parte della lezione è stata tratta dalla lezione svolta · schema della lezione - introduzione -...
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Interfacce e adesione
5a Scuola AIMAT: I Materiali Compositi
Ischia Porto (NA) 15-19 Aprile 2002
Parte della lezione è stata tratta dalla lezione svolta dal prof. Alessandro Pegoretti alla
Schema della lezione
- Introduzione
- Effetto dell’interfaccia sulle proprietà meccaniche dei compositi
- Micromeccanica all’interfaccia: meccanismi di trasferimento degli sforzi
- Misura dell’adesione fibra-matrice: metodi diretti ed indiretti
- Meccanica della frattura all’interfaccia fibra-matrice
- Come migliorare l’adesione fibra-matrice? Cenni sui trattamenti superficiali
The fibre-matrix interface • The interface between fibre and matrix is crucial to
the performance of the composite - in particular fracture toughness; corrosion; moisture resistance.
• Weak interfaces provide a good energy absorption mechanism - composites have low strength and stiffness, but high fracture toughness.
• Strong interface results in a strong and stiff, but brittle composite.
The fibre-matrix interface Adhesion between fibre and matrix is due to one (or more) of 5 main mechanisms:
1. Adsorption and wetting - depending on the surface energies or surface tensions of the two surfaces. Glass and carbon are readily wetted by epoxy and polyester resins, which have lower surface energies.
The fibre-matrix interface - adhesion mechanisms
2. Interdiffusion (autohesion) - diffusion and entanglement of molecules:
The fibre-matrix interface - adhesion mechanisms
3. Electrostatic attraction - important in the application of coupling agents. Glass fibre surface may be ionic due to oxide composition:
The fibre-matrix interface - adhesion mechanisms
4. Chemical bonding - between chemical group in the matrix and a compatible chemical on the fibre surface:
The fibre-matrix interface - adhesion mechanisms
5. Mechanical adhesion - depending on degree of roughness of fibre surface.
Larger surface area may also increase strength of chemical bond.
An interface (2D) or interphase (3D)
is the region of significantly changed chemical composition that constitutes the bond between the matrix
and reinforcement (Metcalfe - 1974)
bulk matrix
bulk fiber
modified matrix
interphase
surface layer
adsorbed material
(after Drzal et al. 1983)
Perche’ interfaccia o interfase?
‘ differential thermal contraction (residual stresses)
‘ different cooling conditions (e.g. carbon fibre is thermally conductive)
‘ matrix contracts during cure (thermosets) ‘ different Poisson´s ratio of fibre and matrix ‘ fibre surface influences cross-link density ‘ crystals can nucleate at fibre contact sizing and binder can be present ‘ water in-take along fibre interface
Why are interfaces in composites important? Surface area !
Fiber filled
df = 10 µm Φf = 0.6
Vc = 1 m3 Vf = 0.6 m3
vf =π4
df2 = 7.854x10−11 m3
fiber
Nf = Vfv f
= 7.639x109
Af = af Nf = π d f (1) Nf = 240.000 m 2
m3
Particulate filled
dp = 5 µm Φp = 0.4
Vc = 1 m3 Vp = 0.4 m3
vp =π6 dp
3 =6.545x10−17 m3
part.
Np = Vpv p
= 6.112x1015
Ap = ap Np = π d p2 N p = 480.000 m 2
m3
Techniques for studying surface structures and composition
- Scanning electron microscopy (SEM)
- Transmission electron microscopy (TEM)
- Scanning tunneling microscopy (STM)
- Atomic force microscopy (AFM)
Microscopy
Spectroscopy
- Auger electron spectroscopy (AES)
- X-ray photoelectron spectroscopy (XPS)
- Secondary ion mass spectroscopy (SIMS)
- Ion scattering spectroscopy (ISS)
- Fourier transformed infrared (FTIR) spectroscopy
- Raman spectroscopy (RS)
- Nuclear magnetic resonance (NMR) spectroscopy
S.Incardona, C.Migliaresi, H.D.Wagner, A.H.Gilbert, G.Marom, Comp.Sci.&Techn. 47, (1993), 43
Photomicrographs of isothermal crystallization of J-Polymer® (DuPont) on a HM pitch based carbon fiber.
30µm
N.Klein, G.Marom, A.Pegoretti, and C.Migliaresi , Composites, 26(10) (1995) 707
Thermo-mechanical properties of transcrystalline layers in PA66 - Kevlar composites by dynamic mechanical thermal analysis (DMTA)
0
1000
2000
3000
4000
5000
6000
-150 -100 -50 0 50 100 150 200
stora
ge m
odul
us (M
Pa)
temperature (°C)
quenched matrix
crystallized matrix
tc matrix
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
-150 -100 -50 0 50 100 150 200
tanδ
temperature (°C)
quenched matrix crystallizedmatrix
tc matrix
Influence of fiber-matrix adhesion on mechanical properties: case of graphite/epoxy composites
M.S.Madhukar, L.T.Drzal, Fiber-matrix adhesion and its effect on composite mechanical properties:
I. Inplane and interlaminar shear behaviour of graphite/epoxy composites, J. Comp. Mater., 25 (1991) 932
II. Longitudinal (0°) and transverse (90°) tensile and flexure behaviour of graphite/epoxy composites, Comp. Mater., 25 (1991) 958
III. Longitudinal (0°) compressive properties of graphite/epoxy composites, J. Comp. Mater., 26 (1992) 310
IV. Mode I and mode II fracture toughness of graphite/epoxy composites, J. Comp. Mater., 26 (1992) 936
Material Tensile Modulus(GPa)
Tensile Strength(MPa)
Interfacial ShearStrength – ISS (MPa)[Fragmentation test]
Interfacial FailureMechanism
AU-4(untreated)
234 3585 37.2 Friction
Fibers(Hercules)
AS-4(surface treated)
234 3585 68.3 Interfacial
AS-4C(epoxy coated AS-4)
234 3585 81.4 Matrix
Matrix Epon 828(DGEBA + mPDA)
3.6 89.6 -- --
Effect of fiber-matrix adhesion on the longitudinal tensile behavior in graphite/epoxy composites fiber
matrix
σL σL
M.S.Madhukar, L.T.Drzal, J. Comp. Mater., 25 (1991) 958
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
0 1 2 3
Longitudinal Tensile Modulus
Longitudinal Tensile Strength
NO
RMA
LIZE
D L
ON
GIT
UD
INA
L D
ATA
NORMALIZED INTERFACIAL SHEAR STRENGTH
M.S.Madhukar, L.T.Drzal, J. Comp. Mater., 25 (1991) 932
fibermatrix
τ
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3
Data 1
Inplane Shear Modulus (45° Tension Test)Inplane Shear Modulus (Iosipescu Shear Test)Inplane Shear Strength (45° Tension Test)Inplane Shear Strength (Iosipescu Shear Test)Interlaminar Shear Strength (Short-Beam Shear Test)
NO
RMA
LIZE
D S
HEA
R D
ATA
NORMALIZED INTERFACIAL SHEAR STRENGTH
Effect of fiber-matrix adhesion on the inplane and interlaminar shear behavior in graphite/epoxy composites
fibermatrix
σT
σT
Effect of fiber-matrix adhesion on the transverse tensile and flexural behavior in graphite/epoxy composites
M.S.Madhukar, L.T.Drzal, J. Comp. Mater., 25 (1991) 958
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 1 2 3
Transverse Tensile ModulusTransverse Flexural ModulusTransverse Tensile StrengthTransverse Flexural Strength
NO
RMA
LIZE
D T
RAN
SVER
SE D
ATA
NORMALIZED INTERFACIAL SHEAR STRENGTH
starter crack
ENF specimen
Effect of fiber-matrix adhesion on Mode II fracture toughness in graphite/epoxy composites
M.S.Madhukar, L.T.Drzal, J. Comp. Mater., 26 (1992) 936
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3
NO
RMA
LIZE
D G
IIC
NORMALIZED INTERFACIAL SHEAR STRENGTH
End Notched Flexure(Mode II Fracture Toughness)
‘Short’ fibres don’t reinforce as effectively as ‘long’ or continuous fibres
• The load transfer mechanism results in end effects which may reduce the fibre stress.
• Difficult to control the alignment of short fibres.
• Randomly-oriented short fibres cannot be packed at such high volume fractions as continuous fibres.
Short fibres are more often used with thermoplastic resins. Processes like injection moulding lead to considerable fibre damage and reduction in length:
Load transfer between matrix and fibre
Under applied tension, load is transferred by shear at the matrix/fibre interface.
At fibre ends, the strain in the matrix is higher than in the fibre:
(Matthews & Rawlings, ‘Composite Materials’, Woodhead)
Micromechanics of stress transfer across the interface
fibermatrix
unloaded case
loadload
loaded case
complex stress field often described by rough models, like
shear-lag model (Cox, 1952)
simplified physical model (Kelly-Tyson, 1965)
Stress variation in a short fibre
(Matthews & Rawlings, ‘Composite Materials’, Woodhead)
Stress variation in a short fibre - experimental evidence
(Matthews & Rawlings, ‘Composite Materials’, Woodhead)
When a stiff fibre is embedded in a relatively flexible matrix, shear stress and strain are a maximum at the fibre ends.
The tensile stress in the fibre, on the other hand, is zero at the fibre end and increases towards the centre. Note low stress at fibre end, increasing to maximum value about 7 radii towards the centre.
• The tensile stress in the fibre thus increases from zero at the ends to a maximum value of σf
max = Ef ε, where e is the strain applied to the composite.
• A fibre is said to be of the critical length if it is just long enough for the tensile stress to reach its maximum value.
L > Lc
L < Lc L = Lc
Lc / 2
fibre
tens
ile s
tress
fib
re te
nsile
stre
ss
σfmax = Ef ε
σfmax = Ef ε
Simple model for critical length Consider a half fibre. The maximum tensile force in the fibre, diameter D, is balanced by the shear force at the fibre/matrix interface, so:
τσ
λ
τσ
τππσ
2
2
24
max
max
2max
fcc
fc
cf
DL
DL
DLD
==
=∴
=
Lc / 2
σfmax
τ centre line
‘λ’ is fibre aspect ratio
Critical fibre length Critical fibre length thus depends on τ, the interfacial or matrix shear strength, and varies according to both fibre and matrix:
matrix fibre Lc (mm) Lc / DAg alumina 0.4 190Cu tungsten 38 20Al boron 1.8 20epoxy boron 3.5 35epoxy carbon 0.2 35polycarbonate carbon 0.7 105polyester glass 0.5 40polypropylene glass 1.8 140alumina SiC 0.005 10
Fibre end effects • Because of the low stress at fibre ends, the average
stress in the fibre will be lower than that in a continuous fibre, even if it is longer than the critical length.
• For fibre length L = 5 Lc, the average fibre stress (σfav)
is about 90% of the maximum stress (σfmax) .
• It can be shown that (for L > Lc):
−=LLc
favf 2
1maxσσ
Stiffness of short fibre composites
For aligned short fibre composites (difficult to achieve in polymers!), the rule of mixtures for modulus in the fibre direction is:
€
E =ηLE fVf + Em(1−Vf )
The length correction factor (ηL) can be derived theoretically. Provided L > 1 mm, ηL > 0.9
For composites in which fibres are not perfectly aligned the full rule of mixtures expression is used, incorporating both ηL and ηo.
Theoretical length correction factor
( )( )2/L
2/Ltanh1L β
β−=η
( )DR2lnDEG8
2f
m=β
00.10.2
0.30.40.50.60.7
0.80.91
0 0.5 1 1.5 2
fibre length (mm)
leng
th c
orre
ctio
n fa
ctor
Theoretical length correction factor for glass fibre/epoxy, assuming inter-fibre separation of 20 D.
Strength of short fibre composites The micromechanics of strength are more complicated than for stiffness. Strength depends on the relative failure strains of fibre and matrix (amongst other things).
Essentially, there is little difference between short and continuous fibre composite strengths once L ≥ 10 Lc.
H.L.Cox “The elasticity and strength of paper and other fibrous materials” Br.J.Appl.Phys. 3, (1952) 72
hp: - linear elastic behavior for matrix and fiber; - perfect adhesion (no debonding).
σf (x) = Ef ε c 1 − cosh [β (L/2−x)]cosh (β L/2)
τf (x) = Ef εc β
rf2
sinh [β (L/2−x)]
cosh (β L/2)
0
200
400
600
800
1000
0 200 400 600 800 1000
σf (M
Pa)
x (µm)
-40
-20
0
20
40
0 200 400 600 800 1000
τ f (MPa
)
x (µm)
A.Kelly, and W.R. Tyson, “Tensile properties of fiber-reinforced metals copper/tungsten and copper/molybdenum” J. Mech. Phys. Solids 13, (1965) 329
hp: - linear elastic behavior for fiber; - elasto-plastic behavior for matrix; - debonding may occur.
L < L t L = L t L > L t
t t
fiber/matrix stress stress,
L < L t L = L L > L
axial fiber stress, σ f
( σ f )* max = E f /E c σ c
τ y τ
(σf )max =τy L
r
Stress transfer at fiber-matrix interface: Kelly-Tyson model
Consideriamo una fibra corta immersa in un cilindro di matrice. Ipotizziamo che:
• La fibra abbia un comportamento perfettamente elastico fino a rottura
• La matrice abbia comportamento elasto-plastico con carico di snervamento uguale a sy
Da un bilancio di forze, si ricava che lo sforzo che agisce sulla fibra all’ascissa x è:
2
0
2)( 2)( rrdxxr
x
mx πσπτπσ ∫ +=
Forza tramessa sulla superficie laterale della
fibra dalla matrice
Forza trasmessa sulla superficie
normale
1 2
o anche:
σf
τ
τ
σf + dσf
( ) ( ) ( ) 044
22
=πτ−π
σ−π
σ+σ=∑ dxddddF fffx
L’ e q u a z i o n e p u o ’ e s s e r e risolta se e’ nota la funzione t(x). Nel caso in esame, a v e n d o l a m a t r i c e c o m p o r t a m e n t o e l a s t o -plastico, t è costante ed u g u a l e a l c a r i c o d i snervamento a taglio ty
ty rappresenta la resistenza al t a g l i o d e l l a m a t r i c e a l l ’ i n t e r f a c c i a . E s s o è approssimativamente uguale a ½ smy
xr yx τσ2
)( =
Lo sforzo applicato alla fibra aumenta linearmente con x
• Per fibre corte, per motivi di simmetria, lo sforzo raggiunge il suo massimo valore, sfmax al centro della fibra, quando cioè x è uguale ad L/2.
rLy
f
τσ =max
L
σf τy
Ma lo sforzo massimo che può accumularsi sulla fibra ha un limite, quello massimo che la fibra vedrebbe se fosse continua. In questo
caso infatti fibra e matrice si deformano delle stesse quantita’
mfc εεε ==f
f
c
c
EEσσ
=
cc
ffcont E
Eσσ =
σf
• Mentre per fibre continue la condizione di sforzo massimo e’ presente su tutta la fibra, per fibre corte essa si verifica soltanto se la fibra è più lunga di una quantità che definiamo “lunghezza di trasferimento di carico (load transfer length), Lt, definibile da:
y
fcontt
dL
τ
σ
2=
L<Lt L=Lt L>Lt
σfcont corrisponde pertanto al piu’ alto dei possibili
valori di σfmax
σ
σfmax
Ma Lt dipende dal carico applicato al composito. Per ogni
valore di sforzo applicato sc esiste un valore corrispondente
di Lt
cc
ff E
Eσσ =max
y
ft
dL
τ
σ
2max=
Lt non e’ un valore unico, ma dipende dal carico applicato al composito: Per ogni valore di sc, esiste un valore di Lt
Ma: aumentando σc, aumenta il valore di Lt, e pertanto il valore di σfmax.Il massimo valore che Lt puo’ assumere è quello che rende il carico applicato sulla fibra uguale al suo carico di rottura, σfb. Quando aumento il carico applicato al composito, aumenta l’σfmax applicato alla fibra, finchè non viene raggiunta la sua resistenza σfb. In queste condizioni la lunghezza della fibra viene definita Lunghezza critica di fibra, Lc. Essa è uguale a:
σc
Lt Lt Lc
y
fbc
dL
τ
σ
2=
• All’aumentare del carico applicato al composito, aumenta il carico trasmesso alla fibra. Il limite del carico che si puo’ raggiungere sulla fibra e’ pero’ rappresentato dalla resistenza della fibra stessa, σfb.
• La lunghezza di fibra che permette il trasferimento da parte della matrice alla fibra di un carico pari alla sua resistenza viene definita Lunghezza critica di fibra, Lc Se la fibra e’ piu’
lunga della lunghezza critica,
raggiunto un determinato carico
sul composito essa si rompe. Se e’ piu’
corta viene espulsa (cede l’interfaccia).
Stress transfer at fiber-matrix interface: Kelly-Tyson model
The “transfer length” Lt is given by: Lt =r Efτy Ec
σc
Lc/2 Lc/2
σc
(σf )max=σfb
and hence: τy = ISS = rLc
σfb
The “critical length” Lc is given by:
Lc =rτy
σfb
Quantitative measurement of fiber-matrix interfacial adhesion: state of the art
HISTORICALLY, TWO GENERAL METHODOLOGIES, BASED ON:
INDIRECT TESTING of collective behaviour of fibers in a matrix (real composites)
- Interface strength interpreted via simplistic model
- Fast but questionable results are obtained
DIRECT TESTING probes interfacial behavior of individual fibers in a matrix (microcomposites)
- More fundamental and accurate information
- Variability within and between techniques
- Issue of relevance to macrocomposites
INDIRECT TEST METHODS - (I)
[±45°] tensile test ASTM D 3518
τ 12 =σ x
2
0
[10°] off-axis tensile test
INDIRECT TEST METHODS - (II) Rail shear test ASTM D 4255
Two rails - tension Three rails - compression
INDIRECT TEST METHODS - (III)
In-plane lap-shear test ASTM D 3518
Transverse tensile test ASTM D 3039
INDIRECT TEST METHODS - (IV)
Short beam interlaminar shear test ASTM D 2344
σxMAX=
3 F L2 B h2
τxyMAX=
3 F4 B h
τxyMAX
σxMAX
=h
2 L
Experimental problems with the short beam interlaminar shear test
Iosipescu shear test ASTM D 5379 INDIRECT TEST METHODS - (V)
Matrix cracking in a 90° specimen
Matrix cracking in a 0° specimen
INDIRECT TEST METHODS - (VI): delamination tests
Modes of interlaminar crack propagation
a) Mode I opening mode b) Mode II sliding shear mode c) Mode III tearing mode
a) b) c)
Mode I Interlaminar fracture toughness Double Cantilever Beam ASTM D 5528
G Ic =P 2
2BdCda
C =δP
C =2 a 3
3 E1 I
where
for the classical beam theory:
INDIRECT TEST METHODS - (VII): delamination tests (cont.)
Mode II Interlaminar fracture toughness
End Notched Flexure specimen
G IIc =9 a 2 P δ
2 B (2 L3 + 3 a 3 )
End Loaded Split specimen
G IIc =9 a 2 P δ
2 B (L3 + 3 a 3 )
DIRECT TEST METHODS - (I) Fiber microdebonding test
ISS = Fp
π d L
Fiber pull-out test
ISS = Fp
π d L
SEM micrograph of PCL droplet on Kevlar 149 fiber.
fiber microdebonding
a)
b)
SEM micrographs of PCL droplet before (a) and after (b) debonding.
A.Gati, M. Sc.Thesis, The Weizmann Institute of Science, Israel (1996)
DIRECT TEST METHODS - (III)
Multi-fiber pull-out test
Y.Qiu and P.Schwartz, Comp.Sci.&Techn. 48 (1993) 5
Microindentation test
t < 3 ÷ 4 d
ISS =Fpπ d t
DIRECT TEST METHODS - (IV): Fiber fragmentation test
load
load
matrix
fiber
ISS =d σ fb(Lc )
2 Lc
σ fb (L) = α LL0
−1/βΓ 1+ 1
β
the “saturation length” Ls is related to the critical length Lc: Lc = 4/3 Ls
average fiber strength, σ fb(L), depends on the fiber length
(generally this dependence follows the Weibull statistics),i.e. :
Fiber fragmentation: test apparatus
Fiber fragmentation observed under polarized light
Glass fibers in PA6 matrix
Carbon fiber in epoxy matrix
Fiber fragmentation in carbon/epoxy composites: effect of temperature
For a “soft” epoxy matrix (Tg = 40°C)
0
10
20
30
40
0 10 20 30 40 50 60
ISS sized fibersISS desized fibersmatrix shear strength
shea
r stre
ss (M
Pa)
temperature (°C)
strain rate = 0.008min -1
M.Detassis, A.Pegoretti, and C.Migliaresi, Comp. Sci. & Techn., 53 (1995) 39.
Fiber fragmentation in carbon/epoxy composites: effect of temperature
For a stiff epoxy matrix (Tg = 150°C)
0
10
20
30
40
50
0 50 100 150 200
ISS sized fibersISS desized fibersmatrix shear strength
shea
r stre
ss (M
Pa)
temperature (°C)
strain rate = 0.008min -1
A.Pegoretti, C.DellaVolpe, M.Detassis, C.Migliaresi, and H.D.Wagner CompositesPartA, 27 (1996) 1067.
Fiber fragmentation in carbon/epoxy composites: effect of strain rate
For a “soft” epoxy matrix (Tg = 40°C)
0
10
20
30
40
50
0 0.005 0.01 0.015
ISS sized fibersISS desized fibersmatrix shear strength
shea
r stre
ss (M
Pa)
strain rate (min -1)
temperature = 20 °C
M.Detassis, A.Pegoretti, and C.Migliaresi, Comp. Sci. & Techn., 53 (1995) 39.
Fiber fragmentation in thermoplastic matrix composites: nylon6/glass fibers
Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.
Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.
Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.
aluminum plate PTFE sheet
nylon-6 film
E-glass fibers
Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.
Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo.
fiber 45 mm
4 mm 90 µ m
Temperature = 300 °C Pressure = 10 kPa (under vacuum) Time = 50 min
load load
Fiber fragmentation in thermoplastic matrix composites: nylon6/glass fibers: effect of temperature
A.Pegoretti, L.Fambri and C.Migliaresi, Polymer Composites, 21 (2000) 466.
0
5
10
15
20
25
30
20 40 60 80 100 120 140 160 180
ISS unsizedISS polyamide sizedISS epoxy sizedmatrix shear strength
shea
r stre
ss (M
Pa)
temperature (°C)
strain rate = 0.008min-1
Fiber fragmentation in thermoplastic matrix composites: nylon6/glass fibers: effect of strain rate
A.Pegoretti, L.Fambri and C.Migliaresi, Polymer Composites, 21 (2000) 466.
0
5
10
15
20
25
30
35
40
10-3 10-2 10-1 100 101
ISS unsizedISS polyamide sizedISS epoxy sizedmatrix shear strength
shea
r stre
ss (M
Pa)
strain rate (min-1)
temperature = 25 °C
What is happening when a fiber breaks in a polymer matrix ?
When a fiber filament breaks, cracks will propagate from the broken fiber end either by: - interfacial debonding; - trasverse matrix cracks; - conical matrix cracks, or combinations of the three modes.
Example: fracture patterns at a broken fiber end depend on fiber/matrix adhesion. glass/epoxy system: a) interfacial debonding); b) radial matrix crack; c) conical matrix crack; d) mixed matrix crack.
A.Pegoretti, M.L.Accorsi and A.T.DiBenedetto, Journal of Materials Science, 31 (1996) 6145.
a) b)
c) d)
Recent trends in fiber/matrix load transfer: a fracture mechanics approach for fiber/matrix debonding.
E-glass fiber in nylon-6 matrix: debonding when fiber fails
load load
10 mm
fiber
debonding
T=25°C
matrix
load load
10 µm
T=100°C
fiber
matrix
debonding
Finite elements modeling of the fiber/matrix debonding
fiber
matrix
fiber fracture point
fiber/matrix debonding zone
Ld
fiber
matrix
fiber fracture point
FEM mesh
A BC
DE
F
z
r
0
5
10
15
20
0 2 4 6 8 10 12 14 16 18 20
strai
n en
ergy
rele
ase
rate
(J/m
2 )
debonding length, Ld (µm)
matrix = epoxy (E=2.9 GPa)fiber = S-glass (E=86.9 GPa)strain = 1%
A.Pegoretti, M.L.Accorsi and A.T.DiBenedetto, Journal of Materials Science, 31 (1996) 6145.
Strain energy release rate for the fiber/matrix debonding - I
fiber
matrix
fiber fracture point
fiber/matrix debonding
Ld
Strain energy release rate for the fiber/matrix debonding - II
0
100
200
300
400
500
0 1 2 3 4 5 6
G (J
/m2 )
strain (%)
elastic
elastic-plastic
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
stre
ss (M
Pa)
strain (%)
epoxy matrix
A.Pegoretti and A.T.DiBenedetto, Composites Part A, 29(9-10) (1998) 1063.
Strain energy release rate for the fiber/matrix debonding - III
A.Pegoretti, M.Fidanza, C.Migliaresi and A.T.DiBenedetto, Composites Part A, 29 (1998) 283.
0
50
100
150
200
250
300
350
unsized polyamide sized epoxy sized
T = 20°CT = 100 °C
Gar
rest (J
/m2 )
fiber surface treatment
Example: E-glass fibers in nylon-6 matrix
Can microcomposites (low volume fraction) be considered as representative for interfaces in macrocomposites (high volume
fraction) ? Problem n° 1: thermal
stresses H.D.Wagner, J.Adhesion, 52 (1995) 131.
Thermal stresses may induce fiber buckling in high modulus fiber embedded in termosetting matrices
Carbon fiber in epoxy matrix
Thermal stresses may induce fiber fracture for high modulus fiber embedded in termoplastic matrices
Carbon fiber in J-polymer
S.Incardona, C.Migliaresi, H.D.Wagner, A.H.Gilbert, G.Marom, Comp.Sci.&Techn. 47, (1993), 43
M.Detassis, A.Pegoretti, C.Migliaresi, H.D.Wagner, J.Mater.Sci, 31 (1996) 2385.
Experimental evaluation of thermal stresses
How can fiber-matrix adhesion be improved ?
Fracture surfaces of epoxy composites after 72 hr in boiling water
Matrix modifications
Surface treatments on fibers
Fibers surface treatments - (I): glass fibers
Typical component of a glass fiber size
• Film-forming resin ... 1-5 %wt
• Antistatic agent……. 0.1 - 0.2 %wt
• Lubricant ………….. 0.1 - 0.2 %wt
• Coupling agent……...0.1 - 0.5 %wt
- SILANE - TITANATE - ZIRCONATE
Fibers surface treatments - (II): silane coupling agents
R-SiX3
R is a group which can react with the resin
X is a group which can hydrolyze to form a silanol group in aqueous solution
a) hydrogen bonding between hydroxyl groups of silanol and glass surface; b) polysiloxane bonded to glass surface; c) organofunctional R-group reacted with polymer
+ H2O → R-Si(OH)3 + 3 HX
Fibers surface treatments - (III):
commercial coupling agents
Fibers surface treatments - (IV): effect of silane coupling agents on the mechanical properties of glass fiber
composites
E.P.Plueddemann, H.A.Clark, L.F.Nelson, and K.R.Hofman Mod.Plast, 39 (1962) 136.
0
100
200
300
400
500
600
700
None Vynil silane Methacrylate silane
DryAfter 2-hr water boil
Flex
ure
stren
gth
of c
ompo
site
(MPa
)
E-glass surface treatment
Fiberglass reinforced polyester composites
Fibers surface treatments - (V) carbon fibers
SURFACE TREATMENT forms chemical bonds to the carbon surface, to give a better cohesion to the resin system of the composite
SIZING is a neutral finishing agent (usually epoxy) to protect the fibers during further processing (eg prepregging) and to act as an interface to the resin system of the composite
Fibers surface treatments - (VI) carbon fibers
Whiskerization Polymer grafting
Pyrolitic carbon deposition
OXIDATIVE NON-OXIDATIVE
Gaseous oxidation
Oxidation in air
Oxidation in oxygen and oxygen containing gases (O3 , CO2)
Catalytic oxidation
Liquid phase oxidation
Chemical (HNO3 , H2O2 KMnO4, NaClO chromic acid)
Electrochemical (HNO3 , NaOH)
Fibers surface treatments - (VII) carbon fibers Chemical groups produced by surface treatments on carbon fibers
J.C.Goan, T.W.Martin, R.Prescott 28th SPI Conf., (1973) Paper 21B.
Fibers surface treatments - (VIII) polymeric fibers
ARAMID FIBERS
- chemical etching/grafting (HCl, H2SO4, NaOH → reactive amino groups fiber damage may occur!) - plasma treatment (in ammonia or argon → 50-400% adhesion increase)
- application of coupling agent (not particularly successfull)
Ultra High Modulus Polyethylene Fibers (UHMPE)
- chemical etching (KMnO2, H2O2, K2Cr2O7 → 6-fold ISS increase in epoxy)
- plasma treatment (in oxygen or air)
M.S.Silverstein, O.Breuer J.Mater.Sci., 28 (1993) 4718.
Fibers surface treatments - (IX): plasma treatment of UHMWPE fibers
C.Della Volpe, L.Fambri, R.Fenner, C.Migliaresi, and A.Pegoretti, J. Mater. Sci., 29 (1994) 3919.
untreated UHMWPE fibers
plasma treated UHMWPE fibers (air, 20 W, 30 min, 10-5 bar)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 1 2 3 4 5
load
(N)
displacement (mm)
untreated fiber
treated fiber
Fp
2 µm
2 µm
Fibers surface treatments - (X): plasma treatment of UHMWPE fibers
Fibers surface treatments - (XI): plasma treatment of UHMWPE fibers
Effect of time Effect of temperature
Stability of plasma treatments
C.Della Volpe, L.Fambri, R.Fenner, C.Migliaresi, and A.Pegoretti, J. Mater. Sci., 29 (1994) 3919.
Matrix modifications
Example: maleic anhydride or acrylic acid grafted onto polypropylene (Polybond™)
J.M.H.Daemen and J. den Besten, Eng. Plastics, 4 (1991) 82.
Books:
• J-K. Kim and Y-W. Mai “Engineered Interfaces in Fiber Reinforced Composites”, Elsevier Oxford (1998)
• E.P. Plueddemann “Silane Coupling Agents” Plenum Press NY 2nd Edition (1991)
• J-P.Donnet and R.C.Bansal “Carbon Fibers” Marcel Dekker NY 2nd Edition (1990)
Conferences:
• IPCM, Interfacial Phenomena in Composite Materials - biennal (next 2003)
• ECCM, European Conference on Composite Materials, biennal (next Brugge – Belgium June 3-7, 2002)
• IPC, Interfaces in Polymer Composites biennal (next, Orlando, FL; December 9-11, 2002)
• ICCI International Conference on Composite Interfaces
Journals:
• Composites Interfaces, VSP.
• Composites Science and Technology and Composites Part A,, Elsevier
• Polymer Composites, Society of Plastics Engineers SPE