Study on residual stresses of thin-walled injection molding

Transcription

1 European Polymer Journal 41 (25) EUROPEAN POLYMER JOURNAL Study on residual stresses of thin-walled injection molding Tong-Hong Wang, Wen-Bin Young * Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 711, Taiwan, ROC Received 4 December 23; received in revised form 6 April 25; accepted 11 April 25 Available online 22 June 25 Abstract The residual stresses of the thin-walled injection molding are investigated in this study. It was realized that the behavior of residual stresses in injection molding parts was affected by different process conditions such as melt temperature, mold temperature, packing pressure and filling time. The layer removal method was used to measure the residual stresses at a thin-walled test sample by a milling machine. This simple method was demonstrated to be adequate for a thin-walled part. Moldings under different conditions were investigated to study the effects of the process conditions on the residual stresses of a thin-walled product using the elastic and viscoelastic models. The mold temperature was found to affect the size of the core region and residual stress on the surface layer of a thin-walled part in our studied range. The packing pressure was insensitive to the residual stresses in the studied high-pressure range. The residual stresses predicted by the viscoelastic model are about the same level and trend as compared to the experimental measurement. Ó 25 Elsevier Ltd. All rights reserved. Keywords: Injection molding; Thin-walled molding; Residual stress; Layer removal 1. Introduction Residual stresses are the stresses left inside the molding product under the condition of no external loads. In the molding process, internal stresses are frozen inside the mold cavity. After demolding, the residual stresses will redistribute and cause the part shrinkage and warpage. Possible thermal stresses may still be introduced into the part after demolding because of further cooling to the room temperature. The residual stresses commonly discussed in injection molding may include the * Corresponding author. Tel.: ; fax: address: youngwb@mail.ncku.edu.tw (W.-B. Young). flow-induced residual stress and thermal induced residual stress. The flow-induced residual stresses include those caused by polymer chain preferential orientations and freeze-off packing pressure, and the thermal induced residual stress is caused by non-uniform cooling of the molding part. Measurement of the residual stresses in a molding part can be performed by either a non-destructive way or a destructive way. The technology of photo-elasticity utilizes the effect that the induced stresses inside a material will diffract the incoming light and form an interaction pattern. This pattern can be related to the stress level and distribution inside the material. Neves and Pouzada [1] measured the molecule orientation in thickness direction using this technology. Treuting and Read [2] used the layer removal method to measure the residual stress in each layer of a molding product. The layer /$ - see front matter Ó 25 Elsevier Ltd. All rights reserved. doi:1.116/j.eurpolymj

2 2512 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) removal method removed a small layer from the surface of the part, leading to a measurable deformation. The deformation shape of the part can be correlated to the residual stress in the removed layer. Deformation shapes for removing consecutive layers are measured until the middle plane of the part. In this way, the distribution of residual stresses through the thickness direction of a part can be measured. Zoetelief et al. [3] used the same method for measuring the through thickness residual stresses. Instead of measuring the part deformation after layer removed, Miller and Ramani [4] used an attached strain gage to estimate the stress in the layer removal method. Except the machining and cutting, Jasen et al. [5] used an excimer laser for the layer removal to avoid the problems of the machining stress. Turnbull et al. [6] made a comparative assessment of techniques for evaluating residual stress in polymers. Emphasis was placed on the layer removal and hole-drilling methods. A more speculative approach, the chemical probe technique, using the sensitivity of the threshold stress for environment stress cracking to particular chemicals, has been developed to characterize near-surface stresses. Chien et al. [7] also had some discussion on the residual stresses for thinwall molded part. In modeling the development of residual stresses in injection molded parts, it was realized that the stress relaxation effect played an important role. Kabanemi et al. [8] used a thermoviscoelastic model with volume relaxation to calculate the residual stresses. A finite element based on plate theory was employed to simulate the injection parts with complex shapes. The thermal and packing pressure variations in injection mold processes were not included in the model calculation; instead a simple thermal equilibrium equation was used. Lee et al. [9] has presented the physical modeling and basic numerical analysis results of the entire injection molding process, in particular with regard to both flow-induced and thermally-induced residual stress and birefringence in an injection molded center-gated disk. Kamal et al. [1] used a three-dimensional numerical simulation to predict internal stresses in injection molded components. The warpage of injection compression molded optical media, such as compact discs and digital video discs, due to asymmetric cooling during production was predicted by Fan et al. [11]. This study used the layer removal method to measure the residual stresses in a thin-walled injection molding part. A simple machine cutting method was used for the layer removal and demonstrated to be adequate in this case. The relative importance of processing parameters on the resulting level of residual stresses was also investigated by numerical simulations using a viscoelastic model. Comparisons with the results from experiments were also discussed. 2. Layer removal stress After Demolding, the surface traction and moment will vanish in a flat molding part as shown in Fig. 1. For the surface in the x-direction, we have the conditions of Z z Z z r x ðzþdz ¼ r x ðzþzdz ¼ ð1þ z z where z is the half thickness. The z-axis is assumed to be in the thickness direction and x-axis is along the flow direction during the injection. When a specified thickness of layer is removed from the surface as shown in Fig. 2, the total force and moment across the crosssection are no longer balanced. The resulting net unit length force and moment in the x-direction can be expressed as Z z1 F x ðz 1 Þ¼ r x ðzþdz ð2þ z Z z1 h M x ðz 1 Þ¼ r x ðzþ z þ z z i 1 dz ð3þ z 2 where z 1 is the left thickness above the original middle plane of the part. Notice that, in calculation of the moment, the new middle plane is shifted down to (z z 1 )/2 after some layers removed from the surface. The net unit x z -z z Fig. 1. The coordinate system and surface tractions on crosssections. x z 1 -z z Fig. 2. Element showing layer to be removed. y y

3 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) L z 1 +z 2z Fig. 3. Determination of the curvature of a deformed bar. length force and moment in the y-direction have the same forms as Eqs. (2) and (3) except the subscript changing from x to y. The bending moment of a plate can be expressed by the bending curvatures [12]. M x ¼ Eðz þ z 1 Þ 3 12ð1 m 2 Þ ½j xðz 1 Þþmj y ðz 1 ÞŠ ð4þ where j x and j y are the curvatures in the x- and y- directions, E is the youngõs modulus, and m is PoisonÕs ratio. Substituting Eq. (4) into (3), one can derive the residual stress in the x-direction E r x ðz 1 Þ¼ ðz 6ð1 m 2 þ z 1 Þ 2 Þ dj x ðz 1 Þ þ m dj yðz 1 Þ dz 1 dz 1 þ4ðz þ z 1 Þ½j x ðz 1 Þþmj y ðz 1 ÞŠ Z z 2 ½j x ðz 1 Þþmj y ðz 1 ÞŠdz ð5þ z The residual stress in the y-direction can be derived by changing the subscript from x to y. For the case of a part with equal stresses and curvatures in x- and y-directions, one has the form for the residual stress as E r x ðz 1 Þ¼ ðz þ z 1 Þ 2 dj x ðz 1 Þ þ 4ðz þ z 1 Þj x ðz 1 Þ 6ð1 mþ dz 1 Z z 2 j x ðz 1 Þdz ð6þ z The bending curvature can be estimated by the following equations: j x ¼ 1 q q ¼ L2 þ 4/ 2 8/ The definitions of L and / are shown in Fig Experimental ð7þ ð8þ A simple strip part with dimensions mm 3 was used in this study. Fig. 4 shows the finite element Fig. 4. The finite element model of the strip part. model of the part and the node place that will be used to show the residual stress distribution in the later study. Material used for the study was ABS (PA-756S from Chi-Mei, Taiwan). Tables 1 3 list some material constants which will be used in the process simulations. An ultra high accuracy laser displacement meter (LC- 24A, Keyence Corp.) was used to measure the deformation of the mid-point location ion the layer removal method. It could measure the displacement with accuracy up to.1 lm. Samples were molded under the conditions of.28 s injection time, 21 C melt temperature, 6 C mold temperature, and 168 MPa packing pressure. The packing time was.5 s and cooling time was 4s. The samples were cut to the size of 1 3 1mm 3 first and glued to the machine table by a double side tape. The first three cutting layers were.2 mm, and the rest of layers were.6 mm until near the middle plane. Totally, 1 layers were removed in the test. In order to minimize the cutting stress and relaxation effects, different samples were used for the cutting of dif- Table 1 Mechanical data and parameters for time temperature shift function Material data Symbol Value YoungÕs modulus E GPa PoissonÕs ratio m.38 Reference temperature T r 373 K Thermal expansion coefficient a K 1 (liquid state) Thermal expansion coefficient a K 1 (glassy state) c c Table 2 Rheological data: cross-wlf viscosity Symbol Value n.2995 s * Pa D Pa s D K D 3 A A K

4 2514 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) Table 3 pvt data: two-domain Tait model Symbol Value b 1m.9999 m 3 /kg b 2m m 3 /kg K b 3m Pa.5617 K 1 b 4m b 1s b 2s b 3s b 4s b 5 b 6 ferent depths. Three samples were used for each depth. The layer removal was performed by a milling machine with the conditions of a 12 mm diameter cutter, a feed rate 25 mm/min, and a spindle speed 1 rpm. In order to understand the cutting stress introduced to the sample during the machining. Some samples were annealed under 9 C for 8 h. After cutting the annealed samples to different depths, the measured deformation and curvature were found to be relatively small in our setup. Therefore, the cutting stress was considered negligible in our system. 4. Numerical simulation of the residual stress For a thin part, the in-plane dimension is larger than the thickness. The shear stresses are neglected in the analysis of the in-mold residual stresses. The stresses to be determined are the three normal stresses. The normal stress, r z, is assumed to be constant in the thickness direction. The polymer is assumed to behave as an isotropic thermorheologically simple solid, in such a manner that stress components are related to histories of strain components and temperature through appropriate relaxation functions. The equations for the deviatoric stresses and bulk stress are [13] s ij ¼ s ¼ Z t Z t G 1 ðn n Þ oe ij ot dt ð9þ G 2 ðn n Þ oðe e thþ ot dt ð1þ where s ij and e ij are the deviatoric stress and strain, s is the bulk stress, e is the average normal strain, and e th is the thermal strain. The modified time scale n is related to the shift function as nðx i ; tþ ¼ and log U ¼ Z t U½T ðx i ; t ÞŠdt c 1ðT T r Þ ðc 2 þ T T r Þ m 3 /kg m 3 /kg K Pa K K K/Pa ð11þ ð12þ where T is the temperature, c 1 and c 2 are material constants, and T r is the reference temperature. The relaxation modulus G 1 and G 2 are described by the following models: G 1 ðtþ ¼2luðtÞ ð13þ G 2 ðtþ ¼3juðtÞ ð14þ and uðtþ ¼ Xm g r exp t ð15þ h r¼1 r where g r, l, and j are material constants, and h r are relaxation times. Due to the condition of the solidification, the analysis of residual stress can be separated into the following three cases: 1. The core region is above the no-flow temperature. Since the core region is still under the packing pressure, r zz will equal to the local melt pressure, P(t), and Dr n zz is equivalent to the variation of local melt pressure at time t n, DP n. The change of in-plane stress can be written as [13] Dr n xx ¼ Drn yy ¼ðuðDn n Þ 1Þr n xx þ a½dp n ðuðdn n Þ 1ÞP n Š þ CðDn n Þða 1Þð3jÞDe n th ð16þ and a ¼ ð 2l þ jþ 3 4l þ j ð17þ 3 2. The entire layers are below the no-flow temperature. As all the layers are below the no-flow temperature and the material does not detach from the mold wall (r zz < ), the boundary condition of no displacement in the thickness direction is employed. One has [13] P nl Dz i Dr n zz ¼ i¼1 ðuðdn n Þ 1Þr n CðDn n Þ zz 3jCðDnn ÞDe n th P nl Dz i i¼1 CðDn n Þ ð18þ Dr n xx ¼ Drn yy ¼ðuðDn n Þ 1Þr n xx þ a Drn zz ðuðdnn Þ 1Þr n zz þ CðDn n Þða 1Þð3jÞDe n th ð19þ 3. The material detached from the mold wall. As the material cools further, the compressive stress in the thickness direction may drop to zero, and the material may detach from the mold wall. At this time, the conditions of r zz = Dr zz = is employed. The variation of in-plane stress becomes [13] Dr n xx ¼ Drn yy ¼ðuðDn n Þ 1Þr n xx þ CðDnn Þð3jÞða 1ÞDe n th ð2þ

5 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) The calculation of the residual stresses requires the simulation of the complete injection molding cycle. This involves a set of mass and energy balance equations together with constitutive relations. Detailed information regarding to the solution of the injection molding cycle and the above residual stress equations can be found in the literature [13,14]. 5. Results and discussion Simulations of the developed residual stresses during the molding process were performed using a code developed in the literature [13] for the viscoelastic model. The commercial code of C-MOLD was used for calculations of the residual stresses using an elastic model. Fig. 5 shows the comparison of the pressure traces from the simulation prediction and experimental measurement at the position of the gate. The melt pressure rises sharply during the filling stage and keeps about the same at the packing stage. As the melt at the gate starts to freeze, the pressure drops at the same time. The predicted pressure was in the same trend as the experimental measured value. For numerical simulation results, the residual stresses of the molding part presented at the following is located at the node position shown in Fig. 4. Fig. 6(a) shows the simulated residual stresses in the thickness direction of samples molded under different melt temperatures using an elastic model. The thickness in the plot was normalized to from 1 to 1. A thin skin layer is under tensile stress while a compression stress in the sublayer. There were not many variations of the residual stresses for different melt temperatures in the range from 2 to 22 C. The effect of different packing pressures from 136 to 168 MPa on the residual stresses is shown in Fig. 6(b). No obvious change was found in this case. The effect of packing pressure on residual stress is usually found in the low packing pressure range. At this range, the packing pressure drops to zero prior to the Pressure (MPa) Measurement Simulation Time (sec.) Fig. 5. Pressure trace at entrance Melt temp. 2 C Melt temp. 21 C Melt temp. 22 C a b c Packing pressure 136MPa Packing pressure 153MPa Packing pressure 168MPa Mold temp. 5 C Mold temp. 6 C Mold temp. 7 C Fig. 6. In-plane residual stress distributions for different: (a) melt temperatures, (b) packing pressures, and (c) mold temperatures calculated by an elastic model. complete glass transition. In the high packing pressure, the pressure distributions for different packing pressures prior to entire glass transition only differ by a constant, resulting in almost the same distribution of residual stresses. However, the average cavity pressure for different packing pressure will be different and cause different shrinkages. Fig. 6(c) shows the effects of different mold temperatures from 5 to 7 C on the through thickness residual stresses. Higher mold temperature tends to increase the tensile stress in the surface, but without obvious effect on the rest of the part. A slightly larger core region was noticed for higher mold temperature. In numerical simulation of the residual stresses of the injection part using the elastic model tends to overestimate the stress level because of the ignorance of the stress relaxation effect. As the melt freezes during the cooling process, the stress relaxation effect is quite fast near the transition point. A large portion of the frozen stress

6 2516 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) melt temp. 2 C melt temp. 21 C melt temp. 22 C a packing pressure 136MPa packing pressure 153MPa packing pressure 168MPa b c mold temp. 5 C mold temp. 6 C mold temp. 7 C Fig. 7. In-plane residual stress distributions for different: (a) melt temperatures, (b) packing pressures, and (c) mold temperatures calculated by viscoelastic model. Table 4 Relaxation data for thermal stress calculation [3] i h i g i e e e e e e Fig. 8. Measured in-plane residual stress distribution. can be relaxed at this moment. Most of the residual stress was built up at the following cooling process with temperature far lower than the transition point. For the numerical simulation using a viscoelastic model, Fig. 7(a) shows the residual stress through the thickness for different melt temperatures. The calculations included both the shear and bulk relaxation. Table 4 lists the relaxation data from literature [3] for ABS plastics. In the core region, the packing pressure relaxes near the glass transition temperature, resulting in lower residual stress. On the other hand, the skin-layer freezeoff at the filling stage under a low pressure. During the packing stage, packing pressure produces an elastic strain in the skin layer, which releases as the packing pressure drops off. The resulting stress is the tensile stress induced by the thermal contraction. The residual stress level shown in Fig. 7(a) is quite low compared those from an elastic model due to the large stress relaxation near and above the glass transition point. Fig. 7(b) shows the effect of the packing pressure on the residual stress. As the case in the elastic model, no major effect can be found in the studied packing pressure range. The effect of mold temperature is shown in Fig. 7(c). The mold temperature has major effect at the stress level at the skin layer since the material at this location is quenched to the mold temperature at the filling stage. As the mold temperature increases, the core region is larger, resulting in more stress relaxation during the packing and less residual stresses. From the experiments, the deformations and curvatures of the samples can be measured. The resulting through thickness residual stresses can thus be calculated using the measured data and Eq. (6). Experimental result (symbols) of the residual stress is shown in Fig. 8 together with the simulation result (solid line). The predicted stress level and trend are close to the experimental measurement. In the core region, the predicted value is quite low as compared to the measured value. The possible reason might be that the used relaxation data overestimates the actual case, leading to the under-estimate of the stress level in the core region. 6. Conclusions The layer removal method was used to measure the residual stresses at a flat thin-walled test sample. Moldings under different conditions were investigated to

7 T.-H. Wang, W.-B. Young / European Polymer Journal 41 (25) study the effects of the process conditions on the residual stresses of a thin-walled product. The mold temperature was found to affect the size of the core region and residual stress on the surface layer of a thin-walled part in our studied range. The packing pressure was found to be insensitive to the residual stresses in the studied high-pressure range. The predicted stress level and trend are close to the experimental measurement in viscoelastic model. The layer removal method was also found to be adequate for a thin-walled part. References [1] Neves NM, Pouzada AS. The use of birefringence for predicting the stiffness of injection molded polycarbonate discs. Polym Eng Sci 1998;38(1): [2] Treuting RG, Read Jr WT. J Appl Phys 1951;22(2): 13. [3] Zoetelief WF, Douven LFA, Housz AJI. Residual thermal stresses in injection molded products. Polym Eng Sci 1996;36(14): [4] Miller K, Ramani K. Process-induced residual stresses in compression molded UHMWPE. Polym Eng Sci 1999; 39(1):11 8. [5] Jansen KMB, Orij JJW, Meijer CZ, Van Dijk DJ. Comparison of residual stress predictions and measurements using excimer laser layer removal. Polym Eng Sci 1999;39(1): [6] Turnbull A, Maxwell AS, Pillai S. Residual stress in polymers evaluation of measurement techniques. J Mater Sci 1999;34(3): [7] Chien RD, Chen SC, Peng HS, Su PL, Chen CS. Investigations on the weldline tensile strength of thin-wall injection molded parts. J Reinf Plast Compos 24; 23(6): [8] Kabanemi KK, Vaillancourt H, Wang H, Salloum G. Residual stresses, shrinkage, and warpage of complex injection molded products: numerical simulation and experimental validation. Polym Eng Sci 1998;38(1): [9] Lee YB, Kwon TH, Yoon K. Numerical prediction of residual stresses and birefringence in injection/compression molded center-gated disk. Part II: Effects of processing conditions. Polym Eng Sci 22;42(11): [1] Kamal MR, Lai-Fook RA, Hernandez-Aguilar JR. Residual thermal stresses in injection moldings of thermoplastics: a theoretical and experimental study. Polym Eng Sci 22;42(5): [11] Fan B, Kazmer DO, Bushko WC, Theriault RP, Poslinski AJ. Warpage prediction of optical media. J Polym Sci Part B: Polym Phys 23;41(9): [12] Timoshenko S, Woninowsky S. Theory of plates and shells. McGraw-Hill; [13] Young WB, Wang J. Residual stress and warpage models for complex injection molding. Int Polym Process 22; 17(3): [14] Young WB. Filling and postfilling analysis of injection/ compression molding. Int Polym Process 2;15(4):