Oct 19, 2016 - The fiber/matrix interface shear stress, which transfers load between fibers and matrix ... energy with theoretical computational value...

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Comparisons of Damage Evolution between 2D C/SiC and SiC/SiC Ceramic-Matrix Composites under Tension-Tension Cyclic Fatigue Loading at Room and 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: Mark Whittaker Received: 3 August 2016; Accepted: 11 October 2016; Published: 19 October 2016

Abstract: In this paper, comparisons of damage evolution between 2D C/SiC and SiC/SiC ceramic-matrix composites (CMCs) under tension–tension cyclic fatigue loading at room and elevated temperatures have been investigated. Fatigue hysteresis loops models considering multiple matrix cracking modes in 2D CMCs have been developed based on the damage mechanism of fiber sliding relative to the matrix in the interface debonded region. The relationships between the fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue peak stress, matrix multiple cracking modes, and interface shear stress have been established. The effects of fiber volume fraction, fatigue peak stress and matrix cracking mode proportion on fatigue hysteresis dissipated energy and interface debonding and sliding have been analyzed. The experimental fatigue hysteresis dissipated energy of 2D C/SiC and SiC/SiC composites at room temperature, 550 ◦ C, 800 ◦ C, and 1100 ◦ C in air, and 1200 ◦ C in vacuum corresponding to different fatigue peak stresses and cycle numbers have been analyzed. The interface shear stress degradation rate has been obtained through comparing the experimental fatigue hysteresis dissipated energy with theoretical values. Fatigue damage evolution in C/SiC and SiC/SiC composites has been compared using damage parameters of fatigue hysteresis dissipated energy and interface shear stress degradation rate. It was found that the interface shear stress degradation rate increases at elevated temperature in air compared with that at room temperature, decreases with increasing loading frequency at room temperature, and increases with increasing fatigue peak stress at room and elevated temperatures. Keywords: ceramic-matrix composites (CMCs); fatigue; damage evolution

1. Introduction Ceramic materials possess high strength and high modulus at elevated temperatures. However, their use as structural components is severely limited due to the brittleness. Continuous fiber-reinforced ceramic-matrix composites (CMCs), are fabricated by incorporating fibers into ceramic matrices, and provide an alternative to conventional ceramics in high temperature applications. CMCs retain the strength, low weight, and high temperature capability while exhibiting less brittleness than ceramics. The CMCs exceed the capability of current nickel super alloys used in high-pressure turbines and provide increased efficiency [1]. The CMCs are subject to fatigue upon cyclic mechanical loads at fixed temperature with both room temperature and elevated temperature examined [2]. Besides, at intermediate temperatures, the chemical attack would cause damage inside of CMCs at constant mechanical load [3]; and creep degradation would occur in CMCs under constant mechanical load and constant temperature [4]. Understanding the damage mechanisms of fatigue represents an important step in the engineering Materials 2016, 9, 844; doi:10.3390/ma9100844

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applications of these materials. For 2D woven C/SiC composite, the fatigue limit stress of 100,000 cycles approaches to 90% tensile strength at room temperature [5]. Under cyclic fatigue loading, the fatigue damage mechanism of matrix multicracking, interface debonding and slipping, and interface wear occur inside of 2D C/SiC composite, leading to more fibers pullout compared with tensile specimen observed in the fracture surface. However, the fatigue life and modulus degradation were affected by the loading frequency [6,7]. When the loading frequency increases to 375 Hz, the fatigue life of 2D C/SiC composite greatly decreases due to localized oxidation at fibers surface caused by internal frictional heating [7]. The post fatigue tensile strength increased after fatigue loading due to a decrease of stress concentrations present near the crossover points of the longitudinal and transverse yarns. At 550 ◦ C in air, there was an increase in cycle to failure at a given stress level when the loading frequency increased from 0.1 to 375 Hz [8], which is different from the trend at room temperature [7]. The oxidation of carbon fibers was almost absent at the high loading frequency of 375 Hz at 550 ◦ C due to internal frictional heating, which caused no reduction in cycles to failure at elevated temperature in comparison to the counterparts at room temperature. At 1200 ◦ C in vacuum, the apparent ratcheting phenomenon was highly relevant to the fatigue behavior of 2D C/SiC composite [9]. For 2D SiC/SiC composite, the fatigue limit stress at 1000 ◦ C in argon is much lower than that at room temperature [10]. At 800 ◦ C in air condition, the stress-strain hysteresis loops at different fatigue cycle numbers, modulus variation over fatigue cycle, cycle history of maximum strain, minimum strain and the width of stress-strain loops, changed with applied cycles [11]. At 1100 ◦ C in air condition, the fatigue life S–N curves for the notched and unnotched specimens were quite similar, however, the fatigue strength of the notched specimens was 10% to 15% less than the unnotched fatigue strength [12]. Under cyclic fatigue loading, the stress-strain hysteresis loops are an effective tool to indicate the fatigue damage mechanisms of CMCs through analyzing fatigue hysteresis modulus or fatigue hysteresis loops area [13–16]. The fiber/matrix interface shear stress, which transfers load between fibers and matrix and affects the damage evolution in CMCs, can be obtained through hysteresis dissipated energy [17,18]. In cross-ply and 2D woven CMCs, the matrix cracking modes involve matrix cracking and interface debonding in the longitudinal plies or yarns occurs under cyclic loading [19,20]. It should be noted that the fatigue damage mechanisms and fatigue life S–N curves of cross-ply or 2D C/SiC and SiC/SiC composites have been analyzed [5–21]. However, the comparisons of fatigue damage evolution versus cycle numbers between C/SiC and SiC/SiC composites using damage parameters of fatigue hysteresis dissipated energy and interface shear stress have not been analyzed, which is important for the real applications on aero engine components. The objective of this paper is to compare the damage evolution in 2D C/SiC and SiC/SiC composites under tension–tension cyclic fatigue loading at room and elevated temperatures. The fatigue hysteresis loops models considering multiple matrix cracking modes in 2D CMCs have been developed based on the damage mechanism of fiber sliding relative to matrix in the interface debonded region. The relationships between fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue peak stress, matrix multiple cracking modes, and interface shear stress have been established. The effects of fiber volume fraction, fatigue peak stress and matrix cracking mode proportion on fatigue hysteresis dissipated energy and interface debonding and slipping have been analyzed. The experimental fatigue hysteresis dissipated energy of 2D C/SiC and SiC/SiC composites at room temperature, 550 ◦ C, 800 ◦ C, and 1100 ◦ C in air, and 1200 ◦ C in vacuum corresponding to different fatigue peak stresses and cycle numbers have been analyzed. The interface shear stress degradation rate has been obtained through comparing the experimental fatigue hysteresis dissipated energy with theoretical computational values. The damage evolution in 2D C/SiC and SiC/SiC composites have been compared using damage parameters of fatigue hysteresis dissipated energy and interface shear stress degradation rate.

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2. Hysteresis Theories Upon first loading to fatigue peak stress σmax , which is greater than the initial cracking stress of transverse and longitudinal ply or yarn, it is assumed that transverse cracks and matrix cracks would Materials 2016, 9, 844 3 of 28 extend throughout the entire laminate cross-section. The multicracking modes in the cross-ply or 2D woven CMCs can be classified into five different modes, as shown in Figure 1, including: [22] 2. Hysteresis Theories 1 2 3 4 5

, which is greater initial cracking stress of Upon first 1: loading to fatigue peak stress σmaxtransverse Cracking mode Transverse cracking in the tow, than withthe debonding at tow boundary. transverse and longitudinal ply or yarn, it is assumed that transverse cracks and matrix cracks Cracking mode 2: Transverse cracking and matrix cracking with perfect fiber/matrix bonding, would extend throughout the entire laminate cross-section. The multicracking modes in the and fracture of fibers occurs in the longitudinal tow. cross-ply or 2D woven CMCs can be classified into five different modes, as shown in Figure 1, Cracking mode including: [22] 3: Transverse cracking and matrix cracking with fiber/matrix debonding and sliding in the longitudinal tow. 1. Cracking mode 1: Transverse cracking in the transverse tow, with debonding at tow boundary. Cracking mode mode 4: Matrix crackingcracking with perfect fiber/matrix bonding, fracture bonding, of fibers occurs 2. Cracking 2: Transverse and matrix cracking with perfectand fiber/matrix in the longitudinal and fracture oftow. fibers occurs in the longitudinal tow. 3. Cracking 3: Transverse cracking matrix cracking with fiber/matrix debonding and in the Cracking modemode 5: Matrix cracking and and fiber/matrix interface debonding and sliding sliding in the longitudinal tow. longitudinal tow. 4.

Cracking mode 4: Matrix cracking with perfect fiber/matrix bonding, and fracture of fibers occurs in loops the longitudinal The hysteresis develop tow. as a result of energy dissipation through frictional sliding between 5. Cracking mode 5: Matrix cracking and fiber/matrix interface debonding and sliding in the fibers and the matrix upon unloading and subsequent reloading. In the matrix cracking modes longitudinal tow.

mentioned above, the interface debonding and sliding occur in the matrix cracking mode 3 and mode 5. The hysteresis loops develop as a result of energy dissipation through frictional sliding between The shape, location and area of hysteresis loops of 2D woven CMCs depend on the interface debonding fibers and the matrix upon unloading and subsequent reloading. In the matrix cracking modes and sliding in cracking in cracking mode 3 and mode 5. The schematic figure for fiber sliding relative mentioned above, the interface debonding and sliding occur in the matrix cracking mode 3 and to matrix upon unloading and reloading illustrated in of Figure 2 [18]. A unit cellon is the extracted mode 5. The shape, location and area ofishysteresis loops 2D woven CMCs depend interfacefrom the CMCs, which contains a single fiber surrounded by a hollow cylinder matrix. The radius is rf , debonding and sliding in cracking in cracking mode 3 and mode 5. Theofschematic figurefiber for fiber 1/2 ). The upon unloading and reloading is illustrated in Figure 2 [18]. A unit cell is crack and thesliding matrixrelative radiustoismatrix R (R = rf /V length of the unit cell is L/2, which is half matrix f extracted from the CMCs, which contains a single fiber surrounded by a hollow cylinder of matrix. spacing, and the interface debonded length is Ld . Upon unloading, counter slip occurs in the interface The fiber radius is rf, and the matrix radius is R (R = rf/Vf1/2). The length of the unit cell is L/2, which is debonded region. The interface debonded region can be divided into two regions, i.e., interface half matrix crack spacing, and the interface debonded length is Ld. Upon unloading, counter slip counter-slip interface slip region. region,The as shown Figure 2a. Thecan interface counter-slip occursregion in the and interface debonded interfaceindebonded region be divided into two length is denoted to bei.e., y. interface Upon reloading, new slipand occurs in the interface debonded The interface regions, counter-slip region interface slip region, as shown in region. Figure 2a. The debonded regioncounter-slip can be divided three regions, i.e., interface new-slip interface counter-slip interface length into is denoted to be y. Upon reloading, new slipregion, occurs in the interface debonded region. interface debonded region can divided into new-slip three regions, i.e.,isinterface region, and interface slipThe region, as shown in Figure 2b. be The interface region denoted to be new-slip region, interface counter-slip region, and interface slip region, as shown in Figure 2b. subsequent The z. Based on the damage mechanism of fiber sliding relative to matrix upon unloading and interface new-slip region is denoted to be z. Based on the damage mechanism of fiber sliding relative reloading, the hysteresis loops can be divided into four different cases, including: 1 2 3 4

to matrix upon unloading and subsequent reloading, the hysteresis loops can be divided into four different cases, including:

Case 1: Interface partially debonds, and fiber completely slides relative to matrix. 1. 2:Case 1: Interface partially debonds, andfiber fiber partially completelyslides slides relative relative totomatrix. Case Interface partially debonds, and matrix. 2. Case 2: Interface partially debonds, and fiber partially slides relative to matrix. Case 3: Interface completely debonds, and fiber partially slides relative to matrix. 3. Case 3: Interface completely debonds, and fiber partially slides relative to matrix. Case Interface completely debonds, completely slides relative to matrix. 4. 4:Case 4: Interface completely debonds,and andfiber fiber completely slides relative to matrix.

(a)

(b)

(c)

(d)

Figure 1. Cont.

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(e) (e)

(f)

(f)

Figure 1. The undamaged state and five damaged modes of cross-ply and 2D woven ceramic Figure 1. 1. The Theundamaged undamaged stateand andfive five damaged damaged modes modes of of cross-ply cross-ply and and 2D woven woven ceramic Figure composites: (a) undamagedstate composite; (b) mode 1: transverse cracking in the transverse2D tow, with ceramic composites: (a) undamaged composite; (b) mode 1: transverse cracking in the transverse tow, with with composites: (a) atundamaged composite; mode 1: cracking transverse in the transverse debonding tow boundary; (c) mode (b) 2: transverse andcracking matrix cracking with perfect tow, debonding at tow tow boundary; (c) mode mode 2:occurs transverse cracking and and matrix cracking with perfect perfect fiber/matrix bonding, and fracture of fibers2: in the longitudinal tow; matrix (d) modecracking 3: transverse debonding at boundary; (c) transverse cracking with cracking bonding, and matrixand cracking withofof fiber/matrix debonding sliding in the longitudinal fiber/matrix bonding, and fracture fibersoccurs occurs inthe theand longitudinal tow; (d) mode modetow; 3: transverse transverse fiber/matrix fracture fibers in longitudinal tow; (d) 3: (e) mode matrix cracking with perfect fiber/matrix debonding bonding, andand fracture of fibers occurs in the cracking and4:matrix matrix cracking with fiber/matrix sliding the longitudinal tow; cracking and cracking with fiber/matrix debonding and sliding inin the longitudinal tow; longitudinal tow; cracking and (f) mode 5: matrix cracking and fiber/matrix interface debonding and sliding (e) mode 4: matrix with perfect fiber/matrix bonding, and fracture of fibers occurs in the (e) mode 4: matrix cracking with perfect fiber/matrix bonding, and fracture of fibers occurs in the in the longitudinal tow [22].

longitudinal tow; tow; and and (f) sliding in longitudinal (f) mode mode 5:5: matrix matrixcracking crackingand andfiber/matrix fiber/matrixinterface interfacedebonding debondingand and sliding the longitudinal tow [22]. in the longitudinal tow [22].

(a)

(b)

Figure 2. The schematic figure for fiber slipping relative to matrix upon: (a) unloading; and (b) reloading [18].

2.1. Matrix Cracking Mode 3(a)

(b)

The unloading strain ɛcu and reloading strain ɛcr corresponding to the interface slip Case 1 and Figure 2.2. The figure forfor fiber slipping relative to matrix upon: (a) unloading; and (b) Figure Theschematic schematic figure fiber relative Case 2 are determined by Equations (1) and (2),slipping respectively [23]. to matrix upon: (a) unloading; and

reloading [18].[18]. (b) reloading cu

i y2

4

2

i 2 y Ld 2 y L Ld

c f

(1)

Ef rf L Ef rf L 2.1. Matrix Cracking Mode V3f_axial Ef 2.1. Matrix Cracking Mode 3 y 2 z ɛcr corresponding to the interface slip Case 1 and 4 strain z ɛcu and reloading The unloading strain 4 The unloading strain εcu strain εcr corresponding to the interface slip Case 1 and V E and E reloading r L E r L (2) Case 2 are determined by Equations(1) Land (2), respectively [23]. y z L 2y 2z L 2 2 Case 2 are determined by Equations 2 (1) and (2), respectively [23]. E r L i y22 i 2 y Ld 2 y L Ld c f the 4 2 fiber elastic (1) τ yfraction along τ (2ythe − loading Ld ) (2ydirection; − L + LEdf)denotes cu theσfiber volume where Vf_axial denotes rf L − (αc − αf ) ∆T (1) ε cu = Vf_axial Ef + 4 Eif rf L − 2 Efi modulus; τi denotes the interface shear cracking space; Ld denotes the Vf_axial Ef E f rf Lstress;EL f denotes the rmatrix fL 2 interface debonded length; y and counter-slip and new-slip length, 2 zinterface i z z2 denotes 4 i y the 4 c r 2the fiber respectively; rf denotes fiber radius; αf, and αc denote thermal expansion y−2zcomposite )2 τ 4τ σ z V f _ a x the E E r L E r L i i (and ia l f f f f4 εf = Vf_axialthe Ef −temperature Ef rf L + Edifference rf L (2)(2) f coefficient, respectively; and ΔTcr denotes between the fabricated LLd + 2y y 2z − 2− 2 Lz) L i L dτi ( L2dy−2y2+z2z)( testing 2 + T cα)∆T f 21 (ΔT = T1 − T0). d − (αc − temperature T 0 and temperature f 2

2

i

cr

f_ a x ia l

f

f

i

f

f

i

d

c

f

Ef

f

d

f

f

Ef

rrf fLL

The unloading strain ɛcu and reloading strain ɛcr corresponding to interface slip Case 3 and Case 4 where Vf_axial denotes thefiber fibervolume volume fraction along theloading loadingdirection; direction;EEf fdenotes denotesthe thefiber fiberelastic elastic f_axial are determined by the Equations (3) and (4), respectively [23]. denotes fraction along the where V

modulus; ττi idenotes denotesthe theinterface interfaceshear shearstress; stress; LL denotes denotes the the matrix matrix cracking cracking space; space; LLdd denotes denotes the the modulus; interface debonded length; y and z denotes the interface counter-slip and new-slip length, respectively; interface debonded length; y and z denotes the interface counter-slip and new-slip length, rf denotes the radius; αf , and αc denote and expansion coefficient, respectively; rf fiber denotes the fiber radius; αf, andthe αc fiber denote thecomposite fiber and thermal composite thermal expansion respectively;respectively; and ∆T denotes difference between the fabricated temperature T0 and coefficient, andthe ΔTtemperature denotes the temperature difference between the fabricated testing temperature T (∆T = T − T ). 1 1 0 temperature T0 and testing temperature T1 (ΔT = T1 − T0). The unloading strain ɛcu and reloading strain ɛcr corresponding to interface slip Case 3 and Case 4 are determined by Equations (3) and (4), respectively [23].

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The unloading strain εcu and reloading strain εcr corresponding to interface slip Case 3 and Case 4 are determined by Equations (3) and (4), respectively [23]. ε cu =

ε cr =

σ Vf_axial Ef

τi y2 τ (2y − L/2)2 −2 i − (αc − αf ) ∆T Ef rf L Ef rf L

(3)

τi z2 τ (y − 2z)2 τ ( L/2 − 2y + 2z)2 +4 i −2 i − (αc − αf ) ∆T Ef rf L Ef rf L Ef rf L

(4)

σ Vf_axial Ef

−4

+4

2.2. Matrix Cracking Mode 5 The unloading strain εcu and reloading strain εcr corresponding to interface slip Case 1 and Case 2 are determined by Equations (5) and (6), respectively [23]. ε cu =

1 Vf_axial Ef

(σ − kσto ) + 4 ε cr =

τi y2 τ (2y − Ld ) (2y + Ld − L) −2 i − (αc − αf ) ∆T Ef rf L Ef rf L

1 Vf_axial Ef

2

(σ − kσto ) − 4 Eτif rzf L +

2 4τi (y−2z) Ef rf L

+ 2 Eτif ( Ld −2y+2z)(rfLLd +2y−2z− L) − (αc − αf ) ∆T

(5)

(6)

where k denotes the proportion of transverse yarns in the entire composite; and σto denotes the axial stress in the transverse yarns. The unloading strain εcu and reloading strain εcr corresponding to interface slip Case 3 and Case 4 are determined by Equations (7) and (8), respectively [23]. ε cu =

1 Vf_axial Ef

(σ − kσto ) + 4

ε cr =

1 Vf_axial Ef

τ (2y − L/2)2 τi y2 −2 i − (αc − αf ) ∆T Ef rf L Ef rf L

(y−2z) (σ − kσto ) − 4 Eτif rzf L + 4 Eτif rf L 2

+2z)2 − 2 Eτif ( L/2−r2y L f

(7)

2

− (αc − αf ) ∆T

(8)

2.3. Hysteresis Dissipated Energy The fatigue hysteresis dissipated energy corresponding to different cycle number is determined by Equation (9) [23]. Z U=

σmax

[ε cu (σ) − ε cr (σ)] dσ

(9)

σmin

where εcu and εcr denote the unloading and reloading strain, respectively. Substituting the unloading and reloading strains of Equations (1)–(4) into (9), the fatigue hysteresis loss energy U3 of matrix cracking mode 3 can be obtained for different interface slips cases; substituting the unloading and reloading strains of Equations (5)–(8) into (9), the fatigue hysteresis loss energy U5 of matrix cracking mode 5 can also be obtained for different interface slip cases. The composite fatigue hysteresis loss energy Uc is determined by Equation (10) [23]. Uc = ηU3 + (1 − η ) U5

(10)

where η denotes the composite damage parameter, i.e., the proportion of matrix cracking mode 3 in the entire matrix cracking modes. By comparing experimental fatigue hysteresis dissipated energy with theoretical computational values, the interface shear stress of CMCs can be obtained [21]. The degradation rate ψ of interface shear stress can be determined by the Equation (11).

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ψ=

τi ( Ninitial ) − τi ( Nfinal ) Nfinal − Ninitial

(11)

where Ninitial and Nfinal denote the initial and final cycle number for estimating interface shear stress, respectively; and τ i (Ninitial ) and τ i (Nfinal ) denote the estimated interface shear stress at the initial and final cycle number, respectively. 3. Discussion Under cyclic fatigue loading, the material properties, i.e., fiber volume content, peak stress, and damage state, i.e., matrix cracking mode proportion, affect the shape, location and area of hysteresis loops. The effect of these factors on interface slip and fatigue hysteresis dissipated energy evolution of matrix cracking mode 3 and mode 5, and composite would be analyzed. 3.1. Effect of Fiber Volume Fraction The effect of fiber volume content on fatigue hysteresis dissipated energy evolution and interface slip of matrix cracking mode 3, mode 5 and the composite is illustrated in Figure 3. When the fiber volume fraction is 40%, the fatigue hysteresis dissipated energy and interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 are illustrated in Figure 3a,b. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing interface shear stress from 12.6 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 63.3 kJ/m3 at the interface shear stress of 7.6 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 3a; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.32 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 16.4 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 3b. For matrix cracking mode 5, the hysteresis dissipated energy increases with decreasing interface shear stress from 2.9 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 31.9 kJ/m3 at the interface shear stress of 3.8 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 3a; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.10 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 6.5 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 3b. When the fiber volume fraction is 45%, the fatigue hysteresis dissipated energy and interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 are illustrated in Figure 3c,d. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing interface shear stress from 8.3 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 51.4 kJ/m3 at the interface shear stress of 6.1 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 3c; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.25 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 12.8 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 3d. For matrix cracking mode 5, the hysteresis dissipated energy increases with decreasing interface shear stress from 2.4 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 26 kJ/m3 at the interface shear stress of 3.1 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 3c; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.07 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 4.8 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 3d. When the fiber volume fraction is 50%, the fatigue hysteresis dissipated energy and interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 are illustrated in Figure 3e,f. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing interface shear stress from 5.5 kJ/m3 at the interface shear stress of 50 MPa to the peak

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with decreasing interface shear stress from 5.5 kJ/m3 at the interface shear stress of 50 MPa to the 3 at0the 3 at the peak of value 41.83 at kJ/m at the interface shearofstress ofand 5 MPa, and decreases kJ/m value 41.8 of kJ/m the3 interface shear stress 5 MPa, decreases to 0 kJ/mto interface interface stressasofshown 0 MPa, shown in Figure 3e; anddebonded the interface debonded length with 2Ld/L shear stressshear of 0 MPa, in as Figure 3e; and the interface length 2Ld /L increases increases with decreasing interface stress from 0.19shear at the interface sheartostress of 50value MPaof to decreasing interface shear stress fromshear 0.19 at the interface stress of 50 MPa the peak theatpeak value of shear 1.0 at the interface shearand stress of 9.9 to MPa, and remains be constant of 1.0shear until 1.0 the interface stress of 9.9 MPa, remains be constant of 1.0tountil the interface the interface shear stress of MPa, as in Figure 3f. For matrix cracking mode 5, the hysteresis stress of 0 MPa, as shown in 0Figure 3f. shown For matrix cracking mode 5, the hysteresis dissipated energy 3 3 dissipated energy increases with shear decreasing shear at stress from 1.8shear kJ/m stress at theofinterface increases with decreasing interface stress interface from 1.8 kJ/m the interface 50 MPa 3 at the shear stressvalue of 50ofMPa the 3peak value of 21.2 kJ/mstress interface sheardecreases stress of to 2.50 MPa, to the peak 21.2tokJ/m at the interface shear of 2.5 MPa, and kJ/m3and at 3 decreases to shear 0 kJ/m at the stress of 0 MPa, as the shown in Figure 3e; andlength the interface the interface stress of 0interface MPa, asshear shown in Figure 3e; and interface debonded 2Ld /L debonded length 2Ld/L increases with decreasing interface stress from 0.05ofat50the interface increases with decreasing interface shear stress from 0.05 at theshear interface shear stress MPa to the shearvalue stressofof1.0 50 at MPa the peakshear valuestress of 1.0ofat3.4 theMPa, interface shear stress of constant 3.4 MPa, of and to peak theto interface and remains to be 1.0remains until the be constant of stress 1.0 until interface shearinstress of3f. 0 MPa, as shown in Figure 3f. interface shear of 0the MPa, as shown Figure Whenmatrix matrixcracking crackingmode mode33proportion proportionηηisis0.2, 0.2,the thecomposite compositefatigue fatiguehysteresis hysteresisdissipated dissipated When energyversus versusinterface interfaceshear shearstress stresscurves curveswhen whenthe thefiber fibervolume volumefraction fractionisis40%, 40%,45% 45%and and50% 50%are are energy illustratedin inFigure Figure3g. 3g.When Whenthe thefiber fibervolume volumefraction fractionisis40%, 40%,the thecomposite compositehysteresis hysteresisdissipated dissipated illustrated energyincreases increases with with decreasing decreasing interface shear stress from 4.8 stress of energy 4.8 kJ/m kJ/m3 3atatthe theinterface interfaceshear shear stress 3 3 5050MPa MPa, and and decreases decreases to to of MPatotothe thepeak peakvalue valueof of 35.4 35.4 kJ/m kJ/m atatthe theinterface interfaceshear shear stress stress of 4.4 MPa, kJ/m33 at the interface shear stress of 00 MPa; MPa; when when the the fiber fibervolume volumefraction fractionisis45%, 45%,the thecomposite composite 00kJ/m hysteresisdissipated dissipatedenergy energyincreases increaseswith withdecreasing decreasinginterface interfaceshear shearstress stressfrom from3.6 3.6kJ/m kJ/m33 at atthe the hysteresis 3 3 interfaceshear shearstress stress 50 MPa to peak the peak 28.8 at kJ/m at the interface shear stress of interface of of 50 MPa to the value value of 28.8ofkJ/m the interface shear stress of 3.6 MPa, 3 at the interface shear stress of 0 MPa; and when the fiber volume 3.6 MPa, and to decreases kJ/m and decreases 0 kJ/m3to at0the interface shear stress of 0 MPa; and when the fiber volume fraction is fraction is 50%, thehysteresis compositedissipated hysteresisenergy dissipated energy increases withinterface decreasing interface shear 50%, the composite increases with decreasing shear stress from 3 3 3 3 stress from 2.5 interface kJ/m at the interface stress of 50 MPa to the peak valueatof kJ/m shear at the 2.5 kJ/m at the shear stress ofshear 50 MPa to the peak value of 23.6 kJ/m the23.6 interface 3 at theto interface shear stress 2.9 MPa,toand decreases 0 kJ/m3 at the stress interface stress of 2.9 MPa, and of decreases 0 kJ/m interface shear of 0shear MPa.stress of 0 MPa. Whenfiber fibervolume volumecontent contentincreases, increases,the thehysteresis hysteresisdissipated dissipatedenergy energyof ofmatrix matrixcracking crackingmode mode3, 3, When mode5 5and and composite the interface same interface sheardecrease, stress decrease, to less interface mode thethe composite at theatsame shear stress due to lessdue interface debonding debonding and between fibers and the matrix. and frictional slipfrictional betweenslip fibers and the matrix.

Figure 3. Cont.

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Figure 3. 3. (a) (a) The The hysteresis hysteresis dissipated dissipated energy energy versus versus interface interface shear shear stress stress curves curves of of matrix matrix cracking cracking Figure f = 40%; (b) the interface debonded length 2L d /L versus interface shear mode 3 and mode 5 when V mode 3 and mode 5 when V f = 40%; (b) the interface debonded length 2Ld /L versus interface shear stress curves curves of of matrix matrix cracking cracking mode mode 33 and and mode mode 55 when when VVff == 40%; 40%; (c) (c) the the hysteresis hysteresis dissipated dissipated stress energy versus versus interface interface shear shear stress stress curves curves of of matrix matrix cracking cracking mode mode 33 and and mode mode 55 when when V Vff = = 45%; energy 45%; (d) the interface debonded length 2L d /L versus interface shear stress curves of matrix cracking (d) the interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 mode 3 and mode V 5 fwhen Vf (e) = 45%; (e) the hysteresis dissipated energy interface versus interface shearcurves stress and mode 5 when = 45%; the hysteresis dissipated energy versus shear stress f = 50%; interface debondedlength length2L 2L /L curves of matrix cracking and mode 5 when of matrix cracking mode mode 3 and 3mode 5 when V f =V50%; (f) (f) thethe interface debonded d d/L versus interface interface shear shear stress stresscurves curvesof ofmatrix matrixcracking crackingmode mode33and andmode mode55when whenVVff == 50%; and (g) the versus versus interface interface shear shear stress stress curve curve when when V Vff = 40%, 45% and composite hysteresis dissipated energy versus 50%, and ηη = 0.2.

3.2. Effect Effect of of Fatigue Fatigue Peak Peak Stress Stress 3.2. The effect effect of of peak peak stress stress on on fatigue fatigue hysteresis hysteresis dissipated dissipated energy energy evolution evolution and and interface interface slip slip of of The matrix cracking mode 3, mode 5 and composite is illustrated in Figure 4. matrix cracking mode 3, mode 5 and composite is illustrated in Figure 4. When the the fatigue fatigue peak peak stress stress is is 150 150 MPa, MPa, the the fatigue fatigue hysteresis hysteresis dissipated dissipated energy energy and and interface interface When debonded length length 2L 2Ldd/L and mode mode 55 debonded /Lversus versusinterface interfaceshear shearstress stress curves curves of of matrix matrix cracking cracking mode mode 33 and are illustrated in Figure 4a,b. For matrix cracking mode 3, the hysteresis dissipated energy increases are illustrated in Figure 4a,b. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing decreasing interface interface shear shear stress stress from from 8.2 8.2 kJ/m kJ/m33 at MPa to to the the with at the the interface interface shear shear stress stress of of 50 50 MPa 3 3 at the interface 3 3 peak value of 44 kJ/m at the interface shear stress of 7 MPa, and decreases to 0 kJ/m peak value of 44 kJ/m at the interface shear stress of 7 MPa, and decreases to 0 kJ/m at the interface shear stress stress of of 00 MPa, MPa, as as shown shown in in Figure Figure4a; 4a;and andthe theinterface interfacedebonded debondedlength length2L 2Ldd/L /L increases with shear increases with decreasing interface interface shear shear stress stress from from 0.34 0.34 at at the the interface interface shear shear stress stress of of 50 50 MPa MPa to to the the peak peak value value of of decreasing 1.0 at the interface shear stress of 17.2 MPa, and remains to be constant of 1.0 until the interface shear 1.0 at the interface shear stress of 17.2 MPa, and remains to be constant of 1.0 until the interface shear stress of of 00 MPa, MPa, as as shown shown in in Figure Figure 4b. 4b. For For matrix matrix cracking cracking mode mode 5, 5, the the hysteresis hysteresis dissipated dissipated energy energy stress 3 increases with with decreasing decreasing interface interface shear shear stress stressfrom from1.9 1.9kJ/m kJ/m3 at of 50 50 MPa MPa increases at the the interface interface shear shear stress stress of 33 3 at 3the to the peak value of 22.2 kJ/m at the interface shear stress of 3.5 MPa, and decreases to 0 kJ/m to the peak value of 22.2 kJ/m at the interface shear stress of 3.5 MPa, and decreases to 0 kJ/m at interface shear stress of of 0 MPa, asasshown the interface interface debonded debondedlength length2L 2Ld d/L /L the interface shear stress 0 MPa, shownininFigure Figure4a; 4a; and and the increases with decreasing interface shear stress from 0.1 at the interface shear stress of 50 MPa to the increases with decreasing interface shear stress from 0.1 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 6.6 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4b.

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peak value of 1.0 at the interface shear stress of 6.6 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4b. When σmax = 200 MPa, the fatigue hysteresis dissipated energy and interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 are illustrated in Figure 4c,d. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing interface shear stress from 18.2 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 76.7 kJ/m3 at the interface shear stress of 9.2 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 4c; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.47 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 23.7 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4d. For matrix cracking mode 5, the hysteresis dissipated energy increases with decreasing interface shear stress from 4.5 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 39.5 kJ/m3 at the interface shear stress of 4.7 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 4c; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.17 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 10 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4d. When σmax = 250 MPa, the fatigue hysteresis dissipated energy and interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 are illustrated in Figure 4e,f. For matrix cracking mode 3, the hysteresis dissipated energy increases with decreasing interface shear stress from 33.8 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 118.1 kJ/m3 at the interface shear stress of 11.3 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 4e; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.6 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 30.1 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4f. For matrix cracking mode 5, the hysteresis dissipated energy increases with decreasing interface shear stress from 8.7 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 61.7 kJ/m3 at the interface shear stress of 5.9 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa, as shown in Figure 4e; and the interface debonded length 2Ld /L increases with decreasing interface shear stress from 0.24 at the interface shear stress of 50 MPa to the peak value of 1.0 at the interface shear stress of 13.5 MPa, and remains to be constant of 1.0 until the interface shear stress of 0 MPa, as shown in Figure 4f. When the proportion of matrix cracking mode 3 is η = 0.2, the composite hysteresis dissipated energy versus interface shear stress curves when the fatigue peak stress is 150 and 200 MPa are illustrated in Figure 4g. When the fatigue peak stress is 150 MPa, the composite hysteresis dissipated energy increases with decreasing interface shear stress from 3.1 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 24.6 kJ/m3 at the interface shear stress of 4.1 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa; when the fatigue peak stress is 200 MPa, the composite hysteresis dissipated energy increases with decreasing interface shear stress from 7.2 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 43.7 kJ/m3 at the interface shear stress of 5.4 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa; and when the fatigue peak stress is 250 MPa, the composite hysteresis dissipated energy increases with decreasing interface shear stress from 13.8 kJ/m3 at the interface shear stress of 50 MPa to the peak value of 68.3 kJ/m3 at the interface shear stress of 6.8 MPa, and decreases to 0 kJ/m3 at the interface shear stress of 0 MPa. When the fatigue peak stress increases, the hysteresis dissipated energy of matrix cracking mode 3, mode 5 and composite at the same interface shear stress increase, due to more interface debonding and frictional slip between fibers and the matrix.

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Figure 4. (a) The hysteresis dissipated energy versus interface shear stress curves of matrix cracking Figure 4. (a) The hysteresis dissipated energy versus interface shear stress curves of matrix cracking mode 3 and mode 5 when σmax = 150 MPa; (b) the interface debonded length 2Ld/L versus interface mode 3 and mode 5 when σmax = 150 MPa; (b) the interface debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 when σmax = 150 MPa; (c) the hysteresis shear stress curves of matrix cracking mode 3 and mode 5 when σmax = 150 MPa; (c) the hysteresis dissipated energy versus interface shear stress curves of matrix cracking mode 3 and mode 5 when dissipated energy versus interface shear stress curves of matrix cracking mode 3 and mode 5 when σmax = 200 MPa; (d) the interface debonded length 2Ld/L versus interface shear stress curves of matrix σmax cracking = 200 MPa; (d)3the interface 2Ld /L(e) versus interface dissipated shear stress curves of matrix = 200 MPa; the hysteresis energy versus mode and mode 5debonded when σmaxlength cracking modeshear 3 andstress mode 5 when σmax =cracking 200 MPa;mode (e) the hysteresis versus = 250 MPa; (f) interface the interface curves of matrix 3 and mode 5dissipated when σmaxenergy shearinterface stress curves of matrix cracking mode 3 and mode 5 when = 250 MPa; mode (f) the3 interface debonded length 2L d/L versus interface shear stress curves σofmax matrix cracking and debonded length 2Ld /L versus interface shear stress curves of matrix cracking mode 3 and mode 5 when σmax = 250 MPa; and (g) the composite hysteresis dissipated energy versus interface shear stress curves when σmax = 150, 200 and 250 MPa, and η = 0.2.

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mode 5 9, when Materials 2016, 844 σmax = 250 MPa; and (g) the composite hysteresis dissipated energy versus interface 11 of 28 shear stress curves when σmax = 150, 200 and 250 MPa, and η = 0.2.

3.3. Effect Effect of of Matrix Matrix Cracking Cracking Mode Mode Proportion Proportion 3.3. The effect cracking proportion η onηfatigue hysteresis dissipated energy versus The effectofofmatrix matrix cracking proportion on fatigue hysteresis dissipated energyinterface versus shear stress curves is illustrated in Figure 5a. When η is 0, there is only matrix cracking mode 5 in the interface shear stress curves is illustrated in Figure 5a. When η is 0, there is only matrix cracking 3 3 composite, thecomposite, composite the hysteresis dissipated energy increases from 2.3 kJ/m from at the2.3 interface shear mode 5 in the composite hysteresis dissipated energy increases kJ/m at the 3 at the interface stress of 50 MPa to the value of 32 kJ/m stress of 3.1 MPa, in interface shear stress of peak 50 MPa to the peak value of 32 kJ/m3 at shear the interface shear stressas ofshown 3.1 MPa, Figure 5a; when η is 1, there is only matrix cracking mode 3 in the composite, the composite hysteresis as shown in Figure 5a; when η is 1, there is only matrix cracking mode 3 in the composite, the 3 at the interface shear stress dissipated energy increases from energy 9.8 kJ/mincreases of 50 MPa toshear the peak value of composite hysteresis dissipated from 9.8 kJ/m3 at the interface stress of 50 3 3 62.5 kJ/m at the interface shear stress of 6 MPa, as shown in Figure 5a; and when 0 < η < 1, there are MPa to the peak value of 62.5 kJ/m at the interface shear stress of 6 MPa, as shown in Figure 5a; and both matrix mode and mode 5 in the composite, when is 0.2, the composite when 0 < η < cracking 1, there are both3matrix cracking mode 3 and mode 5 inηthe composite, when ηhysteresis is 0.2, the 3 3 at the dissipated energy increases from energy 3.8 kJ/mincreases at the interface of 50 MPa toshear the peak value of composite hysteresis dissipated from 3.8shear kJ/mstress interface stress of 50 3 at the interface shear stress 3 35.4 kJ/m of 3.5 MPa; when η is 0.5, the composite hysteresis dissipated MPa to the peak value of 35.4 kJ/m at the interface shear stress of 3.5 MPa; when η is 0.5, the 3 3 at the energy increases from dissipated 6.1 kJ/m3 at the interface shear stress 50 MPa to the peak value 42.5 kJ/m composite hysteresis energy increases from 6.1 of kJ/m interface shearofstress of 50 3 at and at thetointerface shear stress of 4.4 MPa; η isshear 0.8, the composite hysteresis dissipated energy MPa the peak value of 42.5 kJ/m the when interface stress of 4.4 MPa; and when η is 0.8, the 3 at the interface shear stress of 50 MPa to 3 at the 3 increases from 8.3 kJ/m the peak value of 54 kJ/m composite hysteresis dissipated energy increases from 8.3 kJ/m at the interface shear stress of 50 3 at interface shear stress of of 5.754 MPa, shown in Figureshear 5a. With of matrix cracking mode MPa to the peak value kJ/mas the interface stressincreasing of 5.7 MPa, as shown in Figure 5a.3 proportion η, the peak value of hysteresis dissipated energy increases, as shown in Figure 5b; and the With increasing of matrix cracking mode 3 proportion η, the peak value of hysteresis dissipated interfaceincreases, shear stress to the value of hysteresis energy also increases, as energy as corresponding shown in Figure 5b; peak and the interface sheardissipated stress corresponding to the peak shownofinhysteresis Figure 5c.dissipated energy also increases, as shown in Figure 5c. value When matrix 3 proportion η increases, the composite hysteresis dissipated energy matrixcracking crackingmode mode 3 proportion η increases, the composite hysteresis dissipated and theand corresponding interfaceinterface shear stress increase, indicates the hysteresis energy the corresponding shear stress which increase, which that indicates that the dissipated hysteresis energy canenergy approach the peakto value at high interface shear stress.shear stress. dissipated cantoapproach the peak value at high interface

Figure Figure 5. 5. Effect Effect matrix matrix cracking cracking mode mode proportion, proportion, i.e., i.e., ηη == 0, 0, 0.2, 0.2, 0.5, 0.5, 0.8 0.8 and and 1.0, 1.0, on on (a) (a) the the hysteresis hysteresis dissipated dissipated energy energy versus versus interface interface shear shear stress stress curve; curve; (b) (b) the the peak peak value value of of composite composite hysteresis hysteresis dissipated shear stress stress versus versus ηη curve. curve. dissipated energy energy versus versus ηη curve; curve; and and (c) (c) the the corresponding corresponding interface interface shear

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4. Experimental Comparisons 4.1. 2D C/SiC Composite 4.1.1. Room Temperature Li [21] investigated the tension–tension fatigue behavior of cross-ply C/SiC composite at room temperature. The T–700™ carbon (Toray Institute Inc., Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were manufactured by the hot-pressing method. The dog bone-shaped specimens were cut from 150 mm × 150 mm panels by water jet cutting. The test specimens were further coated with SiC of about 20 µm thick by chemical vapor deposition (CVD) to prevent oxidation at elevated temperatures. These processing steps resulted in a material having bulk density about 2.0 g/cm3 , and an open porosity less than 5%. The fatigue tests were conducted in force control with a stress ratio (i.e., minimum stress/maximum stress) of 0.1, and a sinusoidal waveform loading frequency of 10 Hz. The material properties are given by: V f = 40%, Ef = 230 GPa, Em = 350 GPa, rf = 3.5 µm, αf = −0.38 × 10−6 /◦ C, αm = 2.8 × 10−6 /◦ C, and ∆T = −1000 ◦ C. Under fatigue peak stress of σmax = 105 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 6a, in which the proportion of matrix cracking mode 3 is η = 0.8. The experimental and theoretical fatigue hysteresis dissipated energy as a function of interface shear stress is shown in Figure 6b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 36.4 kJ/m3 , and decreases with decreasing interface shear stress to 0 kJ/m3 . The experimental fatigue hysteresis dissipated energy of the 1st cycle lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loop of the 1st cycle corresponds to interface slip Case 2, i.e., interface partially debonds and fiber slides partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear. Staehler et al. [7] observed the interface wear as a result of sliding contact between individual 0◦ fibers within a tow at the loading frequency of 4 Hz. However, no fiber surface abrasions were evident in specimens failed under monotonic tensile loading conditions. Upon cyclic loading, when matrix cracks are present, the matrix slides past the intact fibers. These sliding displacements change the interface shear stress and cause further debonding. The reductions in interface shear stress are attributed to interface wear operating in the fiber coating, especially at those contacts subject to high pressure. The wear process is facilitated by the temperature rise that occurs along the interface, as frictional dissipation proceeds. At high frequencies, the increase in temperature can be large enough to oxidize the fiber coating at room temperature [7]. The wear debris produced during the wear process are particles which have a mild lubricating effect and are easily broken down further during fatigue loading cycles. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 1. The fatigue hysteresis loop of the 100th cycle corresponds to interface slip Case 4, i.e., interface completely debonds and fiber slides completely relative to matrix in the interface debonded region. Shuler et al. [6] investigated the tension–tension fatigue behavior of 2D woven C/SiC composite at room temperature. The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were processed by chemical vapor infiltration (CVI) of SiC into woven 0◦ /90◦ carbon fiber preforms. The test specimens were cut from 200 mm × 200 mm composite panels using diamond tooling into a dog-bone configuration. The composite density ranges from 1.93 to 1.98 g/cm3 . The fatigue tests were performed under force control at a sinusoidal loading frequency of 10 Hz, with a stress ratio (i.e., minimum stress/maximum stress) of 0.1. The material properties are given by: V f = 45%, Ef = 230 GPa, Em = 350 GPa, rf = 3.5 µm, αf = 0, αm = 4.6 × 10−6 /K, and ∆T = −1000 K. Under fatigue peak stress of σmax = 335 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 7a, in which the proportion of matrix cracking mode 3 is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of

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interface shear stress is shown in Figure 7b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 130.4 kJ/m3, and decreases with interface shear stress is shown in Figure 7b. The theoretical fatigue hysteresis dissipated energy 3. The experimental fatigue hysteresis3 dissipated energy of decreasing interface shear stress to 0 kJ/m increases with decreasing interface shear stress to the peak value of 130.4 kJ/m , and decreases with the 1st cycle lies in the right part the fatigue hysteresis dissipated energy versus interface shear 3 . The experimental decreasing interface shear stress to of 0 kJ/m fatigue hysteresis dissipated energy of stress curve. The fatigue hysteresis loop of the 1st cycle corresponds to interface slip Case 2, i.e., the 1st cycle lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress interface partially slides partially relative to to interface matrix inslip theCase interface curve. The fatigue debonds, hysteresisand loopfiber of the 1st cycle corresponds 2, i.e.,debonded interface region. With the number of applied cycles increasing, interface shear stress decreases partially debonds, and fiber slides partially relative to matrix in the interface debonded region. Withwith the increasing cycle number due to interface By comparing experimental hysteresis number of applied cycles increasing, interface wear. shear stress decreases with increasingfatigue cycle number due dissipated with theoretical values, the interface shear dissipated stress corresponding different to interface energy wear. By comparing experimental fatigue hysteresis energy withtotheoretical applied cycles can be estimated, as shown in Table 2. The fatigue hysteresis loops of the 1000th and values, the interface shear stress corresponding to different applied cycles can be estimated, as shown 1,000,000th applied cycle correspond to interface slip Case 4, i.e., interface completely debonds in Table 2. The fatigue hysteresis loops of the 1000th and 1,000,000th applied cycle correspondand to fiber slides completely relative to matrix in the interface debonded region. interface slip Case 4, i.e., interface completely debonds and fiber slides completely relative to matrix in the interface debonded region.

Table 1. The interface shear stress of cross-ply C/SiC composite corresponding to different applied cycles 1. under fatigue peak stress of of σmax = 105 MPa at room temperature. Table The interface shear stress cross-ply C/SiC composite corresponding to different applied cycles under fatigue peak stress of Experimental σmax = 105 MPa at room temperature. Interface Shear Cycle Hysteresis

Stress/MPa Number Dissipated Energy/(kJ/m3) Experimental35Hysteresis 1 7.3 Shear Stress/MPa Interface Cycle Number 3) Dissipated Energy/(kJ/m 3 32 4.0 1 3528 7.3 5 3.2 3 3226 4.0 7 2.8 5 28 3.2 100 21.5 2.1 7 26 2.8 1000 19.4 1.9 100 21.5 2.1 4000 18.2 1.8 1000 19.4 1.9 10,000 16.9 1.6 4000 18.2 1.8 12.8 1.2 10,000 100,000 16.9 1.6 10.7 1.0 100,000 1,000,000 12.8 1.2 1,000,000 10.7 1.0 Table 2. The interface shear stress of 2D woven C/SiC composite corresponding to different applied 335 MPa at room temperature. cycles 2. under fatigue peak stress ofof σmax Table The interface shear stress 2D=woven C/SiC composite corresponding to different applied cycles under fatigue peak stress of σmax = 335 MPa at room temperature.

Cycle Experimental Hysteresis Number Dissipated Energy/(kJ/m3) Experimental Hysteresis Cycle Number1 3) 28.2 Dissipated Energy/(kJ/m 1000 20.3 1 28.2 1,000,000 17.1 1000 20.3 1,000,000

17.1

Interface Shear Stress/MPa Interface 22 Shear Stress/MPa 0.4 22 0.35 0.4 0.35

Figure 6. 6. (a) (a) The The experimental experimental fatigue fatigue hysteresis hysteresis loops loops corresponding corresponding to to different different cycle cycle number; number; and and Figure (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress curve of of cross-ply cross-ply C/SiC C/SiC composite = 105 MPa at room temperature. curve composite under under σσmax max = 105 MPa at room temperature.

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Figure 7. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress Figure 7. 7. (a) (a) The The experimental experimental fatigue fatigue hysteresis hysteresis loops loops corresponding corresponding to to different different cycle cycle number; number; and and Figure curve of 2D woven C/SiC composite under σmax = 335 MPa at room temperature. (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress curve of of 2D 2D woven woven C/SiC C/SiC composite under σσmax = 335 MPa atatroom temperature. curve composite temperature. max = 335 MPa Staehler et al. [7] investigated the under tension–tension fatigueroom behavior of 0°/90° plain-weave C/SiC

composite atetroom temperature.the The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) Staehler al. [7] investigated tension–tension fatigue behavior of ◦0°/90° plain-weave C/SiC Staehler et al. [7] investigated the tension–tension fatigue behavior of 0 /90◦ plain-weave C/SiC fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were manufactured using the CVI composite at room temperature. The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) compositeThe at room temperature. The T–300™ carbon (Toray Institute Inc., Tokyo,toJapan) fiber-reinforced process. 0°/90° fiber preform was given a pyrolytic carbon coating promote composite fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were manufactured using the◦ CVI 3. After silicon carbide matrix composites (C/SiC CMCs) were2.0 manufactured using the CVI process. 0 /90◦ toughness. The0°/90° composite bulk density about g/cmcarbon machining, each testThe specimen process. The fiber preform was was given a pyrolytic coating to promote composite fiber preform was given a pyrolytic carbon coating to promote composite toughness. The composite received a SiC coat via CVD.density The fatigue loading in3.a After sinusoidal waveform loading toughness. Theseal composite bulk was about 2.0was g/cm machining, eachwith test aspecimen bulk density was about 2.0 g/cm3stress . Afterratio machining, each test specimen received a2D SiCwoven seal coat via frequency of 40 Hz. The fatigue was 0.05. The material properties of C/SiC received a SiC seal coat via CVD. The fatigue loading was in a sinusoidal waveform with a loading −6 CVD. The fatigue loading was in a sinusoidal waveform with a loading frequency of 40 Hz. The fatigue composite given f = 45%, Ef = 225 GPa, Em = 430 GPa, rf = 3.5 μm, αf = 1.0 × 10 /°C, αm = 4.8 × frequency are of 40 Hz. by: TheVfatigue stress ratio was 0.05. The material properties of 2D woven C/SiC −6/°C, stress ratio was 0.05. The material properties of 2D woven C/SiC composite are given by: V = 45%, 10 and ΔT = −1000 °C. composite are given by: Vf = 45%, Ef = 225 GPa, Em = 430 rf = 3.5 μm, −α6f =◦1.0 × 10−6/°C, αmf = 4.8◦ × −6 /◦GPa, Ef −6 = 225 GPa, E = 430 GPa, r = 3.5 µm, α = 1.0 × 10 C, α = 4.8 × 10 / C, and ∆T = −1000 to C. m hysteresis loops corresponding Under peak°C.stress of σmax =f 375 MPa, the fatigue f 10 /°C, and fatigue ΔTm= −1000 Under fatigue peak of σmax 375 MPa, the fatigue hysteresis of loops corresponding to different applied cycles arestress illustrated in == Figure 8a, inthe which the proportion matrix cracking mode Under fatigue peak stress of σmax 375 MPa, fatigue hysteresis loops corresponding to applied cycles are illustrated in Figure fatigue 8a, in which the proportion of energy matrix cracking modeof3 3different is η = 0.2. The experimental and theoretical hysteresis dissipated as a function different applied cycles are illustrated in Figure 8a, in which the proportion of matrix cracking mode is η = 0.2.shear The experimental and hysteresisfatigue dissipated energy as a function of interface is shown in theoretical Figure 8b. fatigue The theoretical hysteresis dissipated energy 3 is η = 0.2. Thestress experimental and theoretical fatigue hysteresis dissipated energy as a function of 3 interface shear stress is shown in Figure 8b. The theoretical fatigue hysteresis dissipated energy increases interface to the peak value of 160.7 kJ/m , and then decreases interface with sheardecreasing stress is shown in shear Figurestress 8b. The theoretical fatigue hysteresis dissipated energy 3 , and then decreases increases with decreasing sheartostress to 3the peak value of 160.7 kJ/mhysteresis with decreasing interface interface shear stress 0 kJ/m .the The experimental fatigue 3, and thendissipated increases with decreasing interface shear stress to peak value of 160.7 kJ/m decreases 3 . The experimental fatigue hysteresis with decreasing interface shear stress to 0 kJ/m dissipated energy energy of the 2nd interface cycle lies shear in the stress left part fatigue dissipated versusdissipated interface 3. Thehysteresis with decreasing toof0 the kJ/m experimental fatigueenergy hysteresis of the stress 2nd cycle liesThe in the left part of the fatigue hysteresis dissipated energy versus interface shear shear hysteresis the 2nd cycle corresponds interface slipinterface Case 4, energy of thecurve. 2nd cycle fatigue lies in the left part loop of theoffatigue hysteresis dissipatedto energy versus stress curve. The fatigue hysteresis loop of the 2nd cycle corresponds to interface slip Case 4, i.e., the i.e., thestress interface completely debonds, andloop fiber completely relative to to matrix in the shear curve. The fatigue hysteresis of slips the 2nd cycle corresponds interface slipinterface Case 4, interface completely debonds, andexperimental fiber slips completely relative to matrix inenergy the interface debonded debonded region. By comparing fatigue hysteresis dissipated with theoretical i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface region. By comparing experimental fatigue hysteresis dissipated energycycles with theoretical values, the values, theregion. interface stressexperimental corresponding to different applied can be estimated, as debonded By shear comparing fatigue hysteresis dissipated energy with theoretical interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 3. shown Table 3. values, inthe interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 3.

Figure 8. (a) Figure 8. (a) The The experimental experimental fatigue fatigue hysteresis hysteresis loops loops corresponding corresponding to to different different cycle cycle number; number; and and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress Figure 8. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and max = 375 MPa at room temperature. curve of 2D C/SiC composite under curve 2D woven woven C/SiC compositefatigue underσσ MPa at room temperature. (b) theofexperimental and theoretical hysteresis energy versus interface shear stress max = 375dissipated curve of 2D woven C/SiC composite under σmax = 375 MPa at room temperature.

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Table 3. The interface shear stress of 2D woven C/SiC composite corresponding to different applied cycles under fatigue peak stress of σmax = 375 MPa at room temperature. Cycle Number

Experimental Hysteresis Dissipated Energy/(kJ/m3 )

Interface Shear Stress/MPa

2 107 998 3659 7124 16,931 26,982 36,408 45,961 56,119 66,277 78,275 95,575 227,112 659,419

107.5 84.6 84.3 80.2 80.1 77.3 74.6 73.3 71.9 70.6 69.2 67.9 66.6 62.5 62.3

2.3 1.7 1.68 1.55 1.54 1.48 1.4 1.38 1.32 1.31 1.3 1.28 1.2 1.15 1.14

Li [5] investigated the tension–tension fatigue behavior of 2D woven C/SiC composite at room temperature. The HTA carbon (Toho Tenax, Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were fabricated by laminating 2D plain weave carbon fabrics by liquid silicon infiltration (LSI) method. The fatigue loading was in a sinusoidal waveform with a loading frequency of 10 Hz, and the fatigue stress ratio was 0.1. The material properties of 2D woven C/SiC composite are given by: V f = 50%, Ef = 230 GPa, Em = 350 GPa, rf = 3.5 µm, αf = −0.38 × 10−6 /◦ C, αm = 2.8 × 10−6 /◦ C, and ∆T = −1000 ◦ C. Under fatigue peak stress of σmax = 57 MPa, the fatigue hysteresis loops corresponding different applied cycles are illustrated in Figure 9a, in which the proportion of matrix cracking mode 3 is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of interface shear stress is shown in Figure 9b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 3.2 kJ/m3 , and then decreases with decreasing interface shear stress to 0 kJ/m3 . The experimental fatigue hysteresis dissipated energy of the 11,104th and 33,262nd applied cycles lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loop of the 1st cycle corresponds to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 4. The fatigue hysteresis loops of the 55,493rd and 100,000th applied cycles correspond to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded region. Table 4. The interface shear stress of 2D woven C/SiC composite corresponding to different applied cycles under fatigue peak stress of σmax = 57 MPa at room temperature. Cycle Number

Experimental Hysteresis Dissipated Energy/(kJ/m3 )

Interface Shear Stress/MPa

11,104 33,262 55,493 100,000

1.8 2.4 1.7 1.6

3.7 2.7 0.5 0.45

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9. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and Figure Figure 9. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress curve of 2D woven C/SiC composite under σmax = 57 MPa at room temperature. curve of 2D woven C/SiC composite under σmax = 57 MPa at room temperature. Table 4. The interface shear stress of 2D woven C/SiC composite corresponding to different applied cyclesTemperature under fatigue peak stress of σmax = 57 MPa at room temperature. 4.1.2. Elevated

Experimental Li [21] investigatedCycle the tension–tension fatigue Hysteresis behavior of Interface cross-plyShear C/SiC composite at 800 ◦ C Number Dissipated Energy/(kJ/m3) Stress/MPa in air. The fatigue loading was in a sinusoidal waveform and a loading frequency of 10 Hz, and 11,104 1.8 3.7 the fatigue stress ratio was 0.1. The material properties of cross-ply C/SiC composite are given by: 33,262 2.4 2.7 −6 /◦ C, α = 2.8 × 10−6 /◦ C, and V f = 40%, Ef = 230 GPa, Em55,493 = 350 GPa, rf = 3.5 µm, m 1.7 αf = −0.38 × 10 0.5 ∆T = −200 ◦ C. 100,000 1.6 0.45 Under fatigue peak stress of σmax = 105 MPa, the fatigue hysteresis loops corresponding to 4.1.2. Elevated Temperature different applied cycles are illustrated in Figure 10a, in which the proportion of matrix cracking mode 3 is η = 0.8. Li The theoreticalfatigue fatigue hysteresis dissipated asata 800 function of [21]experimental investigated theand tension–tension behavior of cross-ply C/SiC energy composite °C in air. The stress fatigueisloading was a sinusoidal and a loading of 10dissipated Hz, and theenergy interface shear shown ininFigure 10b. waveform The theoretical fatiguefrequency hysteresis 3 , and fatigue stress ratio was 0.1. The material cross-ply C/SiC composite are given by:then Vf = 40%, increases with decreasing interface shearproperties stress toofthe peak value of 25.6 kJ/m decreases −6/°C, αm = 2.8 × 10−6/°C, and ΔT = −200 °C. 3 E f = 230 GPa, Em = 350 GPa, rf = 3.5 μm, αf = −0.38 × 10 with decreasing interface shear stress to 0 kJ/m . The experimental fatigue hysteresis dissipated energy Under fatigue peak stress of σmax = 105 MPa, the fatigue hysteresis loops corresponding to of the 1st cycle lies in the right part of the fatigue hysteresis dissipated energy versus interface shear different applied cycles are illustrated in Figure 10a, in which the proportion of matrix cracking stress curve. The fatigue hysteresis loop of the 1st cycle corresponds to interface slip Case 2, i.e., the mode 3 is η = 0.8. The experimental and theoretical fatigue hysteresis dissipated energy as a interface partially and fiber partially to matrix in the interface function of debonds, interface shear stressslips is shown in relative Figure 10b. The theoretical fatiguedebonded hysteresisregion. With the number of applied cycles increasing, interface shear stress decreases with increasing dissipated energy increases with decreasing interface shear stress to the peak value of 25.6 kJ/m3, cycle 3. The experimental fatigue and then decreases wear with decreasing interface shear stress to 0 kJ/moxidation, number due to interface and interface oxidation. For interface the oxidation of fiber dissipated energy of the 1st cycle lies in the right part of the fatigue hysteresis dissipated coatinghysteresis is a process such as, energy versus interface shear stress curve. The fatigue hysteresis loop of the 1st cycle corresponds 1 C +interface O2 → CO + O2 →and COfiber slips partially relative to (12) 2 or C debonds, to interface slip Case 2, i.e., the partially 2 matrix in the interface debonded region. With the number of applied cycles increasing, interface 17 of 28 shear stress decreases with increasing cycle number due to interface wear and interface oxidation. For interface oxidation, the oxidation of fiber coating is a process such as,

i.e., theMaterials oxidation material in the form of a gas. 2016, 9,removes 844

C + O2 → CO2 or C + 1 2 O2 → CO

(12)

i.e., the oxidation removes material in the form of a gas.

Figure 10. (a) The experimental fatigue hysteresis loops corresponding to different cycle number;

Figureand 10. (b) (a) the Theexperimental experimental fatigue hysteresis loops corresponding to different cycle number; and and theoretical fatigue hysteresis dissipated energy versus interface shear (b) thestress experimental and theoretical fatigueunder hysteresis dissipated energy versus interface shear stress curve of cross-ply C/SiC composite σmax = 105 MPa at 800 °C in air. ◦ curve of cross-ply C/SiC composite under σmax = 105 MPa at 800 C in air. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 5. The fatigue hysteresis loop of the 100th cycle corresponds to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded region. Table 5. The interface shear stress of cross-ply C/SiC composite corresponding to different applied

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By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 5. The fatigue hysteresis loop of the 100th cycle corresponds to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded region. Table 5. The interface shear stress of cross-ply C/SiC composite corresponding to different applied cycles under fatigue peak stress of σmax = 105 MPa at 800 ◦ C in air. Cycle Number

Experimental Hysteresis Dissipated Energy/(kJ/m3 )

Interface Shear Stress/MPa

1 2 3 4 10 100 500 1000 3000 6000 6600

24.3 20 13 12 9.7 8.6 7.1 6.1 5.4 5.2 5.1

5.5 2.3 1.3 1.2 0.9 0.8 0.6 0.5 0.45 0.43 0.4

Mall and Engesser [8] investigated the tension–tension fatigue behavior of 0◦ /90◦ plain-weave C/SiC composite at 550 ◦ C in air. The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) were manufactured using the CVI method with the reinforcement from plain-weave cloth in a [0/90] lay-up. The T–300 carbon fiber preform was given a pyrolytic carbon coating to promote toughness. The composite density was to be 2.0 g/cm3 . The test specimens were cut from 216 mm × 216 mm composite panels using diamond grinding into a dog-bone configuration. After the machining and cutting, the test specimens were then seal coated with SiC via CVD process. The fatigue tests were conducted in the force control with a stress ratio (i.e., minimum stress/maximum stress) of 0.05, and a sinusoidal waveform loading frequency of 0.1 Hz. The fatigue stress ratio was 0.1. The material properties of 2D woven C/SiC composite are given by: V f = 45%, Ef = 225 GPa, Em = 430 GPa, rf = 3.5 µm, αf = 1.0 × 10−6 /◦ C, αm = 4.8 × 10−6 /◦ C, and ∆T = −500 ◦ C. Under fatigue peak stress of σmax = 350 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 11a, in which the proportion of matrix cracking mode 3 is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of interface shear stress is shown in Figure 11b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 156.7 kJ/m3 , and then decreases with decreasing interface shear stress to 0 kJ/m3 . The experimental fatigue hysteresis dissipated energy of the 100th cycle lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loops of the 100th, 200th, and 212th applied cycles correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 6.

200th, and 212th applied cycles correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental fatigue hysteresis dissipated with theoretical values, the interface shear stress corresponding to different Materials 2016, energy 9, 844 18 of 28 applied cycles can be estimated, as shown in Table 6.

Figure 11. 11. (a) (a)The Theexperimental experimentalfatigue fatigue hysteresis loops corresponding to different number; Figure hysteresis loops corresponding to different cyclecycle number; and and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress stress of curve of 2D woven composite 350 MPa curve 2D woven C/SiCC/SiC composite underunder σ =σmax 350=MPa at 550at◦550 C in°C air.in air. max

Table6.6.The Theinterface interfaceshear shearstress stressof of2D 2Dwoven wovenC/SiC C/SiC composite composite corresponding corresponding to to different different applied applied Table max = 350 MPa at 550 °C in air. cycles under fatigue peak stress of σ ◦ cycles under fatigue peak stress of σmax = 350 MPa at 550 C in air.

Experimental Hysteresis Interface Shear Cycle NumberExperimental Hysteresis Dissipated Energy/(kJ/m3) Interface Stress/MPa Cycle Number Shear Stress/MPa Dissipated Energy/(kJ/m3 ) 100 50.5 18 100 50.5 18 200 53.4 17 200 53.4 17 212 9.79.7 212 93.8 93.8 Rodrigues et al. [9] investigated the tension–tension fatigue behavior of 2D C/SiC composite at Rodrigues et al. [9] investigated the tension–tension fatigue behavior of 2D C/SiC composite at 1200 °C in vacuum. The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) fiber-reinforced silicon 1200 ◦ C in vacuum. The T–300™ carbon (Toray Institute Inc., Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (C/SiC CMCs) was a superposition of several plain weave layers of carbide matrix composites (C/SiC CMCs) was a superposition of several plain weave layers of carbon carbon fiber bundles embedded in a SiC matrix through a CVI process. The composite density is fiber bundles embedded in a SiC matrix through a CVI process. The composite density is about about 2.0 g/cm3. The fatigue tests were performed under force control with a triangular loading cycle 2.0 g/cm3 . The fatigue tests were performed under force control with a triangular loading cycle with a loading frequency of 10 Hz, and a stress ratio (i.e., minimum stress/maximum stress) of 0.1. with a loading frequency of 10 Hz, and a stress ratio (i.e., minimum stress/maximum stress) of The material properties of 2D woven C/SiC composite are given by: Vf = 40%, Ef = 225 GPa, Em = 350 0.1. The material properties−6of 2D woven C/SiC composite are given by: V f = 40%, Ef = 225 GPa, GPa, rf = 3.5 μm, αf = 1.0 × 10 /°C, αm = 4.8 × 10−6/°C, and ΔT = −100 °C. Em = 350 GPa, rf = 3.5 µm, αf = 1.0 × 10−6 /◦ C, αm = 4.8 × 10−6 /◦ C, and ∆T = −100 ◦ C. Under fatigue peak stress of σmax = 300 MPa, the fatigue hysteresis loops corresponding to Under fatigue peak stress of σmax = 300 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 12a, in which the proportion of matrix cracking different applied cycles are illustrated in Figure 12a, in which the proportion of matrix cracking mode 3 mode 3 is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of of interface shear stress is shown in Figure 12b. The theoretical fatigue hysteresis dissipated energy interface shear stress is shown in Figure 12b. The theoretical fatigue hysteresis dissipated energy 3, and increases with decreasing interface shear stress to the peak value of 126 kJ/m then decreases 3 , and then decreases with increases with decreasing interface shear stress to the peak value of 126 kJ/m with decreasing interface shear stress to 30 kJ/m3. The experimental fatigue hysteresis dissipated decreasing interface shear stress to 0 kJ/m . The experimental fatigue hysteresis dissipated energy energy of the 1000th, 100,000th, and 1,000,000th applied cycle lies in the right part of the fatigue of the 1000th, 100,000th, and 1,000,000th applied cycle lies in the right part of the fatigue hysteresis hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loop of the 1st dissipated energy versus interface shear stress curve. The fatigue hysteresis loop of the 1st cycle corresponds to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 7. The fatigue hysteresis loops of the 500,000th, 1,000,000th, 2,100,000th, and 2,600,000th applied cycles correspond to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded region.

increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to different applied cycles can be estimated, as shown in Table 7. The fatigue hysteresis loops of the 500,000th, 1,000,000th, 2,100,000th, and 2,600,000th cycles correspond to interface slip Case 4, i.e., the interface completely debonds, Materials 2016, applied 9, 844 19 of 28 and fiber slips completely relative to matrix in the interface debonded region.

Figure 12. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; Figure 12. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and and (b)experimental the experimental and theoretical fatigue hysteresis dissipated interface shear (b) the and theoretical fatigue hysteresis dissipated energyenergy versusversus interface shear stress max = 300 MPa at 1200 °C in vacuum. stress curve of 2D woven C/SiC composite under σ ◦ curve of 2D woven C/SiC composite under σmax = 300 MPa at 1200 C in vacuum. Table 7. The interface shear stress of 2D woven C/SiC composite corresponding to different applied Table 7. The interface shear stress of 2D woven C/SiC composite corresponding to different applied cycles under fatigue peak stress of σmax = 300 MPa at 1200 °C in vacuum. cycles under fatigue peak stress of σmax = 300 MPa at 1200 ◦ C in vacuum.

Cycle Number

Cycle Number

1000

1000 10,000 10,000 100,000 100,000 500,000 500,000 1,000,000 1,000,000 2,100,000 2,100,000 2,600,000

2,600,000

Experimental Hysteresis Experimental Hysteresis 3) Dissipated Energy/(kJ/m Dissipated Energy/(kJ/m3 ) 30.7 30.7 32.1 32.1 38.6 38.6 30.8 30.8 29.1 29.1 28.6 28.6 25 25

Interface Shear Stress/MPa Interface Shear Stress/MPa 15 14.215 14.2 12 12 0.40.4 0.35 0.35 0.30.3 0.25 0.25

4.2. 4.2. 2D 2D SiC/SiC SiC/SiC Composite Composite 4.2.1. Room Temperature 4.2.1. Room Temperature Shi [11] investigated the tension–tension fatigue behavior of 2D woven SiC/SiC composite at Shi [11] investigated the tension–tension fatigue behavior of 2D woven SiC/SiC composite at room temperature. The Hi-Nicalon™ SiC (Nippon Carbon Co., Ltd., Tokyo, Japan) fiber-reinforced room temperature. The Hi-Nicalon™ SiC (Nippon Carbon Co., Ltd., Tokyo, Japan) fiber-reinforced silicon carbide matrix composites (SiC/SiC CMCs) were manufactured using CVI method whereby silicon carbide matrix composites (SiC/SiC CMCs) were manufactured using CVI method whereby fiber fabrics are first CVD coated with BN before several cycles of CVI to deposit SiC matrix on the fiber fabrics are first CVD coated with BN before several cycles of CVI to deposit SiC matrix on the coated fiber fabrics. The fatigue loading was in a sinusoidal waveform and a loading frequency of coated fiber fabrics. The fatigue loading was in a sinusoidal waveform and a loading frequency of 1.0 1.0 Hz, and the fatigue stress ratio was 0.1. The material properties of 2D woven SiC/SiC composite are Hz, and the fatigue stress ratio was 0.1. The material properties of 2D woven SiC/SiC composite are given by: V f = 40%, Ef = 270 GPa, Em = 300 GPa, rf = 7.0 µm, αf = 5.1 ×−610−6 /◦ C, αm = 4.7−6 × 10−6 /◦ C, given by: Vf = 40%, Ef = 270 GPa, Em = 300 GPa, rf = 7.0 μm, αf = 5.1 × 10 /°C, αm = 4.7 × 10 /°C, and ΔT and ∆T = −1000 ◦ C. = −1000 °C. Under fatigue peak stress of σmax = 150 MPa, the fatigue hysteresis loops corresponding to Under fatigue peak stress of σmax = 150 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 13a, in which the proportion of matrix cracking mode 3 different applied cycles are illustrated in Figure 13a, in which the proportion of matrix cracking is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of mode 3 is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function interface shear stress is shown in Figure 13b. The theoretical fatigue hysteresis dissipated energy of interface shear stress is shown in Figure 13b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 32.1 kJ/m3 , and then decreases with decreasing interface shear stress to 0 kJ/m3 . The experimental fatigue hysteresis dissipated energy of the 121st and 1,200,331st applied cycles lie in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental

increases with decreasing interface shear stress to the peak value of 32.1 kJ/m3, and then decreases with decreasing interface shear stress to 0 kJ/m3. The experimental fatigue hysteresis dissipated energy of the 121st and 1,200,331st applied cycles lie in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in Materials 2016, 9, 844 20 of 28 the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing fatigue hysteresis dissipated energy with theoretical values, the interface shear corresponding to experimental fatigue hysteresis dissipated energy with theoretical values, thestress interface shear stress different applied cycles applied cycles can be estimated, as shown in Table 8. corresponding to different applied cycles applied cycles can be estimated, as shown in Table 8.

Figure 13. (a) (a) The Theexperimental experimentalfatigue fatiguehysteresis hysteresis loops corresponding to different number; Figure 13. loops corresponding to different cyclecycle number; and and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress stress of 2D woven SiC/SiC composite 150 MPa at room temperature. curve curve of 2D woven SiC/SiC composite underunder σ =σmax 150=MPa at room temperature. max

Table Theinterface interface shear stress ofwoven 2D woven SiC/SiC composite corresponding to different shear stress of 2D SiC/SiC composite corresponding to different applied Table 8.8.The applied cyclesfatigue underpeak fatigue peak σmaxMPa = 150 room temperature. cycles under stress of stress σ =of150 at MPa roomattemperature. max

Experimental Hysteresis Interface Shear Cycle NumberExperimental Hysteresis 3) Dissipated Energy/(kJ/m Stress/MPa Interface Shear Stress/MPa Dissipated Energy/(kJ/m3 ) 121 10.4 17 121 10.4 17 331 10.6 16.8 331 10.6 16.8 661 16.316.3 661 10.9 10.9 14.714.7 1241 1241 12.1 12.1 1601 1601 12.7 12.7 14 14 253,561 253,561 13.3 13.3 13.313.3 405,451 14.6 12.1 12.111.4 757,531 405,451 15.5 14.6 11.410 1,200,331757,531 18 15.5 1,200,331 18 10

Cycle Number

Under fatigue peak stress of σmax = 250 MPa, the fatigue hysteresis loops corresponding to Under fatigue peak stress of σmax = 250 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 14a, in which the proportion of matrix cracking mode 3 different applied cycles are illustrated in Figure 14a, in which the proportion of matrix cracking is η = 0.8. The experimental and theoretical fatigue hysteresis dissipated energy as a function of mode 3 is η = 0.8. The experimental and theoretical fatigue hysteresis dissipated energy as a function interface shear stress is shown in Figure 14b. The theoretical fatigue hysteresis dissipated energy of interface shear stress is shown in Figure 14b. The theoretical fatigue hysteresis dissipated energy increases with decreasing interface shear stress to the peak value of 118 kJ/m3 , and then decreases with 3 increases with decreasing interface shear stress to the peak value of 118 kJ/m , and then decreases decreasing interface shear stress to 0 kJ/m3 . The experimental fatigue hysteresis dissipated energy with decreasing interface shear stress to 0 kJ/m3. The experimental fatigue hysteresis dissipated of the 81st, 401st, and 641st applied cycles lie in the right part of the fatigue hysteresis dissipated energy of the 81st, 401st, and 641st applied cycles lie in the right part of the fatigue hysteresis energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip dissipated energy versus interface shear stress curve. The fatigue hysteresis loops correspond to Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in debonded region. With the number of applied cycles increasing, interface shear stress decreases with the interface debonded region. With the number of applied cycles increasing, interface shear stress increasing cycle number due to interface wear and interface oxidation. By comparing experimental decreases with increasing cycle number due to interface wear and interface oxidation. By comparing fatigue hysteresis dissipated energy with theoretical values, the interface shear stress corresponding to experimental fatigue hysteresis dissipated energy with theoretical values, the interface shear stress different applied cycles can be estimated, as shown in Table 9. The fatigue hysteresis loops of the 761st and 332,961st applied cycles correspond to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded region.

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corresponding to different applied cycles can be estimated, as shown in Table 9. The fatigue hysteresis loops of the 761st and 332,961st applied cycles correspond to interface slip Case 4, i.e., the interface completely debonds, and fiber slips completely relative to matrix in the interface debonded Materials 2016, 9, 844 21 of 28 region.

Figure 14. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; Figure 14. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress stress curve of 2D woven SiC/SiC composite under σmax = 250 MPa at room temperature. curve of 2D woven SiC/SiC composite under σmax = 250 MPa at room temperature. Table 9. The interface shear stress of 2D woven SiC/SiC composite corresponding to different Table 9. The interface shear stress of 2D woven SiC/SiC composite corresponding to different applied applied cycles under fatigue peak stress of σmax = 250 MPa at room temperature. cycles under fatigue peak stress of σmax = 250 MPa at room temperature.

Experimental Hysteresis Interface Shear Cycle NumberExperimental Hysteresis Stress/MPa Dissipated Energy/(kJ/m3) Interface Cycle Number Shear Stress/MPa Dissipated Energy/(kJ/m3 ) 81 106 11.1 81 106 107 401 1111.1 401 107 11 641 113 10.1 641 113 10.1 761 5.85.8 761 107 107 1281 105 105 1281 5.65.6 1441 102 102 1441 5.45.4 23,361 93 4.6 23,361 93 4.6 83,161 87 4.2 4.24.1 174,561 83,161 86 87 4.1 4 217,761 174,561 85 86 239,361 217,761 83 85 4 3.9 296,961 239,361 82 83 3.93.8 332,961 80 3.7 296,961 82 3.8 332,961 80 3.7 4.2.2. Elevated Temperature 4.2.2.Shi Elevated Temperature [11] investigated the tension–tension fatigue behavior of 2D woven SiC/SiC composite at ◦ 800 C air. investigated The fatigue loading was in a sinusoidal and loadingSiC/SiC frequency of 1.0 Hz, Shiin[11] the tension–tension fatiguewaveform behavior of 2Da woven composite at and the fatigue stress ratio was 0.1. The material properties of 2D woven SiC/SiC composite are1.0 given 800 °C in air. The fatigue loading was in a sinusoidal waveform and a loading frequency of Hz, −6 ◦ C, α = 4.7 × 10−6 /◦ C, and by: Ef =stress 270 GPa, αf = 5.1 × m = 300 f = 40%, f = 7.0 µm, andVthe fatigue ratioEwas 0.1. GPa, The rmaterial properties of10 2D / wovenmSiC/SiC composite are ◦ ∆T = − 200 C. given by: Vf = 40%, Ef = 270 GPa, Em = 300 GPa, rf = 7.0 μm, αf = 5.1 × 10−6/°C, αm = 4.7 × 10−6/°C, and fatigue peak stress of σmax = 150 MPa, the fatigue hysteresis loops corresponding to ΔT =Under −200 °C. different applied cycles are stress illustrated in Figure in which the proportion matrixcorresponding cracking modeto 3 Under fatigue peak of σmax = 150 15a, MPa, the fatigue hysteresisofloops is η = 0.2. The experimental and theoretical fatigue hysteresis dissipated energy as a function of different applied cycles are illustrated in Figure 15a, in which the proportion of matrix cracking interface stress shown in Figure 15b. The fatigue theoretical fatiguedissipated hysteresisenergy dissipated energy mode 3 isshear η = 0.2. The is experimental and theoretical hysteresis as a function 3 increases with decreasing stress thetheoretical peak value of 32.1hysteresis kJ/m , and then decreases of interface shear stress is interface shown inshear Figure 15b.to The fatigue dissipated energy 3 . The experimental fatigue hysteresis dissipated with decreasing interface shear stress to 0 kJ/m 3 increases with decreasing interface shear stress to the peak value of 32.1 kJ/m , and then decreases energy of the 5th and 36,500th applied lie in3.the part of the fatigue fatigue hysteresis with decreasing interface shear stresscycles to 0 kJ/m Theright experimental hysteresis dissipated dissipated energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip energy of the 5th and 36,500th applied cycles lie in the right part of the fatigue hysteresis dissipated Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental

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energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface Materials 2016, 9, 844 22 of 28 debonded region. With the number of applied cycles increasing, interface shear stress decreases with increasing cycle number due to interface wear and interface oxidation. By comparing experimental fatigue hysteresis hysteresis dissipated dissipatedenergy energywith withtheoretical theoreticalvalues, values,the theinterface interface shear stress corresponding shear stress corresponding to to different applied cycles estimated, shown in Table different applied cycles cancan be be estimated, as as shown in Table 10. 10.

Figure 15. (a) (a) The Theexperimental experimentalfatigue fatiguehysteresis hysteresis loops corresponding to different number; Figure 15. loops corresponding to different cyclecycle number; and and (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear (b) the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress 150 MPa at◦800 in air. stress of 2D woven SiC/SiC composite σmax curve curve of 2D woven SiC/SiC composite underunder σmax = 150= MPa at 800 C in°C air. Table 10.The Theinterface interface shear stress of woven 2D woven SiC/SiC composite corresponding to different Table 10. shear stress of 2D SiC/SiC composite corresponding to different applied ◦ applied cycles under fatigue peak stress of σ max = 150 MPa at 800 °C in air. cycles under fatigue peak stress of σmax = 150 MPa at 800 C in air.

Experimental Hysteresis Interface Shear Cycle Number Experimental Hysteresis 3) Interface Shear Stress/MPa Stress/MPa Dissipated Energy/(kJ/m 3) Dissipated Energy/(kJ/m 5 5.5 32.6 5 5.5 32.6 10 6.5 27.6 10 6.5 27.6 50 21.521.5 50 8.3 8.3 1000 1000 10.6 10.6 16.816.8 15,000 15,000 12.6 12.6 14.114.1 20,000 13.5 13.2 20,000 13.5 13.210.3 25,000 17.3 10.39.5 30,000 25,000 18.7 17.3 32,000 30,000 19.6 18.7 9.5 9 34,000 32,000 20.9 19.6 9 8.5 36,000 23.6 7.5 34,000 20.9 8.5 36,500 26 6.8 36,000 23.6 7.5 36,500 26 6.8 Groner [12] investigated the tension–tension fatigue behavior of 2D woven SiC/SiC composite ◦ C in air. The Nicalon™ SiC (Nippon Carbon Co., Ltd., Tokyo, Japan) fiber-reinforced silicon at 1100 Groner [12] investigated the tension–tension fatigue behavior of 2D woven SiC/SiC composite carbide matrix (SiC/SiC CMCs) were manufactured by chemical infiltrationsilicon (CVI) at 1100 °C in air.composites The Nicalon™ SiC (Nippon Carbon Co., Ltd., Tokyo, Japan) vapor fiber-reinforced method. The fatigue loading was in a triangular waveform and a loading frequency of 1.0 Hz, and carbide matrix composites (SiC/SiC CMCs) were manufactured by chemical vapor infiltration (CVI) the fatigue stress ratio was 0.1. The properties of 2D woven SiC/SiC composite method. The fatigue loading was in material a triangular waveform and a loading frequency of 1.0are Hz,given and −6 /K, α = 2 × 10−6 /K, and by: V = 40%, E = 230 GPa, E = 350 GPa, r = 7.0 µm, α = 3.9 × 10 m m f f f woven SiC/SiC composite are given by: the fatigue stressf ratio was 0.1. The material properties of 2D ∆T = −100 K. V f = 40%, Ef = 230 GPa, Em = 350 GPa, rf = 7.0 μm, αf = 3.9 × 10−6/K, αm = 2 × 10−6/K, and ΔT = −100 K. Under fatigue fatigue peak = 140 MPa, the fatigue hysteresis loops corresponding to Under peak stress stress of of σσmax max = 140 MPa, the fatigue hysteresis loops corresponding to different applied cycles are illustrated in Figure 16a,16a, in which the proportion of matrix crackingcracking mode 3 different applied cycles are illustrated in Figure in which the proportion of matrix is η = 0.2. and theoretical fatigue hysteresis energy as aenergy function mode 3 is The η = experimental 0.2. The experimental and theoretical fatigue dissipated hysteresis dissipated as of a interface shear stress is shown in Figure 16b. The theoretical fatigue hysteresis dissipated energy function of interface shear stress is shown in Figure 16b. The theoretical fatigue hysteresis 3 , and then decreases with increases with decreasing interface shear stress to the peak value of to 28 the kJ/m dissipated energy increases with decreasing interface shear stress peak value of 28 kJ/m3, and 3 . The experimental fatigue hysteresis dissipated energy decreasing interface shear stress to 0 kJ/m 3 then decreases with decreasing interface shear stress to 0 kJ/m . The experimental fatigue hysteresis of the 7249th, 15,381st, and 23,391st applied cycles all lie in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve. The fatigue hysteresis loops correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in Cycle Number

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dissipated energy of the 7249th, 15,381st, and 23,391st applied cycles all lie in the right part of the fatigue hysteresis loops Materials 2016, 9, 844 dissipated energy versus interface shear stress curve. The fatigue hysteresis23 of 28 correspond to interface slip Case 2, i.e., the interface partially debonds, and fiber slips partially relative to matrix in the interface debonded region. With the number of applied cycles increasing, the interface debonded region. With numbercycle of applied cycles shear stress interface shear stress decreases with the increasing number dueincreasing, to interfaceinterface wear and interface decreases with increasing cycle number due to interface wear and interface oxidation. By comparing oxidation. By comparing the experimental fatigue hysteresis dissipated energy with theoretical the experimental fatigue hysteresis energy theoretical values, thecan interface shear stress values, the interface shear stress dissipated corresponding to with different applied cycles be estimated, as corresponding to different applied cycles can be estimated, as shown in Table 11. shown in Table 11.

Figure 16. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; Figure 16. (a) The experimental fatigue hysteresis loops corresponding to different cycle number; and and (b)experimental the experimental and theoretical fatigue hysteresis dissipated energy interface shear (b) the and theoretical fatigue hysteresis dissipated energy versusversus interface shear stress max = 140 MPa at 1100 °C in air. stress curve of 2D woven SiC/SiC composite under σ ◦ curve of 2D woven SiC/SiC composite under σ = 140 MPa at 1100 C in air. max

Table 11. The interface shear stress of 2D woven SiC/SiC composite corresponding to different Table 11. The interface shear stress of 2D woven SiC/SiC composite corresponding to different applied applied cycles under fatigue peak stress of σmax = 140 MPa at 1100 °C in air. cycles under fatigue peak stress of σmax = 140 MPa at 1100 ◦ C in air.

Cycle Number Cycle Number 7249 7249 15,381 15,381 23,391 23,391

Experimental Hysteresis Experimental Hysteresis 3) Dissipated Energy/(kJ/m Dissipated Energy/(kJ/m3 )

3.5

3.58 8 10.8 10.8

Interface Shear Stress/MPa Interface Shear Stress/MPa 38.6 16.6 38.6 16.6 12.3 12.3

4.3. Comparison Analysis 4.3. Comparison Analysis The experimental fatigue hysteresis dissipated energy versus cycle number curves of cross-ply The experimental fatigue hysteresis dissipated energy versus cycle number curves of cross-ply and 2D woven C/SiC composites at room temperature, 550 °C, and 800 °C in air, and 1200 °C in and 2D woven C/SiC composites at room temperature, 550 ◦ C, and 800 ◦ C in air, and 1200 ◦ C in vacuum are illustrated in Figure 17a. For cross-ply C/SiC composite under σmax = 105 MPa at room vacuum are illustrated in Figure 17a. For cross-ply C/SiC composite under σmax = 105 MPa at room temperature and 800 ◦°C in air, 2D woven C/SiC composite under σmax = 335 and 375 MPa at room temperature and 800 C in air, 2D woven C/SiC composite under σmax = 335 and 375 MPa at room temperature, the experimental fatigue hysteresis dissipated energy decreases with increasing cycle temperature, the experimental fatigue hysteresis dissipated energy decreases with increasing cycle number, and lies in the right and left part of the fatigue hysteresis dissipated energy versus interface number, and lies in the right and left part of the fatigue hysteresis dissipated energy versus interface shear stress curve, as shown in Figure 17b. For 2D woven C/SiC composite under σmax = 350 MPa at shear stress curve, as shown in Figure 17b. For 2D woven C/SiC composite under σmax = 350 MPa 550 °C◦in air, the experimental fatigue hysteresis dissipated energy increases with increasing cycle at 550 C in air, the experimental fatigue hysteresis dissipated energy increases with increasing cycle number, and lies in the right part of the fatigue hysteresis dissipated energy versus interface shear number, and lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve, as shown in Figure 17b. For 2D woven C/SiC composite under σmax = 57 MPa at room stress curve, as shown in Figure 17b. For 2D woven C/SiC composite under σmax = 57 MPa at room temperature, and σmax = 300 MPa at 1200 °C in vacuum, the experimental fatigue hysteresis temperature, and σmax = 300 MPa at 1200 ◦ C in vacuum, the experimental fatigue hysteresis dissipated dissipated energy increases first, and then decreases with increasing cycle number, and lies in the energy increases first, and then decreases with increasing cycle number, and lies in the right and right and left part of the fatigue hysteresis dissipated energy versus interface shear stress curve, as left part of the fatigue hysteresis dissipated energy versus interface shear stress curve, as shown in shown in Figure 17b. Figure 17b.

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Figure experimental fatigue fatiguehysteresis hysteresisdissipated dissipatedenergy energyversus versus applied cycles; Figure 17. 17. (a) (a) The The experimental applied cycles; andand (b) (b) the the experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress experimental and theoretical fatigue hysteresis dissipated energy versus interface shear stress curves of curves of cross-ply and 2D woven C/SiC composites at room and elevated temperatures. cross-ply and 2D woven C/SiC composites at room and elevated temperatures.

The interface shear stress degradation rate of cross-ply and 2D woven C/SiC composites at The interface shear stress degradation rate of cross-ply and 2D woven C/SiC composites room and elevated temperatures are illustrated in Table 12. The interface shear stress degradation at room and elevated temperatures are illustrated in Table 12. The interface shear stress rate is the highest for 2D woven C/SiC composite under σmax = 350 MPa at 550 °C in air, i.e., 7.4 × 10◦−2 degradation rate is the highest for 2D woven C/SiC composite under σmax = 350 MPa at 550 C MPa/cycle, due to high fatigue peak stress and low loading frequency of 0.1 Hz, and is the lowest for in air, i.e., 7.4 × 10−2 MPa/cycle, due to high fatigue peak stress and low loading frequency 2D woven C/SiC composite under σmax = 375 MPa at room temperature, i.e., 1.7 × 10−6 MPa/cycle, due of 0.1 Hz, and is the lowest for 2D woven C/SiC composite under σmax = 375 MPa at room to high loading frequency−of 40 Hz. For cross-ply C/SiC composite under the same fatigue peak temperature, i.e., 1.7 × 10 6 MPa/cycle, due to high loading frequency of 40 Hz. For cross-ply stress of σmax = 105 MPa at room temperature and 800 °C in air, the interface shear stress degradation C/SiC composite under the same fatigue peak stress of σmax = 105 MPa at room temperature rate increases at elevated temperature in air, i.e., 7.7 × 10−4 MPa/cycle at elevated temperature and 6.3 and 800 ◦ C in air, the interface shear stress degradation rate increases at elevated temperature −6 × 10 MPa/cycle at room temperature, due to interface oxidation and interface wear. For 2D woven in air, i.e., 7.7 × 10−4 MPa/cycle at elevated temperature and 6.3 × 10−6 MPa/cycle at room C/SiC composite at room temperature, the interface shear stress degradation rate increases with temperature, due to interface oxidation and interface wear. For 2D woven C/SiC composite at room increasing fatigue peak stress, i.e., 2.1 × 10−5 MPa/cycle under σmax = 335 MPa, and 1.6 × 10−4 temperature, the interface shear stress degradation rate increases with increasing fatigue peak stress, MPa/cycle under σmax = 375 MPa, and decreases with increasing loading frequency, i.e., 1.6 × 10−4 i.e., 2.1 × 10−5 MPa/cycle under σmax = 335 MPa, and 1.6 × 10−4 MPa/cycle under σmax = 375 MPa, MPa/cycle at the loading frequency of 10 Hz, and 1.7 × 10−6 MPa/cycle at the loading frequency of 40 and decreases with increasing loading frequency, i.e., 1.6 × 10−4 MPa/cycle at the loading frequency Hz under the same fatigue peak stress of σmax = 375 MPa. − 6 of 10 Hz, and 1.7 × 10 MPa/cycle at the loading frequency of 40 Hz under the same fatigue peak stress of σmax = 375 MPa. Table 12. The interface shear stress degradation rate of C/SiC and SiC/SiC composites at room and elevated Table 12.temperatures. The interface shear stress degradation rate of C/SiC and SiC/SiC composites at room and elevated Items temperatures.

CPItems C/SiC CP C/SiC

2D C/SiC 2D C/SiC

2D SiC/SiC 2D SiC/SiC

σmax/MPa RT 105 T σ max /MPa 800 °C in air 105 RT 105 RT 335 800 ◦ C in air 105 RT 375 RT 335 RT 375 RT 375 RT 57 RT 375 550 °C in air 350 RT 57 1200550 °C◦ C inin vacuum 300 air 350 150 1200 ◦ C RT in vacuum 300 RT 250 RT 150 800 °C 150 RTin air 250 800 ◦°C C ininair 150 1100 air 120 1100 ◦°C C in air 120 1100 in air 140 1100 ◦ C in air 140 1100 ◦°C in air 170 1100 C in air 170 1100 inair air 210 1100 ◦°C C in 210

τinitial/MPa 7.3 τ initial /MPa 5.5 7.3 21.6 5.5 17 21.6 2.3 17 3.7 2.3 18 3.7 15 18 17 15 11.1 17 32.6 11.1 32.6 25.6 25.6 38.6 38.6 30.9 30.9 46.7 46.7

τfinal/MPa Ninitial 1 1 τ final /MPa N initial 0.4 1 1 0.35 11 0.4 0.45 11 0.35 1.14 21 0.45 1 0.45 11,104 1.14 2 9.7 100 0.45 11,104 0.25 1000 9.7 100 10 121 0.25 1000 3.7 81 10 121 6.8 581 3.7 6.8 5 8.9 7062 8.9 7062 12.3 7249 12.3 7249 19.8 1242 19.8 1242 27.8 212 27.8 212

Nfinal ψ/(MPa/Cycle) 1,000,000 6.3 × 10−6 N final ψ/(MPa/Cycle) 6600 7.7 × 10−4 1,000,000 6.3 ××10 10−5−6 1,000,000 2.1 6600 7.7 ××10 10−4−4 100,000 1.6 1,000,000 2.1 ××10 10−6−5 659,419 1.7 100,000 1.6 × 10−5−4 100,000 3.6 × 10 659,419 1.7 × 10−2−6 212 7.4 × 10 −5 100,000 3.6 × 10 −6 2,600,000 5.6 212 7.4 ××10 10−2 1,200,331 5.8 2,600,000 5.6 ××10 10−6−6 −5 332,961 2.2 1,200,331 5.8 ××10 10−6 36,500 7.0 332,961 2.2 ××10 10−4−5 36,500 7.0 ××10 10−4−4 41,696 4.8 41,696 4.8 × 10−3−4 23,391 1.6 × 10 23,391 1.6 × 10−3−3 6780 2.0 × 10 −3 6780 2.0 × 10−2 945 2.6 945 2.6 ××10 10−2

The experimental fatigue hysteresis dissipated energy versus cycle number curves of 2D The experimental fatigue hysteresis dissipated energy versus cycle number curves of 2D SiC/SiC SiC/SiC composite at room temperature, 800 °C, and 1100 °C in air are illustrated in Figure 18a. For composite at room temperature, 800 ◦ C, and 1100 ◦ C in air are illustrated in Figure 18a. For 2D SiC/SiC 2D SiC/SiC composite under σmax = 150 MPa at room temperature and 800 °C in air, and under σmax = 120, 140, 170, and 210 MPa at 1100 °C in air, the experimental fatigue hysteresis dissipated energy

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◦ composite under Materials 2016, 9, 844 σmax = 150 MPa at room temperature and 800 C in air, and under σmax = 120, 25 140, of 28 ◦ 170, and 210 MPa at 1100 C in air, the experimental fatigue hysteresis dissipated energy increases with increases with cyclelies number, and lies parthysteresis of the fatigue hysteresis dissipated increasing cycleincreasing number, and in the right partinofthe theright fatigue dissipated energy versus energy versus interface shear stress in curve, shown in Figure 18b. The hysteresis experimental fatigue interface shear stress curve, as shown Figureas18b. The experimental fatigue dissipated hysteresis first increases, and then decreases with increasing cycle number, energy firstdissipated increases, energy and then decreases with increasing cycle number, and lies in the right and and left lies in the right and left part of the fatigue hysteresis dissipated energy versus interface shear stress part of the fatigue hysteresis dissipated energy versus interface shear stress curve, corresponding to curve, corresponding to SiC/SiC the fatigue loading under of 2D σ SiC/SiC composite undertemperature, σmax = 250 MPa at room the fatigue loading of 2D composite MPa at room as shown in max = 250 temperature, as shown in Figure 18a,b, respectively. Figure 18a,b, respectively. The interface interfaceshear shear stress degradation 2D woven SiC/SiC composite room and The stress degradation rate rate of 2Dofwoven SiC/SiC composite at room at and elevated elevated temperatures are illustrated inThe Table 12. Theshear interface stress degradation rate is for the temperatures are illustrated in Table 12. interface stressshear degradation rate is the highest −2 ◦ − 2 highest for 2D woven SiC/SiC composite under σ max = 210 MPa at 1100 °C in air, i.e., 2.6 × 10 2D woven SiC/SiC composite under σmax = 210 MPa at 1100 C in air, i.e., 2.6 × 10 MPa/cycle, MPa/cycle, and for the2D lowest forSiC/SiC 2D woven SiC/SiCunder composite σmax at= room 150 MPa at room and the lowest woven composite σmax =under 150 MPa temperature, temperature, 5.8 × 10−6 MPa/cycle. For 2D SiC/SiC composite the same fatigue stress i.e., 5.8 × 10−6i.e., MPa/cycle. For 2D SiC/SiC composite under under the same fatigue peakpeak stress of ◦ of σ max = 150 MPa at room temperature and 800 °C in air, the interface shear stress degradation rate σmax = 150 MPa at room temperature and 800 C in air, the interface shear stress degradation −4 MPa/cycle increases at elevated temperature in air,ini.e., × 10 at elevated and 5.8 × rate increases at elevated temperature air,7.0 i.e., 7.0 × 10−4 MPa/cycle at temperature, elevated temperature, −6 MPa/cycle − 6 10 at room temperature, due to interface oxidation and interface wear. For 2D and 5.8 × 10 MPa/cycle at room temperature, due to interface oxidation and interfacewoven wear. SiC/SiC composite at room temperature, interface shear stress degradation rate increases with For 2D woven SiC/SiC composite at roomthe temperature, the interface shear stress degradation rate −6 MPa/cycle increasingwith fatigue peak stress, 5.8 stress, × 10−6 i.e., MPa/cycle under σmax = 150under MPa,σmax and=2.2 10−5 increases increasing fatiguei.e., peak 5.8 × 10 150×MPa, −5 MPa/cycle MPa/cycle under σmax = 250under MPa. σFor woven composite at 1100 °C in air, the and 2.2 × 10 = 250 MPa.SiC/SiC For 2D woven SiC/SiC composite at interface 1100 ◦ C max2D −4 shear degradation rate increases with increasing fatiguewith peakincreasing stress, i.e., fatigue 4.8 × 10 peak MPa/cycle in air, stress the interface shear stress degradation rate increases stress, −2 MPa/cycle under σmax = 210 − 4 − 2 under σ max = 120 MPa, and 2.6 × 10 MPa. i.e., 4.8 × 10 MPa/cycle under σmax = 120 MPa, and 2.6 × 10 MPa/cycle under σmax = 210 MPa. The experimental experimentaland andtheoretical theoretical fatigue hysteresis dissipated energy versus interface shear The fatigue hysteresis dissipated energy versus interface shear stress ◦ stress curves of cross-ply C/SiC 2DSiC/SiC woven SiC/SiC composites °C in air are illustrated in curves of cross-ply C/SiC and 2D and woven composites at 800 Catin800 air are illustrated in Figure 19. Figure 19. The experimental fatigue hysteresis dissipated energy of cross-ply C/SiC composite lies in The experimental fatigue hysteresis dissipated energy of cross-ply C/SiC composite lies in the right and the part rightofand part hysteresis of the fatigue hysteresis dissipated energy versus shear stress curve, left theleft fatigue dissipated energy versus interface shear interface stress curve, corresponding corresponding interface 2 and 4, i.e., the interface partially debonds fiber slips slips to interface slipto Case 2 and slip CaseCase 4, i.e., the Case interface partially debonds and fiber slips and partially partially slips relative to matrix, and the interface completely debonds and fiber slips completely relative to matrix, and the interface completely debonds and fiber slips completely relative to matrix; relative toformatrix; however, forcomposite, 2D woventhe SiC/SiC composite, the hysteresis experimental fatigueenergy hysteresis however, 2D woven SiC/SiC experimental fatigue dissipated just dissipated energy just lies in the right part of the fatigue hysteresis dissipated energy versus lies in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve, interface sheartostress curve, interfacepartially slip Case 2, i.e.,and thefiber interface partially corresponding interface slipcorresponding Case 2, i.e., thetointerface debonds slips partially ◦ debondstoand fiberAtslips partially relative matrix. temperature and 800 °C in air,rate the relative matrix. room temperature andto800 C in At air, room the interface shear stress degradation − 6 interface shear stress degradation rate of 2D woven SiC/SiC composite under σ max = 150 MPa is lower, of 2D woven SiC/SiC composite under σmax = 150 MPa is lower, i.e., 5.8 × 10 MPa/cycle at room −4room i.e., 5.8 × 10−6and MPa/cycle temperature, and 10−4that MPa/cycle at 800 °C incomposite air, than that of temperature, 7.0 × 10at MPa/cycle at 800 ◦ C in 7.0 air, ×than of cross-ply C/SiC under −6 MPa/cycle at − −6 MPa/cycle 4 MPa/cycle ◦C max = 105at MPa, i.e., 6.3 × 10 room temperature, and C/SiC composite under σ σcross-ply = 105 MPa, i.e., 6.3 × 10 room temperature, and 7.7 × 10 at 800 max 7.7air. × 10−4 MPa/cycle at 800 °C in air. in

Figure 18. 18. (a) (a)The Theexperimental experimentalfatigue fatiguehysteresis hysteresis dissipated energy versus applied cycles; (b) Figure dissipated energy versus applied cycles; andand (b) the the experimental and theoretical hysteresis dissipated energyinterface versus interface shear stress experimental and theoretical fatiguefatigue hysteresis dissipated energy versus shear stress curves of curves of 2D wovencomposites SiC/SiC composites at room andtemperatures. elevated temperatures. 2D woven SiC/SiC at room and elevated

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Figure 19. The experimental experimental and theoretical theoretical fatigue fatigue hysteresis hysteresis dissipated dissipated energy energy of of cross-ply cross-plyC/SiC C/SiC ◦ Cin and 2D woven SiC/SiC SiC/SiCcomposites compositesat at800 800°C inair. air.

5. 5. Conclusions Conclusions The comparisons of of damage damage evolution evolution between between 2D 2D C/SiC C/SiC and and SiC/SiC SiC/SiC composites The comparisons composites under under tension–tension cyclic fatigue loading at room and elevated temperatures have been investigated. tension–tension cyclic fatigue loading at room and elevated temperatures have been investigated. The fatigue hysteresis hysteresis loops loops models models considering considering multiple CMCs have have The fatigue multiple matrix matrix cracking cracking modes modes in in 2D 2D CMCs been interface been developed developed based based on on the the damage damage mechanism mechanism of of fiber fiber slipping slipping relative relative to to matrix matrix in in the the interface debonded region. The relationships between fatigue hysteresis loops, fatigue hysteresis dissipated debonded region. The relationships between fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue peak peak stress, stress, matrix matrix multiple multiple cracking cracking modes, modes, and have been energy, fatigue and interface interface shear shear stress stress have been established. cracking mode mode established. The The effects effects of of fiber fiber volume volume fraction, fraction, fatigue fatigue peak peak stress stress and and matrix matrix cracking proportion fatigue hysteresis hysteresis dissipated dissipated energy and interface interface debonding debonding and proportion on on fatigue energy and and slipping slipping have have been been analyzed. Theexperimental experimental fatigue hysteresis dissipated of 2D and SiC/SiC analyzed. The fatigue hysteresis dissipated energy energy of 2D C/SiC andC/SiC SiC/SiC composites ◦ C, 800 ◦ C, and composites at room 550 temperature, 550 1100 °C, ◦800 and ◦1100 °C in air, 1200 °C in vacuum at room temperature, C in°C, air, 1200 C in vacuum corresponding to different corresponding to different fatigue peak stresses and cycle numbers have been analyzed. The fatigue peak stresses and cycle numbers have been analyzed. The interface shear stress degradation interface shearobtained stress degradation rate has been obtained fatigue throughhysteresis comparing experimental fatigue rate has been through comparing experimental dissipated energy with hysteresis dissipated energy with theoretical values. The damage evolution in C/SiC and SiC/SiC theoretical values. The damage evolution in C/SiC and SiC/SiC composites has been compared using composites has beenofcompared using damage parameters of interface fatigue hysteresis energy damage parameters fatigue hysteresis dissipated energy and shear stressdissipated degradation rate. and interface shear stress degradation rate. 1 The interface shear stress degradation rate increases at elevated temperature in air compared with 1. The interface shear stress degradation rate increases at elevated temperature in air compared that at room temperature due to interface and fiber oxidation, decreases with increasing loading with that at room temperature due to interface and fiber oxidation, decreases with increasing frequency at room temperature due to the increasing interface wear rate between fibers and the loading frequency at room temperature due to the increasing interface wear rate between matrix, and increases with increasing fatigue peak stress at room and elevated temperatures due fibers and the matrix, and increases with increasing fatigue peak stress at room and elevated to the increasing interface debonding and slipping extent between fibers and the matrix. temperatures due to the increasing interface debonding and slipping extent between fibers and 2 At 800 ◦ C in air, the experimental fatigue hysteresis dissipated energy of cross-ply C/SiC the matrix. composite under σ = 105 MPa lies in the right and left part of the fatigue hysteresis dissipated 2. At 800 °C in air, max the experimental fatigue hysteresis dissipated energy of cross-ply C/SiC energy versus interface shear stress curve, corresponding to interface slip Case 2 and Case 4, composite under σmax = 105 MPa lies in the right and left part of the fatigue hysteresis which indicates that the interface debonding changes from partially debonding to completely dissipated energy versus interface shear stress curve, corresponding to interface slip Case 2 debonding with increasing cycle number; however, for 2D woven SiC/SiC composite under and Case 4, which indicates that the interface debonding changes from partially debonding to σmax = 150 MPa, the experimental fatigue hysteresis dissipated energy just lies in the right part completely debonding with increasing cycle number; however, for 2D woven SiC/SiC of the fatigue hysteresis dissipated energy versus interface shear stress curve, corresponding composite under σmax = 150 MPa, the experimental fatigue hysteresis dissipated energy just lies to interface slip Case 2, which indicates that the interface debonding remains to be partially in the right part of the fatigue hysteresis dissipated energy versus interface shear stress curve, debonding with increasing cycle number. corresponding to interface slip◦ Case 2, which indicates that the interface debonding remains to 3 At room temperature 800 C in air, cycle the interface be partially debondingand with increasing number.shear stress degradation rate of 2D woven SiC/SiC composite under σ = 150 MPa is lower than thatstress of cross-ply C/SiCrate composite under max 3. At room temperature and 800 °C in air, the interface shear degradation of 2D woven σ = 105 MPa. max SiC/SiC composite under σmax = 150 MPa is lower than that of cross-ply C/SiC composite under σmax = 105 MPa.

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In the present analysis, the effect of mechanical load waveform, i.e., sinusoidal waveform and triangular waveform, on fatigue damage in C/SiC and SiC/SiC composites has not been considered [24], which would be further investigated in the future. Acknowledgments: The author thanks the Science and Technology Department of Jiangsu Province for the funding that made this research study possible. This study has received the support from the Science and Technology Department of Jiangsu Province through 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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