Composites Design and Manufacture (Plymouth University teaching support materials)
Some basic equations and definitions
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Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Anisotropy

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

Further reading:

B Hutchinson, Critical Assessment 16: anisotropy in metals, Materials Science and Technology, September 2015, 31(12), 1393-1401.

Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Fibre volume fraction (Vf)

 Thickness measurement methodResin burn-off method
 Equation:thickness-mathod equationburn-off_equation

where:

The above formulae (albeit with different symbols) appear in CRAG method 1000 Methods of assessment of fibre volume fraction of fibre reinforced plastics [1].

Reference 1: PT Curtis, CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aerospace Establishment Technical Report 88 012, February 1988.  MooDLE

Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Areal Weight of a Fabric (AF)

areal weight equation
where, for a balanced fabric, the parameters are:

Crimp will increase the areal weight by ~1% at 10˚, 3% at 20˚ or 6.5% at 30˚ maximum crimp angle.

Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Rule of Mixtures [1]

ROM equation

where:

 ParameterTypical values/comments
EcYoung's modulus of the composite 
EfYoung's modulus of the fibre 70 GPa (glass), 140 GPa (aramid) or 210 GPa (carbon) for standard grade fibres
EmYoung's modulus of the matrix1-3 GPa (polymers) or 70 GPa (aluminium)
Vffibre volume fraction indicative fibre volume fractions are given in the Table below,
and also see the discussion of compressibility of reinforcements
Vmmatrix volume fraction(1-Vf-Vv)
Vvvoid volume fraction see the discussion at void formation and transport and
division of void content into sub-components, especially for plant fibre composites.
κfibre area correction factor set at unity (1) for circular cross-section fibres
ηdfibre diameter distribution factor for natural fibres set at unity (1) for most man-made fibres
ηlfibre length distribution factor0 (if significantly less than the critical length) or 1 (continuous fibres)
ηofibre orientation distribution factorFibres
  • 1/5 (random 3D all-planes),
  • 1/4 (biaxial on the bias angle),
  • 3/8 (random 2D in-plane),
  • 1/2 (biaxial parallel to the fibres), or
  • 1 (unidirectional parallel to the fibres)

Platelets [2]

  • 8/15 (3-D random platelets)
  • 1 (prefectly oriented material in-plane)

and typical Vf values would be:

Reinforcement form Vf without consolidation Vf with high pressure consolidation
Random in-plane 10% 30%
Woven 30% 60%
Unidirectional 50% 80%

The materials data above is representative and should not be used for 'design' purposes.

BS EN 14272:2011 [3] defines a modification factor, ka, which is a knock-down factor for modulus of elasticity and strength dependent on the surface appearance classes of plywood veneer [4,5].  For appearance classes E, I and II, ka is unity, and these basic mechanical property values are used as the basis of calculations.  For class III, ka is 0.85.  For class IV, and where inner layers are not appearance graded, ka is 0.75.

References

  1. AS Virk, W Hall and J Summerscales, Modulus and strength prediction for natural fibre composites, Materials Science and Technology, July 2012, 28(7), 864-871.
  2. Z Li, RJ Young, NR Wilson, IA Kinloch, C Vallés, Z Li, Effect of the orientation of graphene-based nanoplatelets upon the Young's modulus of nanocomposites, Composites Science and Technology, 8 February 2016, 123, 125–133.
  3. Plywood - calculation method for some mechanical properties, BS EN 14272:2011, British Standards Institution, 2012.  ISBN 978-0-580-69385-4.
  4. Plywood - classification by surface appearance - hardwood, BS EN 635-2:1995, British Standards Institution, 1995.  ISBN 0-580-24769-4.
  5. Plywood - classification by surface appearance - softwood, BS EN 635-3, 1995, British Standards Institution, 1995.  ISBN 0-580-24772-4.
Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Transition temperatures (including glass transition temperature (Tg) ..and.. crystalline melting point (Tm)

In ascending order, the major transition temperatures are normally:

although these key temperatures do not necessarily occur in all cases (e.g. Tc and Tm are only applicable to partially crystalline polymers).

As the temperature rises through the glass transition temperature, short segments of the polymer backbone which had insufficient energy for movement other than atomic vibration, start to move as a group of atoms.  On cooling through this temperature, it is normal to refer to segmental motion being frozen out.  The mechanical properties of the polymer are then:

The crystalline melting point is not applicable to amorphous polymers and is usually only important in thermoplastics.  The crystalline melting point value is normally ~200 (±50) ºC above the glass transition temperature. Tm may be a narrow range of temperatures rather than a single point.

melting point equation
Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Recycling numbers

  1. polyethylene terephthalate (PET or PETE)
  2. high density polyethylene (HDPE)
  3. polyvinyl chloride (PVC, V or vinyl)
  4. low density polyethylene (LDPE)
  5. polypropylene (PP)
  6. polystyrene (PS)
  7. other
Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Types of composite

There are a number of ways in which fibres can be arranged.  In order of increasing stiffness and strength, these are:

At a higher level these layers may be organised in four distinct ways
The terminology is not always consistent, e.g. laminate may be used for monolithic composite materials.

 monolithic  material  all layers aligned parallel
 laminate  structure  orientation changes between layers
 hybrid  structure  more than one type of fibre (e.g. carbon/glass)
 sandwich  structure  composite skins and lightweight core

Laminate stacking sequence

The normal way to concisely record a laminate stacking sequence is, for example:

where the subscripts are:

Thus for n = 2 in the above example, when * denotes the line of symmetry, the sequence will be:

1:  Z Gurdal, RT Hafka and P Hajela, Design and Optimization of Laminated Composite Materials, John Wiley & Sons, 1999.  ISBN 0-471-25276-x.  PU CSH Library

Go direct to .... Anisotropy Areal Weight of Fabric Transition temperatures Glossary of textile terms Fibre volume fraction Recycling numbers Rule of Mixtures Stacking sequence Ashby material indices

Ashby material indices to minimise mass

FunctionFormStiffnessStrength
Tensiontie barρ/Eρ/σy
Bendingbeamρ/E1/2ρ/σy2/3
Bendingpanelρ/E1/3ρ/σy1/2

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Updated by John Summerscales on 11-Sep-2019 14:18. Terms and conditions. Errors and omissions. Corrections.