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.

MEK4540-2012-1.2

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) MEK4540-2012-1.3

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

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• • • •

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

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. MEK4540-2012-1.5

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 MEK4540-2012-1.11

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

Source: http://www.mscsoftware.com/events/vpd2007/emea/presentations/Session-2A-AIRBUS-Bold.pdf MEK4540-2012-1.19

Composites in Airbus designs

Source: http://www.mscsoftware.com/events/vpd2007/emea/presentations/Session-2A-AIRBUS-Bold.pdf MEK4540-2012-1.20

Materials in Boeing 787 Dreamliner

Source: http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_06/article_04_2.html MEK4540-2012-1.21

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 Sandown

HMS Wilton

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. MEK4540-2012-1.30

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 • Tg = glass transition temperature • Tm = melting temperature

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

vc = v f + v m wc w f wm = +

ρc

1

ρc

ρf

=

w f wc

ρf

ρm +

wm wc

ρm

= W f ρ f + Wm ρ m

• Relationship between weight and volume fractions: Wf =

Wm = MEK4540-2012-1.45

wf wc

=

ρf vf ρ c vc

ρm Vm ρc

=

ρf ρc

Vf

We have also the void fraction Vv =

ρ ct − ρ ce ρ ct

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, ε f = ε m = ε c

Then we have i.e. => =>

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Pc = Pf + Pm

Pc = σ c Ac = σ f A f + σ m Am

σc = σ f

Af Ac

+σ m

Am Ac

σ c = σ f V f + σ mVm

since

Vf =

Af Ac

Vm =

Am Ac

Linear elastic case dσ c d σ f dσ m = Vf + Vm dε dε dε

Differentiate wrt. strains:

=> Ec = E f V f + E mVm

– contributions from fibres and matrix are proportional to volume fractions. How much of the forces are taken up by the fibres? ε f = εm = εc

=>

σf Pf

=> P m and

=

σm

Pf Pc

=

=

Ef Em

=> σf

and

σ f Af σ m Am

=

σc

Ef

=

σm Em

=

σc Ec

Ef

=

Ec

Ef Vf E m Vm

σ f Af σ f A f + σ m Am

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σf

=

(E f

E f Em

) (

E m + Vm V f

)

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:

E c = E f V f + E mVm 2.

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

Ec = E f V f +

dσ m Vm dε m

3.

Both fibres and matrix deform non-linearly but following still applies: σ c = σ f V f + σ mVm

4.

Fibres fracture, resulting in fracture of the composite.

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

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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 V f > Vmin : fibre fracture => composite fracture because matrix cannot resist the load after fibres have failed. – Then max. stress in composite is: σ cu = σ fuV f + (σ m )ε (1 − V f ∗ f

•

)

For V f < Vmin : fibre fracture does not give composite fracture beause matrix can still resist the load. We assume the fibres do not carry forces when ε > ε ∗f . – Then max. stress in composite is: σ cu = σ mu (1 − V f

•

*

)

To find Vmin we equate these, so that

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V f = Vmin :

Vmin =

σ mu − (σ m )ε

∗ f

σ fu + σ mu − (σ m )ε

∗ f

Strength and stiffness in longitudinal direction (contd.)

*

• V f < Vmin gives composite strength that is lower than matrix strength σmu, while V f > Vmin can give either higher or lower. •

More useful to define volume fraction Vcrit that gives lower strength limit σmu : σ mu − (σ m )ε σ cu = σ fuV f + (σ m )ε (1 − V f ) ≥ σ mu i.e. Vcrit = σ fu − (σ m )ε ∗ f

∗ f

∗ f

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