Constrained Deformation of Materials (eBook)

Yu-Lin Shen is currently Professor and Interim Chair in the Department of Mechanical Engineering at University of New Mexico. He received his Ph.D. in engineering from Brown University in 1994, and was a post-doctoral research associate at Massachusetts Institute of Technology before joining the faculty of University of New Mexico in 1996. Professor Shen is widely recognized for his research in mechanical behavior of materials, especially in modeling. His numerical modeling experience spans disparate length scales from the continuum level down to atomistics, focusing on mechanical issues related to thin films, composite materials and microelectronic devices and packages. He has published over 140 research papers in these areas, mostly in international journals. In 2005 Professor Shen was elected Fellow of the American Society of Mechanical Engineers (ASME).

Copyright 5
Preface 6
Contents 8
Chapter 1: Introduction 12
1.1 Simple Illustration of Constrained Deformation 13
1.2 Applications 14
1.2.1 Deformation in Micromachined Structures 15
1.2.2 Microelectronic Devices and Packages 16
1.2.3 Materials with Internal Structure 19
1.3 Outline and Scope 20
References 21
Chapter 2: Mechanics Preliminaries 24
2.1 Stress and Strain 24
2.2 Elastic Deformation 26
2.3 Plastic Deformation 27
2.3.1 Uniaxial Response 27
2.3.2 Multiaxial Response 29
2.4 Time-Dependent Deformation 31
2.4.1 Viscoplastic Response 31
2.4.2 Viscoelastic Response 33
2.5 Thermal Expansion and Thermal Mismatch 34
2.5.1 Example: Residual Stress Buildup in a Constrained Rod 35
2.5.2 Example: Thermoelastic Deformation of Bi-material Layers 36
2.6 The Numerical Modeling Approach 39
2.6.1 Example: Sanity Test 39
2.6.2 Example: Proper Interpretation and Use of the Output 41
2.7 Choosing the Appropriate Constitutive Model 43
References 44
Chapter 3: Thin Continuous Films 46
3.1 Basic Elastic-Plastic Response 48
3.1.1 Mechanical Loading 48
3.1.2 Equi-biaxial Stress State and Thermal Loading 50
3.1.2.1 Numerical Example 51
3.2 Yielding and Strain Hardening Characteristics 54
3.3 Film on a Compliant Substrate 58
3.4 Mechanical Deflection of Microbeams 59
3.5 Thermal Deflection of Microbeams 63
3.5.1 Bi-layer Beam 63
3.5.2 Tri-layer Beam 65
3.6 Rate-Dependent Behavior 67
3.6.1 The Deformation Mechanism Approach 68
3.6.2 Stress Evolution During Temperature Cycles 70
3.7 Indentation Loading 74
3.7.1 Indentation-Derived Elastic Modulus and Hardness 76
3.8 Projects 80
References 82
Chapter 4: Patterned Films in Micro-devices 88
4.1 Basic Consideration 89
4.1.1 Elastic Lines on a Thick Substrate 90
4.1.1.1 Model Setup 90
4.1.1.2 Parametric Analysis 92
4.1.2 Elastic-Plastic Lines on a Thick Substrate 95
4.2 Passivated Single-Level Lines 98
4.2.1 Aluminum Interconnects 99
4.2.2 Copper Interconnects 101
4.2.2.1 Elastic Versus Elastic-Plastic Copper Lines 101
4.2.2.2 Influence of Dielectric Material 103
4.3 Complex In-plane Geometries 106
4.4 Multilevel Structures 109
4.4.1 Parallel Lines 110
4.4.2 Copper Lines and Via 110
4.4.3 Stresses in Barrier Layers and Dielectrics 114
4.5 Lines with Pre-existing Flaws 116
4.5.1 Effect of Local Debond 117
4.5.2 Deformation Induced Void Opening 120
4.6 Voiding Damage and Stress Relaxation 122
4.6.1 Voiding Induced Stress Relaxation 122
4.6.2 Time-Dependent Deformation and Void Growth 124
4.7 Projects 125
References 127
Chapter 5: Electronic Packaging Structures 136
5.1 Quantification of Solder Deformation 138
5.1.1 Lap-Shear Model and Stress Evolution 139
5.1.1.1 Model Setup 139
5.1.1.2 Evolution of Stress and Deformation Fields 140
5.1.2 Strain Quantification 142
5.1.2.1 Effect of Solder Constitutive Models 143
5.1.2.2 Effect of Solder Geometry 144
5.1.2.3 Comparison with Experiments 145
5.1.3 Substrate Geometry and Rigidity 148
5.2 Plastic Flow Inside a Solder Joint 151
5.2.1 Elastic-Plastic Analysis 151
5.2.2 Rate-Dependent Model 154
5.3 Side Constraint: Effect of Underfill 158
5.3.1 Shear Loading 158
5.3.1.1 Solder with Copper Substrates 159
5.3.1.2 Solder Adjoining Silicon Chip and Circuit Board 160
5.3.2 Effect of Superimposed Tension 161
5.4 Stress Field Around the Solder Joint 163
5.5 Multi-component Interaction: A Case Study on Transformer Packaging 167
5.5.1 Elastic Analysis 168
5.5.2 Nonlinear Viscoelastic Analysis 171
5.6 Projects 173
References 175
Chapter 6: Heterogeneous Materials 180
6.1 Effective Elastic Response 180
6.1.1 Multilayered Structures 181
6.1.1.1 Numerical Model 182
6.1.1.2 Overall Elastic Constants 183
6.1.2 Long Fiber Composites 184
6.1.3 A Matrix Containing Discrete Particles 187
6.1.3.1 Numerical Model 188
6.2 Effective Plastic Response 191
6.2.1 Effect of Reinforcement Shape 191
6.2.2 Effect of Reinforcement Distribution 195
6.2.2.1 Hexagonal Particle Array 196
6.2.2.2 Effect of Particle Size and Spatial Distribution: Square Array 198
6.2.3 Effect of Thermal Residual Stresses 201
6.2.4 Cyclic Response 205
6.2.5 Explicit Versus Homogenized Two-Phase Structures 207
6.3 Effective Thermal Expansion Response 209
6.3.1 Basic Consideration 210
6.3.2 Effect of Phase Contiguity 213
6.3.2.1 Model Setup 214
6.3.2.2 Composite CTE Without Thermal Residual Stresses 215
6.3.2.3 Composite CTE with Thermal Residual Stresses 217
6.3.3 Composites with Imperfect Metal Filling 219
6.3.3.1 Model Setup 219
6.3.3.2 Effect of Voids 220
6.3.3.3 Effect of Particle Contact 222
6.3.3.4 Comparison with Experiment 224
6.3.4 Viscoelastic Matrix Composites 224
6.3.4.1 Model Setup 225
6.3.4.2 Composites with Solid Fillers 227
6.3.4.3 Composites with Hollow-Sphere Fillers 229
6.4 Internal Deformation Pattern and Damage Implication 230
6.4.1 Cyclic Deformation in Fine and Coarse Lamellar Structure 231
6.4.1.1 Model Setup 231
6.4.1.2 Macroscopic Response and Local Deformation Pattern 233
6.4.1.3 Model Generalization 237
6.4.2 Particle Dispersion and Ductility Enhancement 238
6.4.2.1 Model Setup 239
6.4.2.2 Plastic Deformation Field 240
6.5 Indentation Response 242
6.5.1 Metallic Multilayers: Yield Properties 242
6.5.1.1 Model Setup 243
6.5.1.2 Correlating Hardness and Yield Strength 244
6.5.2 Metal-Ceramic Multilayers 247
6.5.2.1 Model Setup 247
6.5.2.2 Evolution of Stress and Deformation Fields 250
6.5.2.3 Overall Indentation Response 255
6.5.3 Particle-Matrix Systems 258
6.5.3.1 Model Setup 259
6.5.3.2 Indentation Response 260
6.5.3.3 Implications 263
6.6 Projects 265
References 268
Chapter 7: Challenges and Outlook 274
7.1 Material Parameters and Constitutive Models 274
7.2 Technological Relevance 275
7.3 Learning from Nature 276
7.4 Beyond Deformation 277
7.4.1 Case Study: Ductile Failure in Solder Joint 278
7.4.1.1 Model Setup 278
7.4.1.2 Plastic Deformation Field 280
References 283
Index 286