Kennedy / Zheng Flow Analysis of Injection Molds

1. Auflage 2013
ISBN: 978-1-56990-522-7
Verlag: Hanser Publications
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 381 Seiten

Given the importance of injection molding as a process as well as the simulation industry that supports it, there was a need for a book that deals solely with the modeling and simulation of injection molding. This book meets that need. The modeling and simulation details of filling, packing, residual stress, shrinkage, and warpage of amorphous, semi-crystalline, and fiber-filled materials are described. This book is essential for simulation software users, as well as for graduate students and researchers who are interested in enhancing simulation. And for the specialist, numerous appendices provide detailed information on the topics discussed in the chapters.

Contents:

Part 1 The Current State of Simulation: Introduction, Stress and Strain in Fluid Mechanics, Material Properties of Polymers, Governing Equations, Approximations for Injection Molding, Numerical Methods for Solution

Part 2 Improving Molding Simulation: Improved Fiber Orientation Modeling, Improved Mechanical Property Modeling, Long Fiber-Filled Materials, Crystallization, Effects of Crystallizations on Rheology and Thermal Properties, Colorant Effects, Prediction of Post-Molding Shrinkage and Warpage, Additional Issues of Injection-Molding Simulation, Epilogue

Appendices: History of Injection-Molding Simulation, Tensor Notation, Derivation of Fiber Evolution Equations, Dimensional Analysis of Governing Equations, The Finite Difference Method, The Finite Element Method, Numerical Methods for the 2.5D Approximation, Three-Dimensional FEM for Mold Filling Analysis, Level Set Method, Full Form of Mori-Tanaka Model

Autoren/Hrsg.

Kennedy, Peter

Zheng, Rong

Inhaltsverzeichnis

1;Preface;10
2;Notation;22
3;I The Current Status of Simulation;32
3.1;1 Introduction;34
3.1.1;1.1 The Injection Molding Process;34
3.1.2;1.2 Molding Terminology;35
3.1.3;1.3 What is Simulation?;36
3.1.4;1.4 The Challenges for Simulation;37
3.1.4.1;1.4.1 Basic Physics of the Process;37
3.1.5;1.5 Why Simulate Injection Molding?;38
3.1.6;1.6 How Good is Simulation?;39
3.2;2 Stress and Strain in Fluid Mechanics;42
3.2.1;2.1 Stress in Fluids;42
3.2.1.1;2.1.1 The Stress Tensor;42
3.2.1.2;2.1.2 The Extra Stress Tensor;45
3.2.1.3;2.1.3 Rate of Strain Tensor;45
3.2.2;2.2 Newtonian and Non-Newtonian Fluids;46
3.2.3;2.3 The Generalized Newtonian Fluid;47
3.3;3 Material Properties of Polymers;50
3.3.1;3.1 Types of Polymers;50
3.3.2;3.2 Amorphous Polymers;51
3.3.3;3.3 Semi-Crystalline Polymers;51
3.3.4;3.4 Overview of Material Properties for Simulation;52
3.3.5;3.5 Viscosity;53
3.3.6;3.6 Modeling Viscosity;54
3.3.6.1;3.6.1 The Viscosity Function;54
3.3.6.2;3.6.2 The Power Law Model;54
3.3.6.3;3.6.3 The Carreau Model;54
3.3.6.4;3.6.4 The Cross Model;55
3.3.6.5;3.6.5 Incorporation of Temperature Effects ;55
3.3.6.6;3.6.6 The Solidification Problem;56
3.3.7;3.7 Thermal Properties;57
3.3.7.1;3.7.1 Specific Heat Capacity;57
3.3.7.2;3.7.2 Thermal Conductivity;58
3.3.8;3.8 Thermodynamic Relationships;60
3.3.8.1;3.8.1 Expansivity and Compressibility;60
3.3.9;3.9 Pressure-Volume-Temperature (PVT) Data;62
3.3.10;3.10 Fiber Orientation;62
3.3.11;3.11 Shrinkage and Warpage;63
3.4;4 Governing Equations;66
3.4.1;4.1 Introduction;66
3.4.2;4.2 Mathematical Preliminaries;66
3.4.2.1;4.2.1 The Material Derivative;66
3.4.2.2;4.2.2 The Gauss Divergence Theorem;67
3.4.2.3;4.2.3 Reynolds Transport Theorem;68
3.4.2.4;4.2.4 Integration by Parts;68
3.4.3;4.3 Conservation of Mass;69
3.4.4;4.4 Conservation of Momentum;69
3.4.5;4.5 Conservation of Energy;71
3.4.5.1;4.5.1 Relating Specific Energy to Temperature;74
3.4.5.2;4.5.2 The Energy Equation in Terms of Temperature;76
3.4.6;4.6 Boundary Conditions;77
3.4.6.1;4.6.1 Pressure and Flow Rate Boundary Conditions;78
3.4.6.2;4.6.2 Temperature Boundary Conditions;79
3.4.6.3;4.6.3 Mold Deformation Boundary Conditions;79
3.4.6.3.1;4.6.3.1 Thin Cavities;79
3.4.6.3.2;4.6.3.2 Long Cores and Mold Inserts;80
3.4.7;4.7 Fiber-Filled Materials;80
3.4.7.1;4.7.1 Fiber Concentration;80
3.4.7.2;4.7.2 Jeffery's Equation;81
3.4.7.3;4.7.3 A Statistical Approach;82
3.4.7.4;4.7.4 Mechanical Properties;83
3.4.8;4.8 Shrinkage and Warpage;83
3.4.9;4.9 Runners;84
3.5;5 Approximations for Injection Molding;86
3.5.1;5.1 Introduction;86
3.5.2;5.2 Material Property Approximations;87
3.5.3;5.3 Filling, Packing, and Cooling Analysis;87
3.5.3.1;5.3.1 The Thermal Source Term in the Energy Equation;88
3.5.3.2;5.3.2 Viscosity Modeling;88
3.5.3.3;5.3.3 Specific Heat Capacity;89
3.5.3.4;5.3.4 Thermal Conductivity;89
3.5.3.4.1;5.3.4.1 Unfilled Amorphous;89
3.5.3.4.2;5.3.4.2 Unfilled Semi-Crystalline;90
3.5.3.4.3;5.3.4.3 Filled Materials;90
3.5.3.5;5.3.5 No-Flow or Transition Temperature;90
3.5.3.6;5.3.6 Pressure-Volume-Temperature (PVT) Data;92
3.5.3.7;5.3.7 Fiber Orientation, Shrinkage, and Warpage;93
3.5.3.7.1;5.3.7.1 Fiber Orientation Analysis;93
3.5.3.7.2;5.3.7.2 Shrinkage and Warpage Analysis;94
3.5.4;5.4 Summary of Material Assumptions;94
3.5.5;5.5 Governing Equations;95
3.5.6;5.6 The 2.5D Approximation;96
3.5.6.1;5.6.1 Governing Equations in Cartesian Coordinates;97
3.5.6.1.1;5.6.1.1 Conservation of Mass;97
3.5.6.1.2;5.6.1.2 Conservation of Momentum;99
3.5.6.1.3;5.6.1.3 Conservation of Energy;99
3.5.6.2;5.6.2 Estimation of Relevant Terms;100
3.5.6.3;5.6.3 Velocity in the z Direction;102
3.5.6.4;5.6.4 Integration of the Momentum Equations;103
3.5.6.5;5.6.5 Integration of the Continuity Equation;106
3.5.6.5.1;5.6.5.1 Summary of the 2.5D Approximation;108
3.5.7;5.7 Mold Cooling Analysis;109
3.5.8;5.8 Fiber Orientation;111
3.5.8.1;5.8.1 Orientation Tensors;111
3.5.8.2;5.8.2 Folgar-Tucker Equation;112
3.5.8.3;5.8.3 Closure Approximations;112
3.5.8.3.1;5.8.3.1 Linear Closure;113
3.5.8.3.2;5.8.3.2 Quadratic Closure;113
3.5.8.3.3;5.8.3.3 Hybrid Closure;113
3.5.8.3.4;5.8.3.4 Orthotropic Closure;114
3.5.8.3.5;5.8.3.5 The Interaction Coefficient;114
3.5.9;5.9 Shrinkage and Warpage;115
3.5.9.1;5.9.1 Shrinkage Prediction;116
3.5.9.1.1;5.9.1.1 Residual Strain Methods;116
3.5.9.1.2;5.9.1.2 Residual Stress Models;118
3.5.10;5.10 The 2.5D Approximation for Runners;122
3.5.10.1;5.10.1 Conservation of Mass for Runners;122
3.5.10.2;5.10.2 Conservation of Momentum for Runners;124
3.5.10.3;5.10.3 Conservation of Energy for Runners;124
3.5.10.4;5.10.4 Integration of the Momentum Equation for Runners;125
3.5.10.5;5.10.5 Integration of the Continuity Equation for Runners;127
3.6;6 Numerical Methods for Solution;130
3.6.1;6.1 Midplane Methods;130
3.6.1.1;6.1.1 Extraction of a Midplane from a 3D Model;131
3.6.1.2;6.1.2 Dual Domain Analysis for Flow;132
3.6.1.3;6.1.3 Dual Domain Structural Analysis;134
3.6.1.4;6.1.4 Warpage Analysis Using the Dual Domain FEM;137
3.6.2;6.2 3D Analysis;138
3.6.2.1;6.2.1 Finite Volume Methods;138
3.6.2.2;6.2.2 A Pseudo-3D Approach;139
3.6.3;6.3 Warpage and Shrinkage Analysis in 3D;139
3.6.4;6.4 3D Analysis of Runner Systems;140
4;II Improving Molding Simulation;142
4.1;7 Improved Fiber Orientation Modeling;144
4.1.1;7.1 Introduction;144
4.1.2;7.2 ARD Model;145
4.1.2.1;7.2.1 Evolution Equation;145
4.1.2.2;7.2.2 Direct Simulation;146
4.1.2.3;7.2.3 Calculation of CI;147
4.1.3;7.3 RSC Model;148
4.1.4;7.4 Suspension Rheology;149
4.1.5;7.5 Brownian Dynamics Simulation;151
4.2;8 Improved Mechanical Property Modeling;154
4.2.1;8.1 Introduction;154
4.2.2;8.2 Unidirectional Composites;155
4.2.2.1;8.2.1 Effective Stiffness;155
4.2.2.2;8.2.2 Effective Thermal Expansion Coefficients;157
4.2.2.3;8.2.3 Effects of Fiber Concentration and Aspect Ratio;157
4.2.2.3.1;8.2.3.1 Effect of Fiber Concentration;157
4.2.2.3.2;8.2.3.2 Effect of Fiber Aspect Ratio;158
4.2.3;8.3 Fiber Orientation Averaging;161
4.3;9 Long Fiber-Filled Materials;162
4.3.1;9.1 Fiber Orientation Evolution Model;162
4.3.2;9.2 Flow-Induced Fiber Migration Model;163
4.3.3;9.3 Fiber Length Attrition Model;165
4.3.4;9.4 Uniaxial Tensile Strength Model;166
4.3.5;9.5 Flexible Fiber Modeling;167
4.3.5.1;9.5.1 Direct Simulation Methods;167
4.3.5.2;9.5.2 Continuum Modeling;168
4.4;10 Crystallization;172
4.4.1;10.1 Quiescent Crystallization;172
4.4.1.1;10.1.1 The Kolmogoroff-Avrami-Evans Model;173
4.4.1.2;10.1.2 The Rate Equations of Schneider;174
4.4.1.3;10.1.3 Quiescent Nuclei Number Density;175
4.4.1.4;10.1.4 Growth Rate of Spherulites;176
4.4.1.5;10.1.5 Material Characterization;177
4.4.1.5.1;10.1.5.1 Half-Crystallization Time;177
4.4.1.5.2;10.1.5.2 Equilibrium Melting Temperature;177
4.4.1.5.3;10.1.5.3 Crystal Growth Rate;179
4.4.2;10.2 Flow-Induced Crystallization;180
4.4.2.1;10.2.1 Enhanced Nucleation;181
4.4.2.2;10.2.2 Critical Parameters;182
4.4.2.3;10.2.3 Shish-Kebab Structure;183
4.4.2.4;10.2.4 Material Characterization;183
4.5;11 Effects of Crystallization on Rheology and Thermal Properties;186
4.5.1;11.1 Effects of Crystallization on Rheology;186
4.5.1.1;11.1.1 Viscosity-Enhancement-Factor Model;186
4.5.1.2;11.1.2 Two-Phase Model;188
4.5.2;11.2 Effect of Crystallization on PVT;190
4.5.3;11.3 Effect of Crystallization on Specific Heat Capacity;191
4.5.4;11.4 Effect of Crystallization on Thermal Conductivity;192
4.5.4.1;11.4.1 Non-Fourier Thermal Conduction;192
4.5.4.2;11.4.2 Van den Brule's Law for Amorphous Polymers;193
4.5.4.3;11.4.3 Extending the Van den Brule Approach to Semi-Crystalline Polymers;193
4.5.5;11.5 Effect of Crystallization on Heat Transfer;195
4.5.5.1;11.5.1 Stefan's Solution;195
4.5.5.2;11.5.2 Numerical Solution with Crystallization Kinetics;196
4.5.6;11.6 Modification to the Hele-Shaw Equation;197
4.6;12 Colorant Effects;198
4.6.1;12.1 Introduction;198
4.6.2;12.2 Material Characterization;199
4.6.2.1;12.2.1 Morphology;199
4.6.2.2;12.2.2 Specific Heat;200
4.6.2.3;12.2.3 Half-Crystallization Time;200
4.6.2.3.1;12.2.3.1 Quiescent Crystallization;200
4.6.2.3.2;12.2.3.2 Flow-Induced Crystallization;200
4.6.3;12.3 Effect on Shrinkage;202
4.7;13 Prediction of Post-Molding Shrinkage and Warpage;206
4.7.1;13.1 Introduction;206
4.7.2;13.2 Governing Equations;207
4.7.3;13.3 Constitutive Equations;208
4.7.3.1;13.3.1 Viscoelastic Effect;208
4.7.3.2;13.3.2 Thermal Expansion Effect;209
4.8;14 Additional Issues of Injection-Molding Simulation;212
4.8.1;14.1 Weldlines;212
4.8.2;14.2 Core Shift;213
4.8.3;14.3 Non-Conventional Injection Molds;213
4.8.3.1;14.3.1 Overmolding;213
4.8.3.2;14.3.2 Gas-Assisted Injection Molding;214
4.8.3.3;14.3.3 Microcellular Injection Foaming Molding;217
4.8.3.4;14.3.4 Micro-Injection Molding;219
4.8.4;14.4 Viscoelastic Effects;222
4.8.4.1;14.4.1 Flow-Induced Residual Stress and Birefringence;222
4.8.4.2;14.4.2 Viscoelastic Instability;224
4.8.4.3;14.4.3 Viscoelastic Suspensions;225
4.8.5;14.5 Other Numerical Methods;227
4.8.5.1;14.5.1 Molecular Dynamics Simulation;227
4.8.5.2;14.5.2 Meshless Methods;228
4.9;15 Epilogue;232
5;Appendices;234
5.1;A History of Injection-Molding Simulation ;236
5.1.1;A.1 Early Academic Work on Simulation;236
5.1.2;A.2 Early Commercial Simulation;237
5.1.3;A.3 Simulation in the Eighties;239
5.1.3.1;A.3.1 Academic Work in the Eighties;240
5.1.3.1.1;A.3.1.1 Mold Filling;240
5.1.3.1.2;A.3.1.2 Mold Cooling;242
5.1.3.1.3;A.3.1.3 Warpage Analysis;242
5.1.3.2;A.3.2 Commercial Simulation in the Eighties;243
5.1.3.2.1;A.3.2.1 Codes Developed by Large Industrials and Not for Sale;245
5.1.3.2.2;A.3.2.2 Codes Developed by Large Industrials for Sale in the Marketplace;245
5.1.3.2.3;A.3.2.3 Companies Devoted to Developing and Selling Simulation Codes;246
5.1.4;A.4 Simulation in the Nineties;247
5.1.4.1;A.4.1 Academic Work in the Nineties;248
5.1.4.2;A.4.2 Commercial Developments in the Nineties;249
5.1.4.2.1;A.4.2.1 SDRC;249
5.1.4.2.2;A.4.2.2 Moldflow;250
5.1.4.2.3;A.4.2.3 AC Technology/C-MOLD;251
5.1.4.2.4;A.4.2.4 Simcon;251
5.1.4.2.5;A.4.2.5 Sigma Engineering;251
5.1.4.2.6;A.4.2.6 Timon;252
5.1.4.2.7;A.4.2.7 Transvalor;252
5.1.4.2.8;A.4.2.8 CoreTech Systems;252
5.1.5;A.5 Simulation Science Since 2000;252
5.1.5.1;A.5.1 Commercial Developments Since 2000;254
5.1.5.1.1;A.5.1.1 Moldflow;255
5.1.5.1.2;A.5.1.2 Timon;256
5.1.5.1.3;A.5.1.3 CoreTech Systems;256
5.1.5.1.4;A.5.1.4 Autodesk;256
5.1.5.2;A.5.2 Note for Students;256
5.2;B Tensor Notation;258
5.2.1;B.1 Index Notation;258
5.2.2;B.2 Einstein Summation Convention;259
5.2.3;B.3 Kronecker Delta;260
5.2.4;B.4 Alternating Tensor;260
5.2.5;B.5 Product Operations of Two Tensors;261
5.2.6;B.6 Transpose Operation;261
5.2.7;B.7 Transformation of Principal Axes;262
5.2.8;B.8 Gradient of a Field;264
5.2.9;B.9 Unit Vector p and Operator /p;264
5.2.10;B.10 Identities;265
5.3;C Derivation of Fiber Evolution Equations;266
5.3.1;C.1 The Langevin Equation;266
5.3.2;C.2 Probability Density Function and Orientation Tensors;268
5.3.3;C.3 Equations of Change for the Orientation Tensors;269
5.3.3.1;C.3.1 Isotropic Rotary Diffusion Model (Folgar-Tucker Model);270
5.3.3.2;C.3.2 Anisotropic Rotary Diffusion Model;272
5.4;D Dimensional Analysis of Governing Equations ;274
5.4.1;D.1 Conservation of Mass;275
5.4.2;D.2 Conservation of Momentum;276
5.4.3;D.3 The Energy Equation;279
5.4.4;D.4 Summary;281
5.4.4.1;D.4.1 Conservation of Mass;281
5.4.4.2;D.4.2 Conservation of Momentum;281
5.4.4.3;D.4.3 Energy Equation;282
5.5;E The Finite Difference Method;284
5.5.1;E.1 Introduction to the Finite Difference Method;284
5.5.1.1;E.1.1 A Simple Example;286
5.5.2;E.2 Application to Temperature Calculation;288
5.5.2.1;E.2.1 Explicit Methods;288
5.5.2.1.1;E.2.1.1 Stability Criteria for Explicit Methods;289
5.5.2.2;E.2.2 Implicit Methods;289
5.6;F The Finite Element Method ;292
5.6.1;F.1 Basic Terminology;292
5.6.2;F.2 The Finite Element Approach;293
5.6.2.1;F.2.1 Geometric Modeling of the Solution Domain;293
5.6.2.2;F.2.2 Meshing;294
5.6.2.3;F.2.3 Derivation of Element Equations;294
5.6.2.4;F.2.4 Assembly of Element Equations;294
5.6.2.5;F.2.5 Application of Boundary Conditions;295
5.6.2.6;F.2.6 Solution of the System Equations;295
5.6.2.7;F.2.7 Display of Results;295
5.6.3;F.3 The Nature of a Finite Element Solution;296
5.6.4;F.4 Shape Functions;298
5.6.5;F.5 Approximating Nodal Values;298
5.6.5.1;F.5.1 Weighted Residual Methods;299
5.6.6;F.6 Constraint Equations;299
5.6.6.1;F.6.1 Special Case 1: Two Unknowns Equal;302
5.6.6.2;F.6.2 Special Case 2: One Known Constraint;303
5.6.7;F.7 A One-Dimensional Problem Solved Using the FEM;304
5.6.7.1;F.7.1 Meshing;304
5.6.7.2;F.7.2 Derivation of Element Equations;305
5.6.7.3;F.7.3 Assembly;309
5.6.7.4;F.7.4 Application of Boundary Conditions;310
5.6.7.5;F.7.5 Solution of System Equations;312
5.7;G Numerical Methods for the 2.5D Approximation;314
5.7.1;G.1 Overview of Solution Process;314
5.7.1.1;G.1.1 Numerical Methods;315
5.7.2;G.2 Finite Element Formulation for the Pressure Field;316
5.7.2.1;G.2.1 Interpolation Functions;316
5.7.2.2;G.2.2 Area Coordinates;317
5.7.3;G.3 Finite Element Derivation;318
5.7.3.1;G.3.1 Assembly of Element Equations and Solution;326
5.7.4;G.4 Solution of the Energy Equation;327
5.7.4.1;G.4.1 Finite Difference Discretization;327
5.7.4.2;G.4.2 Solution of the Conduction Problem;328
5.7.4.3;G.4.3 Explicit Method;328
5.7.5;G.5 Flow Front Advancement;329
5.7.6;G.6 Runners;329
5.8;H Three-Dimensional FEM for Mold Filling Analysis;334
5.8.1;H.1 Governing Equations;334
5.8.2;H.2 Weak Formulations;335
5.8.3;H.3 Finite Element Matrix Formulations;336
5.8.4;H.4 Solution Procedures;340
5.8.5;H.5 Flow-Front Advancement;341
5.8.6;H.6 Numerical Solution For Temperature Field;342
5.9;I Level Set Method;344
5.10;J Full Form of Mori-Tanaka Model;348
5.10.1;J.1 Eshelby Tensor Components;348
5.10.1.1;J.1.1 Material with Isotropic Matrix and Inclusions;348
5.10.1.2;J.1.2 General Anisotropic Materials;349
5.10.2;J.2 Expanded Mori-Tanaka Equation;350
5.10.2.1;J.2.1 Contracted Notation for Stiffness Tensor and Compliance Tensor;350
5.10.2.2;J.2.2 Inverse of a Matrix ;350
5.10.2.3;J.2.3 Expanded Expression of the Mori-Tanaka Equation;351
5.11;Bibliography;352
5.12;Index;352

Leseproben

Part 1 Current Status of Simulation
1 Introduction
2 Stress and Strain in Fluid Mechanics
3 Material Properties
4 Governing Equations
5 Approximations for Injections Molding

Part 2 Improving Molding Simulations
6 Improved Fiber Orientation Modeling
7 Improved Mechanical Property Modeling
8 Long Fiber Filled Materials
9 Crystallization
10 Effects of Crystallization
11 Colorant Effects on Crystallization and Shrinkage
12 Towards the Prediction of Post-molding Shrinkage and Warpage

Appendices
A History of Injection Molding Simulation
B Tensor Notation
C Dimensional Analysis of Governing Equations
D The Finite Difference Method
E 2D Finite Element Method
F Numerical Methods for the 2.5.D Approximation
G 3D Finite Element Method for Mold Flow Analysis
H Level Set Method

Bibliography

Über Autor(innen)

DEUTSCH:

Peter Kennedy, geboren 1955 in Australien hat Mathematik studiert und in Maschinenbau promoviert. Er arbeitete mehr als 22 Jahre für Moldflow, den ersten kommerziellen Anbieter von Simulations-Software für Spritzgießverfahren.
Rong Zheng, geboren 1947 in China hat 1991 in Computational Rheology an der University of Sydney promoviert. Von 1993 bis 2009 arbeitete er für Moldflow Pty. Ltd. (jetzt Autodesk) u.a. an der Simulation von Spritzgußverfahren
ENGLISH:Peter Kennedy was born in Melbourne, Australia, on the 22nd of November 1955. He studied Mathematics and Education at Melbourne and La Trobe Universities and has a Doctorate in Mechanical Engineering from the Technical University of Eindhoven. After teaching high school mathematics Peter joined Moldflow, the first commercial company to provide simulation software for injection molding. During a total time of 22 years at Moldflow he worked in various positions related to molding simulation and the development of the company's key technologies through internally directed research programs and cooperative projects with academic and industrial research organizations.

Rong Zheng is an Australian citizen and was born in Xiamen, China, in 1947. He obtained a BSc in Mechanical Engineering in 1982 and a Master degree in Polymer Processing in 1985 at South China University of Technology and a PhD in Computational Rheology in 1991 at The University of Sydney, where he continued as a Post-doctoral Fellow from 1991-1993. From 1993 to 2009, he was working in Moldflow Pty. Ltd. (now Autodesk) on research and development of science-based technology for modeling and simulation of injection molding, and was involved as a Chief/Partner Investigator in several collaborative research projects between Moldflow and Universities. He is currently an Adjunct Associate Professor of Mechanical Engineering at the University of Sydney.