Fatigue Damage and Lifetime of Sic/Sic Ceramic-Matrix Composite Under Cyclic Loading at Elevated Temperatures

materials

Article Fatigue Damage and Lifetime of SiC/SiC Ceramic-Matrix Composite under Cyclic Loading at Elevated Temperatures

Longbiao Li

College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao St., Nanjing 210016, China; [email protected]

Academic Editor: Javier Narciso Received: 22 February 2017; Accepted: 30 March 2017; Published: 31 March 2017

Abstract: In this paper, the fatigue damage and lifetime of 2D SiC/SiC ceramic-matrix composites (CMCs) under cyclic fatigue loading at 750, 1000, 1100, 1200 and 1300 ◦C in air and in steam atmosphere have been investigated. The damage evolution versus applied cycles of 2D SiC/SiC composites were analyzed using fatigue hysteresis dissipated energy, fatigue hysteresis modulus, fatigue peak strain and interface shear stress. The presence of steam accelerated the damage development inside of SiC/SiC composites, which increased the increasing rate of the fatigue hysteresis dissipated energy and the fatigue peak strain, and the decreasing rate of the fatigue hysteresis modulus and the interface shear stress. The fatigue life stress-cycle (S-N) curves and fatigue limit stresses of 2D SiC/SiC composites at different temperatures in air and in steam condition have been predicted. The fatigue limit stresses approach 67%, 28%, 39% 17% and 28% tensile strength at 750, 1000, 1100, 1200 and 1300 ◦C in air, and 49%, 10%, 9% and 19% tensile strength at 750, 1000, 1200 and 1300 ◦C in steam conditions, respectively.

Keywords: ceramic-matrix composites (CMCs); fatigue; damage evolution; life prediction; matrix cracking; interface debonding

1. Introduction Ceramic materials possess a high strength and modulus at elevated temperatures. However, their use as structural components is severely limited because of their brittleness. Continuous fiber-reinforced ceramic-matrix composites, by incorporating fibers in ceramic matrices, however, not only exploit their attractive high-temperature strength but also reduce their propensity for catastrophic failure [1]. Many researchers have performed experimental and theoretical investigations on the cyclic fatigue behavior of fiber-reinforced ceramic-matrix composites (CMCs). Mall [2] investigated the effects of moisture on the cyclic fatigue behavior of a 2D SiC/SiC composite at 750 ◦C in air and in a humid environment. It was found that the presence of moisture decreased the fatigue life at a prescribed stress level relative to that without moisture. Michael [3] investigated the tension-tension fatigue behavior of 2D SiC/SiC composite at 1000 ◦C in air and in steam conditions. It was found that the presence of steam significantly degraded the fatigue performance, which accelerated the damage development and fatigue fracture due to oxidation embrittlement. Groner [4] investigated the cyclic fatigue behavior of 2D SiC/SiC composite with two geometries, unnotched and notched, at 1100 ◦C in air. It was found that the fatigue failure of the notched specimens was initiated adjacent to the hole and the failure of the unnotched specimens was initiated at the edge and inherent pores. Jacob [5] investigated the tension-tension fatigue behavior of 2D SiC/SiC composite at 1200 ◦C in air and in steam conditions. The microstructural investigation revealed pronounced oxidation on the fracture surface of specimens

Materials 2017, 10, 371; doi:10.3390/ma10040371 www.mdpi.com/journal/materials Materials 2017, 10, 371 2 of 16 tested in steam. Ruggles-Wrenn and Lee [6] investigated the cyclic fatigue behavior of 2D SiC/SiC composite at 1300 ◦C in air and in steam conditions. It was found that the degradation of the fatigue performance at 1300 ◦C is mainly controlled by the fibers’ strength degradation. Ruggles-Wrenn and Lanser [7] investigated the tension-compression fatigue behavior of 2D woven Nextel™ 720/alumina composite at 1200 ◦C in air and in steam. The fatigue limit stress was achieved at 40% and 35% tensile strength in air and steam environments, respectively, when the maximum cycle number was defined as 100,000 applied cycles. The presence of steam noticeably degrades the tension–compression fatigue performance of the oxide/oxide composite. During cyclic loading, the damage evolution inside the composites should be monitored to predict the lifetime. Maillet et al. [8] investigated the damage evolution of 2D SiC/[Si-B-C] composite at temperatures of 450 ◦C and 500 ◦C using the acoustic emission (AE)-based approach during static fatigue loading. However, the AE-based approach used to damage monitoring is limited at elevated temperatures. Li [9,10] developed a hysteresis dissipated energy–based damage parameter for the damage evolution and life prediction of fiber-reinforced CMCs under cyclic fatigue loading at room and elevated temperatures. In the combustion process, substantial amounts of water vapor are produced from burning hydrocarbon fuels in air. Under equilibrium conditions, 5%–10% of the combustion gas is water vapor. The reactions of SiC fibers with water are therefore a concern. Yao et al. [11] investigated the effects of wet oxidation on the microstructural evolution, fracture mode and mechanical properties of Hi-Nicalon SiC fibers, and found that the water vapor enhances the oxidation rates. Park [12] investigated the effects of different oxidation conditions on the early-stage oxidation behavior of SiC fibers. The steam condition tests clearly yielded a lower O/Si ratio than the air oxidation test, which is likely related to the influence of volatilization on the concentration of the more oxygen-rich component (SiO2). Parthasarathy et al. [13] investigated the experimental grain growth and oxidation kinetics of SiC-based fibers and the accompanying strength degradation in argon, air, and moist air using a mechanistic model. The attendant loss in strength is shown in be captured by the model that proposes increases in the strength-limiting flaw size as being proportional to the grain growth. The objective of this paper is to investigate the fatigue damage evolution and lifetime of 2D SiC/SiC composites at elevated temperatures. The damage development of 2D SiC/SiC composite was analyzed through the damage parameters of fatigue hysteresis dissipated energy, fatigue hysteresis modulus, fatigue peak strain and interface shear stress. The fatigue life stress-cycle (S-N) curves and fatigue limit stress of 2D SiC/SiC composites have been predicted.

2. Damage Parameters and Life Prediction Model

2.1. Damage Parameters Genet et al. [14] investigated the crack network inside of 2D woven SiC/[Si-B-C] composite. It was found that matrix cracks exist in the yarns and the matrix outside of the yarns. Under cyclic fatigue loading, the matrix cracking modes in 2D woven CMCs can be divided into ﬁve different modes, including: [15].

(1) Mode 1: transverse cracking in the transverse tow, with debonding at the tow boundary; (2) Mode 2: transverse cracking and matrix cracking with perfect fiber/matrix bonding and fracture of fibers occurs in the longitudinal tow; (3) Mode 3: transverse cracking and matrix cracking with fiber/matrix debonding and sliding in the longitudinal tow; (4) Mode 4: matrix cracking with perfect fiber/matrix bonding and fracture of fibers occurs in the longitudinal tow; (5) Mode 5: matrix cracking and fiber/matrix interface debonding and sliding in the longitudinal tow. Materials 2017, 10, 371 3 of 16

The transverse yarns run perpendicular to the longitudinal yarns. Upon unloading and reloading, the relative frictional slip occurred in the ﬁber/matrix interface of the matrix cracking mode 3 and mode 5 [16]. For matrix cracking mode 3, the unloading strain εunload and reloading strain εreload are determined by Equations (1) and (2) [17].

 2 ( − )( − + )  σ τi y τi 2y ld 2y lc ld lc  + 4 − 2 − (αc − αf)∆T, ld < VfEf Ef rflc Ef rflc 2 εunload = 2 2 (1)  σ τi y τi (2y − lc/2) lc  + 4 − 2 − (αc − αf)∆T, ld = VfEf Ef rflc Ef rflc 2

 σ τ z2 4τ (y − 2z)2  − 4 i + i  V E E r l E r l  f_axial f f f c f f c  τi (ld − 2y + 2z)(ld + 2y − 2z − lc) lc εreload = +2 − (αc − αf)∆T, ld < (2)  Ef rflc 2  2 2 2  σ τi z τi (y − 2z) τi (lc/2 − 2y + 2z) lc  − 4 + 4 − 2 − (αc − αf)∆T, ld = VfEf Ef rflc Ef rflc Ef rflc 2 where Vf denotes the fiber volume content in the longitudinal direction; Ef denotes the fiber elastic modulus; rf denotes the fiber radius; τi denotes the interface shear stress; lc denotes the matrix crack spacing; ld denotes the interface debonded length; y denotes the interface counter-slip length; z denotes the interface new-slip length; αf and αc denote the fiber and composite thermal expansion coefficient, respectively; ∆T denotes the temperature difference between the fabricated temperature T0 and the testing temperature T1 (∆T = T1 − T0). For matrix cracking mode 5, the unloading strain εunload and reloading strain εreload are determined by Equations (3) and (4) [17].

 2 1 τi y τi (2y−ld)(2y+ld−lc) lc  (σ − kσto) + 4 − 2 − (αc − α )∆T, l < VfEf Ef rflc Ef rflc f d 2 εunload = 2 2 (3) 1 τi y τi (2y−lc/2) lc  (σ − kσto) + 4 − 2 − (αc − α )∆T, l = VfEf Ef rflc Ef rflc f d 2

 2 ( − )2  1 τi z 4τi y 2z  (σ − kσto) − 4 +  VfEf Ef rflc Ef rflc  τ (l − 2y + 2z)(l + 2y − 2z − l ) l  + i d d c − − < c  2 (αc αf)∆T, ld Ef rflc 2 εreload = 2 2 (4)  1 τi z τi (y − 2z)  (σ − kσto) − 4 + 4  VfEf Ef rflc Ef rflc  2  τi (lc/2 − 2y + 2z) lc  − 2 − (αc − αf)∆T, ld = Ef rflc 2 Upon cyclic fatigue loading, the area associated with fatigue hysteresis loops is the energy lost during corresponding cycles, which is deﬁned by Equation (5).

Z σmax U = [εunload(σ) − εreload(σ)]dσ (5) σmin

The fatigue hysteresis dissipated energy of matrix cracking modes 3 and 5 can be derived by inserting the corresponding unloading and reloading strains into Equation (5). The composite fatigue hysteresis dissipated energy is determined by Equation (6).

Uc = ηU3 + (1 − η)U5 (6) where U3 and U5 denote the fatigue hysteresis dissipated energy of matrix cracking modes 3 and mode 5, respectively; and η is the damage parameter determined by the composite’s damage condition. Materials 2017, 10, 371 4 of 16

The fatigue hysteresis modulus E is deﬁned by Equation (7).

σ − σ E = max min (7) εc(σmax) − εc(σmin)

The increasing rate of peak strain φ is deﬁned by Equation (8).

εpeak(Nfinal) − εpeak(Ninitial) φ = (8) Nfinal − Ninitial where εpeak(Nfinal) denotes the peak strain at the final applied cycle number of Nfinal; and εpeak(Ninitial) denotes the peak strain at the initial applied cycle number of Ninitial. The decreasing/increasing rate of the fatigue hysteresis dissipated energy is defined by Equation (9).

Uc(Ninitial) − Uc(Nfinal) ϕ = (9) Nfinal − Ninitial The degradation rate of the fatigue hysteresis modulus Φ is defined by Equation (10).

E(N ) − E(N ) Φ = initial ﬁnal (10) Nﬁnal − Ninitial

The degradation rate of the interface shear stress Ψ is deﬁned by Equation (11).

τ (N ) − τ (N ) Ψ = i initial i ﬁnal (11) Nﬁnal − Ninitial

2.2. Life Prediction Model Under cyclic loading at elevated temperatures, fiber fracture occurred due to gradual interface wear and interface oxidation [18–23]. The global load-sharing assumption is used to determine the load carried by intact and fractured fibers [24]. σ 2lf 2lf = 1 − Pf 1 + T + Pr hTbi (12) Vf lc lc where lf denotes the slip length over which the fiber stress would decay to zero if not interrupted by the far-field equilibrium stresses; and hTbi denotes the average stress carried by broken fibers. h i Pf = χ ζPf a + (1 − η)Pf b + Pf c + Pf d (13)

Pr = Pf c + Pf d (14) where Pfa, Pfb, Pfc and Pfd denote the fiber failure probability of oxidized fibers in the oxidation region, unoxidized fibers in the oxidation region, and fibers in the interface debonded region and interface bonded region, respectively; ζ denotes the oxidation fibers fraction in the oxidized region; and χ denotes the fraction of oxidation in the multiple matrix cracks.

m Lt T Pf a(T) = 1 − exp −2 (15) l0 σ0(t)

m Lt T Pf b(T) = 1 − exp −2 (16) l0 σ0

( m+1 " m+1#) rfT Ld(N) Pf c(T) = 1 − exp − m 1 − 1 − (17) l0(σ0(N)) τi(N)(m + 1) lf(N) Materials 2017, 10, 371 5 of 16

m1 m1   rT LNd  PT 1expf  1 1  fc  m   (17) lN Nm1  lNf   00 i      2rTm  LN PT 1expf 1 d  fd      m LN lN   fo d   f  lNm0011   TlN (18)  s  mm11 Materials 2017, 10, 371    5 of 16 foLNdd LN LN d fo LN dL  111       TlNff r lN f TlNr ff2       m  2rfT Ld(N) where T denotesPf d(T) = the1 − loadexp carried− by intact fibers; rf denotes the fiber× radius;1 − Ld denotes− the interface  m σfo Ld(N) lf(N) debonded length; L denotes theρl0( σmatrix0(N)) crack(m + 1 spacing;) 1 − ρ− denotes the shear-lag model parameter; σfo  T l (N) (18) s #) denotes the fiberσ stressL in(N the) ρ interfaceL (N) m +bonded1 region;L (N) lf denotes σ theL slip(N )length ρL overm+1 which the fiber 1 − fo − d d − 1 − d − 1 − fo − d stress would decayT lfto(N )zero rfif not interruptelf(dN )by the Tfar-fieldlf(N )equilibrium2rf stresses. The time-dependent fiber strength will be controlled by surface defects resulting from oxidation and is where T denotes the load carried by intact fibers; r denotes the fiber radius; L denotes the given by Equation (19) [21]. f d interface debonded length; L denotes the matrix crack spacing; ρ denotes the shear-lag model parameter; σfo denotes the fiber stress in the interface bonded4 region; lf denotes the slip length over which the fiber stress would decay to zero if not1 interruptedKIC by the far-field equilibrium stresses. 00tt,  The time-dependent fiber strength will be controlled by surface defects resulting from oxidation and is  kY 0 given by Equation (19) [21].  4 (19)  1 K 4  KKIC1IC IC  σtt0(t) = σ0, t ≤,  0  4 k Yσ0 kY4 (19)  YktK 1 K0  ( ) = √IC > IC  σ0 t 4 , t Y kt k Yσ0 where KIC denotes the critical stress intensity factor; Y is a geometric parameter; and k is the parabolicwhere rateKIC denotesconstant. the Pa criticalrthasarathy stress intensity et al. [13] factor; investigatedY is a geometric the parameter;strength degradation and k is the parabolic of SiC fibers rate constant. Parthasarathy et al. [13] investigated the strength degradation of SiC fibers in air and in in air and in steam at elevated temperatures. The strength degradation of SiC fibers versus oxidation steam at elevated temperatures. The strength degradation of SiC fibers versus oxidation time curves at time curves750, 1000, at 1100,750, 1000, 1200 and 1100, 1300 1200◦C inand air 1300 andsteam °C in conditionsair and steam are illustrated conditions in Figureare illustrated1, and predicted in Figure 1, and predictedusing Equation using (19). Equation The SiC fiber(19). strength The SiC degradation fiber strength with increasing degradation time inwith SiC/SiC increasing composite time in SiC/SiCat elevated composite temperatures at elevated of 750, temperatures 1000, 1100, 1200of 750, and 1000, 1300 ◦ 1100,C in air 1200 and and stream 1300 was °C predicted in air and using stream was predictedEquation (19), using and Equation is shown in(19), Figure and1 .is shown in Figure 1.

FigureFigure 1. The 1. strengthThe strength degradation degradation of SiC of fibers SiC ﬁbers (a) in (a )air in and air and(b) in (b )steam in steam conditions conditions at elevated at temperatures.elevated temperatures.

WithWith the theincreasing increasing cycle cycle number, number, thethe interface interface shear shear stress stress and fiberand strengthfiber strength decrease decrease due to the due to the interfaceinterface wear and and interface interface oxidation oxidation [25]. [25]. The fiber The failurefiber failure probability probability in the interface in the oxidation interface region, oxidation region,interface interface debonded debonded region andregion interface and bondedinterface region bonded can be region obtained can by combiningbe obtained the by interface combining wear the interfacemodel, wear interface model, oxidation interface model oxidation and fiber strength model degradation and fiber model strength with Equationsdegradation (12)–(14) model [26]. with The evolution of the fiber failure probability versus cycle number curves can be obtained. When the fiber broken fraction approaches the critical value, the composite fatigue fractures. The fatigue limit stress is calculated when the fracture applied cycles approach the maximum cycle number. Materials 2017, 10, 371 6 of 16

Equations (12)–(14) [26]. The evolution of the fiber failure probability versus cycle number curves can be obtained. When the fiber broken fraction approaches the critical value, the composite fatigue fractures. The fatigue limit stress is calculated when the fracture applied cycles approach the maximum cycle number.

3. ExperimentalMaterials 2017, 10, 371Comparisons 6 of 16 Under cyclic loading, the interface shear stress degrades with applied cycles. The interface shear3. Experimental stress degradation Comparisons model developed by Evans has been used to determine the evolution of the interfaceUnder shear cyclic stress loading, [23]. the interface shear stress degrades with applied cycles. The interface shear

stress degradation model developed by Evans has been used to determinej the1 evolution of the interface shear stress [23]. isNbbN000 s11 (20) −1 j (τi(N) − τs)/(τ0 − τs) = (1 + b0) 1 + b0N (20) where τ0 denotes the initial interface shear stress; τs denotes the steady-state interface shear stress; b0 is awhere coefficient;τ0 denotes and thej is initialan exponent interface which shear determines stress; τs denotes the rate the atsteady-state which interface interface shear shear stress stress; drops withb0 isthe a coefficient;number of and cyclesj is N an. exponent which determines the rate at which interface shear stress drops with the number of cycles N. 3.1. Damage Evolution and Lifetime at 750 °C in Air 3.1. Damage Evolution and Lifetime at 750 ◦C in Air Mall [2] investigated the tension-tension fatigue behavior of 2D Syl-iBN/BN/SiC composite under twoMall test [2] environments, investigated the i.e., tension-tension 0% and 60% moisture fatigue behavior content conditions of 2D Syl-iBN/BN/SiC at 750 °C. The composite monotonic under two test environments, i.e., 0% and 60% moisture content conditions at 750 ◦C. The monotonic tensile strength was about 345 MPa. Under σmax = 284 MPa and a 0% moisture content environment, tensile strength was about 345 MPa. Under σ = 284 MPa and a 0% moisture content environment, the peak strain increased from 0.227% at themax 984th applied cycle to 0.26% at the 434,323th applied the peak strain increased from 0.227% at the 984th applied cycle to 0.26% at the 434,323th applied cycle with the increasing rate of the peak strain of ϕ = 7.6 × 10−10/cycle, as shown in Figure 2a; the cycle with the increasing rate of the peak strain of ϕ = 7.6 × 10−10/cycle, as shown in Figure2a; interface shear stress decreased from 25 MPa at the first applied cycle to 22 MPa at the 434,323th the interface shear stress decreased from 25 MPa at the first applied cycle to 22 MPa at the 434,323th applied cycle with the degradation rate of the interface shear stress of Ψ = 6.9 × 10−6 MPa/cycle, as applied cycle with the degradation rate of the interface shear stress of Ψ = 6.9 × 10−6 MPa/cycle, shownas shown in Figure in Figure 2b. 2Theb. Theinterface interface shear shear stress stress degradation degradation model model parameters parameters in in Equation Equation (20) (20) are given in Table 1. Under σmax = 190 MPa (55% σUTS) and a 60% moisture content environment, the peak are given in Table1. Under σmax = 190 MPa (55% σUTS) and a 60% moisture content environment, strainthe peakincreased strain from increased 0.117% from at 0.117%the 1099th at the applied 1099th cycle applied to 0.147% cycle to at 0.147% the 524,587th at the 524,587th applied applied cycle, as showncycle, in as Figure shown 2a, in with Figure the2a, increasing with the increasing rate of the rate peak of thestrain peak of strainϕ = 5.7 of × ϕ10=−10 5.7/cycle;× 10 the−10 /cycle;interface shearthe interfacestress decreased shear stress slowly decreased with slowlyapplied with cycles, applied i.e., cycles,from 25 i.e., MPa from at 25 the MPa first at the applied first applied cycle to 19.4cycle MPa to 19.4at the MPa 524,587th at the 524,587th applied applied cycle, with cycle, the with degradation the degradation rate rateof the of the interface interface shear shear stress stress of Ψ of= Ψ1.0= 1.0× 10×−510 MPa/cycle,−5 MPa/cycle as ,shown as shown in inFigure Figure 2b.2b. The The interface shearshear stress stress degradation degradation model model parametersparameters in in Equation Equation (20) (20) are are given given in in Table Table1 1.. TheThe oxidation oxidation and and embrittlement embrittlement of theof the fiber/matrix fiber/matrix boronboron nitride nitride (BN) (BN) interphase occurred occurred in thein the presence presence of moisture of moisture to form to the form boria the (B2 Oboria3) and (B reacted2O3) and reactedwith SiCwith to SiC form to a form borosilicate a borosilicate melt. When melt. the Wh maximumen the maximum cycle number cycle was numb defineder was to bedefined 1,000,000 to be 1,000,000applied applied cycles, the cycles, fatigue the limit fatigue decreased limit fromdecrease 67%d tensile from strength67% tensile under strength a 0% moisture under a environment 0% moisture environmentto 49% tensile to strength49% tensile under strength a 60% under moisture a 60% environment, moisture asenvironment, shown in Figure as shown2c,d. in Figure 2c,d.

Figure 2. Cont.

Materials 2017, 10, 371 7 of 16 Materials 2017, 10, 371 7 of 16 Materials 2017, 10, 371 7 of 16

Figure 2. (a) The peak strain versus applied cycles with test environment of 0% moisture content Figure 2. ((aa)) The peak strain versus appl appliedied cycles with test environment of 0% moisture content condition and 60% moisture content condition; (b) the interface shear stress versus applied cycle condition andand 60%60% moisturemoisture content content condition; condition; (b )(b the) the interface interface shear shear stress stress versus versus applied applied cycle cycle with with test environment of 0% moisture content condition and 60% moisture content condition; (c) the withtest environment test environment of 0% of moisture 0% moisture content content condition condition and 60% and moisture 60% moisture content content condition; condition; (c) the fatigue(c) the fatiguefatiguelife S-N life life curve S-N S-N withcurve curve test with with environment testtest environmentenvironment of 0% moisture of 0%0% content moisturemoisture condition; contentcontent and condition; condition; (d) with and test and ( environmentd ()d with) with test test ◦ environmentenvironmentof 60% moisture of of 60% 60% content moisture moisture condition content content of 2D conditioncondition SiC/SiC of composite 2D2D SiC/SiCSiC/SiC at composite 750compositeC in air at at [7502 750]. °C °C in in air air [2]. [2].

◦ 3.2.3.2. Damage Damage Evolution Evolution and and Lifetime Lifetime at at 10001000 °C°CC KanufKanuf [3] [[3]3 ]investigated investigatedinvestigated the thethe tension-tensiontension-tension fatiguefafatiguetigue behaviorbehaviorbehavior of ofof 2D 2D2D CGCG CG Nicalon Nicalon™/BN/SiC Nicalon™/BN/SiC™/BN/SiC ◦ compositecomposite under underunder twotwo two test testtest environments, environments,environments, i.e., i.e., in air in and airair in andand steam inin conditions steamsteam conditionsconditions at 1000 C.at at The1000 1000 monotonic °C. °C. The The ◦ monotonicmonotonictensile strength tensile tensile was strength strength about 114was was MPa. aboutabout At 114114 1000 MPa.C in At air, 1010 the0000 °C fatigue°C inin air, air, hysteresis the the fatigu fatigu dissipatede ehysteresis hysteresis energy dissipated dissipated under 3 3 energyenergyσmax =under 80under MPa σ maxσ increasesmax = =80 80 MPa MPa from increases increases 4.6 kJ/m fromfromat the 4.6 second kJ/mkJ/m3 applied3 atat thethe secondcyclesecond to applied 7applied kJ/m cycleat cycle the to 30,000th to 7 kJ/m7 kJ/m applied3 at3 atthe the −5 −3 30,000th30,000thcycle with applied applied the increasing cycle cycle with with rate the the ofincreasing increasing fatigue hysteresis rate of fatiguefatigue dissipated hysteresishysteresis energy dissipated dissipated of φ = 8 ×energy energy10 kJof · ofmφ =φ 8/cycle,= ×8 10 × −105 −5 kJ·mkJ·mas− shown3/cycle,−3/cycle, in as Figureas shown shown3a; inthe in Figure fatigueFigure 3a;3a; hysteresis thethe fatiguefatigue modulus hysteresiseresis decreased modulusmodulus from decreased 1.0decreased at the ﬁrstfrom from applied 1.0 1.0 at at cyclethe the first tofirst 0.9 at the 3022th applied cycle when σ = 80 MPa, and from 1.0 at the ﬁrst applied cycle to 0.91 at the appliedapplied cycle cycle to to 0.9 0.9 at at the the 3022th 3022th applied appliedmax cycle when σσmaxmax == 80 80 MPa, MPa, and and from from 1.0 1.0 at at the the first first applied applied 295th applied cycle when σmax = 100 MPa, asmax shown in Figure3b. The fatigue peak strain increased cyclecycle to to 0.91 0.91 at at the the 295th 295th applied applied cycle cycle whenwhen σmax == 100100 MPa,MPa, as as shown shown in in Figure Figure 3b. 3b. The The fatigue fatigue peak peak strainfrom 0.009%increased at thefrom 30th 0.009% applied at the cycle 30th to applied 0.106% atcycle the to 164122th 0.106% appliedat the 164122th cycle when appliedσmax cycle= 80 when MPa strain increased from 0.009% at the 30th applied cycle to 0.106%− 9at the 164122th applied cycle when withσmax = the 80increasing MPa with rate the ofincreasing the fatigue rate peak of strainthe fatigue of ϕ = peak 5.9 × strain10 /cycle, of ϕ = and5.9 × from 10−9 0.02%/cycle, atand the from 40th σmax = 80 MPa with the increasing rate of the fatigue peak strain of ϕ = 5.9 × 10−9/cycle, and from 0.02%applied at cyclethe 40th to 0.133% applied at cycle the 87,457th to 0.133% applied at the 87,457th cycle when appliedσmax cycle= 100 when MPa withσmax = the 100 increasing MPa withrate the 0.02% at the 40th applied cycle to 0.133% at− the 87,457th applied cycle when σmax = 100 MPa with the increasingof the fatigue rate peak of the strain fatigue of ϕpeak= 1.3 strain× 10 of8 /cycle,ϕ = 1.3 as× 10 shown−8/cycle, in as Figure shown3c; in the Figure interface 3c; the shear interface stress increasing rate of the fatigue peak strain of ϕ = 1.3 × 10−8/cycle, as shown in Figure 3c; the interface sheardecreased stress from decreased 15 MPa from at the 15 second MPa at applied the second cycle applied to 10 MPa cycle at the to 30,000th10 MPa at applied the 30,000th cycle, withapplied the shear stress decreased from 15 MPa at the second applied− cycle to 10 MPa at the 30,000th applied cycle,interface with shear the interface stress degradation shear stress ratedegradation of Ψ = 1.6 rate× of10 Ψ4 =MPa/cycle, 1.6 × 10−4 MPa/cycle, as shown as in shown Figure in3d, Figure andthe 3d, cycle, with the interface shear stress degradation rate of Ψ = 1.6 × 10−4 MPa/cycle, as shown in Figure 3d, andinterface the interface shear stress shear degradation stress degradation model parameters model parameters in Equation in (20)Equation are listed (20) in are Table listed1. The in Table fatigue 1. and the interface shear stress degradation model parameters in Equation (20) are listed in Table 1. Thelimit fatigue approached limit approached 28% tensile strength,28% tensile as shownstrength, in as Figure shown3e. in Figure 3e. The fatigue limit approached 28% tensile strength, as shown in Figure 3e.

Figure 3. Cont.

Materials 2017, 10, 371 8 of 16 Materials 2017, 10, 371 8 of 16

Figure 3. (a) The fatigue hysteresis dissipated energy versus applied cycles; (b) the normalized Figure 3. (a) The fatigue hysteresis dissipated energy versus applied cycles; (b) the normalized hysteresis modulus versus applied cycles; (c) thethe peakpeak strainstrain versusversus appliedapplied cycles;cycles; ((dd)) thethe interfaceinterface shearshear stressstress versusversus appliedapplied cycles;cycles; andand ((ee)) thethe fatiguefatigue lifelife S-NS-N curvescurves ofof 2D2D SiC/SiCSiC/SiC compositecomposite atat 10001000 ◦°CC in air [[3].3].

At 1000 °C in steam, the fatigue hysteresis dissipated energy increased from 1.5 kJ/m3 at the At 1000 ◦C in steam, the fatigue hysteresis dissipated energy increased from 1.5 kJ/m3 at the second applied cycle to 7.7 kJ/m3 at the 190,000th applied cycle with the increasing rate of the fatigue second applied cycle to 7.7 kJ/m3 at the 190,000th applied cycle with the increasing rate of the fatigue hysteresis dissipated energy of φ = 3.2 × 10−5 kJ·m−3/cycle when σmax = 60 MPa, and from 9 kJ/m3 at the hysteresis dissipated energy of φ = 3.2 × 10−5 kJ·m−3/cycle when σ = 60 MPa, and from 9 kJ/m3 second applied cycle to 16.8 kJ/m3 at the 10,000th applied cycle with maxthe increasing rate of the fatigue at the second applied cycle to 16.8 kJ/m3 at the 10,000th applied cycle with the increasing rate of the hysteresis dissipated energy of φ = 7.8 × 10−4 kJ·m−3/cycle when σmax = 100 MPa, as shown in Figure 4a. fatigue hysteresis dissipated energy of φ = 7.8 × 10−4 kJ·m−3/cycle when σ = 100 MPa, as shown The fatigue hysteresis modulus decreased from 1.0 at the first applied cyclemax to 0.76 at the 195,129th in Figure4a. The fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.76 at applied cycle when σmax = 100 MPa, and from 1.0 at the first applied cycle to 0.91 at the 707th applied the 195,129th applied cycle when σmax = 100 MPa, and from 1.0 at the first applied cycle to 0.91 at the cycle when σmax = 60 MPa, as shown in Figure 4b; the fatigue peak strain increased with applied cycles, 707th applied cycle when σmax = 60 MPa, as shown in Figure4b; the fatigue peak strain increased with i.e., from 0.007% at the fifth applied cycle to 0.109% at the 41,323th applied cycle when σmax = 60 MPa applied cycles, i.e., from 0.007% at the fifth applied cycle to 0.109% at the 41,323th applied cycle when with the increasing rate of the fatigue peak strain of ϕ = 2.4 × 10−8/cycle, and from 0.022% at the fifth −8 σmax = 60 MPa with the increasing rate of the fatigue peak strain of ϕ = 2.4 × 10 /cycle, and from applied cycle to 0.08% at the 4098th applied cycle when σmax = 100 MPa with the increasing rate of the 0.022% at the fifth applied cycle to 0.08% at the 4098th applied cycle when σ = 100 MPa with the fatigue peak strain of ϕ = 1.4 × 10−7/cycle, as shown in Figure 4c. The interface shearmax stress decreased from increasing rate of the fatigue peak strain of ϕ = 1.4 × 10−7/cycle, as shown in Figure4c. The interface 15 MPa at the second applied cycle to 3 MPa at the 190,000th applied cycle with the interface shear stress shear stress decreased from 15 MPa at the second applied cycle to 3 MPa at the 190,000th applied cycle degradation rate of Ψ = 6.3 × 10−5 MPa/cycle when σmax = 60 MPa, and from 15 MPa at the second applied with the interface shear stress degradation rate of Ψ = 6.3 × 10−5 MPa/cycle when σ = 60 MPa, cycle to 8 MPa at the 10,000th applied cycle with the interface shear stress degradation ratemax of Ψ = 7 × 10−4 and from 15 MPa at the second applied cycle to 8 MPa at the 10,000th applied cycle with the interface MPa/cycle when σmax = 100 MPa, as shown in Figure 4d, and the interface shear stress degradation model shear stress degradation rate of Ψ = 7 × 10−4 MPa/cycle when σ = 100 MPa, as shown in Figure4d, parameters in Equation (20) are listed in Table 1. The fatigue limitmax approached 10% tensile strength, as and the interface shear stress degradation model parameters in Equation (20) are listed in Table1. shown in Figure 4e. The presence of steam significantly degraded the fatigue performance of the SiC/SiC The fatigue limit approached 10% tensile strength, as shown in Figure4e. The presence of steam composite due to the oxidation of the BN interphase and SiC fibers. In the present analysis, the creep significantly degraded the fatigue performance of the SiC/SiC composite due to the oxidation of strain of the SiC fibers was not considered, leading to the difference between the theoretical analysis and the BN interphase and SiC fibers. In the present analysis, the creep strain of the SiC fibers was not experimental data, as shown in Figure 4c. considered, leading to the difference between the theoretical analysis and experimental data, as shown in Figure4c.

Materials 2017, 10, 371 9 of 16 Materials 2017, 10, 371 9 of 16

Figure 4. ((aa)) The The fatigue fatigue hysteresis hysteresis dissipated dissipated energy energy versus applied cycles; ( (b)) the normalized hysteresis modulus versus applied cycles; ( cc)) the peak strain vers versusus applied cycles; ( d) the interface shear stress versus applied cycles; and (e) the fatiguefatigue lifelife S-NS-N curvescurves ofof 2D2D SiC/SiCSiC/SiC composite at ◦ 1000 °CC in steam [3]. [3].

3.3. Damage Damage Evolution and Lifetime at 1100 °C◦C Groner [[4]4] investigated the tension-tension fatiguefatigue behaviorbehavior ofof 2D2D SiC/SiCSiC/SiC composite at 1100 °C◦C in air. The The monotonic tensile strength waswas aboutabout 230230 MPa.MPa. When σσmax == 120 120 MPa, MPa, the fatigue hysteresis modulus decreased decreased from from 1.0 1.0 at at the first first applied cycle cycle to to 0.72 0.72 at at the 5102th applied applied cycle; cycle; when σmaxmax == 140 140 MPa, MPa ,the the fatigue fatigue hysteresis hysteresis modulus modulus decr decreasedeased from from 1.0 1.0 at atthe the first first applied applied cycle cycle to 0.65to 0.65 at the at the 5341th 5341th applied applied cycle; cycle; when when σmaxσ =max 170= MPa, 170 MPa, the fatigue the fatigue hyster hysteresisesis modulus modulus decreased decreased from 1.0from at 1.0the atfirst the applied first applied cycle to cycle 0.455 to at 0.455the 2042th at the applied 2042th cycle; applied and cycle; when and σmax when = 210 σMPa,max =the 210 fatigue MPa, hysteresisthe fatigue modulus hysteresis decreased modulus from decreased 1.0 at from the first 1.0 atapplied the first cycle applied to 0.35 cycle at tothe 0.35 981th at theapplied 981th cycle, applied as showncycle, as in shown Figure in 5a. Figure The5 a.peak The strain peak strainincreased increased with withapplied applied cycles, cycles, i.e., when i.e., when σmax σ=max 110= MPa, 110 MPa, the peakthe peak strain strain increased increased from from 0.091% 0.091% at atthe the third third applied applied cycle cycle to to 0.151% 0.151% at at the the 246,311th 246,311th applied applied cycle −9 −9 with the increasing increasing rate rate of of the the peak peak strain strain of of ϕϕ = =2.4 2.4 × 10× 10/cycle;/cycle; when when σmax =σ max140 MPa,= 140 the MPa, peak the strain peak increasedstrain increased from 0.142% from 0.142% at the atsecond the second applied applied cycle cycleto 0.278% to 0.278% at the at 22,798th the 22,798th applied applied cycle cycle with with the −8 −8 increasingthe increasing rate rateof the of thepeak peak strain strain of ϕ of = ϕ5.9= × 5.9 10×/cycle;10 /cycle; and when and whenσmax = σ210max MPa,= 210 the MPa, peak the strain peak increased from 0.393% at the fifth applied cycle to 0.475% at the 965th applied cycle with the

Materials 2017, 10, 371 10 of 16

Materials 2017, 10, 371 10 of 16 strain increased from 0.393% at the ﬁfth applied cycle to 0.475% at the 965th applied cycle with the −7 increasing raterate ofof thethe peakpeak strainstrain of ofϕ ϕ= = 8.5 8.5× × 1010−7/cycle,/cycle, as as shown shown in in Figure Figure 55b.b. The fatiguefatigue lifelife S-NS-N ◦ curve is shown in Figure5 5c,c, and and the the fatigue fatigue limit limit approached approached 39% 39% tensile tensile strength strength at at 1100 1100 °CC inin air.air.

Figure 5. (a) The normalized fatigue hysteresis modulus versus applied cycles; ( b) the peak strainstrain versus applied cycles;cycles; andand ((cc)) thethe fatiguefatigue lifelife S-NS-N curvescurves ofof 2D2D SiC/SiCSiC/SiC composite atat 11001100 ◦°CC in air [[4].4].

3.4. Damage Evolution and Lifetime at 1200 °C 3.4. Damage Evolution and Lifetime at 1200 ◦C Jacob [5] investigated the tension-tension fatigue behavior of 2D SiC/SiC composite under two Jacob [5] investigated the tension-tension fatigue behavior of 2D SiC/SiC composite under two test environments, i.e., in air and in steam conditions at 1200 °C. The monotonic tensile strength was test environments, i.e., in air and in steam conditions at 1200 ◦C. The monotonic tensile strength was about 306 MPa. At 1200 ◦°C in air, when σmax = 140 MPa (45.7%σUTS), the fatigue hysteresis dissipated about 306 MPa. At 1200 C in air, when σmax = 140 MPa (45.7%σUTS), the fatigue hysteresis dissipated energy increased from 5.2 kJ/m3 at the 1000th applied cycle to 25 kJ/m3 at the 30,000th applied cycle energy increased from 5.2 kJ/m3 at the 1000th applied cycle to 25 kJ/m3 at the 30,000th applied cycle with the increasing rate of the fatigue hysteresis dissipated energy of φ = 6.8 × 10−4 kJ·m−3/cycle, as with the increasing rate of the fatigue hysteresis dissipated energy of φ = 6.8 × 10−4 kJ·m−3/cycle, shown in Figure 6a. The fatigue hysteresis modulus decreased with applied cycles, i.e., from 1.0 at as shown in Figure6a. The fatigue hysteresis modulus decreased with applied cycles, i.e., from 1.0 at the first applied cycle to 0.6 at the 196,841th applied cycle when σmax = 100 MPa (32.6% σUTS), and the first applied cycle to 0.6 at the 196,841th applied cycle when σmax = 100 MPa (32.6% σUTS), and from from 1.0 at the first applied cycle to 0.444 at the 30,509th applied cycle when σmax = 140 MPa (45.7% 1.0 at the first applied cycle to 0.444 at the 30,509th applied cycle when σmax = 140 MPa (45.7% σUTS), σUTS), as shown in Figure 6b. The fatigue peak strain increased with applied cycles, i.e., from 0.625% as shown in Figure6b. The fatigue peak strain increased with applied cycles, i.e., from 0.625% at at the first applied cycle to 0.724% at the 362th applied cycle when σmax = 140 MPa (45.7% σUTS) and a the first applied cycle to 0.724% at the 362th applied cycle when σmax = 140 MPa (45.7% σUTS) and loading frequency of 0.1 Hz with the increasing rate of the fatigue peak strain of ϕ = 2.7 × 10−6/cycle, a loading frequency of 0.1 Hz with the increasing rate of the fatigue peak strain of ϕ = 2.7 × 10−6/cycle, and from 0.653% at the first applied cycle to 0.776% at the 4360th applied cycle when σmax = 140 MPa and from 0.653% at the first applied cycle to 0.776% at the 4360th applied cycle when σmax = 140 MPa (45.7% σUTS) and a loading frequency of 1.0 Hz with the increasing rate of the fatigue peak strain of (45.7% σUTS) and a loading frequency of 1.0 Hz with the increasing rate of the fatigue peak strain of ϕ = 2.8 × 10−7/cycle, as shown in Figure 6c. The interface shear stress decreased with applied cycles, ϕ = 2.8 × 10−7/cycle, as shown in Figure6c. The interface shear stress decreased with applied cycles, i.e., from 45 MPa at the 1000th applied cycle to 3 MPa at the 30,000th applied cycle with the interface i.e., from 45 MPa at the 1000th applied cycle to 3 MPa at the 30,000th applied cycle with the interface −3 shear stress degradation rate of Ψ = 1.4 × 10 MPa/cycle−3 when σmax = 140 MPa (45.7% σUTS), as shown shear stress degradation rate of Ψ = 1.4 × 10 MPa/cycle when σmax = 140 MPa (45.7% σ ), as in Figure 6d; the interface shear stress degradation model parameters in Equation (20) are listedUTS in shown in Figure6d; the interface shear stress degradation model parameters in Equation (20) are listed Table 1. The fatigue life S-N curve is shown in Figure 6e, and the fatigue limit approached 17% in Table1. The fatigue life S-N curve is shown in Figure6e, and the fatigue limit approached 17% tensile strength at 1200 °C in air. tensile strength at 1200 ◦C in air.

Materials 2017, 10, 371 11 of 16 Materials 2017, 10, 371 11 of 16

Figure 6. (a) The fatigue hysteresis dissipated energy versus applied cycles; (b) the normalized Figure 6. (a) The fatigue hysteresis dissipated energy versus applied cycles; (b) the normalized fatigue hysteresisfatigue hysteresis modulus modulus versus appliedversus applied cycles; (ccycles;) the peak (c) the strain peak versus strain applied versus cycles;applied (d cycles;) the interface (d) the shearinterface stress shear versus stress applied versus cycles; applied and cycles; (e) the and fatigue (e) lifethe S-Nfatigue curves life ofS-N 2D curves SiC/SiC of composite 2D SiC/SiC at 1200composite◦C in airat 1200 [5]. °C in air [5].

At 1200 °C in steam conditions, when σmax = 140 MPa (45.7%σUTS), the fatigue hysteresis At 1200 ◦C in steam conditions, when σ = 140 MPa (45.7%σ ), the fatigue hysteresis dissipated energy increased from 4.5 kJ/m3 at themax 100th applied cycle toUTS 24.6 kJ/m3 at the 10,000th dissipated energy increased from 4.5 kJ/m3 at the 100th applied cycle to 24.6 kJ/m3 at the applied cycle with the increasing rate of the fatigue hysteresis dissipated energy of φ = 2.2 × 10−3 10,000th applied cycle with the increasing rate of the fatigue hysteresis dissipated energy of kJ·m−3/cycle, as shown in Figure 7a. The fatigue hysteresis modulus decreased with applied cycles, φ = 2.2 × 10−3 kJ·m−3/cycle, as shown in Figure7a. The fatigue hysteresis modulus decreased with i.e., from 1.0 at the first applied cycle to 0.36 at the 10,236th applied cycle when σmax = 140 MPa (45.7% applied cycles, i.e., from 1.0 at the ﬁrst applied cycle to 0.36 at the 10,236th applied cycle when σmax σUTS) with the loading frequency of 0.1 Hz, and from 1.0 at the first applied cycle to 0.67 at the 7208th = 140 MPa (45.7% σUTS) with the loading frequency of 0.1 Hz, and from 1.0 at the ﬁrst applied cycle applied cycle when σmax = 140 MPa (45.7% σUTS) with the loading frequency of 10 Hz, as shown in to 0.67 at the 7208th applied cycle when σ = 140 MPa (45.7% σ ) with the loading frequency of Figure 7b. The peak strain increased with maxapplied cycles, i.e., fromUTS 0.036% at the 100th applied cycle 10 Hz, as shown in Figure7b. The peak strain increased with applied cycles, i.e., from 0.036% at the to 0.205% at the 4043th applied cycle with the increasing rate of the peak strain of ϕ = 4.2 × 10−7/cycle 100th applied cycle to 0.205% at the 4043th applied cycle with the increasing rate of the peak strain of when σmax = 140 MPa (45.7%σUTS) with the loading frequency of 0.1 Hz, and from 0.014% at the third ϕ = 4.2 × 10−7/cycle when σ = 140 MPa (45.7%σ ) with the loading frequency of 0.1 Hz, and applied cycle to 0.15% at the 39,737thmax applied cycle withUTS the increasing rate of fatigue peak strain of from 0.014% at the third applied cycle to 0.15% at the 39,737th applied cycle with the increasing rate ϕ = 3.4 × 10−8/cycle when σmax = 140 MPa (45.7% σUTS) with the loading frequency of 10 Hz, as shown of fatigue peak strain of ϕ = 3.4 × 10−8/cycle when σ = 140 MPa (45.7% σ ) with the loading in Figure 7c. The interface shear stress decreased withmax applied cycles, i.e., fromUTS 17 MPa at the 100th frequency of 10 Hz, as shown in Figure7c. The interface shear stress decreased with applied cycles, applied cycle to 3.2 MPa at the 10,000th applied cycle with the interface shear stress degradation rate i.e., from 17 MPa at the 100th applied cycle to 3.2 MPa at the 10,000th applied cycle with the interface of Ψ = 1.39 × 10−3 MPa/cycle, as shown in Figure 7d; the interface shear stress degradation model shear stress degradation rate of Ψ = 1.39 × 10−3 MPa/cycle, as shown in Figure7d; the interface parameters in Equation (20) are listed in Table 1. The fatigue life S-N curve is shown in Figure 7e, and the fatigue limit approached 9% tensile strength at 1200 °C in steam atmosphere.

Materials 2017, 10, 371 12 of 16 shear stress degradation model parameters in Equation (20) are listed in Table1. The fatigue life S-N curve is shown in Figure7e, and the fatigue limit approached 9% tensile strength at 1200 ◦C in steamMaterials atmosphere. 2017, 10, 371 12 of 16

Figure 7.7.( a(a)) The The fatigue fatigue hysteresis hysteresis dissipated dissipated energy energy versus versus applied applied cycles; cycles; (b) the ( normalizedb) the normalized fatigue hysteresisfatigue hysteresis modulus modulus versusapplied versus applied cycles; ( ccycles;) the peak (c) the strain peak versus strain applied versus cycles;applied (d cycles;) the interface (d) the shearinterface stress shear versus stress applied versus cycles; applied and cycles; (e) the and fatigue (e) lifethe S-Nfatigue curves life of S-N 2D curves SiC/SiC of composite 2D SiC/SiC at 1200composite◦C in steamat 1200 [5 °C]. in steam [5].

3.5. Damage Evolution and Lifetime at 1300 °C 3.5. Damage Evolution and Lifetime at 1300 ◦C Ruggles-Wrenn and Lee [6] investigated the tension-tension fatigue behavior of 2D Ruggles-Wrenn and Lee [6] investigated the tension-tension fatigue behavior of 2D TM Hi-NicalonTM/SiC-B4C composite under two test environments, i.e., in air and in steam conditions, at Hi-Nicalon /SiC-B4C composite under two test environments, i.e., in air and in steam conditions, 1300 °C. The monotonic tensile strength was about 311 MPa. At 1300 °C in air, the fatigue hysteresis at 1300 ◦C. The monotonic tensile strength was about 311 MPa. At 1300 ◦C in air, the fatigue hysteresis modulus decreased with applied cycles, i.e., when σmax = 100 MPa, the normalized fatigue hysteresis modulus decreased with applied cycles, i.e., when σmax = 100 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.435 at the 77,639th applied cycle; when modulus decreased from 1.0 at the ﬁrst applied cycle to 0.435 at the 77,639th applied cycle; when σmax = 120 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.389 at the 55,629th applied cycle; when σmax = 130 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.489 at the 19,719th applied cycle; and when σmax = 140 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.389 at the 10,124th applied cycle, as shown in Figure 8a. At 1300 °C in steam conditions, when σmax = 100 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.641 at the 194,352th applied cycle; when σmax = 120 MPa, the normalized fatigue

Materials 2017, 10, 371 13 of 16

σmax = 120 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.389 at the 55,629th applied cycle; when σmax = 130 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.489 at the 19,719th applied cycle; and when σmax = 140 MPa, the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied cycle to 0.389 at the 10,124th applied cycle, as shown in Figure8a. At 1300 ◦C in steam conditions, when Materialsσmax = 1002017,MPa, 10, 371the normalized fatigue hysteresis modulus decreased from 1.0 at the first applied13 of 16 cycle to 0.641 at the 194,352th applied cycle; when σmax = 120 MPa, the normalized fatigue hysteresis hysteresismodulus decreasedmodulus decreased from 1.0 atfrom the 1.0 first at appliedthe first cycleapplied to cycle 0.603 to at 0.603 the 95,469th at the 95,469th applied applied cycle; whencycle; whenσmax = σ 130max MPa= 130, theMPa, normalized the normalized fatigue fatigue hysteresis hysteres modulusis modulus decreased decreased from 1.0 from at the 1.0 first at the applied first appliedcycle to 0.463cycle atto the0.463 70,087th at the applied70,087th cycle; applied and cycle; when andσmax when= 140 σ MPa,max = 140 the normalizedMPa, the normalized fatigue hysteresis fatigue hysteresismodulus decreasedmodulus decreased from 1.0 at from the first1.0 at applied the first cycle applied to 0.431 cycle at to the 0.431 15,414th at the applied 15,414th cycle, applied as shown cycle, asin Figureshown8 b.in TheFigure fatigue 8b. The life S-Nfatigue curves life atS-N 1300 curves◦C inatair 1300 and °C in in steam air and conditions in steam are conditions illustrated are in illustratedFigure8c,d, in and Figure the fatigue8c,d, and limit the approachedfatigue limit 28%approa tensileched strength 28% tensile in air, strength and 19% in air, tensile and strength19% tensile in strengthsteam conditions. in steam conditions.

Figure 8. (a) The normalized fatigue hysteresis modulus versus applied cycles with the test Figure 8. (a) The normalized fatigue hysteresis modulus versus applied cycles with the test environment in air; (b) the normalizednormalized fatigue hysteresis modulusmodulus versus applied cycles with test environment in steam; and ( c) the fatigue life S-N curve with th thee test environment in air; and (d) the fatigue life S-N curve with the environment inin steamsteam ofof 2D2D SiC/SiCSiC/SiC composite composite at at 1300 1300 °C◦C[ [6].6].

Table 1. The parameters of the interface shear stress degradation model for 2D SiC/SiC composite under different peak stresses, loading frequencies and test temperatures.

Temperatures Environment σmax/MPa τ0/MPa τs/MPa b0 j 0% moisture content 284 25 1 1.0 5 × 10−7 750 °C 60% moisture content 190 25 1 1.0 3 × 10−7 Air 100 16 10 2.0 0.2 1000 °C Steam 100 16 3 2.0 0.3 Air 140 45 2 2.0 0.2 1200 °C Steam 140 45 1 2.0 0.3

4. Discussion At 750 °C in air, the fatigue strain increases with applied cycles, and the increasing rate of the peak strain increases with the peak stress and is affected by the test environment, i.e., ϕ = 7.6 × 10−10/cycle when σmax = 284 MPa in a 0% moisture content, and ϕ = 5.7 × 10−10/cycle when σmax = 190

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Table 1. The parameters of the interface shear stress degradation model for 2D SiC/SiC composite under different peak stresses, loading frequencies and test temperatures.

Temperatures Environment σmax/MPa τ0/MPa τs/MPa b0 j 0% moisture content 284 25 1 1.0 5 × 10−7 750 ◦C 60% moisture content 190 25 1 1.0 3 × 10−7 Air 100 16 10 2.0 0.2 1000 ◦C Steam 100 16 3 2.0 0.3 Air 140 45 2 2.0 0.2 1200 ◦C Steam 140 45 1 2.0 0.3

4. Discussion At 750 ◦C in air, the fatigue strain increases with applied cycles, and the increasing rate of the peak strain increases with the peak stress and is affected by the test environment, i.e., ϕ = 7.6 × 10−10/cycle −10 when σmax = 284 MPa in a 0% moisture content, and ϕ = 5.7 × 10 /cycle when σmax = 190 MPa in a 60% moisture content; the fatigue limit decreases from 67% tensile strength under a 0% moisture environment to 49% tensile strength under a 60% moisture environment. At 1000 ◦C, the degradation rate of the fatigue hysteresis modulus is higher in steam conditions than that in air, i.e., from 1.0 at the first applied cycle to 0.76 at the 195,129th applied cycle when σmax = 100 MPa in steam, and from 1.0 at the first applied cycle to 0.91 at the 295th applied cycle when σmax = 100 MPa in air; the increasing rate of the fatigue peak strain is higher in steam conditions than −7 −8 in air, i.e., ϕ = 1.4 × 10 /cycle when σmax = 100 MPa in steam conditions and ϕ = 1.3 × 10 /cycle when σmax = 100 MPa in air, and the fatigue limit stress in steam conditions is less than the fatigue limit stress in air, i.e., 10% tensile strength in steam versus 28% tensile strength in air. At 1100 ◦C in air, the degradation rate of the fatigue hysteresis modulus increases with the fatigue peak stress, i.e., from 1.0 at the first applied cycle to 0.72 at the 5102th applied cycle when σmax = 120 MPa and from 1.0 at the first applied cycle to 0.35 at the 981th applied cycle when σmax = 210 MPa; the increasing rate of the fatigue peak strain increases with the fatigue peak strain, −9 −7 i.e., ϕ = 2.4 × 10 /cycle when σmax = 110 MPa versus ϕ = 8.5 × 10 /cycle when σmax = 210 MPa. The fatigue limit approaches 39% tensile strength at 1100 ◦C in air. At 1200 ◦C, the increasing rate of the fatigue peak strain increases at a low loading frequency, −6 i.e., when σmax = 140 MPa in air, ϕ = 2.7 × 10 /cycle with a loading frequency of 0.1 Hz versus −7 ϕ = 2.8 × 10 /cycle with a loading frequency of 1.0 Hz; when σmax = 140 MPa in steam conditions, ϕ = 4.2 × 10−7/cycle with a loading frequency of 0.1 Hz versus ϕ = 3.4 × 10−8/cycle with a loading frequency of 10 Hz. The fatigue limit stress in steam conditions is less than the fatigue limit stress in air, i.e., 17% tensile strength at 1200 ◦C in air and 9% tensile strength at 1200 ◦C in steam atmosphere. At 1300 ◦C, the degradation rate of the fatigue hysteresis modulus increases with the increasing fatigue peak stress, i.e., in air conditions, from 1.0 at the first applied cycle to 0.435 at the 77,639th applied cycle when σmax = 100 MPa and from 1.0 at the first applied cycle to 0.389 at the 10,124th applied cycle when σmax = 140 MPa; and in steam conditions, from 1.0 at the first applied cycle to 0.641 at the 194,352th applied cycle when σmax = 100 MPa and from 1.0 at the first applied cycle to 0.431 at the 15,414th applied cycle when σmax = 140 MPa. The fatigue limit stress in steam conditions is less than the fatigue limit stress in air, i.e., 28% tensile strength in air and 19% tensile strength in steam conditions.

5. Conclusions The fatigue damage and lifetime of 2D SiC/SiC composites under cyclic fatigue loading at 750, 1000, 1100, 1200 and 1300 ◦C in air and in steam atmosphere have been investigated. The presence of steam accelerated the damage development inside of the SiC/SiC composites, which increased the increasing rate of the fatigue hysteresis dissipated energy and the fatigue peak strain, and the Materials 2017, 10, 371 15 of 16 decreasing rate of the fatigue hysteresis modulus and the interface shear stress. The fatigue limit stresses approached 67%, 28%, 39% 17% and 28% tensile strength at 750, 1000, 1100, 1200 and 1300 ◦C in air, and 49%, 10%, 9% and 19% tensile strength at 750, 1000, 1200 and 1300 ◦C in steam conditions.

1. With the increase of the fatigue peak stress, the degradation rate of the fatigue hysteresis modulus and the interface shear stress increases, and the increasing rate of the fatigue peak strain and the fatigue hysteresis dissipated energy increases. 2. With the decrease of the loading frequency, the degradation rate of the fatigue hysteresis modulus and the interface shear stress increases, and the increasing rate of the fatigue peak strain and the fatigue hysteresis dissipated energy increases.

Acknowledgments: The work reported here is supported by the Natural Science Fund of Jiangsu Province (Grant No. BK20140813), and the Fundamental Research Funds for the Central Universities (Grant No. NS2016070). The author also wishes to thank three anonymous reviewers and editors for their helpful comments on an earlier version of the paper. Conﬂicts of Interest: The author declares no conﬂict of interest.

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