Sharif Rahman The University of Iowa Iowa City, IA 52245 tochastic Multiscale Fracture Analysis of 3D Functionally Graded Media 2009 ASME PVP Conference, Prague, Czech Republic, July 2009 Work supported by NSF (CMS-0409463) Arindam Chakraborty Structural Integrity Associates San Jose, CA 95138
Fracture reliability of 3D graded composite using novel statistical method
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Sharif RahmanThe University of Iowa
Iowa City, IA 52245
Stochastic Multiscale Fracture Analysis of 3D Functionally Graded Media
2009 ASME PVP Conference, Prague, Czech Republic, July 2009
intensityConstituent properties of SiC & Al indep. LN variables(Means of E: 419.2, 69.7 GPa; Means of : 0.19, 0.34)
= i =1 kN/cm2; o = 0.6 kN/cm2
Part. rad. = 0.48 cm
Nearly700 RVs( = 0.4)
EXAMPLE
Global Responses (Two Samples)
Sample 1 Sample 2
EXAMPLE Mode-I SIFs (Univariate)
0 5 10 15 20
KI, MPa m1/2
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
10 20 30 40 50
KI, MPa m1/2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
10 20 30 40 50 60 70
KI, MPa m1/2
0.00
0.02
0.04
0.06
0.08
0.10
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
AB
16 cm
16
cm
8 cm
4 cm
C
o
i
Crack
1x
2x
3x
EXAMPLE Modes-II and –III SIFs (Univariate)
-16 -14 -12 -10 -8 -6 -4 -2 0
KII, MPa m1/2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
0 5 10 15 20
KII, MPa m1/2
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
-6 -4 -2 0 2 4 6 8
KII, MPa m1/2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Prob
abil
ity
dens
ity
func
tion
Concurrent (=0.4)
Concurrent (=0.2)
0 2 4 6 8 10
KIII, MPa m1/2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40P
roba
bili
ty d
ensi
ty f
unct
ion
Concurrent (=0.4)
Concurrent (=0.2)
0 2 4 6 8 10 12 14
KIII, MPa m1/2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
0 2 4 6 8 10
KIII, MPa m1/2
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Pro
babi
lity
den
sity
fun
ctio
n
Concurrent (=0.4)
Concurrent (=0.2)
0 10 20 30 40 50 60 70
KIc, MPa m1/2
10 -3
10 -2
10 -1
10 0
PF(K
Ic)
Tip C
Tip A
Tip B
=0.2
=0.4
EXAMPLE
Conditional Probability of Fracture Initiation
A
B
16 cm
16
cm
8 cm
4 cm
C
o
i
Crack
1x
2x
3x
CONCLUSIONS/FUTURE WORK
A moment-modified polynomial dimensional decomposition method was developedFourier-polynomial expansionsMCS/control variatemoment-modified random output
Efficiently generates SIF distributions
Probability of fracture initiation varies significantly along the crack front
Future work: Crack growth, cohesive zone models, particle-matrix debonding, dynamic & thermal fracture, etc.