Numerical simulation of the polymer forming by hot embossing process

Transcription

1 èe Congrès Français de Mécanique Besançon, 9 août au septebre Nuerical siulation of the polyer foring by hot ebossing process Résué: G. CHENG, J.C. GELIN, T. BARRIERE FEMTO-ST Institut, Applied Mechanics Departent, 4 Rue de l épitaphe, 5 BESANCON Ce travail concerne la odélisation theroécanique par éléents finis du procédé d estapage à chaud des polyères theroplastiques. Le principe consiste à chauffer une plaque de polyère à une tepérature au-delà de la tepérature de transition, entre deux plateaux rigides indéforables, dont l un possède des otifs icrostructuraux. Différents paraètres atériaux ont été testés lors de la siulation du procédé de copression à chaud afin d étudier leurs influences au cours de procédé de ise en fore. Les résultats nuériques obtenus sont très encourageants. Abstract: This work concerns the nuerical odelling of the hot ebossing process by using finite eleent ethod. The process consists to the upsetting of a theroplastic plate with an adapted teperature and to replicate the icrostructures between two rigid die structured oulds. The different aterial characterisations of polyers have been taken into account in order to deterine the ain processing paraeters. The hot ebossing siulation has been realized by FEM. The results obtained are in proper agreeent with the experts. Mots clefs: Hot ebossing process, polyers Introduction In the developent of icro technologies, the size of the icrostructures continuously decreases fro icro and sub-icro to nano scales with the fast developent of the icro systes and devices. The topographical surface state of the functional coponents becoes ore and ore coplex and the aterials used also becoe ore coplex. Well-known conventional technologic such as injection oulding, hot ebossing and casting process have been extensively used at the icro-replication scale. Hot ebossing is now becoing a proising anufacturing processes, which is well suited for producing dedicated icrostructures with high aspect ratios and sall distortions [-]. However, larger diffusion of the hot ebossing process is liited due to the lack of adequate characterisation and process optiization. To face the future requireents, reliable coputer odels and siulation tools for hot ebossing processes are necessary []. Due to the high processing teperature in ebossing conditions, the visco-elastic properties of the polyer ay have an effect on the foring process. In this paper, a reliable constitutive odel is applied to describe the aterial properties of PMMA during the hot ebossing process by using COMSOL Multiphysics software. Description of hot ebossing process Hot ebossing process is a polyer replication process that is investigated in different laboratories [][4]. This process is especially well suited for anufacturing sall and ediu batch of icro-coponents []. This process can be divided into four sequential stages (figure ): Heating stage: Heat a polyer plate to glass transition teperature between lower and upper icro structured plates, Copression stage: The upper ould ove down and ebosses the polyer plate with an iposed pressure at the hot ebossing teperature, Cooling stage: Cool down the polyer plate to the deoulding teperature, Deoulding stage: Open the ould to obtain the polyer plate with icro structured cavities.

2 èe Congrès Français de Mécanique Besançon, 9 août au septebre Upper Mould Polyer Plate Lower Mould Pressure Upper Mould Lower Mould Upper Mould Lower Mould Heating stage Copression stage and cooling stage Deoulding stage FIG. The different stages of hot ebossing process: heating, copression, cooling and deoulding stage A polyer plate is inserted between two copression plates. The thickness of the polyer plate depends on the depth of the cavities. The surface of the polyer ust cover the structured part of the oulds. The oulds and the polyer plate are heated up to the glass transition teperature in vacuu, which is above the polyer s softening teperature. The upper ould oves down to copress the polyer plate into the icro-structured cavities until the axiu ebossing force is reached. During the replication period, the teperature is always kept up to the hot ebossing teperature. The variation of the teperature and pressure during the hot ebossing process is related in figure [5]. After the filling of the cavities, the polyer plate is cooled down below the softening teperature. In order to avoid the shrinkage and sinking arks, the ebossing force is aintained during the cooling stage. The upper ould lift and the structure part can be deoulded. Teperature Tg Pressure Tie Heating Copression Cooling Deoulding FIG. Profile of the hot ebossing pressure and teperature, which shows the variation of teperature and pressure during hot ebossing process [5] The hot ebossing process is ore flexible, copared to other icro anufacturing processes, such as injection oulding and casting. Different oulds can be used in hot ebossing process and the experiental processing conditions are ore extended copared to injection oulding process. Due to the fact that the highest teperature in hot ebossing is above the softening teperature, and the polyer need to be heated above the elting teperature in the injection process. Nowadays, the research activities are focused to find low-cost production processes, so the hot ebossing process is well suited for that [].. Modelling of the hot ebossing process The siulation of the hot ebossing process is one of the ost popular subjects in the icrostructure field in recent years. Thanks to the quick developing of the FEM siulation tools, the hot ebossing process can be analysed with various FEM software, such as Abaqus, Cosol, Ls-dyna. The hot ebossing process is coplex and is difficult to define only one FEM tool to siulate the whole process [6]. The siulation of the hot ebossing process can be divided into several steps: the heating process siulation, the ebossing process siulation and the deoulding process siulation. The hot ebossing process siulation covers the aterial behaviour, the characterization of contact friction between polyer and oulds, the echanical and theral conditions [7]. The deoulding process step is the ost iportant one, because the risk of destroying icrostructures is highest during this processing [6]. Due to the coplexity of the hot ebossing process, the work involved in the heating and copression stage, not include the deoulding one. In order to siplify the odelling process, the linear viscoelastic odel has been applied for taking into account the evolution of the aterial behaviour. The contact and friction between polyer and oulds have been Tie

3 èe Congrès Français de Mécanique Besançon, 9 août au septebre taken into account during the process odelling. The theral conditions have been treated by using a variable Young due to the softening of the polyer at high teperature. The odelling of the hot ebossing process has been carried out by using COMSOL Multiphysics software.. Definition of behaviour law A theroplastic polyer Poly (ethylethacrylate) (PMMA) has been selected in the siulation of the hot ebossing process. The deforation of the polyer occurs principally at the copressing stage. Therefore the odelling of the echanical behaviour needs to be able to describe the evolution of the viscoelastic behaviour beyond the glass transition teperature. A linear viscoelastic odel has been selected to describe the aterial behaviour at the copressing stage, for which the stress depends linearly on the strain and its tie derivatives (strain rate). It is assued that the viscous part of the deforation is incopressible, so that the volue change is purely elastic. The total stress tensor is in the for of: σ K[ ε α ( T )] Ι + σ () vol T ref where K is the bulk odulus, α is the coefficient of theral expansion, the strain tensor is decoposed as: ε ε vol Ι + ε d () where the voluetric strain is defined as: d ε trace ε ] () vol [ ij The stress deviator is expressed as follows: t ε d σ d Γ( t t') dt' (4) t' where the function Γ(t ) is called the relaxation odulus function that can describe the evolution of the aterial shear odulus during the relaxation tie. The generalized Maxwell odel, which is the ost general for of the linear odel for viscoelasticity, has been introduced for this approach. The odel can be represented by a purely viscous daper and a purely elastic spring connected in series. It takes into account that the relaxation does not occur at a single tie, but at a distribution of ties. The function can be expressed as: Γ( t) G + N G t exp( ) τ where G is the shear odulus of aterial, τ is the relaxation tie constant of the daper and the stiffness of the spring in the sae branch. (5) G represents. Siulation of the hot ebossing process The copression odelling has been realized under diensions axisyetric geoetrical assuption (figure ). A polyer plate has been copressed between two rigid and non deforable plates, which have a Young s odulus and a Poisson ratio corresponding to those of structure steel (table ). The three blocks in the odel are constructed respectively in the software. The interfaces between the polyer and steel plates are treated as contact pairs. The diensions of the polyer disc equals to 4 in diaeter and 5 of thickness. A suitable Young s odulus has been applied for the polyer disc, in order to properly account the theral conditions at high teperature. Therefore, the polyer Young s odulus is equal to 8 MPa and the Poisson ratio is equal to.4 (table ). The processing geoetry odel has been eshed with free triangular eleents. The rigid plates have been supposed to be undeforable, so a uch ore coarse esh size has been applied. The deforation of the PMMA plate is ore iportant for the odelling. Therefore, the eleent size of the polyer plate is uch finer in order to iprove the siulation accuracy. The eleent size for the polyer and two plates is related in table. Material Density (Kg/³) Young s odulus (MPa) Poisson ratio Upper and lower ould (in steel) 785. Polyer plate (PMMA) Table. Viscoelastic paraeters for PMMA plate and oulds

4 èe Congrès Français de Mécanique Besançon, 9 août au septebre Syetry axis 5 Contact pair 5 FIG. Mesh of the geoetry of tooling syste and polyer disc between two rigid oulds used for siulation of hot ebossing process Material Eleent type Max. eleent size () Min. eleent size () Eleent nuber Upper and lower ould Free triangular(three nodes) Polyer plate Free triangular(three nodes) Table. Description of eleent size of the PMMA plate and the steel oulds.. Siulation of the heating process The heating stage has been siulated using COMSOL Multiphysics software for Heat Transfer physic odelling, which is used for siulating the evolution of teperature in the PMMA and upper and lower plates during the heating stage. The PMMA glass transition teperature is equal to 5 C [8]. The ai of the heating stage is to heat the PMMA to the teperature above the glass transition teperature. In the siulation of the heating process, the polyer plate is heated by two steel oulds, which have an initial teperature 6 C. The tie-dependent study is selected in order to see the evolution of teperature in the polyer plate. The boundary theral conditions during the heating stage are described as follows: The initial value of abient teperature has been fixed to C, so as the polyer plate The initial value of teperature in the steel oulds has been fixed to 6 C The whole odel is axisyetric with the reference axis R. The theral aterial properties of the polyer plate and the discs are described in table. These paraeters describing the physical behaviour of the aterials used could be obtained directly in the database of the COMSOL software. Material Glass transition teperature [ C] Heat capacity at constant pressure [J/(Kg* C)] Theral conductivity [W/(* C)] Upper and lower ould (in steel) Polyer plate (PMMA) Table. Physical paraeters of the polyer plate and discs A Tie Dependent Solver has been used to calculate the internal teperature of the polyer PMMA during the whole heating stage. The heating tie has been defined in the range fro to s with a step equal to s. The teperature contours in the tools and ebossed aterial can be observed as follows (figure 4): T s 4 T s

5 èe Congrès Français de Mécanique Besançon, 9 août au septebre T 4s T s FIG. 4 Teperature contour in the ebossed plate and oulding plates when Ts, Ts, T4s and Ts According to the figure 4, at the beginning of the heating process (Ts) the teperature in the oulds and polyer plate corresponds the initial conditions of the odel. During the heating process, the distribution of the teperature in the odel is syetric because of the syetric boundary conditions iposed. At the end of the process (Ts), the polyer plate has been heated to nearly 5 C and the whole odel has alost the sae teperature... Siulation of the copression process The copression stage has been siulated by applying a constant pressure at the external surface of the upper disc. In order to obtain the rigid and undeforable oulding plates, a uch larger value of the Young s odulus has been applied in the copression process. The contact friction between the polyer surface and the ould disc surface has been taken into account by using the contact pair in the software. The value of the Young s odulus is equal to 8 MPa, which corresponds the PMMA proprieties at high teperature. The alternative for of Equation (5) is N t Γ( t) G[ µ + µ exp( )] τ where the constant µ are such that N 5 µ (7) In the siulation, a four-ter Generalized Maxwell aterial has been applied in order to describe the viscoelastic property of the polyer. The paraeters for the odel are as follows: µ. 54 ; µ.4, τ s ; µ.8, τ s ; µ.9, τ s ; µ.5, τ s. 4 4 The viscoelastic properties have a strong dependence on the teperature for any polyers, therefore an assuption is used in these aterials. A change in the teperature can be transfored directly into a change in the tie scale. A WLF (Willias-Landel-Ferry) equation has been applied in order to describe the relaxation tie α (T ) : T C( T T ) Log( α T ) (8) C + ( T T ) where T is the glass transition teperature of the aterial, C and Care aterial constants: C 7. 44, C 5.6. The boundary conditions in the siulation of the copression process are as follows: The lower ould die is fixed during the ebossing process A upsetting load P 5 N has been applied in the exterior surface of the upper disc The whole odel is considered as axisyetric with the reference axis R. The viscoelastic aterial date (instantaneous) for the polyer: G 7MPa, K MPa (6)

6 èe Congrès Français de Mécanique Besançon, 9 août au septebre The reference teperature for the viscoelastic aterial is 5 C The contact friction coefficient for the contact pair is... FIG. 5 Total displaceent for an iposed pressure equal to P5N/ applied to the exterior surface of the upper disc In the copression stage, both discs have been supposed rigid and non deforable, this is clearly observed in figure 5. During copression by the rigid disc, the polyer plate exhibits a significant deforation. The free boundary surface of the polyer plate exhibits a large displaceent in the horizontal direction. The contact friction conditions have been taken into account for the siulation, so a slip oveent of the polyer plate in the contact surface could be observed in figure 5. The deforation of the PMMA plate is not syetric with the horizontal axis, due to the pressure applied on the external surface of the upper disc when the lower disc is always fixed. The PMMA layers closed to the upper disc exhibit ore displaceent than the lower PMMA layers. Conclusions The developents presented in that paper corresponds to a first investigations for the nuerical siulation of the hot ebossing process based on COMSOL Multiphysics software (4.a). The heating process and the copressing process have been siulated in this analysis. A viscoelastic aterial odel has been applied for the polyer in order to describe the aterial properties at high teperature. The contact and friction conditions between the polyer plate and the ould tool are taken into account in order to be close to the reality conditions. Reaining probles associated the hot ebossing process siulation are now in progress in the laboratory. References [] Heckele M., Schoburg W.K., Review on icro olding of theroplastic polyers, Microech Microeng. Journal, 4, -4, 4. [] Worgull M., Hétu J.-F., Kabanei K.K., Heckele M., Modeling and optiization of the hot ebossing process for icro- and nanocoponent fabrication, Microsy. Techno.,, , 6. [] Worgull M., Heckele M., New aspects of siulation in hot ebossing, Microsy. Techno.,, 4-47, 4. [4] Sahli M., Millot C., Roques-Cares C., Khan Malek C., Barriere T., Gelin J.C., Quality assessent of polyer replication by hot ebossing and icro-injection oulding processes using scanning echanical icroscopy, Materials Processing Technology. Journal, 9, , 9. [5] Liu C., Li J.M., Liu J.S., Wang L.D., Deforation behavior of solid polyer during hot ebossing process, Microel. Eng., 87, -7,. [6] Worgull M., Kabanei K.K., Marcotte J.-P, Hétu J.-F., Heckele M., Modeling of large area hot ebossing, Microsyste Technology., 4, 6-66, 8. [7] Jena R.K., Chen X., Yue C.Y., La Y.C., Viscosity of COC polyer (TOPAS) near the glass transition teperature, Experiental and odeling, 9, 9-98,. [8] Lin C.-T., Kuo S.-W., Huang C.-F., Chang F.-C., Glass transition teperature enhanceent of PMMA through copolyerization with PMAAM and PTCM ediated by hydrogen bonding, Polyer, 5, ,. 6