# Material for 3rd Year Engineering Materials (Polymers)

## Solutions

Following some students' enquiries, here are the solutions and marking scheme to the Summer 2004 exam paper [PDF, 412kb]. The marking scheme for question 5 is not marked on the PDF, but it is pretty straight forward.
1. Maxwell 
2. Kelvin 
3. Standard-Linear-Solid plus Discussion 
4. Numerical calculation 
To give a total of 20 marks for the question

### A note on Question 5

When answering this question, some people misinterpreted the expression for creep compliance in Question 5, and interpreted one or both of the minus signs as multiplications. The misinterpretations gave rise to a less-realistic viscoelastic model, and it is important to see why. If we interpret it correctly, then at t=0, the value of D begins as (omitting units) 2-exp(0)=2-1=1. As t increases, the exponential term decreases from one towards a limit of zero. This means that D gradually increases from 1.0 towards a limit of 2.0-0.0=2.0

This is plotted in the figure shown (click for a full-size view), where the red curve shows the correct interpretation. Also plotted are other ways that D was interpreted. By comparing these with the behaviour discussed in the first parts of Question 5, it is easy to see that these alternative models are not at all realistic.

## Handouts

### Lectures

1. Lecture 1 -- Introduction (no handout available)
2. Lecture 2 -- Polymerisation reactions
3. Lecture 3 -- RMM, MWD, Material properties, Crystallisation, Amorphous/Crystalline structures, Glass transition temperature
Acetates:  Or all in one file
4. Lecture 4 -- Introduction to Viscoelasticity Acetate: 5. Lecture 5 -- Viscoelasticity (no handout available online, short lecture)
Acetates:      Or all in one file
6. Lecture 6 -- Maxwell model, Kelvin model and Standard Linear Solid
Acetates:   Or all in one file
7. Lecture 7 -- Viscoelasticity, Boltzmann Superposition
Acetates: (note that the second worked problem is Q.6 from Summer 1999)    Or all in one file