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Georg J. Schmitz og Ulrich Prahl
(2016)
John Wiley & Sons
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Handbook of Software Solutions for ICME
Georg J. Schmitz og Ulrich Prahl
(2016)
Sprog: Engelsk
John Wiley & Sons, Incorporated
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Detaljer om varen
- 1. Udgave
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: John Wiley & Sons (Oktober 2016)
- Forfattere: Georg J. Schmitz og Ulrich Prahl
- ISBN: 9783527693580
As one of the results of an ambitious project, this handbook provides a well-structured directory of globally available software tools in the area of Integrated Computational Materials Engineering (ICME). The compilation covers models, software tools, and numerical methods allowing describing electronic, atomistic, and mesoscopic phenomena, which in their combination determine the microstructure and the properties of materials. It reaches out to simulations of component manufacture comprising primary shaping, forming, joining, coating, heat treatment, and machining processes. Models and tools addressing the in-service behavior like fatigue, corrosion, and eventually recycling complete the compilation. An introductory overview is provided for each of these different modelling areas highlighting the relevant phenomena and also discussing the current state for the different simulation approaches. A must-have for researchers, application engineers, and simulation software providers seeking a holistic overview about the current state of the art in a huge variety of modelling topics. This handbook equally serves as a reference manual for academic and commercial software developers and providers, for industrial users of simulation software, and for decision makers seeking to optimize their production by simulations. In view of its sound introductions into the different fields of materials physics, materials chemistry, materials engineering and materials processing it also serves as a tutorial for students in the emerging discipline of ICME, which requires a broad view on things and at least a basic education in adjacent fields.
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Detaljer om varen
- Hardback: 632 sider
- Udgiver: John Wiley & Sons, Incorporated (December 2016)
- Forfattere: Georg J. Schmitz og Ulrich Prahl
- ISBN: 9783527339020
As one of the results of an ambitious project, this handbook provides a well-structured directory
of globally available software tools in the area of Integrated Computational Materials
Engineering (ICME).
The compilation covers models, software tools, and numerical methods allowing describing
electronic, atomistic, and mesoscopic phenomena, which in their combination determine the
microstructure and the properties of materials. It reaches out to simulations of component
manufacture comprising primary shaping, forming, joining, coating, heat treatment, and
machining processes. Models and tools addressing the in-service behavior like fatigue, corrosion,
and eventually recycling complete the compilation.
An introductory overview is provided for each of these different modelling areas highlighting the
relevant phenomena and also discussing the current state for the different simulation approaches.
A must-have for researchers, application engineers, and simulation software providers seeking
a holistic overview about the current state of the art in a huge variety of modelling topics.
This handbook equally serves as a reference manual for academic and commercial software developers
and providers, for industrial users of simulation software, and for decision makers seeking
to optimize their production by simulations. In view of its sound introductions into the different
fields of materials physics, materials chemistry, materials engineering and materials processing
it also serves as a tutorial for students in the emerging discipline of ICME, which requires a broad
view on things and at least a basic education in adjacent fields.
of globally available software tools in the area of Integrated Computational Materials
Engineering (ICME).
The compilation covers models, software tools, and numerical methods allowing describing
electronic, atomistic, and mesoscopic phenomena, which in their combination determine the
microstructure and the properties of materials. It reaches out to simulations of component
manufacture comprising primary shaping, forming, joining, coating, heat treatment, and
machining processes. Models and tools addressing the in-service behavior like fatigue, corrosion,
and eventually recycling complete the compilation.
An introductory overview is provided for each of these different modelling areas highlighting the
relevant phenomena and also discussing the current state for the different simulation approaches.
A must-have for researchers, application engineers, and simulation software providers seeking
a holistic overview about the current state of the art in a huge variety of modelling topics.
This handbook equally serves as a reference manual for academic and commercial software developers
and providers, for industrial users of simulation software, and for decision makers seeking
to optimize their production by simulations. In view of its sound introductions into the different
fields of materials physics, materials chemistry, materials engineering and materials processing
it also serves as a tutorial for students in the emerging discipline of ICME, which requires a broad
view on things and at least a basic education in adjacent fields.
List of Contributors XVII Preface XXVII 1 Introduction 1 Georg J. Schmitz and Ulrich Prahl
1.1 Motivation 1
1.2 What is ICME? 2
1.3 Industrial Needs for ICME 4
1.4 Present ICME 9
1.5 Scope of this Book 11
1.6 Structure of the Book 13 2 Modeling at the Process and Component Scales 19
2.1 Overview of Processing Methods and Process Chains 21 Ralph Bernhardt and Georg J. Schmitz
2.1.1 History of Metalworking 22
2.1.2 History of Modeling of Manufacturing Processes 23
2.1.3 Overview of Processing Methods 25
2.1.4 Processes and Process Chains 26
2.1.5 Benefits of Modeling Process Chains 27
2.1.6 Available Modeling Tools at Component Scale 29
2.2 Primary Shaping Processes 35 Christoph Broeckmann, Christian Hopmann, Georg J. Schmitz, Sree Koundinya Sistla, Marcel Spekowius, Roberto Spina, and Chung Van Nguyen
2.2.1 Overview 35
2.2.1.1 Solidification and Crystal Growth 36
2.2.2 Casting 36
2.2.3 Plastics Processing 38
2.2.4 Sintering 41
2.2.5 Additive Manufacturing 44
2.2.6 Typical Applications of Simulations in Primary Shaping Processes 44
2.2.7 Phenomena to be Modeled 48
2.2.8 Basic Equations to be Solved 51
2.2.9 Initial and Boundary Conditions 54
2.2.10 Required Data and their Origin 55
2.2.11 Simulation Codes in the Area of Primary Shaping 58
2.3 Forming Processes 81 Stephan Hojda and Markus Bambach 2.3.1 Overview: Manufacturing Process Forming 81
2.3.2 Phenomena Occurring during Forming Processes 81
2.3.3 Modeling and Simulation Methods 85
2.3.4 Typical Applications of Forming Simulations 86
2.3.5 Initial and Boundary Conditions 87
2.3.6 Required Data and their Origin 88
2.3.7 Numerical Aspects 90
2.3.8 Software Codes 91
2.4 Heat Treatment 97 Martin Hunkel
2.4.1 Introduction into Heat Treatment 97
2.4.2 Heat Transfer in and out of a
Part 98
2.4.3 Microstructure 101
2.4.4 Mechanical Behavior during Heat Treatment 104
2.4.5 Thermochemical Treatment 105
2.4.6 Heat Treatment Simulation 107
2.5 Joining Processes 111 Ulrike Beyer, Gerson Meschut, Stephan Horstmann, and Ralph Bernhardt
2.5.1 Introduction 111
2.5.2 Basics and Definitions 112
2.5.3 Welding 115
2.5.4 Joining by Forming 120
2.5.5 Software for Joining Processes 128
2.6 Thick Coating Formation Processes 135 Kirsten Bobzin, Mehmet Ã?te, Thomas Frederik Linke, and Ilkin Alkhasli
2.6.1 Overview 135
2.6.2 Typical Applications of Coating Simulations 136
2.6.3 Phenomena Occurring During Coating Formation 137
2.6.4 Basic Equations to Model the Phenomena 139
2.6.5 Initial and Boundary Conditions 140
2.6.6 Process Modeling on the Example of Thermal Spraying 140
2.6.7 Conclusion 150
2.6.8 Software Tools 151
2.7 Thin-Film Deposition Processes 157 Andreas Pflug, Michael Siemers, ThomasMelzig, Martin Keunecke, Lothar Schäfer, and Günter Bräuer
2.7.1 Introduction 157
2.7.2 Overview of Thin-Film Deposition Methods 159
2.7.3 Modeling of Thin-Film Deposition as a Multiscale Problem 165
2.7.4 Software Codes 172
2.8 Machining 19 André Teixeira, Markus Krömer, and Roland Müller
2.8.1 Introduction to Machining Processes 191
2.8.2 General Aspects of Machining Simulations 196
2.8.3 Combination of Analytic-Geometric Simulation Models and FEM Simulation Models 200
2.8.4 Simulation of Surface Integrity Modifications 201
2.8.5 Summary 204
2.8.6 Simulation Tools for Machining Processes 204
2.9 Fatigue Modeling: From Microstructure to Component Scale 209 Mohamed Sharaf and Sebastian Münstermann
2.9.1 Influence Factors on Component Fatigue Limit 209
2.9.2 Micromechanics as a Modeling Approach 211
2.9.3 Numerical Representation of Microstructure 212
2.9.4 Cyclic Elastoplasticity of Crystals and Microsubstructures 213
2.9.5 The Notion of Fatigue Indicator Parameters (FIPs) 216
2.9.6 Fatigue Limit as a Function of Microstructure 218
2.9.7 Software Tools for Modeling Fatigue 223
2.10 Corrosion and Its Context in Service Life 227 Daniela Zander, Daniel Höche, Johan Deconinck, and Theo Hack
2.10.1 Overview 227
2.10.2 Corrosion Modeling and Applications 229
2.10.3 Industrial Demands in ICME-Related Corrosion Modeling 238
2.10.4 Software Tool-Related Corrosion Modeling 240
2.10.5 Future Tasks and Limits 244
2.10.6 Acknowledgments 244
2.11 Recycling Processes 247 Klaus Hack, Markus A. Reuter, Stephan Petersen, and Sander Arnout
2.11.1 Overview 247
2.11.2 Materials-Centric versus Product-Centric Approach 248
2.11.3 General Phenomena: LED Lamp Recycling as an Example 249
2.11.4 Methods Available 251
2.11.5 Thermochemical Aspects of Recycling 252
2.11.6 Recycling of Aluminum 255
2.11.7 Recycling of Zinc: Fuming 258
2.11.8 Valorization of "Wastes" 262
2.11.9 Summary of Simulation Tools 265 3 Microstructure Modeling 269 Markus Apel, Robert Spatschek, Franz Roters, Henrik Larsson, Charles-André Gandin, Gildas Guillemot, Frigyes Podmaniczky, László Gránásy, Georg J. Schmitz, and Qing Chen
3.1 Overview and Definitions 269
3.1.1 What is a Microstructure and why it is Important? 269
3.2 How to Describe and Store a Microstructure? 271
3.2.1 Digital Microstructures 273
3.3 Phenomena Affecting Microstructure Evolution 273
3.4 Basic Equations/Models 275
3.5 Models for Microstructure Evolution 276
3.5.1 Overview 276
3.5.2 Example for Integral Models 276
3.5.3 Nucleation Models 279
3.5.4 Diffusion Models 286
3.5.5 Precipitation Models 289
3.5.6 Cellular Automaton Models 292
3.5.7 Monte Carlo Potts Models 295
3.5.8 Phase-Field and Multiphase-Field Models 296
3.5.9 Phase-Field Crystal Models 300
3.5.10 Crystal Plasticity 304
3.6 Software Tools 308 4 Thermodynamics 325 Tore Haug-Warberg, Long-Qing Chen, Ursula Kattner, Bengt Hallstedt, André Costa e Silva, Joonho Lee, Jean-Marc Joubert, Jean-Claude Crivello,Fan Zhang, Bethany Huseby, and Olle Blomberg
4.1 Overview 325
4.2 Basic Concepts and Principles 326
4.2.1 The Concept of theThermodynamic State 326
4.2.2 Fundamental Relations and Canonical State Variables 327
4.2.3 Equations of State (EOS) 330
4.2.4 Euler Integration of EOS into a Fundamental Relation 332
4.2.5 The Principle ofThermodynamic Equilibrium 333
4.3 Thermodynamic Modeling 335
4.3.1 Gibbs and Helmholtz Energy Residuals 336
4.3.2 Excess Gibbs Energy 337
4.4 The CALPHAD Approach 340
4.4.1 History 341
4.4.2 Crystallography and Models of Phases 342
4.4.3 Models of Composition Dependence 345
4.4.4 Model of Nanosize Effect 346
4.4.5 CALPHAD Databases 348
4.4.6 Database Development and Parameter Optimization 350
4.4.7 Phase Names 353
4.4.8 Reference States 356
4.4.9 Database Formats 356
4.4.10 Extensions 360
4.4.11 Limitations and Challenges 363
4.5 Deriving Thermodynamics from Ab Initio Calculations 364
4.5.1 DFT Methodology 365
4.5.2 Heat of Formation 366
4.5.3 Mixing Enthalpy 367
4.5.4 Lattice Vibrations 368
4.6 Use of Thermodynamics at Larger Scales 370
4.7 Applications and Success Stories 373
4.8 Software Tools 378 5 Discrete Models: Down to Atoms and Electrons 385 Seyed Masood Hafez Haghighat, Ignacio Martin-Bragado, Cláudio M.Lousada, and Pavel A. Korzhavyi
5.1 Overview and Definitions 385
5.2 Discrete and Semidiscrete Mesoscopic Models in Materials Science 386
5.2.1 Discrete Dislocation Dynamics 386
5.2.2 Monte Carlo Method 391
5.3 Atomistic Simulations: Models and Methods 394
5.3.1 Kinetic Monte Carlo 394
5.3.2 Molecular Dynamics 398
5.4 Electronic StructureMethods 401
5.4.1 Approximate Solutions to the Electronic Wave Function 403
5.4.2 Density Functional Theory (DFT) 407
5.5 Potentials, Force Fields, and Effective Cluster Interactions 411
5.6 Software Tools in the Area of Discrete Modeling 412 6 Effective Properties 433 Ludovic Noels, Ling Wu, Laurent Adam, Jan Seyfarth, Ganesh Soni, Javier Segurado, Gottfried Laschet, Geng Chen, Maxime Lesueur, Mauricio Lobos, Thomas Böhlke, Thomas Reiter, Stefan Oberpeilsteiner, Dietmar Salaberger, Dieter Weichert, and Christoph Broeckmann
6.1 Computational Homogenization Methods and Codes: An Overview 433
6.1.1 Review of Homogenization Methods for Heterogeneous Materials 433
6.1.2 Homogenization in Industrial Application: Current State of the Art 442
6.2 Finite Element-Based Homogenization 447
6.2.1 Effective Properties of Polycrystalline Materials 447
6.2.2 Variation of the Effective Elastic Properties During γ â?? α Phase Transformation of a Low-Carbon Steel, Simulated by the Phase-Field Method 449
6.2.3 A Direct Method-Based Statistical Prediction of the Effective Strengths of Particulate-Reinforced Metal Matrix Composite 452
6.2.4 Effective Elastic Properties of Semicrystalline Thermoplastic Microstructures of Injection-Molded Parts 454
6.2.5 On the Effective Mechanical Properties of Discontinuous Fiber Composites (DF
1.1 Motivation 1
1.2 What is ICME? 2
1.3 Industrial Needs for ICME 4
1.4 Present ICME 9
1.5 Scope of this Book 11
1.6 Structure of the Book 13 2 Modeling at the Process and Component Scales 19
2.1 Overview of Processing Methods and Process Chains 21 Ralph Bernhardt and Georg J. Schmitz
2.1.1 History of Metalworking 22
2.1.2 History of Modeling of Manufacturing Processes 23
2.1.3 Overview of Processing Methods 25
2.1.4 Processes and Process Chains 26
2.1.5 Benefits of Modeling Process Chains 27
2.1.6 Available Modeling Tools at Component Scale 29
2.2 Primary Shaping Processes 35 Christoph Broeckmann, Christian Hopmann, Georg J. Schmitz, Sree Koundinya Sistla, Marcel Spekowius, Roberto Spina, and Chung Van Nguyen
2.2.1 Overview 35
2.2.1.1 Solidification and Crystal Growth 36
2.2.2 Casting 36
2.2.3 Plastics Processing 38
2.2.4 Sintering 41
2.2.5 Additive Manufacturing 44
2.2.6 Typical Applications of Simulations in Primary Shaping Processes 44
2.2.7 Phenomena to be Modeled 48
2.2.8 Basic Equations to be Solved 51
2.2.9 Initial and Boundary Conditions 54
2.2.10 Required Data and their Origin 55
2.2.11 Simulation Codes in the Area of Primary Shaping 58
2.3 Forming Processes 81 Stephan Hojda and Markus Bambach 2.3.1 Overview: Manufacturing Process Forming 81
2.3.2 Phenomena Occurring during Forming Processes 81
2.3.3 Modeling and Simulation Methods 85
2.3.4 Typical Applications of Forming Simulations 86
2.3.5 Initial and Boundary Conditions 87
2.3.6 Required Data and their Origin 88
2.3.7 Numerical Aspects 90
2.3.8 Software Codes 91
2.4 Heat Treatment 97 Martin Hunkel
2.4.1 Introduction into Heat Treatment 97
2.4.2 Heat Transfer in and out of a
Part 98
2.4.3 Microstructure 101
2.4.4 Mechanical Behavior during Heat Treatment 104
2.4.5 Thermochemical Treatment 105
2.4.6 Heat Treatment Simulation 107
2.5 Joining Processes 111 Ulrike Beyer, Gerson Meschut, Stephan Horstmann, and Ralph Bernhardt
2.5.1 Introduction 111
2.5.2 Basics and Definitions 112
2.5.3 Welding 115
2.5.4 Joining by Forming 120
2.5.5 Software for Joining Processes 128
2.6 Thick Coating Formation Processes 135 Kirsten Bobzin, Mehmet Ã?te, Thomas Frederik Linke, and Ilkin Alkhasli
2.6.1 Overview 135
2.6.2 Typical Applications of Coating Simulations 136
2.6.3 Phenomena Occurring During Coating Formation 137
2.6.4 Basic Equations to Model the Phenomena 139
2.6.5 Initial and Boundary Conditions 140
2.6.6 Process Modeling on the Example of Thermal Spraying 140
2.6.7 Conclusion 150
2.6.8 Software Tools 151
2.7 Thin-Film Deposition Processes 157 Andreas Pflug, Michael Siemers, ThomasMelzig, Martin Keunecke, Lothar Schäfer, and Günter Bräuer
2.7.1 Introduction 157
2.7.2 Overview of Thin-Film Deposition Methods 159
2.7.3 Modeling of Thin-Film Deposition as a Multiscale Problem 165
2.7.4 Software Codes 172
2.8 Machining 19 André Teixeira, Markus Krömer, and Roland Müller
2.8.1 Introduction to Machining Processes 191
2.8.2 General Aspects of Machining Simulations 196
2.8.3 Combination of Analytic-Geometric Simulation Models and FEM Simulation Models 200
2.8.4 Simulation of Surface Integrity Modifications 201
2.8.5 Summary 204
2.8.6 Simulation Tools for Machining Processes 204
2.9 Fatigue Modeling: From Microstructure to Component Scale 209 Mohamed Sharaf and Sebastian Münstermann
2.9.1 Influence Factors on Component Fatigue Limit 209
2.9.2 Micromechanics as a Modeling Approach 211
2.9.3 Numerical Representation of Microstructure 212
2.9.4 Cyclic Elastoplasticity of Crystals and Microsubstructures 213
2.9.5 The Notion of Fatigue Indicator Parameters (FIPs) 216
2.9.6 Fatigue Limit as a Function of Microstructure 218
2.9.7 Software Tools for Modeling Fatigue 223
2.10 Corrosion and Its Context in Service Life 227 Daniela Zander, Daniel Höche, Johan Deconinck, and Theo Hack
2.10.1 Overview 227
2.10.2 Corrosion Modeling and Applications 229
2.10.3 Industrial Demands in ICME-Related Corrosion Modeling 238
2.10.4 Software Tool-Related Corrosion Modeling 240
2.10.5 Future Tasks and Limits 244
2.10.6 Acknowledgments 244
2.11 Recycling Processes 247 Klaus Hack, Markus A. Reuter, Stephan Petersen, and Sander Arnout
2.11.1 Overview 247
2.11.2 Materials-Centric versus Product-Centric Approach 248
2.11.3 General Phenomena: LED Lamp Recycling as an Example 249
2.11.4 Methods Available 251
2.11.5 Thermochemical Aspects of Recycling 252
2.11.6 Recycling of Aluminum 255
2.11.7 Recycling of Zinc: Fuming 258
2.11.8 Valorization of "Wastes" 262
2.11.9 Summary of Simulation Tools 265 3 Microstructure Modeling 269 Markus Apel, Robert Spatschek, Franz Roters, Henrik Larsson, Charles-André Gandin, Gildas Guillemot, Frigyes Podmaniczky, László Gránásy, Georg J. Schmitz, and Qing Chen
3.1 Overview and Definitions 269
3.1.1 What is a Microstructure and why it is Important? 269
3.2 How to Describe and Store a Microstructure? 271
3.2.1 Digital Microstructures 273
3.3 Phenomena Affecting Microstructure Evolution 273
3.4 Basic Equations/Models 275
3.5 Models for Microstructure Evolution 276
3.5.1 Overview 276
3.5.2 Example for Integral Models 276
3.5.3 Nucleation Models 279
3.5.4 Diffusion Models 286
3.5.5 Precipitation Models 289
3.5.6 Cellular Automaton Models 292
3.5.7 Monte Carlo Potts Models 295
3.5.8 Phase-Field and Multiphase-Field Models 296
3.5.9 Phase-Field Crystal Models 300
3.5.10 Crystal Plasticity 304
3.6 Software Tools 308 4 Thermodynamics 325 Tore Haug-Warberg, Long-Qing Chen, Ursula Kattner, Bengt Hallstedt, André Costa e Silva, Joonho Lee, Jean-Marc Joubert, Jean-Claude Crivello,Fan Zhang, Bethany Huseby, and Olle Blomberg
4.1 Overview 325
4.2 Basic Concepts and Principles 326
4.2.1 The Concept of theThermodynamic State 326
4.2.2 Fundamental Relations and Canonical State Variables 327
4.2.3 Equations of State (EOS) 330
4.2.4 Euler Integration of EOS into a Fundamental Relation 332
4.2.5 The Principle ofThermodynamic Equilibrium 333
4.3 Thermodynamic Modeling 335
4.3.1 Gibbs and Helmholtz Energy Residuals 336
4.3.2 Excess Gibbs Energy 337
4.4 The CALPHAD Approach 340
4.4.1 History 341
4.4.2 Crystallography and Models of Phases 342
4.4.3 Models of Composition Dependence 345
4.4.4 Model of Nanosize Effect 346
4.4.5 CALPHAD Databases 348
4.4.6 Database Development and Parameter Optimization 350
4.4.7 Phase Names 353
4.4.8 Reference States 356
4.4.9 Database Formats 356
4.4.10 Extensions 360
4.4.11 Limitations and Challenges 363
4.5 Deriving Thermodynamics from Ab Initio Calculations 364
4.5.1 DFT Methodology 365
4.5.2 Heat of Formation 366
4.5.3 Mixing Enthalpy 367
4.5.4 Lattice Vibrations 368
4.6 Use of Thermodynamics at Larger Scales 370
4.7 Applications and Success Stories 373
4.8 Software Tools 378 5 Discrete Models: Down to Atoms and Electrons 385 Seyed Masood Hafez Haghighat, Ignacio Martin-Bragado, Cláudio M.Lousada, and Pavel A. Korzhavyi
5.1 Overview and Definitions 385
5.2 Discrete and Semidiscrete Mesoscopic Models in Materials Science 386
5.2.1 Discrete Dislocation Dynamics 386
5.2.2 Monte Carlo Method 391
5.3 Atomistic Simulations: Models and Methods 394
5.3.1 Kinetic Monte Carlo 394
5.3.2 Molecular Dynamics 398
5.4 Electronic StructureMethods 401
5.4.1 Approximate Solutions to the Electronic Wave Function 403
5.4.2 Density Functional Theory (DFT) 407
5.5 Potentials, Force Fields, and Effective Cluster Interactions 411
5.6 Software Tools in the Area of Discrete Modeling 412 6 Effective Properties 433 Ludovic Noels, Ling Wu, Laurent Adam, Jan Seyfarth, Ganesh Soni, Javier Segurado, Gottfried Laschet, Geng Chen, Maxime Lesueur, Mauricio Lobos, Thomas Böhlke, Thomas Reiter, Stefan Oberpeilsteiner, Dietmar Salaberger, Dieter Weichert, and Christoph Broeckmann
6.1 Computational Homogenization Methods and Codes: An Overview 433
6.1.1 Review of Homogenization Methods for Heterogeneous Materials 433
6.1.2 Homogenization in Industrial Application: Current State of the Art 442
6.2 Finite Element-Based Homogenization 447
6.2.1 Effective Properties of Polycrystalline Materials 447
6.2.2 Variation of the Effective Elastic Properties During γ â?? α Phase Transformation of a Low-Carbon Steel, Simulated by the Phase-Field Method 449
6.2.3 A Direct Method-Based Statistical Prediction of the Effective Strengths of Particulate-Reinforced Metal Matrix Composite 452
6.2.4 Effective Elastic Properties of Semicrystalline Thermoplastic Microstructures of Injection-Molded Parts 454
6.2.5 On the Effective Mechanical Properties of Discontinuous Fiber Composites (DF
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