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Joining and Welding Research Institute, Osaka University
H. Serizawa and H. MurakawaJoining and Welding Research Institute,
Osaka University
SiC/SiC Creep Strength- New FEM Analysis of Time-Dependent Crack Growth
in SiC/SiC Composites -
International Town Meeting on SiC/SiCDesign and Material Issues for Fusion Systems
Oak Ridge National Laboratory, January 18-19,2000
Joining and Welding Research Institute, Osaka University
Fiber Bridging Zone in SiC/SiC Composites
&
SiC/SiC CompositePre-existing Cracks (or Pores)
caused by manufacturing methods (CVI, CVD, PIP)
Structural MaterialsVarious Loads are Applied
Fiber Bridging Zone1) Matrix Cracking2) Fiber Bridge Cracks3) Fiber Creep
Joining and Welding Research Institute, Osaka University
Creep of SiC/SiC Composites
Methods of estimating the crack propagation in compositesprevious methods … microscopicnew method … macroscopic
crack growthdetermined by the creep rate of
bridging fibersModeling in this study
Fiber
MatrixCrack
Fiber Bridging Zone → Interface Elements
Other Zone → Ordinary Elements
(Interface Potential )mf φφφ +≡
・One interface element was assumed to represent many fibers and matrices in bridging zone.・Interface potential was defined as same as the simple rule of mixture.
Joining and Welding Research Institute, Osaka University
Interface Element
Potential function(Lennard-Jones type potential energy)
+
−
+
=nn
rr
rr
δδγφ
0
0
2
0
0 22
:surface energy per unit areaδ :crack openingγ2
n , 0
r :material constants
before crack propagation during crack propagation
maxσ
Forc
e
Displacement
Relation between crack openingdisplacement and bonding stress
A A
BB
CC
DD
A
A
B
B
CC
DD
δ・ The fracture behavior can be regarded as the formation of a new surface, which is represented by interface element based on the interface potential energy.
Joining and Welding Research Institute, Osaka University
C
PLB
h3hδ
P Reinforcement plateAdhesive
Substrate Plating thin film
Schematic Illustration of Peeling Test
Joining and Welding Research Institute, Osaka University
0 5 10 15 20 25 30Displacement (mm)
0
5
10
15
20
25
Load
(N)
ComputationExperiment
r0 = 0.5 mmn = 4
2γ = 0.4 kN/mE = 60 GPah = 1.21 mm
2γ = 0.3 kN/mE = 33 GPah = 0.94 mm
Comparison between Experiment and Computation
・The computational results excellently agreed with the experimental results.
Joining and Welding Research Institute, Osaka University
Interface Potential of Interface Element
One Interface Element
Many Fibers and Matrices in Bridging Zone
+
⋅−
+
⋅≡
+
⋅−
+
⋅≡
+≡
n
m
mn
m
mmm
n
f
fn
f
fff
mf
rr
rr
rr
rr
δδγφ
δδγφ
φφφ
0
0
2
0
0
0
0
2
0
0
22
22
Interface Potential
Time Dependency
Joining and Welding Research Institute, Osaka University
Objectives
To develop a new Time-Dependent Interface Elementfor introducing the creep property of fibersinto the interface element
To apply the Time-Dependent Interface Elementfor analyzing time-dependent crack growthespecially slow crack growth of SiC/SiC composite
Joining and Welding Research Institute, Osaka University
Theory of Two Methods (General and New)
displacement increment of interface element
ce δδδ ∆+∆=∆:eδ∆
:cδ∆
elastic displacement incrementcreep displacementincrement
tA mc ∆⋅⋅=∆ σδassumption
(creep law):σ stress:t∆ time increment
potential function
( )
+
−
+
=n
ef
fn
ef
ff
ef r
rr
rδδ
γδφ0
0
2
0
0 22
:σ stress:t∆ time increment
increment of 0fr
tBr mf ∆⋅⋅=∆ σ0
initial value : 0fr
assumption
( ) ( )( )
( )( )
+
−
+
=n
f
fn
f
fff tr
trtr
trt
δδγδφ
0
0
2
0
0 22,
potential function
General New
Joining and Welding Research Institute, Osaka University
fiber
Theory of New Method
∗ increment of ∗ initial value :
:σ stress:t∆ time increment
0frtBrf ∆⋅⋅=∆ σ0
0frassumption
potential function
bonding stress
( ) ( )( )
( )( )
+
−
+
+
+
−
+
=n
m
mn
m
mm
n
f
fn
f
ff r
rr
rtr
trtr
trt
δδγ
δδγδφ
0
02
0
0
0
0
2
0
0 2222,
( )( )
( )( )
( )
+
−
+
⋅+
+
−
+
⋅=
∂∂
++++ 12
0
01
0
0
0
12
0
0
1
0
0
0
44 n
m
mn
m
m
m
m
n
f
fn
f
f
f
f
rr
rr
rn
trtr
trtr
trn
δδγ
δδγ
δφ
matrix
Joining and Welding Research Institute, Osaka University
a
3.4
5.5
4050
20
(unit:mm)
Load
Initial Crack Length : a = 1.1
Schematic Illustration of Four-Point Bending Test
・The reinforcements of the composites were 2-dimensional, plain-weave Hi-Nicalon fiber mats, which were stacked in the direction of thickness, and the matrices were deposited by chemical vapor infiltration.・The crack propagated from the tip of the notch in the direction, which is parallel to the applied load.
Joining and Welding Research Institute, Osaka University
Load
Interface Elements Ordinary Elements
x
yA
B
Model and Mesh Division for Analysis
・Because of the symmetry of the problem, only the half of the specimen was used.・The time dependent interface elements were arranged along the crack propagation path.・Only the mode-I type crack propagation parallel to y-axis was taken into account according to the experimental results.
Joining and Welding Research Institute, Osaka University
0.0x100
5.0x104
1.0x105
1.5x105
2.0x105
Time (s)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Disp
lace
men
t (m
m)
Displacement-Time Curve during Time-DependentCrack Growth in SiC/SiC Composite
SiC/SiC Composites1200℃, Ar (<20ppm O2)Applied Load = 556 N
・The area in time-displacement curve, where the displacement was more than 0.06 mm, was compared with calculation results since the rate of change of the displacement, with respect to time, was minimal.
Joining and Welding Research Institute, Osaka University
0.0x100
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
Time (s)
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Disp
lace
men
t (m
m)
ExperimentComputation (General)Computation (New)
s/Nm103.3s/Nm103.8
mm02.0 ,kN/m5.02mm06.0 m,/kN182
318
3200
0
⋅=⋅=====
−
−
xBxA
rr
mm
ff
γγ
Comparison between Experiment and Computationsin Time-Dependent Crack Growth
・Although both calculation results simulated the stage-II slow crack growth, the result using the new method represented not only the stage-II slow crack growth but also the stage-III crack growth.
Joining and Welding Research Institute, Osaka University
0.0x100
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
Time (s)
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Disp
lace
men
t (m
m)
200 N
556 N700 N
800 N
s/Nm103.3mm02.0 ,kN/m5.02mm06.0 m,/kN182
3180
0
⋅=====
−xBrr
mm
ff
γγ
Calculated Displacement-Time Curvesunder Various Applied Load
・The transition time from stage-II to stage III decreased with increasing applied load, similar to the general creep deformation. Therefore the new method is considered to be useful for analyzing such a creep behavior.
Joining and Welding Research Institute, Osaka University
6.0E+2
4.0E+22.0E+20.0-2.0E+2-4.0E+2-6.0E+2-8.0E+2-1.0E+3
44000 s
134000 s
248300 s
(MPa)
Deformations and Stress Distributionnear Crack Path
・The crack propagation behavior was clearly demonstrated and the stress relaxation behavior at the crack tip was also calculated.
Joining and Welding Research Institute, Osaka University
A B
-400-300-200-100
0100200300400500600700
Stre
ss (
MPa
)
44000 sFiberMatrix
-400-300-200-100
0100200300400500600700
Stre
ss (
MPa
)
FiberMatrix
134000 s
-400-300-200-100
0100200300400500600700
Stre
ss (
MPa
)
248300 sFiberMatrix
Stress Changes of Fiber and Matrixalong Crack Path
・The stress of matrix became almost zero. On the other hand, thestress of fiber maintained around 200 MPa after the crack propagated since the fiber was assumed to continue to creep.
Joining and Welding Research Institute, Osaka University
Conclusion
In order to analyze crack propagation behavior in SiC/SiC composite, a new computer simulation method using time dependent interface elements was developed and applied to time-dependent crack growth in SiC/SiC composites. The conclusions can be summarized as follows.
(1) The time-dependent crack growth in SiC/SiC composite was simulated by two methods, in which the creep property was introduced into the interface elements according to :
1) the general method of FEM analysis2) a new method making the best use of the potential function.
In both cases, the stage-II slow crack growth of a general creep deformation was simulated.
(2) By using the new method, not only the stage-III crack growth but also transition phenomena from stage-II to stage-III could be simulated. So the new method is considered to have the potential capability to model all stages of time-dependent crack growth behavior in SiC/SiC composite.