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EBB 220/3Polymer Physics
Characteristics of;Thermoplastic (amorphous & semicrystalline) thermoset rubber
Linear & crosslink system? Differences between
vulcanizing and curing?
INTRODUCTIONINTRODUCTION
INTRODUCTIONINTRODUCTION
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.
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
Structure
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.
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.
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.
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.
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.
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.
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.
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.
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.
Polymer Structure/Property relationships
Example of Thermoplastic Polymers
Example of Thermoplastic Polymers
EBB 220/3PRINCIPLE OF
VISCO-ELASTICITY
INTRODUCTIONINTRODUCTION
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.
The response of polymeric materials with stress or strain that been applied dependent on :
1. Loading rate
2. Loading time
The differences between materials behaviour are :
1. Elastic materials
2. Viscous materials
3. Visco-elasticity
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
Behaviour of elastic materialBehaviour of elastic material
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.
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.
Behaviour of viscous materialBehaviour of viscous material
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.
dt
de
= viscosity
de/dt = strain rate
• The behaviour of linear elastic were given by Hooke’s law:
Ee
E= Elastic modulus
= Stress
e=strain
de/dt = strain rate
d/dt = stress rate
= viscosity
ordt
deE
dt
d
• The behaviour of linear viscous were given by Newton’s Law:
dt
de
** This equation only applicable at low strain
Summary: Hooke’s law (elastic) & Newton’s Law (plastic)
Summary: Hooke’s law (elastic) & Newton’s Law (plastic)
• Behaviour of most polymer is in between behaviour of elastic and viscous materials.
1. At low temperature & high strain rate, Polymer demonstrate elastic behaviour,
2. At high temperature & low strain rate, Polymer demonstrate viscous behaviour
3. At intermediate temperatures & rate of strain Polymer demonstrate visco-elastic
behaviour
Visco elastic behaviourVisco elastic behaviour
• Polymer is called visco- elastic because:
• Showing both behaviour elastic & viscous behaviour
• Instantaneously elastic strain followed by viscous time dependent strain
• 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:
1. Elastic spring with modulus which follows Hooke’s law
2. Viscous dashpots with viscosity which follows Newton’s law.
• The models are used to explain the phenomena creep and stress relaxation of polymers involved with different combination of this two basic elements.
Mechanical ModelMechanical Model
CREEP STRESS RELAXATION
Constant strain is applied the stress relaxes as function of time
Constant stress is applied the strain relaxes as function of time
• The common mechanical model that use to explain the viscoelastic phenomena are:
1. Maxwell• Spring and dashpot align in series
2. Voigt• Spring and dashpot align in parallel
3. Standard linear solid• One Maxwell model and one spring align
in parallel.
• 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 springViscous dashpot
Maxwell ModelMaxwell Model
• Overall stress , 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:
ds eee
ds
anddt
deE
dt
d s
dt
ded
• For Maxwell model, the strain rate is given as
• In creep case, the stress at therefore d/dt = 0. The equations can be written as:
• Maxwell model can predict the Newtonian behaviour the strain is predict to increase with time
dt
d
Edt
de 1
0
dt
de
.
• The behavior of Maxwell model during creep loading (constant stress, strain is predicted to increased linearly with time
This is not the viscoelastic behaviour of polymeric materials de/dt decreased with time
• May be this model is useful to predict the behaviour of polymeric materials during stress relaxation.
• In this case, the strain is constant e=e0 applied to the system given de/dt =0
• then
• Integration at t=0 given
dt
d
Edt
de 1
dt
d
E
10
dtEd
Et
eksp0= earlier stress
• The term E is constant for Maxwell model and sometimes can be refered as time relaxation, 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
00
teksp
• 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.
Voigt ModelVoigt Model
Viscous dashpot
Elastic spring
• 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 d in every elements are additive and the overall stress are
• Equation for spring and dahpot can be written as:
and
ds eee
ds
Ees dt
ded
• 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 so d/dt = 0. The equation can be written as:
• The simple differential equation given by:
Ee
dt
de
0
Ee
dt
de
Et
ekspE
e 10
• Constant ratio E can be replace with time relaxation,
• Changes in strain with time for Voigt model that having creep are given by:
0
0 1
teksp
Ee
Figure shows polymer behavior under creep deformation strain rate decreased with time
e and t=
• 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:
0Ee
or
0Ee
Behavior of Voigt model at different loading Stress relaxation
• 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.
Standard linear solidStandard linear solid
• 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
Viscous dashpot
Elastic spring
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:
a) creepb) Stress relaxationc) Constant stress rated) Constant strain rate
General time dependent behaviour
General time dependent behaviour
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 – Hooke’s law
Viscous component – Newton’s law
Deformation of polymeric materials combination of Hooke’s law and Newton’s law.
INTRODUCTIONINTRODUCTION
CREEP STRESS RELAXATION
Constant strain is applied the stress relaxes as function of time
Constant stress is applied the strain relaxes as function of time
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
(a) Creep(a) Creep
During stress relaxation: Strain is constant Stress decreased slowly with time. For elastic solid the stress is constant
(b) Stress Relaxation(b) Stress Relaxation
The increasing strain with time is not linear. It becoming more steep with:
1. Increasing time
2. Increasing stress rate
(c) Constant stress rate(c) Constant stress 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
(d) Constant strain rate(d) Constant strain rate
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.
Creep phenomenonCreep phenomenon
There were 3 stages of creep:
1. Primary Creep– The slope of strain vs time decreased with time.
2. Secondary creep – Constant strain rate.
3. Tertiary creep – the strain rate increased rapidly until rupture (formation of crack, yielding and etc).
3 creep stages3 creep stages
Creep strain,
Rupture
Time, t
Graph for strain curve at constant loading.
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.
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.
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:1. Isometric curve – stress versus time
2. Modulus creep curve – modulus versus time
3. Isochronous curve – stress versus strain
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.
Isometric curveIsometric 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.
Modulus curveModulus 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.
Isochronous curveIsochronous curve
The knowledge of knowing to interpret of creep graphs are useful for materials engineer.
Data from creep graph gives us the information about:
1. The rupture/deformation of the materials
2. Yield and shape change of the materials.
3. Can estimating the life time of the materials
Can choose the materials based on materials applications.
The use of creep graphThe use of creep graph
Can comparing various types of polymeric materials during design because:
The stress for materials were plotted at time for the specific loading being applied.
Isochronous curveIsochronous curve
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.
Example of the problemExample of the problem
From graph creep modulus decreased with increasing time showing the visco-elastic behaviour.
This graph were useful because modulus were needed in engineering deflection.
Modulus curveModulus curve
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.
Example of the applicationExample of the application
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.
Isometric curveIsometric curve
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.
Example of applicationExample of application
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?
Example of the exams questionExample of the exams question
Effect of glass transition and temperature on creep Below Tg? In the Tg region? Above Tg?
• 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.
SummarySummary
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?
Example of the exams questionExample of the exams question
Thank you
