You are previewing The Physics of Deformation and Fracture of Polymers.
O'Reilly logo
The Physics of Deformation and Fracture of Polymers

Book Description

Demonstrating through examples, this book presents a mechanism-based perspective on the broad range of deformation and fracture response of solid polymers. It draws on the results of probing experiments and considers the similar mechanical responses of amorphous metals and inorganic compounds to develop advanced methodology for generating more precise forms of modelling. This, in turn, provides a better fundamental understanding of deformation and fracture phenomena in solid polymers. Such mechanism-based constitutive response forms have far-reaching application potential in the prediction of structural responses and in tailoring special microstructures for tough behaviour. Moreover, they can guide the development of computational codes for deformation processing of polymers at any level. Applications are wide-ranging, from large strain industrial deformation texturing to production of precision micro-fluidic devices, making this book of interest to both advanced graduate students and to practising professionals.

Table of Contents

  1. Cover
  2. Half Title Page
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. Symbols
  9. Frequently used abbreviations
  10. Chapter 1: Structure of non-polymeric glasses
    1. 1.1 Overview
    2. 1.2 Glass formability in metallic alloys
    3. 1.3 Atomic packing in disordered metallic solids
    4. 1.4 Energetic characterization of the structure of metallic glasses
      1. 1.4.1 The atomic site stress tensor
      2. 1.4.2 Calorimetry
    5. 1.5 Free volume
    6. 1.6 Viscosity of glass-forming liquids
    7. 1.7 Structural relaxations
      1. 1.7.1 A computational model
      2. 1.7.2 Kinetic models of structural relaxations in metallic glasses
    8. 1.8 The distributed character of structural relaxations and the glass transition
    9. 1.9 The dependence of the glass-transition temperature on cooling rate
    10. 1.10 Crystallization in bulk metallic glasses
    11. 1.11 Deformation-induced alterations of atomic structure in sub-cooled liquids and glasses
    12. 1.12 The range of metallic alloys that have been obtained as bulk metallic glasses
    13. 1.13 The structure of amorphous silicon
    14. 1.14 Characterization of the structure of amorphous silicon
    15. Suggested further reading on structure of non-polymeric glasses
    16. References
  11. Chapter 2: Structure of solid polymers
    1. 2.1 Overview
    2. 2.2 Structure of polymers
    3. 2.3 Molecular architecture
    4. 2.4 Molecular weight
    5. 2.5 Structure of amorphous polymers
      1. 2.5.1 Molecular-structure models of amorphous polymers
      2. 2.5.2 Chemically specific molecular-structure models of amorphous polymers
      3. 2.5.3 Chemically non-specific models of amorphous polymer structure
      4. 2.5.4 Experimental means of characterization of the structure of glassy polymers
    6. 2.6 Crystalline polymers
      1. 2.6.1 The fringed-micelle model of semi-crystalline polymers
      2. 2.6.2 Spherulites
      3. 2.6.3 Hedrites
      4. 2.6.4 Polymer single crystals
      5. 2.6.5 Crystallization from the melt and growth of spherulites
    7. 2.7 Defects in polymer crystals
      1. 2.7.1 Overview
      2. 2.7.2 Chain defects
      3. 2.7.3 Lattice defects
    8. 2.8 Chain-extended polymers
    9. Suggested further reading on structure of solid polymers
    10. References
  12. Chapter 3: Constitutive connections between stress and strain in polymers
    1. 3.1 Overview
    2. 3.2 Stresses and strains
      1. 3.2.1 Stresses
      2. 3.2.2 Strains
    3. 3.3 Linear elasticity of polymers
    4. 3.4 Plasticity of polymers
      1. 3.4.1 Generalized yield conditions
      2. 3.4.2 The associated-flow rule
    5. 3.5 Thermally activated deformation
    6. References
  13. Chapter 4: Small-strain elastic response
    1. 4.1 Overview
    2. 4.2 Small-strain elasticity in crystals
      1. 4.2.1 The generalized Hooke’s law
      2. 4.2.2 Orthorhombic crystals or orthotropic solids
      3. 4.2.3 Hexagonal crystals
      4. 4.2.4 Cubic crystals
      5. 4.2.5 Isotropic materials
      6. 4.2.6 Temperature and strain dependence of elastic response
    3. 4.3 Theoretical determination of elastic constants of polymers
      1. 4.3.1 Glassy polymers
      2. 4.3.2 Crystalline polymers
    4. 4.4 Elastic response of textured anisotropic polymers
    5. 4.5 Elastic properties of heterogeneous polymers
      1. 4.5.1 Methods of estimating the elastic properties of heterogeneous polymers
      2. 4.5.2 The self-consistent method
      3. 4.5.3 The Eshelby inclusion method of Chow
    6. References
  14. Chapter 5: Linear viscoelasticity of polymers
    1. 5.1 Introduction
    2. 5.2 Phenomenological formalisms of viscoelasticity
      1. 5.2.1 Uniaxial creep or stress-relaxation response
      2. 5.2.2 Dynamic relaxation response
      3. 5.2.3 Temperature dependence of viscoelastic relaxations
    3. 5.3 Viscoelastic relaxations in amorphous polymers
      1. 5.3.1 The α-relaxation
      2. 5.3.2 The free-volume model of the α-relaxation
      3. 5.3.3 Dependence of the α-relaxation on the chemical structure of molecules
      4. 5.3.4 Secondary relaxations in the glassy regime
      5. 5.3.5 Effect of physical aging on the relaxation spectra of polymers
      6. 5.3.6 Secondary relaxations in polycarbonate of bisphenol-A
    4. 5.4 Shear relaxations in partially crystalline polymers
    5. 5.5 Some problems of viscoelastic-stress analysis
    6. 5.6 Non-linear viscoelasticity
    7. Suggested further reading on linear viscoelasticity of polymers
    8. References
  15. Chapter 6: Rubber elasticity
    1. 6.1 Overview
    2. 6.2 Molecular characteristics of rubbers
      1. 6.2.1 Distinctive features of rubbers
      2. 6.2.2 The chemical constitution of rubbers
    3. 6.3 Thermodynamics of rubbery behavior
    4. 6.4 The Gaussian statistical model of rubber elasticity
    5. 6.5 The non-Gaussian statistical model of rubber elasticity
      1. 6.5.1 The freely jointed single chain
      2. 6.5.2 Langevin networks
      3. 6.5.3 Comparison of the Langevin-network model with experiments
    6. 6.6 Modes of deformation in rubber elasticity
      1. 6.6.1 Conditions for general response
      2. 6.6.2 Uniaxial tension or compression
      3. 6.6.3 Equi-biaxial stretch
      4. 6.6.4 Plane-strain tension and pure shear
      5. 6.6.5 Simple shear
      6. 6.6.6 Plane-strain compression flow in a channel die
    7. 6.7 Gaussian rubbery-type response in glassy polymers
    8. References
  16. Chapter 7: Inelastic behavior of non-polymeric glasses
    1. 7.1 Overview
    2. 7.2 The mechanism of plasticity in non-polymeric glasses
    3. 7.3 The kinematics of plasticity in glassy solids by shear transformations
    4. 7.4 Nucleation of shear transformations under stress
      1. 7.4.1 The elastic strain energy of a shear transformation in the unstressed solid
      2. 7.4.2 The Gibbs free energy of nucleation of the shear transformation under stress
      3. 7.4.3 Stages in the nucleation of the shear transformation
    5. 7.5 Yielding in metallic glasses
      1. 7.5.1 Behavior at low temperatures, T ≪ Tg
      2. 7.5.2 Temperature dependence of the yield stress, T ≪ Tg
      3. 7.5.3 Analysis of the experimental results on yield behavior of metallic glasses at low temperatures
      4. 7.5.4 Yielding in metallic glasses at temperatures close to Tg
      5. 7.5.5 Changing kinetics of plasticity near Tg
    6. 7.6 Post-yield large-strain plastic response of glassy solids: strain softening and strain hardening
      1. 7.6.1 Features of large-strain plastic flow of glassy solids
      2. 7.6.2 Plastic-flow-induced increase in the liquid-like material fraction, ψ
      3. 7.6.3 Plastic-strain-induced changes in structure and the kinetics of associated evolutions of ψ
      4. 7.6.4 Kinetics of large-strain plastic flow of glasses at T ≪ Tg
      5. 7.6.5 Kinetics of large-strain plastic flow of glasses at T close to Tg
      6. 7.6.6 Multi-axial deformation: correspondences of shear, tension, and compression at low temperatures
    7. 7.7 The strength-differential effect in disordered solids
    8. 7.8 Shear localization
      1. 7.8.1 The phenomenology of shear localization in metallic glasses
      2. 7.8.2 The mechanics of shear localization
      3. 7.8.3 Temperature rises associated with shear localization
      4. 7.8.4 The flow state
    9. Appendix. Plastic-floor-induced structural alterations: the relation between flow dilatations of free volume and liquid-like material
    10. References
  17. Chapter 8: Plasticity of glassy polymers
    1. 8.1 Overview
    2. 8.2 The rheology of glassy polymers
      1. 8.2.1 Important provisos
      2. 8.2.2 The phenomenology of plastic flow in glassy polymers
    3. 8.3 The mechanism of plastic flow in glassy polymers
      1. 8.3.1 Computer simulation of plastic flow
      2. 8.3.2 Simulation results in polypropylene
      3. 8.3.3 Simulation results in polycarbonate
    4. 8.4 Temperature dependence of yield stresses of glassy polymers
    5. 8.5 The kinetic model of plastic yield in glassy polymers
      1. 8.5.1 Temperature dependence of the plastic resistance
      2. 8.5.2 The thermal activation parameters
      3. 8.5.3 A kinetic model of flow of linear-chain glassy polymers
    6. 8.6 Large-strain plastic flow in glassy polymers
      1. 8.6.1 Development of post-yield large-strain plastic flow
      2. 8.6.2 A model for post-yield plastic flow of glassy polymers
      3. 8.6.3 Stored energy and Bauschinger back strains
      4. 8.6.4 The strength-differential effect and the multi-axial yield condition
    7. 8.7 Strain hardening in glassy polymers
    8. 8.8 Comparison of experiments and simulations on the yielding and large-strain plastic flow of glassy polymers
    9. References
  18. Chapter 9: Plasticity of semi-crystalline polymers
    1. 9.1 Overview
    2. 9.2 Mechanisms of plastic deformation
    3. 9.3 Plasticity of two semi-crystalline polymers: high-density polyethylene (HDPE) and polyamide-6 (Nylon-6)
      1. 9.3.1 Methodology of deformation
      2. 9.3.2 Plastic strain-induced alterations of spherulite morphology in Nylon-6 in uniaxial tension
      3. 9.3.3 Large-strain plastic flow in HDPE in plane-strain compression
      4. 9.3.4 Large-strain plastic flow in monoclinic Nylon-6 induced by plane-strain compression
      5. 9.3.5 Measurement of critical resolved shear stresses in textured HDPE and Nylon-6 and their normal-stress dependence
    4. 9.4 The kinetics of plastic flow in semi-crystalline polymers
      1. 9.4.1 Modes of dislocation nucleation in lamellae
      2. 9.4.2 The strain-rate expression
      3. 9.4.3 The dominant nucleation mode
      4. 9.4.4 Activation volumes
      5. 9.4.5 Temperature dependence of the plastic resistance
    5. 9.5 Simulation of plastic-strain-induced texture development in HDPE
      1. 9.5.1 Characteristics of the simulation
      2. 9.5.2 Basic assumptions of the model
      3. 9.5.3 Constitutive relations
      4. 9.5.4 Composite inclusion
      5. 9.5.5 Interaction law and solution procedure
      6. 9.5.6 Parameter selection in the model
      7. 9.5.7 Predicted results of the composite model and comparison with experiments
    6. Suggested further reading on plasticity of semi-crystalline polymers
    7. References
  19. Chapter 10: Deformation instabilities in extensional plastic flow of polymers
    1. 10.1 Overview
    2. 10.2 Deformation instabilities in extensional plastic flow of polymers
    3. 10.3 Conditions for impending localization in extensional deformation
      1. 10.3.1 Basic shear response
      2. 10.3.2 Basic extensional response
    4. 10.4 Stability of extensional plastic flow
    5. 10.5 The effect of strain-rate sensitivity on stability in extensional plastic flow
      1. 10.5.1 In the onset of necking
      2. 10.5.2 In the post-necking behavior
    6. 10.6 Plastic drawing of polymers
    7. References
  20. Chapter 11: Crazing in glassy homo- and hetero-polymers
    1. 11.1 Overview
    2. 11.2 The phenomenology of crazing in glassy homo-polymers
    3. 11.3 Simulation of cavitation in a glassy polymer at the atomic level
    4. 11.4 Craze initiation
      1. 11.4.1 Experimental observations
      2. 11.4.2 Intrinsic crazing
      3. 11.4.3 Tension–torsion experiments
    5. 11.5 A craze-initiation model
    6. 11.6 Comparison of the predictions of the craze-initiation model with experiments
    7. 11.7 Craze growth
      1. 11.7.1 Craze stresses
      2. 11.7.2 Craze microstructure
      3. 11.7.3 Craze-growth experiments
    8. 11.8 A craze-growth model
    9. 11.9 Comparison of the craze-growth model with experiments
    10. 11.10 Crazing in block copolymers
      1. 11.10.1 Morphology of diblock copolymers
      2. 11.10.2 Crazing experiments in PS/PB diblock copolymers
      3. 11.10.3 A model of craze growth in a PS/PB diblock copolymer with spherical PB domains
      4. 11.10.4 Comparison of the predictions of the craze-growth model in PS/PB diblock copolymers with experiments
    11. References
  21. Chapter 12: Fracture of polymers
    1. 12.1 Overview
    2. 12.2 Cracks and fracture
      1. 12.2.1 Two complementary perspectives in crack mechanics
      2. 12.2.2 Cracks in LEFM
      3. 12.2.3 The energy-release rate GI in LEFM with crack extension
    3. 12.3 Cracks with plastic zones
      1. 12.3.1 The pervasiveness of plasticity at the crack tip
      2. 12.3.2 Cracks with small-scale yielding (SSY)
      3. 12.3.3 Crack-tip fields with contained plasticity
      4. 12.3.4 Crack fields in fully developed plasticity
    4. 12.4 Stability of crack advance
    5. 12.5 Intrinsic brittleness of polymers
    6. 12.6 Brittle-to-ductile transitions in fracture
    7. 12.7 Mechanisms and forms of fracture in polymers
      1. 12.7.1 The crack-tip process zone
      2. 12.7.2 The role of chain scission in polymer fracture
      3. 12.7.3 Fracture of unoriented polymers
      4. 12.7.4 Cohesive separation
      5. 12.7.5 Fracture in glassy polymers involving crazing
      6. 12.7.6 Molecular-scission-controlled fracture of oriented semi-crystalline polymers
      7. 12.7.7 Fracture toughnesses of a selection of polymers
    8. 12.8 Impact fracture of polymers
      1. 12.8.1 Application of fracture mechanics to impact fracture
      2. 12.8.2 Fracture of polymers at high strain rate
    9. Suggested further reading on fracture of polymers
    10. References
  22. Chapter 13: Toughening of polymers
    1. 13.1 Overview
    2. 13.2 Strategies of toughening of polymers
    3. 13.3 Different manifestations of toughness in polymers
    4. 13.4 The generic fracture response of polymers in uniaxial tension
    5. 13.5 Toughening of crazable glassy polymers by compliant particles
      1. 13.5.1 Types of compliant composite particles
      2. 13.5.2 Brittleness of glassy homo-polymers and alleviating it through craze plasticity
      3. 13.5.3 The mechanism of toughening in particle-modified crazable glassy polymers
      4. 13.5.4 Elasticity of compliant particles
      5. 13.5.5 Craze initiation from compliant particles and the craze-flow stress
      6. 13.5.6 The role of compliant-particle size in toughening glassy polymers
      7. 13.5.7 A model for the craze-flow stress of particle-toughened polystyrene
      8. 13.5.8 Special HIPS blends prepared to evaluate the toughening model
      9. 13.5.9 Comparison of the behavior of special HIPS blends with model predictions
    6. 13.6 Diluent-induced toughening of glassy polymers
      1. 13.6.1 Different manifestations of toughening with diluents
      2. 13.6.2 Factors affecting diluent toughening of PS
      3. 13.6.3 A model of diluent-induced toughening of glassy polymers
      4. 13.6.4 Comparison of the diluent-induced-toughening model with experiments
    7. 13.7 Toughening of semi-crystalline polymers
      1. 13.7.1 Toughness of unmodified HDPE and polyamides of Nylon-6 and -66
      2. 13.7.2 Toughening semi-crystalline polymers by particle modification
    8. 13.8 Toughening of brittle thermosetting polymers
    9. References
  23. Author index
  24. Subject index