Damage development and lifetime prediction of cross-ply ceramic-matrix composites subjected to cyclic loading at room and elevated temperatures

Abstract

In this paper, the damage development and lifetime prediction of fibre-reinforced ceramic-matrix composites subjected to cyclic loading at elevated temperatures in oxidising atmosphere have been investigated. Considering the damage mechanisms of matrix cracking, interface debonding, interface wear and interface oxidation, the damage evolution of fatigue hysteresis dissipated energy, fatigue hysteresis modulus, fatigue peak strain, interface shear stress and broken fibres fraction have been analysed. The relationships between damage parameters and internal damage of matrix cracking, interface debonding and slipping, and fibres fracture have been established. The experimental fatigue hysteresis, interface slip lengths, peak strain, and the fatigue life curves of cross-ply CMCs under cyclic loading at elevated temperature have been predicted. The different fatigue behaviour in unidirectional and cross-ply CMCs at room and elevated temperatures subjected to low-cycle and high-cycle fatigue has been discussed.

Keywords

Ceramic-matrix composites airworthiness damage evolution oxidation matrix multicracking interface debonding

Introduction

Ceramic-matrix composites (CMCs) possess high strength-to-weight ratio at elevated temperatures, and are being designed and developed for hot section components in commercial aero engine [1]. As new materials, the CMCs need to meet the airworthiness certification requirements, and it is necessary to analyse the degradation, damage, and failure mechanisms subjected to cyclic loading at different temperatures and environments.

Many researchers performed the experimental and theoretical investigations on cyclic fatigue behaviour of fibre-reinforced CMCs. McNulty and Zok [2] investigated the low-cycle fatigue behaviour of unidirectional, cross-ply and 2D woven CMCs at room temperature. The damage evolution subjected to fatigue loading was correlated with matrix cracks and stress/strain hysteresis loops. The degradation of the interface shear stress and fibres strength was the major reason for the low-cycle fatigue fracture of CMCs. Yasmin and Bowen [3] performed the experimental investigations on cross-ply SiC/CAS–II composite under monotonic, static, cyclic and a combination of static and cyclic loadings at room temperature and 800°C in air. When the maximum cycle number is defined to be 1,000,000 applied cycles, the fatigue limit of the composite at 800°C reduced to half of its room temperature value. Kim and Liaw [4] investigated the high-cycle fatigue behaviour of unidirectional and cross-ply SiC/CAS composites using the infra-red thermography. The temperature changes during high-cycle fatigue testing were monitored and correlated with the damage evolution inside of CMCs, and can be divided into three regions, i.e. the initial constant temperature region, increasing temperature region, and final temperature rising failure region. Lara-Curzio [5] developed a micromechanical model to predict the reliability and lifetime of unidirectional CMCs subjected to stresses beyond the first matrix cracking stress at elevated temperature. It was shown that the oxidation of the fibre coating leads to changes in the stress distribution of fibres and exposure of the fibres to the environment, and the oxidation of the fibres leads to fibre strength degradation and ultimately composite fracture. Ruggles-Wrenn et al. [6] investigated the tension–tension fatigue behaviour of 2D woven SiC/SiC composite at 1200°C in air and in steam environment. The fatigue limit and fatigue lifetime decreases with increasing loading frequency from 0.1 to 10 Hz in both test environments, and the presence of steam significantly degraded the fatigue performance. Ruggles-Wrenn and Lanser [7] investigated the tension–compression fatigue behaviour of 2D woven Nextel™ 720/alumina composite at 1200°C in air and in steam. The fatigue limit stress was achieved at 40 and 35% tensile strength in air and steam environment, respectively, when the maximum cycle number is defined to be 100,000 applied cycles. The presence of steam noticeably degrades the tension–compression fatigue performance of the oxide/oxide composite. Ruggles-Wrenn and Lee [8] investigated the tension–tension fatigue behaviour of 2D woven SiC/SiC composite with an inhibited matrix at 1300°C in air and in steam condition. The fatigue limit stress is higher in steam environment than that in air, which indicates that the presence of steam appears to have a moderately beneficial effect on tension–tension fatigue at 1300°C. During cyclic loading, the damage evolution inside the composites should be monitored to predict the lifetime. Maillet et al. [9] investigated the damage evolution of 2D woven SiC/[Si–B–C] composite at temperatures of 450 and 500°C using the acoustic emission (AE) based approach during static fatigue loading. However, the AE-based approach used to damage monitoring is limited at elevated temperature. Longbiao [10,11] developed a hysteresis dissipated energy-based damage parameter for damage evolution and life prediction of fibre-reinforced CMCs under cyclic fatigue loading at room and elevated temperatures.

The objective of this paper is to investigate the damage development and lifetime prediction in fibre-reinforced CMCs under cyclic fatigue loading at room and elevated temperatures. The damage parameters based on the hysteresis loops models considering the combination effects of interface wear and interface oxidation, i.e. the fatigue hysteresis dissipated energy, fatigue hysteresis modulus and fatigue peak strain, have been used to monitor the damage evolution inside of CMCs. The experimental fatigue hysteresis, the interface slip lengths, peak strain and the fatigue life of cross-ply SiC/MAS composite under cyclic fatigue loading at 566 and 1093°C in air have been predicted. The comparisons between unidirectional and cross-ply CMCs subjected to low-cycle, high-cycle fatigue loading at room and elevated temperatures have been analysed.

Theoretical analysis

The unit cell contained a single fibre surrounded by a hollow cylinder of matrix is extracted from the ceramic composite system, as shown in Figure 1. The fibre radius is r_f, and the matrix radius is R (R = r_f/V_f^1/2). At elevated temperatures, the oxidative gas can enter into the internal of the composite and oxidise the interphase and fibres, as shown in Figure 2. Under cyclic loading, the interface shear stress decreases due to interface wear and interface oxidation at elevated temperature. The interface debonded region can be divided into two regions, including: (1) the interface oxidation region, i.e. x∈[0, ξ], τ_i(x) = τ_f; and (2) the interface wear region, i.e. x∈[ξ, l_d], τ_i(x) = τ_i(N) [12]. (1) where τ₀ denotes the initial interface shear stress; τ_s denotes the steady-state interface shear stress; b₀ is a coefficient; and j is an exponent which determines the rate at which the interface shear stress drops with the number of cycle N.

Based on the interface debonding and interface slipping between the fibre and the matrix inside of the composite, the fatigue hysteresis loops of CMCs under cyclic loading can be divided into four different cases, including: (i)

Case 1: the interface oxidation region and the interface wear region is less than the matrix crack spacing, and the interface counter-slip upon unloading and the interface new-slip upon reloading is equal to the interface debonded length.

(ii)

Case 2: the interface oxidation region and the interface wear region is less than the matrix crack spacing, and the interface counter-slip upon unloading and the interface new-slip upon reloading is less than the interface debonded length.

(iii)

Case 3: the interface oxidation region and the interface wear region is equal to the matrix crack spacing, and the interface counter-slip upon unloading and the interface new-slip upon reloading is less than the matrix crack spacing.

(iv)

Case 4: the interface oxidation region and the interface wear region is equal to the matrix crack spacing, and the interface counter-slip upon unloading and the interface new-slip upon reloading is equal to the matrix crack spacing.

When the interface oxidation region and the interface wear region is less than the matrix crack spacing, the unloading and reloading stress–strain relationship is determined by Equation (2) [13] (2a) (2b) where V_f denotes the fibre volume content; E_f denotes the fibre elastic modulus; y and z denote the interface counter-slip length and interface new-slip length, respectively; l_d and l_c denote the interface debonded length and matrix crack spacing, respectively; ρ denotes the shear-lag model parameter; α_f and α_c denote the fibre and composite thermal expansion coefficient, respectively; and ΔT denotes the temperature difference between the fabricated temperature T₀ and testing temperature T₁ (ΔT = T₁−T₀).

When the interface oxidation region and the interface wear region is equal to the matrix crack spacing, the unloading and reloading stress–strain relationship is determined by Equation (3) [13] (3a) (3b) The fatigue hysteresis dissipated energy is defined by Equation (4) (4) where ε_{c_unload} and ε_{c_reload} denote the unloading and reloading strain, respectively.

The global load sharing (GLS) assumption is used to determine the load carried by intact and fracture fibres. (5) where l_f denotes the slip length over which the fibre stress would decay to zero if not interrupted by the far-field equilibrium stresses; and denotes the average stress carried by broken fibres. (6) (7) where P_fa, P_fb, P_fc and P_fd denote the fibre failure probability of oxidised fibres in the oxidation region, unoxidised fibres in the oxidation region, fibres in the interface debonded region and interface bonded region, respectively; ζ denotes the oxidation fibres fraction in the oxidised region; and χ denotes the fraction of oxidation in the multiple matrix cracks. (8a) (8b) (8c) (8d) where T denotes the load carried by intact fibres; σ_fo denotes the fibre stress in the interface bonded region; l_f denotes the slip length over which the fibre stress would decay to zero if not interrupted by the far-field equilibrium stresses. The time-dependent fibre strength will be controlled by surface defects resulting from oxidation and is given by Equation (9) [5] (9) where K_IC denotes the critical stress intensity factor; Y is a geometric parameter; and k is the parabolic rate constant.

With increasing cycle number, the interface shear stress and fibres strength decrease due to the interface wear and interface oxidation. The fibres failure probability in the interface oxidation region, interface debonded region and interface bonded region can be obtained by combining the interface wear model, interface oxidation model and fibre strength degradation model with Equations (5)–(8). The evolution of fibres failure probability versus cycle number curves can be obtained. When the fibre broken fraction approaches to the critical value, the composite fatigue fractures. The fatigue limit stress is calculated when the fracture applied cycles approach to the maximum cycle number.

Experimental comparisons

Steiner [14] investigated the cyclic fatigue behaviour of cross-ply SiC/MAS composite at elevated temperatures in air. The material properties of cross-ply SiC/MAS composite are listed in Table 1. The tension–tension fatigue tests at 566 and 1093°C in air were performed under the load control at a triangular waveform with the loading frequency of 1 and 10 Hz and the fatigue load ratio, i.e. minimum to maximum stress, of 0.1, and the maximum number of applied cycles was defined to be 1,000,000 applied cycles. At 566°C in air, the tensile strength was about 292 MPa, as shown in Figure 3, and the fatigue peak stresses were 137, 120 and 103 MPa, as shown in Figure 4(a). At 1093°C in air, the tensile strength were about 209 MPa, as shown in Figure 3, and the fatigue peak stresses were 137, 120, 103 and 96 MPa, as shown in Figure 4(b).

Table 1

The material properties of SiC/MAS and SiC/CAS composites.

	SiC/MAS [14]	SiC/CAS [2]	SiC/MAS [2]	SiC/CAS [4]
E_f/GPa	200	210	210	190
E_m/GPa	138	95.5	138	90
V_f/%	40	38	40	40
r_f/μm	7.5	7.5	7.5	7.5
α_f/10⁻⁶× °C⁻¹	4	3.1	3.1	3.1
α_m/10⁻⁶× °C⁻¹	2.4	4.5	2.4	4.5
ΔT/°C	−1000	−1000	−1000	−1000
m	2	2	2	2

The fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue hysteresis modulus, and fatigue peak strain versus applied cycles, and the fatigue life of cross-ply SiC/MAS composite under different fatigue peak stresses at elevated temperatures have been predicted.

Cross-ply SiC/MAS at 566°C in air with the loading frequency of 1 Hz

When the fatigue peak stress is σ_max = 137 MPa, the experimental fatigue hysteresis dissipated energy decreases from 5.4 kJ m⁻³ at the 4th applied cycle to 4.4 kJ m⁻³ at the 230th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 5.5 kJ m⁻³ at the 1st applied cycle to 4.1 kJ m⁻³ at the 1000th applied cycle, corresponding to the interface slip Case 4, i.e. the interface oxidation and wear region is equal to the matrix crack spacing, and the interface slip length is also equal to the matrix crack spacing, as shown in Figure 5(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.62 at the 476th applied cycle, as shown in Figure 5(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 5(c), in which the experimental fatigue peak strain increases from 0.34% at the first applied cycle to 0.409% at the 442th applied cycle.

When the fatigue peak stress is σ_max = 120 MPa, the experimental fatigue hysteresis dissipated energy decreases from 4.6 kJ m⁻³ at the 3rd applied cycle to 3.2 kJ m⁻³ at the 105th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 4.8 kJ m⁻³ at the 1st applied cycle to 2.7 kJ m⁻³ at the 1000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 5(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.699 at the 9532th applied cycle, as shown in Figure 5(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 5(c), in which the experimental fatigue peak strain increases from 0.26% at the first applied cycle to 0.303% at the 7350th applied cycle.

When the fatigue peak stress is σ_max = 103 MPa, the experimental fatigue hysteresis dissipated energy decreases from 2.8 kJ m⁻³ at the 4th applied cycle to 2.4 kJ m⁻³ at the 920th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 3.0 kJ m⁻³ at the 1st applied cycle to 2.3 kJ m⁻³ at the 1000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 5(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.889 at the 546,253th applied cycle, as shown in Figure 5(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 5(c), in which the experimental fatigue peak strain increases from 0.239% at the first applied cycle to 0.253% at the 242,935th applied cycle.

The fatigue life S–N curves of cross-ply SiC/MAS composite at 566°C in air with the loading frequency of 1 Hz are illustrated in Figure 6(a). The fatigue limit stress approaches to 15% tensile strength. The broken fibres fraction versus applied cycles curves at the fatigue peak stresses of 0.4 and 0.35 tensile strength are illustrated in Figure 6(b). When σ_max = 0.4σ_UTS, the broken fibres fraction increases from 3.6% at the first applied cycle to 47% at the 71,484th applied cycle; and when σ_max = 0.35σ_UTS, the broken fibres fraction increases from 2.3% at the first applied cycle to 49.2% at the 114,537th applied cycle.

Cross-ply SiC/MAS at 566°C in air with the loading frequency of 10 Hz

When the fatigue peak stress is σ_max = 137 MPa, the experimental fatigue hysteresis dissipated energy decreases from 6.5 kJ m⁻³ at the 2nd applied cycle to 3.6 kJ m⁻³ at the 7730th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 6.9 kJ m⁻³ at the 1st applied cycle to 2.6 kJ m⁻³ at the 10,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 7(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.67 at the 9902th applied cycle, as shown in Figure 7(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 7(c), in which the experimental fatigue peak strain increases from 0.293% at the first applied cycle to 0.329% at the 9857th applied cycle.

When the fatigue peak stress is σ_max = 120 MPa, the experimental fatigue hysteresis dissipated energy decreases from 2.5 kJ m⁻³ at the 6th applied cycle to 1.3 kJ m⁻³ at the 6149th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 2.59 kJ m⁻³ at the 1st applied cycle to 1.39 kJ m⁻³ at the 10,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 7(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.75 at the 106,813th applied cycle, as shown in Figure 7(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 7(c), in which the experimental fatigue peak strain increases from 0.227% at the first applied cycle to 0.269% at the 102,538th applied cycle.

When the fatigue peak stress is σ_max = 103 MPa, the experimental fatigue hysteresis dissipated energy decreases from 1.3 kJ m⁻³ at the 2nd applied cycle to 0.6 kJ m⁻³ at the 2073th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 1.5 kJ m⁻³ at the 1st applied cycle to 0.8 kJ m⁻³ at the 10,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 7(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.89 at the 508,814th applied cycle, as shown in Figure 7(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 7(c), in which the experimental fatigue peak strain increases from 0.205% at the first applied cycle to 0.221% at the 513,725th applied cycle.

The fatigue life S–N curves of cross-ply SiC/MAS composite at 566°C in air with the loading frequency of 10 Hz are illustrated in Figure 8(a). The fatigue limit stress approaches to 30% tensile strength. The broken fibres fraction versus applied cycles curves at the fatigue peak stresses of 0.47, 0.41 and 0.35 tensile strength are illustrated in Figure 8(b). When σ_max = 0.47σ_UTS, the broken fibres fraction increases from 5.9% at the first applied cycle to 49.9% at the 21,465th applied cycle; when σ_max = 0.41σ_UTS, the broken fibres fraction increases from 3.9% at the first applied cycle to 50% at the 33,936th applied cycle; and when σ_max = 0.35σ_UTS, the broken fibres fraction increases from 2.4% at the first applied cycle to 50% at the 244,079th applied cycle.

Cross-ply SiC/MAS at 1093°C in air with the loading frequency of 1 Hz

When the fatigue peak stress is σ_max = 137 MPa, the experimental fatigue hysteresis dissipated energy decreases from 43.8 kJ m⁻³ at the 4th applied cycle to 32.8 kJ m⁻³ at the 25th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 50 kJ m⁻³ at the 1st applied cycle to 27.1 kJ m⁻³ at the 100th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 9(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.515 at the 24th applied cycle, as shown in Figure 9(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 9(c), in which the experimental fatigue peak strain increases from 0.575% at the first applied cycle to 0.631% at the 25th applied cycle.

When the fatigue peak stress is σ_max = 120 MPa, the experimental fatigue hysteresis dissipated energy decreases from 34.9 kJ m⁻³ at the 3rd applied cycle to 22.5 kJ m⁻³ at the 75th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 38.5 kJ m⁻³ at the 1st applied cycle to 21.2 kJ m⁻³ at the 100th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 9(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.55 at the 89th applied cycle, as shown in Figure 9(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 9(c), in which the experimental fatigue peak strain increases from 0.557% at the first applied cycle to 0.623% at the 87th applied cycle.

When the fatigue peak stress is σ_max = 103 MPa, the experimental fatigue hysteresis dissipated energy decreases from 25.5 kJ m⁻³ at the 4th applied cycle to 6.5 kJ m⁻³ at the 10,608th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 28.8 kJ m⁻³ at the 1st applied cycle to 5.57 kJ m⁻³ at the 11,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 9(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.64 at the 10,416th applied cycle, as shown in Figure 9(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 9(c), in which the experimental fatigue peak strain increases from 0.443% at the first applied cycle to 0.559% at the 20,329th applied cycle.

When the fatigue peak stress is σ_max = 96 MPa, the experimental fatigue hysteresis dissipated energy decreases from 16 kJ m⁻³ at the 3rd applied cycle to 4.4 kJ m⁻³ at the 33,299th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 17.4 kJ m⁻³ at the 1st applied cycle to 3.3 kJ m⁻³ at the 33,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 9(a).

The fatigue life S–N curves of cross-ply SiC/MAS composite at 1093°C in air with the loading frequency of 1 Hz are illustrated in Figure 10(a). The fatigue limit stress approaches to 39% tensile strength. The broken fibres fraction versus applied cycles curves at the fatigue peak stresses of 0.65, 0.57, 0.49, 0.46, and 0.41 tensile strength are illustrated in Figure 10(b). When σ_max = 0.65σ_UTS, the broken fibres fraction increases from 18.3% at the first applied cycle to 49.8% at the 44th applied cycle; when σ_max = 0.57σ_UTS, the broken fibres fraction increases from 12.7% at the first applied cycle to 49.9% at the 295th applied cycle; when σ_max = 0.49σ_UTS, the broken fibres fraction increases from 8.3% at the first applied cycle to 50% at the 14,887th applied cycle; when σ_max = 0.46σ_UTS, the broken fibres fraction increases from 6.9% at the first applied cycle to 50% at the 59,868th applied cycle; and when σ_max = 0.41σ_UTS, the broken fibres fraction increases from 4.9% at the first applied cycle to 50% at the 550,861th applied cycle.

Cross-ply SiC/MAS at 1093°C in air with the loading frequency of 10 Hz

When the fatigue peak stress is σ_max = 137 MPa, the experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.56 at the 349th applied cycle, as shown in Figure 11(b). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 11(c), in which the experimental fatigue peak strain increases from 0.523% at the first applied cycle to 0.577% at the 360th applied cycle.

When the fatigue peak stress is σ_max = 103 MPa, the experimental fatigue hysteresis dissipated energy decreases from 13 kJ m⁻³ at the 6th applied cycle to 4.6 kJ m⁻³ at the 12,783th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 14.6 kJ m⁻³ at the 1st applied cycle to 5 kJ m⁻³ at the 100,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 11(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.74 at the 98,898th applied cycle, as shown in Figure 11(b).

When the fatigue peak stress is σ_max = 96 MPa, the experimental fatigue hysteresis dissipated energy decreases from 8.1 kJ m⁻³ at the 6th applied cycle to 3.6 kJ m⁻³ at the 37,439th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 9 kJ m⁻³ at the 1st applied cycle to 3.6 kJ m⁻³ at the 38,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 11(a). The experimental and theoretical normalised fatigue hysteresis modulus decreases rapidly at the initial applied cycles, i.e. from 1.0 upon first loading to 0.87 at the 49,974th applied cycle, as shown in Figure 11(b).

When the fatigue peak stress is σ_max = 86 MPa, the experimental fatigue hysteresis dissipated energy decreases from 7.2 kJ m⁻³ at the 6th applied cycle to 3.3 kJ m⁻³ at the 10,311th applied cycle, and the theoretical fatigue hysteresis dissipated energy decreases from 8.2 kJ m⁻³ at the 1st applied cycle to 2.7 kJ m⁻³ at the 38,000th applied cycle, corresponding to the interface slip Case 4, as shown in Figure 11(a). The experimental and theoretical fatigue peak strain versus applied cycle curves are illustrated in Figure 11(c), in which the experimental fatigue peak strain increases from 0.4% at the first applied cycle to 0.456% at the 105,923th applied cycle.

The fatigue life S–N curves of cross-ply SiC/MAS composite at 1093°C in air with the loading frequency of 10 Hz are illustrated in Figure 12(a). The fatigue limit stress approaches to 42% tensile strength. The broken fibres fraction versus applied cycles curves at the fatigue peak stresses of 0.65, 0.49, and 0.46 tensile strength are illustrated in Figure 12(b). When σ_max = 0.65σ_UTS, the broken fibres fraction increases from 17.8% at the first applied cycle to 49.9% at the 384th applied cycle; when σ_max = 0.49σ_UTS, the broken fibres fraction increases from 8% at the first applied cycle to 50% at the 75,600th applied cycle; and when σ_max = 0.46σ_UTS, the broken fibres fraction increases from 6.7% at the first applied cycle to 50% at the 262,479th applied cycle.

Discussion

McNulty and Zok [2] investigated the tensile and tension–tension fatigue behaviour of unidirectional and cross-ply SiC/CAS and SiC/MAS composites at room temperature. The material properties of cross-ply SiC/CAS and SiC/MAS composite are listed in Table 1. The loading frequency was 0.5 Hz and the stress ratio was 0.05. For SiC/CAS composite at room temperature, the tensile strength of the unidirectional composite was approximately 454 MPa; and the tensile strength of the cross-ply composite was about 254 MPa, as shown in Figure 13(a). The fatigue hysteresis loops of the unidirectional SiC/CAS composite corresponding to the first, 5th, 10th, 120th and 40,000th applied cycles are illustrated in Figure 13(b). The fatigue hysteresis dissipated energy first increases and then decreases with applied cycles, due to the degradation of interface shear stress, and the fatigue hysteresis loops correspond to the interface slip Case 2 and 3. The fatigue life S–N curves of unidirectional and cross-ply SiC/CAS composite are illustrated in Figure 13(c,d). For the unidirectional SiC/CAS composite, the fatigue limit approaches to about 60% tensile strength; and for the cross-ply SiC/CAS composite, the fatigue limit approaches to about 55% tensile strength when the maximum cycle number is defined to be 1,000,000 applied cycles.

For SiC/MAS composite at room temperature, the tensile strength of the unidirectional composite was approximately 413 MPa; and the tensile strength of the cross-ply composite was about 298 MPa, as shown in Figure 14(a). The fatigue hysteresis loops of the unidirectional SiC/MAS composite corresponding to the first, 11th, 110th, and 1000th applied cycles are illustrated in Figure 14(b). The fatigue hysteresis dissipated energy decreases with applied cycles, and the fatigue hysteresis loops correspond to the interface slip Case 4, i.e. the interface completely debonding and the fibre completely sliding relative to the matrix in the interface debonded region. The fatigue life S–N curves of unidirectional and cross-ply SiC/MAS composites at room temperature are illustrated in Figure 14(c,d). For the unidirectional SiC/MAS composite, the fatigue limit approaches to approximately 70% tensile strength; and for the cross-ply SiC/MAS composite, the fatigue limit approaches to about 55% tensile strength when the maximum cycle number is defined to be 1,000,000 applied cycles.

Kim and Liaw [4] investigated the tensile and fatigue behaviour of unidirectional and cross-ply SiC/CAS composites at room temperature. The material properties of cross-ply SiC/CAS composite are listed in Table 1. The loading frequency was 20 Hz and the stress ratio was 0.1. For SiC/CAS composite at room temperature, the tensile strength of the unidirectional composite was approximately 251 MPa; and the tensile strength of the cross-ply composite was about 184 MPa, as shown in Figure 15(a). The fatigue life S–N curves of unidirectional and cross-ply SiC/CAS composites at room temperature are illustrated in Figure 15(b,c). For the unidirectional SiC/CAS composite, the fatigue limit approaches to approximately 65% tensile strength; and for the cross-ply SiC/MAS composite, the fatigue limit approaches to about 60% tensile strength when the maximum cycle number is defined to be 1,000,000 applied cycles.

However, at elevated temperatures in air, the fatigue limit of cross-ply CMCs is significantly reduced. At 566°C in air, the fatigue limit stress approaches to about 15% tensile strength under the loading frequency of 1.0 Hz, and 30% tensile strength under the loading frequency of 10 Hz. At 1093°C in air, the fatigue limit stress approaches to about 39% tensile strength under the loading frequency of 1.0 Hz, and 42% tensile strength under the loading frequency of 10 Hz.

Conclusions

In this paper, the damage evolution and lifetime prediction of cross-ply CMCs subjected to cyclic loading at room and elevated temperatures in air have been investigated. The experimental fatigue hysteresis dissipated energy, fatigue hysteresis modulus, fatigue peak strain, interface slip and fatigue lifetime of cross-ply SiC/CAS and SiC/MAS composite under cyclic loading at room temperature, and elevated temperature of 566 and 1093°C in air have been predicted. (i)

With increasing of fatigue peak stress, the interface debonding and slip lengths increase, leading to the increase of degradation rate of fatigue hysteresis dissipated energy and fatigue hysteresis modulus, and increasing rate of fatigue peak strain.

(ii)

With increasing of oxidation temperature, the interface debonding and slip lengths increases, leading to more damage inside of CMCs even under low peak stress.

(iii)

At room temperature, for the unidirectional SiC/CAS composite, the fatigue limit approaches to about 60% tensile strength; and for the cross-ply SiC/CAS composite, the fatigue limit approaches to about 55% tensile strength when the loading frequency was 0.5 Hz.

(iv)

At room temperature, for the unidirectional SiC/CAS composite, the fatigue limit approaches to approximately 65% tensile strength; and for the cross-ply SiC/MAS composite, the fatigue limit approaches to about 60% tensile strength when the loading frequency was 20 Hz.

(v)

At room temperature, for the unidirectional SiC/MAS composite, the fatigue limit approaches to approximately 70% tensile strength; and for the cross-ply SiC/MAS composite, the fatigue limit approaches to about 55% tensile strength.

(vi)

At 566°C in air, the fatigue limit stress was about 15 and 30% tensile strength at the loading frequency of 1 and 10 Hz; however, at 1093°C in air, the fatigue limit stress was about 39 and 42% tensile strength at the loading frequency of 1 and 10 Hz.

Footnotes

Acknowledgements

The author thanks the anonymous reviewers and the editors for their valuable comments on the previous manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

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