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Micro-Injection Moulding
From Process to Modelling
Première édition
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.
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Spécifications
- Éditeur
- Presses universitaires de Louvain
- Partie du titre
-
Numéro 30
- Auteur
- Cécile Jeggy,
- Collection
- Thèses de l'École polytechnique de Louvain
- Langue
- anglais
- Catégorie (éditeur)
- Sciences appliquées > Science des matériaux et procédés
- Catégorie (éditeur)
- Sciences appliquées
- BISAC Subject Heading
- TEC000000 TECHNOLOGY & ENGINEERING
- Code publique Onix
- 06 Professionnel et académique
- CLIL (Version 2013-2019 )
- 3069 TECHNIQUES ET SCIENCES APPLIQUEES
- Date de première publication du titre
- 01 janvier 2004
- Type d'ouvrage
- Thèse
Livre broché
- Date de publication
- 01 janvier 2004
- ISBN-13
- 9782930344553
- Ampleur
- Nombre de pages de contenu principal : 289
- Code interne
- 2930344555
- Format
- 16 x 24 x 1,5 cm
- Poids
- 306 grammes
- Prix
- 23,30 €
- ONIX XML
- Version 2.1, Version 3
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Sommaire
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