Injection Molding

Preface

Part I: Background and Overview

1 Injection Molding: Introduction and General Background

1.1 Scope

1.2 Introduction

1.2.1 Polymer Processing

1.2.1.1 The Plastics Processing System

1.2.1.2 Processing Properties of Polymers and Their Compounds

1.2.2 Injection Molding

1.2.2.1 Introduction

1.2.2.2 General Injection Molding Process Sequence

1.3 Injection Molding Process Characteritics

1.3.1 The Plastication Stage

1.3.1.1 The Melting Zone

1.3.1.2 Temperature distribution in the nozzle

1.3.2 The Filling Stage

1.3.2.1 Flow Lines and Weld Lines

1.3.2.2 Jetting

1.3.2.3 Fountain Flow

1.3.3 Heat Transfer in the Cavity

1.3.3.1 Measurement of Temperature Distribution in the Cavity

1.3.3.2 Numerical Simulation of Heat Transfer in Injection Molding

1.3.3.3 Crystallization Kinetics

1.4 Microstructure of Injection Molded Parts

1.4.1 Crystallinity

1.4.1.1 Effect of Crystallinity and Orientation on Birefringence and Tensile Modulus

1.4.2 Morphology

1.4.3 Residual Stresses

1.4.3.1 Calculation of Residual Stresses

1.4.4 Microstructure of Fiber Reinforced Thermoplastics

1.4.4.1 Fiber Length and Concentration Distributions

1.4.4.2 Matrix Crystallinity

1.4.4.3 Fiber and Matrix Orientation

1.4.4.4 Composites Incorporating Conductive Fibers

1.4.5 Distribution of Cure in Thermosets

1.5 Properties of Injection Molding Compounds and Products

Symbol List

References

Part II: Injection Molding Machinery and Systems

2 Injection Molding Machines, Tools, and Processes

2.1 Injection Molding Machines

2.1.1 Types of Injection Molding Machines

2.1.1.1 Horizontal Injection Molding Machines

2.1.1.2 Vertical Injection Molding Machines

2.1.1.3 Hybrid Injection Molding Machine Composed of Vertical and Horizontal Units

2.1.2 Screw and Barrel Unit

2.1.2.1 In-Line Screw Type Injection Molding Machines

2.1.2.2 Screw Design for Injection Molding Machines

2.1.2.3 Barrels for Injection Molding Machines

2.1.3 Driving Principles

2.1.3.1 Hydraulic Injection Molding Machines

2.1.3.2 Electric Injection Molding Machines

2.1.3.2.1 Control Systems for an Electric Injection Molding Machine

2.1.3.2.2 Injection Mechanism for an Electric Machine

2.1.3.2.3 Nozzle Contact Mechanism for an Electric Injection Molding Machine

2.1.3.2.4 Electric Clamping Mechanism

2.1.3.2.5 Electric Ejection Mechanism

2.1.3.3 Man-Machine Interface and Communication Control

2.1.3.3.1 Man-Machine Interface for an Injection Molding Machine

2.1.3.3.2 Communication Control

2.1.4 Process Control

2.1.4.1 Control of the Filling Process

2.1.4.2 Control of the Hold-Pressure Switching Process

2.1.4.3 Control of the Hold-Pressure Process

2.1.4.4 Control of the Metering Process

2.1.4.5 Control of the Mold Opening/Closing Process

2.1.4.6 Temperature Control of Each Barrel And Nozzle

2.1.4.7 Control of the Injection Compression Process

2.2 Molds for Injection Molding

2.2.1 Functions of Mold Components

2.2.2 Classification of Molds

2.2.2.1 Cold Runner Mold Systems

2.2.2.1.1 2-Plate Molds

2.2.2.1.2 3-Plate Molds

2.2.2.2 Hot Runner Mold Systems

2.2.3 Sprue, Runners, and Gates

2.2.3.1 Runners

2.2.3.2 Gates

2.2.3.3 Gate Balance

2.2.3.4 Air Vents

2.2.4 Ejection Mechanisms

2.2.4.1 Ejector Pins

2.2.4.2 Sleeve and a Stripper Plate

2.2.4.3 Air Ejector

2.2.5 Mold Cooling

2.2.6 Temperature Control Methods and Mechanisms

2.2.6.1 Liquid Medium Control

2.2.6.2 Electric Heater Control

2.3 Injection Molding Processes

2.3.1 In-Mold Build-Up Injection Molding (DSI)

2.3.2 Conventional Processes

2.3.3 DSI Molding Process

2.3.3.1 Injection Welding Mechanism

2.3.3.2 Advantages of the DSI molding process

2.3.3.3 Product Examples of the DSI Molding Process

2.3.4 Multi-Material Injection Molding

2.3.4.1 Multi-Material Molding Techniques

2.3.4.2 Application Examples for the M-DSI Molding Process

2.3.5 Super-High Speed Injection Molding

2.3.5.1 Effects of High-Speed Injection

2.3.5.2 High-Speed Injection Molding Machines

2.3.5.3 Example of Ultra High-Speed Injection Molding

2.3.6 In-Mold Coating Injection Molding

2.3.6.1 Surface Decoration Techniques

2.3.6.2 Simultaneous Transfer Molding

2.3.7 Insert Injection Molding Process

2.3.7.1 Insert Molding Machines

2.3.8 Sandwich Injection Molding

2.3.8.1 Process Outline

2.3.8.2 Construction of Sandwich Nozzles

2.3.8.3 Features of Sandwich Molding

2.3.9 Plastic Magnet Injection Molding

2.3.9.1 Molding System and Magnetic Field Generating Methods

2.3.9.2 Important Issues with Injection Molding of Plastic Magnets

2.3.9.3 Key Points of Mold Design for Plastic Magnets

2.3.10 Long-Glass Fiber Reinforced Injection Molding

2.3.10.1 Long Fiber Reinforced Plastics Injection Molding

2.3.10.2 Properties of Long Glass Fiber (GF) Reinforced Plastics

2.3.10.3 Applications of Long-Fiber Molding to Large-Size Products

References

3 The Plasticating System for Injection Molding Machines

3.1 Introduction

3.2 The Plasticating System

3.3 Operation of Plasticating Screw Machines

3.3.1 Proper Operation

3.4 The Melting Process

3.5 Basic Screw Design

3.5.1 PS Injection Molding Case Study

3.6 High-Performance Screw Designs

3.7 Secondary Mixing Processes and Devices

3.7.1 Dynamic Mixers

3.8 Screw Design Issues Causing Resin Degradation

3.9 Non-Return Valve

Nomenclature

References

4 Non-Conventional Injection Molds

4.1 Introduction

4.2 Molds for Multi-Material Molding

4.2.1 Co-Injection

4.2.2 Overmolding

4.3 Injection Units, Layout, and Runner System

4.3.1 Equipment

4.3.2 Hot Runners

4.3.3 Material Interactions

4.4 Molds for Injection-Welding

4.5 Molds for Backmolding

4.5.1 Molding over Textiles or Fabrics

4.5.2 In-Mold Labeling

4.5.3 In-Mold Decoration

References

5 Gas Assisted Injection Molding

5.1 Introduction

5.1.1 Gas Assisted Injection Molding

5.1.2 Advantages and Limitations of GAIM

5.1.3 Materials for GAIM

5.2 Molding Equipment and Process

5.2.1 Gas Injection Unit and Injection Nozzle

5.2.2 Gas Injection into the Part

5.2.3 Gas Nozzle

5.2.4 Pressure Development during the Molding Process

5.2.5 Gas Penetration Behavior in Molded Parts

5.2.6 Gas Venting and Recycling

5.2.7 Moldability Diagram for GAIM

5.3 Process Modeling

5.4 Part/Mold Designs and Molding Guidelines

5.4.1 Gas Channel Geometry

5.4.2 Gas Channel Layout

5.4.3 Effect of Gravity

5.4.4 Residual Wall Thickness Distribution

5.4.5 Gas Dissolution into the Polymer

5.4.6 Gas Fingering

5.4.7 Unstable Gas Penetrations

5.4.8 Weld Lines Caused by the Flow-Lead Effect

5.4.9 Molding of Fiber Reinforced Materials

5.5 Concluding Remarks

List of symbols

References

6 Water Injection Techniques (WIT)

6.1 Introduction

6.2 Processing Technology

6.2.1 Course of Process

6.2.2 Process Variants

6.2.2.1 Short-Shot Process

6.2.2.2 Full-Shot Process

6.2.2.3 Full-Shot Process with Overspill

6.2.2.4 Melt Push Back Process

6.2.2.5 Core Pulling Process

6.2.2.6 Rinsing/Flushing Process

6.2.3 Comparison between GAIM and WIT

6.2.3.1 Limitations of GAIM

6.2.3.2 Cycle Times

6.2.3.3 Part Properties

6.2.3.3.1 Residual Wall Thicknesses (RWT)

6.2.3.3.2 Shrinkage/Warpage

6.2.3.3.3 Fluid-Sided Surface Qualities

6.2.3.3.4 Typical Part Defects

6.3 Plant and Injector Technology

6.3.1 Concepts and Operation Technology for Water Pressure Generating Units

6.3.2 Injector Technology for Water Injection Technique

6.3.2.1 Demands on WIT Injectors

6.3.3 Classification and Presentation of Different WIT-Injectors

6.3.3.1 Operating Method

6.3.3.2 Operating Direction

6.3.3.3 Alignment in the Mold

6.3.4 General Design Remarks for WIT Injectors

6.3.4.1 Excellent Process Reliability

6.3.4.2 Specific Controllability

6.4 WIT Compatible Part Design

6.4.1 Injector Embedding

6.4.2 General Design Guidelines for WIT Articles

6.4.3 Tubular Articles

6.4.3.1 Cross Sections

6.4.3.2 Aspect Ratio

6.4.3.3 Curves and Redirections

6.4.3.4 Change of Diameter

6.4.4 Compact Parts with Integrated Thick-Walled Sections

List of Abbreviations and Symbols

References

Part III: Injection Molding of Complex Materials

7 Flow Induced Fiber Micro-Structure in Injection Molding of Fiber Reinforced Materials

7.1 Introduction

7.2 Observations

7.2.1 Fiber Length Distribution

7.2.2 Fiber Concentration

7.2.3 Fiber Orientation

7.2.3.1 Orientation Mechanisms

7.2.3.2 Qualitative Observations

7.2.3.3 Quantification Tools: Orientation Distribution Function, Orientation Tensors

7.2.3.4 Experimental Methods

7.2.3.5 Results

7.3 Calculation of Fiber Orientation

7.3.1 Orientation Models

7.3.1.1 The Standard Model

7.3.1.2 Choice of the Interaction Coefficient and the Closure Approximation

7.3.1.2.1 Value of the Interaction Coefficient

7.3.1.2.2 The Closure Approximation Issue

7.3.1.3 Discussion of the Standard Model

7.3.1.4 Application to Injection Molding

7.3.2 Rheological Models

7.3.2.1 Overview on Rheological Measurements

7.3.2.2 Introduction to Behavior Laws

7.4 Conclusions

List of Symbols

References

8 Injection Foam Molding

8.1 Introduction

8.2 Injection Foam Molding Technologies: Background

8.2.1 Structural-Foam Molding

8.2.1.1 Low-Pressure Foam Molding

8.2.2 High-Pressure Foam Molding

8.2.2.1 Co-Injection Foam Molding

8.2.2.2 Gas Counter-Pressure Foam Molding

8.2.2.3 Sequential Injection Foam Molding

8.2.3 Microcellular Injection Foam Molding

8.2.3.1 Background on Microcellular Foam Processing

8.2.3.2 Development of Microcellular Injection Foam Molding

8.2.3.2.1 Batch Microcellular Processing

8.2.3.2.2 Semi-Continuous Microcellular Processing

8.2.3.2.3 Continuous Microcellular Processing

8.2.3.2.4 Microcellular Injection Foam Molding

8.3 Fundamentals of Foam Injection Molding

8.3.1 Foaming Additives

8.3.1.1 Cell-Nucleating Agents

8.3.1.2 Blowing Agents

8.3.1.2.1 Chemical Blowing Agents

8.3.1.2.2 Physical Blowing Agents

8.3.2 Thermophysical and Rheological Properties of Polymer/Gas Mixtures

8.3.2.1 Solubility and Diffusivity

8.3.2.1.1 Solubility

8.3.2.1.2 Diffusivity

8.3.2.2 Viscosity of Polymer/Gas Mixtures

8.3.2.3 Surface Tension of Polymer/Gas Mixtures

8.3.3 Formation of Foamable Compositions

8.3.3.1 Foamable Compositions in CBA Processing

8.3.3.2 Foamable Compositions in PBA Processing

8.3.3.3 Dissolution of Gas in Polymers

8.3.4 Cell Nucleation

8.3.4.1 Homogeneous and Heterogeneous Nucleation

8.3.4.1.1 Homogeneous Nucleation

8.3.4.1.2 Heterogeneous Nucleation

8.3.4.2 Nucleation and Pressure Profiles during Filling

8.3.5 Filling and Cell Growth

8.3.5.1 Geometric Singularity and Weld Lines

8.3.5.2 Void Fraction Control

8.3.5.3 Cell Growth in a Mold

8.4 Foam Molding Machines and Applications

8.4.1 Foam Molding Machines

8.4.2 Applications

8.5 Future Developments

List of Symbols and Abbreviation

References

9 Powder Metal Injection Molding

9.1 Opportunity

9.2 Process Overview

9.3 Feedstock

9.3.1 Powders

9.3.2 Binders

9.3.3 Compounds

9.4 Part and Tool Design

9.4.1 Part Design

9.4.2 Mold Design

9.5 Molding

9.5.1 Equipment

9.5.2 Operations

9.6 Debinding

9.7 Sintering

9.7.1 Fundamentals

9.7.2 Furnaces

9.7.3 Setters

9.8 Post Sintering Treatments

9.8.1 Heat Treatment

9.8.2 Hot Isostatic Pressing

9.8.3 Secondary Operations

9.9 Material Properties

List of Symbols

References

Acknowledgements

10 Micro Injection Molding

10.1 Introduction

10.2 Why Is Polymer Processing so Interesting for Microsystems Engineering?

10.3 The Process Specialties of Micro Injection Molding

10.3.1 Types of Micro Components

10.3.2 Machine Technology for Micro Injection Molding

10.3.3 Fabrication of Microstructured Mold Inserts For Micro Injection Molding

10.3.4 Special Types of Micro Injection Molding

10.3.5 Simulation

10.4 Micro Reaction Injection Molding

10.4.1 Reactive Resin Polymerization Methods

10.4.2 Thermally Initiated Reaction Injection Molding of LIGA-Structures

10.4.3 Development of Light Induced Reaction Molding (Photomolding) Techniques

10.4.4 UV-Embossing of Photocurable Systems

10.4.5 Photomolding of Composites

10.5 Micro Powder Injection Molding (MicroPIM)

10.5.1 Introduction to MicroPIM

10.5.2 Metal and Ceramic Powders for PIM

10.5.3 Commercially Available PIM Feedstocks and Binders

10.5.4 Binder Systems for MicroPIM

10.5.5 Compounding Feedstocks for MicroPIM

10.5.6 Rheology Measurements of PIM Feedstocks

10.5.7 Machinery for MicroPIM

10.5.8 Molding Tools for MicroPIM

10.5.9 Patterning Process for PIM Microparts

10.5.9.1 Debinding of MicroPIM Green Compacts

10.5.9.2 Sintering Process for MicroPIM Parts

10.5.10 MicroPIM Research

10.6 Two-Component Micro Injection Molding (2C-MicroPIM)

10.6.1 Machine Technology for Micro Two-Component Injection Molding

10.6.2 Mold Technology for Two-Component Micro Injection Molding

10.6.3 Contact-Strength for the Multi-Component Injection Molding

10.6.4 Sequence of the Two-Component Micro Injection Molding Process

10.6.5 Variothermal Mold Temperature Control for Two-Component Injection Molding

10.6.6 Applications of Multi-Component Injection Molding

10.6.6.1 Insert Injection Molding

10.6.6.2 Overmolding

10.6.6.3 In-Mold Assembly

10.6.6.4 3D-MID-Technology

10.6.6.5 Two-Component Powder Injection Molding

10.7 Summary and Outlook

List of Abbreviations

References

Part IV:Process Visualization, Control, Optimization, and Simulation

11 Internal Visualization of Mold Cavity and Heating Cylinder

11.1 Introduction

11.2 Dynamic Visualization Techniques for the Inside of the Mold Cavity

11.2.1 Overview of Dynamic Visualization Techniques

11.2.1.1 Light transmission method

11.2.1.2 Light Reflection Method

11.2.1.3 Light-Section Method

11.2.2 Glass-Inserted Mold (2D, 3D)

11.2.3 Back-Lighting Mold

11.2.4 Laser-Light-Sheet Mold

11.2.5 Runner-Exchanging System

11.2.6 Automatic Tracking System under High Magnifications

11.2.7 Visualization Technique for Ultra-High-Speed Injection Molding

11.3 Static Visualization Techniques for the Inside of a Mold Cavity

11.3.1 Overview of Static Visualization Techniques

11.3.1.1 Plugging of Colored Materials

11.3.1.2 Lamination of Colored Materials

11.3.2 Runner-Exchanging System and Gate-Magnetization Method

11.4 Visualization Heating Cylinder

11.4.1 Overview of Visualization Techniques for the Inside of a Heating Cylinder

11.4.2 Glass-Inserted Heating Cylinder

11.4.3 Visualization Unit inside Hopper Throat, Check-Ring, and Reservoir Areas

11.4.4 Image Processing Method for Laminated Slit Images

References

12 Injection Molding Control

12.1 Introduction

12.2 Basic Concepts and Elements of Control Systems

12.2.1 Basic Control System Structure

12.2.1.1 Open Loop System

12.2.1.2 Closed-Loop System

12.2.2 Basic Elements of Control Systems

12.2.2.1 Controlled Variables in Injection Molding

12.2.2.2 Actuators in Injection Molding

12.2.2.3 Measurement of Output Variables

12.2.2.4 The Controller

12.3 Control Applications

12.3.1 Machine Sequence Control

12.3.2 Adaptive Control

12.3.2.1 Dynamic Analysis of Injection Molding Process Variables

12.3.2.2 Adaptive Control Background

12.3.2.3 RLS Estimation

12.3.2.4 Pole Placement Design

12.3.2.5 Solving the Diophantine Equation

12.3.2.6 Direct Implementation of Adaptive Pole-Placement Control

12.3.2.7 Improvement I – Anti-Windup Estimation

12.3.2.8 Improvement II – Adaptive Feedforward Control

12.3.2.9 Improvement III – Cycle-To-Cycle Adaptation

12.3.2.10 Test of Different Conditions

12.3.2.11 Summary

12.3.3 Model Predictive Control

12.3.3.1 MPC Background

12.3.3.2 GPC Design for Injection Velocity

12.3.3.3 Step Response Comparison of GPC and Pole-Placement

12.3.3.4 Adaptive GPC Experiments with Different Conditions

12.3.3.5 Summary

12.3.4 Fuzzy Model Based Control [16]

12.3.4.1 Fuzzy Inference System

12.3.4.2 Fuzzy Multi-Model and Application to Injection Velocity

12.3.4.3 Fuzzy Multi-Model Predictive Control

12.3.4.4 On-Line Identification of Model Parameters of Rule Consequents

12.3.4.5 Batch Learning of Membership Function Parameters of Rule Premises

12.3.4.6 Experimental Test of Fuzzy Multi-Model Based Predictive Control

12.3.4.7 Summary

12.3.5 Iterative Learning Control [18]

12.3.5.1 Iterative Learning Control Background

12.3.5.2 P-Type Learning Control Algorithm

12.3.5.3 Optimal Iterative Learning Controller

12.3.5.4 Robust and Convergence Analysis

12.3.5.5 Selection of the Weighting Matrices

12.3.5.6 Injection Velocity Control with Optimal ILC

12.3.5.7 Summary

12.3.6 Statistical Process Monitoring of Injection Molding

12.3.7 Statistical Process Monitoring for Continuous Processes

12.3.8 Statistical Monitoring of Batch Processes

12.3.9 Stage-Based Statistical Monitoring of Injection Molding [61–63]

12.3.9.1 Fault #1: Material Disturbance

12.3.9.2 Fault #2: Check-Ring Failure

12.4 Control Perspective and Challenges for Injection Molding

12.4.1 Control Perspective

12.4.2 Major Challenges of Injection Molding Control

12.4.2.1 Implementation of Robust Control Algorithms

12.4.2.2 New Measurements

12.4.2.3 Comprehensive Quality Modeling

12.4.2.4 Closed-Loop Quality Control

12.4.2.5 Process and Control Performance Monitoring

References

13 Optimal Design for Injection Molding

13.1 Introduction

13.2 Basic Equations for the Mold Filling Problem

13.2.1 Mathematical Model: Hele-Shaw and Energy Equations

13.2.2 Boundary Conditions

13.2.3 Numerical Discretization

13.3 Optimization Techniques

13.3.1 Optimization Concept

13.3.2 Optimization Problems

13.3.3 Numerical Solution of Optimization Problems

13.3.3.1 Zero-Order Methods

13.3.3.2 First- and Second-Order Methods

13.3.3.3 Combination of Zero-Order and Gradient-Based Methods

13.4 Gradient-Based Methods and Sensitivity Analysis

13.4.1 Direct Sensitivity Equation Method

13.4.2 Adjoint Equation Method

13.4.3 Comparison of Solution Methods

13.4.4 Choice of a Method

13.5 Optimal Design for Injection Molding

13.5.1 Problem Parameters

13.5.2 Problem Definition

13.5.3 Direct Sensitivity of the State Equations

13.5.4 Sensitivity Formulation of the Objective Function

13.5.5 Parameterization of the Injection Pressure and Sensitivities

13.5.6 Sensitivities of the Function Constraints

13.5.7 Flow-Front Tracking and Sensitivities

13.5.8 Parameterization of the Flow Domain and Sensitivities

13.6 Algorithm

13.7 Illustrative Applications

13.7.1 Automotive Part: Single Gate Optimization

13.7.2 Automotive Lens: Multiple Gate Optimization

13.7.3 Multiple Gate Optimization: More than One Optimal Solution

13.8 Conclusions

List of Symbols and Abbreviations

References

14 Development of Injection Molding Simulation

14.1 Introduction

14.2 The Molding Process

14.3 The Problem

14.3.1 Basic Physics of the Process

14.3.2 Material Properties

14.3.3 Geometric Complexity of Mold and Part

14.3.4 Process Stability

14.4 Why Simulate Injection Molding?

14.5 Early Academic Work on Simulation

14.5.1 Boundary Conditions and Solidification

14.6 Early Commercial Simulation

14.7 Simulation in the 1980s

14.8 Academic Work in the 1980s

14.8.1 Mold Filling

14.8.2 Mold Cooling

14.8.3 Warpage Analysis

14.8.4 Fiber Orientation

14.9 Commercial Simulation in the 1980s

14.9.1 Codes Developed by Large Industrials and not for Sale

14.9.1.1 General Electric

14.9.1.2 Philips/Technical University of Eindhoven

14.9.2 Codes developed by Large Industrials for Sale in the Marketplace

14.9.2.1 SDRC

14.9.2.2 GRAFTEK

14.9.3 Companies Devoted to Developing and Selling Simulation Codes

14.9.3.1 AC Technology

14.9.3.2 Moldflow

14.9.3.3 Simcon Kunststofftechnische Software GmbH

14.10 Simulation in the 1990s

14.11 Academic Work in the 1990s

14.12 Commercial Developments in the 1990s

14.12.1 SDRC

14.12.2 Moldflow

14.12.3 AC Technology/C-MOLD

14.12.4 Simcon

14.12.5 Sigma Engineering

14.12.6 Timon

14.12.7 Transvalor

14.12.8 CoreTech Systems

14.13 Simulation Science since 2000

14.14 Commercial Developments since 2000

14.14.1 Moldflow

14.14.2 Timon

14.14.3 Core Tech Systems

14.15 The Simulation Market Today

14.16 Conclusion

14.17 Appendix: 2.5D Analysis

14.17.1 Material Properties

14.17.2 Geometric Considerations

14.17.3 Simplification by Mathematical Analysis

14.18 Acknowledgments

References

15 Three-Dimensional Injection Molding Simulation

15.1 Introduction

15.1.1 Process Background

15.1.2 Historical Background on 3D Simulation

15.1.3 General Numerical Techniques for 3D Injection Molding Simulation

15.1.3.1 Constitutive Equations

15.1.3.2 Boundary Conditions

15.1.4 Numerical Issues in 3D Injection Molding

15.2 Temperature Independent Flows and Finite Element Techniques

15.2.1 Generalized Stokes Problem

15.2.1.1 Mixed Finite Elements for Newtonian Flows

15.2.1.2 More General Viscous Resolution

15.2.2 Extension to Weakly Isothermal Compressible Flows

15.2.3 Extension to Navier and Stokes Equations

15.2.4 Extension to Viscoelastic Flows

15.2.4.1 Viscoelasticity and Constitutive Models

15.2.4.2 Flow Determination for Viscoelastic Materials

15.3 Free Surface Determination

15.3.1 Techniques to Determine the Interface

15.3.2 The VOF (Volume of Fluid Method)

15.3.2.1 Resolution of the Transport Equation

15.3.2.2 Advantages and Disadvantages of the VOF Method

15.3.3 The Level Set Method

15.3.3.1 Mathematical Considerations

15.3.3.2 Resolution of the Transport Equation

15.3.3.3 Advantages and Disadvantages of the Level Set Method

15.4 Thermomechanical Coupling

15.4.1 Material Properties Coupling

15.4.2 The Temperature Balance Equation

15.4.3 Numerical Solution

15.5 Advanced Computational Techniques

15.5.1 Meshing

15.5.1.1 Generation and Anisotropic Adaptation of Static Interfaces

15.5.1.2 Multidomain and Interface Capturing

15.5.2 Parallel Computing

15.5.3 Application to Filling Simulation with Mold Coupling

15.6 Application to a 3D Part

15.7 Conclusion

Acknowledgements

Appendixes

Appendix 15.1: Viscosity Equations

Appendix 15.2: Tait Equation Parameters

Notations

References

16 Viscoelastic Instabilities in Injection Molding

16.1 Introduction

16.2 Background, Literature Review

16.3 Experimental Motivation

16.4 Analysis

16.5 Numerical Modelling: Governing Equations

16.6 Numerical Modelling: Finite Element Analysis

16.7 Domain Perturbation Technique

16.8 Results

16.8.1 Steady State Results

16.8.2 Stability Results

16.9 Discussion

Symbols and Notation

References

Part V: Microstructure Development, Characterization, and Prediction

17 Evolution of Structural Hierarchy in Injection Molded Semicrystalline Polymers

17.1 Introduction

17.2 Fundamentals of the Injection Molding Process

17.2.1 Experiences of Polymer Chains in a Typical Injection Molding Machine

17.2.2 Flow Behavior into Injection Molding Cavities

17.3 Structure Development in Injection Molded Fast Crystallizing Polymers

17.3.1 Polyethylene (PE)

17.3.2 Polypropylene (PP)

17.3.3 Polyoxymethylene (POM) and Other Fast Crystallizing Polymers

17.3.4 Injection Molded PVDF and its Blends with PMMA

17.3.5 Polyamides (PA)

17.3.6 Effect of Platelet Type Nanoparticles in Injection Molding

17.3.7 Influence of Nano Clay on the Crystallization and Orientation – Summary

17.3.8 Structure Development in Thermotropic Liquid Crystalline Polymers

17.4 Structure Development in Injection Molded Slowly Crystallizing Polymers

17.4.1 General Characteristics of Structure Development in Slow Crystallizing Polymers

17.4.2 Poly(Phyenylene Sulfide) (PPS)

17.4.3 Effect of Molecular Weight

17.4.4 Poly(Ether Ether Ketone) PEEK

17.4.5 Syndiotactic Polystyrene (s-PS)

17.4.6 Polyethylene Naphthalate (PEN)

17.4.7 Structure Characteristics of Injection Molded Slowly Crystallizing Polymers – Summary

17.5 Simulation of the Structure Development During Injection Molding Process

17.6 General Summary

Abbreviations

References

18 Modeling Aspects of Post-Filling Steps in.Injection Molding

18.1 Introduction

18.1.1 The Post-Filling Stages

18.1.2 State of the Art on Post-Filling Modeling

18.1.3 Outline

18.2 Understanding Pressure Evolution

18.2.1 The Evolution of Pressure Curves During Injection Molding

18.2.1.1 The Filling Stage

18.2.1.2 The Packing-Holding Stage

18.2.1.3 The Cooling Stage

18.2.2 Pressure Curves Inside the Runners During Cooling

18.3 A Suitable Modeling of the Process

18.3.1 Modeling the Packing – Holding Stage

18.3.2 Modeling the Cooling Stage

18.3.3 Time-Depending Heat Transfer Coefficient

18.4 Relevant Aspects of Rheological Behavior

18.4.1 The Effect of Pressure on Viscosity

18.5 Mold Deformation

18.5.1 Effect of Mold Deformation on the Packing Stage

18.5.2 Effect of Mold Deformation on the Cooling Stage

18.5.3 Effect of Mold Deformation on Pressure Evolution and on Gate Sealing Time

18.6 Molecular Orientation

18.6.1 Experimental Evidences

18.6.2 Modeling the Evolution of Orientation

18.6.2.1 Leonov Model

18.6.2.2 Non-Linear Maxwell Model

18.6.3 Results of Modeling for Amorphous Materials

18.7 Semi-Crystalline Polymers

18.7.1 Effect of Crystallinity on Material Properties

18.7.1.1 Effect of Crystallinity on Rheology

18.7.1.2 Effect of Crystallinity on Specific Volume

18.8 Morphology Evolution During the Post-Filling Stages

18.9 Concluding Remarks

Nomenclature

References

19 Volumetric and Anisotropic Shrinkage in.Injection Moldings of Thermoplastics

19.1 Introduction

19.2 Theoretical Analysis

19.2.1 Volumetric Shrinkage

19.2.2 Anisotropic Shrinkage

19.3 Comparison Between Simulations and Experiments

19.3.1 Volumetric Shrinkage

19.3.2 Anisotropic Shrinkage

19.4 Conclusions

19.5 Acknowledgement

Nomenclature

References

20 Three-Dimensional Simulation of Gas-Assisted and Co-Injection Molding Processes

20.1 Introduction

20.2 Background

20.3 Mathematical Modeling and Formulations

20.3.1 Conservation of Mass and Momentum

20.3.2 Conservation of Energy

20.3.3 Boundary and Initial Conditions

20.3.4 The Compressibility Effects

20.4 Front Capturing Methods for Co-Injection Molding

20.4.1 The VOF and phase field methods

20.4.2 The Level-Set Method

20.4.3 Use of Level-Set in Co-Injection Molding

20.5 Numerical Implementation

20.5.1 A Finite Element Method

20.5.1.1 Momentum-Continuity Equations

20.5.1.2 Energy Equation

20.5.1.3 Level-Set Equation

20.5.2 Solution Algorithm

20.6 Validation Cases and Applications

20.6.1 Gas-Assisted Injection Molding

20.6.1.1 Gas-Assisted Injection of a Plate with a Flow Channel

20.6.1.2 Secondary Penetration in Gas-Assisted Injection

20.6.1.3 Gas-Assisted Injection of a Thick Part

20.6.2 Co-Injection Molding

20.6.2.1 Co-Injection of a Side Gated Rectangular Plate

20.6.2.2 Co-Injection of a Center-Gated Rectangular Plate

20.6.2.3 Co-Injection of a C-Shaped Plate

20.6.3 Simulation of Breakthrough in Co-Injection Molding

20.7 Conclusions

List of Symbols and Abbreviations

References

21 Co-Injection Molding of Polymers

21.1 Introduction

21.2 Technology

21.3 Experimental Studies

21.3.1 Effect of Process Parameters on Skin-Core Structure

21.3.2 Breakthrough Phenomenon

21.3.3 Interfacial Instability

21.3.4 Mechanical Properties

21.3.5 Microstructure

21.3.6 Biomedical Applications

21.4 Modeling of the Co-Injection Molding Process

21.4.1 Simulation Approaches

21.4.2 Comparison between Simulation and Experiment

21.5 Conclusions

Nomenclature

References

Subject Index