FIBRE-MATRIX DEBONDING IN TRANSVERSE CYCLING LOADING...
Transcript of FIBRE-MATRIX DEBONDING IN TRANSVERSE CYCLING LOADING...
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
Fatigue is by far the most common type of failure of structures in service
Fatigue in structures
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
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
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
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
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.
Ø 20 µm
Increasingload
cycles
Ø
Single-fibre composite test
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.
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
-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
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
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
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
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)
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)
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
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
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
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
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
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)
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.
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
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.