EBB 220/3 Polymer Physics

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EBB 220/3Polymer Physics
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INTRODUCTION

• Characteristics of
• Thermoplastic (amorphous semicrystalline)
• thermoset
• rubber
• Linear crosslink system?
• Differences between
• vulcanizing and curing?

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INTRODUCTION
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Structure

• The structural properties of a polymer relate to
  the physical arrangement of monomers along the
  backbone of the chain.
• Structure has a strong influence on the other
  properties of a polymer.

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Structure

• The simplest form of polymer molecule is a
  straight chain or linear polymer, composed of a
  single main chain. The flexibility of an
  unbranched chain polymer is characterized by its
  persistence length.
• A branched polymer molecule is composed of a main
  chain with one or more substituent side chains or
  branches.
• A cross-link suggests a branch point from which
  four or more distinct chains emanate. A polymer
  molecule with a high degree of crosslinking is
  referred to as a polymer network

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Monomer arrangement in copolymers

• Monomers within a copolymer may be organized
  along the backbone in variety of ways.
• Alternating copolymers possess regularly
  alternating monomer residues
• Random copolymers have a random sequence of
  monomer residue types
• Block copolymers have two or more homopolymer
  subunits linked by covalent bonds. Block
  copolymers with two or three distinct blocks are
  called diblock copolymers and triblock
  copolymers, respectively.

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Tacticity in polymers

• This property describes the relative
  stereochemistry of chiral centers in neighboring
  structural units within a macromolecule. There
  are three types isotactic, atactic, and
  syndiotactic.
• Precise knowledge of tacticity of a polymer also
  helps understanding at what temperature a polymer
  melts, how soluble it is in a solvent and its
  mechanical properties.

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Melting point

• The term "melting point" when applied to polymers
  suggests not a solid-liquid phase transition but
  a transition from a crystalline or
  semi-crystalline phase to a solid amorphous
  phase.
• Though abbreviated as simply "Tm", the property
  in question is more properly called the
  "crystalline melting temperature".
• Among synthetic polymers, crystalline melting is
  only discussed with regards to thermoplastics, as
  thermosetting polymers will decompose at high
  temperatures rather than melt.

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Glass transition temperature (Tg)

• A parameter of particular interest in synthetic
  polymer manufacturing is the glass transition
  temperature (Tg), which describes the temperature
  at which amorphous polymers undergo a second
  order phase transition from a rubbery, viscous
  amorphous solid to a brittle, glassy amorphous
  solid.
• The glass transition temperature may be
  engineered by altering the degree of branching or
  cross-linking in the polymer or by the addition
  of plasticizer.

The Space Shuttle Challenger disaster was caused
by rubber O-rings that were below their glass
transition temperature on an unusually cold
Florida morning, and thus could not flex
adequately to form proper seals between sections
of the two solid-fuel rocket boosters.
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Polymer Structure/Property relationships

• Chain length
• Increasing chain length tends to decrease chain
  mobility, increase strength and toughness, and
  increase the glass transition temperature (Tg).
• This is a result of the increase in chain
  interactions such as Van der Waals attractions
  and entanglements that come with increased chain
  length.
• These interactions tend to fix the individual
  chains more strongly in position and resist
  deformations and matrix breakup, both at higher
  stresses and higher temperatures.

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Polymer Structure/Property relationships

• Branching
• Branching of polymer chains also affect the bulk
  properties of polymers.
• Long chain branches may increase polymer
  strength, toughness, and Tg due to an increase in
  the number of entanglements per chain.
• Random length and atactic short chains, on the
  other hand, may reduce polymer strength due to
  disruption of organization.
• Short side chains may likewise reduce
  crystallinity due to disruption of the crystal
  structure. Reduced crystallinity may also be
  associated with increased transparency due to
  light scattering by small crystalline regions. A
  good example of this effect is related to the
  range of physical attributes of polyethylene.
• High density polyethylene (HDPE) has a very low
  degree of branching, is quite stiff, and is used
  in applications such as milk jugs. Low density
  polyethylene (LDPE), on the other hand, has
  significant numbers of short branches, is quite
  flexible, and is used in applications such as
  plastic films.

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Polymer Structure/Property relationships

• Chemical cross-linking
• Cross linking tends to increase Tg and increase
  strength and toughness.
• Cross linking consists of the formation of
  chemical bonds between chains.
• Among other applications, this process is used to
  strengthen rubbers in a process known as
  vulcanization, which is based on cross linking by
  sulfur. Car tires, for example, are highly cross
  linked in order to reduce the leaking of air out
  of the tire and to toughen their durability.
  Eraser rubber, on the other hand, is not cross
  linked to allow flaking of the rubber and prevent
  damage to the paper.

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Polymer Structure/Property relationships

• Inclusion of plasticizers
• Inclusion of plasticizers tends to lower Tg and
  increase polymer flexibility.
• Plasticizers are generally small molecules that
  are chemically similar to the polymer and create
  gaps between polymer chains for greater mobility
  and reduced interchain interactions.
• A good example of the action of plasticizers is
  related to polyvinylchlorides or PVCs.
• A uPVC or unplasticized polyvinylchloride is used
  for things such as pipes. A pipe has no
  plasticizers in it because it needs to remain
  strong and heat resistant. Plasticized PVC is
  used for clothing for a flexible quality.
  Plasticizers are also put in some types of cling
  film to make the polymer more flexible.

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Polymer Structure/Property relationships

• Degree of crystallinity
• Increasing degree of crystallinity tends to make
  a polymer more rigid. It can also lead to greater
  brittleness.
• Polymers with degree of crystallinity approaching
  zero or one will tend to be transparent, while
  polymers with intermediate degrees of
  crystallinity will tend to be opaque due to light
  scattering by crystalline / glassy regions.

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Example of Thermoplastic Polymers
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Example of Thermoplastic Polymers
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EBB 220/3PRINCIPLE OFVISCO-ELASTICITY
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INTRODUCTION

• The differences between the polymeric materials
  behaviour and materials with totally elastic
  behaviours are
• Time dependent characteristics
• Temperature dependent characteristics
• Polymeric materials will show the properties that
  dependent on stress strain ? that will
  influence when the loading being applied.

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• The response of polymeric materials with stress
  or strain that been applied dependent on
• Loading rate
• Loading time
• The differences between materials behaviour are
• Elastic materials
• Viscous materials
• Visco-elasticity

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Behaviour of elastic material

• Elastic behaviour is instantaneous/immediate.
• The total deformation (or strain) occurs the
  instant the stress is applied or release.
• Upon release of the external stress the
  deformation is totally recovered (deformation is
  reversible)
• The specimens assumes its original deformation

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Elastic materials

• The spring (in the following figure) represents
  the elastic portion (usually short term) of a
  plastic material's response to load.
• When a load is applied to the spring, it
  instantly deforms by an amount proportional to
  the load. When the load is removed, the spring
  instantly recovers to its original dimensions.
• As with all elastic responses, this response is
  independent of time and the deformation is
  dependent on the spring constant.

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Behaviour of viscous material

• Deformation or strain is not instantaneously.
• In response to an applied stress- deformation is
  delayed or dependent with time.
• This deformation is not reversible or completely
  recovered after stress is released.

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Viscous Behavior

• The dash-pot in the following figure represents
  the viscous portion of a plastic's response.
• The dash-pot consists of a cylinder holding a
  piston immersed in a viscous fluid. The fit
  between the piston and cylinder is not tight.
• When a load is applied, the piston moves slowly
  in response. The higher the loading, the faster
  the piston moves. If the load is continued at the
  same level, the piston eventually bottoms out
  (representing failure of the part). The viscous
  response is generally time- and rate-dependent.

h viscosity de/dt strain rate
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Summary Hookes law (elastic) Newtons Law
(plastic)

• The behaviour of linear elastic were given by
  Hookes law

or

• The behaviour of linear viscous were given by
  Newtons Law

• E Elastic modulus
• s Stress
• e strain
• de/dt strain rate
• ds/dt stress rate
• h viscosity

This equation only applicable at low strain
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Visco elastic behaviour

• Behaviour of most polymer is in between behaviour
  of elastic and viscous materials.
• At low temperature high strain rate,
• Polymer demonstrate elastic behaviour,
• At high temperature low strain rate,
• Polymer demonstrate viscous behaviour
• At intermediate temperatures rate of strain
• Polymer demonstrate visco-elastic behaviour

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• Polymer is called visco- elastic because
• Showing both behaviour elastic viscous
  behaviour
• Instantaneously elastic strain followed by
  viscous time dependent strain

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Mechanical Model

• Methods that used to predict the behaviour of
  visco-elasticity.
• They consist of a combination of between elastic
  behaviour and viscous behaviour.
• Two basic elements that been used in this model
• Elastic spring with modulus which follows Hookes
  law
• Viscous dashpots with viscosity h which follows
  Newtons law.
• The models are used to explain the phenomena
  creep and stress relaxation of polymers involved
  with different combination of this two basic
  elements.

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STRESS RELAXATION
CREEP
Constant strain is applied ? the stress relaxes
as function of time
Constant stress is applied ? the strain relaxes
as function of time
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• The common mechanical model that use to explain
  the viscoelastic phenomena are
• Maxwell
• Spring and dashpot ? align in series
• Voigt
• Spring and dashpot ? align in parallel
• Standard linear solid
• One Maxwell model and one spring ? align in
  parallel.

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Maxwell Model

• Maxwell model consist of spring and dashpot in
  series and was developed to explain the
  mechanical behaviour on tar.
• On the application of stress, the strain in each
  elements are additive.
• The total strain is the sum of strain in spring
  dashpot. The stress each elements endures is the
  same.

Elastic spring
Viscous dashpot
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• Overall stress s, overall strain e in the system
  is given by
• es strain in spring and ed strain in dashpot
  dashpot
• Because the elements were in series ? the stress
  is the same for all elements,
• Equations for spring and dashpot can be written
  as

and
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• For Maxwell model, the strain rate is given as
• In creep case, the stress at s s0 therefore
  ds/dt 0. The equations can be written as
• Maxwell model can predict the Newtonian behaviour
  ? the strain is predict to increase with time

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• .

• The behavior of Maxwell model during creep
  loading (constant stress, s0 ?strain is predicted
  to increased linearly with time

This is not the viscoelastic behaviour of
polymeric materials ? de/dt decreased with time
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• May be this model is useful to predict the
  behaviour of polymeric materials during stress
  relaxation.
• In this case, the strain is constant ee0 applied
  to the system given de/dt 0
• then
• Integration at t0 s s0 given

?
so earlier stress
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• The term h/E is constant for Maxwell model and
  sometimes can be refered as time relaxation, t0
  written as
• The exponential decreased in stress can be
  predicted ? give a better representation of
  polymeric materials behaviour.

• Stress were predicted completely relaxed with
  time period ? it is not the normal case for
  polymer

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Voigt Model

• Can also known as the Kelvin model.
• It consists of a spring and dashpot in parallel.
• In application of strain, the stress of each
  element is additive, and the strain in each
  element is the same.

Elastic spring
Viscous dashpot
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• The parallel arrangement of spring and dashpot
  gives the strain e are the same for the system
  given by
• es strain in spring and ed strain in
  dashpot
• Because the elements in parallel ? stress s d in
  every elements are additive and the overall
  stress are
• Equation for spring and dahpot can be written as

and
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• For Voigt model, the strain rate are
• The accuracy of prediction the mechanical
  behaviour of Voigt model can be confirm.
• In creep case, stress is s so so ds/dt 0.
  The equation can be written as
• The simple differential equation given by

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• Constant ratio h/E can be replace with time
  relaxation, t0.
• Changes in strain with time for Voigt model that
  having creep are given by

Figure shows polymer behavior under creep
deformation? strain rate decreased with time
e ?so /.E and t
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• Voigt model fails to predict the stress
  relaxation behaviour of polymer
• When the strain is constant at e0 and de/dt 0
  the equation shows
• ? The linear response is shown in the figure

or
Behavior of Voigt model at different loading ?
Stress relaxation
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Standard linear solid

• As shown
• Maxwell model can accurately predict the
  phenomenon stress relaxation to a first
  approximation.
• Voigt Model can accurately predict the phenomenon
  creep to a first approximation.
• Standard linear solid model was developed to
  combined the Maxwell and Voigt model ? to
  describe both creep stress relaxation to a
  first approximation.

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Elastic spring
Viscous dashpot

• In consist ? one Maxwell elements in parallel
  with a spring.
• The presence on this second spring will stop the
  tendency of Maxwell element undergoing viscous
  flow during creep loading ? but will still allow
  the stress relaxation to occur

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General time dependent behaviour

• The true mechanical properties that appropriate
  with time for polymeric materials dependent on ?
  types of stress or cycle of strain that been
  used.
• Changes in stress an strain with time (t), can
  be shown in simple schema of polymer tensile.
• It can be categorized based on 4 different
  deformation behaviour as
• creep
• Stress relaxation
• Constant stress rate
• Constant strain rate

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INTRODUCTION

• It is difficult to predict the creep and stress
  relaxation for polymeric materials.
• It is easier to predict the behaviour of
  polymeric materials with the assumption ? it
  behaves as linear viscoelastic behaviour.
• Deformation of polymeric materials can be divided
  to two components
• Elastic component Hookes law
• Viscous component Newtons law
• Deformation of polymeric materials ? combination
  of Hookes law and Newtons law.

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STRESS RELAXATION
CREEP
Constant strain is applied ? the stress relaxes
as function of time
Constant stress is applied ? the strain relaxes
as function of time
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(a) Creep

• During Creep loading
• A constant load were applied to the specimen at
• t 0,
• The strain increased quickly at the beginning but
  become slowly with time after a long period of
  deformation.
• For elastic solid ? the strain rate is constant

Constant stress
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(b) Stress Relaxation

• During stress relaxation
• Strain is constant
• Stress decreased slowly with time.
• For elastic solid ? the stress is constant

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(c) Constant stress rate

• The increasing strain with time is not linear.
• It becoming more steep with
• Increasing time
• Increasing stress rate

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(d) Constant strain rate

• The increasing stress with time is not linear.
• The slope of the curve decreased with time
• The slope become more steep with the increasing
  strain rate

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Creep phenomenon

• It were the general behaviour of polymeric
  materials and very important in engineering.
• It can estimates the strength or the ability to
  sustained the stress that been applied
  permanently or constant.
• Creep ? polymer is stressed at a constant level
  for a given a time and the strain increases
  during that time periods.
• Creep can be used to estimate the life times of
  materials
• Frequently run at temperatures where thermal
  degradation is significant ? data can be used to
  estimate of the elevate-temperature life of
  materials.

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3 creep stages

• There were 3 stages of creep
• Primary Creep The slope of strain vs time
  decreased with time.
• Secondary creep Constant strain rate.
• Tertiary creep the strain rate increased
  rapidly until rupture (formation of crack,
  yielding and etc).

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Creep strain, e
Rupture
Time, t
Graph for strain curve at constant loading.
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• After beginning of strain, specimen will having a
  slowly shape changes with time until the
  yielding occur that caused a rupture.
• At primer area ?
• Area of early stage of deformation when creep
  rate is decreased with time (slope of the curve
  decreased with time).
• Polymeric materials having the increased in creep
  resistance or strain hardening.

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• Secondary area ?
• Area where the creep rate where almost constant
• Creep rate were explained by the equilibrium in
  between strain hardening and the ability to
  maintain/ retain its shape.
• Tertier area ?
• Where creep accelerate and rupture occurred.
• Creep happens due to changes in microstructure.
• Happen at higher stress for ductile materials.
• Decreased in cross-section that make the rupture
  or creep rate increased rapidly.

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• Creep test normally run in extension/ tension
  test. (but can be done in shear, compression or
  flexural test)
• Creep rate of polymeric materials were dependent
  on loading, time and temperatures.
• Polymeric components will deformed rapidly at
  higher temperatures.
• Creep results can been shown as
• Isometric curve stress versus time
• Modulus creep curve modulus versus time
• Isochronous curve stress versus strain

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Isometric curve

• Stress that being applied will dependent on time.
• At beginning ? stress is higher due to bonding
  forces between atoms is higher.
• After a few moments ? slippage between atoms
  occur and the polymer crystallization rate
  decreased then the strain were increased with
  time.

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Modulus curve

• The elasticity of certain materials exists due to
  the materials decomposition of chain to become
  more order.
• If the measurements is taken in the short
  periods? the decomposition of chain folding had
  not happened ? polymer are more like persistent
  materials.
• This graph is very useful in determination of
  materials rigidity and persistent ? based on the
  life span of the materials.

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Isochronous curve

• The slope of the graph is equivalent to the
  modulus Young, E which is the determination the
  resistance towards the neighbouring separation of
  the atoms.
• Modulus is the rigidity or the resistance of
  materials towards shapes changes.
• The high modulus values ? resulting from small
  strain changes due to the applied stress.

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The use of creep graph

• The knowledge of knowing to interpret of creep
  graphs are useful for materials engineer.
• Data from creep graph gives us the information
  about
• The rupture/deformation of the materials
• Yield and shape change of the materials.
• Can estimating the life time of the materials
• Can choose the materials based on materials
  applications.

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Isochronous curve

• Can comparing various types of polymeric
  materials during design because
• ? The stress for materials were plotted at time
  for the specific loading being applied.

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Example of the problem

• One of the engineer has to design rigid structure
  can sustained the continuous load for 1000 hours
  with the strain not more than 2 .
• Question
• What is the maximum stress can be allowed?
• Solution
• Need to make a comparison from graph strain
  versus time for different stress for 1000 hours.
  ? strain at different stress can be resolved.
• Graph stress versus strain at 1000 hours can be
  plotted ? the maximum stress allowed can be
  obtained.

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Modulus curve

• From graph ? creep modulus decreased with
  increasing time showing the visco-elastic
  behaviour.
• This graph were useful because modulus were
  needed in engineering deflection.

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Example of the application

• To chosen the life span of component that being
  designing at modulus curve ? the modulus value is
  called design modulus.
• The stress of the modulus is determine according
  to the alternative
• If stress being determine ? The values should be
  taken from the modulus curve with the stress
  value is nearly to the value that needed.
• If the stress needed not yet been determine ?
  Need to choose the modulus curve with the
  conservative stress value and need to be checked
  before starting the calculation.

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Isometric curve

• With observing materials behaviour during stress
  relaxation ? can estimate the long term materials
  behaviour.
• Materials long term service can be estimate when
  the certain stress being applied not more than
  the rupture of the materials.

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Example of application

• For one bottle lid under constant strain for very
  long period ? low stress relaxation is needed.
• That bottle lid will fail if the stress decreased
  instantly.
• Time is a the main factor that will influenced
  the mechanical properties of the bottle lid
  because
• At very short loading time ? higher stresses is
  needed for particular strain.
• At long term loading ? lower stresses is needed
  to get the particular strain.

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Example of the exams question

• What is definition of visco-elasticity?
• Please gives the differences between
  visco-elastic behavior and totally elastic
  behavior.
• Gives the advantages of creep properties in
  materials engineering?

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Effect of glass transition and temperature on
creep

• Below Tg?
• In the Tg region?
• Above Tg?

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Summary

• There were a lots of attempts to discover more
  complex model that can give a good approximation
  to predict viscoelastic behaviour of polymeric
  materials.
• When the elements used is increased ?
  mathematical can be more complex.
• It can be emphasis that mechanical models can
  only gives mathematical representations for
  mechanical behaviour only ? it not much help to
  predict the behaviour of viscoelasticity at
  molecular level.

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Example of the exams question

• What is the purpose of mechanical model in
  visco-elasticity theories?
• Gives a brief description how the chosen
  mechanical model can be used to estimate the
  creep or stress relaxation behavior for polymeric
  materials?

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Thank you