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The zero shear rate viscosity (g0) is represented by
Here, D1, D2, D3, A1, and A~2 are data-fitted coefficients [14]. In this paper, MOLDFLOW software was utilized using CAD model to simulate injection molding process with same processing conditions as experiment. The material properties of polycarbonate built in MOLDFLOW matching experiments have been used for all simulation. The residual stress and temperature distribution throughout the part have been extracted as input data for following thermal deformation. For the numerical analysis of thermal deformation, ABAQUS software was used by importing the results from MOLDFLOW, assuming that injection molded part is a linear elastic body. The constitutive equation of a linear elastic body becomes
Here, rr is the residual stress of parts calculated during injection process, K is the bulk modulus, and a is the thermal expansion coefficient of material with the functional relationship to specific volume. For accurate modeling of specific volume, the following Tait’s state equation was used:
Here, V0(T), B(T), and Tg are defined by the following equations：
Here, all coefficients starting with b in Eqs. (10)–(12) are predefined values. Tg stands for glass transition temperature. Thermal deformation analysis was conducted after part ejection from mold.
Subject will experience the temperature change falling from mold temperature to atmospheric value. Finally, we measured the difference of dimension between initial CAD model and final geometry using HYPERMESH software similarly to experiments. Figure 2 shows the schematic description of our numerical analysis procedure.
Figures 2(a) and 2(b) represent initial CAD design and filling phenomena simulated by MOLDFLOW software, respectively. For thermal deformation, ABAQUS software was used by importing the results from MOLDFLOW and finally deformed shape was 100 times magnified and illustrated in Fig. 2(c). Figure 2(d) shows measuring quantity of final deformation by HYPERMESH program. In order to check the reliability of numerical results, mesh convergence tests have been performed. With considering time efficiency and accuracy, 2,800,000 and 300,000 meshes were used for battery and front cover, respectively.
Fig. 2 Schematic description of the developed numerical analysis procedure (a) initial CAD design, (b) injection molding process by MOLDFLOW, (c) thermal deformation process by ABAQUS,and (d) deformation measurement by HYPERMESH
3 Result and Discussion
3.1 Validation of Numerical Model.
In order to validate the proposed numerical model, we measured the specific dimensions of final product from both numerical analysis and experimental test which had experienced overall deformation through injection and cool down process. At first, we tried to compare the deformation amount in average sense. In industrial standpoint, dissimilar shrinkage rate with respect to width and height could be the most important design perspective during initial CAD model. Most mold practitioner utilize a little bit larger mold cavity considering the shrinkage at the final stage. Usually uniform expansion rate could be assumed in vertical and horizontal direction but directional size difference turns out to be significant as compared to initial CAD data. This size discrepancy could result in mismatching parts during assembling process.
We have defined the averaged deformation amounts along width and height, defined as W and H for battery cover, respectively.