Mechanics of Paper Products

Description

This graduate level textbook focuses on the mechanical properties and performance of products made of fiber-based materials such as paper and board. The book aims to help students develop effective skills for solving problems of product performance and engineering challenges in new product development. Therefore the material is organized with a problem-based approach - a practical example of product performance is presented and then the relevant mechanics are analyzed to deduce which material properties control the performance. Problem-based approach to help students to develop effective skills for solving problems in new product development Paper and board specific topics such as loading and strength of board boxes, stress-strain behavior, fracture mechanics, creep and hygroexpansion and micromechanics of paper products, extension to biocomposites High quality color illustrations 1 The challenge 2 Paper as an engineering material 2.1 Introduction 2.2 Linear elasticity of paper 2.2.1 Elastic constants 2.2.2 Typical stiffness values for paper 2.3 Stress-strain behavior of paper 2.3.1 In-plane tensile loading 2.3.2 Visco-elastic effects 2.3.3 Other loading modes 2.4 Multi-axial strength 2.5 Mechanical properties in relation to the papermaking process 2.5.1 Preparation of papermaking fibers 2.5.2 Effect of the paper machine Part I: Structural strength 3 Packaging performance 3.1 Introduction 3.2 Paper-based packaging materials 3.2.1 Corrugated board 3.2.2 Box manufacturing process 3.2.3 Carton board 3.3 Loads imposed on boxes 3.4. Strength of boxes 3.4.1 Short-term compressive loading 3.4.2 Empirical models for static box strength 3.4.3 Finite element models 3.4.4 Long-term loading 3.5 Summary 4 Behavior of corners in carton board boxes 4.1 Introduction 4.2 Folding of a multiply carton board 4.3 Creasing 4.4 Important material properties 4.5 Final remarks 5 Fracture properties 5.1 Introduction 5.2 Examples of practical applications of fracture mechanics 5.2.1 Mode I failure under in-plane tension 5.2.2 Out-of-plane delamination 5.3 Crack tip modeling in paper materials 5.3.1 Characteristic length scale and the basis of crack tip modeling 5.3.2 Linear elastic fracture mechanics LEFM 5.3.3 Nonlinear fracture mechanics using J-integral 5.3.4 Cohesive zone models 5.3.5 Continuum damage mechanics modeling of paper 5.3.6 Delamination of paper materials 5.4 Compressive failure 5.5 Summary Part II: Dynamic stability 6 Web dynamics in paper transport systems 6.1 Introduction 6.2 Dynamics of web transport 6.2.1 Basic formulation of web transport problems 6.2.2 The case of an axially moving web 6.2.3 Moving thread problem 6.2.4 Fluttering of a two-dimensional web 6.3 Concluding remarks 7 Creep and relaxation 7.1 Introduction 7.2 Relaxation and creep as phenomena 7.3 Modeling of time-dependence 7.3.1 Linear behavior 7.3.2 Nonlinearity 7.3.3 Recoverability 7.3.4 Time scales 7.4 Creep and relaxation properties of paper 7.4.1 Creep 7.4.2 Stress relaxation 7.4.3 Tensile versus compressive creep 7.4.4 Effect of the papermaking process and furnish 7.5 Moisture effects 7.5.1 Softening with moisture 7.5.2 Accelerated creep 7.6 Prediction of box lifetime 7.6.1 Creep response of a box 7.6.2 Previous equations for box lifetime 7.6.3 Derivation of a new equation for box lifetime 7.6.4 Accounting for variability 7.7 Summary 8 Statistical aspects of failure of paper products 8.1 Introduction 8.2 Practical examples 8.2.1 Web breaks in a printing press and on a paper machine 8.2.2 Stacking performance of boxes 8.3 Statistical approaches for failure in materials or systems 8.3.1 The chain model 8.3.2 The bundle model 8.3.3 Time-dependent, statistical failure model 8.4 Statistical failure of paper 8.4.1 Strength distributions 8.4.2 Factors controlling strength distributions 8.4.3 Strength scaling 8.4.4 Web break prediction 8.5 Research front of statistical failure of paper 8.6 Concluding remarks Part III: Reactions to moisture and water 9 Moisture-induced deformations 9.1 Introduction 9.2 Moisture-induced deformations 9.2.1 Hygroexpansion of paper 9.2.2 Effect of moisture history 9.3 Fluting 9.3.1 Tension wrinkling 9.3.2 Effect of small scale strain variations 9.3.3 Fluting vs. cockling 9.4 Summary 10 Mechanics in printing nip for paper and board 10.1 Introduction 10.2 Nip mechanics in offset printing of paper 10.3 Nip mechanics in flexo post printing of corrugated board 10.4 Micro-fluidics of ink in printing nip 10.5 Concluding remarks Part IV: Material properties 11 Micromechanics 11.1 Introduction 11.2 Fiber network structure 11.2.1 Two-dimensional network 11.2.2 Densification mechanisms 11.2.3 Statistical geometry of real fiber networks 11.2.4 Key structural factors when engineering the mechanical properties of paper 11.3 Elastic modulus 11.3.1 The effect of paper density 11.3.2 The shear-lag mechanism 11.3.3 The activation mechanism 11.3.4 Elastic modulus of activated fiber network 11.3.5 Key factors when engineering the elastic modulus of paper 11.4 Stress-strain behavior, creep, and bond opening 11.5 Fracture process in the fiber network 11.5.1 Microscopic observations 11.5.2 Micromechanical description of the fracture process 11.6 Hygroexpansion 11.7 Final remarks 12 Wood biocomposites – extending the property range of paper products 12.1 Introduction 12.2 Material components: fibers and polymers 12.2.1 Plant fiber structure 12.2.2 Polymer matrices and binders 12.3 Micromechanics of fiber composites 12.3.1 Weight fraction and volume fraction 12.3.2 Elastic properties in unidirectional composites 12.3.3 Elastic properties in short fiber composites 12.3.4 Interfacial strength in short fiber composites 12.4 Composites data: wood fiber/thermoplastic 12.5 Composites data: wood fiber/thermoset 12.6 Nano-fibrillated cellulose materials 12.6.1 Cellulosic “nano-paper” 12.6.2 Nano-composites 12.7 Conclusions Index