Polymer Behaviour 2

Question 1

What is the Kelvin-Voigt Model

Answer 1

The KV model gives an acceptable first approximation to creep and recovery behaviour, but does not account for stress relaxation. It is a spring and a dashpot which is in parallel.

Question 2

What is the Maxwell Model

Answer 2

The Maxwell model can account for stress relaxation but is poor in its description of creep and recovery. It is a spring and a dashpot which is in series.

Question 3

What is the Standard Linear Solid Model (SLS)

Answer 3

Another model consisting of elements in series and parallel is known as the standard linear solid model. It is a combination of the KV and Maxwell models. Similar form to KV model for recovery, similar form to Maxwell for stress relaxation. It is a spring and a dashpot which has a (something in series) spring and dashpot in series, with another spring in parallel (something in parallel).

Unlike Maxwell or KV model, SLS model shows all the significant characteristics (creep, recovery, relaxation) of viscoelastic polymers.

Question 4

What is Boltzmann Superposition Principle

Answer 4

BSP is a useful method to compute time-dependent strain in a linear viscoelastic polymer subjected to varying stress. We can calculate the strain caused by the corresponding change of the stress and sum these strains at any arbitrary time.

Question 5

What is the concept of linear viscoelasticity

Answer 5

In both models, the creep compliance is a function of time for a given material and these models are, therefore, only applicable to Linear Viscoelastic Polymers.

Linear viscoelasticity is normally applied to polymers subjected to small strain. The mechanical behaviour of a viscous liquid is time dependant. At low rates of strain it obeys Newton’s law:

Question 6

What would the graph look like for KV model?
Creep (Under constant stress)
Relaxation (Fixed Strain)
Recovery (Stress Free)

Answer 6

Strain (Y-axis) Vs. Time (X-axis) : Looks like a slide

Constantly increasing (exponentially) from zero to a point
Holds constant
Constantly decreasing (exponentially) to zero.

Stress (Y-axis) Vs. Time (X-axis) : Looks like a cliff

Holds constant at some stress value
Holds constant at some stress value during relaxation too
Drops to zero

Question 7

What would the graph look like for Maxwell model?
Creep (Under constant stress)
Relaxation (Fixed Strain)
Recovery (Stress Free)

Answer 7

Strain (Y-axis) Vs. Time (X-axis) : Looks like a hill and then steps downwards. ALWAYS STRAIGHT LINES

An instantaneous strain is present, increasing (linear) from instantaneous strain to a point
Holds constant.
Drops to some value of strain and then remains constant

Stress (Y-axis) Vs. Time (X-axis) : Looks like a downward hill

Holds constant at some stress value.
Constantly decreases (linearly) to some stress value.
Drops to zero and has a permanently set stress.

Question 8

What would the graph look like for SLS model?
Creep (Under constant stress)
Relaxation (Fixed Strain)
Recovery (Stress Free)

Answer 8

Strain (Y-axis) Vs. Time (X-axis) : Looks like a slide

Constantly increasing (exponentially) from zero to a point
Holds constant
Constantly decreasing (exponentially) to zero.

Stress (Y-axis) Vs. Time (X-axis) : Looks like a smaller slide

Holds constant at some stress value
Constantly decreases (exponentially) to some stress value.
Drops to zero

Question 9

How would you calculate the strain at any time using creep compliance formula (Boltzmann Superposition Principle)?

Answer 9

strain[t] = D(t-ui)*Change in stress at that time

D(t-ui) = 1/E + (t-t[i])/n

Where t[i] = initial time
n = dashpot symbol