Delamination Under High Cycle Fatigue Composite

8/10/2019 Delamination Under High Cycle Fatigue Composite

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Albert Turon, Josep Costa

AMADE. Universitat de Girona

Pedro P. CamanhoDEMEGI. Universidade do Porto

Carlos G. Dvila

NASA Langley Research Center

Simulation of delamination under high cycle

fatigue in composite materials

COMPTEST200610th-12th April. Universidade do Porto


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COMPTEST2006 10th-12th April. Universidade do Porto

Girona


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Introduction

Delamination: Interlaminar crack formation and/or propagation

Approaches to the study of delamination:

(1) Direct application of Fracture Mechanics Delamination propagation

Virtual Crack Closure Technique (VCCT), J integral

(2) Damage Mechanics Initiation and propagation of delamination

Cohesive Zone Model approach, based on the Dugdale-Barenblatt concept:Acohesive 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.


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Quasi static model


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Damage Mechanics models

Constitutive equations model the constitutive behaviour of the cohesive

zone.

Initiation criteria

Propagation criteria21 3 4 5

P

P

0 F

1

2

4 5

3K

(1-d)K

0

0

Gc


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=

=

t.tt.. Gr

r,Frd

( )

( ) ( )( )0ft

0tft

tt

ss

0t

r

rrG

rGd

ts0max,rmaxr

=

=

=

( ) ( ) 0,;0,; .. = tttt rFrrFr 0

Kuhn-Tucker conditions forloading/unloading/neutral load conditions

Evolution of internal variables

Initiation

Propagation

d = 0.9d = 0.5

d = 0.1

3

shear

Damage evolution under quasi-static loading


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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


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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


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Simulation results (II)

x

25

25-25

-25

9090

25 mm

0.7

92mm

z

yF

F


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High cycle fatigue


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Fatigue loading

max

min

(1-d )k0

1

2

t

u

1

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 +=


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a damage evolution law as a function of the number of cycles is

established a priori, Peerlings law, for example:

The parameters of the law (C, , ) 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 torelate damage evolution to crack growth rates.

Damage evolution with the number of cycles

=

a

CeN

dd


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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)

N

A

AN

=

d

d

dd

A

Ad

d=A

1

A=

d

d

cGA

A =d

=

dd

d A

G

Ac

(1-d)K

0

f


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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 Rices model:

Damage evolution with the number of cycles (III)

N

A

AN

=

d

d

dd

NA

AA

NA

NA CZ

Ae

e

CZ

=

dd

NA

AA

NA

CZ =

d

( )23

32

9

oCZ

GEbA

=


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G is computed from the constitutive equation

Crack growth rate (II)

G

max

min

0

f

Gmax

max

Gmin

min

m

cG

GC

N

A

=

1

2

t

u


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Different approaches:

(1) Damage Mechanics

(2) Fracture Mechanics

Summary of damage evolution under cyclic loading

N

A

AN

=

d

d

dd

A

Ad

d=

cGA

A =d

N

A

AN CZ

=

1d

N

A

A

G

N CZ

c

=

dd

cyclicstatic ddd +=

Experimental

Constitutive model


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Determination of cycle jump Ni

Fixed

Variable

Integration of the constitutive equation

Cycle jump strategy

i

i

i1i NN

+=+

ddd

maxd

d

i

i

N

N

t

u Ni-1 Ni Ni+1


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Two elements connected by only one decohesion element:

Results


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Crack growth velocity under mode I loading:

Results (II)


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Delamination Under High Cycle Fatigue Composite

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