delamination under high cycle fatigue composite
TRANSCRIPT
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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
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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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