Mechanics of Paper Products (eBook)

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Kaarlo Niskanen, Mid Sweden University, Sundsvall, Sweden.

Preface 6
List of Contributing Authors 8
Contents 10
1 The challenge 16
2 Paper as an engineering material 20
2.1 Introduction 20
2.2 Linear elasticity of paper 21
2.2.1 Elastic constants 21
2.2.2 Typical stiffness values for paper 24
2.3 Stress-strain behavior of paper 26
2.3.1 In-plane tensile loading 26
2.3.2 Visco-elastic effects 30
2.3.3 Other loading modes 30
2.4 Multi-axial strength 32
2.5 Mechanical properties in relation to the papermaking process 34
2.5.1 Preparation of papermaking fibers 34
2.5.2 Effect of the paper machine 37
Part I: Structural strength 42
3 Packaging performance 44
3.1 Introduction 44
3.2 Paper-based packaging materials 45
3.2.1 Corrugated board 45
3.2.2 Box manufacturing process 48
3.2.3 Carton board 49
3.3 Loads imposed on boxes 50
3.4. Strength of boxes 53
3.4.1 Short-term compressive loading 53
3.4.2 Empirical models for static box strength 57
3.4.3 Finite element models 59
3.4.4 Long-term loading 62
3.5 Summary 63
4 Behavior of corners in carton board boxes 68
4.1 Introduction 68
4.2 Folding of a multiply carton board 70
4.3 Creasing 74
4.4 Important material properties 78
4.5 Final remarks 78
5 Fracture properties 82
5.1 Introduction 82
5.2 Examples of practical applications of fracture mechanics 84
5.2.1 Mode I failure under in-plane tension 84
5.2.2 Out-of-plane delamination 87
5.3 Crack tip modeling in paper materials 88
5.3.1 Characteristic length scale and the basis of crack tip modeling 88
5.3.2 Linear elastic fracture mechanics LEFM 90
5.3.3 Nonlinear fracture mechanics using J-integral 91
5.3.4 Cohesive zone models 94
5.3.5 Continuum damage mechanics modeling of paper 96
5.3.6 Delamination of paper materials 98
5.4 Compressive failure 100
5.5 Summary 102
Part II: Dynamic stability 106
6 Web dynamics in paper transport systems 108
6.1 Introduction 108
6.2 Dynamics of web transport 109
6.2.1 Basic formulation of web transport problems 109
6.2.2 The case of an axially moving web 110
6.2.3 Moving thread problem 115
6.2.4 Fluttering of a two-dimensional web 120
6.3 Concluding remarks 122
7 Creep and relaxation 126
7.1 Introduction 126
7.2 Relaxation and creep as phenomena 127
7.3 Modeling of time-dependence 129
7.3.1 Linear behavior 129
7.3.2 Nonlinearity 130
7.3.3 Recoverability 131
7.3.4 Time scales 132
7.4 Creep and relaxation properties of paper 134
7.4.1 Creep 135
7.4.2 Stress relaxation 137
7.4.3 Tensile versus compressive creep 138
7.4.4 Effect of the papermaking process and furnish 139
7.5 Moisture effects 141
7.5.1 Softening with moisture 141
7.5.2 Accelerated creep 142
7.6 Prediction of box lifetime 144
7.6.1 Creep response of a box 144
7.6.2 Previous equations for box lifetime 146
7.6.3 Derivation of a new equation for box lifetime 147
7.6.4 Accounting for variability 148
7.7 Summary 149
8 Statistical aspects of failure of paper products 154
8.1 Introduction 154
8.2 Practical examples 154
8.2.1 Web breaks in a printing press and on a paper machine 154
8.2.2 Stacking performance of boxes 157
8.3 Statistical approaches for failure in materials or systems 158
8.3.1 The chain model 159
8.3.2 The bundle model 160
8.3.3 Time-dependent, statistical failure model 162
8.4 Statistical failure of paper 164
8.4.1 Strength distributions 165
8.4.2 Factors controlling strength distributions 166
8.4.3 Strength scaling 167
8.4.4 Web break prediction 169
8.5 Research front of statistical failure of paper 171
8.6 Concluding remarks 172
Part III: Reactions to moisture and water 176
9 Moisture-induced deformations 178
9.1 Introduction 178
9.2 Moisture-induced deformations 178
9.2.1 Hygroexpansion of paper 178
9.2.2 Effect of moisture history 182
9.3 Fluting 186
9.3.1 Tension wrinkling 186
9.3.2 Effect of small scale strain variations 189
9.3.3 Fluting vs. cockling 192
9.4 Summary 193
10 Mechanics in printing nip for paper and board 196
10.1 Introduction 196
10.2 Nip mechanics in offset printing of paper 197
10.3 Nip mechanics in flexo post printing of corrugated board 201
10.4 Micro-fluidics of ink in printing nip 203
10.5 Concluding remarks 206
Part IV: Material properties 210
11 Micromechanics 212
11.1 Introduction 212
11.2 Fiber network structure 213
11.2.1 Two-dimensional network 213
11.2.2 Densification mechanisms 215
11.2.3 Statistical geometry of real fiber networks 216
11.2.4 Key structural factors when engineering the mechanical properties of paper 220
11.3 Elastic modulus 221
11.3.1 The effect of paper density 221
11.3.2 The shear-lag mechanism 223
11.3.3 The activation mechanism 225
11.3.4 Elastic modulus of activated fiber network 226
11.3.5 Key factors when engineering the elastic modulus of paper 230
11.4 Stress-strain behavior, creep, and bond opening 231
11.5 Fracture process in the fiber network 235
11.5.1 Microscopic observations 235
11.5.2 Micromechanical description of the fracture process 236
11.6 Hygroexpansion 240
11.7 Final remarks 242
12 Wood biocomposites – extending the property range of paper products 246
12.1 Introduction 246
12.2 Material components: fibers and polymers 251
12.2.1 Plant fiber structure 251
12.2.2 Polymer matrices and binders 255
12.3 Micromechanics of fiber composites 257
12.3.1 Weight fraction and volume fraction 257
12.3.2 Elastic properties in unidirectional composites 258
12.3.3 Elastic properties in short fiber composites 259
12.3.4 Interfacial strength in short fiber composites 261
12.4 Composites data: wood fiber/thermoplastic 262
12.5 Composites data: wood fiber/thermoset 263
12.6 Nano-fibrillated cellulose materials 265
12.6.1 Cellulosic “nano-paper” 265
12.6.2 Nano-composites 267
12.7 Conclusions 267
Index 270