injection analysis.pdf

Introduction Weld lines are formed during mold fi lling whenever two separated melt streams recombine. This occurs either due to injection through multiple gates or as a conse- quence of fl ow around an obstacle. Two main types of weld lines are usually distinguished. Cold or stagnat- ing weld line is formed by a head-on impingement of two melt fronts without additional fl ow after that. Hot or fl owing weld lines occur when two melt streams continue to fl ow after their lateral meeting. Since weld lines often result in reduced mechanical strengths and/or poor optical surface appearance of injection molded parts there have been a great number of investigations about the eff ect of processing condi- tions on the weld lines. Malguarnera and Manisali (1981) measured the weld line strength for several types of polymers and found that melt and mold temperature had a remarkable infl uence on the weld line strength. Criens and Mosle (1983) investigated the infl uence of design and processing parameters on the mechanical properties of a plate with hole. They rec- ognized that the eff ect of melt temperature changes from polymer to polymer. Kim and Suh (1986) have shown that increasing melt temperature can lead to a deterioration of weld line strength just below the degradation temperature. Injection pressure, injection speed, holding time and holding pressure have also beeninvestigatedandonlylittle eff ecthasbeen observed (Piccarolo and Saiu 1988). Recently, Liu et al. (2000) designed their experiments according to the Taguchi?s method and showed again that the melt and mold temperature are the principle factors aff ect- ing weld line properties of injection molded thermo- plastics. It should be noted that the sensibility of weld lines depends not only on the material properties and the processing conditions, but also on the testing methods applied (Selde n 1997). Although in the literature mechanical weakness of weld lines is usually explained by (1) lack of diff usion Tham Nguyen-Chung Flow analysis of the weld line formation during injection mold fi lling of thermoplastics Received: 10 February 2003 Accepted: 22 October 2003 Published online: 19 December 2003 ? Springer-Verlag 2003 Abstract To studythe weld line formation of colliding fl ow fronts the fi lling of a mold cavity was sim- ulated. The thermo-rheological fi ndings were used to investigate the sources of weld line weakness. In this way critical areas of the inter- face in regard to the lack of inter- diff usion and the inappropriate molecular orientation were found to be placed near the surface of the fi nished parts. The main source for the weld line weakness seems to be the V-notch that arises due to the poorly bonded region near the sur- face in combination with the large shrinkage as a result of extremely high molecular orientations induced at the end of the fi lling. Further- more, the empirical knowledge was confi rmed that weld lines are rather more sensitive to the local fl ow sit- uation than the global processing conditions. Melt and mold temper- atures can be considered to be the most important factors which infl u- ence the weld line strength. Keywords Polymer Injection molding Thermoplastics Weld line Simulation Rheol Acta (2004) 43: 240245 DOI 10.1007/s00397-003-0339-2 ORIGINAL CONTRIBUTION In part presented at the 6th European Con- ference on Rheology, Erlangen, 2002 T. Nguyen-Chung Institut fu r Allgemeinen Maschinenbau und Kunststoff technik, Chemnitz University of Technology, 09107 Chemnitz, Germany E-mail: tham.nguyen.chungmb.tu-chemnitz.de of polymer molecules, (2) unfavorable molecular ori- entation at the interface, and (3) formation of a V-notch at the surface of injection molded parts (Kim and Suh 1986; Fellahi et al. 1995), little was known about the interrelationship between these factors. Kim and Suh (1986) analyzed the fi rst and second factors separately and then integrated them to predict the strength of weld lines. In their theoretical approach for the diff usion process the temperature gradient across the part thickness was neglected. Tomari et al. (1990) clarifi ed the V-notch structure and its eff ect on the strength of general purpose polystyrene injection mol- dings. They measured the weld strength of dog bone type tensile specimens the surface of which was par- tially eliminated by milling. Their results suggested that the V-notch eff ect is caused rather by a poorly bonded layer near the surface than the fi ne groove on the surface. It is also worth noting that the V-notch may be also attributed to the air entrapped at the interface between the fl ow fronts (Hagerman 1973) or volumetric shrinkage during cooling (Piccarolo and Saiu 1988). To date, modeling of the weld line mainly focuses on predicting the weld line position and investigating the infl uence of the thermo-rheological situation on the measured weld line strengths. However, most of the simulation is based on the pressure drop formulation, which does not give detailed information about the fl ow situation at the advancing front. There have been only a few papers on simulation of the weld line for- mation considering the full fl ow history. Wei et al. (1987) calculated the stress which a viscoelastic melt exhibits in a fl ow past obstacles by assuming that the kinematics are close to those of a shear-thinning fl uid such as the Carreau model. The calculated values of molecular orientation showed a highly oriented region surrounding the weld interface just downstream of the obstacle, which was verifi ed by experiments using the rheo-optical method. Mavridis et al. (1988) simulated the situation of colliding fl ow fronts for a Newtonian fl uid and showed that the orientation of polymer molecules at a stagnating weld line is mainly deter- mined by the fountain fl ow before the collision occurs. Recently, Nguyen-Chung et al. (1998) investigated the fl ow mechanisms behind an obstacle clarifying the infl uence of the thermo-rheological history of the melt on the performance of the weld line. The presented paper represents a non-isothermal simulation of the weld line formation due to collision of two fl ow fronts. This way the aforementioned sources of the weld line weakness and their interrelationship can be investi- gated with regard to the fl ow history and the thermo- rheological situation, which as a whole enables a better understanding of the mechanisms of the weld line formation. Simulation Simulation has been carried out of a viscous fl uid fi lling a rectan- gular cavity from both ends (Fig. 1). By considering the symmetry a quarter of the cavity was modeled as two-dimensional geometry. Neglecting gravity and surface tension means that the free surfaces can be assumed to be initially fl at, the fl uid being at rest. The mass, momentum and energy conservation equations for an incompressible fl uid can be written as follows: r ? t 01 q t t t ? r t ? ?rp r ? ? s2 qcp T t t ? rT ? r ? krT ? s : _ ? c3 where t, t, T, p, ? s, _ ? c, q, cpand k denote time, velocity vector, temperature, hydrostatic pressure, deviatoric stress tensor, rate of deformation tensor, density, specifi c heat and heat conductivity respectively. The constitutive equation for a generalized Newtonian fl uid was used: ? s 2g T; _ c _ ? c;_ ? c 1 2 r t r tT4 with the viscosity given by the Bird-Carreau model (Bird et al. 1977): g g01 kc _ c 2 hin?1 2 ;_ c ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 2_ ? c : _ ? c p 5 For temperature dependence the Arrhenius model was applied on the viscosity at a reference temperature T0: g _ c;T aTg aT_ c;T0;aT exp a 1 T ? 1 T0 ? 6 Fig. 1 Initial state (top) and boundary conditions (bottom) for a fi lling simulation of a rectangular cavity 241 The following boundary conditions complete the statement of the problem: at the inlet a constant velocity and a constant tem- perature of the melt are assumed; no-slip condition and a constant mold temperature are imposed on the wall (Table 1); at the sym- metry lines symmetry conditions are applied; at the fl ow front zero surface traction is applied and heat transport through this surface is neglected. With the commercial code FIDAP (Fluent 1998), the Galerkin fi nite element method was used to solve the continuity, momentum, and energy equations which are discretized by standard procedures, using a mixed formulation in which pressure is interpolated one order lower than velocity and temperature. The free surfaces are tracked by using the VOF method applied on a fi xed mesh (Hirt and Nichols 1981). An additional equation is to be solved together with the governing fl ow equations: F t t ? rF 07 whereby F is defi ned as a material density function. It has a value of unity in a fi lled section of the fl ow domain and is zero outside of the fl uid. At the free surface itself this function has a value between 0 and 1. As material, polystyrene 165 H (supplied by BASF, Ludwigshafen, Germany) has been used. The thermo-rheological properties and the coeffi cients of the viscosity model are shown in Table 2. Results Results will be shown using the non-dimensionalized variables as follows: v? v v0 ; t? t t0 ;t? t t0 v0 ; _ c ? _ c v0 t0 ; p? p v0 g0T0t0 8 with a characteristic length v0=0.004 m, a characteristic velocity m0=0.1 m/s, and a zero-shear-rate viscosity g0(T0)=3760 Pas. The fl ow fronts at diff erent times (Fig. 2) show that the weld line is formed as expected from the middle of the cavity towards the wall. In Fig. 3 the path lines of selected material elements can be observed which are originally positioned on the fl at fl ow front. The distance between the originally fl at fl ow front and the weld line position is large enough so that the fl ow front has been fully developed before the weld line is formed. It can be seen that the weld line consists of the material elements coming from the core region of the cavity where they generally did not have experienced large deformations (Nguyen-Chung and Mennig 2001). Only during the transition from the fl at to the fully developed fl ow front may deformations occur, but that is rather an exception due to the specifi c problem defi nition. On the whole, deformations at the weld line must be mostly subjected to the local fl ow situation. At the interface the material elements change their fl ow direction and continue to move along the thickness direction. During these times interdiff usion may occur. In the core the contact time above the solidifi cation temperature is longer than in the outer region so that a stronger degree of interdiff usion can be expected there. By contrast, in the layer near the wall, the contact time is very short since the material elements arriving there will be frozen-in immediately before contact with their counterparts can be established (for example the mate- rial element numbered 8). This results in a layer with poor bonding as found by Tomari et al. (1990). Themolecularorientationhasbeenfrequently investigated by tracing a great number of material ele- ments which are fi rstly placed on a straight line (Coyle et al. 1987). However, in that way it is not possible to distinguish between the absolute deformations that strongly depend on the observation time and the relative deformations that are a measurement for molecular orientation. In this work, several groups of material Table 1 Processing parameters ParametersValues Melt temperature TF503 ?K Mould temperature TW333 ?K Inlet velocity v00.1 m/s Table 2 Material properties of polystyrene 165 H PropertiesValues Melt density q892 kg/m3 Specifi c heat cp1968 J/kgK Thermal conductivity k0.14 W/mK Reference temperature T0503 ?K Zero-shear-rate viscosity g0(T0)3760 Pas Time constant k0.15 s Power law index n0.23 Arrhenius coeffi cient a10,842 Fig. 2 Development of the fl ow fronts 242 elements were traced. Each group forms a circle and locates originally on the straight fl ow front (Fig. 4). By comparing the deformations of the circles at diff erent times the relative deformations of the melt and so the development of the fl ow induced molecular orientation can be visualized. It shows again that the high orienta- tion at the weld line is a result of rather the local deformations along the interface than of the general deformation at the fl ow front. In the past, Mavridis et al. (1988) also recognized that there was signifi cant exten- sional deformation at the surface of the advancing fl ow front which would lead to a perpendicular orientation to the wall. The authors pointed out the analogy of the colliding fl ow fronts to the planar stagnation fl ow which was originally used by Tadmor (1974) as a model to describe the fountain fl ow. However, in the same paper Mavridis et al. (1988) compared the stretching of material bands at the fl ow front with those at the weld line and recognized that the stretching due to fountain fl ow is much larger leading to the assumption that the fountain fl ow may be mostly responsible for the anisotropy at weld lines of injection molded parts. This assumption is not quite correct due to the fact that dif- ferent tracking times were compared to each other, i.e., the material bands at the fountain fl ow were traced longer than those at the colliding fl ow fronts. Actually, Fig. 4 shows that the fountain fl ow, which leads to high deformations at the mold wall (Nguyen-Chung and Mennig 2001) producing pronounced molecular orien- tation parallel to the wall, aff ects only the regions far away from the weld line. As the two fl ow fronts meet, the extension along the weld line can be considered to be the main source for the molecular orientation perpen- dicular to the wall. Furthermore, the largest extension rate was found to occur near the cavity surface just before the cavity has been fully fi lled (Fig. 5). In the core the extension rates are at a lower level all the time like in case of a steady-state planar extensional fl ow. Fig. 3 Path lines of material elements originally positioned on the straight fl ow front Fig. 4 Deformations of circular volume elements Fig. 5 Extension rates along the weld line just before the end of fi lling 243 The reason for the increasing extension rates towards the wall was the increasing velocity, which occurred due to the small eff ective cavity remaining in the last fi lled region while the average fl ow rate was kept constant (Fig. 6). As a consequence of this local fl ow situation a high degree of molecular orientation perpendicular to the wall can be expected near the cavity surface which is therefore assumed to be the most sensitive area of the weld line region. Furthermore, a hypothesis may be postulated that not only the poor bonding but also the high molecular orientation leads to formation of the V-notch, since the relaxationoforientationleadstoinhomogeneous shrinkages which are more pronounced near the weld surface than elsewhere. This can be verifi ed by experi- ment with test specimens created by two-component injection molding of diff erently colored melts of the same material. After having been annealed above the glass transition temperature the test specimens show large shrinkage at the weld surface indicating high molecular orientation in the region (Fig. 7). Due to the decreasing eff ective cavity mentioned above the pressure drops near the wall region are also very high (Fig. 8), so that a further increase of the pressure level at the last fi lled region to compensate the shrinkage will have little eff ect. It should be noted that the V-notch could be still a direct result of an incomplete fi lling under improper processing conditions which may be even aggravated by the entrapped air or contaminants as supposed by other authors. However, unavoidable inhomogeneous shrink- age, which deteriorates the bonding additionally, seems to be an important source for the V-notches (Haufe et al. 1999). Conclusions The empirical knowledge about the sources of the weld line weakness have been confi rmed by simulation results. It can be shown that the critical areas of the weld line interface are placed near the surface of the fi nished parts. The main source for the weld line weakness seems to be the V-notch. First, it is a result of the poor bonding since there is insuffi cient time for the polymer molecules to diff use across the interface. Second, the molecular ori- Fig. 6 Increasing velocity at the last fi lled region due to decreasing eff ective cavity Fig. 7 Comparison of test specimens before (top) and after (bottom) having been annealed above the glass transition temper- ature Fig. 8 Pressure distribution across the interface just before the end of the fi lling 244 entation on the surface of the part which used to be parallel to the wall ends up being parallel to the weld line. That is unfavorable for mechanical strength. Fur- thermore, the high orientation produces large shrinkage near the wall, mostly in direction parallel to the weld line which may be an additional source of the V-notch. On the whole, the sources of weld line weakness are more sensitive to the local fl ow situations than the global conditions so that, as expected, melt and mold temper- atures can be considered to be the most important processing parameters which infl uence the weld line strength. Moreover, well-known possibilities like local heating or mechanical techniques to smear the interface such as push-pull, which directly infl uence the local fl ow situation are eff ective methods to improve the weld line strength. Acknowledgement The author would like to thank the DFG (Deutsche Forschungsgemeinschaft) for the fi nancial support of the investigation. References Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymeric liquids, vol 1. Wiley, New York Coyle DJ, Blake JW, Macosko CW (1987) The kinematics of fountain fl ow in mold fi lling.