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.