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- Sprache: Englisch
This book presents state-of-the-art investigation on the properties of ceramic-matrix composites subjected to tensile and fatigue loading at different testing conditions. It helps designer to better design components for civil aircrafts or aero engines.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Preface
Acknowledgments
1 Introduction
1.1 Tensile Behavior of CMCs at Elevated Temperature
1.2 Fatigue Behavior of CMCs at Elevated Temperature
1.3 Stress Rupture Behavior of CMCs at Elevated Temperature
1.4 Vibration Behavior of CMCs at Elevated Temperature
1.5 Conclusion
References
2 First Matrix Cracking of Ceramic-Matrix Composites at Elevated Temperature
2.1 Introduction
2.2 Temperature-Dependent Matrix Cracking Stress of C/SiC Composites
2.3 Temperature-Dependent Matrix Cracking Stress of SiC/SiC Composite
2.4 Time-Dependent Matrix Cracking Stress of C/SiC Composites
2.5 Time-Dependent Matrix Cracking Stress of Si/SiC Composites
2.6 Conclusion
References
3 Matrix Multiple Cracking Evolution of Fiber-Reinforced Ceramic-Matrix Composites at Elevated Temperature
3.1 Introduction
3.2 Temperature-Dependent Matrix Multiple Cracking Evolution of C/SiC Composites
3.3 Temperature-Dependent Matrix Multiple Cracking Evolution of SiC/SiC Composites
3.4 Time-Dependent Matrix Multiple Cracking Evolution of C/SiC Composites
3.5 Time-Dependent Matrix Multiple Cracking Evolution of SiC/SiC Composites
3.6 Conclusion
References
4 Time‐Dependent Tensile Behavior of Ceramic‐Matrix Composites
4.1 Introduction
4.2 Theoretical Analysis
4.3 Results and Discussion
4.4 Experimental Comparisons
4.5 Conclusion
References
5 Fatigue Behavior of Ceramic‐Matrix Composites at Elevated Temperature
5.1 Introduction
5.2 Theoretical Analysis
5.3 Experimental Comparisons
5.4 Conclusion
References
6 Stress Rupture of Ceramic-Matrix Composites at Elevated Temperature
6.1 Introduction
6.2 Stress Rupture of Ceramic-Matrix Composites Under Constant Stress at Intermediate Temperature
6.3 Stress Rupture of Ceramic-Matrix Composites Under Stochastic Loading Stress and Time at Intermediate Temperature
6.4 Stress Rupture of Ceramic-Matrix Composites Under Multiple Load Sequence at Intermediate Temperature
6.5 Conclusion
References
7 Vibration Damping of Ceramic-Matrix Composites at Elevated Temperature
7.1 Introduction
7.2 Temperature-Dependent Vibration Damping of CMCs
7.3 Time-Dependent Vibration Damping of CMCs
7.4 Conclusion
References
Index
End User License Agreement
List of Tables
Chapter 4
Table 4.1 Material properties of SiC/SiC minicomposites.
Table 4.2 Material properties of C/SiC composites.
Chapter 5
Table 5.1 Interface debonding and slip state in CMCs.
Table 5.2 Cyclic‐dependent damage evolution of 2.5D woven self‐healing Hi‐Nic...
Table 5.3 Cyclic‐dependent damage evolution of 2.5D woven self‐healing Hi‐Nic...
Table 5.4 Cyclic‐dependent damage evolution of 2D woven self‐healing Hi‐Nical...
Chapter 6
Table 6.1 Material properties of SiC/SiC composite.
Table 6.2 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.3 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.4 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.5 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.6 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.7 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.8 Evolution of the time-dependent stress rupture of SiC/SiC composite...
Table 6.9 The strain, interface debonding and oxidation ratio, and broken fib...
Table 6.10 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.11 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.12 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.13 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.14 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.15 The strain, interface debonding and oxidation ratio, and broken fi...
Table 6.16 Experimental and theoretical strain, interface debonding and oxida...
Table 6.17 Experimental and theoretical strain, interface debonding and oxida...
Table 6.18 The experimental and theoretical strain, interface debonding and o...
Table 6.19 Effect of fiber volume on stress rupture of SiC/SiC composite unde...
Table 6.20 Effect of matrix crack spacing on stress rupture of SiC/SiC compos...
Table 6.21 Effect of interface shear stress in slip region on stress rupture ...
Table 6.22 Effect of interface shear stress in oxidation region on stress rup...
Table 6.23 Effect of temperature on stress rupture behavior of SiC/SiC compos...
Chapter 7
Table 7.1 Effect of fiber volume on composite damping, interface debonding, a...
Table 7.2 Effect of matrix crack spacing on composite vibration damping, inte...
Table 7.3 Effect of interface debonding energy on composite damping, interfac...
Table 7.4 Effect of steady-state interface shear stress on composite damping,...
Table 7.5 Effect of interface frictional coefficient on composite damping, in...
Table 7.6 Effect of fiber volume on time-dependent composite vibration dampin...
Table 7.7 Effect of vibration stress on time-dependent composite vibration da...
Table 7.8 Effect of matrix crack spacing on time-dependent composite vibratio...
Table 7.9 Effect of interface shear stress on time-dependent composite vibrat...
Table 7.10 Effect of temperature on time-dependent composite vibration dampin...
Table 7.11 Experimental and predicted time-dependent composite vibration damp...
Table 7.12 Experimental and predicted time-dependent composite vibration damp...
Table 7.13 Experimental and predicted time-dependent composite vibration damp...
List of Illustrations
Chapter 2
Figure 2.1 Effect of fiber volume (i.e.
V
f
= 30% and 35%) on (a) the matrix ...
Figure 2.2 Effect of interface shear stress (i.e.
τ
0
= 30 and 40 MPa) o...
Figure 2.3 Effect of interface frictional coefficient (i.e.
μ
= 0.03 an...
Figure 2.4 Effect of interface debonding energy (i.e. Γ
d
...
Figure 2.5 Effect of interface debonding energy (i.e. Γ
m
...
Figure 2.6 Tensile stress–strain curves of 2D C/SiC composite at (a)
T
= 973...
Figure 2.7 (a) Experimental and theoretical matrix cracking stress versus en...
Figure 2.8 Effect of fiber volume on (a) the matrix cracking stress versus t...
Figure 2.9 Effect of interface shear stress on (a) the matrix cracking stres...
Figure 2.10 Effect of interface frictional coefficient on (a) the matrix cra...
Figure 2.11 Effect of the interface debonding energy on (a) the matrix crack...
Figure 2.12 Effect of matrix fracture energy on (a) the matrix cracking stre...
Figure 2.13 Experimental tensile stress–strain curves of Nicalon™ SiC/PyC/Si...
Figure 2.14 Experimental tensile stress–strain curves of Nicalon™ SiC/BN/SiC...
Figure 2.15 Experimental and predicted matrix cracking stress versus the tem...
Figure 2.16 (a) The matrix cracking stress versus temperature curves when
V
f
Figure 2.17 (a) The matrix cracking stress versus temperature curves when
τ
...
Figure 2.18 (a) The matrix cracking stress versus temperature curves when
τ
...
Figure 2.19 (a) The matrix cracking stress versus temperature curves when
μ
...
Figure 2.20 (a) The matrix cracking stress versus temperature curves when...
Figure 2.21 (a) The matrix cracking stress versus temperature curves when...
Figure 2.22 (a) Experimental and predicted matrix cracking stress versus tem...
Figure 2.23 (a) The matrix cracking stress versus temperature curves when...
Figure 2.24 (a) The matrix cracking stress versus temperature curves when...
Figure 2.25 (a) The matrix cracking stress versus temperature curves when...
Figure 2.26 (a) The matrix cracking stress versus temperature curves when...
Figure 2.27 (a) The matrix cracking stress versus temperature curves when...
Figure 2.28 Experimental and predicted matrix cracking stress versus tempera...
Chapter 3
Figure 3.1 (a) The matrix cracking density versus applied stress curves when...
Figure 3.2 (a) The matrix cracking density versus applied stress curves when...
Figure 3.3 (a) The matrix cracking density versus applied stress curves when...
Figure 3.4 (a) The experimental and theoretical matrix cracking density vers...
Figure 3.5 (a) The matrix cracking density versus applied stress curves when...
Figure 3.6 (a) The matrix cracking density versus applied stress curves when...
Figure 3.7 (a) The matrix cracking density versus applied stress curves when...
Figure 3.8 (a) The matrix cracking density versus applied stress curves when...
Figure 3.9 (a) The matrix cracking density versus applied stress curves when...
Figure 3.10 (a) The experimental and theoretical matrix cracking density ver...
Figure 3.11 (a) The matrix cracking density versus applied stress curves for...
Figure 3.12 (a) The matrix cracking density versus applied stress curves for...
Figure 3.13 (a) The matrix cracking density versus applied stress curves for...
Figure 3.14 (a) The matrix cracking density versus applied stress curves for...
Figure 3.15 (a) The experimental and theoretical matrix cracking density ver...
Figure 3.16 (a) The matrix cracking density versus applied stress curves for...
Figure 3.17 (a) The matrix cracking density versus applied stress curves for...
Figure 3.18 (a) The matrix cracking density versus applied stress curves for...
Figure 3.19 (a) The matrix cracking density versus applied stress curves for...
Figure 3.20 (a) The matrix cracking density versus applied stress curves for...
Figure 3.21 (a) The matrix cracking density versus applied stress curves for...
Figure 3.22 (a) The experimental and theoretical matrix cracking density ver...
Figure 3.23 (a) The experimental and theoretical matrix cracking density ver...
Chapter 4
Figure 4.1 Effect of fiber volume on (a) the time‐dependent tensile stress–s...
Figure 4.2 Effect of fiber radius on (a) the time‐dependent tensile stress–s...
Figure 4.3 Effect of matrix Weibull modulus on (a) the time‐dependent tensil...
Figure 4.4 Effect of the matrix cracking characteristic strength on (a) the ...
Figure 4.5 Effect of matrix cracking saturation spacing on (a) the time‐depe...
Figure 4.6 The effect of the interface shear stress on (a) the time‐dependen...
Figure 4.7 Effect of interface debonding energy on (a) the time‐dependent te...
Figure 4.8 Effect of fiber strength on (a) the time‐dependent tensile stress...
Figure 4.9 Effect of fiber Weibull modulus on (a) the time‐dependent tensile...
Figure 4.10 Effect of the oxidation time on (a) the time‐dependent tensile s...
Figure 4.11 (a) Experimental and predicted tensile stress–strain curves for ...
Figure 4.12 (a) Experimental and predicted tensile stress–strain curves for ...
Figure 4.13 (a) Experimental and predicted tensile stress–strain curves for ...
Figure 4.14 (a) Experimental and predicted tensile stress–strain curves for ...
Figure 4.15 (a) Experimental and predicted tensile stress–strain curves; (b)...
Figure 4.16 (a) Experimental and predicted tensile stress–strain curves; (b)...
Figure 4.17 (a) Experimental and predicted tensile stress–strain curves; (b)...
Figure 4.18 (a) Experimental and predicted tensile stress–strain curves; (b)...
Chapter 5
Figure 5.1 Unit cell of damaged CMCs upon (a) unloading and (b) reloading.
Figure 5.2 Tensile curve of 2.5D woven self‐healing Hi‐Nicalon™ SiC/[Si‐B‐C]...
Figure 5.3 Experimental Δ
W
/
W
e
versus cycle number curves of 2...
Figure 5.4 (a) Experimental and predicted internal friction parameter Δ ...
Figure 5.5 Tensile curve of 2.5D woven self‐healing Hi‐Nicalon™ SiC/[Si‐B‐C]...
Figure 5.6 Experimental internal friction parameter Δ
W
/
W
...
Figure 5.7 (a) Experimental and predicted internal friction parameter Δ
W
/...
Figure 5.8 Tensile curve of 2D woven self‐healing Hi‐Nicalon™ SiC/[SiC‐B
4
C] ...
Figure 5.9 Experimental cyclic‐dependent dissipated energy (Δ...
Figure 5.10 (a) Experimental and predicted dissipated energy Δ...
Figure 5.11 (a) Experimental and predicted interface shear stress versus cyc...
Figure 5.12 (a) Experimental and predicted interface shear stress versus cyc...
Chapter 6
Figure 6.1 Effect of the fiber volume (i.e.
V
f
= 20%, 30%, and 40%) on (a) t...
Figure 6.2 Effect of the constant peak stress level (i.e.
σ
max
= 150, 2...
Figure 6.3 Effect of the space between saturation matrix cracking (i.e.
l
sat
Figure 6.4 Effect of the interface shear stress in slip region (i.e.
τ
i
Figure 6.5 The effect of the interface shear stress in oxidation region (i.e...
Figure 6.6 Effect of the Weibull modulus of the fiber (i.e.
m
f
= 4, 5, and 6...
Figure 6.7 Effect of the environmental temperature (i.e.
T
= 600, 700, and 8...
Figure 6.8 (a) Evolution of the time-dependent stress rupture curves of expe...
Figure 6.9 (a) Evolution of the time-dependent stress rupture curves of expe...
Figure 6.10 (a) Evolution of the time-dependent stress rupture curves of exp...
Figure 6.11 Effect of stochastic stress (i.e.
σ
s
= 200, 220, 240, 260, ...
Figure 6.12 Effect of stochastic stress (i.e.
σ
s
= 240 MPa) and time in...
Figure 6.13 Effect of fiber volume (i.e.
V
f
= 20%, 25%, 30%, 35%, and 40%) o...
Figure 6.14 Effect of saturation matrix crack spacing (i.e.
l
sat
= 100, 150,...
Figure 6.15 Effect of the interface shear stress in the slip region (i.e.
τ
...
Figure 6.16 Effect of interface shear stress in the oxidation region (i.e....
Figure 6.17 Effect of environment temperature (i.e.
T
= 750, 800, 850, 900, ...
Figure 6.18 (a) The experimental and predicted strain versus time curves; (b...
Figure 6.19 (a) Experimental and predicted strain versus time curves; (b) th...
Figure 6.20 (a) Experimental and predicted strain versus time curves; (b) th...
Figure 6.21 Diagram of multiple loading sequence.
Figure 6.22 Effect of fiber volume (i.e.
V
f
= 25%, 30%, and 35%) on (a) the ...
Figure 6.23 Effect of saturation matrix crack spacing (i.e.
l
sat
= 150, 200,...
Figure 6.24 Effect of interface shear stress in the slip region (i.e.
τ
Figure 6.25 Effect of interface shear stress in the oxidation region (i.e....
Figure 6.26 Effect of temperature (i.e.
T
= 700, 800, and 900 °C)...
Figure 6.27 (a) Experimental and predicted composite strain versus time curv...
Figure 6.28 (a) Experimental and predicted composite strain versus time curves;...
Figure 6.29 (a) Experimental and predicted composite strain versus time curves;...
Chapter 7
Figure 7.1 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.2 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.3 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.4 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.5 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.6 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.7 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.8 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.9 (a) Composite damping versus temperature curves; (b) the fraction...
Figure 7.10 (a) Composite damping versus temperature curves; (b) the fractio...
Figure 7.11 (a) Experimental and predicted composite damping versus temperat...
Figure 7.12 Effect of fiber volume on (a) time-dependent composite vibration...
Figure 7.13 Effect of vibration stress on (a) time-dependent composite vibra...
Figure 7.14 Effect of matrix crack spacing on (a) time-dependent composite v...
Figure 7.15 Effect of interface shear stress on (a) time-dependent composite...
Figure 7.16 Effect of oxidation temperature on (a) time-dependent composite ...
Figure 7.17 (a) Experimental and predicted time-dependent composite vibratio...
Figure 7.18 (a) Experimental and predicted time-dependent composite vibratio...
Figure 7.19 (a) Experimental and predicted time-dependent composite vibratio...
Figure 7.20 Experimental and predicted time-dependent composite vibration da...
Guide
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Table of Contents
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High Temperature Mechanical Behavior of Ceramic-Matrix Composites
Longbiao Li
Author
Prof. Longbiao LiNanjing Univ. of Aeronautics &AstronautCollege of Civil AviationNo. 29 Yudao St.210016 NanjingChina
CoverCover Design: WileyCover Image: © Iuzvykova Iaroslava/Shutterstock
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Print ISBN: 978-3-527-34903-6ePDF ISBN: 978-3-527-83177-7ePub ISBN: 978-3-527-83178-4oBook ISBN: 978-3-527-83179-1
Preface
Monolithic ceramic is a kind of brittle material. The properties of the material will be greatly reduced by microdefects, which limit the practical application of ceramics in many fields. However, the inherent brittleness of ceramic materials can be improved by a continuous or discontinuous ceramic fiber or carbon fiber reinforcement, namely, ceramic-matrix composites (CMCs). This dispersed second phase can improve the fracture toughness of ceramic materials. The main mechanism is that the crack bridging effect in the process of fracture can make the matrix materials connect with each other, disperse the fracture energy by the way of fiber debonding, and fiber pulling out to prevent the fracture of the material. Compared with the monolithic ceramic, the mechanical behavior of CMCs has many different characteristics. Understanding the failure mechanisms and internal damage evolution represents an important step to ensure reliability and safety of CMCs. This book focuses on the high-temperature mechanical behavior of CMCs as follows:
Temperature- and time-dependent first matrix cracking stress of fiber-reinforced CMCs is investigated using the energy balance approach. The temperature-dependent micromechanical parameters are incorporated into the analysis of the microstress analysis, interface debonding criterion, and energy balance approach. Relationships between the first matrix cracking stress, interface debonding, temperature, and time are established. Effects of fiber volume, interface shear stress, interface frictional coefficient, interface debonding energy, matrix fracture energy, temperature, and time on the first matrix cracking stress and interface debonding length are discussed. Experimental first matrix cracking stress and interface debonding of C/SiC and SiC/SiC composites at elevated temperature are predicted.
Temperature- and time-dependent matrix cracking evolution of fiber-reinforced CMCs is investigated using the
critical matrix strain energy
(
CMSE
) criterion. Temperature-dependent interface shear stress, Young's modulus of the fibers and the matrix, matrix fracture energy, and the interface debonding energy are considered in the microstress field analysis, interface debonding criterion, and matrix multiple cracking evolution model. Effects of fiber volume, interface shear stress, interface debonding energy, matrix fracture energy, temperature, and time on matrix multiple cracking evolution and interface debonding are discussed. Experimental matrix multiple cracking evolution and fiber/matrix interface debonding of C/SiC and SiC/SiC composite at elevated temperatures are predicted.
Time-dependent tensile damage and fracture of fiber-reinforced CMCs are investigated considering the interface and fiber oxidation. Time-dependent damage mechanisms of matrix cracking, interface debonding, fiber failure, and interface and fiber oxidation are considered in the analysis of the tensile stress–strain curve. Experimental time-dependent tensile stress–strain curves, matrix cracking, interface debonding, and fibers failure of different SiC/SiC and C/SiC composites are predicted for different oxidation durations.
Cyclic-dependent damage development in self-healing 2.5D woven Hi-Nicalon™ SiC/[Si-B-C] and 2D woven Hi-Nicalon SiC/[SiC-B
4
C] composites at
T
= 600 and 1200 °C is investigated. Cyclic-dependent damage parameters of internal friction, dissipated energy, Kachanov's damage parameter, and broken fiber fraction are obtained to analyze damage development in self-healing CMCs. Relationships between cyclic-dependent damage parameters and multiple fatigue damage mechanisms are established. Experimental fatigue damage evolution of self-healing Hi-Nicalon SiC/[Si-B-C] and Hi-Nicalon SiC/[SiC-B
4
C] composites are predicted. Effects of fatigue peak stress, testing environment, and loading frequencies on the evolution of internal damage and final fracture are analyzed.
Time-dependent deformation, damage, and fracture of fiber-reinforced CMCs that were exposed to stress rupture loading at intermediate environmental temperatures are investigated. The composite microstress field and tensile constitutive relationship of the damaged CMCs were examined to characterize their time-dependent damage mechanisms. Relationships between stress rupture lifetime, peak stress level, time-dependent composite deformation, and evolution of internal damages are established. Effects of composite material properties, composite damage state, and environmental temperature on stress rupture lifetime, time-dependent composite deformation, and evolution of the internal damages of SiC/SiC are analyzed. Experimental stress rupture lifetime, time-dependent composite deformation, and composite internal damage evolution of SiC/SiC composite subjected to the stress rupture loading are evaluated.
A micromechanical temperature-dependent vibration damping model of fiber-reinforced CMCs is developed. Temperature-dependent damage mechanisms of matrix cracking, interface debonding and slip, and fiber fracture contribute to the vibration damping of damaged CMCs. Temperature-dependent fiber and matrix strain energy and dissipated energy density are formulated of composite constituent properties and damage-related microparameters of matrix crack spacing, interface debonding and slip length, and broken fibers fraction. Relationships between temperature-dependent composite damping, temperature-dependent damage mechanisms, temperature, and oxidation duration are established. Effects of composite constituent properties and composite damage state on temperature-dependent composite vibration damping of SiC/SiC and C/SiC composites are analyzed. Experimental temperature-dependent composite vibration damping of 2D SiC/SiC and C/SiC composites are predicted.
I hope this book can help the material scientists and engineering designers to understand and master the high-temperature mechanical behavior of CMCs.
Longbiao Li
30 November 2020
Nanjing, PR China
Acknowledgments
I am grateful to my wife Li Peng and my son Sheng-Ning Li for their encouragement.
A special thanks to Dr. Shaoyu Qian and Katherine Wong for their help with my original manuscript.
I am also grateful to the team at Wiley for their professional assistance.
1Introduction
Monolithic ceramic is a kind of brittle material. The properties of the material will be greatly reduced by microdefects, which limit the practical application of ceramics in many fields. However, the inherent brittleness of ceramic materials can be improved by continuous or discontinuous ceramic fiber or carbon fiber reinforcement, namely, ceramic-matrix composites (CMCs). This dispersed second phase can improve the fracture toughness of ceramic materials. The main mechanism is that the crack bridging effect in the process of fracture can make the matrix materials connect with each other, disperse the fracture energy by the way of fiber debonding, and fiber pulling out to prevent the fracture of the material [1, 2].
Compared with the superalloy, fiber-reinforced CMCs can withstand higher temperature, reduce cooling air flow, and improve the turbine efficiency. The density of fiber-reinforced CMCs is 2.0–2.5 g/cm3, which is only 1/4–1/3 of superalloy. CMCs have already been applied to aeroengine combustion chambers, nozzle flaps, turbine vanes, and blades. For example, the CMC nozzle flaps and seals manufactured by SNECMA have already been used for more than 10 years in the M88 and M53 aeroengines. The CMC tail nozzle designed by SAFRAN Group of France passed the commercial flight certification of European Union Aviation Safety Agency (EASA) and completed its first commercial flight on the CFM56-5B aeroengine on 16 June 2015. National Aeronautics and Space Administration (NASA) has prepared and tested the CMC turbine guide vanes and turbine blade disc components in the Ultra-Efficient Engine Technology (UEET) project. General Electric (GE) tested the CMC combustor and high-pressure turbine components in the ground test of GEnx aeroengine. The CMC turbine blades were successfully tested on the F414 engine, which are planned to be used in GE90 series aeroengines. The engine weight is expected to be reduced by 455 kg, accounting for about 6% of the total weight of GE90-115 aeroengine. The LEAP (Leading Edge Aviation Propulsion) series aeroengine developed by CFM company adopts CMC components. The LEAP-1A, 1B, and 1C aeroengine provides power for Airbus A320, Boeing 737MAX, and COMAC C919, respectively.
Compared with polymer matrix composites (PMCs), CMCs have some similarities, including anisotropy, braided structure, high strength/high modulus fibers, manufacturing process sensitivity, and diversity, but there are also differences, such as high operation temperature (>500 °C), diversity of material constituents (i.e. oxide matrix, nonoxidized matrix, carbide matrix, silicon nitride matrix, carbon matrix, etc.) and processing methods (i.e. reaction bonding [RB], hot pressing sintering [HPS], precursor infiltration and pyrolysis [PIP], reactive melt infiltration [RMI], chemical vapor infiltration [CVI], slurry infiltration and hot pressing [SIPH], CVI-PIP, CVI-RMI, and PIP-HP), low matrix failure strain, complex degradation/damage/failure mechanisms at elevated temperature, difficult connection of structures in high-temperature environment, and high requirement of nondestructive testing and repair technology.
To ensure the reliability and safety of their use in aircraft and aeroengine structures, it is necessary to investigate the tensile, fatigue, stress rupture, and vibration behavior of CMCs at elevated temperature.
1.1 Tensile Behavior of CMCs at Elevated Temperature
The stress–strain curve of CMCs under tensile load appears obviously nonlinear. The tensile stress–strain curve can be divided into three regions, i.e. elastic region, nonlinear region, and secondary linear region before failure. In region I, there is no damage in the material during initial loading, and the tensile stress–strain curve is linear. With the increase of stress, microcracks appear in the matrix-rich area or matrix defects. The initial matrix cracking stress is defined as σmc. These microcracks can only be detected by means of acoustic emission (AE), microscopic observation of specimen surface, and temperature measurement of sample surface. When the stress reaches the proportional limit stress, the accumulation of matrix cracks makes the stress–strain curve deflect, and the stress–strain curve is nonlinear, which marks the beginning of region II. In region II, the matrix cracks propagate along the vertical load direction while the number of matrix cracks increases. When the cracks extend to the fiber/matrix interface, the cracks deflect along the fiber/matrix interface, and debonding occurs at the fiber/matrix interface. With the increase of stress, when the slip zones of adjacent matrix cracks overlap each other, the matrix cracks reach saturation. The saturated stress of matrix cracks is defined as σsat. When the matrix crack is saturated, the region III of the stress–strain curve starts, and the external load is mainly borne by the fiber. The tangent modulus of the stress–strain curve is about VfEf (Vf is the volume content of the fiber and Ef is the elastic modulus of the fiber). With the increase of the stress, some fibers fail, and the failed fibers continue to carry through the shear stress at the fiber/matrix interface. When the fibers broken fraction reaches the critical value, the composite fracture occurs.
The tensile stress–strain behavior reflects the strength of the composite material to resist the damage of external tensile loading. The tensile properties (i.e. proportional limit stress, matrix crack spacing, tensile strength, and fracture strain) can be obtained from the tensile stress–strain curves and can be used for component design [3–5]. Jia et al. [6] investigated the relationship between the interphase and tensile strength of SiC fiber monofilament. The tensile strength of the SiC fiber monofilament decreases with the increasing coating layers. The SiC fibers with single boron nitride (BN) coating have the high monofilament strength retention of about 70%, 42.1% with two BN coatings, and 32.3% with four BN coatings. The minicomposite comprises one single fiber tow, interphase, and matrix and can be used to optimize the fiber–matrix interfacial zone and to generate micromechanical data necessary for modeling the mechanical behavior [7]. Almansour [8], Sauder et al. [9], and Yang et al. [10] performed investigations on the tensile behavior of SiC/SiC minicomposites with different fiber types and interface properties. Shi et al. [11] performed an investigation on the variability in tensile behavior of SiC/SiC minicomposite. The tensile strength of the SiC/SiC minicomposite satisfied the Weibull distribution. He et al. [12] performed an investigation on the tensile behavior of SiC/SiC minicomposites with different interphase thickness. The tensile strength and fiber pullout length increase with the interphase thickness. Chateau et al. [13] investigated the damage evolution and final fracture in SiC/SiC minicomposite using the in situ X-ray microtomography under tensile loading. Zeng et al. [14] performed experimental and theoretical investigations on the tensile damage evolution of unidirectional C/SiC composite at room temperature. Ma et al. [15], Wang et al. [16], Liang and Jiao [17], and Hu et al. [18] performed investigations on the tensile damage and fracture of 2.5D and 3D CMCs. The nonlinearity appears in the tensile curves along both the warp and weft directions. Under tensile loading, the matrix cracking first occurs because of the local stress concentration of the pores inside of the composite, and the transverse cracks and longitudinal interlaminar cracks result in the final brittle fracture of the composite. The acoustic emission technique is used to monitor the damage evolution of a 3D needled C/SiC composite [19]. The damage signal contained three main frequencies of 240, 370, and 455 kHz corresponding to the damage mechanisms of the interface damage, matrix damage, and fiber fracture, respectively. Wang et al. [20] compared the tensile behavior of C/SiC composites with different fiber preforms. The minicomposite has the largest strength, modulus, and strain energy density to failure in contrast to the lowest values of the 2D composite and the intermediate properties of the 3D composite. The tensile behavior of CMCs is affected by temperature [21–23]. For the unidirectional C/SiC composite at 1300 °C, the composite tensile strength was σUTS = 374 MPa and the composite tensile modulus was Ec = 134 GPa, and at 1450 °C, the composite tensile strength was σUTS = 338 MPa and the composite tensile modulus was Ec = 116 GPa. For the 2D SiC/SiC composite, the fracture strain at 1200 °C is higher than that at room temperature because of the interface oxidation. For the 3D C/SiC composite, when the temperature increases from room temperature to 1500 °C, the composite elastic modulus and the strain for saturation matrix cracking remained unchanged; the first matrix cracking stress, matrix cracking saturation stress, and fracture stress all increased first with temperature to the peak value at the temperature range of 1100–1300 °C and then decreased with temperature. Luo and Qiao [24] investigated the effect of loading rate on tensile behavior of 3D C/SiC composite at room temperature, 1100, and 1500 °C. At room temperature, the fracture stress increased with loading rate; at 1500 °C, the fracture stress decreased with loading rate; and at 1100 °C, the fracture stress remained the same without changing with loading rate. At elevated oxidizing temperature, the applied stress opens the existing cracks and allows for easier ingress of oxygen to the fibers [25, 26]. Under thermal and mechanical load cycling in oxidative environment, the strain is damage dependent and a combination of physical mechanism in the form of matrix microcracking and fiber debonding and chemical mechanism of fiber oxidation. Li et al. [27, 28] and Li [29] developed a micromechanical approach to predict the tensile behavior of CMCs with different fiber preforms considering multiple damage mechanisms. Li [30] predicted the time-dependent proportional limit stress of C/SiC composites with different fiber volumes, interface properties, and matrix damage. Li [31] analyzed matrix multi-cracking of fiber-reinforced CMCs considering the interface oxidation and compared the matrix cracking evolution of C/SiC composite with/without the interface oxidation. Martinez-Fernandez and Morscher [32] investigated the tensile properties of single tow Hi-Nicalon™ SiC/PyC/SiC composite at room temperature, 700, 950, and 1200 °C. The elevated temperature stress rupture behavior was dependent on the precrack stress, and the stress rupture life increases with the decreasing precrack stress. Forio et al. [33] investigated the lifetime of SiC multifilament tows under static fatigue in air at a temperature range of 600–700 °C. A slow-crack-growth mechanism is considered in the analysis of delayed failure of SiC/SiC minicomposite under low stress state. Morscher and Cawley [34] investigated the time-dependent strength degradation of woven SiC/BN/SiC composite at intermediate temperatures. The strength degradation is dependent on the kinetics for fusion of fibers to one another, the number of matrix cracks, and the applied stress state. Larochelle and Morscher [35] investigated the tensile stress rupture behavior of woven Sylramic–iBN/BN/SiC composite at 550 and 750 °C in a humid environment. The stress rupture strengths decreased with respect to time with the rate of decrease related to the temperature and the amount of moisture content. Pailler and Lamon [36] developed a micromechanics-based model of fatigue/oxidation for CMCs considering thermally induced residual stresses and kinetics of interphase degradation or crack healing. Santhosh et al. [37, 38] investigated the time-dependent deformation and damage of 2D SiC/SiC composite under multiaxial stress and dwell fatigue at 1204 °C. Morscher et al. [39] investigated the damage evolution and failure mechanisms of 2D Sylramic–iBN SiC/SiC composite under tensile creep and fatigue loading at 1204 °C in air condition. The damage development was the growth of matrix cracks and increasing number of matrix cracks with stress and time. Four dominant failure criterions are present in the literature for modeling matrix crack evolution of CMCs: maximum stress theories, energy balance approach, critical matrix strain energy (CMSE) criterion, and statistical failure approach. The maximum stress criterion assumes that a new matrix crack will form whenever the matrix stress exceeds the ultimate strength of the matrix, which is assumed to be single valued and a known material property [40]. The energy balance failure criteria involve calculation of the energy balance relationship before and after the formation of a single dominant crack as originally proposed by Aveston et al. [41]. The progression of matrix cracking as determined by the energy criterion is dependent on matrix strain energy release rate. The energy criterion is represented by Zok and Spearing [42] and Zhu and Weitsman [43]. The concept of a CMSE criterion presupposes the existence of an ultimate or critical strain energy limit beyond which the matrix fails. Beyond this, as more energy is placed into the composite, the matrix, unable to support the additional load, continues to fail. As more energy is placed into the system, the matrix fails such that all the additional energy is transferred to the fibers. Failure may consist of the formation of matrix cracks, the propagation of existing cracks, or interface debonding [44]. Statistical failure approach assumes matrix cracking is governed by statistical relations, which relate the size and spatial distribution of matrix flaws to their relative propagation stress [45].
In Chapter 2 “First Matrix Cracking of Ceramic-Matrix Composites at Elevated Temperature,” the temperature- and time-dependent first matrix cracking stress of fiber-reinforced CMCs is investigated using the energy balance approach. The temperature-dependent micromechanical parameters of fiber and matrix modulus, fiber/matrix interface shear stress, interface debonding energy, and matrix fracture energy are incorporated into the analysis of the microstress analysis, fiber/matrix interface debonding criterion, and energy balance approach. Relationships between the first matrix cracking stress, fiber/matrix interface debonding, temperature, and time are established. Effects of fiber volume, interface shear stress, interface frictional coefficient, interface debonding energy, matrix fracture energy, temperature and time on the first matrix cracking stress, and interface debonding length are discussed. Experimental first matrix cracking stress and interface debonding of C/SiC and SiC/SiC composites at elevated temperature are predicted.
In Chapter 3, “Matrix Multiple Cracking Evolution of Fiber-Reinforced Ceramic-Matrix Composites at Elevated Temperature,” the temperature- and time-dependent matrix cracking evolution of fiber-reinforced CMCs is investigated using the CMSE criterion. The temperature-dependent fiber/matrix interface shear stress, Young's modulus of the fibers and the matrix, matrix fracture energy, and the fiber/matrix interface debonding energy are considered in the microstress field analysis, fiber/matrix interface debonding criterion, and matrix multiple cracking evolution model. Effects of fiber volume, fiber/matrix interface shear stress, fiber/matrix interface debonding energy, matrix fracture energy, temperature and time on matrix multiple cracking evolution, and fiber/matrix interface debonding are discussed. Experimental matrix multiple cracking evolution and fiber/matrix interface debonding of C/SiC and SiC/SiC composite at elevated temperatures are predicted.
In Chapter 4, “Time-Dependent Tensile Behavior of Ceramic-Matrix Composites,” time-dependent tensile damage and fracture of fiber-reinforced CMCs are investigated, considering the interface and fiber oxidation. Time-dependent damage mechanisms of matrix cracking, interface debonding, fiber failure, and interface and fiber oxidation are considered in the analysis of the tensile stress–strain curve. Experimental time-dependent tensile stress–strain curves, matrix cracking, interface debonding, and fiber failure of different SiC/SiC and C/SiC composites are predicted for different oxidation duration.
1.2 Fatigue Behavior of CMCs at Elevated Temperature
For CMCs, because of the low fracture toughness of the matrix, there is no fatigue damage in the matrix itself. The degradation of interface or fiber properties is the main cause of fatigue damage. The interface degradation is mainly caused by interface layer fracture, wear, thermal residual stress release, and temperature rise at the interface; fiber degradation is caused by defects on the fiber surface during the interface wear process. It is found that the strength of the fiber decreases obviously after fatigue failure. The decrease of interfacial shear stress leads to the increase of interfacial debonding length with the increase of cycle, resulting in the increase of residual strain and decrease of modulus. The characteristic length and load of fiber increase with the decrease of interfacial shear stress. At the same time, the strength of fiber decreases because of interface wear, which further increases the probability of fiber fracture. When the percentage of fiber fracture reaches the critical value, the modulus of the composite decreases sharply, and the fatigue failure occurs.
At elevated temperature, oxidation is the key factor to limit the application of CMCs on hot section load-carrying components of aeroengine. Combining carbides deposited by CVI process with specific sequences, a new generation of SiC/SiC composite with self-healing matrix has been developed to improve the oxidation resistance [46, 47]. The self-sealing matrix forms a glass with oxygen at high temperature and consequently prevents oxygen diffusion inside the material. At low temperature of 650–1000 °C in dry and wet oxygen atmosphere, the self-healing 2.5D Nicalon™ NL202 SiC/[Si-B-C] with a pyrolytic carbon (PyC) interphase exhibits a better oxidation resistance compared to SiC/SiC with PyC because of the presence of boron compounds [48]. The fatigue lifetime duration in air atmosphere at intermediate and high temperature is considerably reduced beyond the elastic yield point. For the Nicalon SiC/[Si-B-C] composite, the elastic yield point is about σ = 80 MPa. The lifetime duration was about t = 10–20 hours at T = 873 K and less than t = 1 hour at T = 1123 K under σmax = 120 MPa. For the self-healing Hi-Nicalon™ SiC/SiC composite, a duration of t = 1000 hours without failure is reached at σmax = 170 MPa, and a duration higher than t = 100 hours at σmax = 200 MPa at T = 873 K [49]. For the self-healing Hi-Nicalon SiC/[SiC-B4C] composite, at 1200 °C, there was little influence on fatigue performance at f = 1.0 Hz but noticeably degraded fatigue lifetime at f = 0.1 Hz with the presence of steam [50, 51]. Increase in temperature from T = 1200 to 1300 °C slightly degrades fatigue performance in air atmosphere but not in steam atmosphere [52]. The crack growth in the SiC fiber controls the fatigue lifetime of self-healing Hi-Nicalon SiC/[Si-B-C] at T = 873 K, and the fiber creep controls the fatigue lifetime of self-healing SiC/[Si-B-C] at T = 1200 °C [53]. The typical cyclic fatigue behavior of a self-healing Hi-Nicalon SiC/[Si-B-C] composite involves an initial decrease of effective modulus to a minimum value, followed by a stiffening, and the time-to-the minimum modulus is in inverse proportion to the loading frequency [54]. The initial cracks within the longitudinal tows caused by interphase oxidation contribute to the initial decrease of modulus. The glass produced by the oxidation of self-healing matrix may contribute to the stiffening of the composite either by sealing the cracks or by bonding the fiber to the matrix [55]. The damage evolution of self-healing Hi-Nicalon SiC/[Si-B-C] composite at elevated temperature can be monitored using acoustic emission (AE) [56, 57]. The relationship between interface oxidation and AE energy under static fatigue loading at elevated temperature has been developed [58]. However, at high temperature above 1000 °C, AE cannot be applied for cyclic fatigue damage monitoring. The complex fatigue damage mechanisms of self-healing CMCs affect damage evolution and lifetime. Hysteresis loops related with cyclic-dependent fatigue damage mechanisms [59–61]. The damage parameters derived from hysteresis loops have already been applied for analyzing fatigue damage and fracture of different nonoxide CMCs at elevated temperatures [62–65]. However, the cyclic-dependent damage evolution and accumulation of self-healing CMCs are much different from previous analysis results especially at elevated temperatures.
In Chapter 5, “Fatigue Behavior of Ceramic-Matrix Composites at Elevated Temperature,” cyclic-dependent damage development in self-healing 2.5D woven Hi-Nicalon SiC/[Si-B-C] and 2D woven Hi-Nicalon SiC/[SiC-B4C] composites at T = 600 and 1200 °C are investigated. Cyclic-dependent damage parameters of internal friction, dissipated energy, Kachanov's damage parameter, and broken fiber fraction are obtained to analyze damage development in self-healing CMCs. Relationships between cyclic-dependent damage parameters and multiple fatigue damage mechanisms are established. Experimental fatigue damage evolution of self-healing Hi-Nicalon SiC/[Si-B-C] and Hi-Nicalon SiC/[SiC-B4C] composites are predicted. Effects of fatigue peak stress, testing environment, and loading frequencies on the evolution of internal damage and final fracture are analyzed.
1.3 Stress Rupture Behavior of CMCs at Elevated Temperature
At the intermediate temperature, SiC/SiC composite lifetime is decreased because of interface oxidation and lowered fiber content following exposure to stress rupture loading [66]. At elevated temperature range of 700–1200 °C, the SiC/SiC minicomposite with the PyC interphase exhibited severe damages of oxidation embrittlement, and the SiC/SiC minicomposite with the BN interphase showed only mild degradation subjected to the stress rupture loading [67]. Martinez-Fernandez and Morscher [32] investigated the monotonic tensile, stress rupture under constant load, and low-cycle fatigue of single tow Hi-Nicalon, PyC interphase, and CVI SiC matrix minicomposites at room temperature, 700, 950, and 1200 °C in air atmosphere. The stress rupture behavior at elevated temperature depended on the precracking stress level. However, for the 2D woven melt-infiltrated (MI) Hi-Nicalon SiC/SiC composite, the stress rupture properties were obvious worse than the SiC/SiC minicomposite properties under similar testing conditions because of complex fiber preform and damage evolution mechanisms [68]. Verrilli et al. [69] investigated the lifetime of C/SiC composite at elevated temperatures of 600 and 1200 °C subjected to the stress rupture loading in different environments. Stress rupture lives in air and in steam containing environments were similar at a low stress level of 69 MPa at an elevated temperature of 1200 °C. The fiber oxidation rate correlated with the composite stress rupture lifetime in the various environments. In the theoretical research area, Marshall et al. [70] and Zok and Spearing [42] applied the fracture mechanics approach to explore nonsteady first matrix cracking stress and multiple matrix cracking in fiber-reinforced CMCs. The energy balance relationship before and after the matrix cracking is established considering the mutual inference factors of the stress field between the adjacent matrix cracks. Curtin [45] investigated multiple matrix cracking in CMCs in the presence of matrix internal flaws. Evans [71] reported a method to predict design and life problems in fiber-reinforced CMCs. In addition, a connection between the macro-mechanical behavior and constituent properties of CMCs was established based on these predictions. McNulty and Zok [72] investigated the low-cycle fatigue damage mechanism and reported predictive damage models to describe the low-cycle CMC fatigue life. The degradation of the interface properties and fiber strength controls the fatigue life of CMCs. Lara-Curzio [73] established a micromechanical model for fiber-reinforced CMC reliability and time-to-failure estimation, particularly following the application of stresses greater than the first matrix cracking stress. The relationship between internal damage mechanisms and lifetime was established. In addition, the stress and temperature influences on the fiber-reinforced CMCs were investigated. Halverson and Curtin [74] developed a micromechanically based model for composite strength, and stress rupture lifetime of oxide/oxide fiber-reinforced CMCs considering the degradation of the fiber, matrix damage, and fiber pullout. Casas and Martinez-Esnaola [75] produced a fiber-reinforced CMC micromechanical creep-oxidation model, which was used to characterize oxidation at the CMC interface and the matrix, fiber creep, and fiber degradation with respect to time. Pailler and Lamon [36] developed a micromechanics-based model for the thermomechanical behavior of minicomposites based on multi-matrix cracking and fiber failure, which was derived from a fracture statistics-based model. Dassios et al. [76] analyzed the micromechanical behavior and micromechanics of crack growth resistance and bridging laws. The contributions of intact and pulled-out fibers on the bridging strain were discussed. Baranger [77] developed a reduced constitutive law to characterize the complex material behavior and applied the constitutive law to the mechanical modeling of SiC/SiC composites. Li [78–80] developed micromechanical damage models and constitutive relationship of cross-ply CMCs subjected to the dwell-fatigue loading at elevated temperature. Li et al. [27, 28] and Li [29] developed a micromechanical constitutive relationship to predict the damage and fracture of different fiber-reinforced CMCs subjected to tensile loading considering multiple damage mechanisms. Nonetheless, the above research did not consider fiber-reinforced CMC time-dependent deformation, damage, and fracture following the application of stress rupture loading at intermediate environmental temperatures.
In Chapter 6, “Stress Rupture of Ceramic-Matrix Composites at Elevated Temperature,” time-dependent deformation, damage, and fracture of fiber-reinforced CMCs that were exposed to stress rupture loading at intermediate environmental temperatures are investigated. The composite microstress field and tensile constitutive relationship of the damaged CMCs were examined to characterize their time-dependent damage mechanisms. Relationships between stress rupture lifetime, peak stress level, time-dependent composite deformation, and evolution of internal damages are established. Effects of composite material properties, composite damage state, and environmental temperature on stress rupture lifetime, time-dependent composite deformation, and evolution of the internal damages of SiC/SiC are analyzed. Experimental stress rupture lifetime, time-dependent composite deformation, and composite internal damage evolution of SiC/SiC composite subjected to the stress rupture loading are evaluated.
1.4 Vibration Behavior of CMCs at Elevated Temperature
Failure analysis shows that approximately two-thirds of the failures are related to vibration and noise, leading to reduced operational control accuracy, structural fatigue damage, and shortened safety life. Therefore, studying the damping performance of fiber-reinforced CMCs and improving their reliability in the service environment is an important guarantee for the safe service of CMCs in various fields. Compared with metals and alloys, CMCs have many unique damping mechanisms because of internal structure and complex damage mechanisms [81–85]. Hao et al. [86] performed computational and experimental analysis on the modal parameters and vibration response of C/SiC bolted fastenings. The composite vibration damping affects the vibration amplitude of CMC components. Zhang [87] investigated the vibration characteristics of a CMC panel subjected to high temperature and large gradient thermal environment and performed damping measurement experiments of CMC panels in the thermal environment. The effect of thermal environment on the natural frequency and vibration damping of CMCs was analyzed. Huang and Wu [88] performed natural frequencies and acoustic emission testing of 2D SiC/SiC composite subjected to tensile loading. The natural frequencies decrease with increasing tensile stress because of internal damages. Natural frequency and vibration damping are affected by the damage state of CMCs [89]. Energy dissipation of frictional sliding between matrix cracks is the main mechanism for the damping of unidirectional or cross-ply CMCs at room temperature [90]. The damping of CMCs is also affected by the fabrication method [91], property of the fiber [91], internal damages inside of CMCs [82, 92], and interphase thickness [93]. At elevated temperature, the temperature-dependent damage mechanisms affect the mechanical behavior and vibration damping of CMCs [94–99].
In Chapter 7 “Vibration Damping of Ceramic-Matrix Composites at Elevated Temperature,” a micromechanical temperature-dependent vibration damping model of fiber-reinforced CMCs is developed. Temperature-dependent damage mechanisms of matrix cracking, interface debonding and slip, and fiber fracture contribute to the vibration damping of damaged CMCs. Temperature-dependent fiber and matrix strain energy and dissipated energy density are formulated of composite constituent properties and damage-related microparameters of matrix crack spacing, interface debonding and slip length, and broken fiber fraction. Relationships between temperature-dependent composite damping, temperature-dependent damage mechanisms, temperature, and oxidation duration are established. Effects of composite constituent properties and composite damage state on temperature-dependent composite vibration damping of SiC/SiC and C/SiC composites are analyzed. Experimental temperature-dependent composite vibration damping of 2D SiC/SiC and C/SiC composites is predicted.
1.5 Conclusion
In this chapter, tensile, fatigue, stress rupture, and vibration behavior of fiber-reinforced CMCs are briefly introduced. In the following chapters, detailed formation about the matrix cracking, matrix multiple cracking, tensile, fatigue, stress rupture, and vibration behavior of fiber-reinforced CMCs are given:
Chapter 2
: First Matrix Cracking of Ceramic-Matrix Composites at Elevated Temperature.
Chapter 3
: Matrix Multiple Cracking Evolution of Fiber-Reinforced Ceramic-Matrix Composites at Elevated Temperature.
Chapter 4
: Time-Dependent Tensile Behavior of Ceramic-Matrix Composites.
Chapter 5
: Fatigue Behavior of Ceramic-Matrix Composites at Elevated Temperature.
Chapter 6
: Stress Rupture of Ceramic-Matrix Composites at Elevated Intemperature.
Chapter 7
: Vibration Damping of Ceramic-Matrix composites at Elevated Temperature.
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