Polymer viscoelasticity : stress and strain in practice

902 Pages·2000·40.243 MB·English

by  Evaristo Riande, et al

~oundingE ditor
Professor
Clemon University
Clemson, South Carolina
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H~ndbooko f Polyolefins, Second
by C~~~elVi~sai le
MARCEL
MARCEL DEKKER, INC. NEWY ORK BASEL
DEKKER
rar-y of ~on~re~sast alo~in~-in-Publi~ation
Polymer viscoelasticity :s tress and strain in practice / Evaristo
Riande .. . [ et al.].
p. cm. -( Plastics engineering :5 5)
Includes bibliographical references and index.
ISBN 0-8247-7904-5 (alk. paper)
1. Polymers-Viscosity. 2. Viscoelasticity. I. Riande,
Evaristo. 11. Series: Plastics engineering (Marcel Dekker, Inc.);
55.
TA455.PBP694 2000
620.1 '9204232-dc21 99-40874
CIP
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This book is concerned mainly with the study of the viscoelastic responseO f
isotropic macro~oleculars ystems to mechanical force fields.O wing to
diverse influences on the viscoelastic behavior in multiphase systems (e.g.,
changes in morphology and interfaces by action of the force fields, interac-
tions between phases, etc.), it is difficult to relate the measured rheological
functions to the intrinsic physical properties of the systems and, as a result,
the viscoelastic behavior ofp olymerb lends and liquid crystals is not
addressed in this book.
We have approached the subject in such a way that the book will meet
the require~entso f the beginner in the study of viscoelastic properties of
polymers as well as those of the experienced worker in other type of materi-
als. With this in mind, Chapters 1 and 2 are introductory and discuss aspects
related to chemicald iversity, topology, molecular heterodispersity, and
states of aggregation of polymers (glassy, crystalline, and rubbery states)
to familiarize those who are not acquainted with polymers with molecular
parameters that condition the marked viscoelastic behavior of these materi-
als. Chapters I and 2 also discuss melting processesa nd glass transition, and
factors affecting them.
Owing to the coil conformation of molecular chains, polymers above
the glass-transition te~peraturee xhibit high entropic elasticity. Chapter 3
discusses, using thermodynamic approaches, the relationship between stress
and entropic elasticity in rubbery networks. The equation of state between
stress and defor~ationin rubber elasticity is established through random-
flight statistics. Swelling methods are described that enable infomation to
be obtained on the topology of the networks, Vulcanizing systems,a dditives
iii
iv Preface
(antioxidants, softeners and plasticizers, reinforcers), and applications are
reviewed, as are elastomeric materials and thermoplastic elastomers com-
mercially available. Chapter 3 also provides a summary of some aspects
related to rubbers of interest in engineering.
Chapter 4 outlines operations of symmetry on ideal solids that show
how the number of independentc omponents of the modulus tensor
diminishes as the number of symmetrye lements in the solidi ncreases.
This analysis leads to the formulation of the generalized ooke’s law utiliz-
ing both elastic modulus and elastic complia~cesfo r am hous solid mate-
rialsT. hese re~ationships,c onvenientlym odified, are further usedi n
viscoelasticity. In this chapter the generalizedl awo fN ewton for ideal
liquids is also stated.
Chapters 5 and 6 discuss how the mechanical characteristics of a mate-
rial (solid, liquid, or viscoelastic) can be defined by comparing the mean
relaxation time and the time scale ofb oth creep and relaxation experiments,
in which the transient creep compliance function and the transient relaxa-
tion modulus for viscoelastic materials can be determined. These chapters
oltzmann superposition principle can be applied to predict
the evolution of either the deformation or the stress for c
discontinuo~sm echanical histories in linear viscoelasticity.
relationships between transient compliance functions and transient relaxa-
tion moduli are obtained, and interrelations between viscoelastic functions
in the time and frequency domains are given.
xperimental methods to measure the viscoelastic functions in the time
quency domain are described in Chapter 7.
thermorheolo~cals imple systems, the time-tem~erature correspon-
dence principleh olds. Chapter 8 gives examples of isotherrnfso r compliance
functions and relaxation moduli. The shift factors are expressed in terrns of
terminal viscoelastic parameters, and the temperature dependence of the
ctors is interpreted int e rms of the freev olume and the ua-
he chapter outlines methods for determining the mole ght
entanglements, and analyzes the in~uenceo f diluents and plastici-
zers on the viscoelastic functions.
Chapter 9 examines transient and nontransient viscoelastic functions in
terms of the retardation times (compliance functions) and relaxation times
axation moduli) andc o mpares retardation and relaxation times.
thods to determine retardation and relaxation spectra from c o ~ ~ l i a ~ ~ e
functions and relaxation spectra, respectively, are presented.
echanical modelst hat represent the evolution of the viscoelastic func-
tions in the time and frequency domain are described inC hapter 10. Chapter
11 discusses experimental scaling laws for viscosity, equilib~umr ecovery
Preface V
compliance, and terminal relaxation times in terms of molecular models
(spring-bead and reptation theories).
In the glassy state, long-range motions are frozen and onlyl ocal
motions are pe~ittedT. he viscoelastic behavior of polymers in the glassy
state di sis cusseind 2, with emphasis on the mechanisms that
could produce the sub- elaxations. The glass-rubber relaxation is
discussedi n terms of the equation. Aginge ffects on the glass rubber
relaxation are analyz as the effeocc t fr ystalline entities on the
relaxation viscoelastic behavior of se~icrystallinep olymers.
The stress in viscoelastic liquids at steady-state conditions is defined, in
simple shear flow,b y the shear rate and two normal stress differences.
Chapter 13r eviews the evolution of both the normal stress differenc~s
and the viscosityw ith increasing shear ratef or different
e~iquantitativea pproaches are used in which the critical shear rate at
which the viscosity starts to drop in non-~ewtonianf luids is estimate^.
The effects of shear rate, concentration, and temperature on die swell are
qualitatively analyzed, and some basic aspects of the elongational flow are
discussed. This process is useful to understand, at least qualitatively, the
rheological fundamentals of polymer processing.
As strain increases, the stress-strain isochrones deviate
and some phenomena arise in polymeric materials in bulk.
plastic material, permanent or irreversible changes occur
stress,d efined as yields tress.e cause thermoplastics and thermosets in
engineering applications fail b yielding-thati s,b y the onset of plastic
defor~ation-plastic deformation is closely associated with the technolo
of polymers. Chapter 14 presents an overview of yielding and deformation
behavior in polymers. Theoretical approaches that have been developed to
account for yield strength are outlined in this chapter. Polymers can fail in
many other ways. Chapter 14 also discusses the analysis of the stress-strain
curves of polymeric materials and enables their classification as brittle or
ductile materials as well as establishing testing conditions for the ductile-
brittle transition. The processes that take place when a polymer is fractur~~
are described, as are crazing phenomena, characteristics of thermoplastic
polymers. Crazing represents an intermediate state betweenm icroscopic
fracture and yielding, and it is often a precursor to brittle fracture,
Finally, the impact strength and fatigue are examined.
Among the main disadvantages of using polymers as structural compo-
nents in engineering are their low stiffness and strength. To improve these
properties, reinforced polymers or polymeric matrix composites are pre-
pared. Chapter 15 provides an overview of these materials, mainly fiber-
reinforced composites since they exhibit the best mechanical properties.