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FIBRE-MATRIX DEBONDING IN TRANSVERSE CYCLING LOADING OF UNIDIRECTIONAL COMPOSITE PLIES
E. CORREA*, E.K. GAMSTEDT** AND F. PARÍS*
* Group of Elasticity and Strength of MaterialsSchool of EngineeringUniversity of Seville
Sevilla, SPAIN
** KTH Solid Mechanics
Stockholm, SWEDEN
COMPTEST 2006, Porto, 10-12 April 2006
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Fatigue is by far the most common type of failure of structures in service
Fatigue in structures
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Transverse plies in laminates
Transverse plies are very used in multidirectional composite laminates
+ Increase stiffness in the 90º direction+ Increase strength in the 90º direction+ Prevent from splitting
…but they are the first plies to show cracks
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T-T and T-C fatigueσmax
Log N
Tension-tension
Tension-compression
σ
tσ
t
From experimental evidence T-C cycling load has been
shown to be more deleterious than T-T cycling load in
laminates containing transverse plies and even in
pure unidirectional laminates
WHY?
Tension-tensionR = 0.1
Tension-compressionR = –1
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T-T and T-C fatigue
Delamination+
buckling
Fibre breakage
Compression
Multidirectional laminates
First ply damage: transverse cracking
Tension
Unidirectional laminates
What happens at micromechanical level?
Formation process of transverse cracks Matrix/Inter-fibre failure
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Damage initiation at the interface
60-70º
60-70º
Growth along the interface
Kinking
Coalescence
Matrix/ Inter-Fibre failure
(*) París, F., Correa, E. and Mantič, V., ‘Study of kinking in transversal interface cracks between fibre and matrix’, In: ECCM-10, Composites for the future, ESCM, Brugge (Belgium), 2002.
Micromechanical analysis based on Interfacial Fracture Mechanics
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Single-fibre composite test
(*) Gamstedt EK, Sjögren BA, ‘Micromechanisms in tension-compression fatigue of composite laminates containing transverse plies’, Comp Sci Tech 1999; 59: 167-178.
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Ø 20 µm
Increasingload
cycles
Ø
Single-fibre composite test
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Why does damage increase in compression? BEM Model
Experimental Results
-The first cycle of T-T load produces a debond angle corresponding to a value between 60º and 70º. The next few T-T cycles only produce a very small growth, reaching a constant level that is maintained in subsequent cycles.
-T-C cycles also produce
crack growth.
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BEM Model
∫Δ+
Δ+Δ+ +=Δαα
αααθαθααα θσσ
δαα duuG rrrr })()()(){(
21),(
Energy Release Rate
Fibre radius: a=23x10-6 m
002
3
FIBRA
MATRIZ
α
Fondo inferior
Fondo superior
a
2
3
FIBRE
MATRIX
θd
a σ0σ0
Material Properties
34.0102.2
21.0106.79
10
=ν=
=ν=mm
ff
PaxEPaxE
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-1.5
-1
-0.5
0
0.5
1
1.5
0 20 40 60 80 100 120 140 160 180
α (º)
σrr
/σ0,
σr θ
/σ0
Damage initiation at the interface
σrrσrθ
FIBRE
MATRIX
α σ0σ0
Goodier
The radial stress can be considered as the responsible for the origin of damage An initial debond centred in 0º is chosen for this analysis
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70 80 90 100 110 120 130Debonding angle, θ d (º)
ER
R(G
/G0)
Energy Release Rate. Tension case
GIGIIG
00
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
0000
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
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Evolution of the contact zone. Tension case
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120Debonding angle, θ d (º)
Con
tact
Zon
e (º
)
Element size
Polynomial approximation
(order 2)
θd=45ºθd=60ºθd=90º
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Morphology of the crack. Tension case
ExternalTension
θd=60ºMATRIX
FIBRE
ExternalTension
Material 1-Stiff
Material 2-CompliantAllowed near-tip slip direction
Large near-tip contact zone
External load
Material 1-Stiff
Material 2-CompliantAllowed near-tip slip direction
Large near-tip contact zone
External load
00
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
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Energy Release Rate. Compression case
GIGIIG
003
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
00003
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Debonding angle, θ d (º)
ER
R(G
/G0)
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70 80 90 100 110 120 130Debonding angle, θ d (º)
ER
R(G
/G0)
Energy Release Rate comparison
G (C-0)G (T-0)
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0
10
20
30
40
50
60
70
0 20 40 60 80 100 120Debonding angle, θ d (º)
Bub
ble
exte
nsio
n (º
)Evolution of the separation zone. Compression case
Element size
Polynomial approximation
(order 2)
θd=40ºθd=60ºθd=75ºθd=90º
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Morphology of the crack. Compression case
ExternalCompression
θd=45ºMATRIX
FIBRE
undeformed positionof the interface
δur
ExternalCompression
Material 1-Stiff
Material 2-Compliant
“Bubble”
Not allowed near-tip slip direction
Extremely small near-tip contact zone
rc Mat. 2
Mat. 1
“Bubble”
External load
localsliding
direction
Material 1-Stiff
Material 2-Compliant
“Bubble”
Not allowed near-tip slip direction
Extremely small near-tip contact zone
rc Mat. 2
Mat. 1
“Bubble”
External load
localsliding
direction
Material 1-Stiff
Material 2-Compliant
“Bubble”
Not allowed near-tip slip direction
Extremely small near-tip contact zone
rc Mat. 2
Mat. 1
“Bubble”
External load
localsliding
direction
00
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
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0
10
20
30
40
50
60
70
80
90
100
110
120
0 20 40 60 80 100 120
Debonding angle, θ d (º)
ψG
(º)
Tension case. Damage prediction: ψG
Hutchinson and Suo (1992)
)(intintGcGG ψ≥
)()(tan int
int
aGaG
I
IIG
2
ΔΔ=ψ
Energetic phase angle (ψG)
Δa=0.5ºΔa: length of the virtual crack extension
3020 .. ≤≤ λ
λ: fracture mode sensitivity parameter
))(tan()( intintG
21Gc 11GG ψλψ −+=
00
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
0000
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
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Compression case. Damage prediction: ψG
Hutchinson and Suo (1992)
)(intintGcGG ψ≥
)()(tan int
int
aGaG
I
IIG
2
ΔΔ=ψ
Energetic phase angle (ψG)
Δa=0.5ºΔa: length of the virtual crack extension
3020 .. ≤≤ λ
λ: fracture mode sensitivity parameter
))(tan()( intintG
21Gc 11GG ψλψ −+=
-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140
Debonding angle, θ d (º)
ψG
(º)
00
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
0000
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
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Damage prediction: Gc
))(tan()( intintG
21Gc 11GG ψλψ −+=
-150 -130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130 150
ψ G (º)
Apparent(friction
considered)Intrinsic
(friction not considered)
Open Model Contact Model
small bubblegrowing bubble
closing opening zone contact zone
compliant
stiff
compliant
stiff
compliant
stiff
compliant
stiff
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
apparent
Tension case. Damage prediction: Gc(ψG)
00
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
0000
2
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
Tensile cycles will produce debondings that will propagate till a crack extension of 60º-70º at the end of the first cycle applied, not founding numerical support for these cracks to go on growing in later tensile cycles (same value of load)
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Compression case. Damage prediction: Gc(ψG)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
00
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
0000
3
FIBRA
α
Fondo inferior
Fondo superior
a2
3
FIBRE
MATRIX
θda σ0σ0
For an initial debonding around θd =60º, a compressive cycle will cause an unstable growth till a position above 100º.
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Compression case. Damage prediction: Gc(ψG)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
apparent
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30 40 50 60 70 80 90 100 110 120Debonding angle, θ d (º)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
apparent
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
G (θd) /G0Gc(ψG(θd), λ=0.25)Gc(ψG(θd), λ=0.2)
apparent
The BEM conclusions agree with the experimental results showing the capability of compressive cycles to make the crack grow from its stable position after the tensile cycles to a final debonding of around 110º
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Conclusions and future works
• The more deleterious effect of Tension-Compression fatigue than Tension-Tension fatigue has been investigated at micromechanical level.
• The damage is originated by transverse cracks. Transverse cracks are initiated from coalescence of fibre-matrix debonds.
• Experimental tests (single fibre specimens) have been carried out in order to examine debond growth under Tension-Tension and Tension-Compression fatigue.
• A BEM model has been developed and Fracture Mechanics concepts have been applied to find an explanation of damage origin at micromechanical level.
• Experimental and numerical studies lead to the same conclusions, having found an explanation for the damaging effect of compressive load excursions in fatigue.
• The results obtained may be used to formulate a fatigue growth law at micromechanical level to predict the onset of transverse cracking.