1、Numerical Simulation of Residual Stress in Injection MoldingXI Guo-dong, ZHOU Hua-min, LI De-qun (State Key Laboratory of Mold &Die Technology, Huazhong University of Science and Technology, Wuhan 430074, China)Abstract: Distribution and history of residual stress in plaque-like geometry aresimulate
2、d based on linear thermoviscoelastic model, to explore the mechanics and evolution of residual stress in injection molding process. Results show that the residual stress distribution through thickness is almost the same along flow path and the stress value near the end is a litter higher than that n
3、ear the gate.CLC number: TQ 320.66；O 345 Document code: A Article ID:1003-4951(2006)01-0017-07Keywords: injection molding; residual stress; numerical simulation; thermoviscoelastic1 IntroductionInjection molding is a flexible production technique for the manufacturing of polymer product. A typical i
4、njection molding process consists of four stages: filling, packing, cooling and ejection of product. During these processes, residual stress is produced due to high pressure and cooling, which induce the warpage and shrinkage of product. To make the product with high precision, it is important to si
5、mulate the pressure and thermal effect induced residual stress in the processes. Residual stress of injection molding has received more and more attention recently. Many researchers15 calculated the residual stress and shrinkage in the process by using different models.In general, the study of resid
6、ual stress is focused on the theoretical analysis with an isolated model. It does not take into account the specifics of injection molding and correlate with the packing and cooling analysis. In this study, distribution and history of residual stress in plaque-like geometry is simulated based on lin
7、ear thermoviscoelastic model, where the effects of pressure, thermal history and stress relaxation are jointly investigated.The numerical calculation model is built by finite difference method in time duration with layered discretization along thickness and under the specified boundary conditions. T
8、he developed simulation system is used to calculate the residual stress of typical injection molded parts.2 Model Problem2.1 Linear Thermoviscoelastic ModelTemperature and pressure induced stresses arise from inhomogeneous cooling of the part in combination with the hydrostatic pressure. For cooling
9、, the relaxation time increases and becomes comparable to the filling and packing time; therefore accurate prediction of thermal stress would require viscoelastic constitutive equations.But within the limit of infinitesimal strains variation the behavior of viscoelastic material is well described by
10、 the theory of linear viscoelasticity. Most injection mould products are very thin, we can take the flow direction as 1-dimensional and the local thickness direction as the 3-direction and build the local coordinates. The total stress tensor ij can be split into a hydrostatic pressure h P and an ext
11、ra stress part ij 6Where G1 is bulk relaxation function, G2 is shear relaxation function, th is thermal strain, mis spherical strain tensor,ij extra strain tensor and (t) is the material time.2.2 Basic Assumptions and Boundary ConditionsFor simplifying the calculation of thermally and pressure induc
12、ed stress in the injection molding process, the following assumptions are made:(1) We take the flow direction as the 1-direction and the local thickness direction as the 3-direction and build the local coordinates; (2) While in the mold, the material is locally constrained in the in-plane directions
13、 by three dimensional features of the part (bosses, ribs and other walls), so the in-plane strain is assumed to be equal to 0; (3) The normal stress 33 is constant in the thickness direction of the product and equals the reverse of cavity pressure; (4) As long as the cavity pressure is non-zero ( 0
14、33 ), the material sticks to the mold walls; (5) Mold elasticity is neglected and the warpage of wokpiece in the mold is not taken into account.3 Results and DiscussionTo study the evolution and distribution of stress, simulation is performed for a fan-gated specimen (300752.5 mm) as shown in Fig.1.
15、 A minimum complexity approach is proposed to emphasize the process physics, which would result in a better understanding of the transition that takes place during the molding. The material used was ABS (Novodur P2X of Bayer). The material parameters and the main processing parameters are listed in
16、Table 1 and Table 2, respectively.Fig.1 Rectangular strip mold3.1 Evolution of Cavity PressureAccording to the Basic Assumptions (3),normal stress equals the negative of the packing pressure in simulation. Therefore, the evolution of cavity pressure shows the variation of normal stress. Fig.2 shows the calculated pressure history at different locations along the flowpath, including the pressure profiles near the gate, quarter to
