MEK4540-2012-1.1

MEK4540 Komposittmaterialer og konstruksjoner Composite materials and structures

Innledning materialer ensrettede kompositter Introduction materials unidirectional composites

MEK4540-2012-1.2

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.

MEK4540-2012-1.3

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)

MEK4540-2012-1.4

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 (byning og

knekning) Kompositter i ANSYS Sandwichmaterialer Sandwichbjelker og -plater Sammenfyninger Kortfiberkompositter Produksjonsmetoder Mekanisk prving Dimensjonering og regelverk

MEK4540-2012-1.5

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.

MEK4540-2012-1.6

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

MEK4540-2012-1.7

Classification of composite materials From Agarwal, Broutman & Chanrashekhara

and multi-layered composites having same properties in each layer

Layers with different materials

MEK4540-2012-1.8

Microscopy

MEK4540-2012-1.9

Composites properties

UD = unidirectional = ensrettet

QI = quasi-isotropic

= kvasi-isotrop

MEK4540-2012-1.10

Applications

MEK4540-2012-1.11

Offshore/subsea Tension leg, tether

Riser

Subsea protection cover

MEK4540-2012-1.12

Offshore/subsea

MEK4540-2012-1.13

Ships/boats

MEK4540-2012-1.14

Naval ships

MEK4540-2012-1.15

Sports and leisure equipment

MEK4540-2012-1.16

Cars

MEK4540-2012-1.17

Trains (Flytoget)

MEK4540-2012-1.18

Aircraft

MEK4540-2012-1.19

Composites in Airbus designs

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

MEK4540-2012-1.20

Composites in Airbus designs

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

MEK4540-2012-1.21

Materials in Boeing 787 Dreamliner

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

MEK4540-2012-1.22

Aircraft development over the years

MEK4540-2012-1.23

Wind energy

The blades can be as long as 62 m

MEK4540-2012-1.24

Buildings and bridges

MEK4540-2012-1.25

British naval vessels in GRP

HMS Wilton

HMS Sandown

GRP is used here for its non-magnetic properties

MEK4540-2012-1.26

Sandown class mine-hunter

Midship section

MEK4540-2012-1.27

Sandwich catamarans (SES)

Midship section

MEK4540-2012-1.28

Visby Class Swedish Navy

72 m long CFRP sandwich with PVC core

MEK4540-2012-1.29

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

MEK4540-2012-1.30

Materials carbon fibres Carbon and graphite fibres

Graphite fibres: 99% Carbon Carbon fibres: 8095% Carbon

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

MEK4540-2012-1.31

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

MEK4540-2012-1.32

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!

MEK4540-2012-1.33

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

MEK4540-2012-1.34

Matrix materials polymers

Poly = many Mer = part

E.g. polyethylene [- CH2 CH2 -]n

Linear

Branched

Cross-linked

MEK4540-2012-1.35

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.

MEK4540-2012-1.36

Polymer mechanical properties temperature dependence

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

MEK4540-2012-1.37

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

MEK4540-2012-1.38

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 100-180C

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

Merkapto Low temperature, rapid curing

Exotherm HMS - allergies

MEK4540-2012-1.39

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.

MEK4540-2012-1.40

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

MEK4540-2012-1.41

Properties of fibre composites

MEK4540-2012-1.42

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 Poissons ratio

Strength tension, compression, shear various directions

MEK4540-2012-1.43

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

MEK4540-2012-1.44

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 ==

MEK4540-2012-1.45

Relationships between densities, volume and weight fractions

Relationship between densities c , f , m

=> =>

=> =>

Relationship between weight and volume fractions:

mfc www +=

mmffcc vvv +=

f

c

f

cc

ff

c

ff Vv

vww

W

===

m

c

mm VW

=

ct

cectvV

=

c

mm

c

ff v

vV

vv

V ==

c

mm

c

ff w

wW

ww

W ==

mmff

c

mm

c

ffc

VVvv

vv

+=

+=

m

m

f

f

c

c www

+=

mmff

m

cm

f

cf

c

WW

wwww

+=

+=1

We have also the void fraction

mfc vvv +=

MEK4540-2012-1.46

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 ==

mfc PPP +=

mmffccc AAAP +==

c

mm

c

ffc A

AAA

+=

c

mm

c

ff A

AV

AA

V == mmffc VV +=

MEK4540-2012-1.47

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

EEE

==

( ) ( )fmmfmf

mmff

ff

c

f

VVEEEE

AAA

PP

+=

+=

cmf == =>

m

f

m

f

mm

ff

m

f

VV

EE

AA

PP

==

=>

c

f

c

f

m

f

m

f

EE

EE

==

=> and

and

m

mf

fc Vd

dV

dd

dd

+= =>

MEK4540-2012-1.48

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 Vd

dVEE

+=

mmffc VV +=

MEK4540-2012-1.49

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 f

( ) ( )fmffucu VVf

+= 1

( )( )

+

=

f

f

mmufu

mmuV

min

( )fmucu V= 1

*

MEK4540-2012-1.50

Strength and stiffness in longitudinal direction (contd.)

gives composite strength that is lower than matrix strength mu, while

can give either higher or lower.

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

f += 1

( )( )

=

f

f

mfu

mmuV

crit

minVV f < minVV f >

*