Injection moulding contraction and the pressurevolume-time

Transcription

1 Polimery, No. 4, 2007, pp Injection moulding contraction and the pressurevolume-time relation B. Kowalska Politechnika Lubelska, ul Nadbytrzyck 236, , Lublin, Poland Selected from International Polymer Science and Technology, 34, No. 5, 2007, reference PT 07/04/280; transl. serial no Translation submitted by E.A. Inglis Heat processing contraction is a measure of the change in volume and shape of the moulding while cooling during injection moulding. Volume contraction and linear contraction are distinguished [1 3], and the value of each of these is not identical in all sites in he product. This variation is caused primarily by the non-uniformly decreasing temperature of the polymer during cooling. This is due partly to the low heat conductivity which changes with drop in temperature and the high heat expansion of the polymer which also changes under these conditions [1 and 2]. As a result, a considerable and spatially varying cooling rate gradient is formed, owing to which the structure of the polymer becomes heterogeneous and anisotropic to varying degrees. In the analysis of volume contraction it is helpful to be able to interpret the p-v-t graphs describing the process of injection, since changes in the specific volume of the plastic relate to most of the phases of this process [1 4]. For instance, during the injection phase there is a marked reduction in the specific volume of the molten polymer due to its compressibility. During the compression phase, under conditions of isobaric cooling, the volume of the polymer in the cavity is reduced. On the other hand, during the cooling phase the individual layers solidify at different rates and under different pressures and are characterised during hardening by different specific volumes. The thicker the moulding the more marked is this type of differentiation. Hence after the polymer has passed into the solid state under atmospheric pressure there is a change in shape and a decrease in volume of the moulding, and the various layers of the contracting polymer have different specific volumes. Insufficient knowledge of the thermodynamic state of the polymer described by the p-v-t relation (especially in the case of partly crystalline polymers) as well as excessive simplifi cations in simulation calculations result in less effectiveness of the process and also mean that the mouldings do not meet the required quality criterion. Therefore, when using these relations during injection moulding it is necessary to determine the kinetic crystallisation parameters for the conditions under which the process is taking place. This allows us to take account of the differences in the phase transition temperatures and also the changes in the specific volume of the polymer in the solid state. Correct analysis of the p-v-t relations and their derivatives is also an indispensable tool in modern computer simulation, especially of the phases of compression and cooling of the moulding during injection moulding. The variable specific volumes are also input data in numerical simulations employed for designing of injection moulds. If we know the changes in properties of the polymer as a function of time this permits us to speed up the optimisation and planning studies and improve the effective control of the process [5 8]. The calculation procedures used in simulation programs require inputting specific data into the program. These include rheological model parameters and parameters of the thermodynamic equation of state of the polymer. The most important of these are the coefficients of thermal expansion and compressibility. The main objective of the simulation studies described here was to compare the volume contraction of the mouldings and their deformation obtained using the p-v-t relations corresponding to conditions of slow and rapid cooling of the polymer, keeping identical remaining conditions of injection moulding Smithers Rapra Limited T/41

2 BASES AND MODELLING ASSUMPTIONS OF THE INJECTION MOULDING PROCESS Simulation of the flow through the mould and the volume contraction and deformation of the mouldings was carried out using the Moldflow Plastics Insight ver. 4.1 program [9 and 10], which is available at the Department of Plastics Processing and Production Equipment at Czestochowa Polytechnic. This program is an integral part of the programming package made by SERC called I-Deas Master Series 8, and its modular structure enables the formation of specific system configurations depending on the particular tasks to be performed. For the simulation we have to input data on the shape and dimensions of the moulding, the constructional elements of the mould, properties of the polymer, conditions of moulding and type of moulding machine. The basis for modelling of he injection moulding process is the assumption that the fl ow of the polymer in he mould channels is locally two-dimensional fl ow [11 13]. This assumption is fundamental, since the mouldings are usually thin-walled products, a fact which allows us to ignore flow in the direction of the thickness of the moulding. It is also assumed that the liquid polymer behaves like a generalised Newtonian fluid. The basic equations that have to be solved are equations of conservation of mass (continuity equation), conservation of movement and conservation of energy. Solving generalised equations of this type relating to processes as complex as injection moulding is not possible, and therefore we have to introduce a series of simplifying assumptions. These relate both to the properties of the polymer and the range of applicability of the equation. Such simplifications can be made by assuming the parameters of shape of the mould cavity and also restricting considerations applying to the moulding cavity and the flow channels. The next step is to introduce the so-called no-flow temperature, which is understood to be the temperature at which the polymer behaves like a solid body. This temperature definition allows us to use in the simulation equations derived for a fluid, which thus do not refer to solidified layers. It is assumed at this point that the rate components of the solidified polymer acquire values close to zero near the cavity walls. It is also assumed that the polymer flow is symmetrical with respect to the central surface of the moulding cavity. Specific data concerning the form of the basic equations, the method of their solution and also an analysis of the simplifying assumptions are described in he literature [11, 13 20]. In the simulation studies, for calculations of the pressure distribution we used the finite elements method, for calculations of the temperature distribution we used the method of finite differences and to determine the passage of the front of the fl owing polymer we used the control volume method [21 23]. The simulation additionally requires the use of the rheological equation of state of the polymer, which determines the relation between the viscosity of the polymer (η) and the shear rate (γ. ). From many known mathematical rheological models [11, 24 27] we selected for our studies the 7-parameter Cross-WLF rheological model. This is a combination of the Cross model and the WLF model which as is well-known [28 30] provides a fairly accurate mathematical description of the rheological properties of a polymer. In the database of the Moldflow Plastics Insight program can be found values for the parameters of this model corresponding to the conditions opf the simulation. The Cross model takes the following form [28 31]: ( ) η0 T, p ηγ (, T, p)= ηγ τ * 1 n where T is the temperature, p is the pressure, n and τ* are constant parameters of the model (τ* denotes the shear stress at which the liquid polymer begins to show the properties of a fluid thinned by shear), and η 0 is the viscosity at a shear rate tending to zero. Changes in η 0 as a function of temperature can be described by means of the WLF model: A T T * ( )= A + ( T T *) 1 η 0 T, p D 1 exp 2 in which ( ) (1) (2) T * ( p)= D2+ D3 p (3) and A = A + D p where D 1, D 2, D 3, A 1 and A ~ 2 are constant parameters of he WLF model. These parameters together with the constants of the Cross model form the 7-parameter Cross-WLF model. Their values with regard to the simulation conditions are determined on the basis of the data in the program (Table 1). It is necessary to know the p-v-t relation for simulation of the pressure phase and also to determine the volume contraction and deformation of the mouldings. In the calculations we employed the Tait experimental equation described in the literature [30, 34 37], separately for the solid state and liquid state of the polymer. The parameters of the Tait equation during slow and rapid cooling of Malen P type J-400 isotactic polypropylene manufactured by Basell Orlen Polyolefins (4) T/42 International Polymer Science and Technology, Vol. 34, No. 8, 2007

3 Table 1. Values of Cross-WLF model parameters Parameter N τ*, Pa D 1, Pa s D 2, K D 3, K/Pa A 1 A 2, K Value Figure 1. Finite element network of central channel and runner (1), polymer sol;idified in the gate (2) and measurement sample (3). were determined in reference 37. These results were used in the present study to calculate the contraction and deformation of the moulding made from this same polymer; its characteristics (data supplied by the manufacturer) are also contained in ref. 37. A solid model of the moulding was drawn using the Master Modeler of the I-Deas Ms8 pack, and it was divided into finite elements with the Mesh modulus of the same computer package. The model shows the sprue (the shaped elements in the central channel, runners and gate) and the measurement sample. The model was divided into 34,293 tetrahedral (3D) finite elements of the measurement sample and 81 linear (1D) elements of the sprue and solidified polymer in the gate (Figure 1). From a database giving details of processing machines we selected the KM 65/160/C1 injection moulding machine produced by Krauss Maffei. Computerised control of this machine permits accurate setting of the moulding conditions and control of the various phases of the process. In the simulation we used data relating to the moulding conditions selected from the literature [2,3, 38] (Table 2). The p-v-t relations employed were obtained from previously presented reports [37 and 39]. We used a rate of cooling of 5 C/min and arpid cooling conditions with regard to the rate of crystallisation. Table 2. Injection moulding conditions adopted for the simulation Symbol of specimen Moulding pressure p d, Mpa Injection speed v w, m/s of injection, t w Time, s of pressure, t d Temperature of cylinder T ( C) in zone: of cooling, t ch I II III IV Smithers Rapra Limited T/43

4 RESULTS OF THE SIMULATION Changes in the volume contraction (S v ) as a function of time were determined at selected nodal points of the moulding shown in Figure 2. Analysis of cooling referred to the central layer of the polymer. The contraction values shown in Figure 3 correspond to the parameters of Tait s model determined with slow cooling of the polymer, whereas those shown in Figure 4 were obtained from adjusted values of the Tait model parameters corresponding to rapid cooling [37]. These graphs show an initial sudden drop in the value of S v, followed b7 an increase and levelling out. The most marked differences in S v relate to point 1 which is closest to the entry of the polymer into the mould cavity. This may be caused by reverse flow of the liquid polymer following the switchover to clamping pressure whish prevents increase in S v. Also, the interaction of the polymer and the cavity wall in the form of friction and adhesion (preceded by absorption) may impede increase in the contraction. After reaching equilibrium, or at the point where the contraction of the polymer overcomes the impediments, volume contraction begins. The different pressure and temperature values at different points of the moulding and also their differing changes with time have the effect that the contraction determined at these points is not the same [40]. Examination of Figures 3 and 4 shows that the values of S v found under conditions of different cooling rates differ considerably. In the case of rapid cooling (Figure 4) the lowest contraction on completion of the moulding process is 10.4% and is found at point No. 1 (compare Figure 2), whereas the highest volume contraction is 10.8% is observed at node No.3. These values are considerably than those obtained using Tait equation parameters for slow cooling, where the minimum S v (No.1) = 13.9% and the maximum S v (No.3) = 14.4%. Figure 2. View of PP moulding with indicated direction of flow of he polymer into the gate. Nodal points (1,2,3) are indicated, at which the cooling curves were determined. Figure 3. Dependence of volume contraction (S v ) on time (t) determined at selected points (1,2, 3 see Figure 2) for PP moulding (Table 2, symbol 25.1) obtained using Tait equation parameters with slow cooling of the polymer. T/44 International Polymer Science and Technology, Vol. 34, No. 8, 2007

5 Figure 4. Dependence of volume contraction (S v ) on time (t) at selected points (1,2,3 see Figure 2) of PP moulding (symbol 25.1 in Table 2) obtained using Tait equation parameters with fast cooling of the polymer. Figure 5. Distribution of volume contraction (S v, coloristic scale) in PP moulding (symbol 25.1 in Table 2) obtained using Tait equation parameters with a) rapid cooling of polymer and b) slow cooling of polymer Smithers Rapra Limited T/45

6 Thus the volume contraction found in conditions corresponding to the real process (more rapid cooling) is lower than with slow cooling of the polymer (the relative differences reach 35%). Also, the uneven distribution of contraction in he various layers of the polymer and its changes in the initial period of the pressure phase are more evident with rapid cooling. In order to visualise the distribution of contraction through the whole moulding we carried out a simulation, which gave the values of S v shown in Figure 5.In this case also we analysed conditions of rapid (Figure 5(a)) and slow cooling of the moulding (Figure 5(b)). In both of the variants considered there are differences in the distribution and values of contraction at the various points of each of the mouldings, and the variability pf contraction is visible both on he surface and in the interior of the mouldings. The deformation resulting from the contraction distribution is shown in Figure 6. In this case there is distribution of he deformations through the thickness and over the entire surface of the moulding. With rapid cooling of the polymer the deformations are thus than with slow cooling, which completely confirms the observations mentioned previously. CONCLUSIONS It is seen from the simulation experiments that the various parameters of the Tait thermodynamic equation of state used for the calculations affect the volume contraction of the injection mouldings. These parameters, defined on the basis of standard measurements of p-v-t, or under slow cooling conditions of the polymer have the effect that the volume contraction values are higher than with rapid cooling, and the differences can be as great as 35%. The deformation of the moulding depends in the same way on the rate of cooling. The results observed in the different layers of the moulding also vary from each other. This is a result of the differentiated gradient of the polymer cooling rate and the fact that the individual layers of the moulding solidify under different real pressures, leading to specific stresses in the polymer. Figure 6. Deformation of PP moulding (symbol 25.1 in Table 2) obtained using Tait equation parameters with a) rapid cooling of polymer and b) slow cooling of polymer. T/46 International Polymer Science and Technology, Vol. 34, No. 8, 2007

7 During rapid cooling of the polymer the time taken for the formation of a fully developed crystalline structure is too short, and for this reason there is less volume contraction than there is with slow cooling. This is undesirable, however, since as a result of further structural changes in the partly crystalline polymer there is increased secondary contraction of the mouldings. From the studies we can assume that the conditions adopted for establishing the p-v-t relation have a substantial effect on the calculated values of volume contraction and deformation of the polypropylene mouldings. Therefore the parameters of the equation of state should be determined under conditions of rapid cooling of the polymer characteristic of the injection moulding process. REFERENCES 1. R. Sikora, Fundamentals of polymer processing, Lublin R. Sikora, Processing of polymers, WE, Warsaw A. Smorawinski, Injection moulding technology, WNT, QWarsaw H. Zawistowski, Theory of the formation of properties of products in injection moulding in Application and processing of polymeric matrerials (ed. J. Koszul), Czestochowa 1998, p X. Guo and A.I. Isaev, Int. Polym. Process., 114, 1999, p.377 and X. Guo et al., Polym. Eng. Sci., 39, 1999, p.2096 and J. Guo and K.A. Narh, Polym. Eng. Sci., 41, 2001, p M.R. Kamal and P.G. Lafleur, Polym. Eng. Sci., 22, 1982, p C-Mold Design Guide. A resource for plastics engineers, C-Mold Ithaca, New York C-mold Reference Manual, C-Mold Ithaca, New York P. Kennedy, Flow analysis of injection moulds, Hanser Publishers, Munich-Vienna-New York K. Wilczynski, Rheology in plastics processing, WNT, Warsaw L.C. Tucker, Fundamentals of computer modelling for polymer processing, Carl Hanser Verlag, Munich-Vienna-New York A.N. Alexandrou and A. Ahmed, Polym. Eng. Sci., 33, 1993, p M. Buchmann et al., Polym. Eng. Sci., 37, 1997, p B.S. Chen and W.H. Liu, Polym. Eng. Sci., 34, 1994, p M.R. Kamal and S. Kenig, Polym. Eng. Sci., 12, 1972, p.294 and M.R. Kamal and P.G. Lafleur, Polym. Eng. Sci., 22, 1982, p W. Michaeli et al., Int. Polym. Process., 16, 2001, p T.D. Papathanasiou and M.R. Kamal, Polym. Eng. Sci., 33, 1993, p J.P. Greee, Polym. Eng. Sci., 37, 1997, p J. Koszkul et al., Simulation of injection mould fiilimng using the program Moldflow Plastic Insight in he collection Polymer materials and their processing, Czestochowa Polytechnic 2000, p Ho-S. Lee, Polym. Eng. Sci., 37, 1997, p P.J. Carreau et al., Rheology of polymeric systems. Principles and applications, Hanser D. De Kee et al., Useful rheological models for industrial applications, J. Ferguson and Z. Kemlowski, Applied rheology of fluids, Lodz O. Verhoyen and F. Dupret, J. Non-newtonian Fluid Mech., 74, 1998, p Yu.L. Liyong et al., Polym. Eng. Sci., 44, 2004, p K.M. Jansen et al., Int. Polym. Process., 13, 1998, p H.H. Chiang et al., Polym. Eng. Sci., 31, 1991, p.116 and L. Yu et al., Polym. Eng. Sci., Polym. Eng. Sci., 44, 2004, p W. Michaeli and P. Niggemeier, Kunststoffe Plast Europe, 89, 1999, p P.A. Tanguy and J.M. Grygiel, Polym. Eng. Sci., 33, 1993, p S. Han and K.K. Wang, Int. Polym. Process., 12, 1997, p S. Han and K.K. Wang, Int. Polym. Process., 17, 2002, p Smithers Rapra Limited T/47

8 36. B. Kowalska and R. Sikora, Polimery, 48, 2003, p B. Kowalska, Polimery, 51, 2006, p Z. Zawistowski and S. Zieba, Setting up injection moulding, Plastech, Warsaw B. Kowalska, Polimery, 52, 2007, No P. Postawa, Polimery, 50, 2005, p.201. T/48 International Polymer Science and Technology, Vol. 34, No. 8, 2007