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Advanced Ceramics and Composites 5 Series Editor: Longbiao Li Longbiao Li Vibration Behavior in Ceramic-Matrix Composites Advanced Ceramics and Composites Volume 5 Series Editor Longbiao Li , College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China The book series “Advanced Ceramics and Composites” publishes insights and latest research results on advanced ceramics and composites, as well as the applications of these materials. The intent is to cover all the technical contents, applications, and multidisciplinary aspects of Advanced Ceramics and Composites. The objective of the book series is to publish monographs, reference works, selected contributions from specialized conferences, and textbooks with high quality in the field advanced ceramics and composite materials. The series provides valuable references to a wide audience in research community in materials science, research and development personnel of ceramic and composite materials, industry practi- tioners and anyone else who are looking to expand their knowledge of ceramics and composites. Longbiao Li Vibration Behavior in Ceramic-Matrix Composites Longbiao Li College of Civil Aviation Nanjing University of Aeronautics and Astronautics Nanjing, Jiangsu, China ISSN 2662-9305 ISSN 2662-9313 (electronic) Advanced Ceramics and Composites ISBN 978-981-19-7837-1 ISBN 978-981-19-7838-8 (eBook) https://doi.org/10.1007/978-981-19-7838-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore To My Son Shengning Li Preface Ceramic-matrix composites (CMCs) possess a great potential for the application in hot-section components of aeroengines due to their low density, high-temperature resistance, and oxidation resistance. The high-temperature components in aeroengines mainly include combustion chambers, turbines, and nozzles. Currently, the temperature resistance limit of high-temperature alloys is maintained around 1100 oC, but the application of CMCs increases the temperature resistance of hot- section components to 1200–1350 oC, and the mass of CMC components is usually 1/4–1/3 of the mass of nickel-based alloy components, which can reduce the specific fuel consumption by increasing the operating temperature and reducing the mass of components. This book focuses on the vibration behavior in CMCs, as follows: • The vibration natural frequency of 2D SiC/SiC composite under tensile loading was investigated. Nonlinear damage and fracture are mainly attributed to damage mechanisms of matrix cracking, interface debonding, and fibers fracture. Under cyclic loading/unloading, hysteresis loops appeared due to internal frictional slip between the fiber and the matrix and the natural frequency were obtained for different peak stress. A micromechanical tensile and cyclic loading/unloading constitutive model was adopted to predict the tensile curves. Microdamage param- eters of interface debonding ratio and broken fibers fraction were used to char- acterize tensile damage and fracture. Relationships between natural frequency, interface debonding, and fibers fracture were established. • The vibration damping in fiber-reinforced CMCs was investigated considering fibers debonding and fracture. Micromehcanical vibration damping models were developed considering multiple damage mechanisms. Relationships between the damping of CMCs, damping of fiber and the matrix, damping caused by frictional slip between the fiber and the matrix, and fiber debonding and fracture were established. Effects of fiber volume, matrix crack spacing, interface shear stress, interface debonding energy, fiber strength and fiber Weibull modulus on the damping of CMCs, interface debonding and slip between the fiber and the matrix, and fiber broken fraction were analyzed. Experimental damping of 2D C/SiC composite was predicted. vii viii Preface • The temperature-dependent vibration damping in C/SiC composites with different fiber preforms under different vibration frequencies was investigated. A micromechanical temperature-dependent vibration damping model was developed to estab- lish the relationship between composite damping, material properties, internal damage mechanisms, and temperature. Effects of fiber volume, matrix crack spacing, and interface properties on temperature-dependent vibration damping of CMCs and interface damage were analyzed. Experimental temperature-dependent composite damping of 2D and 3D C/SiC composites was predicted for different loading frequencies. • A time-dependent vibration damping model of fiber-reinforced CMCs was developed. Considering time-and temperature-dependent interface damages of oxidation, debonding, and slip, relationships between composite vibration damping, material properties, internal damages, oxidation duration, and temperature were established. Effects of material properties, vibration stress, damage state, and oxidation temperature on time-dependent composite vibration damping and interface damages of C/SiC composite were discussed. • A cyclic-dependent vibration damping model of fiber-reinforced CMCs was developed. Combining cyclic-dependent damage mechanisms, damage models, and dissipated energy model, relationships between composite vibration damping, cyclic-dependent damage mechanisms, vibration stress, and applied cycle number were established. Effects of material properties and damage state on composite vibration damping were analyzed for different applied cycle number and vibration stress. Experimental composite vibration damping of 2D and 3D C/SiC composites without/with coating was predicted for different vibration frequencies and applied cycle number. I hope this book can help the material scientists and engineering designers to understand and master the vibration behavior of ceramic-matrix composites. Nanjing, China Longbiao Li September 2022 Contents 1 Introduction ................................................... 1 1.1 Application Background of Ceramic-Matrix Composites ......... 1 1.2 Vibration Behavior in Ceramic-Matrix Composites .............. 3 1.2.1 Vibration Natural Frequency of CMCs .................. 3 1.2.2 Vibration Damping of CMCs .......................... 5 1.3 Summary and Conclusions ................................... 11 References ..................................................... 14 2 Vibration Natural Frequency of Ceramic-Matrix Composites ...... 15 2.1 Introduction ............................................... 15 2.2 Materials and Experimental Procedures ........................ 16 2.3 Theoretical Models ......................................... 16 2.4 Results and Discussions ..................................... 17 2.5 Summary and Conclusions ................................... 19 References ..................................................... 20 3 Vibration Damping of Ceramic-Matrix Composites Considering Fiber Debonding and Fracture ....................... 21 3.1 Introduction ............................................... 21 3.2 Micromechanical Damping Models of Ceramic-Matrix Composites ................................................ 22 3.2.1 Damping in Intact Ceramic-Matrix Composites ........... 24 3.2.2 Damping in Damaged Ceramic-Matrix Composites ....... 25 3.3 Result and Discussion ....................................... 28 3.3.1 Effect of Fiber Volume on Damping of Ceramic-Matrix Composites ......................................... 28 3.3.2 Effect of Matrix Crack Spacing on Damping of Ceramic-Matrix Composites ........................ 30 3.3.3 Effect of Interface Shear Stress on Damping of Ceramic-Matrix Composites ........................ 31 3.3.4 Effect of Interface Debonding Energy on Damping of Ceramic-Matrix Composites ........................ 31 ix x Contents 3.3.5 Effect of Fiber Strength on Damping of Ceramic-Matrix Composites ........................ 33 3.3.6 Effect of Fiber Weibull Modulus on Damping of Ceramic-Matrix Composites ........................ 35 3.3.7 Comparison of Damping of Ceramic-Matrix Composites without/with Considering Fiber Failure ....... 37 3.4 Experimental Comparison ................................... 39 3.5 Summary and Conclusion ................................... 41 References ..................................................... 41 4 Temperature-Dependent Vibration Damping of Ceramic-Matrix Composites .................................. 43 4.1 Introduction ............................................... 43 4.2 Temperature-Dependent Micromechanical Vibration Damping Models ........................................... 44 4.3 Results and Discussions ..................................... 47 4.3.1 Effect of Fiber Volume on Temperature-Dependent Damping of C/SiC Composite ......................... 48 4.3.2 Effect of Matrix Crack Spacing on Temperature-Dependent Damping of C/SiC Composite .......................................... 48 4.3.3 Effect of Interface Debonding Energy on Temperature-Dependent Damping of C/SiC Composite .......................................... 50 4.3.4 Effect of Steady-State Interface Shear Stress on Temperature-Dependent Damping of C/SiC Composite .......................................... 52 4.4 Experimental Comparisons .................................. 54 4.4.1 2D C/SiC ........................................... 54 4.4.2 3D C/SiC ........................................... 58 4.5 Discussions ................................................ 67 4.6 Summary and Conclusions ................................... 68 References ..................................................... 68 5 Time-Dependent Vibration Damping of Ceramic-Matrix Composites .................................................... 71 5.1 Introduction ............................................... 71 5.1.1 Time-Dependent Micromechanical Vibration Damping Models .................................... 72 5.2 Results and Discussion ...................................... 75 5.2.1 Effect of Fiber Volume on Time-Dependent Vibration Damping of C/SiC Composite ......................... 76 5.2.2 Effect of Vibration Stress on Time-Dependent Vibration Damping of C/SiC Composite ................. 79 5.2.3 Effect of Matrix Crack Spacing on Time-Dependent Vibration Damping of C/SiC Composite ................. 82