Simulation of delamination under high cycle fatigue in...

Albert Turon, Josep CostaAMADE. Universitat de Girona

Pedro P. CamanhoDEMEGI. Universidade do Porto

Carlos G. DávilaNASA Langley Research Center

Simulation of delamination under high cycle fatigue in composite materials

COMPTEST200610th-12th April. Universidade do Porto

COMPTEST2006 10th-12th April. Universidade do Porto

Girona


Introduction

• Delamination: Interlaminar crack formation and/or propagation

Approaches to the study of delamination:

(1) Direct application of Fracture Mechanics Delamination propagationVirtual Crack Closure Technique (VCCT), J integral …

(2) Damage Mechanics Initiation and propagation of delaminationCohesive Zone Model approach, based on the Dugdale-Barenblatt concept: A

cohesive damage zone -or softening plasticity- is developed ahead of the crack tip

• There are numerical tools to analyze initiation or propagation of delamination under quasi-static loading, but “not” under cycling load.


• Quasi - static model

• High cycle fatigue

• Damage evolution law

• Cycle jump strategy

• Results

• Conclusions

OUTLINE


Quasi static model


Damage Mechanics models

Constitutive equations model the constitutive behaviour of the cohesive zone.

τInitiation criteria

Propagation criteria 21 3 4 5P

P

Δ0 ΔF Δ

1

2

4 5

3K

(1-d)K

0

τ0

Gc


( ) ( )λλ

λλ

∂∂=

∂∂=

t.tt.. Grr,Frd

( )

( ) ( )( )0ft

0tft

tt

ss

0t

rrrG

rGd

ts0max,rmaxr

ΔΔΔΔ

λ

−−=

=

≤≤⎭⎬⎫

⎩⎨⎧=

( ) ( ) 0, ; 0, ; ..

=≤≥ tttt rFrrFr λλ0

• Kuhn-Tucker conditions for loading/unloading/neutral load conditions

• Evolution of internal variables

Initiation

Propagation

d = 0.9d = 0.5d = 0.1

�3

�shear

Damage evolution under quasi-static loading


Implemented using Decohesion Elements

• Zero-thickness elements placed at the interfaces of Solid Elements

• Simulate the cohesive forces of the interface

In different element technologies such as

• Elements with Embedded Interfaces

Finite element implementation


0

100

200

300

400

500

600

700

800

0 2 4 6 8 10 12

Displacement [mm]

Load

[N]

ENF

MMB (GII/GT=50%)

MMB (GII/GT=20%)

Experimental

Numerical

MMB (GII/GT=80%)

DCB

Simulation results


Simulation results (II)

x

25º

25º-25º

-25º

90º90º

25 mm

0.7

92

mm

z

yF

F


High cycle fatigue


Fatigue loading

�max

�min

�

�

(1-d )k0

1

2

t

u1

2

1

2

t

u

• Low cycle fatigue Cycle by cycle analyses

• High cycle fatigue

• Damage evolution with the number of cycles

• Cycle jump strategy

cyclicstatic ddd +=


• … a damage evolution law as a function of the number of cycles isestablished a priori, Peerling’s law, for example:

→ The parameters of the law (C, λ, β) have to be adjusted calibrating the whole numerical model with experimental results.

• In this presentation: The evolution of the damage variable was derived by linking Fracture Mechanics and Damage Mechanics to relate damage evolution to crack growth rates.

Damage evolution with the number of cycles

βλ

ΔΔ⎟⎠⎞

⎜⎝⎛

=∂∂

a

CeN

dd


The evolution of the damage variable is related with the evolution of the crack surface:

Different approaches:

(1) Damage Mechanics

(2) Fracture Mechanics

Damage evolution with the number of cycles (II)

NA

AN ∂∂

∂∂=

∂∂ d

d

dd

AAdd =

A1

A=

∂∂

d

d

cGAA Ξ=d

Ξ∂∂=

∂∂ dd

d AG

Ac

Δ

τ

Ξ

(1-d)K

Δ0 Δf


…the crack growth rate equals to the sum of the damaged surface growth rate in the cohesive zone:

…the area of the cohesive zone can be computed using Rice’s model:

Damage evolution with the number of cycles (III)

NA

AN ∂∂

∂∂=

∂∂ d

d

dd

NA

AA

NA

NA CZ

Ae

e

CZ∂∂≈

∂∂=

∂∂ ∑

∈

dd

NA

AA

NA

CZ ∂∂=

∂∂ d

( )23

329

oCZGEbA

τπ=


→ Experimental characterization

Crack growth rate

log(dA/dN)

log(ΔG)

Region IIIRegion IIRegion I

ΔGth

Gc

1m

m

cGGC

NA

⎟⎠

⎞⎜⎝

⎛=

∂∂ Δ

NA

AA

NA

CZ ∂∂=

∂∂ d


ΔG is computed from the constitutive equation

Crack growth rate (II)

Δ

τ

ΔG

ΔmaxΔminΔ0 Δf

Δ

τ

Gmax

Δmax

Δ

τ

Gmin

Δmin

m

cGGC

NA

⎟⎠

⎞⎜⎝

⎛=

∂∂ Δ

1

2

t

u


Different approaches:

(1) Damage Mechanics

(2) Fracture Mechanics

Summary of damage evolution under cyclic loading

NA

AN ∂∂

∂∂=

∂∂ d

d

dd

AAdd =

cGAA Ξ=d

NA

AN CZ ∂∂=

∂∂ 1d

NA

AG

N CZ

c

∂∂

Ξ∂∂=

∂∂ dd

cyclicstatic ddd +=

Experimental

Constitutive model


Determination of cycle jump ΔNi

→ Fixed→ Variable

Integration of the constitutive equation

Cycle jump strategy

i

i

i1i NN

Δ∂∂+=+ ddd

maxdd ΔΔ ≤∂∂ i

iN

N

t

u ΔNi-1 ΔNi ΔNi+1


Two elements connected by only one decohesion element:

Results


Crack growth velocity under mode I loading:

Results (II)


• A thermodynamically consistent Interface Damage Model has been formulated.

• The Interface Damage Model has been modified to simulate high cycle fatigue loading.

• The evolution of the damage variable was derived by linking Fracture Mechanics and Damage Mechanics.

• The model reproduce test data without the need of additional parameters that are typically used in other fatigue growth models.

Concluding remarks

Simulation of delamination under high cycle fatigue in...

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