Crack opening model for unidirectional ceramic matrix composites at elevated temperature

Author’s Accepted Manuscript Crack opening model for unidirectional ceramic matrix composites at elevated temperature C.-P. Yang, F. Jia

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S0272-8842(18)31616-X https://doi.org/10.1016/j.ceramint.2018.06.172 CERI18616

To appear in: Ceramics International Received date: 22 April 2018 Accepted date: 20 June 2018 Cite this article as: C.-P. Yang and F. Jia, Crack opening model for unidirectional ceramic matrix composites at elevated temperature, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.06.172 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Crack opening model for unidirectional ceramic matrix composites at elevated temperature C. -P. Yang a*, F. Jia b a

Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, China b

School of Mechano-Electronic Engineering, Xidian University, Xi’an, China

Abstract: Crack opening displacement (COD) is a key parameter determining the gas diffusion regime and the associated oxidation kinetics of ceramic matrix composites (CMCs) in high temperature oxidative atmosphere. In this paper, COD of an isolated tunneling crack in unidirectional CMCs is formulated based on shear-lag theory. The model simultaneously considers the coupling effects of applied stress, environmental temperature and interface degradation. Both the elastic constants of the constituents and the interface slipping stress are regarded as temperature-dependent parameters. And, interface recession length was introduced to quantify oxidation effect on crack opening behavior of CMCs. Reasonability of the model was validated by comparing the predictions with experimental data of single tow SiC/BN/SiC composites. Besides, parametric analysis was performed with C/SiC composites, revealing that tension stress contributes to open matrix crack, while temperature acts the opposite . But, temperature effect on crack healing is weakened by interfacial friction. With aggravated interface oxidation, matrix crack closure can hardly be achieved for new interface debonding generates, resulting in linear increase of crack opening. Key word: ceramic matrix composites (CMCs); crack opening displacement (COD); elevated temperature *

Corresponding author. Email: [email protected] (C. –P. Yang) 1

1. Introduction Continuous fiber reinforced ceramic matrix composites (CMCs) have been proposed as advanced materials suitable for aerospace and gas turbine engine parts [1]. Therefore, the service environment for such materials involves high temperature and oxidative gases. Unfortunately, a large amount of original porosities and thermal cracks have been observed existing in CMCs [2]. Moreover, when external load is imposed, new coating and matrix cracks will generate, except for the extension of the original ones. Such defects would serve as avenues for the ingress of oxidative atmosphere into the interior of the composites, leading to oxidation damage and lifetime decline of CMCs at high temperatures [3, 4]. Towards in-depth oxidation of CMCs, the opening displacement of those tunneling cracks has been demonstrated to be a key factor that dominates gas diffusion regimes and the oxidation kinetics of the constituents [5], i.e., fibers, interphase and matrix. And, crack opening displacement (COD) relates significantly to environmental temperature, applied stress and oxidative damage. Influence of imposed stress as well as thermal residual stress was included in classical COD formulation [6-7]. However, this room-temperature model did not thoroughly consider the impacting mechanism of temperature, which not only dominates the thermal expansion extent, but also changes the elastic properties of the constituents and the interfacial frictional resistance. Moreover, oxidation upon COD has rarely been investigated. In order to predict the thermal-mechanical-oxygenic coupling lifetime and/or the post-oxidation property of CMCs, it is necessary to develop a new matrix crack opening model which should in-

2

corporate the effects of stresses, temperature and oxidation simultaneously. From microscopic conception, formulation of COD models generally involves interface debonding and/or recession, and meanwhile fiber sliding. Most analyses of fiber debonding and sliding have been based on shear-lag approach with various degrees of approximation. Some concise models assume that sliding along a debonded interface is resisted by a constant shear stress. And, this approximation has turned out to be satisfactorily good for many experiments [8]. Consequently, in this paper, such shear-lag assumption is followed to establish a new thermal-mechanical-oxygenic coupled model for matrix crack opening description. 2. Theoretical framework 2.1 Crack opening at loading temperature 2.1.1 Crack opening upon loading In order to determine the original crack opening displacement of a unidirectional ceramic matrix composite subjected to a tensile load larger than the matrix cracking stress, a minicomposite model [8] is adopted here, and the stress distribution in the fiber as well as in the matrix around an isolated crack [9] is schematically shown in Fig.1 (a). Once matrix crack appears upon mechanical loading, interface debonding would also occur in the minicomposite. The debonding length on either sides of the crack can be evaluated by

Ld3 

Rf EmVm ( c   th   i ) 2 Vf Ec

(1)

where 𝜎c is the imposed stress; 𝑅f is the fiber radius; 𝜏 is the interfacial slipping stress; 𝑉f and 𝑉m are the volume fraction of the fiber and matrix, respectively; 𝐸m is 3

the elastic modulus of the matrix; 𝐸c = 𝐸f 𝑉f + 𝐸m 𝑉m with 𝐸f the elastic modulus of the fiber. The interfacial debonding stress 𝜎i takes the following form

Em i Rf

i  1

c1

(2)

where 𝛤i is the interface debonding energy, 𝑐1 is a coefficient defined in Ref. [10]. The thermal misfit stress 𝜎th = 𝑞m 𝐸c ⁄𝐸m with 𝑞m the axial residual stress in the matrix and is theoretically predicted by

qm  Ef EmVf 1 Ec

(3)

where Ω1 is the misfit strain taking the following expression 1   m (Tp )   m (T0 )   f (Tp )   f (T0 )

(4)

where 𝛼f and 𝛼m are the specific thermal expansion coefficients of the fiber and matrix, respectively; 𝑇p is the processing temperature of the composite, and 𝑇0 is the initial temperature upon mechanical loading. Within the debonding region, deformation of the fiber and the matrix is inco nsistent, unlike the case in the bonded region. The matrix slides backward along fiber direction against the crack plane. The overall contractive displacement is m  load 

Rf EmVm 2   ( c   i ) 2  2 Vf Ec2  th

(5)

On the contrary, relative extension generates in the fiber, which is f  load 



Rf EmVm c ( c   th   i )  Vf Ec2 Rf Em2Vm2  ( c   th ) 2   i2 

(6)

2 Vf2 Ef Ec2

Summation of the relative shrinkage of the matrix and the relative extension of the fiber provides the crack opening displacement, which obeys the formulation given 4

below eload 

Rf EmVm ( c   th ) 2   i2  2 Vf2 Ef Ec

(7)

The above equation is reasonable at random loading temperature.

Fig.1. Stress profiles of the fiber and the matrix around an isolated matrix crack for the minicomposite subjected to (a) tensile load at initial temperature 𝑇0 and (b) tensile load at elevated temperature 𝑇. 2.2.2 Crack opening upon unloading Unloading the composite from the top stress 𝜎c to a lower 𝜎u accompanies by redistribution of the internal stresses, as is shown by the dash lines in Fig. 1 (a). Deduction of the relative contraction of the matrix gives

5

m  unload 

Rf EmVm  th ( c   th   i )  Vf Ec2

RE V  f m m2 ( c   u ) 2  2( u   th   i ) 2  4 Vf Ec

(8)

Meanwhile, the relative extension of the fiber can be estimated by f  unload 

Rf EmVm  (   th   i )  Vf2 Ef Ec u c



Rf Em2Vm2  (   th   i )  Vf2 Ef Ec2 th c



Rf Em2Vm2 (   u ) 2  2( u   th   i ) 2  4 Vf2 Ef Ec2  c

(9)

Combining Eq.(8) and Eq.(9) gives COD upon unloading as follows

eu  eload 

Rf EmVm ( c   u ) 2 2 4 Vf Ef Ec

(10)

For complete unloading, i.e., 𝜎u = 0, it becomes

eu 

Rf EmVm  2(   th ) 2   c2  2 i2  4 Vf2 Ef Ec  c

(11)

It is noted that Eqs.(7), (10) and (11) are consistent with the widely-accepted formulations presented in Refs. [6, 10‒11], and they are reasonable at random loading temperature as long as the sliding zones of adjacent matrix cracks do not overlap . 2.2 Crack opening at elevated temperature 2.2.1 Crack opening during heating up Application of CMCs in aerospace field has great possibility to encounter the rmal-mechanical coupled environment. When heating up CMCs, the internal thermal residual stresses will be relieved continuously until the processing temperature is reached, and then the thermal stresses will reversely get higher and higher as temperature continues to rise. In order to model crack healing behavior based on the mini-

6

composite model, thermal stresses in the constituents must be estimated first. At operating temperature 𝑇 (𝑇

𝑇0 ), the thermal stress in the matrix becomes qmT  EfT EmTVf 2 EcT

(12)

Note here that the superscript “T” denotes the parameter value at operating temperature 𝑇 (similarly hereinafter). The thermal misfit strain Ω2 between the fiber and matrix is given by 2   m (Tp )   m (T )   f (Tp )   f (T )

(13)

T T T⁄ T The corresponding thermal misfit stress of the composite becomes 𝜎th = 𝑞m 𝐸c 𝐸m .

Considering the variation of the interface property at high temperature, the interfacial slipping stress is now regarded as function of 𝑇 for thermal mismatch and/or chemical effect. And, another parameter was introduced to facilitate the following deduction, which relates to temperature 𝑇 as

RfVm EmT L  T T ( c   thT   iT ) 2 Vf Ec d 4

(14)

Also, the debonding stress 𝜎i is considered changing with temperature because it relates to temperature-dependent material parameters. For minicomposite that holds a stress of 𝜎c during heating up from 𝑇0 , Fig.1 (b) presents the thermo-mechanical coupled stress profiles of the fiber and matrix by the dash lines. As a reference, the solid lines describe the stress diagram upon pure mechanical loading at initial loading temperature. If the interface debonding length on either side of the crack remains 𝐿𝑑3 , the additional contraction of the matrix due to thermal effect within the debonding region can be calculated by

7

m  th-mech  2  m (T )   m (T0 )  Ld3



2 Vf  TVf d 2 d d  d 2  (Ld3 ) 2  T  ( L4 )  ( L3 )  2L3 L4  RfVm Em RfVm Em

(15)

Meanwhile, the extra elongation of the fiber can be evaluated by f  th-mech  2  f (T )   f (T0 )  Ld3

2 Ld 2 Ld  2 (Ld3 ) 2  c 3  c T3 Rf Ef Vf Ef Vf Ef

(16)

T   T (Ld3 ) 2  (Ld4 ) 2  2Ld3 Ld4  Rf Ef

m f Note here that 𝛿th−mech = 𝛿th−mech = 0 when 𝑇 equals to 𝑇0 . Combination of Eq.(15)

and Eq.(16) gives the thermal-mechanical coupled crack opening formulation for unidirectional CMCs. It is m f e(T )  eload   th-mech   th-mech

 eload  23 Ld3  

2 Ec ( Ld3 ) 2 2 c Ld3 ( Ef  EfT )  Rf Vm Em Ef Vf Ef EfT

(17)

 T EcT

( Ld3 ) 2  2 Ld3 Ld4  ( Ld4 ) 2  Rf Vm E E T f

T m

where the misfit strain Ω3 has the following form

3  m (T )  m (T0 )  f (T )  f (T0 )

(18)

It should be noted that Eq.(17) characterizes a fundamental mechanism that thermal expansion within the debonding region is restrained by some extent due to inte rfacial resistance. If engineering elastic constants are temperature independent and thermal misfit is absent between the fiber and the matrix, Eq.(17) would be equivalent to Eq.(7). Meanwhile, Eq.(17) is reasonable under the condition that

Em ET ( c   th   i )  mT ( c   thT   iT )  0 Ec Ec

(19)

If matrix crack closure is not achieved up to the highest temperature defined by the 8

above inequality, the further thermal expansion of the constituents within the debon ding zone is certainly to be free.

Fig.2. Stress profiles of the fiber and the matrix around an isolated matrix crack for the minicomposite with new interface debonding. A special case is that 𝜏 T decreases with increasing temperature, leading to a possibility that the interface debonding tip moves forward. At certain temperature 𝑇n (𝑛 = 1, 2, ⋯ , 𝑁), 𝑇n

𝑇n−1, the maximum interface debonding length may become

|𝐿𝑑4 (𝑇n )|, and |𝐿𝑑4 (𝑇n )|

|𝐿𝑑4 (𝑇n−1 )|. Under such case, the shear-lag based stress pro-

files for the fiber and the matrix are depicted in Fig.2. And, the extra contraction of the matrix turns into m  th-mech  2  m (T )   m (T0 )  Ld4 (Tn )

 2 ( c   th )  Ld4 (Tn )  Ld3  Ec 

T d d 2 Vf ( Ld3 ) 2 2 Vf L4 (Tn ) L4 (Tn )  RfVm Em RfVm EmT

At the same time, further extension of the fiber may present, which is

9

(20)

f  th-mech  2  f (T )   f (T0 )  Ld4 (Tn )

V E  2  m m  th   c   Ld4 (Tn )  Ld3  Ec  Vf Ef  d T d d 2 ( Ld3 ) 2 2 c Ld3 2 c L4 (Tn ) 2 L4 (Tn ) L4 (Tn )     Rf Ef Vf Ef Vf EfT Rf EfT

(21)

Then, COD at 𝑇n can be evaluated by

e(Tn )  eload  23 Ld4 (Tn ) 

2 th d 2 Ld L4 (Tn )  Ld3   c 3  Ef Vf Vf Ef

(22)

d T T d d 2 Ec ( Ld3 ) 2 2 c L4 (Tn ) 2 Ec L4 (Tn ) L4 (Tn )    Rf Vm Em Ef Vf EfT Rf Vm EfT EmT

If engineering elastic constants are irrelevant to temperature and thermal mismatch is absent between the constituents, Eq.(22) would be identical to Eq.(17) and Eq.(7). Additionally, at temperature 𝑇 between 𝑇n and 𝑇n+1, the value of COD can be obtained by modifying Eq.(22), as e(T )  eload  23 Ld4 (Tn )  

2 Ec ( Ld3 ) 2 2 th d 2 Ld3 c d  L ( T )  L   4 n 3 V E Rf Vm Em Ef Ef Vf f f

 T EcT

 L (Tn )  2 L L (Tn )  ( L )    Rf Vm EfT EmT  d 4

2

d 4

d 4

d 2 4

(23) 2 c Ld4 (Tn ) Vf EfT

When 𝑇 = 𝑇n , the above equation will degenerate to Eq.(22). Besides, Eq.(23) is valid when 𝑇 is lower than 𝑇n+1. 2.2.2 Crack opening during oxidation In this section the influence of interface corrosion on crack opening behavior is considered, without addressing the oxidation kinetics [12]. As is known, interface oxidation leads to detachment between the fiber and matrix, which completely eliminates the internal stress of the minicomposite within the interface recession length [13]. Thus,

10

such stress relaxation usually result in enlargement of COD.

Fig.3. Stress distribution in the fiber and the matrix for the minicomposite with rel atively short interface recession length. According to the stress diagram shown in Fig.3, the solution for crack opening displacement of the minicomposite with interface recession length of 𝑑 at elevated temperatures can be directly obtained by modification of the previously proposed models. If 𝐿𝑑max = 𝐿𝑑3 and the recession length satisfies the following condition: 0  d  Ld3  Ld4

(24)

the previously established Eq.(17) is then transformed into e(T )  eload  23 Ld3   

2d c Vf EfT

2 Ec ( Ld3 ) 2 2 c Ld3 2 c ( Ld3  d )   Rf Vm Em Ef Vf Ef Vf EfT

(25)

 T EcT ( Ld3  d ) 2  2( Ld3  d ) Ld4  ( Ld4 ) 2  Rf Vm EfT EmT

where 𝑒load is given by Eq.(7). Moreover, if 𝑑 complies with the condition below Ld3  Ld4  d  L 2  Ld4

(26)

with 𝐿 the crack spacing, new debonding will occur, and Eq.(25) is then changed into 11

e(T )  eload  23 ( Ld4  d ) 

2d c Vf EfT

2 th 2 c Ld3 d d   d  L4  L3   Ef Vf  Vf Ef

(27)

T T d d d 2 Ec ( Ld3 ) 2 2 Ec L4 L4 2 c L4    Rf Vm Em Ef Rf Vm EfT EmT Vf EfT

Another degradation case is that new debonding generate due to significant decline of interface slipping stress at certain temperatures, as stated previously. At temperature 𝑇n (𝑛 = 1, 2, ⋯ , 𝑁), if |𝐿𝑑4 (𝑇n )|

𝐿𝑑3 and |𝐿𝑑4 (𝑇n )|

|𝐿𝑑4 (𝑇n−1 )|, COD of the

minicomposite with interface recession length of 𝑑 (≤ 𝐿⁄2 − |𝐿𝑑4 (𝑇n )|) can be obtained by e(Tn )  eload  23  Ld4 (Tn )  d  

2 th 2d 2 Ld d  Ld4 (Tn )  Ld3   T c  c 3  Ef Vf Ef Vf Vf Ef

(28)

d T T d d 2 Ec ( Ld3 ) 2 2 c L4 (Tn ) 2 Ec L4 (Tn ) L4 (Tn )    Rf Vm Em Ef Vf EfT Rf Vm EfT EmT

When 𝑑 = 0, the above equation will degenerate to Eq.(22). At temperatures between 𝑇n and 𝑇n+1, if 𝑑 ≤ |𝐿𝑑4 (𝑇n )| − |𝐿𝑑4 |, the value of COD can be determined by e(T )  eload  23 Ld4 (Tn )   

2d c 2 Ld3 c  Vf EfT Vf Ef

2 c Ld4 (Tn ) 2 Ec ( Ld3 ) 2 2 th d d  L ( T )  L   4 n 3 Rf Vm Em Ef Ef Vf Vf EfT

(29)

 T EcT

 Ld4 (Tn )  d 2  2  Ld4 (Tn )  d  Ld4  ( Ld4 ) 2   Rf Vm E E  T f

T m

However, if |𝐿𝑑4 (𝑇n )| − |𝐿𝑑4 | < 𝑑 ≤ 𝐿⁄2 − |𝐿𝑑4 |, COD can be provided by e(T )  eload  23  Ld4 (Tn )  d  T T d d 2d c 2 Ld3 c 2 Ec L4 (Tn ) L4 (Tn )    Vf EfT Vf Ef Rf Vm EmT EfT



2 c Ld4 (Tn ) 2 Ec ( Ld3 ) 2 2 th   d  Ld4 (Tn )  Ld3   Rf Vm Em Ef Vf Ef Vf EfT 12

(30)

It is assumed that in Eqs.(25), (27)‒(30) thermal expansion of the fiber and matrix is unconstrained within the interface recession length. It is necessary to identify first the interfacial degradation degree before application of Eq.(25) and Eqs.(27)‒(30) in order to discern the in-depth gas diffusion regimes and the associated oxidation kinetics of unidirectional CMCs. Moreover, the crack closure time under various situations can be resolved through the corresponding models once the oxidation kinetics of the interface is identified. 3. Model application and discussion 3.1 Temperature-dependent parameters The specific thermal expansion coefficient of SiC can be expressed as [14]

 m  1.8276T  0.0178T 2  1.5544 105 T 3 4.5246 109 T 4

(31)

Eq.(31) is valid in the temperature range 125−1273K. Contrarily, the coefficient of thermal expansion at temperatures above 1273K is assumed as constant 5.0×10-6/K. Meanwhile, the elastic modulus of dense SiC at elevated temperatures can be empirically formulated as [14]  962  EmT  460  0.04T exp     T 

(32)

Eq.(32) is accurate enough in the temperature range 300−1800K. On the other hand, the elastic modulus of carbon fibers at elevated temperatures can be empirically expressed as [15]

EfT  230 1  2.86  10 4 exp T 324  

(33)

The above equation is available from room temperature to 2273 K. The longitudinal

13

thermal expansion coefficients of the fiber can be described as [16]

 f  2.529 104  1.569 106 T  2.228 109 T 2

(34)

1.877 1013 T 3  1.288 1016 T 4 Eq.(34) is valid in the temperature range 300−2500K.

Except the temperature-dependent parameters, the other required material constants are all given in Table 1. Table 1. Material constants for typical ceramic matrix composites Value Parameter

Symbol

Unit SiC/SiC

C/SiC

Fiber radius

Rf

μm

5.0 [17]

3.5 [5]

Volume fraction of fibers

Vf

%

13 [17]

40 [5, 9]

Volume fraction of matrix

Vm

%

87 [17]

60 [5, 9]

Poisson’s ratio of fiber and matrix

ν

—

0.2

0.2 [9]

Interface debonding energy

Гi

J/m2

0 [17]

0.1 [9]

Special micromechanical parameter

c1

—

3.5 (calculated)

1.2 (calculated)

Interfacial slipping stress at room temperature

τ

MPa

2.0 [17]

20 (assigned)

Processing temperature

Tp

K

—

1273 [5, 9]

Room temperature

T0

K

300 (assigned)

300 (assigned)

3.2 Model validation with SiC/SiC composite It should be noted here that in-situ measurement of COD in high temperature oxidative atmosphere is extremely hard. And, only a few experimental data is available for evaluating the present model. Bale et al. [17] had successfully measured the crack opening displacements in single-tow SiC/BN/SiC composites loaded in tension at room temperature and 1750°C. The experimental results are presented in Fig.4. The determined interfacial sliding stress at room temperature is 2MPa, while at 1750°C it decreases to 0.4MPa [17]. The predictions provided by Eq.(7) and Eq.(22) are also depicted in Fig.4 for comparison. And, good agreements can be seen between the experimental data and the corresponding model predictions, revealing the reasonability 14

and applicability of the suggested model. Moreover, it is concluded from Fig.4 that decreased interfacial slipping stress enhances matrix crack opening for weakened interfacial resistance and new debonding generated.

Fig.4. Comparison between model predictions and the experimental results of SiC/SiC composites. 3.3 Parametric analysis with C/SiC composite Parametric analysis is performed towards C/SiC composites, of which dramatic thermal misfit exists between the fiber and the matrix, in order to illustrate the general influences of applied stress, interface slipping stress, environment temperature and interface oxidation upon crack opening behavior of ceramic matrix composites. 3.3.1 Evolution of COD with temperature Fig.5 presents the evolution features of COD with temperature under different tensile stresses for unidirectional C/SiC composites. The interfacial slipping stress is assumed unchanged at elevated temperatures, i.e., 𝜏 = 𝜏 T = 20MPa. It is clearly seen that COD decreases with increasing temperature, in a quasi-linear manner. However, an opposite tendency is observed for COD variation along with tensile stress. It is obviously that the imposed tensile stress contributes to open matrix cracks, while tem15

perature acts reversely.

Fig.5. Evolution of COD with temperature for unidirectional C/SiC composites under different stress levels. In addition, the synergistic effects of interfacial slipping stress and temperature on COD of unidirectional C/SiC composites are also investigated. The theoretical results are exhibited in Fig.6 (a) and (b) for stress-holding and as-fabricated materials, respectively. At certain temperature, it is observed that the larger the interfacial sliding stress is, the narrower the crack opening becomes, similar to the phenomenon presented in Fig.4. And, the decreasing rate of COD versus temperature becomes larger when the interface slipping stress turns down. The reason for these phenomena is that the interfacial slipping stress acts to impede matrix expanding forward along the fiber when heating up the composite, and hinder the matrix contracting backward when cooling the material. Under different stress levels, similar variation features of COD with interfacial sliding stress are observed. However, we notice that the stress-holding composite generates higher COD, while the as-fabricated material presents the lower. Besides, the dropping rate of COD with temperature for stress-holding material is relatively small. Such theoretical results can legitimately account for the experimental 16

phenomenon that the load-carrying composite is more vulnerable to high temperature oxidative atmosphere [12, 18].

Fig.6. Effect of interface slipping stress on COD evolution for unidirectional C/SiC composites at elevated temperatures: (a) 𝜎c = 500MPa and (b) 𝜎c = 0MPa. 3.3.2 Evolution of COD with recession length In this section, influence of interface recession length on crack opening behavior is examined quantitatively. For load-carrying C/SiC composites, COD evolution with interface recession length is much complicated as shown in Fig.7 where the effects of temperature, applied stress and interfacial slipping stress are all taken into account. On the early stage, COD appears to decrease as recession length grows, in a parabolic style. New interface debonding occurs beyond the inflection point for serious interface oxidation, leading to linear increase of COD. Under such situation, matrix crack closure can hardly be achieved if interface corrosion continues. Moreover, the width of crack opening declines slightly due to tensile deformation of carbon fiber within the interface recession length before new interface debonding generates. Afterwards, crack opening is enhanced significantly, analogous to the phenomenon presented in Fig.4, for thermal stress relaxation in the new fiber-matrix debonded zone. Generally, the life17

time of ceramic matrix composites without coating protection is surprisingly short once matrix cracks emerge. Moreover, it decreases significantly with increasing load at the same temperature [19, 20].

Fig.7. Evolution of COD with interface recession length for stress-holding material under: (a) σ c =300MPa, τ=10MPa; (b) τ=10MPa, T=700°C; (c) σ c =300MPa, T=700°C. 4. Conclusions A new matrix crack opening model is established based on shear-lag theory. The model simultaneously considers the influence of tensile stress, environmental temperature and fiber-matrix interface degradation on crack opening behavior of unidirectional CMCs. The model has potential in dealing with thermal-mechanical-oxygenic coupled problems of CMCs in high temperature oxidative atmosphere. 18

Theoretical and experimental results demonstrate that crack opening displacement of ceramic matrix minicomposite increases with increasing tensile stress, while decreases with elevated temperature due to thermal expansion of the matrix along fiber direction. But, temperature effect on crack healing can be weakened by fiber-matrix friction resistance. Under the same thermo-mechanical loading, COD usually declines with increasing interface slipping stress. Meanwhile, the healing rate of COD with temperature also decreases when interfacial slipping stress increases. Oxidation of carbon or BN interface initially has negative effect on crack opening of CMCs for relieving interfacial friction. With enlarged oxidation region, slight reduction of crack opening displacement usually occurs due to tensile deformation of the fiber within the interface recession length. When interface oxidation aggravates, new interface debonding definitely generates, resulting in accelerated matrix crack opening. Under such case, matrix crack closure can hardly be achieved. Acknowledgements This work was supported by the National Science Foundation of China (Grant No. 11702217) and the Basic Research Funds of Northwestern Polytechnical University (Grant No. JC20110219). The authors also thank Profs. Litong Zhang and Laifei Cheng for providing of the specimens. References 1.

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