SiC composites in a combustion wind tunnel

Composites Science and Technology 88 (2013) 178–183

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Stressed oxidation life predication of 3D C/SiC composites in a combustion wind tunnel Xin’gang Luan ⇑, Laifei Cheng, Congwei Xie Science and Technology on Thermostructural Composite Materials Laboratory, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China

a r t i c l e

i n f o

Article history: Received 10 June 2013 Received in revised form 27 July 2013 Accepted 7 September 2013 Available online 16 September 2013 Keywords: A. Ceramic–matrix composites (CMCs) B. Creep C. Damage mechanics D. Scanning electron microscopy (SEM) Oxidation

a b s t r a c t To improve safety and reliability, a method which can predict the life of C/SiC structures in severe environments accurately is need for designers. A multi-zone load bearing model for stressed oxidation of 3D C/SiC was suggested. Based on the model, the life prediction functions for wind tunnel environments were derived from the nature of oxidation of carbon fibers. Most of material and environmental parameters are taken into consideration. The former include properties of carbon fiber (i.e., density, modulus and thermal expansion coefficient (CTE)), CTE of SiC matrix, braid angle of fiber perform, and thickness of sample. The latter involve gas flow velocity, gas composites, molar fraction of oxidant, load and temperature. The effects of temperature, load, atmosphere pressure and partial pressure of oxygen were also introduced to the equation by the width of crack. It is proved by the experimental results that the predication results are accurate under the loading ranging from 100 to 160 MPa in a wind tunnel. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Carbon fiber-reinforced silicon carbide composite (C/SiC) is one of the promising ceramic matrix composites (CMC). It has been highly expected to serve as gas turbine hot section components because of its low specific weight and high specific strength over a large temperature range compared to superalloys, its great damage tolerance compared to monolithic ceramics and the great potential for reducing component weights and cooling flow requirements [1,2]. To improve safety and reliability, designers who wish to use C/ SiC need a method to accurately predict the life of C/SiC structures as a function of material parameters and experimental parameters such as preform architecture, gas velocity, oxidant concentration, temperature and stress. One of the more formidable obstacles to the widespread use of C/SiC composites is the oxidation of carbon fibers at medium to high temperatures in a gas turbine environment in which high-speed oxidizing gases and a creep loading coexist. Based on an oxidation dynamic model supposed by Lamouroux et al., a few models have been built to predict the mass loss of C/SiC after oxidized under the conditions without loading [3–7]. All works model the oxidation of C/SiC based on the physical nature of oxidation of carbon, however, it is impossible to predict the service life of C/SiC structures accurately because no preform architecture, gas velocity and stress were concerned in all those models. ⇑ Corresponding author. Tel.: +86 29 88495071. E-mail address: [email protected] (X. Luan). 0266-3538/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2013.09.001

Thomas et al. [8] employ a phenomenological based stress rupture model using a Probabilistic Residual Strength (PRS) technique to predict the stressed oxidation life of C/SiC composites. The model considers the material’s initial static strength, applied load, duration of loading, time-to-failure and intermediate residual strength as random variables. However, the model needs a series of tests to calibrate some constant parameters before being used for each material and atmosphere. A strain response model is developed to estimate the strain of 2D C/SiC with time in presence of mechanical fatigue and static oxidizing atmosphere [9], which may be employed to predict the lifetime of 2D C/SiC components when they have strain limitation. Some numerical model [10–12] are developed to simulate the oxidation behaviors of 2D C/SiC composite materials and structures. However, they also cannot predict the lifetime directly. The purpose of this paper is to develop a mathematic method for the life prediction of C/SiC based on the physical nature of oxidation of carbon fibers. All factors related to the life of C/SiC, i.e. preform architecture, gas velocity, oxidant concentration, temperature and stress are considered in this method. It can be used directly without calibration.

2. Experimental Carbon fiber (T-300 Japan Toray) was employed. Fibrous preform was prepared by the three-dimensional braid method and supplied by the Nanjing Institute of Glass Fiber. The volume fraction of fibers in the preform was 40–45%. The composite was

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prepared by a low-pressure chemical vapor infiltration (LPCVI) process. The preform was deposited with pyrolytic carbon (PyC) as interlayer using butane and densified with SiC as a matrix using methyltrichlorosilane (MTS). The dog bone shaped specimens were cut from the prepared composite plates and a two-layer SiC coating was deposited to seal the open ends of the fibers and open pores. Cross-section of gauge is rectangular with the size of 3  4 mm2. For a standard 3D C/SiC composite, the thickness of the PyC interlayer was 200 nm and the thickness of the SiC coating was 40 lm. The samples were exposed in the high temperature combustion gas wind tunnel in which the combustion gas came from the burning of aviation kerosene in air. Its air–fuel ratio, total pressure and gas velocity were 27.8, 1 atm and 240 m/s, respectively. In the combustion gas, the molar fraction of CO2, O2, N2 and H2O was 0.0788, 0.083, 0.7459 and 0.0927, respectively. The gas flow was directly impinging on the specimen that was vertical to it. The diameter of heated zone was 30 mm. The temperature of the gas flow were 1200 °C, 1300 °C and 1500 °C which were detected by a platinum–rhodium thermocouple nearby the specimen during the tests. The tensile creep loads (i.e., 60, 100, 120, 160, 240 MPa), perpendicular to the flame, were supplied by a hydraulic servo frame (INSTRON 8872).

gases. Because the directionality of convective mass transfer caused by the flow of high-speed gas, oxidation of the composite material starts from windward side of the specimen and then progresses to its lee side. The stressed oxidation model in wind tunnels, namely Multi-zone Load Bearing (MLB) Model, is shown in Fig. 1(b). Every zone (II) repeat the same failure process following the stressed oxidation model. According to the results from Ref. [13], the lifetime of 3D C/SiC composites is mostly shorter than 1 h when NS is bigger than NTS and temperatures are above 1000 °C. However, the lifetime might be longer than 30 h when the specimens are exposed in the conditions where NS is smaller than 0.25 and temperatures are above 1000 °C. Only when NS ranges from 0.25 to NTS, the limited lifetime of the composites need be predicated. In this case, oxidation of carbon fibers in the load-bearing area is controlled by gas in-diffusion through cracks in the matrix.

3.2. Main function Based on the MLB model mentioned above, assuming the oxidation rate of every load-bearing area is the same in the same condition, the total degradation of composites (Doxid) is the sum of degradation of every load-bearing area (Da):

3. Life predication functions

Doxid ¼ 1  rnps ¼ N a  Da ¼

3.1. Stress rupture model According to the previous paper [13], during the stressed oxidation, the load is bore by a load-bearing region which includes just part of fibers of 3D C/SiC composites as shown in Fig. 1(a). At the first stage of the stressed oxidation test, only zone (I) and zone (II) exist. Zone (I) keeps the properties of as-prepared composite, while zone (II) bears the loading. After zone (II) cannot bear the loading due to the oxidation of carbon fibers, a new zone (II) detaches from zone (I) to bear the loading, and then the old zone (II) becomes zone (III). So, when the stress is small, there will occur several zone(III)s before the sample fails. The damage mechanisms of a standard 3D C/SiC composite in combustion wind tunnels depend on normalized threshold stress (NTS), as reported in Ref. [13]. When normalized stress (NS, i.e., the ratio of loading/maximal tensile strength) is below NTS, the composite is damaged region by region along the direction of flowing gas; and the oxidation of the fibers in the load-bearing region, i.e. zone (II), is controlled by the crack in-diffusion of oxidizing

1 rns  1t

where Na is the number of load-bearing area which is the reciprocal of average NS (rns), rnps is defined to the normalization stress corresponding to the maximal loading (i.e., the ratio of max loading/ maximal tensile strength), 1t is the total effective load-bearing width (m), 1 is oxidation width of load-bearing area (m). Da can be calculated based on Fig. 2, where e, d, l are crack width, crack depth and crack length, respectively. To simplify the calculation, several hypotheses need be taken into account. (1) High speed gas passes through the crack as a laminar flow. (2) Components of gas at z = 0 are the same as those at the surface of a specimen for each load-bearing area. (3) Effect of oxidation of SiC on crack width can be ignored. In the wind tunnel condition where t1 > 200 m/s, diffusive mass transfer can be neglected. So, when a high speed gas flows

Gas

(I) (II)

(III)

(III) (II)

(III)

(II) (I)

(a) Model of part fiber load-bearing

ð1Þ

(b) Stressed oxidation model

(I) fiber broken area; (II) fiber load-bearing area; (III) fiber no-load area Fig. 1. Degradation models of carbon fibers of C/SiC composite under tensile stress in wind tunnels.

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y l

NO2 ¼

x

e

z

Oxide Oxidizing Gas

NC ¼

Fig. 2. Stressed oxidation schematic of load-bearing area in 3D C/SiC.

through a crack, molar flux of oxygen through unit area in unit time is as follow:

qg tZ Mg

x1

ð2Þ

where qg is gas density (kg/m3), tz is gas speed in a crack (m/s), Mg is molar mass of gas (kg/mol), and v1 is molar fraction of oxygen at z = 1. Velocity boundary layer and concentration boundary layer will built up when combustion gas flows through the cracks. Based on the theory of boundary layer, assuming the combustion gas is an incompressible steady flow in the cracks and the velocity increases lineally from the crack wall to the center, thickness of boundary layer and velocity in boundary layer can be expressed as [14]:

tz y ¼ t1 dz

ð3Þ sffiffiffiffiffiffiffiffiffiffiffiffi lz

dz ¼ 5:0

ð4Þ

qg t1

tz

sffiffiffiffiffiffiffiffiffiffiffiffi

qg t31 1 1 2 l

ð5Þ

The thickness of concentration boundary layer is written as [14]:

dD ¼ 4:53Rez1=2 Sc1=3 ¼ 4:53 dz

l t1 zqg

!1=2   Dqg 1=3

l

ð6Þ

where dD is the thickness of concentration boundary layer at crack depth z (m), Re is Reynolds number, Sc is Schmidt number, and D is gas diffusion coefficient (m2/s). Utilizing Eq. (6) and taking Eq. (4) into account, dD can be obtained:

dD ¼ 22:65

1=3

l D t1 q2=3 g 2=3

ð7Þ

Assuming that the concentration of oxygen in boundary layer also increases linearly, the concentration distribution of oxygen in concentration boundary layer is expressed as:

vz y ¼ v0 dD

ð8Þ

where vz is molar fraction of oxygen at crack depth of z (m). At the position of y = e/2, when z = 1, v1 is:

v1 ¼

t1 q2=3 g ev0 45:3l2=3 D1=3

D

1

 12

ð10Þ

ð9Þ

Substituting Eqs. (5) and (9) into Eq. (2), NO2 can be obtained as:

e2 v0 qg13=6 t5=2 1

1

226:5M g l7=6 D1=3

 1 2

ð11Þ

Eq. (11) describes consumption rate of C phase when stressed oxidation is controlled by diffusion. The effect of temperature on NC is embodied by gas diffusivity D, oxidation width 1, crack width e and gas velocity t1. Assuming the distance of fiber degradation is d1 during time dt, the weight change of material can be obtained:

DW ¼ d1  S  V f  q

ð12Þ

or DW ¼ NC  S  dt  M

ð13Þ

where q is the density of C phase, Vf is the volume fracture of fiber and S is the crack cross-sectional area, NC is the consumption rate of C phase and M is the molar mass of carbon. Combining Eqs. (11)–(13), the formula below can be derived:

e2 v0 qg13=6 t5=2 d1 M 1 1 ¼  12  Vf  q dt 226:5M g l7=6 D1=3

ð14Þ

Taking boundary condition, 1 = 0 when t = 0, into account, the equation becomes: 3

where tz is gas velocity in boundary layer at crack depth z (m/s), t1 is ambient gas velocity (m/s), dz is thickness of velocity boundary layer at crack depth z (m), y is distance from crack wall whose maximum is e/2 , l is gas viscosity (Pa s), qg is gas density (kg/m3). At the position of y = e/2, when z = 1, tz has the following relation:

e ¼ 10

t

453M g l

N O2 is the molar flux of oxygen through unit area in unit time, which also can be regarded as consumption rate of oxygen in unit area. Based on the reaction 2C + O2 = 2CO, consumption rate of C phase (NC) can be expressed as:

d

NO2 ¼

13=6 5=2 1 7=6 1=3

e 2 v0 q g

12 ¼

13=6 5=2 1 7=6 1=3

3e2 v0 qg

t

453M g l

D

M t Vf q

ð15Þ

According to stressed oxidation model in the wind tunnel as shown in Fig. 1(b), the sample will break when the residual carbon fiber can not bear the loading, in other words, total number of damaged carbon fibers excesses the maximal number of bearing fibers. The failure criterion of composite materials should be derived from Eq. (1):

1 ¼ ð1  rnps Þ  rns  1t ¼ ð1  rnps Þ  rns  kt  h  V 1=3 f

ð16Þ

where kt is preform structure tortuousness factor which is not less than 1, h is the thickness of specimen at the gas direction. According to ideal gas function, qg = PMg/RT. With this and Eqs. (15) and (16) in consideration, the lifetime of C/SiC composite is available:

tc=sic ¼ Na  t ¼

qðkt hV f Þ 453ðRTÞ13=6 l7=6 D1=3 ð1  rnps Þ3=2 r1=2 ns  5=2 M 3e2 x0 P13=6 M 7=6 t 1 g

3=2

ð17Þ where tc/sic is the lifetime of composite with unit of s, P is the total pressure of environment (= 1.01  105 Pa in this case), R is universal gas constant (= 8.314 J/mol K). In Eq. (17), the first part includes all environmental factors affecting the life of composite material in wind tunnel, i.e. gas velocity, partial pressure of oxygen, combustion components, stress and temperature; the second part covers major material parameters, i.e. fiber volume fraction, fiber properties, fiber perform structure and specimen size. The effect of temperature also will be introduced to Eq. (17) through the crack width e, gas viscosity l and gas diffusion coefficient D. 3.3. Crack width function The crack width e is controlled by thermal expansion mismatch of free carbon fiber and free matrix as well as mechanical

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x

Table 1 Viscosity coefficient in Pa s  105 for components in combustion gas at various temperature and at a nominal pressure of 1 atm [16].

fiber

α

x

e

L

matrix

Fig. 3. Schematic of free carbon fiber and matrix in 3D C/SiC.

extension of free carbon fiber. Those free carbon fibers and matrices come from matrix cracking and interlayer debonding during the composite cools down from the processing temperature, as shown in Fig. 3. No contribution is made to the crack width by those bonded fiber and matrix because they expand or extend together. At room temperature, the length of free fiber (L) satisfies the equation:

L  cos a ¼ 2x þ e0

ð18Þ

where x is the length of free matrix (m), e0 is crack width at room temperature (m), a is braiding angle of fiber preform (°). According to Fig. 3, crack width will change with temperature as following:

eT ¼ e0 þ L cos a  af ðT  293Þ  2xam ðT  293Þ

ð19Þ

where eT is the crack width at temperature T (unit: m), af is coefficient of thermal expansion of carbon fiber (K1), am is coefficient of thermal expansion of matrix (K1), T is Kelvin temperature (K). The crack of 3D C/SiC heals at 1173 K [15]. This means eT = 0 when T = 1173 K. So, combining Eqs. (18) and (19), the length of free fiber and matrix can be obtained:

x¼

1:136  103 þ af  e0 2ðam  af Þ

ð20Þ

L¼

1:136  103 þ am  e0 ðam  af Þ cos a

ð21Þ

Putting them into Eq. (19), the equation of crack width changed with temperature is gained:

eT ¼ ½1  1:136  103 ðT  293Þ  e0

ð22Þ

Assuming no more interlayer debonding occurs during stressed oxidation, the total crack width resulted from thermal expansion and mechanical extension is as follow:

e ¼ eT þ L  r=Ef ¼ ½1  1:136  103 ðT  293Þ  e0 þ

1:136  103 þ am r   e0 ðam  af Þ cos a Ef ð23Þ

where r is mechanical loading (MPa), Ef is elastic module of carbon fiber (GPa). 3.4. Viscosity and molecular weight of combustion gas Gas viscosity also is an important parameter for the life prediction of C/SiC in the high temperature combustion wind tunnel. Combustion gas is a multi-component mixture mainly consisting of CO2, O2, N2 and H2O. The viscosity of combustion gas can be calculated utilizing Wilke’s formula as follows [16]:

lmix ¼

n X i¼1

xi l Pn i j¼1 xj Uij

ð24Þ

T (K)

O2

N2

CO2

H2O

1200 1300 1400 1500 1600 1700 1800

5.466 5.761 6.048 6.327 6.599 6.864 7.124

4.599 4.845 5.084 5.317 5.545 5.767 5.984

4.346 4.586 4.819 5.046 5.267 5.482 5.693

4.665 5.095 5.513 5.920 6.318 6.703 7.075

2  1=2 1 Mi 41 þ Uij ¼ pffiffiffi 1 þ Mj 8

li lj

!1=2   32 1=4 Mj 5 Mi

ð25Þ

where subscript i and j denote composites in the combustion gas, x,

l and M are molar fraction of component, viscosity coefficient, and molar mass of component, respectively. All the values needed for calculation are listed in Tables 1 and 2. Molecular weight of combustion gas is calculated based on the rule of mixtures [17]:

Mg ¼ xA M A þ xB MB þ xC M C þ xD M D

ð26Þ

where M is molecular weight, x is molar fraction of each composite in combustion gas, and the different subscripts stand for different components. 3.5. Effective diffusion coefficient of multicomponent gas The gas diffusion coefficient in multicomponent combustion gas can be calculated according to the approximated but practically important concept proposed by Wilke [18], which enables us to estimate rates of diffusion in multicomponent systems from the well-established binary diffusion coefficients. The relevant expression is as follow:

Dm;A ¼

xB DAB

1  xA C D þ DxAC þ DxAD  

ð27Þ

where Dm,A is the effective diffusion coefficient of component A [m2/ s] and DAB, DAC, DAD, . . . are the binary diffusion coefficients of component A through components B, C, and D, respectively [m2/s]. Those can be found in Table 3. 4. Stressed oxidation life calculation and verification In this work, stressed oxidation lifetime of 3D C/SiC is tested under creep loading in high temperature wind tunnel. All material parameters and environmental parameters are listed in Table 4. According to the material parameters, Eq. (23) can be specified as following:

e ¼ 0:5331  106  0:4544  109 T þ 0:4175  108 r

ð28Þ

Based on the environmental parameters, viscosity and diffusion coefficient of combustion gas calculated by using Eqs. (24), (25), and (27) are as follows:

l ¼ 0:0021T þ 1:1329

ð29Þ

DO2 ¼ 0:0035T  2:0789

ð30Þ

The molecular weight of combustion gas (Mg) is 0.028677 kg/mol in accordance with Eq. (26). In the environments with coexisting high speed gas and high tensile loading, cracks will be wide enough to ignore the effect of perform structure on convective mass transfer. This means kt

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Table 2 Quantity (Mj/Mi)1/4 and (1 + Mi/Mj)1/2 for components in combustion gas [16]. j

(1 + Mi/Mj)1/2

(Mj/Mi)1/4

i

O2

N2

CO2

H2O

O2

N2

CO2

H2O

O2 N2 CO2 H2O

– 1.36949 1.5412 1.2502

1.46363 – 1.6034 1.28182

1.31419 1.27929 – 1.18717

1.66619 1.59846 1.85549 –

– 1.03380 0.92342 1.15444

0.96731 – 0.89323 1.11670

1.08293 1.11953 – 1.25018

0.86622 0.89549 0.79988 –

Table 3 Diffusion coefficient in m2/s  104 for components in combustion gas at various temperatures and at a nominal pressure of 1 atm [16]. T (K)

O2–N2

O2–CO2

O2–H2O

1200 1300 1400 1500 1600 1700 1800

2.1903 2.5028 2.8314 3.1756 3.5351 3.9095 4.2986

1.6934 1.9366 2.1924 2.4604 2.7404 3.0321 3.3353

3.0124 3.4482 3.9069 4.3878 4.8904 5.4141 5.9584

Table 4 Parameters for stressed oxidation lifetime predication of 3D C/SiC. Material parameters

rUTS (MPa) Ef (GPa) af (106 K1) am (106 K1) a (°) e0 (lm) [15] Vf q (kg/m3) M (kg/mol) h (m)

Environmental parameters 386 230 0.7 4.5 24 0.4 0.4–0.45 1760 0.012 0.0032

t1 (m/s) vO2 vH2O vCO2 vN2 r (MPa) T (°C)

240 0.083 0.0927 0.0788 0.7459 60,100,120,160,240 1200,1300,1500

should be 1. Because water vapor will react with carbon fiber as well as oxygen, x0 should be the sum of theirs molar fraction, i.e., 0.1757. Combining Eqs. (17), (28), (29) and (30) and employing all the parameters listed in Table 5, effects of temperature and tensile loading on the stressed oxidation lifetime of 3D C/SiC under the wind tunnel can be calculated as shown in Fig. 4. The error bars are attributed to the change of volume fraction of carbon fibers. The calculation results are highly consistent with the experimental results under the conditions of tensile loading ranging from 100 to 160 MPa (i.e., NS ranging from 0.25 to 0.4). Beyond the range, the lifetime will be overestimated to some degree. For the loading of 60 MPa, the overestimation is due to the lack of consideration of diffusion mass transfer in the functions of life predication. The reason is because the oxidation of carbon fiber is mainly controlled by the diffusion mass transfer while the loading is below 100 MPa or the NS is below 0.25 [19]. For the case of 240 MPa, the overprediction is attributed to the underestimate of crack width because the hypothesis of no more debonding happening between fiber and matrix during tests is incorrect in this circumstance. When the loading is 160 MPa (i.e., NS = 0.414), the oxidation mechanism is sensitive to temperature because the crack width is in the critical condition. The lifetime of composite is tend to the results under a bigger stress due to a bigger crack width at 1200 °C, however, the lifetime is close to that under a smaller stress due to a smaller width at 1300 °C. 5. Conclusions Based on the MLB model, the predication functions of stressed oxidation lifetime in a high temperature composite wind tunnel

Fig. 4. Stressed oxidation lifetimes changed with temperature under different creep loadings.

for 3D C/SiC have been derived from the physical nature of oxidation of carbon fiber and mass transfer of high velocity multicomponent gas. Compared with the experimental results, the predication results are accurate under the loading range from 100 to 160 MPa in the wind tunnel. When the loading is below 100 MPa, the predication results are larger than the experimental results because the dominant oxidation mechanism of carbon fiber switches from convective mass transport to diffusion mass transfer. When the loading is above 160 MPa, the predication results are also larger than the experimental values. The reason, however, is the lack of consideration of the extra crack opening resulted from the debonding between fiber and matrix under the higher loading. It is expected that the functions also can be used to predicate the stressed oxidation life of 3D C/SiC under fatigue loads in the wind tunnel. The ways are taking the average load for r in Eq. (28) as well as treating the corresponding NS of average load and maximal load as rns and rnps in Eq. (17), respectively.

Acknowledgments The work is supported by National Basic Research Program of China (973 Program) (2011CB605806) and 111 Project (B08040). The authors also acknowledge the financial support of Natural Science Foundation of China (Contract No. 51002121).

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