Polymer viscoelastic model for calculating internal stress of injection

Date：2014-06-26 15:58:10

        Injection molding is a molding method of the polymer is important. In the forming process, the polymer to withstand the temperature and the force, a stress within the article. The size of the internal stress has a significant impact on the use of the article. On the one hand, the internal stress can cause warpage after releasing the workpiece, dimensional accuracy affected; the other hand, will reduce the internal stress of the mechanical properties of the workpiece, in particular the tensile strength and impact strength, optical properties of the products and apparent quality have varying degrees of impact. Mechanisms and processes in the study of vertical injection molding machine injection molding process stress formation and development, quality control of injection molded article has important significance. Numerous studies indicate that the internal stress of the injection molded article mainly from thermal stress.
        Currently, for the calculation of thermal stress has built a number of different viscoelastic model.
        From the vertical injection molding machine injection molding process characteristics and the characteristics of the polymer starting constitutive behavior, based on the injection of creep experiments, constructed the new vertical injection molding machine stress calculation model and validate numerical example .
        Mechanical model of a problem for ease of illustration, the following as an example to the flat parts stress analysis process within the injection formation and its characteristics. Polymer melt into the cavity, the cooling effect of the mold in contact with the mold wall will be the first melt is cooled and solidified, the solid - liquid interface with time and continuous advance inwardly. Ignore the tension applied to the melt and the solidified layer and the frictional force between the mold wall on the solidified layer, as shown in FIG solidified layer in the stress state of the injection mold 1, wherein, z representative of the part thickness direction, x, y respectively. representative length direction and the width direction of the article. Generally, the thickness of the injection molded article is much smaller than its length and width. Vertical injection molding machines during the cooling process, due to the geometry of the mold and the article, the article in the thickness direction of the inner surface and the shear deformation is difficult, especially in complex shapes injection molded article. For amorphous polymers, ignoring its current orientation of anisotropy caused, may introduce the following assumptions:
        (1) products in the x direction, the total strain Ex (t) = Ey (t) y = 0 direction, wherein, t is time.
        (2) shear strain Exz (t) = Eyz (t) = Exy (t) = 0.
        Pressure (3) on both sides of the solidified layer is exposed to pressure at the pressure values ​​used in the simulation result of packing, i.e. Rz (t) = p (t) where, p (t) is a packing pressure, MPa.
        Injection cooling process, the polymer viscoelastic behavior mainly for creep and stress relaxation. When building the mechanical model, one should consider the description of viscoelastic materials can express their constitutive relations, on the other hand is to establish its solving boundary value problems. On this basis, the number of viscoelastic and viscous component elements constituting a mechanical model for stress analysis calculations. From the basic theory of knowledge viscoelastic, viscoelastic materials can be discrete elastic element and viscous components --- Hooker spring and characterization of Newtonian mechanics model clay pot with a combination of different ways.
        Cooling the injection molding process, mainly due to the strain layer is solidified viscous strain E1, elastic strain E2, E3 heat shrinkage strain and the strain Ez dwell pressure in the thickness direction. Since the vertical injection molding machine does not consider the flow stress, the polymer in the cavity just solidified, it can be regarded as a natural viscoelastic body. As the temperature drops, solidified layer is first generated heat shrinkable strain. Pressure at this time, if the role of the solidified layer in a thickness direction of the strain produced by the Poisson's ratio of the polymer, the inner surface of the strain can be converted to strain solidified layer, it is considered in this lateral strain, denoted E4.
        Since the total strain is zero, the initial strain solidified layer mainly by thermal strain and transverse strain components. Viscous behavior due to the lag, the initial stress field of elastic stress field, the mechanical behavior described by spring. Subsequently, the elastic stress field while continuing to heat strain and transverse strain effects, on the other hand the impact of polymer viscous strain gradually, four-element model of the mechanical characterization of the interactions between them can be shown in Figure 2. It is based on Maxw ell mechanical model, an increase of two elastic rods, used to describe the temperature and pressure at the impact of the strain on the solidified layer vertical injection molding machine.
        L is the viscosity coefficient of the polymer maker, E is the elastic modulus, A is the thermal expansion coefficient, M is the Poisson ratio. Mechanical model of the injection stress calculations using the model by introducing transverse strain, stress can be calculated within the complex into simple plane stress calculations. Springs and dampers to characterize the viscoelastic properties of the polymer itself and its impact on the internal stress; while thermal strain and transverse strain to characterize the material to promote the formation of internal stress field outside the carrier, and it is closely related to the injection molding process conditions.
        When the temperature and holding pressure changes, two elastic rods generate heat strain increment $ E3 and transverse strain increment $ E4, which will force the spring elastic strain increment $ E2, solidified layer formed inside the elastic of a certain size stress field. Under the effect of the stress, sticky pot begins to move, resulting viscous strain $ E1, so that the elastic strain $ E2 has reply, the solidified layer of the original elastic stress - strain fields change accordingly.
        The final stress within the solidified layer - depends on the elastic strain effects and viscous effects combined result, which reflects the injection molded polymer temperature, Paul viscoelastic constitutive behavior under pressure effect. When the viscosity coefficient is large clay pots, these models into elastic model. When the clay pot viscosity coefficient is very small, sticky strain sufficient to completely or mostly elastic strain recovery, viscous flow available which describes the state of the polymer.
        Two constitutive equation
        According to the physical model and assumptions described in solidified layer of stress within the constitutive equation can be written as R (t) = E (T) E2 (t) = - E (T) [E1 (t) + E3 (t) + E4 (t)] (1) where, T is the temperature, K.
        The above equation indicates: solidification during cooling, depending on the instantaneous stress in the internal parts of the elastic response of the material, and with the development of viscous flow of the material change. Formula (1), the thermal strain and transverse strain, respectively E3 (t + $ t) = E3 (t) + A (T) $ T (2) E4 (t) = P (t) M (T) / E (T) (3) According to Newton's law, the viscous strain of E1 (t) = Qt0R (t) L (T) dt (4) can be seen from the formula (1) to (4), shown in Figure 2 mathematical expression in the form of mechanical model is not complicated, the question is how to get the true and accurate polymer performance parameters, especially the elastic modulus E (T) and sticky pot viscosity coefficient L (T).
        In previous studies, the establishment of the constitutive equations often stress relaxation model by genetic integration. Chinese scholars have also conducted many discussed. In fact, vertical injection molding machine cooling solidified layer is viscoelastic state variable temperature, variable temperature relaxation to obtain accurate experimental data very difficult. Further, the polymer of the E (T), L (T) and other physical parameters which change with the change of the machining path, the polymer is heated to a temperature equal to the measured properties of the melt is not cooled to the same temperature performance, which is exactly what we need. To solve this problem, this paper describes a new approach to polymer injection cooling process E (T) changes and L (T) is. The elastic deformation characteristics of the polymer, when subjected to a uniform pressure on the workpiece by p) V) T state equation can be expressed as the strain body H = 3E = V - V0 V0 = - 01 0894ln [1 + p B (T) ] = -. 0 0894ln [1 + RB (T)] B (T) = b3, le-b4, l (T-b5) T> Tg (p) b3, s e-b4, s (T-b5) T         The glass transition temperature Tg. Thermal expansion coefficient variation with temperature available p) V) derived T equation of state. Poisson's ratio is less impact on the strain, to simplify the calculation process, which can be regarded as a constant.
        3 Results and Discussion
        The stress calculations required temperature and holding pressure field generated by Z-mold analysis software available. Injection molding process conditions: injection temperature 195 e, injection pressure 65MPa, holding pressure was 10MPa, 3 0MPa and 50MPa, dwell time 5s, mold temperature was 50 e and 70 e, using flat seam gate, a two-mode cavity. Workpiece size: 140mm @ 60mm @ 21 5mm, the materials used for the PS.
        Which is calculated as follows:
        (1) Select the time step $ t. Set temperature T 0 is the start of the injection molded article stress calculation, the solidification temperature is the corresponding time is 0. If the elastic modulus of the known temperature, the thermal expansion coefficient, $ t after the time of solidification temperature drop $ t, by the formula (2), (3) the initial calculated E03 and E04.
        (2) Since the viscous strain hysteresis, without regard to the impact, i.e., E03 = 0. Thus, E02 = - (E03 + E04), into equation (1) to get the current time of stress R0.
        (3) using equation (10) to get sticky pot temperature viscosity coefficient of the current.
        (4) the next time step, using the formula (2) to (4) were obtained E11, E13 and E14, will be substituted into the formula (1), R1 must stress the current moment. Repeating the above calculation process. Figure 3 is a holding pressure of 50MPa, the simulation under different stress PS injection mold temperature calculation results with the experimental results. Figure 4 is a mold temperature of 70 e, simulation under different vertical injection molding machine holding pressure calculations. As can be seen, improved vertical injection molding machine mold temperature, the injection will have to reduce stress. This is because the higher the mold temperature, the more easily the polymer creep, so that the inner strengthening plastic stress response effects, stress decreased. By comparison with the experimental results, the model accuracy. This is mainly due to the calculation of the model, taking into account temperature, strain on the performance parameters of the polymer, so that it can more truly reflect the changes in their viscoelastic and influence the development of the internal stress. Generally, it is believed the polymer in the mold cavity is rapidly cooled to a temperature below its glass transition, geometry of macromolecular structure in different levels of the system are all key / freeze 0 lost motion capability. In fact, / freeze 0 structure is a metastable structure, there is a tendency to shift the steady-state structure. When the polymer has just solidified from a macro point of view, the glass transition temperature of the polymer is under, but the local area is still in the transition region, the macromolecular chains have some athletic ability and the consequent changes in the structure and properties of polymers the higher the temperature, the greater the stress, this change more rapidly, the viscoelastic polymer exhibits more significant effect. Studies on the structure and mechanical properties of the polymers has been confirmed in the glass transition temperature of the polymer elastic modulus less change, and the simulation results of Figure 3 can be used to obtain a good interpretation of these theories. Consider injection under the glass transition temperature of the polymer viscoelastic behavior is an effective way to stress the numerical simulation of injection molding precision. Figure 4 reflects the influence of packing pressure injection molding parts of sub-surface stress formation. Vertical injection molding machine pressure at the surface stress has little effect on the formation and development, and close to the central portion of the stress with Paul while reducing the pressure has increased. This may be due to the holding pressure decreased during the holding pressure parts feeding parts causes insufficient decrease in density, shrinkage increases.
        4 Conclusion
        (1) The results show that the physical model used to calculate the vertical injection molding machine to cool the internal stress of this article build real and effective, and its related formulas viscoelastic constitutive equation derived therefrom can be well described by injection cooling process viscoelastic behavior of polymers and their impact internal stress development.
        (2) Studies have shown that the viscoelastic behavior of vertical injection molding machine in glassy polymers under the internal stress of the formation and development can not be ignored. Consider the performance parameters change with temperature glassy polymer vertical injection molding machine, and thus lead to lower its viscoelastic response model can get more realistic calculations, and the calculation process is more simple.

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