<TitleType>01</TitleType> <TitleText>Thèses de l'Université catholique de Louvain (UCL)</TitleText>

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COM.ONIXSUITE.9782930344553 03 01 Presses universitaires de Louvain 02 2930344555 03 9782930344553 15 9782930344553 10 BC <TitleType>01</TitleType> <TitleText>Thèses de l'Université catholique de Louvain (UCL)</TitleText> Numéro 30 Thèses de l'École polytechnique de Louvain 30 <TitleType>01</TitleType> <TitleText>Micro-Injection Moulding</TitleText> <Subtitle>From Process to Modelling</Subtitle> 01 GCOI 29303100229470 1 A01 Cécile Jeggy Jeggy, Cécile Cécile Jeggy 1 01 eng 289 00 289 03 TEC000000 29 2012 3069 TECHNIQUES ET SCIENCES APPLIQUEES 24 INTERNET Science des matériaux et procédés 24 INTERNET Sciences appliquées 93 T 01 06 01 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding.The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling.Besides giving insight into the process, this work demonstrates the importance of visco-elastic effects and investigates further related issues. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an appropriate viscoelastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low. In this case, the model admissibility from a mathematical and thermodynamic point of view is not guaranteed. This admissibility is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micromixer design and prototyping is presented as an application of this promising process. 03 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding.The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling.Besides giving insight into the process, this work demonstrates the importance of visco-elastic effects and investigates further related issues. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an appropriate viscoelastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low. In this case, the model admissibility from a mathematical and thermodynamic point of view is not guaranteed. This admissibility is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micromixer design and prototyping is presented as an application of this promising process. 02 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a... 01 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding. The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling. Besides giving insight into the process, this work demonstrates the importance of visco-elastic effects and investigates further related issues. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an appropriate viscoelastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low. In this case, the model admissibility from a mathematical and thermodynamic point of view is not guaranteed. This admissibility is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micromixer design and prototyping is presented as an application of this promising process. 03 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding. The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling. Besides giving insight into the process, this work demonstrates the importance of visco-elastic effects and investigates further related issues. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an appropriate viscoelastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low. In this case, the model admissibility from a mathematical and thermodynamic point of view is not guaranteed. This admissibility is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micromixer design and prototyping is presented as an application of this promising process. 02 Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very... 04 Introduction 1 1 The process 11 1.1 Description of micro-injection moulding................................................................ 12 1.1.1 Classical injection moulding........................................................................ 12 1.1.2 Particularities of micro-injection moulding ................................................. 25 1.2 Equipment ............................................................................................................. 30 1.2.1 Machine ...................................................................................................... 30 1.2.2 Mould ......................................................................................................... 33 1.2.3 Micro-cavity................................................................................................ 35 1.2.4 Inductive heating......................................................................................... 42 1.2.5 Quality control ............................................................................................ 43 1.3 Materials................................................................................................................ 44 1.3.1 General requirements .................................................................................. 44 1.3.2 Materials used in micro-injection moulding ................................................ 45 1.3.3 Materials selected in the Brite project.......................................................... 46 1.4 Micromoulding experiments .................................................................................. 50 1.4.1 Machine ...................................................................................................... 50 1.4.2 Test micro-structures................................................................................... 51 1.4.3 Processing conditions.................................................................................. 53 1.4.4 Quality control ............................................................................................ 57 1.5 Experimental results............................................................................................... 58 1.5.1 Initial trial session ....................................................................................... 58 1.5.2 Second trial session ..................................................................................... 65 1.6 Interpretation of experimental results ..................................................................... 67 1.6.1 Flow filling pattern...................................................................................... 67 1.6.2 Material....................................................................................................... 70 1.6.3 Crucial processing parameters ..................................................................... 70 1.6.4 Visco-elasticity ........................................................................................... 71 1.7 Simulation tool required......................................................................................... 71 1.7.1 Why classical injection moulding simulation tools do not apply for micro-injection moulding ?................................................ 72 1.7.2 Requirements for a simulation tool adapted to micro-injection moulding .... 73 1.8 Conclusion............................................................................................................. 74 2 CONTENTS 2 Modelling 77 2.1 Modelling .............................................................................................................. 78 2.1.1 On the problem of modelling....................................................................... 78 2.1.2 Physical effects ........................................................................................... 79 2.1.3 Restriction of the study................................................................................ 80 2.1.4 Need for a constitutive equation .................................................................. 83 2.2 Visco-elasticity ...................................................................................................... 85 2.2.1 Polymer and flow nature ............................................................................. 85 2.2.2 Visco-elastic models ................................................................................... 86 2.2.3 Criteria to choose a model ........................................................................... 95 2.2.4 Giesekus model........................................................................................... 96 2.3 Dimensional analysis ............................................................................................. 98 2.3.1 Geometrical considerations ......................................................................... 98 2.3.2 Flow considerations..................................................................................... 99 2.3.3 Dimensionless equations ........................................................................... 100 2.3.4 Dimensionless numbers............................................................................. 101 2.3.5 Final equations for the flow....................................................................... 103 2.4 Boundary conditions ............................................................................................ 105 2.4.1 Boundary conditions to be prescribed........................................................ 105 2.4.2 Types of boundary conditions ................................................................... 106 2.4.3 Strong/weak imposition of boundary conditions ....................................... 107 2.4.4 Particular conditions for micro-injection moulding ................................... 108 2.5 Conclusion........................................................................................................... 109 3 Material characterization 111 3.1 Choice of a material ............................................................................................. 112 3.1.1 Criteria...................................................................................................... 113 3.1.2 PC Lexan HF1110R characteristics ........................................................... 114 3.2 Degradation check ............................................................................................... 114 3.2.1 Experimental method ................................................................................ 116 3.2.2 Results ...................................................................................................... 117 3.2.3 Conclusion ................................................................................................ 117 3.3 Determination of dynamic moduli G’ and G’’ ...................................................... 118 3.3.1 Principle.................................................................................................... 119 3.3.2 Experimental procedure............................................................................. 121 3.3.3 Results ...................................................................................................... 121 3.3.4 Comments................................................................................................. 124 3.3.5 Master curves............................................................................................ 124 3.4 Determination of the relaxation time spectrum ..................................................... 127 3.4.1 Method...................................................................................................... 127 3.4.2 Results ...................................................................................................... 129 3.4.3 Comments and discussion ......................................................................... 130 3.5 Determination of the non-linear parameter ....................................................... 133 3.5.1 Steady shear data....................................................................................... 133 3.5.2 Fitting of mobility parameter ................................................................ 134 3.6 Conclusion........................................................................................................... 137 3 CONTENTS 4 Giesekus model, a theoretical analysis .................................................139 4.1 Introduction ......................................................................................................... 139 4.1.1 Second law of thermodynamics ................................................................. 141 4.1.2 Mathematical instabilities.......................................................................... 141 4.1.3 Literature review ....................................................................................... 144 4.2 Characteristics method......................................................................................... 147 4.2.1 Principle.................................................................................................... 147 4.2.2 Covariant and contravariant coordinates .................................................... 148 4.2.3 Quasi-linear form ...................................................................................... 149 4.3 Characteristic sheets............................................................................................. 151 4.3.1 Definition.................................................................................................. 151 4.3.2 Demonstrations ......................................................................................... 153 4.3.3 Application to Giesekus model.................................................................. 157 4.4 Evolutionary character of the system.................................................................... 159 4.4.1 Evolution and non evolution...................................................................... 159 4.4.2 Propagation speed ..................................................................................... 162 4.4.3 Evolution criteria....................................................................................... 163 4.5 Extra-stress histories ............................................................................................ 164 4.5.1 Equations in an intrinsic framework .......................................................... 165 4.5.2 Evolution of positive definiteness.............................................................. 167 4.5.3 Possible return to initial stress configuration.............................................. 169 4.5.4 Application to Beris admissibility criterion................................................ 173 4.6 Formulation of the Second Law ........................................................................... 176 4.6.1 Free energy form....................................................................................... 177 4.6.2 Dimensionless form of the Second Law........................... 180 4.6.3 Constraints imposed by the Second Law.................................................... 180 4.7 Thermodynamic admissibility .............................................................................. 183 4.7.1 Study of........................................................183 4.7.2 Study of................................................................................ 190 4.7.3 Constraints on K........................................................................................ 191 4.8 Conclusion........................................................................................................... 197 5 Numerical algorithm .................................................199 5.1 _-splitting method for time discretization ............................................................. 200 5.1.1 Operator splitting ...................................................................................... 201 5.1.2 Time splitting............................................................................................ 203 5.1.3 Numerical issues ....................................................................................... 208 5.2 Weak formulations............................................................................................... 208 5.2.1 Treatment of the strong formulations......................................................... 209 5.2.2 Continuous weak formulations .................................................................. 211 5.3 Finite element solution......................................................................................... 213 5.3.1 Spatial discretization ................................................................................. 213 5.3.2 Stokes solver ............................................................................................. 217 5.3.3 Transport solver ........................................................................................ 221 5.4 Conclusion........................................................................................................... 230 4 CONTENTS 6 Application of micro-injection moulding .................................................231 6.1 Static micro-mixer ............................................................................................... 231 6.1.1 Electrochemical sensor.............................................................................. 231 6.1.2 Micro-mixing problematics ....................................................................... 232 6.2 Design ................................................................................................................. 234 6.2.1 Micro-mixing concept ............................................................................... 234 6.2.2 Macro-mixing experimental apparatus....................................................... 234 6.2.3 Macro-mixing experimental results ........................................................... 234 6.2.4 Suggested micro-mixing unit design.......................................................... 236 6.3 Prototype ............................................................................................................. 238 6.3.1 Prototype manufacturing ........................................................................... 239 6.3.2 Prototype testing ....................................................................................... 240 6.3.3 Micro-mixing tests .................................................................................... 240 6.4 Micro-moulded mixer devices.............................................................................. 240 6.4.1 Mould making........................................................................................... 240 6.4.2 Moulding trials.......................................................................................... 241 6.4.3 Mixing evaluation ..................................................................................... 242 6.5 Conclusion........................................................................................................... 245 Conclusions .................................................247 Appendix A Stiffness matrix for Stokes problem .................................................251 Bibliography .................................................261 99 BE 07 03 01 https://pul.uclouvain.be/resources/titles/29303100229470/images/34ad9bc83e3c72c62281cb2c744ac966/THUMBNAIL/9782930344553.jpg 20160216 02 https://pul.uclouvain.be/book/?GCOI=29303100229470 06 3052405007518 Presses universitaires de Louvain 01 06 3052405007518 Presses universitaires de Louvain Louvain-la-Neuve BE 04 20040101 2004 01 WORLD 01 9.45 in 02 6.30 in 03 1.63 in 08 16.50 oz 01 24 cm 02 16 cm 03 1.63 cm 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