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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 (bøyning og
knekning) • Kompositter i ANSYS • Sandwichmaterialer • Sandwichbjelker og -plater • Sammenføyninger • Kortfiberkompositter • Produksjonsmetoder • Mekanisk prøving • 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”: 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.
MEK4540-2012-1.31
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<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
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 100-180°C
• 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 – Poisson’s 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 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 +=
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 εεε ==
mfc PPP +=
mmffccc AAAP σσσ +==
c
mm
c
ffc A
AAA
σσσ +=
c
mm
c
ff A
AV
AA
V == mmffc VV σσσ +=
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
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
+= =>
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 V
dd
VEEεσ
+=
mmffc VV σσσ +=
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 <
minVV f =
∗> fεε
( ) ( )fmffucu VVf
−+= ∗ 1εσσσ
( )( ) ∗
∗
−+
−=
f
f
mmufu
mmuV
ε
ε
σσσ
σσmin
( )fmucu V−= 1σσ
*
MEK4540-2012-1.50
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 >
*