SiC/SiC Creep Strengtharies.ucsd.edu/LIB/MEETINGS/0001-SiCSiC/Serizawa.pdf · 0.08 0.10 0.12 mm)...

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


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


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.


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.


C

PLB

h3hδ

P Reinforcement plateAdhesive

Substrate Plating thin film

Schematic Illustration of Peeling Test


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.


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


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


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


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


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.


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.


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.


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.


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.


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.


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.


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.

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