Moreover, the study parameter is needed in future works to confirm the impact factors.

Acknowledgment This study was supported by the Research Grant of Sogang University (No. 201210031). The support is gratefully acknowledged.

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Kai Jin earned his B.S. degree from the School of Automotive Engineering, Harbin Institute of Technology, Weihai, China in 2010. He is currently studying at Sogang University, Seoul, South Korea to receive his Ph.D. degree from the Department of Mechanical Engineering in 2015. His research interests are die casting and injection molding process analysis.

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Naksoo Kim is currently a professor at the Department of Mechanical Engineering, Sogang University, Seoul, South Korea. He received his B.S. and M.S. degrees from the Department of Mechanical Design, Seoul National University, Seoul, South Korea in 1982 and 1984, respectively. He then went on to receive his Ph.D. from UC Berkeley, California, USA. Dr. Kim has worked for the Engineering Research Center for Net Shape Manufacturing at Ohio State University as a senior researcher and at Hongik University as an assistant professor. Dr. Kim’s research interests are metal forming plasticity, computer-aided process analysis, and optimal design.