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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Fachliteratur
- Sprache: Englisch
Guides researchers and practitioners toward developing highly reliable ceramic-matrix composites
The book systematically introduces the thermomechanical fatigue behavior of fiber-reinforced ceramic-matrix composites (CMCs) and environmental barrier coatings, including cyclic loading/unloading tensile behavior, cyclic fatigue behavior, dwell-fatigue behavior, thermomechanical fatigue behavior, and interface degradation behavior. It discusses experimental verification of CMCs and explains how to determine the thermomechanical properties. It also presents damage evolution models, lifetime prediction methods, and interface degradation rules.
Thermomechanical Fatigue of Ceramic-Matrix Composites offers chapters covering unidirectional ceramic-matrix composites and cross-ply and 2D woven ceramic-matrix composites. For cyclic fatigue behavior of CMCs, it looks at the effects of fiber volume fraction, fatigue peak stress, fatigue stress ratio, matrix crack spacing, matrix crack mode, and woven structure on fatigue damage evolution. Both the Dwell-fatigue damage evolution and lifetime predictions models are introduced in the next chapter. Experimental comparisons of the cross-ply SiC/MAS composite, 2D SiC/SiC composite, and 2D NextelTM 720/Alumina composite are also included. Remaining sections examine: thermomechanical fatigue hysteresis loops; in-phase thermomechanical fatigue damage; out-of-phase thermomechanical fatigue; interface degradation models; and much more.
-Offers unique content dedicated to thermomechanical fatigue behavior of ceramic-matrix composites (CMCs) and environmental barrier coatings
-Features comprehensive data tables and experimental verifications
-Covers a highly application-oriented subject?CMCs are being increasingly utilized in jet engines, industrial turbines, and exhaust systems
Thermomechanical Fatigue of Ceramic-Matrix Composites is an excellent book for developers and users of CMCs, as well as organizations involved in evaluation and characterization of CMCs. It will appeal to materials scientists, construction engineers, process engineers, and mechanical engineers.
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Seitenzahl: 611
Veröffentlichungsjahr: 2019
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Table of Contents
Cover
1 Cyclic Loading/Unloading Tensile Fatigue of Ceramic‐Matrix Composites
1.1 Introduction
1.2 Unidirectional Ceramic‐Matrix Composites
1.3 Cross‐Ply and 2D Woven Ceramic‐Matrix Composites
1.4 2.5D and 3D Ceramic‐Matrix Composites
1.5 Conclusions
References
2 Cyclic Fatigue Behaviors of Ceramic‐Matrix Composites
2.1 Introduction
2.2 Materials and Experimental Procedures
2.3 Hysteresis‐Based Damage Parameters
2.4 Results and Discussions
2.5 Experimental Comparisons
2.6 Discussions
2.7 Conclusions
References
3 Dwell‐Fatigue Behavior of Ceramic‐Matrix Composites
3.1 Introduction
3.2 Theoretical Analysis
3.3 Results and Discussions
3.4 Experimental Comparisons
3.5 Conclusions
References
4 Thermomechanical Fatigue Behaviors of Ceramic‐Matrix Composites
4.1 Introduction
4.2 Theoretical Analysis
4.3 Thermomechanical Fatigue Hysteresis Loops
4.4 In‐phase Thermomechanical Fatigue Damage
4.5 Out‐of‐phase Thermomechanical Fatigue
4.6 Thermomechanical Fatigue with Different Phase Angles
4.7 Conclusions
References
5 Interface Degradation of Ceramic‐Matrix Composites Under Thermomechanical Fatigue Loading
5.1 Introduction
5.2 Interface Degradation Models
5.3 Experimental Comparisons
5.4 Conclusions
References
Index
End User License Agreement
List of Tables
Chapter 5
Table 5.1 The fiber/matrix interface frictional coefficient of unidirec...
Table 5.2 The fiber/matrix interface frictional coefficient of unidirec...
Table 5.3 The fiber/matrix interface frictional coefficient of unidirec...
Table 5.4 The fiber/matrix interface frictional coefficient of unidirec...
Table 5.5 The fiber/matrix interface frictional coefficient of unidirec...
List of Illustrations
Chapter 1
Figure 1.1 The unit cell of the Budiansky–Hutchinson–Evans shear‐lag model...
Figure 1.2 (a) The fatigue hysteresis loops at different fatigue peak stre...
Figure 1.3 (a) The matrix cracking density versus the applied stress when ...
Figure 1.4 (a) The fatigue hysteresis loops at different fatigue peak stre...
Figure 1.5 (a) The fatigue hysteresis loops at different fatigue peak stre...
Figure 1.6 (a) The broken fibers fraction versus applied stress curve; (b)...
Figure 1.7 The cyclic loading/unloading tensile stress–strain curve of uni...
Figure 1.8 (a) The matrix multiple cracking on the side surface; and (b) t...
Figure 1.9 The experimental and theoretical matrix cracking density versus...
Figure 1.10 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.11 (a) The fatigue hysteresis loops; and (b) the fiber/matrix int...
Figure 1.12 (a) The fatigue hysteresis loops; (b) the interface slip lengt...
Figure 1.13 (a) The cyclic loading/unloading stress–strain curves; (b) the...
Figure 1.14 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.15Figure 1.15 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.16Figure 1.16 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.17Figure 1.17 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.18Figure 1.18 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.19 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.20 (a) The cyclic loading/unloading fatigue hysteresis loops; (b)...
Figure 1.21 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.22Figure 1.22 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.23 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.24 (a) The cyclic loading/unloading fatigue hysteresis curves; (b...
Figure 1.25 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.26Figure 1.26 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.27Figure 1.27 (a) The fatigue hysteresis loops; and (b) the inter...
Figure 1.28 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.29 (a) The matrix cracking density versus the applied stress curv...
Figure 1.30 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.31 (a) The fatigue hysteresis loops; (b) the interface slip lengt...
Figure 1.32 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.33 (a) The fatigue hysteresis loops; and (b) the interface slip l...
Figure 1.34 (a) Undamaged composite; (b) mode 1; (c) mode 2; (d) mode 3; (...
Figure 1.35 The fiber axial stress distribution for the interface slip Cas...
Figure 1.36 The fiber axial stress distribution for the interface slip Cas...
Figure 1.37 The fiber axial stress distribution for the interface slip Cas...
Figure 1.38 The fiber axial stress distribution for the interface slip Cas...
Figure 1.39 The fiber axial stress distribution for the interface slip Cas...
Figure 1.40 The fiber axial stress distribution for the interface slip Cas...
Figure 1.41 The fiber axial stress distribution for the interface slip Cas...
Figure 1.42 The fiber axial stress distribution for the interface slip Cas...
Figure 1.43 (a) The fatigue hysteresis loops of matrix cracking mode 3 and...
Figure 1.44 (a) The fatigue hysteresis loops of matrix cracking mode 3 and...
Figure 1.45 (a) The fatigue hysteresis loops of matrix cracking mode 3 and...
Figure 1.46 (a) The fatigue hysteresis loops of matrix cracking mode 3 and...
Figure 1.47 (a) The fatigue hysteresis loops of matrix cracking mode 3 and...
Figure 1.48 (a) The fatigue hysteresis loops of single matrix cracking mod...
Figure 1.49 The loading/unloading tensile stress–strain curve of cross‐ply...
Figure 1.50 (a) The experimental and predicted fatigue hysteresis loops; (...
Figure 1.51 (a) The experimental and predicted fatigue hysteresis loops; (...
Figure 1.52 (a) The experimental and predicted fatigue hysteresis loops; (...
Figure 1.53 (a) The experimental and predicted fatigue hysteresis loops; (...
Figure 1.54 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.55 (a) The experimental and analytical model predicted fatigue hy...
Figure 1.56 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.57 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.58 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.59 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.60 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.61 (a) The experimental and predicted fatigue hysteresis loops; a...
Figure 1.62 The cyclic loading/unloading hysteresis loops of 2.5D C/SiC co...
Figure 1.63 The experimental and theoretical hysteresis loops of 2.5D C/Si...
Figure 1.64 The cyclic loading/unloading hysteresis loops of 3D braided C/...
Figure 1.65 The experimental and theoretical hysteresis loops of 3D braide...
Figure 1.66 The cyclic loading/unloading hysteresis loops of 3D needled C/...
Figure 1.67 The experimental and theoretical hysteresis loops of 3D needle...
Chapter 2
Figure 2.1 The fiber/matrix interface shear stress versus applied cycle nu...
Figure 2.2 The effect of fiber volume content on (a) the fatigue hysteresi...
Figure 2.3 The effect of fatigue peak stress on (a) the fatigue hysteresis...
Figure 2.4 The effect of fatigue stress ratio on (a) the fatigue hysteresi...
Figure 2.5 The effect of matrix crack spacing on (a) the fatigue hysteresi...
Figure 2.6 The undamaged state and five damaged modes of cross‐ply ceramic...
Figure 2.7 The effect of matrix cracking mode on (a) the fatigue hysteresi...
Figure 2.8 The fatigue hysteresis dissipated energy versus the interface s...
Figure 2.9 (a) The experimental and predicted fiber/matrix interface shear...
Figure 2.10 (a) The fatigue hysteresis dissipated energy versus the fiber/...
Figure 2.11 (a) The experimental and predicted fiber/matrix interface shea...
Figure 2.12 (a) The theoretical fatigue hysteresis dissipated energy versu...
Figure 2.13 (a) The theoretical fatigue hysteresis dissipated energy versu...
Figure 2.14 (a) The theoretical fatigue hysteresis dissipated energy versu...
Figure 2.15 (a) The theoretical fatigue hysteresis dissipated energy versu...
Figure 2.16 (a) The theoretical fatigue hysteresis dissipated energy versu...
Figure 2.17 (a) The interface shear stress versus cycle number curve; (b) ...
Figure 2.18 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.19 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.20 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.21 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.22 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.23 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 2.24 (a) The fiber/matrix interface shear stress versus the applied...
Figure 2.25 (a) The interface shear stress versus the applied cycle number...
Figure 2.26 (a) The fiber/matrix interface shear stress versus the applied...
Figure 2.27 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.28 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.29 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.30 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.31 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.32 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.33 (a) The interface shear stress versus the applied cycle number...
Figure 2.34 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.35 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.36 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.37 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.38 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.39 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.40 (a) The fiber/matrix interface shear stress versus the applied...
Figure 2.41 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.42 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.43 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.44 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.45 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.46 (a) The fiber/matrix interface shear stress versus the applied...
Figure 2.47 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.48 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.49 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.50 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.51 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.52 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.53 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.54 (a) The fiber/matrix interface shear stress versus the applied...
Figure 2.55 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.56 (a) The theoretical and experimental hysteresis loops and (b) ...
Figure 2.57 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.58 (a) The theoretical and experimental hysteresis loops and (b) ...
Figure 2.59 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.60 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.61 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.62 (a) The interface shear stress versus the applied cycle number...
Figure 2.63 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.64 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.65 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.66 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.67 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.68 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.69 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.70 (a) The interface shear stress versus the applied cycle number...
Figure 2.71 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.72 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.73 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.74 (a) The theoretical and experimental fatigue hysteresis loops ...
Figure 2.75 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.76 (a) The interface shear stress versus cycle number curve and (...
Figure 2.77 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 2.78 (a) The interface shear stress versus the applied cycle number...
Figure 2.79 The fatigue life S–N curves of unidirectional, cross‐ply, 2D, ...
Figure 2.80 (a) The fatigue hysteresis modulus
E
n
/
E
0
versus cycle numb...
Figure 2.81 The fatigue hysteresis loops corresponding to (a) unidirection...
Figure 2.82 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 2.83 The fatigue life S–N curves of unidirectional, cross‐ply, 2D, ...
Figure 2.84 The schematic of fibers oxidation in multiple cracked C/SiC co...
Figure 2.85 (a) The fatigue hysteresis modulus
E
n
/
E
0
versus cycle numb...
Figure 2.86 The fatigue hysteresis loops of (a) unidirectional C/SiC; (b) ...
Figure 2.87 (a) The fatigue hysteresis dissipated energy versus cycle numb...
Figure 2.88 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 2.89 (a) The fatigue hysteresis dissipated energy versus interface ...
Figure 2.90 (a) The interface shear stress versus cycle number and (b) the...
Figure 2.91 (a) The interface shear stress versus cycle number and (b) the...
Chapter 3
Figure 3.1 The unit cell of Budiansky–Hutchinson–Evans shear‐lag model.
Figure 3.2 The schematic of oxidation effects into composite.
Figure 3.3 The schematic figure for fiber sliding relative to the matrix u...
Figure 3.4 The schematic of cyclic fatigue loading and cyclic fatigue load...
Figure 3.5 (a) The fatigue hysteresis dissipated energy versus the applied...
Figure 3.6 (a) The fatigue hysteresis dissipated energy versus the applied...
Figure 3.7 (a) The fatigue hysteresis dissipated energy versus the applied...
Figure 3.8 (a) The fatigue hysteresis dissipated energy versus the applied...
Figure 3.9 (a) The fatigue hysteresis dissipated energy versus the applied...
Figure 3.10 (a) The experimental fatigue hysteresis loops corresponding to...
Figure 3.11 (a) The experimental and analytical model fatigue hysteresis l...
Figure 3.12 (a) The experimental fatigue hysteresis loops corresponding to...
Figure 3.13 (a) The experimental and theoretical predicted fatigue life S–...
Figure 3.14 (a) The experimental fatigue hysteresis loops corresponding to...
Figure 3.15 (a) The fatigue hysteresis loops corresponding to different ap...
Figure 3.16 (a) The experimental and analytical model predicted fatigue li...
Figure 3.17 (a) The experimental and theoretical fatigue hysteresis dissip...
Figure 3.18 (a) The experimental and analytical model fatigue hysteresis d...
Figure 3.19 (a) The experimental and analytical model predicted fatigue pe...
Figure 3.20 (a) The fatigue peak strain versus cycle number curves under
σ
...
Chapter 4
Figure 4.1 The schematic figure for fiber slipping relative to matrix upon...
Figure 4.2 (a) The fatigue hysteresis loops under in‐phase/out‐of‐phase th...
Figure 4.3 (a) The fatigue hysteresis loops under in‐phase/out‐of‐phase th...
Figure 4.4 (a) The fatigue hysteresis loops under in‐phase/out‐of‐phase th...
Figure 4.5 (a) The fatigue hysteresis loops under in‐phase/out‐of‐phase th...
Figure 4.6 (a) The fatigue hysteresis loops under in‐phase and out‐of‐phas...
Figure 4.7 (a) The fatigue hysteresis loops under the in‐phase and out‐of‐...
Figure 4.8 (a) The experimental and analytical model fatigue hysteresis lo...
Figure 4.9 (a) The experimental and analytical model fatigue hysteresis lo...
Figure 4.10 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.11 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.12 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.13 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.14 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.15 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.16 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.17 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.18 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.19 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.20 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.21 (a) The experimental and analytical model fatigue hysteresis l...
Figure 4.22 (a) The fatigue hysteresis dissipated energy versus the fiber/...
Figure 4.23 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 4.24 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 4.25 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 4.26 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 4.27 (a) The fatigue hysteresis dissipated energy versus the interf...
Figure 4.28 (a) The fatigue hysteresis dissipated energy versus the cycle ...
Figure 4.29 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.30 (a) The fatigue hysteresis dissipated energy versus the cycle ...
Figure 4.31 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.32 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.33 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.34 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.35 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.36 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.37 (a) The fatigue hysteresis modulus versus the cycle number cur...
Figure 4.38 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.39 (a) The fatigue hysteresis dissipated energy versus the cycle ...
Figure 4.40 The schematic of thermomechanical fatigue loading correspondin...
Figure 4.41 (a) The fatigue hysteresis loops corresponding to the cycle nu...
Figure 4.42 (a) The fatigue hysteresis loops corresponding to the differen...
Figure 4.43 (a) The fatigue hysteresis loops corresponding to the differen...
Figure 4.44 (a) The fatigue hysteresis loops corresponding to the differen...
Figure 4.45 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.46 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.47 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.48 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.49 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.50 (a) The fatigue hysteresis dissipated energy versus the applie...
Figure 4.51 (a) The experimental and analytical model predicted fatigue hy...
Figure 4.52 The experimental and theoretical predicted fatigue peak strain...
Chapter 5
Figure 5.1 The fiber axial stress distribution upon unloading and subseque...
Figure 5.2 The fiber axial stress distribution during unloading and subseq...
Figure 5.3 The fiber axial stress distribution during unloading and subseq...
Figure 5.4 The fiber axial stress distribution during unloading and subseq...
Figure 5.5 (a) The fatigue hysteresis loops of different fiber/matrix inte...
Figure 5.6 The experimental and analytical model fatigue hysteresis dissip...
Figure 5.7 The experimental and predicted fatigue hysteresis loops of unid...
Figure 5.8 The experimental and analytical model fatigue hysteresis dissip...
Figure 5.9 The experimental and analytical model fatigue hysteresis loops ...
Figure 5.10 The experimental and analytical model fatigue hysteresis dissi...
Figure 5.11 The experimental and analytical model predicted fatigue hyster...
Figure 5.12 The experimental and analytical model fatigue hysteresis dissi...
Figure 5.13 The experimental and predicted fatigue hysteresis loops of uni...
Figure 5.14 The experimental and analytical model fatigue hysteresis dissi...
Figure 5.15 The experimental and predicted fatigue hysteresis loops of uni...
Figure 5.16 The fiber/matrix interface frictional coefficient versus the n...
Figure 5.17 (a) The experimental and analytical model fatigue hysteresis l...
Figure 5.18 (a) The experimental and analytical model fatigue hysteresis l...
Figure 5.19 (a) The experimental and analytical model fatigue hysteresis l...
Figure 5.20 (a) The experimental and analytical model fatigue hysteresis l...
Figure 5.21 (a) The experimental and analytical model fatigue hysteresis d...
Figure 5.22 (a) The experimental and analytical model fatigue hysteresis l...
Figure 5.23 (a) The experimental fatigue hysteresis dissipated energy vers...
Figure 5.24 (a) The experimental and analytical model fatigue hysteresis d...
Guide
Cover
Table of Contents
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Thermomechanical Fatigue of Ceramic-Matrix Composites
Longbiao Li
Copyright
Author
Longbiao Li
Nanjing University of Aeronautics and
Astronaut
College of Civil Aviation
No. 29 Yudao St.
210016 Nanjing
China
Cover
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1Cyclic Loading/Unloading Tensile Fatigue of Ceramic‐Matrix Composites
1.1 Introduction
Ceramic materials possess high strength and modulus at elevated temperature, but their use as structural components is severely limited due to their brittleness. Continuous fiber‐reinforced ceramic‐matrix composites (CMCs), by incorporating fibers in ceramic matrices, not only exploit their attractive high‐temperature strength but also reduce the propensity for catastrophic failure (Naslain 2004; Cheng 2010; Li 2013, 2016a,b).
As the strain‐to‐failure of the matrix tends to be less than that of the fibers, the first noticeable damage event under tensile loading in the fiber direction is the occurrence of matrix cracks perpendicular to the loading direction (Ramakrishnan and Arunachalam 1993; Dalmaz et al. 1996). The matrix cracks will develop, and some matrix cracks will deflect along the fiber/matrix interface as the load increases (Chiang 2001). When multiple matrix cracking, interface debonding, and sliding occur, interface shear stress transfers loads between the fiber and matrix, which is critical for the nonlinear behavior of the C/SiC CMCs (Curtin 2000).
Upon unloading and subsequent reloading, stress–strain hysteresis loops develop due to the frictional sliding that occurs along any interface debonded region (Rouby and Reynaud 1993; Evans et al. 1995; Reynaud 1996; Mei and Cheng 2009). Kotil et al. (1990) firstly performed an investigation on the effect of interface shear stress on the shape and area of the hysteresis loops. Pryce and Smith (1993) investigated the effect of interface partially debonding on the hysteresis loops based on the assumption of purely frictional load transfer between the fiber and matrix. Based on the Pryce–Smith model, Keith and Kedward (1995) investigated the effect of hysteresis loops when fiber/matrix interface is completely debonded. Solti et al. (1995) investigated the effect of hysteresis loops when fiber/matrix interface was chemically bonded and partially debonded by adopting the maximum interface shear stress criterion to determine the interface debonded length. Ahn and Curtin (1997) investigated the effect of matrix stochastic cracking on hysteresis loops by assuming the two‐parameter Weibull distribution of matrix flaw and compared with the Pryce–Smith model. Li et al. (2009) investigated the effect of interface debonding and fiber Poisson contraction on hysteresis loops when fiber/matrix interface was chemically bonded. It was found that after unloading completely, the residual strain and the area of the hysteresis loops decrease as the interface debonded energy and interface frictional coefficient increase. Li and Song (2010a, 2011a) developed an approach to estimate interface shear stress and interface frictional coefficient of CMCs from hysteresis loops. It was found that the interface shear stress and interface frictional coefficient degraded as cycle increased, and the degradation rate depends on the fatigue maximum stress, fatigue load ratio, and loading rate. Fantozzi and Reynaud (2009) investigated the fatigue hysteresis behavior of bi‐ or multidirectional (cross‐weave, cross‐ply, 2.5D, [0/+60/−60]n) with SiC or C long fiber‐reinforced SiC, MAS‐L, Si‐B‐C, or C matrix at room temperature and at high temperature under inert and oxidation atmosphere. It was found that the macroscopic hysteresis behavior of these materials was not always controlled by the friction at the fiber/matrix interfaces but can be controlled by the friction at the yarn/matrix, yarn/yarn, or ply/ply interface. By assuming that the mechanical behavior of the composite is mainly controlled by the mechanical behavior of the longitudinal yarns, the hysteresis loop shape variation of theses composites during cyclic loading was analyzed. It should be noted that the models mentioned earlier do not consider the effect of fiber failure on hysteresis loops. Upon unloading and subsequent reloading, the fracture and intact fibers both slip in the interface debonded region, which affect the shape, area, and location of the hysteresis loops (Kun and Herrmann 2000; Yang and Mall 2003; Li and Song 2011b).
In this chapter, the cyclic loading/unloading hysteresis behavior of CMCs with different fiber preforms, i.e. unidirectional, cross‐ply, 2D and 2.5D woven, 3D braided, and 3D needled, are investigated. Based on fiber sliding mechanisms, the hysteresis loop models considering different interface slip cases are developed. The matrix crack spacing and interface debonding length are obtained by matrix cracking statistical model and fracture mechanics interface debonding criterion. The two‐parameter Weibull model is used to describe fiber strength distribution. The stress carried by the intact and fracture fibers at the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing (GLS) criterion. The axial stress distribution of the intact fibers is determined based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region. The unloading interface counter slip length and reloading interface new slip length are determined by the fracture mechanics approach. The effects of fiber volume fraction, matrix cracking density, interface shear stress, interface debonded energy, and fiber failure on the hysteresis loops, hysteresis dissipated energy, hysteresis width, and hysteresis modulus are analyzed. The hysteresis loops, hysteresis dissipated energy, and hysteresis modulus of unidirectional, cross‐ply, 2D and 2.5D woven, 3D braided, and 3D needled CMCs are predicted.
1.2 Unidirectional Ceramic‐Matrix Composites
The cyclic loading/unloading hysteresis loops of unidirectional CMCs are investigated for different fiber volume fraction, matrix cracking density, fiber/matrix interface shear stress, and interface debonded energy with and without considering fiber failure. The experimental C/SiC, C/Si3N4, SiC/Si3N4, and SiC/CAS composites are predicted for different peak stresses. The peak stress affects the interface debonding and sliding and also the hysteresis loops.
1.2.1 Materials and Experimental Procedures
1.2.1.1 C/SiC Composite
The unidirectional T‐700™ C/SiC composites were manufactured by the hot‐pressing method, which offered the ability to fabricate dense composites via a liquid phase sintering method at a low temperature. The fibers have an average diameter of 7 μm and come on a spool as a tow of 12K fibers. The volume fraction of fibers was approximately 42%. Low pressure chemical vapor infiltration (CVI) was employed to deposit approximately 5–20 layers of PyC/SiC with the mean thickness of 0.2 μm in order to enhance the desired nonlinear/non‐catastrophic tensile behavior. The nano‐SiC powder and sintering additives were ball milled for four hours using SiC balls. After drying, the powders were dispersed in xylene with polycarbonsilane (PCS) to form the slurry. Carbon fiber tows were infiltrated by the slurry and wound to form aligned unidirectional composite sheets. After drying, the sheets were cut to a size of 150 mm × 150 mm and pyrolyzed in argon. Then, the sheets were stacked in a graphite die and sintered by hot pressing.
The dog‐bone shaped specimens, with 120 mm length, 3.2 mm thickness, and 4.5 mm width in the gage section, were cut from the 150 mm × 150 mm panels by water cutting. Specimens were further coated with SiC of about 20 μm thick by chemical vapor deposition (CVD) to prevent oxidation at high temperature. These processing steps resulted in a material having bulk density about 2.0 g/cm3 and an open porosity below 5%.
The cyclic loading/unloading tensile experiments at room temperature were conducted on an MTS Model 809 servo hydraulic load frame (MTS Systems Corp., Minneapolis, MN) equipped with edge‐loaded grips, operated at a loading rate of 2.0 MPa/s. Gage‐section strains were measured using a clip‐on extensometer (Model No. 634.12F‐24, MTS Systems Corp., modified for a 25 mm gage length). Direct observations of matrix cracking were made using HiROX optical microscope. Matrix crack densities were determined by counting the number of cracks in a length of about 15 mm.
1.2.1.2 C/Si3N4 and SiC/Si3N4 Composites
THORNEL P25™ (Amoco, USA) carbon fiber‐reinforced silicon nitride matrix (Ube Industries, Japan) composite (C/Si3N4 CMCs) was prepared by Joint Research Centre, Petten, NL. In order to promote liquid phase sintering of silicon nitride, the powder mixture for the preparation of the slurry contains 10% by weight of Al2O3 and Y2O3. The individual unidirectional fibrous preforms were infiltrated by the mixture of Si3N4, Al2O3, and Y2O3. The densification process was conducted by sintering under load of 27 MPa at a temperature of 1700 °C for 30 minutes and 1650 °C for 60 minutes. The final dimensions of the composite panels were fixed to be 72 mm × 45 mm × 3.9 mm to control the fiber volume fraction and ensure the reproducibility of the process. The fiber volume fraction of C/Si3N4 composite was about 40%, and the average density was 2.6–2.7 g/cm3. The porosity of the composite is less than 1%.
The Hi‐Nicalon™ SiC (Nippon Carbon Co., Ltd., Tokyo, Japan) fiber‐reinforced silicon nitride (Ube Industries, Japan) matrix composite (SiC/Si3N4 CMCs) was also fabricated by Joint Research Centre, Petten, NL. The pyrolytic carbon (PyC) interphase was deposited on the Hi‐Nicalon fibers by CVD. Based on the interface bonding condition between fibers and matrix, the SiC/Si3N4 composite can be divided into two cases, i.e. type A composite, where the carbon coating is perfectly attached to SiC fibers, indicating strong interface bonding; and type B composite, where the adhesion between SiC fibers and carbon coating is low. The volume fraction of the composite was about 30%, and the average density was 2.8–2.95 g/cm3. The porosity of the composite is less than 3%.
The mechanical testing specimen was rectangle in shape with dimensions of 72 mm × 7 mm × 1.5 mm for C/Si3N4 composite and 72 mm × 7 mm × 1.2 mm for SiC/Si3N4 composite according to the French AFNOR standardization (French National Organization for Standardization, 1989). Cyclic loading/unloading tensile and tension–tension fatigue tests of unidirectional C/Si3N4 and SiC/Si3N4 composites were conducted on an Instron Model 8511 servo hydraulic load frame (INSTRON System Corp., Norwood, Massachusetts, USA). The clamping stresses performed on the surface of the specimens are less than 5 MPa for C/Si3N4 composite and 9 MPa for SiC/Si3N4 composite. The longitudinal deformation was measured with the aid of an extensometer Schenk knife of 14 mm. The cyclic tensile loading/unloading tests were conducted under strain control with the loading rate of 0.05 mm/min. During tensile loading, the test is interrupted regularly, and the applied stress is maintained using the load control mode to make replicas on the front surface of the specimen, in order to in situ measure the matrix cracking density at different applied stress levels.
1.2.1.3 SiC/CAS Composite
Nicalon™ SiC fiber‐reinforced calcium aluminosilicate glass ceramic matrix laminates were manufactured by hot‐pressing prepreg. Tensile coupons, 80 mm by 20 mm, were cut from the laminates. Abraded and etched aluminum end tags were bonded to specimens for ease of gripping in wedge grips. Quasi‐static tests were carried out using Instron 1175 under displacement control at a crosshead speed of 0.05 mm/min. Direct observations of matrix cracking were made using optical and scanning electron microscopy of the polished coupon edges. Crack densities were determined by counting the number of cracks in a gage length of about 15 mm.
1.2.2 Theoretical Analysis
1.2.2.1 Stress Analysis
Upon first loading to the peak stress of σmax, which is higher than the initial matrix cracking stress σmc, it is assumed that matrix cracks run across the cross section of the composites and fiber/matrix interface debonds. To analyze stress distributions in the fiber and the matrix, a unit cell is extracted from the CMCs, as shown in Figure 1.1. The unit cell contains a single fiber surrounded by a hollow cylinder of matrix. The fiber radius is rf, and the matrix radius is . The length of the unit cell is lc/2, which is just the half matrix crack space. The fiber/matrix interface debonding length is ld. At the matrix crack plane, fibers carry all the loads (σ/Vf), where σ denotes far‐field applied stress and Vf denotes fiber volume fraction. The shear‐lag model adopted by Budiansky–Hutchinson–Evans (Budiansky et al. 1986) is applied to perform stress and strain calculations in the interface debonded region (x ∈ [0, ld]) and interface bonded region (x ∈ [ld, lc/2]):
where Vm denotes the matrix volume fraction, τi denotes the fiber/matrix interface shear stress, and ρ denotes the shear‐lag parameter (Budiansky et al. 1986).
where Gm denotes matrix shear modulus, and
σfo and σmo denote fiber and matrix axial stress in the interface bonded region, respectively:
where Ef, Em, and Ec denote fiber, matrix, and composite elastic modulus, respectively. αf, αm, and αc denote fiber, matrix, and composite thermal expansion coefficient. ΔT denotes the temperature difference between the fabricated temperature T0 and testing temperature T1 (ΔT = T1 − T0). The axial elastic modulus of composite is approximated by the rule of mixture:
Figure 1.1 The unit cell of the Budiansky–Hutchinson–Evans shear‐lag model.
When the fiber fails, the fiber axial stress distribution in the interface debonded region and bonded region is determined using the following equation:
where T denotes the intact fiber axial stress at the matrix cracking plane.
1.2.2.2 Matrix Cracking
When loading of fiber‐reinforced CMCs, cracks typically initiate within the composite matrix since the strain‐to‐failure of the matrix is usually less than that of the fiber. The matrix crack spacing decreases with applied stress above the initial matrix cracking stress σmc and may eventually attain saturation at stress σsat. There are four dominant failure criterions for modeling matrix cracking evolution of unidirectional CMCs, i.e. the maximum stress criterion (Daniel and Lee 1993), the energy balance approach (Aveston et al. 1971; Zok and Spearing 1992; Zhu and Weitsman 1994), the critical matrix strain energy criterion (Solti et al. 1995), and the statistical failure approach (Curtin 1993). The brittle nature of the matrix material and the possible formation of initial cracks distribution throughout the microstructure suggest that a statistical approach to matrix crack evolution is warranted in CMCs. The tensile strength of the brittle matrix is assumed to be described using the two‐parameter Weibull distribution. The matrix failure can be determined using the following equation (Curtin 1993):
where σm denotes the tensile stress in the matrix and σR and m denote the matrix characteristic strength and matrix Weibull modulus, respectively. To estimate the instantaneous matrix crack space with increasing applied stress, it leads to the following equation:
where lc denotes the instantaneous matrix crack space and lsat denotes the saturation matrix crack space. Using Eqs. 1.10 and 1.11, the instantaneous matrix crack space can be determined using the following equation (Curtin 1993):
1.2.2.3 Interface Debonding
When matrix crack propagates to the fiber/matrix interface, it deflects along the fiber/matrix interface. There are two approaches to the problem of fiber/matrix interface debonding, i.e. the shear stress approach (Hsueh 1996) and the fracture mechanics approach (Gao et al. 1988). It has been proved that the fracture mechanics approach is preferred to the shear stress approach for interface debonding (Sun and Singh 1998). The fracture mechanics approach is adopted in the present analysis. The interface debonding criterion can be described using the following equation (Gao et al. 1988):
where denotes the fiber load at the matrix crack plane, wf(0) denotes the fiber axial displacement at the matrix crack plane, and v(x) denotes the relative displacement between the fiber and the matrix. The axial displacement of fiber and matrix can be determined using the following equations:
Using Eqs. 1.14 and 1.15, the relative displacement between the fiber and matrix can be described using the following equation:
Substituting wf(x = 0) and v(x) into Eq. (1.13), it forms the following equation
To solve Eq. 1.17, the interface debonding length can be determined using the following equation:
1.2.2.4 Fiber Failure
There are relatively fewer models for the fiber failure of CMCs compared with analyses for damage mechanisms, such as matrix cracking and interface debonding. As fibers begin to break, the loads dropped by the broken fibers must be transferred to the intact fibers in the cross section. Two dominant failure criterions are present in the literature for modeling fiber failure: GLS and Local Load Sharing (LLS). The GLS criterion assumes that the load from any one fiber is transferred equally to all other intact fibers in the same cross‐section plane. The GLS assumption neglects any local stress concentrations in the neighborhood of existing breaks and is expected to be accurate when the interface shear stress is sufficiently low. Models that include GLS explicitly have been developed by Thouless and Evans (1988), Cao and Thouless (1990), Sutcu (1989), Schwietert and Steif (1990), Curtin (1991), Weitsman and Zhu (1993), Hild et al. (1994), Zhu and Weitsman (1994), Curtin et al. (1998), Paar et al. (1998), and Liao and Reifsnider (2000). The LLS assumes that the load from the broken fiber is transferred to the neighborhood intact fibers and is expected to be accurate when the interface shear stress is sufficiently high. Models that include LLS explicitly have been developed by Zhou and Curtin (1995), Dutton et al. (2000), and Xia and Curtin (2000).
The two‐parameter Weibull model is adopted to describe fiber strength distribution, and the GLS assumption is used to determine the loads carried by the intact and fracture fibers (Curtin 1991):
where 〈Tb〉 denotes the load carried by the broken fibers and P(T) denotes the fiber failure volume fraction (Curtin 1991):
where mf is the fiber Weibull modulus and σc is the fiber characteristic strength of a length δc of fiber:
where lo is the reference length and σo is the fiber reference strength of a length of lo of fiber.
When fiber fractures, the fiber stress drops to zero at the break, and the stress in the fiber builds up through the stress transfer across the fiber/matrix interface shear stress:
The sliding length lf required to build the fiber stress up to its previous intact value is given by the following equation:
The probability distribution f(x) of the distance x of a fiber break from reference matrix crack plane, provided that a break occurs within a distance ±lf, is constructed based on the Weibull statistics by Phoenix and Raj (1992):
where x ∈ [0, lf].
Using Eqs. 1.22 and 1.24, the average stress carried by the broken fiber is given by the following equation:
Substituting Eq. (1.25) into Eq. (1.19) leads to the following equation:
The load carried by the intact fibers T at the matrix crack plane for different applied stress can be obtained by solving Eq. (1.26), and then the fiber failure volume fraction can be obtained by substituting T into Eq. (1.20). When the load carried by the intact fibers reach the maximum value, composites fail. The composite ultimate tensile strength σUTS is given by the following equation:
1.2.2.5 Hysteresis Theories
When CMCs are under tensile loading, matrix cracking occurs first. As the applied stress increases, the amounts of the matrix cracks increase, partially matrix cracks deflect along fiber/matrix interface, and some matrix cracks propagate penetration through fibers, which makes fiber fracture. The interface debonded length, which includes the effect of fiber failure, is given by the following equation:
It is shown from Eq. (1.28) that, when none of the fibers fails, T = σ/Vf and ldf = ld. When ldf < lc/2, the fiber/matrix interface partially debonds; and when ldf = lc/2, the fiber/matrix interface completely debonds. Two cases of hysteresis loops are discussed in the following: (i) the interface partially debonding and the fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading; and (ii) the interface completely debonding and the fiber sliding relative to matrix in the entire matrix crack spacing upon unloading and subsequent reloading.
1.2.2.5.1 Interface Partially Debonding
When the fiber/matrix interface partially debonds, the unit cell can be divided into the interface debonded region (x ∈ [0, ldf]) and the interface bonded region (x ∈ [ldf, lc/2]). Upon unloading to the applied stress of σ (σmin < σ < σmax), the interface debonded region can be divided into the interface counter slip region (x ∈ [0, y]) and the interface slip region (x ∈ [y, ldf]).
The fiber axial stress distribution upon unloading is given by the following equation:
where
where TU denotes the stress carried by the intact fibers at the matrix crack plane upon unloading, which satisfied the relationship of the following equation:
Upon reloading to the applied stress of σ, slip again occurs near the matrix cracking plane over a distance of z, which denotes the new slip region. The interface debonded region can be divided into the new slip region (x ∈ [0, z]), counter slip region (x ∈ [z, y]), and slip region (x ∈ [y, ldf]).
The fiber axial stress distribution upon reloading is given by the following equation:
where
where TR denotes the stress carried by the intact fibers at the matrix crack plane upon reloading, which satisfies the relationship of the following equation:
where Tm satisfies the relationship of the following equation:
1.2.2.5.2 Completely Debonding of Interface
When the fiber/matrix interface completely debonds, the unit cell can be divided into the interface counter slip region (x ∈ [0, y]) and slip region (x ∈ [y, lc/2]) upon unloading.
The fiber axial stress distribution upon unloading is given by the following equation:
where
where TU denotes the stress carried by the intact fibers at the matrix crack plane upon unloading, which satisfies Eq. (1.31).
Upon reloading, the unit cell can be divided into the interface new slip region (x ∈ [0, z]), interface counter slip region (x ∈ [z, y]), and slip region (x ∈ [y, lc/2]). The fiber axial stress distribution upon reloading is given by the following equation:
where
where TR denotes the stress carried by the intact fibers at the matrix crack plane upon reloading, which satisfies Eq. (1.34).
1.2.2.5.3 Hysteresis Loops and Hysteresis‐Based Parameters
When damage forms within the composite, the composite strain can be determined using the following equation, which assumes that the composite strain is equivalent to the average strain in an undamaged fiber:
Substituting Eq. (1.29) into Eq. (1.40), the unloading stress−strain relationship for the interface partially debonding is given by the following equation:
Substituting Eq. (1.32) into Eq. (1.40), the reloading stress−strain relationship for the interface partially debonding is given by the following equation:
Substituting Eq. (1.36) into Eq. (1.40), the unloading stress−strain relationship for the interface completely debonding is given by the following equation:
Substituting Eq. (1.38) into Eq. (1.40), the reloading stress−strain relationship for the interface completely debonding is given by the following equation:
The area associated with the hysteresis loops is the dissipated energy during corresponding cycle, which is defined as the following equation:
where εc_unload and εc_reload denote unloading and reloading strain, respectively. Substituting unloading and reloading strains corresponding to the interface partially and completely debonding into Eq. (1.45), the hysteresis dissipated energy U can be obtained.
The hysteresis width Δε is defined by the following equation:
The hysteresis modulus E is defined by the following equation:
1.2.3 Results and Discussion
The fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue hysteresis width, and fatigue hysteresis modulus of unidirectional SiC/CAS composite are analyzed for different fiber volume fraction, matrix cracking density, fiber/matrix interface shear stress, and interface debonded energy.
1.2.3.1 Effect of Fiber Volume Fraction on Fatigue Hysteresis Loops and Fatigue Hysteresis‐Based Damage Parameters
The fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue hysteresis width, and fatigue hysteresis modulus of SiC/CAS composite are shown in Figure 1.2 for fiber volume fractions of Vf = 30% and 40%.
Figure 1.2 (a) The fatigue hysteresis loops at different fatigue peak stresses when the fiber volume fraction is Vf = 30%; (b) the fatigue hysteresis loops at different fatigue peak stresses when the fiber volume fraction is Vf = 40%; (c) the fatigue hysteresis dissipated energy for different fatigue peak stresses when the fiber volume fraction is Vf = 30% and 40%; (d) the fatigue hysteresis width for different fatigue peak stresses when the fiber volume fraction is Vf = 30% and 40%; and (e) the fatigue hysteresis modulus for different fatigue peak stresses when the fiber volume fraction is Vf = 30% and 40%.
When the fiber volume is Vf = 30%, the fatigue hysteresis dissipated energy increases with fatigue peak stress, i.e. from U = 22.3 kJ/m3 at the fatigue peak stress of σmax = 200 MPa to U = 178.6 kJ/m3 at the fatigue peak stress of σmax = 400 MPa; the fatigue hysteresis width increases with the fatigue peak stress, i.e. from Δε = 0.016% at the fatigue peak stress of σmax = 200 MPa to Δε = 0.067% at the fatigue peak stress of σmax = 400 MPa; and the fatigue hysteresis modulus decreases with the fatigue peak stress, i.e. from E = 99.8 GPa at the fatigue peak stress of σmax = 200 MPa to E = 85.5 GPa at the fatigue peak stress of σmax = 400 MPa.
When the fiber volume is Vf = 40%, the fatigue hysteresis dissipated energy increases with the fatigue peak stress, i.e. from U = 5.8 kJ/m3 at the fatigue peak stress of σmax
