Deformation and Flow of Polymeric Materials

564 Pages·2014·15.345 MB·English

by  Helmut Münstedt, Friedrich Rudolf Schwarzl (auth.)

Helmut Münstedt
Friedrich Rudolf Schwarzl
Deformation
and Flow of
Polymeric
Materials
Deformation and Flow of Polymeric Materials
Helmut Münstedt Friedrich Rudolf Schwarzl
•
Deformation and Flow
of Polymeric Materials
123
Helmut Münstedt
Friedrich Rudolf Schwarzl
Lehrstuhl fürPolymerwerkstoffe
Friedrich-Alexander-Universität
Erlangen-Nürnberg
Erlangen
Germany
ISBN 978-3-642-55408-7 ISBN 978-3-642-55409-4 (eBook)
DOI 10.1007/978-3-642-55409-4
Springer Heidelberg NewYork Dordrecht London
LibraryofCongressControlNumber:2014940158
(cid:2)Springer-VerlagBerlinHeidelberg2014
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Preface
Duringthelastfewdecades,theuseofpolymericmaterialshasgrownsothatthey
form the most important class of materials if counted by volume and it can be
regardedascertainthattheirgrowthrateswillremainhighinthefuture.Whileat
the beginning of the era of polymers Chemistry was the predominant science,
EngineeringandPhysicshavebecome moreandmorerequisitefor the successful
development of polymeric materials. Engineering, as the efficient production of
materialsofgoodqualityandtheirhighlysophisticatedprocessinghavedeveloped
into key factors of economic success; and Physics, as material properties have
become decisive for specific applications and the continuing innovation and
improvement of products. These requirements cannot be fulfilled without a
fundamental knowledge of polymeric materials and a profound understanding of
the relations between the molecular structure of polymers and their physical and
processing properties.
These developments and the increasing number of joint uses of various mate-
rials in highly sophisticated technical products led to the foundation of special
institutes devoted to materials science at some universities about 40 years ago.
Besides classical materials like metals, glass, and ceramics, polymers became a
central point of academic teaching and research. This book has its origin in lec-
tures for students in the field of polymeric materials within the Department of
MaterialsScienceandProcessingattheFriedrich-Alexander-UniversityErlangen-
Nürnberg. Its main intention is to teach the basics about polymers necessary for
everybody working with these materials. One part is based on the textbook
‘‘Polymermechanik,’’ which appeared in 1990, the other stems from more recent
lectures.
Thebookfollows twomainguidelines.Oneisaquantitativedescriptionofthe
molecular structure, though this has sometimes had to be simplified due to its
complexnature.Theotherpresentsrelationshipsbetweenmolecularquantitiesand
materialproperties,whichcoverthesolidandthemoltenstate.Thetemperatureis
the key external parameter according to which the mechanical behavior is com-
prehensively discussed. Nevertheless, this work has to be regarded neither as a
complete text book on the mechanics of polymer materials nor on their rheology.
Rather, it is meant to discuss these fields from a common viewpoint, which
encompasses the transitions between the solid and molten states.
v
vi Preface
‘‘Tools’’aredescribedinsofarastheyarebelievedtobenecessaryforadeeper
understanding of the results presented. They comprise measuring devices as well
as mathematical formalisms required for dealing with large deformations.
Muchspaceisdevotedtothelineartheoryofviscoelasticityasitiscoherentin
itself and allows quantitative insights into relations between properties and
molecular structure. Theories covering the nonlinear viscoelastic regime which
dominates processing are not yet in a state of development enabling quantitative
descriptionsofpropertiesandprocesseswithageneralitycomparabletothelinear
behavior. This has to be said, although many theories have been published since
1990, the year of the appearance of ‘‘Polymermechanik.’’ Nevertheless, an over-
viewofconstitutiveequationsbasedonvariousmodelsisgivenandsomeoftheir
predictions are compared with experimental findings.
Inmanypartsofthebook,resultsofinvestigationsperformedattheInstituteof
Polymer Materials are presented. They are examples of how research and estab-
lished knowledge can become complementary parts of teaching. Regarding the
references,longlists,whichcouldeasilybeobtainedtodayfromvariouselectronic
bibliographies, have deliberately been avoided. Instead, a selection of original
literature is cited, which opens the door to deeper information for those who are
interested in more details.
The book is written from our experience of teaching the knowledge on poly-
mericmaterials,which wethinktobeuseful forpeopleinterestedandengagedin
this class of materials. We hope it will be helpful for students to consolidate and
broaden their knowledge, to researchers in the field of polymers at various insti-
tutions, and even to those working in industry, whenever they would like to get
some fundamental questions answered, which arise from dealing with polymers.
As it is obvious from the reference lists, the originality and actuality of the
results presented in this book are based, to a high degree, on the research of
doctoral students under the guidance of the authors of this book. Particularly
appreciated are the contributions from the theses of:
Dr. Dietmar Auhl Dr. Robert Greiner
Dr. Hans-Jürgen Grieß Dr. Joachim Kaschta
Dr. Daniela Hertel Dr. Günther Link
Dr. Jens Hepperle Dr. Walter Pfandl
Dr. Claus Gabriel Dr. Michael Wolf
Dr. Ute Maria Kessner Dr. Franz Zahradnik
Dr. Stefan Kurzbeck
Dr. Julia Maria Resch
Dr. Martin Schwetz
Dr. Florian Stadler
Dr. Jens Stange
Dr. Thomas Steffl
Dr. Erik Wassner
Dr. Friedrich Wolff
Preface vii
H.MünstedtthanksDr.UteMariaKessner,Dr.MartinSchwetz,andDr.Friedrich
Wolffforreadingpartsofthemanuscript,Dr.FlorianStadlerforfruitfuldiscussions
andM.Sc.UteZeitlerforhersupportinpreparingcomputer-basedversionsofmany
ofthefigures.
F.R.SchwarzlwishestorememberthelateDr.ir.J.Heijboerwithwhommany
fruitful discussions in the field of secondary relaxation mechanisms of polymers
were held. He wishes also to thank Prof. Dr. H. Janeschitz-Kriegl for a life-long
friendship and scientific cooperation in Graz, Delft, Linz, and Erlangen, Prof. Dr.
ir.L.C.E.Struikfortheverystimulatingdiscussionsconcerningthesolidstateof
polymersinDelftandProf.Dr.M.H.Wagner,TechnicalUniversityBerlin,forthe
introduction to his theories on polymer rheology.
Erlangen, March 2014 Helmut Münstedt
Friedrich Rudolf Schwarzl
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 General Aspects of Polymeric Materials . . . . . . . . . . . . . . . . 1
1.2 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 General Classification of Polymeric Materials . . . . . . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Physical Structure of Macromolecules. . . . . . . . . . . . . . . . . . . . . 7
2.1 Structure and Brownian Motion of Macromolecules. . . . . . . . 7
2.2 Molar Mass and Molar Mass Distribution . . . . . . . . . . . . . . . 10
2.3 The Random Walk Problem in Three Dimensions . . . . . . . . . 19
2.4 Macromolecules in Solution. . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Statistical Shape of Linear Macromolecules in H-Solution . . . 31
2.6 Statistical Shape of Macromolecules in Good Solvents. . . . . . 35
2.7 Analysis of Branched Macromolecules . . . . . . . . . . . . . . . . . 37
2.8 Size of Macromolecules in the Glassy and Molten State. . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 Experimental Methods to Determine Molecular Quantities . . . . . 43
3.1 Osmometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Viscometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Gel Permeation Chromatography . . . . . . . . . . . . . . . . . . . . . 68
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Structure and States of Polymers . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 Classification of Polymeric Materials . . . . . . . . . . . . . . . . . . 77
4.2 Molecular Structure of Amorphous Polymers. . . . . . . . . . . . . 87
4.3 States of Order of Uncross-Linked Amorphous Polymers . . . . 89
4.4 Influence of Molar Mass and Cross-Linking Density . . . . . . . 94
4.5 Semicrystalline Polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.5.1 Features of Crystallinity . . . . . . . . . . . . . . . . . . . . . 99
4.5.2 States of Order. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.5.3 Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
ix
x Contents
4.6 The Specific Volume of Polymers . . . . . . . . . . . . . . . . . . . . 111
4.6.1 The Specific Volume of Amorphous Polymers. . . . . . 111
4.6.2 The Free Volume Theory . . . . . . . . . . . . . . . . . . . . 115
4.6.3 Volume Relaxation and Physical Aging . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5 Linear Viscoelastic Deformation Behavior in Simple Shear . . . . . 121
5.1 Theoretical Description of the Deformation Behavior
of Polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 Creep, Creep Recovery, and Stress Relaxation. . . . . . . . . . . . 122
5.3 The Principle of Superposition. . . . . . . . . . . . . . . . . . . . . . . 127
5.4 Relaxation and Retardation Spectra . . . . . . . . . . . . . . . . . . . 130
5.5 The Creep Recovery Experiment . . . . . . . . . . . . . . . . . . . . . 137
5.6 The Creep Compliance of Amorphous Polymers . . . . . . . . . . 140
5.7 Relations Between Creep and Stress Relaxation. . . . . . . . . . . 149
5.8 Oscillatory Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.9 Approximate Relations Between Measurable Viscoelastic
Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.10 The Viscoelastic Behavior of Amorphous Polymers
in Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6 Time-Temperature Shift of Mechanical Properties. . . . . . . . . . . . 189
6.1 The Significance of the Time-Temperature Shift for the
Description of the Deformation Behavior of Polymers . . . . . . 189
6.2 The Time-Temperature Shift Principle . . . . . . . . . . . . . . . . . 190
6.3 The Time-Temperature Shift of the Glass-Rubber
Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.4 The Time-Temperature Shift in the Flow Region
of Amorphous Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.5 The Time-Temperature Shift in the Flow Region
of Semicrystalline Polymers. . . . . . . . . . . . . . . . . . . . . . . . . 210
6.6 The Time-Temperature Shift of Secondary Transitions
in the Glassy State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
7 Linear Viscoelastic Deformation Under Three-Dimensional
Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7.1 The Stress Tensor and the Equations for the
Balance of Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7.2 The Strain Tensor for Small Deformations . . . . . . . . . . . . . . 227
7.3 The Rheological Equation of State for Isotropic
Linear Elastic Materials (Hookean Theory of Elasticity). . . . . 230
Contents xi
7.4 The Rheological Equation of State for Isotropic Linear
Viscoelastic Materials at Small Deformations . . . . . . . . . . . . 231
7.5 Simple Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
7.6 Isotropic Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.7 Uniaxial Tensile Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
7.8 The Viscoelastic Functions for Amorphous Uncross-Linked
Polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
8 Fundamentals of the Rheology of Large Deformations. . . . . . . . . 243
8.1 Kinematics of Large Deformations. . . . . . . . . . . . . . . . . . . . 243
8.2 Deformation Gradient and Finite Strain Tensors. . . . . . . . . . . 247
8.3 Relative Deformation Gradient and Relative Strain
Tensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
8.4 The Rate of Strain Tensor. . . . . . . . . . . . . . . . . . . . . . . . . . 254
8.5 Dynamics of Deformable Bodies . . . . . . . . . . . . . . . . . . . . . 256
8.6 Eigenvalues and Invariants of the Stress Tensor. . . . . . . . . . . 259
8.7 Transformation of the Strain Tensors and the Rate of Strain
Tensor to Principal Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
8.7.1 Time-Dependent Simple Shear. . . . . . . . . . . . . . . . . 268
8.7.2 Multidimensional Time-Dependent
Incompressible (Isochoric) Extension . . . . . . . . . . . . 271
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
9 Large Deformations of Polymers. . . . . . . . . . . . . . . . . . . . . . . . . 275
9.1 Stress-Strain Behavior of Polymeric Materials. . . . . . . . . . . . 275
9.2 Rheological Equation of State for Isotropic Elastic
Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
9.3 Rheological Equation of State for the Ideal Rubber . . . . . . . . 284
9.4 Statistical Theory of Rubber Elasticity . . . . . . . . . . . . . . . . . 289
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
10 Equations of State for Polymer Melts . . . . . . . . . . . . . . . . . . . . . 297
10.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
10.2 Rheological Equation of State for the Elastic Liquid
After Lodge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
10.2.1 The Constitutive Equation. . . . . . . . . . . . . . . . . . . . 298
10.2.2 The Lodge Liquid in Time-Dependent
Simple Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
10.2.3 The Lodge Liquid in a Stressing Experiment
in Simple Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
10.2.4 The Lodge Liquid in Shear Creep and Creep
Recovery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305