TIME-DEPENDENT MATRIX MULTI-FRACTURE OF SiC/SiC …€¦ · Ceramics-Silikáty 63 (2), 131-148...

Ceramics-Silikáty 63 (2), 131-148 (2019)www.ceramics-silikaty.cz doi: 10.13168/cs.2019.0005

Ceramics – Silikáty 63 (2) 131-148 (2019) 131

TIME-DEPENDENT MATRIX MULTI-FRACTURE OFSiC/SiC CERAMIC-MATRIX COMPOSITESCONSIDERING INTERFACE OXIDATION

LI LONGBIAO

College of Civil Aviation, Nanjing University of Aeronautics and AstronauticsNo.29 Yudao St., Nanjing 210016, PR China

E-mail: [email protected]

Submitted October 4, 2018; accepted January 7, 2019

Keywords: Ceramic-matrix composites (CMCs), Matrix multi-cracking, Time-dependent, Interface oxidation

In this paper, the time-dependent matrix multi-cracking of SiC/SiC ceramic-matrix composites (CMCs) has been investigated considering the fibre/matrix interface oxidation. The time-dependent interface oxidation length and temperature-dependent fibre/matrix interface shear stress in the oxidation and the de-bonded region, the interface de-bonded energy, the fibre and matrix modulus and the matrix fracture energy are considered in the analysis for the micro stress field, the interface debonding criterion and the critical matrix strain energy model. The effects of the fibre volume fraction, the fibre/matrix interface shear stress, the fibre/matrix interface frictional coefficient, the fibre/matrix interface de-bonded energy and the matrix fracture energy on the matrix multi-cracking density and the interface oxidation ratio of SiC/SiC composite are discussed for the different temperatures and oxidation time. The experimental matrix multi-cracking density and fibre/matrix interface oxidation ratio are predicted for unidirectional and mini SiC/SiC composites at different testing temperatures and oxidation time.

INTRODUCTION

Ceramic materials possess high specific strengthand a specific modulus at elevated temperatures. Buttheir use as structural components is severely limiteddue to their brittleness. Continuous fibre-reinforcedceramic-matrix composites (CMCs), by incorporating fibres in the ceramic matrices, not only exploit theirattractive high-temperature strength, but also reducethe propensity for catastrophic failure [1, 2, 3]. The en- vironment inside the hot section CMC componentsis harsh and the composite is typically subjected to complex thermomechanical loading, which can lead to matrix multi-cracking [4, 5]. These matrix cracks form paths for the ingressof the environmentoxidising thefibresandleadingtoaprematurefailure[6,7,8,9,10].The density and openings of these cracks depend on the fibre architecture, the fibre/matrix interface bondingintensity,theappliedloadandtheenvironments[11,12,13]. It is important todevelopanunderstandingof thematrixmulti-crackingdamagemechanismsatelevatedtemperatures considering the oxidation damage mecha-nisms. [14] Many researchers performed experimental and theoretical investigationson thematrixmulti-cracking

evolutionoffibre-reinforcedCMCs [15,16,17,18,19,20, 21]. Morscher et al. [22] established the relationships for the stress-dependent matrix cracking of a 2D SiC/SiC composite, which was related to the stress in the load-bearing SiC matrix. Morscher and Gordon [23] monitored the matrix cracking of a SiC/SiC matrix composite using acoustic emission (AE) and electrical resistance (ER). Racle et al. [24] established the rela-tionship between the characteristic time of a 25 % total fatigue lifetime and the beginning of the matrix cracking usingAE.However,inthestudiesmentionedabove,thetime-dependent matrix multi-cracking of the SiC/SiC composite at an elevated temperature considering theinterfaceoxidationhasnotbeeninvestigated. In this paper, the time-dependent matrix multi-crackingofaSiC/SiCcompositehasbeeninvestigatedconsidering the fibre/matrix interface oxidation. Thetime-dependent interface oxidation length and tempe-rature-dependent fibre/matrix interface shear stress inthe oxidation and de-bonded region, the interface de-bondedenergy,thefibreandmatrixmodulusandmatrixfracture energy are considered in the analysis for the microstressfield,theinterfacedebondingcriterionandthe criticalmatrix strain energymodel.The effects ofthefibrevolumefraction,thefibre/matrixinterfaceshear

https://doi.org/10.13168/cs.2019.0005

Li L.

132 Ceramics – Silikáty 63 (2) 131-148 (2019)

stress, the fibre/matrix interface frictional coefficient,the fibre/matrix interface de-bonded energy and thematrix fracture energy on the matrix multi-cracking densityandthefibre/matrixinterfaceoxidationratioofthe SiC/SiC composite are discussed for the differenttemperatures and oxidation time. The experimental matrix multi-cracking density and the fibre/matrixinterface oxidation ratio for the unidirectional and mini SiC/SiC composites at different testing temperaturesand oxidation time are predicted.

THEORETICAL ANALYSIS

Time-dependent stress analysis

ThecompositewiththefibrevolumefractionofVf is loaded by a remote uniform stress σ normal to the crack plane, as shown inFigure 1.Thefibre radius isrf, and the matrix radius is R (R = rf/Vf

1/2). The length of the unit cell is half a matrix crack spacing lc/2, and the interface oxidation length and interface de-bonded length are ζ and ld, respectively. The time-dependentfibre and matrix axial stress and the fibre/matrixinterface shear stress distributions can be determined using the following equations:

z l t Td c, ,exp , , ,

z l t T l t T × − ∈

V r V rmo d mo

z z t T

t T l t T t Tf i

f fT T2 , 2 , ,

V Vτ τσ ζ ζ σ

+ + − −

t T z t T z t T l t Tζ ζ ζ+ − ∈f if f2 , 2 , , , , ,T TV Vτ τ

2 , 0, ,ff

m f

dm f m f

m

m f m f

df

( , , )

2

TVV r

V r V rz t T

r

τζ

σ

ρ

∈

= −

( )

( ) ( )

( ) ( )

( )

( ) ( ) ( ) ( )

( )( )( )

( )( )

( )

f iT T2 2τ τ

τ ζ

τ ζ

z l t T, ,d cexp , , ,

z l t T l t T × − ∈

, , ,t T l t T t Tmo dV r rσ ζ ζ− − −

i d, , , ,T z t T l t T

, 0, ,T z t T f

mi

f f f

df

, ,2

2

Vz t T

r

ρτ

ρ

∈ ∈=

−

( )

( ) ( )

( ) ( ) ( )

( )( )

( )

( )

( )

( )

( ) ( )

T t 2

bϕ

( )ζ (t,T ) = φ1 (T ) 1 – exp –

Aτi (T ) = τ0 + µ

|αrf (T ) – αrm (T )|(Tm – T )

Aτf (T ) = τs + µ

|αrf (T ) – αrm (T )|(Tm – T )

Ec (T )σfo = σ + Ef (T )(αlc – αlf ) ΔT

Ef (T )

Ec (T )σmo = σ + Em (T )(αlc – αlm ) ΔT

Em (T )

d c× − ∈, ,z l t T l t T

exp , , ,z l t T

fo mo dV r r, , ,t T l t T t T

T Tf i2 2τ τσ σ ζ ζ

+ − − −

, , , , , ,V r r

t T z t T z t T l t Tζ ζ ζ

z z T

T Tf i2 2− − − ∈

τ τ

( )

( )f

f f

df f f

fm

f f f

df

2, 0

, ,

2

TV r

z t TV

r

τσ ζ

σ

σ

ρ

− ∈

= −

,

( )

( )

( )

( )

( )( ) ( ) ( )

( )( )( )

( )

( )( )( )

(1)

(2)

(3)

(5)

(6)

(7)

(8)

where

(4)

Time-dependent matrix multi-fracture of SiC/SiC ceramic-matrix composites considering interface oxidation


where Ef (T), Em (T) and Ec (T) denote the temperature-dependentfibre,matrixandcompositeelasticmodulus,respectively;αrf and αrmdenotethefibreandmatrixra- dial thermal expansion coefficient, respectively; αlf, αlm and αlcdenotethefibre,matrixandcompositeaxialthermalexpansioncoefficient,respectively;and∆T de-notesthetemperaturedifferencebetweenthefabricatedtemperature T0 and the testing temperature T1 (∆T = = T1 ‒T0).

Time-dependentfibre/matrixinterface debonding

The fracture mechanics approach is adopted in the presentanalysistodeterminethefibre/matrixinterfacede-bonded length. [25]

(9)

where F(= πrf2/Vf)denotes thefibre loadat thematrix

cracking plane; wf (z = 0) denotes the fibre axial dis-placement at the matrix cracking plane and v(z) denotes the relative displacement between the fibre and thematrix.Basedonthefibreandmatrixaxialstressdistri-butionasdescribedinEquations1and2,thefibreandmatrix axial displacements of wf (z) and wm (z) can be described using the following equations:

γd (T ) = – ∫ τi (T ) dz4�rf

F21

∂ld

∂wf (z = 0)∂ld

ld(t,T)

0

∂v (z)

c d

d d

, / 2 ,

l t T l t T

, , ,T Tf i2 2τ τ

, , ,l t T t T l t T

ζ ζ

T t T l t T tmo dσ ζ ζ + − − − f f f fE T V r r

f f fr E T E TT T l t Ti fo cτ σ

− − + −

f f f fd d, 2 , , ,l t T z t T l t T t T z

V E T r E T = − − − −

E Tw z dz

( )c ,f2

ff

f 2 2

2

f m

, ,

,2

l t T

z

z t T

T

r V

σ

τσ

ζ

ρ

=

∫

f

1 exp

T

rρ

− × − −

( )

( )

( )( )

( )

( )( )

( )

( )( )

( )

( )

( )

( ) ( ) ( ) ( )

( )

( ) ( )

( )

( )

( )

( )

( )

( )

( )

, / 2 ,

c d

l t T l t T

2 , 2 , ,V T V T

mo dT t T l t T t TE T r V r V

σ ζ ζ − − − −

( ),m2

mm

f f 2 2d

f m m

2f i mo cd d

f m m m

f f f if

m f m f m

, ,

2 , , ,

,, , ,

2

cl t T

z

z t Tw z dz

E T

V Tt T l t T t T z

r V E T

V T T l t Tl t T t T l t T

r V E T E T

r

σ

τζ ζ

τ σζ

τ τρ

=

= − −

+ − + −

∫

f

1 expr

ρ

− × − −

( )

( )

( )

( )

( )

( )

( )( )

( )

( )

( )

( )

( )

( )

( )

( )

( )( )( )

( )

( )

( )

( )

( )

( )

(10)

(11)

MatrixMatrix Fiber

Slip region

Oxidation region

Crack plane

τ iτ f

σ/Vf

z

Figure 1. The schematic of the shear-lag model considering the interface oxidation and debonding.

Li L.


Therelativedisplacementofv(z)betweenthefibreandthematrixcanbedescribedusingthefollowingequation:

Substituting wf (z = 0) and v(z) into Equation 9, leads to the following equation:

SolvingEquation13,thefibre/matrixinterfacede-bondedlengthcanbedeterminedbythefollowingequation:

τc iE T T − −

f f f m m fV E T r V E T E T

( )

c f 2 2d d

2d

f m m f

f c f imo d

m m f f f

, 2 , , ,

, ,

2 , 2 , ,

1 ex

v (z) = |wf (z) – wm (z)|

E T Tl t T z t T l t T t T z

l t T t Tr V E T E T

r E T T TT t T l t T t T

V E T E T r r

τσ ζ ζ

ζ

τ τσ ζ ζ

ρ

= − − − −

+ − − −

× − c d

f

, / 2 ,p

l t T l t Tr

ρ − −

( )

( )

( )

( )( )

( )( )

( )( ) ( )

( )( )

( ) ( )( )

( )

( )

( )

( )

( )

( )

( )( )

( )

( )

τ σV E T f f cV E T E T

σr V E T+ − =

t T t T− + +ρ ρf f f m m f m m fV E T r V E T E T V E T E Tf i c f c f iτ σ τ τ τr T E T T E T T T

ζ ζ, ,

f f f m m f

ζ ζ ζd d, , , , ,l t T t T t T l t T t TV E T r V E T E T

f m m f m m fr V E T E T V E T E T

T E T T Ti c f iτ σ τ τ− − + −

2 22c i c i

d d

22

f

f f

, , , ,

2

2

,

E T T E T Tl t T t T l t T t T

Tt T

τ τζ ζ

ρ

ζ

− + −

−2

f m md2 0

4Tγ

( ) ( )( ) ( )

( )( ) ( )

( )

( ) ( ) ( )( )( )

( )( )

( )( )

( )( )

( ) ( )( ) ( )

( ) ( )( ) ( )

( )

( ) ( )( ) ( )

( )

( ) ( ) ( ) ( )

( )( )( )

( )

( )( )

( )

t T l t T t T T

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23i c2f

d mo dm f

4, , 4 , , ,3

4 , , ,

,4 , , ,3 2

T TA V VU t T t T l t T t T t TE V r T V r

V T T t T l t T t Tr V

T l t TV l t T t T l t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ σ

= + −

+ −

+ − + −

( )

f mo f if fd mo

m f m f

c d

f

2f if f f

d mom f m f

22 , 2 , ,

, / 2 ,1 exp

2 , 2 , ,2

r T T TV VV r V r

l t T l t Tr

T Tr V Vt T l t T t T TV r V r

σ τ τζ ζ σ

ρ

ρ

τ τζ ζ σ

ρ

+ + − −

− × − −

+ + − −

c d

f

, / 2 ,1 exp 2

l t T l t Tr

ρ − × − −

( )

( ) ( )

( )

( ) ( ) ( )( )

( )( )( )

( )( )

( ) ( ) ( )

( )( )( )

( ) ( )( )

( )

( )( )( )

( ) ( )

( ) ( ) ( )

( )( )

( )( )

t T l t T t T T

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23i c2f

d mo dm f

4, , 4 , , ,3

4 , , ,

,4 , , ,3 2




τ τζ ζ ζ

τ τ ζ ζ

τζ σ

= + −

+ −

+ − + −

( )

f mo f if fd mo

m f m f

c d

f

2f if f f

d mom f m f

22 , 2 , ,

, / 2 ,1 exp

2 , 2 , ,2

r T T TV VV r V r

l t T l t Tr


σ τ τζ ζ σ

ρ

ρ

τ τζ ζ σ

ρ

+ + − −

− × − −

+ + − −

c d

f

, / 2 ,1 exp 2

l t T l t Tr

ρ − × − −

( )

( ) ( )

( )

( ) ( ) ( )( )

( )( )( )

( )( )

( ) ( ) ( )

( )( )( )

( ) ( )( )

( )

( )( )( )

( ) ( )

( ) ( ) ( )

( )( )

( )( )

t T l t T t T T

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23i c2f

d mo dm f

4, , 4 , , ,3

4 , , ,

,4 , , ,3 2




τ τζ ζ ζ

τ τ ζ ζ

τζ σ

= + −

+ −

+ − + −

( )

f mo f if fd mo

m f m f

c d

f

2f if f f

d mom f m f

22 , 2 , ,

, / 2 ,1 exp

2 , 2 , ,2

r T T TV VV r V r

l t T l t Tr


σ τ τζ ζ σ

ρ

ρ

τ τζ ζ σ

ρ

+ + − −

− × − −

+ + − −

c d

f

, / 2 ,1 exp 2

l t T l t Tr

ρ − × − −

( )

( ) ( )

( )

( ) ( ) ( )( )

( )( )( )

( )( )

( ) ( ) ( )

( )( )( )

( ) ( )( )

( )

( )( )( )

( ) ( )

( ) ( ) ( )

( )( )

( )( )

c iE T Tf m m f m m fT V E T r V E T E T

ζ γ= − + − − + d d, 1 ,l t T t T T2

f f2

i f c i

12 2r r

T V E T Tτ στ τ ρ ρ τ

( )( ) ( )

( )( ) ( )

( )( )

( )( )

( ) ( )

(12)

(13)

(16)

(14)

Time-dependent matrix multi-fracture

The temperature-dependent matrix strain energy can be described using the following equation: [26]

(15)

where Am is the cross-section area of the matrix in the unit cell. When the interface is partially de-bonded, substi-tuting the matrix axial stress in Equation 2 into Equation 15, the matrix strain energy can be described using the following equation:Um (t,T ) = ∫ ∫ σm (z,t,T ) dzdAm2Em (T )

1 lc(T )

Am 02



When the interface is completely de-bonded, the matrix strain energy can be described using the follo-wing equation:

(17)

The critical matrix strain energy of Umcr can be de-scribed using the following equation:

(18)

where K (k ∈ [0,1]) is the critical matrix strain energy parameter; l0 is the initial matrix crack spacing; and σmocr (T) can be described using the following equation:

(19)

where σcr (T) denotes the temperature-dependent critical stress corresponding to the composite’s proportional limitstressdefinedbytheACKmodel:[15]

(20)

where γm (T) denotes the temperature-dependent matrix fracture energy. Thematrixmulti-crackingevolutioncanbedeter-mined using the following equation:

Um (σ,t,T) = Ucrm (σcr,T) (21)

RESULTS AND DISCUSSIONS

The ceramic composite system of SiC/SiC is used forthecasestudyanditsmaterialpropertiesaregivenby: Vf = 30 %, rf =7.5μm,Ef = 230 GPa, γm=15J∙m-2, γd=0.4J∙m-2, τ0 = 10 MPa, αrf = 2.9 × 10-6K-1 and αlf = = 3.9 × 10-6K-1. The temperature-dependent SiC matrix elastic mo-dulus of Em (T) can be described using the following equation: [27]

(22)

The temperature-dependent SiC matrix axial and radial thermal expansion coefficients of αlm (T) and αrm (T) can be described using the following equation, respectively:[27]

(23)

The temperature dependent fibre/matrix interfacede-bonded energy of ζd (T) and the matrix fracture energy of ζm (T) can be described using the following equations,respectively:[28]

(24)

(25)

where To denotes the reference temperature; Tm denotes the fabricated temperature; γd

o and γmo denote thefibre/

matrix interface de-bonded energy and the matrix frac-ture energy at the reference temperature of To; and CP (T) can be described using the following equation:

CP (T) = 76.337 + 109.039 × 10-3 T – – 6.535 × 105 T--2 – 6.535 × 10-6 T-2 (26)

Theeffectsof thefibrevolumefraction, thefibre/matrixinterfaceshearstress,thefibre/matrixinterfacefrictional coefficient, the fibre/matrix interface de-bonded energy and the matrix fracture energy on the time-dependent matrix multi-cracking density and the interface oxidation ratio are discussed.

Effectofthefibrevolumefraction

The effect of the fibre volume fraction (i.e.,Vf = 25 %, 30 % and 35 %) on the time-dependent matrix multi-cracking and the fibre/matrix interface oxidationratio of the SiC/SiC composite at T =873K,973 Kand1073 K for the oxidation time of t = 1 h and 3 h are shown in Figure 2. When Vf = 25 % at T = 873 Kandt = 1 h, the matrix multi-cracking density increases from φ = 1.2/mm at σcr = = 110 MPa to φ = 11.9/mm at σsat = 120 MPa,andthefibre/matrixinterfaceoxidationratiodecreasesfromζ/ld = 6 % to ζ/ld = 3.4 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.67 mm at σcr = 110 MPa to φ = 10.7/mm at σsat =123 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 16.6 % to ζ/ld = 9.8 %. At T = 973 Kandt = 1 h, the matrix multi-cracking den-sity increases from φ = 0.24/mm at σcr = 104 MPa to φ = = 9.2/mm at σsat = 133 MPa, and the interface oxidation ratio decreases from ζ/ld = 16.7 % to ζ/ld = 9.5 %; and at

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23if

dm f

4, , 4 , , ,3

4 , , ,

4 , ,3

T TA V VU t T t T l t T t T t TE V r V r


TV l t T t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ

= + −

+ −

+ −

( )

( )( )

( )

( )

( )

( )( )

( )( )

( )

( )( ) ( ) ( )

αlm (T ) = αrm (T ) = +4.5246 · 10-9 T 3, T ∈ [125-1273 K]

5.0 · 10-6 / K, T > 1273 K

–1.8276 + 0.0178T – 1.5544 · 10-5 T 2

γ γd d

= −

o

m

o

o 1

T

PTT

PT

C T dTT

C T dT

∫∫

( )( )

( )

γ γm m

= −

o

m

o

o 1

T

PTT

PT

C T dTT

C T dT

∫∫

( )( )

( )

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23if

dm f

4, , 4 , , ,3

4 , , ,

4 , ,3



TV l t T t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ

= + −

+ −

+ −

( )

( )( )

( )

( )

( )

( )( )

( )( )

( )

( )( ) ( ) ( )

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23if

dm f

4, , 4 , , ,3

4 , , ,

4 , ,3



TV l t T t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ

= + −

+ −

+ −

( )

( )( )

( )

( )

( )

( )( )

( )( )

( )

( )( ) ( ) ( )

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23if

dm f

4, , 4 , , ,3

4 , , ,

4 , ,3



TV l t T t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ

= + −

+ −

+ −

( )

( )( )

( )

( )

( )

( )( )

( )( )

( )

( )( ) ( ) ( )

2 2f f3 2m f f

m dm m f m f

22f

f i df m

23if

dm f

4, , 4 , , ,3

4 , , ,

4 , ,3



TV l t T t TV r

τ τζ ζ ζ

τ τ ζ ζ

τζ

= + −

+ −

+ −

( )

( )( )

( )

( )

( )

( )( )

( )( )

( )

( )( ) ( ) ( )

Umcr (T ) = kAm l02

21Em (T )σmocr (T )

460

350T

962Em (T ) = 460 – 0.04T exp – , T ∈ [300-1773 K]

σmocr (T ) = σcr (T ) + Em (T ) [αlc (T ) – αlm (T )] ∆T Ec (T )

Em (T )

1/32 2f f c i m

cr c lc lm2f m m

6V E T E T T TT E T T T

r V E Tτ γ

σ α α

= − − ∆Τ

( )( ) ( ) ( )

( )( )

( ) ( ) ( )

1/32 2f f c i m

cr c lc lm2f m m

6V E T E T T TT E T T T

r V E Tτ γ

σ α α

= − − ∆Τ

( )( ) ( ) ( )

( )( )

( ) ( ) ( )

Li L.


t = 3 h, the matrix multi-cracking density increases from φ = 0.17/mm at σcr = 104 MPa to φ = 7.4/mm at σsat = = 140 MPa, and the interface oxidation ratio decreases from ζ/ld = 40.5 % to ζ/ld = 25.1 %. At T = 1073 Kand

t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 96 MPa to φ = 7/mm at σsat = 144 MPa, and the interface oxidation ratio decreases from ζ/ld = = 6.7 % to ζ/ld = 21.1 %; and at t = 3 h, the matrix multi-

100 120 140 1600

0.2

0.4

0.6

1.0

0.8

ζ (ld

)Stress (MPa)

T=873K/t=1hT=873K/t=3hT=973K/t=1hT=973K/t=3hT=1073K/t=1hT=1073K/t=3h

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


140 160 180 200 220120

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


140 160 180 200 220 240 260 280

100 120 140 160 1800

2

4

6

10

8

12

14

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


200 220 240120 140 160 1800

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


140 160 180 200 220 240 260 2800

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


Figure2.ThematrixcrackingdensityversustheappliedstresscurvesforthedifferentoxidationtemperatureandtimewhenVf = 25%(a),30%(c),35%(e);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperatureand time when Vf = 25 % (b), 30 % (d), 35 % (f).

b) Vf = 25 %

d) Vf = 30 %

f) Vf = 35 %

a) Vf = 25 %

c) Vf = 30 %

e) Vf = 35 %



cracking density increases from φ = 0.09/mm at σcr = = 96.3 MPa to φ = 5.0/mm at σsat = 144 MPa, and the interface oxidation ratio decreases from ζ/ld = 72.8 % to ζ/ld = 48.9 %. When Vf = 30 % at T = 873 Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.47/mm at σcr = 146 MPa to φ = 10.36/mm at σsat = 167 MPa, and thefibre/matrixinterfaceoxidationratiodecreasesfromζ/ld = 5.6 % to ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.35/mm at σcr = 146 MPa to φ = 3.4/mm at σsat = 170 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.6 % to ζ/ld = 9.3 %. At T =973K and t = 1 h, the matrix multi-cracking density increases from φ = 0.21/mm at σcr = 134 MPa to φ = 8.46/mm at σsat = 178 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.9 % to ζ/ld = 9.1 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 134 MPa to φ = 6.9/mm at σsat = 186 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 38.9 % to ζ/ld = 24.3 %. At T =1073K and t = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 122 MPa to φ = 6.7/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 35.7 % to ζ/ld = 20.7 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.09/mm at σcr = 122 MPa to φ = 4.8/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 71.5 % to ζ/ld = 48.2 %. When Vf = 35 % at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.35/mm at σcr = 180 MPa to φ = 9.75/mm at σsat = 215 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.5 % to ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.28/mm at σcr = 180 MPa to φ = 8.9/mm at σsat = 219 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.4 % to 9.2 %. At T =973Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 165 MPa to φ = 8.2/mm at σsat = = 223 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.9 % to ζ/ld = 9.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 165 MPa to φ = 6.7/mm at σsat = 234 MPa, and the interface oxidation ratio decreases from ζ/ld = 38.8 % to ζ/ld = 24.3 %. At T =1073Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 148 MPa to φ = 6.6/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 36 % to ζ/ld = 21 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.09/mm at σcr = 148 MPa to φ = 4.8/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 71.9 % to 48.7 %.

Effectofthefibre/matrixinterface shear stress

The effect of interface shear stress (i.e., τ0 = 15, 20 and 25 MPa) on the time-dependent matrix multi-crackingandthefibre/matrixinterfaceoxidationratioof

the SiC/SiC composite at T =873K,973Kand1073Kfor t = 1 h and 3 h are shown in Figure 3. When τ0 = 15 MPa at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.34/mm at σcr = 191 MPa to φ = 10.33/mm at σsat = 234 MPa, and the interface oxidation ratio decreases from ζ/ld = 6 % to ζ/ld = 3.5 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.27/mm at σcr = 191 MPa to φ = 9.3/mm at σsat = 240 MPa, and the interface oxidation ratio decreases from ζ/ld = 16.6 % to ζ/ld = 10.2 %. At T =973Kandt = 1 h, the matrix multi-cracking densi-ty increases from φ = 0.21/mm at σcr = 176 MPa to φ = = 8.7/mm at σsat = 245 MPa, and the interface oxidation ratio decreases from ζ/ld = 17.1 % to ζ/ld = 10.1 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 176 MPa to φ = 7/mm at σsat = = 258 MPa, and the interface oxidation ratio decreases from ζ/ld = 40.6 % to ζ/ld = 26.3 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 159 MPa to φ = 7/mm at σsat = = 239 MPa, and the interface oxidation ratio decreases from ζ/ld = 37.5 % to ζ/ld = 22.8 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 159 MPa to φ = 4.8/mm at σsat = 239 MPa, and the interface oxidation ratio decreases from ζ/ld = 71.7 % to ζ/ld = 50.9 %. When τ0 = 20 MPa at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.34/mm at σcr = 201 MPa to φ = 10.89/mm at σsat = 251 MPa, and the interface oxidation ratio decreases from ζ/ld = 6.5 % to ζ/ld = 3.9 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.27/mm at σcr = 201 MPa to φ = 9.7/mm at σsat = 260 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 17.7 % to ζ/ld = 11 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.22/mm at σcr = 186 MPa to φ = 9.26/mm at σsat =265 MPa, and the interface oxidation ratio decreases from ζ/ld = 18.2 % to ζ/ld = 11 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 186 MPa to φ = 7.3/mm at σsat = 280 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 42.3 % to ζ/ld = 28.1 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 169 MPa to φ = 7.4/mm at σsat = 254 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 39 % to ζ/ld = 24.5 %; and at t = 3 h, the mat-rix multi-cracking density increases from φ = 0.09/mm at σcr = 169 MPa to φ = 4.9/mm at σsat = 254 MPa, and the interface oxidation ratio decreases from ζ/ld = 72.1 % to ζ/ld = 52.9 %. When τ0 = 25 MPa at T =873Kandt = 1 h, the ma-trix multi-cracking density increases from φ = 0.35/mm at σcr = 211 MPa to φ = 11.4/mm at σsat = 270 MPa, and the interface oxidation ratio decreases from ζ/ld = 7 % to ζ/ld = 4.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.28/mm at σcr = 211 MPa to φ = 10.2/mm at σsat = 277 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 18.8 % to ζ/ld = 11.8 %.

Li L.


At T =973Kandt = 1 h, the matrix multi-cracking den-sity increases from φ = 0.23/mm at σcr = 195 MPa to φ = 9.7/mm at σsat = 282 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 19.3 % to ζ/ld = 11.8 %;

and at t = 3 h, the matrix multi-cracking density increa-ses from φ = 0.15/mm at σcr = 195 MPa to φ = 7.5/mm at σsat = 293 MPa, and the interface oxidation ratio de-creases from ζ/ld = 43.8 % to ζ/ld = 29.7 %. At T =1073K

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)Stress (MPa)


140 160 180 200 220 240 260 280 300

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)


300 320160 180 200 220 240 260 280Stress (MPa)

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


180 200 220 300 320240 260 280

300160 180 200 220 240 260 2800

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


300 320160 180 200 220 240 260 2800

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


0

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)


Stress (MPa)180 200 220 300 320240 260 280

Figure3. Thematrixcrackingdensityversus theapplied stresscurves for thedifferentoxidation temperatureand timewhen τ0=15MPa(a),20MPa(c),25MPa(e);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperature and time when τ0 = 15 MPa (b), 20 MPa (d), 25 MPa (f).

b) τ0 = 15 MPa

d) τ0 = 20 MPa

f) τ0 = 25 MPa

a) τ0 = 15 MPa

c) τ0 = 20 MPa

e) τ0 = 25 MPa



and t = 1 h, the matrix multi-cracking density increases from φ = 0.16/mm at σcr = 178 MPa to φ = 7.7/mm at σsat = 268 MPa, and the interface oxidation ratio decreases from ζ/ld = 40.4 % to ζ/ld = 26.1 %; and at t = 3 h, the ma-

trix multi-cracking density increases from φ = 0.09/mm at σcr = 178 MPa to φ = 5/mm at σsat = 268 MPa, and the interface oxidation ratio decreases from ζ/ld = 72.6 % to ζ/ld = 54.6 %.

0

0.2

0.4

0.6

0.8

0.1

0.3

0.5

0.7

ζ (ld

)Stress (MPa)


140 160 180 200 220 240 260 280

0

0.2

0.4

0.6

0.8

0.1

0.3

0.5

0.7

ζ (ld

)

Stress (MPa)


140 160 180 200 220 240 260 280

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


180 200 220140 160 240 260 280

140 160 180 200 220 240 260 2800

2

4

6

10

8

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


0

2

4

6

10

8

Mat

rix c

rack

ing

dens

ity (m

m-1

)


Stress (MPa)180 200 220140 160 240 260 280

140 160 180 200 220 240 260 2800

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


Figure4. Thematrixcrackingdensityversus theapplied stresscurves for thedifferentoxidation temperatureand timewhen τf=1MPa(a),3MPa(c),5MPa(e); the interfaceoxidation ratioversus theappliedstresscurves for thedifferentoxidationtemperature and time when τf = 1 MPa (b), 3 MPa (d), 5 MPa (f).

b) τf = 1 MPa

d) τf = 3 MPa

f) τf = 5 MPa

a) τf = 1 MPa

c) τf = 3 MPa

e) τf = 5 MPa

Li L.


The effect of interface shear stress (i.e., τf = 1, 3 and 5 MPa) on the time-dependent matrix multi-cracking and thefibre/matrix interfaceoxidationof theSiC/SiCcomposite at T =873K,973Kand1073Kfort = 1 h and 3 h are shown in Figure 4. When τf = 1 MPa at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.34/mm at σcr = 180 MPa to φ = 9.6/mm at σsat = 214 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.5 % to ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.27/mm at σcr = 180 MPa to φ = 8.6/mm at σsat = 220 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 15 % to ζ/ld = 9.1 %. At T =973Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.19/mm at σcr = 165 MPa to φ = = 7.9/mm at σsat = 225 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.4 % to ζ/ld = 9 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.13/mm at σcr = 165 MPa to φ = 6.3/mm at σsat = = 237 MPa, and the interface oxidation ratio decreases from ζ/ld = 36.2 % to ζ/ld = 23.3 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.13/mm at σcr = 148 MPa to φ = 6.3/mm at σsat = = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 33.5 % to ζ/ld = 20 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.07/mm at σcr = 148 MPa to φ = 4.2/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 62.7 % to ζ/ld = 44.3 %. When τf = 3 MPa at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.35/mm at σcr = 180 MPa to φ = 9.7/mm at σsat = 214 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.5 % to ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.28/mm at σcr = 180 MPa to φ = 8.7/mm at σsat =220 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.2 % to ζ/ld = 9.2 %. At T =973Kandt = 1 h, the matrix multi-cracking densi-ty increases from φ = 0.2/mm at σcr = 165 MPa to φ = = 8.0/mm at σsat = 224 MPa, and the interface oxidation ratio decreases from ζ/ld = 15.6 % to ζ/ld = 9.1 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 165 MPa to φ = 6.5/mm at σsat = 236 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 37.5 % to ζ/ld = 23.8 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 148 MPa to φ = 6.4/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 34.7 % to ζ/ld = 20.5 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.08/mm at σcr = 148 MPa to φ = 4.5/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 67 % to ζ/ld = 46.4 %. When τf = 5 MPa at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.35/mm at σcr = 180 MPa to φ = 9.7/mm at σsat = 214 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.5 % to

ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.29/mm at σcr =180 MPa to φ = 8.9/mm at σsat = 220 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 15.4 % to ζ/ld = 9.3 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 165 MPa to φ = 8.2/mm at σsat = 224 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 15.9 % to ζ/ld = 9.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 165 MPa to φ = 6.7/mm at σsat = 234 MPa, and the interface oxidation ratio de-creases from ζ/ld = 38.8 % to ζ/ld = 24.3 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr =148 MPa to φ = 6.6/mm at σsat = 222 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 36 % to ζ/ld = 21 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 148 MPa to φ = 4.8/mm at σsat = 222 MPa, and the interface oxidation ratio decreases from ζ/ld = 72 % to ζ/ld = 48.7 %.

Effectofthefibre/matrixinterfacefrictionalcoefficient

The effect of the fibre/matrix interface frictionalcoefficient (i.e., μ = 0.05, 0.1 and 0.15) on the time-dependent matrix multi-cracking and the fibre/matrixinterface oxidation ratio of the SiC/SiC composite at T =873K,973Kand1073Kfor t = 1 h and 3 h are shown in Figure 5. When μ = 0.05 at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 1.2/mm at σcr = 128 MPa to φ = 9.9/mm at σsat = 136 MPa, and the interface oxidation ratio decreases from ζ/ld = 4.9 % to ζ/ld = 2.7 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.71/mm at σcr = 128 MPa to φ = 9.2/mm at σsat = 138 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 13.8 % to ζ/ld = 7.9 %. At T = 973 K and t = 1 h, the matrix multi-crackingdensity increases from φ = 0.21/mm at σcr = 120 MPa to φ = 7.9/mm at σsat = 151 MPa, and the interface oxidation ratio decreases from ζ/ld = 14.5 % to ζ/ld = 7.9 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.16/mm at σcr = 120 MPa to φ = 6.7/mm at σsat = 156 MPa, and the interface oxidation ratio decreases from ζ/ld = 37.1 % to ζ/ld = 21.7 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 110 MPa to φ = 6.3/mm at σsat = = 162 MPa, and the interface oxidation ratio decreases from ζ/ld = 34.8 % to ζ/ld = 18.8 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 110 MPa to φ = 4.8/mm at σsat = 166 MPa, and the interface oxidation ratio decreases from ζ/ld = 73.7 % to ζ/ld = 46.1 %. When μ = 0.1 at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.47/mm at σcr = 146 MPa to φ = 10.3/mm at σsat = 167 MPa, and the



interface oxidation ratio decreases from ζ/ld = 5.6 % to ζ/ld = 3.2 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.35/mm at σcr = 146 MPa to φ = 9.4/mm at σsat = 170 MPa, and the interface oxida-

tion ratio decreases from ζ/ld = 15.6 % to ζ/ld = 9.3 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.21/mm at σcr = 134 MPa to φ = 8.4/mm at σsat = 178 MPa, and the interface oxidation

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)Stress (MPa)


140 160 180100 120 200

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


120 200 220140 160 180

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


180 200 220 240120 140 160

100 120 140 160 180 2000

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


160 180 200 220120 1400

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


0

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)


Stress (MPa)180 200 220 240120 140 160

Figure5. Thematrixcrackingdensityversus theapplied stresscurves for thedifferentoxidation temperatureand timewhen µ=0.05(a),0.10(c),0.15(e);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperatureand time when µ = 0.05 (b), 0.10 (d), 0.15 (f).

b) µ = 0.05

d) µ = 0.10

f) µ = 0.15

a) µ = 0.05

c) µ = 0.10

e) µ = 0.15

Li L.


ratio decreases from ζ/ld = 15.9 % to ζ/ld = 9.1 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 134 MPa to φ = 6.9/mm at σsat = 186 MPa, and the interface oxidation ratio decreases from ζ/ld = 38.9 % to ζ/ld = 24.3 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 122 MPa to φ = 6.7/mm at σsat = = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 35.7 % to ζ/ld = 20.7 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 122 MPa to φ = 4.8/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 71.5 % to ζ/ld = 48.2 %. When μ = 0.15 at T =873Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.4/mm at σcr = 160 MPa to φ = 10.9/mm at σsat = 193 MPa, and the interface oxidation ratio decreases from ζ/ld = 6.3 % to ζ/ld = 3.7 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.31/mm at σcr = 160 MPa to φ = 9.8/mm at σsat = 198 MPa, and the interface oxidation ratio decreases from ζ/ld = 17.1 % to ζ/ld = 10.5 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.22/mm at σcr = 147 MPa to φ = 8.9/mm at σsat = 201 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 17.2 % to ζ/ld = 10.2 %; and at t = 3 h, the matrix multi-cracking density increa-ses from φ = 0.15/mm at σcr = 147 MPa to φ = 7.2/mm at σsat = 212MPa, and the interface oxidation ratio decreases from ζ/ld = 40.7 % to ζ/ld = 26.5 %. At T =1073Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 132 MPa to φ = 7/mm at σsat = 198 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 36.9 % to ζ/ld = 22.4 %; and at t = 3 h, the matrix multi-cracking density increases from φ = = 0.09/mm at σcr = 132 MPa to φ = 4.8/mm at σsat = = 198MPa, and the interface oxidation ratio decreases from ζ/ld = 71 % to ζ/ld = 50.1 %.

Effectofthefibre/matrixinterfacede-bonded energy

The effect of the fibre/matrix interface de-bondedenergy (i.e., γd = 0.3, 0.5 and 0.7 J∙m-2) on the time-dependent matrix multi-cracking and the fibre/matrixinterface oxidation ratio of the SiC/SiC composite at T =873K,973Kand1073Kfor t = 1 h and 3 h are shown in Figure 6. When γd =0.3J∙m-2 at T =873Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.7/mm at σcr = 146 MPa to φ = 10.3/mm at σsat = 160 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.2 % to ζ/ld = 3.1 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.49/mm at σcr = 146 MPa to φ = 9.4/mm at σsat = 164 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 14.7 % to ζ/ld = 9.0 %. At T = 973 K and t = 1 h, the matrix multi-cracking

density increases from φ = 0.24/mm at σcr = 134 MPa to φ = 8.4/mm at σsat = 171 MPa, and the interface oxidation ratio decreases from ζ/ld = 14.7 % to ζ/ld = 8.7 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.16/mm at σcr = 134 MPa to φ = 6.9/mm at σsat = 179 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 36.5 % to ζ/ld = 23.3 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 122 MPa to φ = 6.7/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 32.6 % to ζ/ld = 19.6 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 122 MPa to φ = 4.8/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 67.3 % to ζ/ld = 46.3 %. When γd=0.5J∙m-2 at T =873Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.3/mm at σcr = 146 MPa to φ = 10.3/mm at σsat = 173 MPa, and the interface oxidation ratio decreases from ζ/ld = 5.9 % to ζ/ld = 3.3 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.29/mm at σcr = 146 MPa to φ = 9.4/mm at σsat = 176 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 16.5 % to ζ/ld = 9.6 %. At T =973Kandt = 1 h, the matrix multi-cracking den-sity increases from φ = 0.2/mm at σcr = 134 MPa to φ = = 8.4/mm at σsat = 184 MPa, and the interface oxidation ratio decreases from ζ/ld = 17.1 % to ζ/ld = 9.5 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 134 MPa to φ = 6.9/mm at σsat = 192 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 41.2 % to ζ/ld = 25.2 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 122 MPa to φ = 6.7/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 38.9 % to ζ/ld = 21.7 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm at σcr = 122 MPa to φ = 4.8/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 75.6 % to ζ/ld = 50 %. When γd=0.7J∙m-2 at T =873Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.3/mm at σcr =146 MPa to φ = 10.3/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 6.7 % to ζ/ld = 3.6 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.24/mm at σcr = 146 MPa to φ = 9.4/mm at σsat = 186 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 18.2 % to ζ/ld = 10.2 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 134 MPa to φ = 8.4/mm at σsat = 202 MPa, and the interface oxidation ratio decreases from ζ/ld = 19.7 % to ζ/ld = 10.3 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.15/mm at σcr = 134 MPa to φ = 6.9/mm at σsat = 202 MPa, and the interface oxidation ratio decrea-ses from ζ/ld = 46 % to ζ/ld = 27 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from



φ = 0.16/mm at σcr = 122 MPa to φ = 6.8/mm at σsat = = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 46 % to ζ/ld = 23.8 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.09/mm

at σcr = 122 MPa to φ = 4.9/mm at σsat = 183 MPa, and the interface oxidation ratio decreases from ζ/ld = 84.1 % to ζ/ld = 53.6 %.

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)


240100 120 140 160 180 200 220Stress (MPa)

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


120 200 220140 160 180

0

0.2

0.4

0.6

1.0

0.8

ζ (ld

)

Stress (MPa)


120 200 220140 160 180

160 180 200 220 240100 120 1400

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


160 180 200 220120 1400

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


0

2

4

6

10

8

12

Mat

rix c

rack

ing

dens

ity (m

m-1

)


Stress (MPa)180 200 220120 140 160

Figure6. Thematrixcrackingdensityversus theapplied stresscurves for thedifferentoxidation temperatureand timewhen γd=0.3J∙m-2(a),0.5J∙m-2(c),0.7J∙m-2(e);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperature and time when γd=0.3J∙m-2(b),0.5J∙m-2(d),0.7J∙m-2 (f).

b) γd=0.3J∙m-2

d) γd=0.5J∙m-2

f) γd=0.7J∙m-2

a) γd=0.3J∙m-2

c) γd=0.5J∙m-2

e) γd=0.7J∙m-2

Li L.


Effectofthematrixfractureenergy Theeffectofthematrixfractureenergy(i.e.,γm = 20, 25 and 30 J∙m-2) on the time-dependent matrix multi-crackingandthefibre/matrixinterfaceoxidationratioof

the SiC/SiC composite at T =873K,973Kand1073Kfor t = 1 h and 3 h are shown in Figure 7. When γm=20J∙m-2 at T =873Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.3/mm

0

0.2

0.4

0.6

0.8

0.1

0.3

0.5

0.7

ζ (ld

)Stress (MPa)


140 160 180 200 220 240120

Stress (MPa)


180 200 220140 160 240 260 2800

0.2

0.4

0.6

0.8

0.1

0.3

0.5

0.7

ζ (ld

)

0

0.2

0.4

0.6

0.8

0.1

0.3

0.5

0.7

ζ (ld

)


Stress (MPa)180 200 220 240 260160 280

0

2

4

6

10

8

Mat

rix c

rack

ing

dens

ity (m

m-1

)


Stress (MPa)180 200 220 240120 140 160

140 160 180 200 220 240 260 2800

2

4

6

8

1

3

5

7

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)


Stress (MPa)


180 200 220 240 260160 2800

2

4

6

8

1

3

5

7

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Figure7. Thematrixcrackingdensityversus theapplied stresscurves for thedifferentoxidation temperatureand timewhen γm=20J∙m-2(a),25J∙m-2(c),30J∙m-2(e);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperature and time when γm=20J∙m-2(b),25J∙m-2(d),30J∙m-2 (f).

b) γm=20J∙m-2

d) γm=25J∙m-2

f) γm=30J∙m-2

a) γm=20J∙m-2

c) γm=25J∙m-2

e) γm=30J∙m-2



at σcr = 162 MPa to φ = 8.4/mm at σsat = 195 MPa, and the interface oxidation ratio decreases from ζ/ld = 4.8% to ζ/ld = 2.8 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.24/mm at σcr = 162 MPa to φ = 7.8/mm at σsat = 199 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 13.6 % to ζ/ld = 8.2 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.18/mm at σcr =149 MPa to φ = 7.1/mm at σsat = 204 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 13.7 % to ζ/ld = 8 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.13/mm at σcr = 149 MPa to φ = 6/mm at σsat = 212 MPa, and the interface oxidation ratio decreases from ζ/ld = 34.4 % to ζ/ld = 21.6 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.13/mm at σcr = 135 MPa to φ = 5.8/mm at σsat = = 203 MPa, and the interface oxidation ratio decreases from ζ/ld = 30.9 % to ζ/ld = 18.2 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.08/mm at σcr = 135 MPa to φ = 4.3/mm at σsat = 203 MPa, and the interface oxidation ratio decreases from ζ/ld = 64.7 % to ζ/ld = 43.6 %. When γm=25J∙m-2 at T =873Kandt = 1 h, the ma-trix multi-cracking density increases from φ = 0.23/mm at σcr = 175 MPa to φ = 7.3/mm at σsat = 218 MPa, and the interface oxidation ratio decreases from ζ/ld = 4.3 % to ζ/ld = 2.6 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 175 MPa to φ = 6.8/mm at σsat = 222 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 12.2 % to ζ/ld = 7.5 %. At T =973Kandt = 1 h, the matrix multi-cracking den-sity increases from φ = 0.15/mm at σcr = 162 MPa to φ = 6.2/mm at σsat = 243 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 12.3 % to ζ/ld = 7.3 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.12/mm at σcr = 162 MPa to φ = 5.4/mm at σsat = 234 MPa, and the interface oxidation ratio de-creases from ζ/ld = 31.3 % to ζ/ld = 19.8 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.12/mm at σcr = 146 MPa to φ = 5.2/mm at σsat = 220 MPa, and the interface oxidation ratio decreases from ζ/ld = 27.7 % to ζ/ld = 16.5 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.08/mm at σcr = 146 MPa to φ = 4.0/mm at σsat = 220 MPa, and the interface oxidation ratio decreases from ζ/ld = 60 % to ζ/ld = 40.4 %. When γm =30J∙m-2 at T =873Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 187 MPa to φ = 6.5/mm at σsat = 239 MPa, and the interface oxidation ratio decreases from ζ/ld = 4 % to ζ/ld = 2.4 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.17/mm at σcr = 167 MPa to φ = 6.1/mm at σsat = 242 MPa, and the interface oxida-tion ratio decreases from ζ/ld = 11.3 % to ζ/ld = 6.9 %. At T = 973 K and t = 1 h, the matrix multi-cracking density increases from φ = 0.14/mm at σcr = 172 MPa to

φ = 5.6/mm at σsat = 243 MPa, and the interface oxidation ratio decreases from ζ/ld = 11.2 % to ζ/ld = 6.7 %; and at t = 3 h, the matrix multi-cracking density increases from φ = 0.11/mm at σcr = 172 MPa to φ = 4.9/mm at σsat = 253 MPa, and the interface oxidation ratio decreases from ζ/ld = 29.1 % to ζ/ld = 18.4 %. At T =1073Kand t = 1 h, the matrix multi-cracking density increases from φ = 0.11/mm at σcr = 156 MPa to φ = 4.8/mm at σsat = = 234 MPa, and the interface oxidation ratio decreases from ζ/ld = 25.4 % to ζ/ld = 15.3 %; and at t = 3 h, the ma-trix multi-cracking density increases from φ = 0.07/mm at σcr = 156 MPa to φ = 3.7/mm at σsat = 234 MPa, and the interface oxidation ratio decreases from ζ/ld = 56.3 % to ζ/ld = 37.9 %.

EXPERIMENTAL COMPARISONS

The experimental and theoretical matrix multi-cracking density and the fibre/matrix interface oxidation ratio of the unidirectional SiC/SiC [29] and mini SiC/SiC [30] composites composite at room temperature, T =773K,873K,973Kand1073Kfort = 1 h and 3 h are predicted, as shown in Figures 8 and 9.

The unidirectional SiC/SiC composite

Beyerleetal.[29]investigatedthedamageevolutionof the matrix multi-cracking in the unidirectional SiC/SiC composite. At room temperature, the matrix multi-crackingevolutionstartsatσcr = 240 MPa and approaches saturation at σsat = 320 MPa; and the matrix cracking density increases from φ = 1.1/mm to φ = 13/mm. At T =773K,thematrixmulti-crackingdensityin-creases from φ = 0.5/mm at σcr = 222 MPa to φ = 12.4/mm at σsat = 311 MPa; at T =773Kandt=1h,thematrixmulti-cracking density increases from φ = 0.36/mm at σcr = 222 MPa to φ = 11.9/mm at σsat = 272 MPa, and the interface oxidation ratio decreases from ζ/ld = 2 % at σcr = 222 MPa to ζ/ld = 1.1 % at σsat = 272 MPa; and at T =773Kandt=3h,thematrixmulti-crackingdensityin-creases from φ = 0.34/mm at σcr = 222 MPa to φ = 11.5/mm at σsat = 273 MPa, and the interface oxidation ratio de-creases from ζ/ld = 5.8 % at σcr = 222 MPa to ζ/ld = 3.4 % at σsat = 273 MPa. At T = 873 K, the matrix multi-cracking densityincreases from φ = 0.45/mm at σcr = 206 MPa to φ = = 11.2/mm at σsat = 288 MPa; at T =873Kandt = 1 h, the ma-trix multi-cracking density increases from φ = 0.25/mm at σcr = 206 MPa to φ = 10.3/mm at σsat = 288 MPa, and the interface oxidation ratio decreases from ζ/ld = 8.3 % at σcr = 206 MPa to ζ/ld = 4.6 % at σsat = 288 MPa; and at T =873Kandt = 3 h, the matrix multi-cracking density increases from φ = 0.21/mm at σcr = 206 MPa to φ = 9.4/mm at σsat = 288 MPa, and the interface oxidation ratio de-creases from ζ/ld = 22.3 % at σcr = 206 MPa to ζ/ld = 13 % at σsat = 288 MPa.

Li L.


At T =973K,thematrixmulti-crackingdensityin-creases from φ = 0.4/mm at σcr = 188 MPa to φ = 10.2/mm at σsat = 263 MPa; at T =973Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.21/mm at σcr = 188 MPa to φ = 8.8/mm at σsat =263 MPa, and the interface oxidation ratio decreases from ζ/ld = 26.3 % at σcr = 188 MPa to ζ/ld = 13.7 % at σsat = 263 MPa; and at T =973Kandt = 3 h, the matrix multi-cracking density in-creases from φ = 0.15/mm at σcr = 188 MPa to φ = 7.1/mm at σsat = 263 MPa, and the interface oxidation ratio decreases from ζ/ld = 57.2 % at σcr = 188 MPa to ζ/ld = = 34.5 % at σsat = 263 MPa. At T =1073K,thematrixmulti-crackingdensityin-creases from φ = 0.35/mm at σcr = 169 MPa to φ = 9.4/mm at σsat = 236 MPa; at T =1073Kandt = 1 h, the matrix multi-cracking density increases from φ = 0.2/mm at σcr = 169 MPa to φ = 7.7/mm at σsat = 236 MPa, and the

interface oxidation ratio decreases from ζ/ld = 65.7 % at σcr = 169 MPa to ζ/ld = 33.2 % at σsat = 236 MPa; and at T =1073Kandt = 3 h, the matrix multi-cracking density increases from φ = 0.11/mm at σcr = 169 MPa to φ = 5.2/mm at σsat = 236 MPa, and the interface oxidation ratio de-creases from ζ/ld = 1 at σcr = 169 MPa to ζ/ld = 68.1 % at σsat = 236 MPa.

The mini SiC/SiC composite

Zhangetal.[30]investigatedthedamageevolutionof the matrix multi-cracking in the mini-SiC/SiC com-posite. At room temperature, the matrix multi-cracking evolutionstartsfromtheappliedstressofσcr = 135 MPa and approaches saturation at σsat = 250 MPa; the matrix multi-cracking density increases from φ = 0.4/mm to φ = = 2.4/mm.

Stress (MPa)

T=773K/t=1hT=773K/t=3hT=873K/t=1hT=873K/t=3hT=973K/t=1hT=973K/t=3hT=1073K/t=1hT=1073K/t=3h

300160 180 200 220 320240 260 2800

0.2

0.4

0.6

1.0

0.8

1.2ζ

(ld)

220 24080 100 120 140 160 180 2000

0.1

0.2

0.3

0.5

0.4

0.6

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)

T = 973 K / t = 3 hT = 1073 K / t = 3 hT = 1173 K / t = 3 h

0

2

4

6

10

8

12

14

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)200 250 450300 350 400

Exp. dataRoom temp.T=773KT=773K/t=1hT=773K/t=3hT=873KT=873K/t=1hT=873K/t=3hT=973KT=973K/t=1hT=973K/t=3hT=1073KT=1073K/t=1hT=1073K/t=3h

320 36040 80 120 160 200 240 2800

0.5

1.0

1.5

2.5

2.0

3.0

Mat

rix c

rack

ing

dens

ity (m

m-1

)

Stress (MPa)

Experimental dataRoom temperatureT = 973 K / t = 3 hT = 1073 K / t = 3 hT = 1173 K / t = 3 h

Figure8. Theexperimentalandtheoreticalmatrixcrackingdensityversustheappliedstresscurvesfor thedifferentoxidationtemperatureandtime(a);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperatureandtime of the unidirectional SiC/SiC composite (b).

Figure9. Theexperimentalandtheoreticalmatrixcrackingdensityversustheappliedstresscurvesfor thedifferentoxidationtemperatureandtime(a);theinterfaceoxidationratioversustheappliedstresscurvesforthedifferentoxidationtemperatureandtime of the mini SiC/SiC composite (b).

b)

b)

a)

a)



At T =973Kandt = 3 h, the matrix multi-cracking density increases from φ = 0.06/mm at σcr = 112 MPa to φ = 2/mm at σsat = 140 MPa, and the interface oxidation ratio decreases from ζ/ld = 9.8 % to ζ/ld = 4.6 %. At T =1073Kandt = 3 h, the matrix multi-cracking density increases from φ = 0.04/mm at σcr = 98.4 MPa to φ = 1.9/mm at σsat = 136 MPa, and the interface oxidation ratio decreases from ζ/ld = 23.7 % to ζ/ld = 11.6 %. At T =1173Kandt = 3 h, the matrix multi-cracking density increases from φ = 0.03/mm at σcr = 83.4 MPa to φ = 1.7/mm at σsat = 133 MPa, and the interface oxidation ratio decreases from ζ/ld = 46.2 % to ζ/ld = 24.5 %.

CONCLUSIONS

In this paper, the time-dependent matrix multi-cracking of SiC/SiC composite has been investigatedconsidering the fibre/matrix interface oxidation. Theeffects of the fibre volume fraction, the fibre/matrixinterfaceshearstress,thefibre/matrixinterfacefrictionalcoefficient, thefibre/matrix interfacede-bondedenergyand the matrix fracture energy on the matrix multi-crackingdensityandthefibre/matrixinterfaceoxidationratio of the SiC/SiC composite have been discussedfor the different temperatures and oxidation time. Theexperimentalmatrixmulti-crackingdensityandthefibre/matrix interface oxidation ratio for the unidirectional and mini SiC/SiC composite at the different testingtemperaturesandoxidationtimehavebeenpredicted.Withanincreasingtemperature,thefirstmatrixcrackingstress of the SiC/SiC composite decreases due to the decreasing of the fibre/matrix interface shear stress inthe de-bonded region. Withanincreasingofoxidationtimeatanelevatedtemperature, the saturation matrix cracking density of the SiC/SiC composite decreases, due to the decreasing of the interface shear stress in the oxidation region.

Acknowledgements

The work reported here is supported by the Funda-mental Research Funds for the Central Universities (Grant No. NS2016070).

REFERENCES

1. Christin F. (2002): Design, fabrication, and application of thermostructural composites (TSC) like C/C, C/SiC, and SiC/SiC composites. Advanced Engineering Materials, 4(12), 903-912. doi: 10.1002/adem.200290001

2. Naslain R. (2004): Design, preparation and properties of non-oxide CMCs for application in engines and nuclear reactors:anoverview.Composites Science and Technology, 64(2), 155-170. doi: 10.1016/S0266-3538(03)00230-6

3. Zhu D. (2018). Aerospace ceramic materials: thermal, en-vironmental barrier coatings and SiC/SiC ceramic matrix composites for turbine engine applications. NASA/TM-2018-219884.

4. Cox B. N., Marshall D. B. (1996): Crack Initiation in Fiber‐Reinforced Brittle Laminates. Journal of the American Ceramic Society, 79(5), 1181-1188. doi: 10.1111/j.1151-2916.1996.tb08570.x

5. SevenerK.M.,TracyJ.M.,ChenZ.,KiserJ.D.,DalyS.(2017): Crack opening behavior in ceramic matrix com-posites. Journal of the American Ceramic Society, 100(10), 4734-4747. doi: 10.1111/jace.14976

6. Filipuzzi L., Camus, G., Naslain R., Thebault J. (1994): OxidationmechanismsandKineticsof1D‐SiC/c/SiC com-posite materials: I, an experimental approach. Journal of the American Ceramic Society, 77(2), 459-466. doi: 10.1111/ j.1151-2916.1994.tb07015.x

7. LamourouxF.,NaslainR.,JouinJ.M.(1994):Kineticsandmechanismsofoxidationof2DwovenC/SiCcomposites:II, theoretical approach. Journal of the American ceramic society, 77(8), 2058-2068. doi: 10.1111/j.1151-2916.1994.tb07097.x

8. VerrilliM.J.,OpilaE.J.,CalominoA.,KiserJ.D.(2004):EffectofEnvironmentontheStress‐RuptureBehaviorofaCarbon‐Fiber‐Reinforced Silicon Carbide Ceramic Matrix Composite. Journal of the American Ceramic Society, 87(8), 1536-1542. doi: 10.1111/j.1551-2916.2004.01536.x

9. HalbigM.C.,McGuffin‐Cawley J. D., Eckel A. J., Brewer D.N.(2008):OxidationKineticsandstresseffectsfortheoxidationofcontinuouscarbonfiberswithinamicrocrackedC/SiC ceramic matrix composite. Journal of the American ceramic society, 91(2), 519-526. doi: 10.1111/j.1551-2916. 2007.02170.x

10.Li.L.(2017):Modelingmatrixcrackingoffiber-reinforcedceramic-matrix composites under oxidation environmentatelevatedtemperature.Theoretical and Applied Fracture Mechanics, 87, 110-119. doi: 10.1016/j.tafmec.2016.11.003

11. Smith C. E., Morscher G. N., Xia Z. H. (2008): Monitoring damage accumulation in ceramic matrix composites using electrical resistivity. Scripta Materialia, 59(4), 463-466. doi: 10.1016/j.scriptamat.2008.04.033

12. Simon C., Rebillat F., Herb V., Camus G. (2017): Moni-toringdamageevolutionofSiCf/[SiBC]mcompositesusingelectrical resistivity: Crack density-based electromecha-nical modeling. Acta Materialia, 124, 579-587. doi: 10.10 16/j.actamat.2016.11.036

13.GowayedY.,OjardG.,SanthoshU., JeffersonG. (2015):Modeling of crack density in ceramic matrix composites. Journal of Composite Materials, 49(18), 2285-2294. doi: 10.1177/0021998314545188

14. Parthasarathy T. A., Cox B., Sudre O., Przybyla C., Cinibulk M.K.(2018):Modelingenvironmentallyinducedpropertydegradation of SiC/BN/SiC ceramic matrix composites. Journal of the American Ceramic Society, 101(3), 973-997. doi: 10.1111/jace.15325

15.AvestonJ.,CooperG.A.,KellyA.(1971).ThePropertiesof Fiber Composites. in: Proceedings of National Physical Laboratory. Guildford, IPC Science and Technology Press. pp. 15−26.

16.Beyerle D. S., Spearing S. M., Zok F.W., EvansA. G.(1992): Damage and failure in unidirectional ceramic-matrix composites. Journal of the American Ceramic Society, 75(10), 2719-2725. doi: 10.1111/j.1151-2916.1992.tb05495.x

Li L.


17.HolmesJ.W.,ChoC.(1992):ExperimentalObservationsof Frictional Heating in Fiber‐Reinforced Ceramics. Journal of the American Ceramic Society, 75(4), 929-938. doi: 10.1111/j.1151-2916.1992.tb04162.x

18.Kuo W. S., Chou T. W. (1995): Multiple Cracking ofUnidirectional and Cross‐PlyCeramic Matrix Composites. Journal of the American Ceramic Society, 78(3), 745-755. doi: 10.1111/j.1151-2916.1995.tb08242.x

19.LiL.(2017):Modelingfirstmatrixcrackingstressoffiber-reinforced ceramic-matrix composites considering fiberfracture. Theoretical and Applied Fracture Mechanics, 92, 24-32. doi: 10.1016/j.tafmec.2017.05.004

20.Li L. (2017): Synergistic effects of fiber debonding andfracture on matrix cracking in fiber-reinforced ceramic-matrix composites. Materials Science and Engineering: A, 682, 482-490. doi: 10.1016/j.msea.2016.11.077

21. Li L. (2018). Damage, fracture and fatigue of ceramic-matrix composites. Springer Nature Singapore Pte Ltd. doi: 10.1007/978-981-13-1783-5

22.MorscherG.N.,SinghM.,KiserJ.D.,FreedmanM.,BhattR. (2007): Modeling stress-dependent matrix cracking and stress–strain behavior in 2D woven SiC fiber reinforcedCVI SiC composites. Composites Science and Technology, 67(6), 1009-1017. doi: 10.1016/j.compscitech.2006.06.007

23. Morscher G. N., Gordon N. A. (2017): Acoustic emission and electrical resistance in SiC-based laminate ceramic com-posites tested under tensile loading. Journal of the Euro- pean Ceramic Society, 37(13), 3861-3872. doi: 10.1016/ j.jeurceramsoc.2017.05.003

24. Racle E., Godin N., Reynaud P., Fantozzi G. (2017): Fatigue lifetime of ceramic matrix composites at intermediate tem-perature by acoustic emission. Materials, 10(6), 658. doi: 10.3390/ma10060658

25.GaoY.C.,MaiY.W.,CotterellB.(1988):Fractureoffiber-reinforced materials. Zeitschrift für angewandte Mathe-matik und Physik ZAMP, 39(4), 550-572. doi: 10.1007/BF00948962

26. Solti J.P., Mall S., Robertson D. D. (1995): Modeling damage in unidirectional ceramic-matrix composites. Com-posites Science and Technology, 54(1), 55-66. doi: 10.1016/ 0266-3538(95)00041-0

27.SneadL.L.,NozawaT.,KatohY.,ByunT.S.,KondoS.,Petti D. A. (2007): Handbook of SiC properties for fuel per-formance modeling. Journal of Nuclear Materials, 371(1-3), 329-377. doi: 10.1016/j.jnucmat.2007.05.016

28. Wang R., Li W., Li D., Fang D. (2015): A new temperatu-re dependent fracture strength model for the ZrB2–SiC composites. Journal of the European Ceramic Society, 35(10), 2957-2962. doi: 10.1016/j.jeurceramsoc.2015.03. 025

29.Beyerle D. S., Spearing S. M., Zok F.W., EvansA. G.(1992): Damage and failure in unidirectional ceramic–matrix composites. Journal of the American Ceramic Society, 75(10), 2719-2725. doi: 10.1111/j.1151-2916.1992.tb05495.x

30. Zhang S., Gao X., Chen J., Dong H., Song Y. (2016): Strength model of the matrix element in SiC/SiC com-posites. Materials & Design, 101, 66-71. doi: 10.1016/j.matdes.2016.03.166

TIME-DEPENDENT MATRIX MULTI-FRACTURE OF SiC/SiC …€¦ · Ceramics-Silikáty 63 (2), 131-148...

Documents

Transcript of TIME-DEPENDENT MATRIX MULTI-FRACTURE OF SiC/SiC …€¦ · Ceramics-Silikáty 63 (2), 131-148...