In this video I'm going to discuss what is viscoelasticity and why polymeric material shows viscoelastic behavior
I will also discuss the simple viscoelastic models and their simplified equations
Which can be very helpful in solving exam questions
So let's first discuss. What is viscoelasticity?
Visco-elasticity is a type of deformation which consists of both elastic and viscous deformation.
Elastic deformation is a recoverable deformation which means the sample or the material can return to its original shape
Once the applied force is removed
Whereas viscous deformation is a non-recoverable deformation
which means applied force leads to a permanent deformation of the sample.
The example of elastic deformation is a stretching of rubber bands and
example of viscous deformation is flow of fluids like water or honey.
It seems odd that polymers are solid at room temperature, but they may deform like a liquid
Before going into why it will deform like liquids. Let's first discuss how polymer deform under stress?
Here we can see that at a small deformation
stress increases linearly with strain. This region is called elastic region and
deformation is called elastic deformation
Because sample can return to its original shape if the force is removed.
But once the deformation reaches to yield point sample starts to deform permanently.
After yield point the deformation is called viscous deformation and here we can see that
deformation is occurring without increasing in stress.
Now let's discuss why polymeric material shows both elastic and viscous deformation
Here I'm not going to get into the in-depth analysis of the molecular mechanism or use mathematical model to explain the
deformation behavior
But I will discuss some key parameters and I will provide a general understanding of molecule motion
responsible for the viscoelastic behavior
Those who are interested to learn more about the molecular mechanism, a reference is provided in the slide
In my previous video
introduction to polymer
I have provided some explanation and example of how polymeric material differ from other chemical and metallic materials
the major difference is
polymeric materials consists of long-chain molecules as a result in addition to chemical forces
like ionic Van Der Waals and non-polar interactions
polymer chain also interact through entanglement points. In a semi-crystalline polymer
crystals also act as an entanglement points
Another point, which is different in polymeric material is a polymer chain can have motion at different timescale
from atomic vibration to full chain diffusion
This mobility occurs at different time scale.
Diffusion of large segments of chain occurs at much slower speed than diffusion of small segments
because of this
polymeric materials show time dependent deformation.
So in absence of external force that typical forces which governs the morphology of the polymer chain is listed here
due to these forces chain remains in an entangled state and
Continuously collides with each other to form our lowest possible energy state.
This state is a highly disordered form.
When an external force is applied it leads to alignment of some polymer chain in the force direction
whereas other chains tries to pull them back to original position through entanglement points.
At small deformation bond stretching and chain straightening can take place.
Both this deformation is like stretching a spring, so they will return to its original shape once force is removed.
On the other hand if the polymer chain is deformed further or the load is applied for long time
Then chain breakage and chain slippage can occur.
Both phenomena would result in a permanent change in
the polymer morphology. As a result when the force is removed,
the chain will not be able to return to its original shape and it will attain a new equilibrium State.
In summary
we can say that bond stretching and chain straightening leads to elastic deformation
and change slippage and chain breakage leads to plastic deformation. As polymer
undergoes both these type of deformation under stress
the polymeric material shows viscoelastic behavior.
It is very clear that the molecule mechanism of elastic and plastic deformation is not only complex
But also extremely specific to a polymer.
Since it depends on
chemical nature of the chain, molecular weight, percent crystallinity, deformation type and many other factors
so to avoid the complication scientists have developed different models to explain and understand the viscoelastic behavior of polymeric materials.
Three of the most common models are Maxwell model, Kelvin Voigt model and
standard linear viscoelastic model.
The Maxwell model consists of a spring and a dashpot connected in series.
The spring corresponds to elastic deformation and dashpot to viscous deformation.
The creep and recovery behavior of Maxwell model can be represented by a very simple equation as shown here.
We can see that when force is applied there is an instant energy deformation due to a stretching of spring
Further deformation takes place due to deformation of dashboard.
Once the force is removed
Spring returns to its original shape leading to recovery of the deformation.
One limitation of this model is that it does not predict creep or
constant stress condition accurately because
this model suggests that strain will increase linearly with time. However
polymers for the most part shows the strain rate decrease with time
Anyways, Maxwell model is very good in understanding the deformation and recovery behavior of soft solids
like thermoplastic polymer in the vicinity of their melting point.
Second model is Kelvin and Voigt model in this model spring and dashpot is connected in parallel.
This model can also be represented by very simple equation as shown in the slide
We can see that once the force is applied. There is no instantaneous deformation
Since dashpot cannot deform instantaneously
At constant stress the model is quite realistic as it predicts strain to decrease with time.
Thus the model is extremely good for modeling creep in materials.
But with regards to relaxation the model is much less accurate
however
this model can be used to predict the deformation behavior
at low loading for organic polymers rubber and wood.
In more complex but comprehensive model is a SLV model
SLV model is the combination of maxwell and Kelvin Voigt model and represented by
the equation shown in the slide.
It is the simplest model that accurately describe both the creep and stress relaxation behavior of a viscoelastic material.
Using these models we can easily derive the spring constant and viscosity of the dashpot.
corresponding to a particular polymer. Which can help us to predict the material behavior under different condition
This is very important aspect when designing a load-bearing structure.
Here we can see the simplified version of the viscoelastic equation representing different model.
The simplified form shows the simple relationship between stress and strain
so if
the constants are given,
then it will be very easy to calculate the deformation at different time.
In exam it is important that the units of this parameter should be in one form only. If you have any question
please comment below.
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