MEK4540-2012-1.1

MEK4540 Komposittmaterialer og –konstruksjoner Composite materials and structures

Innledning – materialer – ensrettede kompositter Introduction – materials – unidirectional composites

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MEK4540 Teaching schedule • Normally lectures will be on Wednesdays from 12.15-14.00 and

practice sessions will be on Thursdays from 12.15-14.00.

• However, there will be several deviations from this:

– Lecture no. 2 will be held on Thursday 23.08.2012 in place of the practice session.

– There will be no lecture on Wednesday 29.08.2012.

– There will be a practice session on Thursday 30.08.2012.

– There will also be deviations in September and early October.

• The full schedule will be published within 1-2 days.

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Preliminaries • Language:

– PowerPoint presentations in English – Text books in English – Norwegian + English technical terms will be provided where possible – Spoken language Norwegian or English – Assignments (“obligs”) handed out in English – Students may hand in solutions in English or Norwegian – Written or oral examination in Norwegian or in English if requested

• Text books: – Main text:

B.D. Agarwal, L.J. Broutman and K. Chanrashekhara: Analysis and Performance of Fiber Composites, 3rd ed.

– Composite plates – additional material: D. Zenkert and M. Battley: Foundations of Fibre Composites – Ch. 5 and parts of Ch. 8 to be handed out

– Sandwich beams and plates: D. Zenkert: Introduction to Sandwich Construction (student edition – KTH)

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Course content – Kursets innhold • Introduction and definitions • Component materials • Unidirectional composites • Orthotropic lamina (plies)

and laminates • Laminated plates (bending

and buckling) • Composites in ANSYS • Sandwich materials • Sandwich beams and plates • Joints • Short fibre composites • Production methods • Mechanical testing • Design criteria and rules

• Innledning og definisjoner • Materialkomponenter • Ensrettede kompositter • Ortotrope lag og laminater • Laminerte plater (bøyning og

knekning) • Kompositter i ANSYS • Sandwichmaterialer • Sandwichbjelker og -plater • Sammenføyninger • Kortfiberkompositter • Produksjonsmetoder • Mekanisk prøving • Dimensjonering og regelverk

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Definitions • A composite material is a material that consists of one or more

discontinuous components (particles/fibres/reinforcement) that are placed in a continuous medium (matrix)

• In a fibre composite the matrix binds together the fibres, transfers loads between the fibres and protects them from the environment and external damage.

• The fibres carry the loads.

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Main classes

• Particulate composites – Various geometrical shapes (cubes, spheres, flakes, etc.) – Various materials (rubber, metal, plastics, etc.) – Have generally low strength. – Will not be treated further in this course.

• Fibre composites – Discontinuous or – Continuous

• See next slide for further divisions

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Classification of composite materials From Agarwal, Broutman & Chanrashekhara

and multi-layered composites having same properties in each layer

Layers with different materials

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Microscopy

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Composites – properties

UD = unidirectional = ensrettet

QI = quasi-isotropic

= kvasi-isotrop

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Applications

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Offshore/subsea Tension leg, tether

Riser

Subsea protection cover

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Offshore/subsea

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Ships/boats

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Naval ships

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Sports and leisure equipment

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Cars

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Trains (Flytoget)

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Aircraft

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Composites in Airbus designs

http://www.mscsoftware.com/events/vpd2007/emea/presentations/Session-2A-AIRBUS-Bold.pdf Source:

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Composites in Airbus designs

http://www.mscsoftware.com/events/vpd2007/emea/presentations/Session-2A-AIRBUS-Bold.pdf Source:

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Materials in Boeing 787 Dreamliner

http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_06/article_04_2.html Source:

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Aircraft development over the years

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Wind energy

The blades can be as long as 62 m

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Buildings and bridges

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British naval vessels in GRP

HMS Wilton

HMS Sandown

GRP is used here for its non-magnetic properties

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Sandown class mine-hunter

Midship section

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Sandwich catamarans (SES)

Midship section

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Visby Class – Swedish Navy

• 72 m long • CFRP sandwich with PVC core

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Materials – glass fibres

• Types: E-glass (+ S-glass, C-glass and D-glass) • Production method

– Spun from molten glass

• Properties – Low cost – Moderately high strength – Low stiffness – Low wear resistance – Sensitive to moisture – Sizing (coating / surface preparation): 2 types/purposes:

• To protect the fibres and keep them together during further processing (weaving etc.). Removed before use.

• To improve adhesion (also called coupling agents) – organofunctional silanes

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Materials – carbon fibres • Carbon and graphite fibres

– “Graphite fibres”: ≥ 99% Carbon – “Carbon fibres”: 80–95% Carbon

• Production – Organic fibres: PAN, rayon and pitch – Stretched and stabilised at 200°C – Pyrolysis at 1500°C (inert atmosphere) – Grafitisation at 3000°C (inert atmosphere)

• strong covalent bonds in longitudinal direction of fibre.

• Important to note – Carbon fibres can be of several types, with widely differing

properties. – Normally supplied with sizing for use with epoxy resins – use

with polyester and vinylester requires special sizing.

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Materials – other fibre types

• Aramid (Kevlar, Twaron) – Aromatic polyamide – Spun from solution in acid

• HPPE – High performance polyethylene – UHMW-PE – ultra-high-molecular-weight polyethelene – Spun from solution and then stretched – Dyneema and Spectra – Properties roughly similar to aramid

• Boron, SiC

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Fibre properties

Tensile modulus [GPa]

Tensile strength [MPa]

Tensile strain at failure [%]

Density [g/cc]

E-glass 72 2000 -2500 3 2.5

High-stiffness carbon

500-800 2100 0.9-1.8 2

High-strength carbon

250-350 3100-4500 0.3-0.4 1.8

Kevlar 49 124 3600 1.4

UHMWPE 118 2500 0.97

NB: Carbon fibres are available with a wide range of properties!

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Reinforcement architecture • UD fabric or tape • Multiaxial “non-crimp” knitted fabric

– straight fibres i layers with defined directions, stitched together

• Woven fabric – fibres in 0/90 directions, not straight

• Chopped strand mat (CSM) – short fibres randomly oriented

• Continuous strand mat – long fibres randomly oriented

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Matrix materials – polymers

• Poly = many • Mer = part

• E.g. polyethylene [- CH2 – CH2 -]n

• Linear

• Branched

• Cross-linked

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Matrix materials

• Thermoplastics – Polyethylene (PE), polypropylene (PP) (=polyolefin), PMMA, PVC,

PS, – ABS, PC, POM, PET, TPU – Linear or branched molecule chains (are not chemically bound to

each other) – Can be melted down and re-used

• Thermosets – Polyester (unsaturated), Epoxy, Vinylester, Polyimide, Phenolic – Cross linked – chains are chemically bound to each other – Cannot be melted down and re-used – Supplied as prepolymer (resin) which hardens when initiator or

hardener is added.

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Polymer mechanical properties – temperature dependence

Thermoplastic, amorphous • Linear or branched chains • Transparent • PS, PC, PMMA • Can only be used at T<Tg

Thermosets • Crosslinked chains • Used at T<Tg

• Tg = glass transition temperature • Tm = melting temperature

Semi-crystalline • Not transparent • Normally linear chains • Can only be used at T<Tm • Brittle at T<Tg

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Unsaturated polyester • Prepolymer: Linear chain dissolved in styrene

– Styrene participates in curing process and reduces viscosity – Addition of inhibitors and accelerators

• Production of polyester resin – Saturated dibasic acid

• Phthalic acid anhydride – most used, cheapest • Isophthalic acid • Adipin acid – flexibility

– Unsaturated dibasic acid • Fumaric acid • Maleic acid

– Glycol • Propylene glycol – most used • Ethylene or diethylene glycol

• Curing: Styrene, retarded by inhibitor, addition of initiator results in cross linking

– Addition polymerisation, no by-products, EXOTHERM – Styrene – HMS for open processes

• Tighter cross-linking gives higher Tg, but a more brittle material

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Epoxy

• Epoxy group • Linear prepolymer (resin)

– Ordinary Epichlorohydrin + Bisphenol A = DGEBA – Curing system – cross-linking – Polyamines – cured at room temperature

• Curing by additive polymerisation – no by-products – Carboxyl acid anhydride – cured at 100-180°C

• Complex reaction – gives (small amounts) H2O as by-product but high temperature expels water.

– Merkapto • Low temperature, rapid curing

• Exotherm • HMS - allergies

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Vinylester

• Chemical structure resembles epoxy, but cured as polyester

• Prepolymer based on DGEBA + organic acid dissolved in styrene or other monomer

• Also found as rubber-modified vinylester with high strain to failure.

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Properties of matrix materials

Tensile modulus [Gpa]

Tensile strength [MPa]

Density [g/cc]

Tmax

[°C]

Polyester 2-4 30 - 100 1.3 40-90

Vinylester 3.0-3.5 70 - 80 1.2 ~100

Epoxy 3-4 50 - 130 1.2

160

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Properties of fibre composites

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Properties of UD (uni-directional) composites

Following must be studied: • Fibre content by both volume and weight • Stiffness

– E-modulus in both longitudinal and transverse directions – G-modulus – Poisson’s ratio

• Strength – tension, compression, shear – various directions

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Nomenclature • m – matrix • f – fibre, reinforcement • c – composite • 1 – longitudinal direction • 2 og 3 – transverse direction • 1,2,3 also denoted L,T,T’

• Laminate – composite built up from several layers,

often with fibres in different directions • UD ply – layer with all fibres in same direction

– Properties are different in transverse and longitudinal directions

• UD composite – all plies have same fibre direction • Other possibilities:

– Layers with fibres in 2 perpendicular directions (e.g. woven fabrics) – “cross-ply”

– Laminate with layers in several directions

laminate

ply

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UD composites: Volume and weight fractions • Ratio between amounts of fibre and matrix can be described by use of

– fibre volume fraction or – fibre weight fraction

• Has importance for mechanical properties

Volume fraction vc volume of composite vm volume of matrix vf volume of fibres Definition of volume fractions:

mfc vvv +=

c

mm

c

ff v

vV

vv

V ==

Weight fraction wc weight of composite wm weight of matrix wf weight of fibres Definition of weight fractions:

mfc www +=

c

mm

c

ff w

wW

ww

W ==

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Relationships between densities, volume and weight fractions

• Relationship between densities ρc , ρf , ρm

=> =>

=> =>

• Relationship between weight and volume fractions:

mfc www +=

mmffcc vvv ρρρ +=

f

c

f

cc

ff

c

ff V

vv

ww

Wρρ

ρρ

===

m

c

mm VW

ρρ

=

ct

cectvV

ρρρ −

=

c

mm

c

ff v

vV

vv

V ==

c

mm

c

ff w

wW

ww

W ==

mmff

c

mm

c

ffc

VVvv

vv

ρρ

ρρρ

+=

+=

m

m

f

f

c

c wwwρρρ

+=

mmff

m

cm

f

cf

c

WW

wwww

ρρ

ρρρ

+=

+=1

We have also the void fraction

mfc vvv +=

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Strength and stiffness in longitudinal (fibre) direction • Assumptions:

– Fibres are • uniform wrt. properties and diameter • continuous and parallel through entire

composite – Perfect adhesion between matrix and fibres. – Pf, Pm, Pc are the respective forces – Af, Am, Ac are the respective areas – Respective strains are equal,

• Then we have i.e.

=>

=> since

cmf εεε ==

mfc PPP +=

mmffccc AAAP σσσ +==

c

mm

c

ffc A

AAA

σσσ +=

c

mm

c

ff A

AV

AA

V == mmffc VV σσσ +=

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Linear elastic case Differentiate wrt. strains:

– contributions from fibres and matrix are proportional to volume fractions.

How much of the forces are taken up by the fibres?

mmffc VEVEE +=

c

c

m

m

f

f

EEEσσσ

==

( ) ( )fmmf

mf

mmff

ff

c

f

VVEEEE

AAA

PP

+=

+=

σσσ

cmf εεε == =>

m

f

m

f

mm

ff

m

f

VV

EE

AA

PP

==σσ

=>

c

f

c

f

m

f

m

f

EE

EE

==σσ

σσ=> and

and

m

mf

fc Vd

dV

dd

dd

εσ

εσ

εσ

+= =>

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Non-linear elastic case Generally a composite deforms according to linear theory. The deformation sequence is as follows:

1. Fibres and matrix undergo linear elastic deformation. Following still applies:

2. Fibres deform linearly while matrix enters a non-linear phase:

3. Both fibres and matrix deform non-linearly but following still applies:

4. Fibres fracture, resulting in fracture of the composite.

Several possible types of failure dependent on fibre fraction and fibre brittleness:

mmffc VEVEE +=

m

m

mffc V

dd

VEEεσ

+=

mmffc VV σσσ +=

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• To find Vmin we equate these, so that :

Strength and stiffness in longitudinal direction (contd.) • Vmin = min. fibre volume fraction for composite

fracture to be determined by fibre fracture as opposed to matrix fracture

• For : fibre fracture => composite

fracture because matrix cannot resist the load after fibres have failed. – Then max. stress in composite is:

• For : fibre fracture does not give composite fracture beause matrix can still resist the load. We assume the fibres do not carry forces when . – Then max. stress in composite is:

minVV f >

minVV f <

minVV f =

∗> fεε

( ) ( )fmffucu VVf

−+= ∗ 1εσσσ

( )( ) ∗

∗

−+

−=

f

f

mmufu

mmuV

ε

ε

σσσ

σσmin

( )fmucu V−= 1σσ

*

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Strength and stiffness in longitudinal direction (contd.)

• gives composite strength that is lower than matrix strength σmu, while

can give either higher or lower.

• More useful to define volume fraction Vcrit that gives lower strength limit σmu : i.e. ( ) ( ) mufmffucu VV

fσσσσ ε ≥−+= ∗ 1

( )( ) ∗

∗

−

−=

f

f

mfu

mmuV

ε

ε

σσ

σσcrit

minVV f < minVV f >

*