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Modeling of crack growth initiation in wood timber: an approach by the G q v integral. DUBOIS Frédéric. MECHANICS AND MODELLING OF MATERIALS AND STRUCTURES OF CIVIL ENGINEERING University of Limoges, Civil Engineering Department, Egletons, France. - PowerPoint PPT Presentation
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UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
DUBOIS Frédéric
Modeling of crack growth initiation in wood timber:
an approach by the Gv integral
MECHANICS AND MODELLING OF MATERIALS AND STRUCTURES OF CIVIL ENGINEERING
University of Limoges, Civil Engineering Department, Egletons, France
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
DUBOIS Frédéric
Modeling of crack growth initiation in wood timber:
an approach by the Gv integral
MECHANICS AND MODELLING OF MATERIALS AND STRUCTURES OF CIVIL ENGINEERING
University of Limoges, Civil Engineering Department, Egletons, France
Thermodynamic approach
Modeling of the linear viscoelastic behavior
Viscoelastic fracture algorithm
Numerical validation
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Thermodynamic approach
Thermodynamic functions for viscoelasticity
t
0
klijklij dtJt
Elastic strain energy
dVttUV
e F
klij
t
0
ijklt
0
ddt2J
tJ2
2
1tF
Energy balance
vise WUW
V eU visW
WS
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Thermodynamic approach
Thermodynamic functions for viscoelasticity
t
0
klijklij dtJt
Energy balance
V eU visW
WS
vise WUW
Viscous dissipation work
dVdtWV
vis
t
-0
D
klij
t
0
t
0
ddt2Jt D
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Thermodynamic approach
Griffith fracture energy balance
Ue Wvis
V
Ws
Wa a
state (a)
state (b)
a
W
a
W
a
U
a
W svise
svisew GGGG
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Thermodynamic approach
Viscoelastic energy release rate
Ue Wvis
V
Ws
W
svisew GGGG
Energy release rate
a
UG e
v
Viscoelastic energy release rate
Ws
Crack growth initiation criterion
sv GG
a
G
a
G sv
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Modeling of the linear viscoelastic behavior
Incremental formulation
oijkl
1ijkl
mijkl
Mijkl
kl kl
ijkl
oijklk
1ijklk m
ijklk M
ijklk
1ijkl m
ijkl M
ijkl
oijkl
1ijkl
mijkl
Mijkl
kl kl
ijkl
oijklk
1ijklk m
ijklk M
ijklk
1ijkl m
ijkl M
ijkl
1m
M
mijkl
oijklijkl
l,kijklij
Finite difference integration 1nnn t~tt M
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Modeling of the linear viscoelastic behavior
Finite element algorithm
1~
ntFntextFntuTK
dT BMBTK 1 dntT
ntF 1~
1~ MB
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Free energy partition
dVttUV
e F
klij
t
0
ijklt
0
ddt2J
tJ2
2
1tF
dVk2
1
dVk2
1
dVk
2
1
k2
1
U
V
mkl
mij
mijkl
M
1m
V
okl
oij
oijkl
V
M
1m
mkl
mij
mijkl
okl
oij
oijkl
e
dVk2
1
dVk2
1
dVk
2
1
k2
1
U
V
mkl
mij
mijkl
M
1m
V
okl
oij
oijkl
V
M
1m
mkl
mij
mijkl
okl
oij
oijkl
e
+ Kelvin Voigt properties
Viscoelastic fracture algorithm
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Viscoelastic energy release rate partition
a
UG e
v
dV
V
mkl
mij
mijklk
a
M
m
dV
V
okl
oij
oijklk
a
dV
V
M
m
mkl
mij
mijklk
okl
oij
oijklk
avG
2
1
1
2
11
2
1
2
1
dV
V
mkl
mij
mijklk
a
M
m
dV
V
okl
oij
oijklk
a
dV
V
M
m
mkl
mij
mijklk
okl
oij
oijklk
avG
2
1
1
2
11
2
1
2
1
Viscoelastic fracture algorithm
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Viscoelastic energy release rate partition
M
m
mvGo
vGvG
1dV
V
pkl
pij
pijklk
apvG
2
1
Elastic energy release rate definition
a
peUp
vG
dVttUV
p
e pF p
klpij
pijkl
p k2
1 F
Viscoelastic fracture algorithm
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Path-independent Integral G
Viscoelastic fracture algorithm
klijijklkW 2
1
a
WG
G
1x
2x
Failure zone
1x
2x
Failure zone
dCC jkkiuijkkWG ,,,
02
11
02
01
C
02
11
02
01
C
pvGGeneralization for
²
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Path-independent Integral Gv
Viscoelastic fracture algorithm
dCC jkkiuijkkWG ,,,
klijijklkW 2
1pkl
pij
pijkl
p k2
1 F
a
W
Ga
peUp
vG
dCuGC
j,kp
k,i
p
ijk,kpp
v
F
M
m
mvGo
vGvG
1
pij
pijklk
lk
pij
,
Elastic stress :
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Geometry and mesh definition
Numerical validation
200mm
200mm
100mm
tP
tP
Mesh details around the crack tip
Crack
P t 10MPa
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
oJJ tt
Viscoelastic properties
Numerical validation
200/exp1580/exp121 ttt
LRGRRERRELR
RRELRLLE
/100
0/1/
0//1
oJMPa15000ELL
MPaRRE 600
MPaLRG 700
4.0LR
Pine spruce
Creep function
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Creep loading : analytic solution
Numerical validation
Correspondence principletC
K)t(G
2 t87,19tG
Gv method
200/t200/t
80/t80/t
vexp2exp5
exp2exp28136.0tG
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Creep loading : analytic solution
Numerical validation
0
20
40
60
80
100
120
140
160
180
0 100 200 300 400 500 600 700 800 900 1000
Time (min)
Ene
rgy
rele
ase
rate
(N
/mm
-1)
Correspondence principleAnalytic solution
GGv
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Creep loading : numerical simulation by Gv
Numerical validation
0
20
40
60
80
100
120
140
160
180
0 100 200 300 400 500 600 700 800 900 1000
Time (min)
Vis
coel
asti
c en
ergy
rel
ease
rat
e (N
mm
-1)
Analytic solutionNumeric simulation
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Creep loading : Path-independence integration for Gv
Numerical validation
Crack lips
C6C5C4C3C2
Crack lips
C6C5C4C3C2
Crown C1 C3 C5 C7simulation error 11,15% 0,73% 0,64% 0,58%
Crown C9 C11 C13 C15simulation error 0,54% 0,51% 0,49% 0,47%
Crown C17 C19 C21 C23simulation error 0,45% 0,44% 0,42% 0,41%
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Conclusion
Conclusion and Perspectives
Separation of the free energy and the viscous dissipation
for the crack growth initiation process
Development of the new path-independence integral Gv
Adaptation of the approach with an orthotropic viscoelastic behavior algorithm using the finite element method
Development of the energy partition by using a generalized Kelvin Voigt model for the mechanical behavior
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
Perspectives
Conclusion and Perspectives
Generalization for mixed mode fracture by using a M integral type
Adaptation for the crack growth process
Generalization for aging behavior for the mechano-sorptive effects
UNIVERSITE
DE LIMOGES
Mechanics and Modeling of Materials and Structures of Civil Engineering University of Limoges, Boulevard Jacques Derche, 19300 Egletons, France
DUBOIS Frédéric
Modeling of crack growth initiation in wood timber:
an approach by the Gv integral
MECHANICS AND MODELLING OF MATERIALS AND STRUCTURES OF CIVIL ENGINEERING
University of Limoges, Civil Engineering Department, Egletons, France
