LaminateFatigueDamageandFiberFracture · 2017-01-23 · LaminateFatigueDamageandFiberFracture G.Eyer1,C.Hochard1;2,O.Montagnier1;3,J-P.Charles1;2 1:LaboratoiredeMécaniqueetd’Acoustique,Marseille,France

Laminate Fatigue Damage and Fiber Fracture

G. Eyer1, C. Hochard1,2, O. Montagnier1,3, J-P. Charles1,2

1 : Laboratoire de Mécanique et d’Acoustique, Marseille, France

2 : Université d’Aix-Marseille, Marseille, France

3 : Centre de Recherche de l’Armée de l’Air, Salon de Provence, France

Objectives

Failure prediction of laminated structuresTraction, shear, compression...Static and fatigue loadsVarious materials

Gabriel Eyer 1 / 16 ICFC 2015

Objectives

Failure prediction of laminated structuresTraction, shear, compression...Static and fatigue loadsVarious materials

1- Material behaviorDamage evolution

Fiber failure

2- Structure behaviorNon local criteria


Objectives

Micro-Cracks

e1

e2

Speech of C. Hochard :

Matrix Damage Under

Combined Transverse/Shear

Loads in Static and Fatigue


Fiber failure



Objectives

e1

e2

Fiber failure


Fiber failure



Objectives

Micro-Cracks

e1

e2 ⇒e1

e2

Fiber failure


Fiber failure


Gabriel Eyer 1 / 16 ICFC 2015x

Objectives

Micro-Cracks

e1

e2 ⇒e1

e2

Fiber failure


Fiber failure


Gabriel Eyer 1 / 16 ICFC 2015x

Outline

1- Influence of damage on fiber failure=⇒ Homogeneous case

• Experimental set up• Experimental results for traction and compression• Model

2- Link with the structure=⇒ Case of a stress concentration

• Motivation• Experimental results


Influence of fatigue damage on fiber failureMethod

Measure of the initial stiffnessCompute the damageEffect of damage on tensile strengthAnd what about compression ?

F2

time

F2-F2e1

e2

σ2

ε2E20


+/- θ

+/- θ



E2 = E2 (1 - d)0

Damage

F2

time

F2-F2

σ2

ε2E2

Micro-Cracks

e1

e2


+/- θ

+/- θ



F1

time

F1

-F1

e1

e2

σ1

ε1

σ1max

ε1max

?Gabriel Eyer 3 / 16 ICFC 2015

u

u



d

σ1max

?1




F1

time

F1

-F1

e1

e2

-σ1

-ε1

σ1min

?ε1min


u

u



dσ1min

1

?Gabriel Eyer 3 / 16 ICFC 2015

Influence of fatigue damage on fiber failureExperimental set up

d = dtarget

Cyclic Torsional Load

No

Monitored by image correlation

Compressive test

Yes

Tensile test

Fibers aligned ?No Static Torsional Load

Method used to introduce damage Digital Image Correlation device

Material : woven carbon/epoxy (0◦ in the direction of the tube)

Cyclic Load → High damageDigital Image Correlation device

Damage measurementHomogeneous field (strain, damage)Fibers alignmentGabriel Eyer 4 / 16 ICFC 2015

Influence of fatigue damage on fiber failureExperimental set up

d = dtarget

Cyclic Torsional Load

No

Monitored by image correlation

Compressive test

Yes

Tensile test

Fibers aligned ?No Static Torsional Load

Method used to introduce damage

-0.04 -0.02 0 0.02 0.04-50

0

50

Shear Strain (%)

Equ

ival

ent S

tres

s (M

Pa) d = 0.00

d = 0.63d = 0.95

~ 500 cycles

~ 1000 cycles

Damage measurement : d = 1 − E

E0

Material : woven carbon/epoxy (0◦ in the direction of the tube)

Cyclic Load → High damageDigital Image Correlation device

Damage measurementHomogeneous field (strain, damage)Fibers alignmentGabriel Eyer 4 / 16 ICFC 2015

Influence of fatigue damage on fiber failureTensile test

0 1 2 30

20

40

60

Displacement (mm)

Ten

sile

load

(kN

)

Undamaged tubeDamaged tube (d~0.75)

Behavior of the material with two different damages

Modelisation⇓σ11 = E11.ε11

Results

Linear materialStiffness is not affected by the damageStrength decreases when damage increases



0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

Damage

Ulti

mat

e te

nsile

str

ain

(%)

Evolution of the ultimate tensile strain versus the damage

Modelisation⇓if d ≤ 0.8 εmax11(d) = εmax11(d=0)

else εmax11(d) = εmax11(d=0) . k

Results

Linear materialStiffness is not affected by the damageStrength decreases when damage increases


k < 1


Confirmation with a quantitative test (temperature ↗)

σmax = 800MPa

Safe 1055/ES18 Material under tension

σmax = 320MPa

Uncured 1055/ES18 Material under tension

σmax = 480MPa

Post cured at 190◦ 1055/ES18 Material under tension



Confirmation with a quantitative test (temperature ↗)

0 50 100 150 2000

250

750

1000

Temperature (°C)

Experiments

Ten

sile

str

engt

h (M

Pa)

500

GlassTemperature

Temperature ⇔ DamageStrength decreases according to the temperature


Influence of fatigue damage on fiber failureCompressive test

-1.5 -1 -0.5 0-600

-500

-400

-300

-200

-100

0

Strain (%)

Equ

ival

ent S

tres

s (M

Pa) d = 0.00

d = 0.63d = 0.95Failure

d = 0.25d = 0.50

Behavior of the material with different damages

Modelisation⇓σ11 = E11.ε11.(1+ α.ε11)

Results

Non linear behaviorStiffness is not affected by the damageCompressive strength is significantly affected by the damage


Influence of fatigue damage on fiber failureCompressive test

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

DamageUlti

mat

e co

mpr

essi

ve s

trai

n (%

)

Model : εc=εd=0.(1-d)Experiments

Evolution of the ultimate tensile strain versus the damage

Modelisation⇓εmin11(d) = ε

min11(d=0).(1− d)

Results

Non linear behaviorStiffness is not affected by the damageCompressive strength is significantly affected by the damage


Outline


• Description of the set up• Experimental results for traction and compression• Model

2- Link with the structure=⇒ Case of a stress concentration=⇒ Focus on compressive results

• Motivation• Experimental results


Link with the structureMotivation

Compressive test : plate with a hole

0 0.5 1 1.5 2 2.5 3 3.5-2.5

-2

-1.5

-1

-0.5

0

x (mm)

Loca

l str

ain

(%) ε∞

εmin

εminhomogeneous

Local strain : plate with a hole

Non local criteria

High local strainLocal criteria⇒ Underestimate the structureNon local criteria

"Point stress""Average stress"

ε =1

V

∫V

ε V = g(Lc)

⇒ New parameter : Lc = f(d) ?


Link with the structureMotivation

Compressive test : plate with a hole

Local strain : plate with a hole

Non local criteria

High local strainLocal criteria⇒ Underestimate the structureNon local criteria

"Point stress""Average stress"

ε =1

V

∫V

ε V = g(Lc)

⇒ New parameter : Lc = f(d) ?


Link with the structureMethod

Different samples for different strain fields

Width = 20mm

Length = 80 −→ 150mm

Thickness = 6.7mm (52plies) (to avoid buckling)Material : UD T700/M21



Introduction of the damage (with images...)

Pi

u

-u

u

Time

Damage

Time

Stop the cyclic load

d1

d4

d3

d2

Different damages for each plate Pi



Introduction of the damage (with images...)

Pi

Compressive testPi1

Fibers are aligned in the direction of the sampleTests have to be performed for each plate Pi


Link with the structureUndamaged samples

Comparison of the different samples

0 0.5 1 1.5 2 2.5 3 3.5-2.5

-2

-1.5

-1

-0.5

0

Loca

l str

ain

(%)

x (mm)

Caracteristic length (point stress)

εmin

Local criteria is not efficientIntroduction of a characteristic length

Ld=0c = 0.5mm et εd=0min ∼ −1.5%

Very sensitive parameter with a point stress method !Gabriel Eyer 13 / 16 ICFC 2015

Link with the structureUndamaged samples


0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

Characteristique length (average stress)

εmin

Ave

rage

d st

rain

(%

)

x (mm)

Local criteria is not efficientIntroduction of a characteristic length

Ld=0c = 1mm et εd=0min ∼ −1.5%

Less sensitive parameter for the average stress method !Gabriel Eyer 14 / 16 ICFC 2015

Link with the structureDamaged samples


0 1 2 3 4 5-2

-1.5

-1

-0.5

Distance du bord (mm)

Déf

orm

atio

n lo

cale

inte

rpol

ée (

%)

Longueur caractéristique (point stress)

, Characteristic length is not affected by damageLP−Sc ∼ 0.5mm et LA−Sc ∼ 1mm

, Good agreement with the model identified on tubes


Link with the structureDamaged samples


0 0.2 0.4 0.6 0.8 1-1.5

-1

-0.5

0

Damage

Ulti

mat

e co

mpr

essi

ve s

trai

n (%

)

Model identified with tubes

Experiments

, Characteristic length is not affected by damageLP−Sc ∼ 0.5mm et LA−Sc ∼ 1mm

, Good agreement with the model identified on tubes


Summary


• Stiffness is not affected by damage• Tensile strength decreases with very high damage• Compressive strength decreases significantly with damage

2- Link with the structure=⇒ Case of a stress concentration

• Introduction of a characteristic length• Lc does not evolve according to the damage• Validation of the identified model


Thank you.

I’ll do my best to answer your questions.

Laminate Fatigue Damage and Fiber Fracture

G. Eyer1, C. Hochard1,2, O. Montagnier1,3, J-P. Charles1,2

1 : Laboratoire de Mécanique et d’Acoustique, Marseille, France

2 : Université d’Aix-Marseille, Marseille, France

3 : Centre de Recherche de l’Armée de l’Air, Salon de Provence, France

More slides ?

Micro-mechanics approach

First Micromodel - Rosen 1964⇓Postulate⇓

Micro-buckling of fibers

, Matrix stiffness is a very sensitiveparameter

σmin = −E2

1− νf= −

E02.(1− d2)

1− νf

/ Bad agreement with experiments



"Kink-Band"

Budiansky and Fleck 1993Garland et al 2001Jumahat et al 2001Feld et al 2001

... ...

, Improvement of the modelPlasticityMatrix damageAlignment of fibers...

/ ± Predictive model

⇒ Damage plays an important role !Need to be compared to experiments



"Kink-Band"


... ...






"Kink-Band"


... ...





Experiments on tubesHow to avoid of the buckling ?

Numerical predictions of the buckling loads are complex !Imperfections,Non-linear material...

An experimental method is proposed (based on analytic results)

σbuckle =E√

3(1−ν2)

tR

E : Young Modulus

t : Thickness

R : Mean radius

ν : Poisson factor Failure caused by

BUCKLING

0 1 2 3 4 5 6 7 8 99 10 11 12 13 14 150

500

1000

1500

2000

2500

3000

3500

Number of plies

Equ

ival

ent S

tres

s (M

Pa)

Buckling without knockdown factorBuckling with knockdown factorMaterial rupture

Failure caused by

MATERIAL

Theoretical curve σfailure = f(nplies)


Experiments on tubesHow to avoid of the buckling ?

Numerical predictions of the buckling loads are complex !Imperfections,Non-linear material...

An experimental method is proposed (based on analytic results)

σbuckle =E√

3(1−ν2)

tR

E : Young Modulus

t : Thickness

R : Mean radius

ν : Poisson factor Failure caused by

MATERIALFailure caused by

BUCKLING

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

Number of plies

Equ

ival

ent

Str

ess

(MP

a)Theoretical buckling without KdFTheoretical buckling with KdFMaterial strengthExperimental stress leading to failure

3 5 7 9 11

Theoretical curve σfailure = f(nplies)


Samples with stress concentrationUndamaged samples

Method to interpolate the strain

x

y

εyy = 0.0 %

εyy= -1.7 %

0 2 4 6 8 10-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Position de la facette suivant l'axe horizontal (mm)

Déf

orm

atio

n da

ns l'

axe

de l'

épro

uvet

te (

%)

mesureinterpolation

Measure is complex close to the edge of the sampleInterpolation is neededDetermination of the degree of the polynomial with a FEsimulationIdentification of the coefficient with DIC


Samples with stress concentrationUndamaged samples

Method to interpolate the strain

x

y

εyy = 0.0 %

εyy= -1.7 %

0 2 4 6 8 10-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Position de la facette suivant l'axe horizontal (mm)

Déf

orm

atio

n da

ns l'

axe

de l'

épro

uvet

te (

%)

mesureinterpolation

Measure is complex close to the edge of the sampleInterpolation is neededDetermination of the degree of the polynomial with a FEsimulationIdentification of the coefficient with DIC


ManufacturingTubes

Pompe à vide

Aluminium

Composite

Peel ply

Feutre

Sac à vide

Tissu thermorétractable

Cured in a oven (4 hours)Temperature = 180◦

Compaction = Vacuum + Thermo-shrinkable tissue + Thermaldilatation (aluminum)


Test on plates ±45◦

Side effects

ε=0.0 %

ε=0.4 %

Zone homogène

Effet de bord

Effet de bord

Measure with DIC

Followed with DICHomogeneous field in the middle


Documents

LaminateFatigueDamageandFiberFracture · 2017-01-23 · LaminateFatigueDamageandFiberFracture G.Eyer1,C.Hochard1;2,O.Montagnier1;3,J-P.Charles1;2 1:LaboratoiredeMécaniqueetd’Acoustique,Marseille,France