1. Composites: basics and terminology
John Summerscales
CAN-LHR 27 Sep 15
LGW-HKG 19 Sep 17

2. Reading for a degree Each lecture has: PowerPoint slides on extranet
these need JS “soundtrack” (i.e. lectures)
individual lecture webpages on extranet
also read these to reinforce your learning
… and to really understand the topic follow up the references and/or review papers

3. Support materials http://www.fose1.plymouth.ac.uk/sme/mats3472 3

4. Structure of module MATS347
one lecturer
John Summerscales (JS)
two themes
materials selection and characterisation
manufacturing processes
assessed by one coursework report + one 3h examination
Complemented by MATS348 (next term)t by module MATS348 final report

5. Support materials http://www.fose1.plymouth.ac.uk/sme/mats232
Lecture & practical schedule Review papers
Free e-books Subject index

6. Support materials for module
home page on Extranet
BSc MATS232:
BEng/MEng MATS347:
MATS347 lectures, notes and PowerPoint:
Schedule on MooDLE home page
case studies
home page also includes:
subject index
map of local composites companies
links to Library Reading Lists
and many other useful resources ;-)
see MooDLE student portal for assessments

7. LinkedIn professional networking site composites graduates from PU
connections for placement & employment
British Composites Society
other composites groups

8. Practical manufacture and test of a composite plate
attendance at Health and Safety lecture is an essential prerequisite for coursework
list of attendees circulated for signature
if your name is not on the list, you will not be allowed to do the practical
if you do not do the practical you will fail the coursework element and hence the module.

9. Civil and structural engineering
Bridges
Rehabilitation
Enhanced carrying capacity of offshore rigs
Repairs to LUL tunnels, plus bridges & pipework
Cladding
(~30 years) Mondial/Montedison House
Buildings
(not so) temporary structures

10. Outline of this lecture
anisotropy
fibre volume fraction (Vf)
basic rule-of-mixtures
glass transition temperature (Tg)
crystalline melting point (Tm)
stacking sequence notation

11. Anisotropy Degree of anisotropy Principal axes Properties Example
Isotropic
Orthogonal
Constant regardless of direction
Metals
Square symmetric
Two different principal axes
Unidirectional fibres or woven cloth
Orthotropic
Three different principal axes
Unidirectional weave with light weft
Anisotropic
Any angle
Constant relative to axes
Filament wound tube or many crystals
Aeolotropic
May change with position
Timber

12. Fibre volume fraction (Vf)
n = the number of layers
AF = the areal weight of the fabric
ρf = density of the fibre, and
t = the thickness of the laminate.

13. Areal weight of fabric (AF)
For a balanced fabric, the parameters are:
Nf = number of filaments per tow
NT = number of tows in unit width of fabric
rf = radius of the fibre cross-section
ρf = density of the fibre
crimp increases areal weight by ~1% at 10˚, 3% at 20˚ or 6.5% at 30˚ maximum crimp angle.

14. Basic rule-of-mixtures 1
Elastic properties (e.g. density or modulus) of composite calculated by rule-of-mixtures
EC = κ . ηd . ηL . ηO . Vf . Ef + Vm . Em
if the first term of the equation is large, the second term can be neglected

15. Basic rule-of-mixtures 2a
The parameters are:
EX = modulus of component x
Vx = volume fraction of component x
subscripts (x) are c, f and m for composite, fibre and matrix respectively

16. Basic rule-of-mixtures 2b
κ = fibre area correction factor*
ηd = fibre “diameter” distribution factor*
ηL = fibre length distribution factor
ηO = fibre orientation distribution factor
* these two factors are set to unity for man-made fibres (but see lecture MATS347A9 on natural fibres)

17. Basic rule-of-mixtures 3
ηL = fibre length distribution factor
1 for continuous fibres
fractional for long fibres
0 if fibre below a “critical length”

18. Basic rule-of-mixtures 4
ηO = fibre orientation distribution factor
a weighted function of fibre alignment, essentially cos4θ:
1 for unidirectional
1/2 for biaxial aligned with the stress
3/8 for random in-plane
1/4 for biaxial fabric on the bias angle

19. Basic rule-of-mixtures 5
Vf = fibre volume fraction
for random
for fabrics
for unidirectional
consolidation pressure:
no pressure gives the lower value
Vf increases with pressure

20. Basic rule-of-mixtures 6
figures below are lowest values i.e. for standard fibres
Ef = elastic modulus of fibre
glass = ~70 GPa (equivalent to aluminium)
aramid = ~140 GPa
carbon = ~210 GPa (equivalent to steel)

21. Transition temperatures in ascending order
Tg = glass transition temperature
Tc = peak crystallisation temperature
Tm = crystalline melting point typically Tm = Tg + 200±50°C nb: no melting point in amorphous materials
Tv = topology freezing transition temperature in vitrimers (viscosity = 1012 Pa s)
Tp = processing temperature typically Tp = Tm + ~30°C for “semi”-crystalline polymers
Tg follows cure temperature in thermosets
Td = degradation/decomposition temperature may limit Tp (especially for PVC)

22. Glass transition temperature (Tg)
Temperature at which segmental motion of the chain is frozen out
below Tg polymer is elastic/brittle
above Tg polymer is viscoelastic/tough
more rigorous than heat distortion temperature
Tg for thermoplastics = Tm - ~200°C
Tg for thermosets follows cure temp.

23. Crystalline melting point (Tm)
all polymers have a Tg
only some polymers have a Tm
they must be able to form crystals
normally a regular repeating structure
rarely 100% crystalline
polymers may degrade before melting
usually the case for thermoset

24. Composites
How fibres can be arranged in order of increasing stiffness and strength:
3-D random
e.g. injection moulding grades.
planar random
e.g. moulding compounds, chop strand mat, random swirl.
quasi-isotropic (QI)
e.g. continuous fibres oriented at 0°/-45°/90°/+45° or 0°/60°/120°.
bidirectional
e.g. woven fabrics or cross-plied UD laminates at 0 °/90 °.
unidirectional (UD)
e.g. pultrusions and aligned monolithic fibre composites.

25. Four types of fibre-reinforced composite
monolithic (material)
all layers aligned parallel
laminate (structure - see next slides)
orientation changes between layers
hybrid (structure – MATS347 lecture A6)
more than one type of fibre (e.g. carbon/glass)
sandwich (structure – MATS347 A10)
composite skins and lightweight core

26. Laminate stacking sequence notation
typical laminate stacking sequence is:
[0º/+45º/-45º/90º]ns
where the subscripts are:
n is the number of repeats of the sequence
Q indicates antisymmetric laminate
s means the laminate is symmetric
T is the total number of plies
overbar denotes that the laminate is symmetric about the mid-plane of the ply
Thus for n = 2 above, the sequence will be:
0º/+45º/-45º/90º/0º/+45º/-45º/90º*90º/-45º/+45º/0º/90º/-45º/+45º/0º
with * denoting the line of symmetry.

27. I-beam vs stacking sequence
Beam stiffness reduces from left to right:
Laminated composite plate: 0° layer or 90° layer
Equivalent beam: high EI vs low EI segments

28. Formative assignment (research–informed teaching/RIT)
identify a laminate analysis package
Autodesk Helius Composite software was the choice of last years’ students
use it to determine
the flexural stiffness of a hybrid beam
UD aramid interleaved with woven glass
the flexural stiffness of a sandwich panel
bias-angle carbon fibre skins on a polymer foam core
use rule of mixtures to calculate the tensile stiffness of the above beams
consider why the numbers differ
you will need this skill for the summative coursework assignment

29. Key points of this lecture
resources on Student Portal and Extranet
anisotropy
fibre volume fraction (Vf)
basic rule-of-mixtures
glass transition temperature (Tg)
crystalline melting point (Tm)
stacking sequence notation