Structural Health Monitoring of Aerospace Composites

 
 
Academic Press
  • 1. Auflage
  • |
  • erschienen am 8. September 2015
  • |
  • 470 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-12-410441-9 (ISBN)
 

Structural Health Monitoring of Aerospace Composite Structures offers a comprehensive review of established and promising technologies under development in the emerging area of structural health monitoring (SHM) of aerospace composite structures.

Beginning with a description of the different types of composite damage, which differ fundamentally from the damage states encountered in metallic airframes, the book moves on to describe the SHM methods and sensors currently under consideration before considering application examples related to specific composites, SHM sensors, and detection methods. Expert author Victor Giurgiutiu closes with a valuable discussion of the advantages and limitations of various sensors and methods, helping you to make informed choices in your structure research and development.


  • The first comprehensive review of one of the most ardent research areas in aerospace structures, providing breadth and detail to bring engineers and researchers up to speed on this rapidly developing field
  • Covers the main classes of SHM sensors, including fiber optic sensors, piezoelectric wafer active sensors, electrical properties sensors and conventional resistance strain gauges, and considers their applications and limitation
  • Includes details of active approaches, including acousto-ultrasonics, vibration, frequency transfer function, guided-wave tomography, phased arrays, and electrochemical impedance spectroscopy (ECIS), among other emerging methods


Dr. Giurgiutiu is an expert in the field of Structural Health Monitoring (SHM). He leads the Laboratory for Active Materials and Smart Structures at the University of South Carolina. He received the award Structural Health Monitoring Person of the Year 2003 and is Associate Editor of the international journal Structural Health Monitoring.
  • Englisch
  • Saint Louis
  • |
  • USA
Elsevier Science
  • 23,00 MB
978-0-12-410441-9 (9780124104419)
012410441X (012410441X)
weitere Ausgaben werden ermittelt
  • Front Cover
  • Structural Health Monitoring of Aerospace Composites
  • Copyright Page
  • Dedication
  • Contents
  • 1 Introduction
  • 1.1 Preamble
  • 1.2 Why Aerospace Composites?
  • 1.3 What are Aerospace Composites?
  • 1.3.1 Definition of Aerospace Composites
  • 1.3.2 High-Performance Fibers for Aerospace Composites Applications
  • 1.3.3 High-Performance Matrices for Aerospace Composites Applications
  • 1.3.4 Advantages of Composites in Aerospace Usage
  • 1.3.5 Fabrication of Aerospace Composites
  • 1.4 Evolution of Aerospace Composites
  • 1.4.1 Early Advances
  • 1.4.2 Composite Growth in the 1960s and 1970s
  • 1.4.3 Composites Growth Since the 1980s
  • 1.5 Today's Aerospace Composites
  • 1.5.1 Boeing 787 Dreamliner
  • 1.5.2 Airbus A350 XWB
  • 1.6 Challenges for Aerospace Composites
  • 1.6.1 Concerns About the Aerospace Use of Composites
  • 1.6.2 The November 2001 Accident of AA Flight 587
  • 1.6.3 Fatigue Behavior of Composite Materials
  • 1.6.4 The Future of Composites in Aerospace
  • 1.7 About This Book
  • References
  • 2 Fundamentals of Aerospace Composite Materials
  • 2.1 Introduction
  • 2.2 Anisotropic Elasticity
  • 2.2.1 Basic Notations
  • 2.2.2 Stresses-The Stress Tensor
  • 2.2.3 Strain-Displacement Relations-The Strain Tensor
  • 2.2.4 Stress-Strain Relations
  • 2.2.4.1 Stiffness Tensor
  • Compliance Tensor
  • 2.2.4.2 From Tensor Notations to Voigt Matrix Notation
  • 2.2.4.3 Stiffness Matrix
  • 2.2.4.4 Compliance Matrix
  • 2.2.4.5 Stress-Strain Relations for an Isotropic Material
  • 2.2.5 Equation of Motion in Terms of Stresses
  • 2.2.6 Equation of Motion in Terms of Displacements
  • 2.3 Unidirectional Composite Properties
  • 2.3.1 Elastic Constants of a Unidirectional Composite
  • 2.3.2 Compliance Matrix of a Unidirectional Composite
  • 2.3.3 Stiffness Matrix of a Unidirectional Composite
  • 2.3.4 Estimation of Elastic Constants from the Constituent Properties
  • 2.3.4.1 Estimation of the Longitudinal Modulus EL
  • 2.3.4.2 Estimation of the Transverse Modulus ET
  • 2.3.4.3 Estimation of Poisson Ratio ?LT
  • 2.3.4.4 Estimation of the LT Shear Modulus GLT
  • 2.3.4.5 Estimation of Transverse Shear Modulus G23
  • 2.3.4.6 Matrix-Dominated Approximations
  • 2.4 Plane-Stress 2D Elastic Properties of a Composite Layer
  • 2.4.1 Plane-Stress 2D Compliance Matrix
  • 2.4.2 Plane-Stress 2D Stiffness Matrix
  • 2.4.3 Rotated 2D Stiffness Matrix
  • 2.4.4 Rotated 2D Compliance Matrix
  • 2.4.5 Proof of RTR-1=T-t
  • 2.5 Fully 3D Elastic Properties of a Composite Layer
  • 2.5.1 Orthotropic Stiffness Matrix
  • 2.5.2 Rotated Stiffness Matrix
  • 2.5.3 Equations of Motion for a Monoclinic Composite Layer
  • 2.5.4 Rotated Compliance Matrix
  • 2.5.5 Note on the Use of Closed-Form Expression in the C and S matrices
  • 2.5.6 Proof of RTR-1=T-t in 3D
  • 2.6 Problems and Exercises
  • References
  • 3 Vibration of Composite Structures
  • 3.1 Introduction
  • 3.1.1 Displacements for Axial-Flexural Vibration of Composite Plates
  • 3.1.2 Stress Resultants
  • 3.2 Equations of Motion in Terms of Stress Resultants
  • 3.2.1 Derivation of Equations of Motion from Free Body Diagram
  • 3.2.2 Derivation of Axial-Flexural Equations from Stress Equations of Motion
  • 3.2.2.1 Integration of u-Equation of Motion
  • 3.2.2.2 Integration of v-Equation of Motion
  • 3.2.2.3 Integration of w-Equation of Motion
  • 3.2.2.3.1 Calculation of Out-of-Plane Shear Resultant Nxz
  • 3.2.2.3.2 Calculation of Out-of-Plane Shear Resultant Nyz
  • 3.2.2.3.3 The w-Equation of Motion in Terms of Moment Stress Resultants
  • 3.2.3 Summary of Equations of Motion in Terms of Stress Resultants
  • 3.2.4 Strains in Terms of Displacements
  • 3.2.5 Strains in Terms of Mid-Surface Strains and Curvatures
  • 3.3 Vibration Equations for an Anisotropic Laminated Composite Plate
  • 3.3.1 Stress-Strain Relations for an Anisotropic Laminated Composite Plate
  • 3.3.2 Stresses in Terms of Mid-Surface Strains and Curvatures for an Anisotropic Laminated Composite Plate
  • 3.3.3 Stress Resultants in Terms of Mid-Surface Strains and Curvatures for an Anisotropic Laminated Composite Plate
  • 3.3.3.1 Matrix Representation of Stresses and Stress Resultants
  • 3.3.3.2 Stress Resultants through Stress Integration across the Thickness of an Anisotropic Laminated Composite Plate (ABD ...
  • 3.3.4 Equations of Motion in Terms of Displacements for an Anisotropic Laminated Composite Plate
  • 3.3.5 Vibration Frequencies and Modeshapes of an Anisotropic Laminated Composite Plate
  • 3.4 Vibration Equations for an Isotropic Plate
  • 3.4.1 Isotropic Stress-Strain Relations
  • 3.4.2 Stresses in Terms of Mid-Surface Strains and Curvatures for an Isotropic Plate
  • 3.4.3 Stress Resultants for an Isotropic Plate
  • 3.4.3.1 ABD Matrices for an Isotropic Plate
  • 3.4.4 Equations of Motion in Terms of Displacements for an Isotropic Plate
  • 3.4.5 Vibration Frequencies and Modeshapes of an Isotropic Plate
  • 3.4.5.1 Axial Vibration of an Isotropic Plate
  • 3.4.5.2 Flexural Vibration of an Isotropic Plate
  • 3.5 Special Cases
  • 3.5.1 Symmetric Laminates
  • 3.5.2 Isotropic Laminates
  • 3.6 Problems and Exercises
  • References
  • 4 Guided Waves in Thin-Wall Composite Structures
  • 4.1 Introduction
  • 4.1.1 Overview
  • 4.1.2 Problem Setup
  • 4.1.3 State of the Art in Modeling Guided-Wave Propagation in Laminated Composites
  • 4.1.4 Chapter Layout
  • 4.2 Wave Propagation in Bulk Composite Material-Christoffel Equations
  • 4.2.1 Equation of Motion in Terms of Displacements
  • 4.2.2 Christoffel Equation for Bulk Composites
  • 4.3 Guided Waves in a Composite Ply
  • 4.3.1 Guided Wave as a Superposition of Partial Waves
  • 4.3.2 Coherence Condition-Generalized Snell's Law
  • 4.3.3 Christoffel Equation for a Lamina
  • 4.3.4 Stresses
  • 4.3.4.1 Stress-Displacement Relation
  • 4.3.4.2 Stress-Displacement Relations under x2-Invariant Conditions
  • 4.3.4.3 Stresses in a Monoclinic Lamina under x2-Invariant Conditions
  • 4.3.4.4 Boundary Tractions for a Monoclinic Lamina
  • 4.3.4.5 Boundary Tractions in Terms of Wave Propagation
  • 4.3.5 State Vector and Field Matrix
  • 4.3.6 Dispersion Curves
  • 4.3.6.1 Boundary Conditions at Upper and Lower Faces of the Lamina
  • 4.3.6.2 Search for the Solution
  • 4.3.6.3 Modeshapes
  • 4.4 Guided-Wave Propagation in a Laminated Composite
  • 4.4.1 Global Matrix Method (GMM)
  • 4.4.2 Transfer Matrix Method (TMM)
  • 4.4.3 Stiffness Matrix Method (SMM)
  • 4.5 Numerical Computation
  • 4.6 Problems and Exercises
  • References
  • 5 Damage and Failure of Aerospace Composites
  • 5.1 Introduction
  • 5.2 Composites Damage and Failure Mechanisms
  • 5.2.1 Fiber and Matrix Stress-Strain Curves
  • 5.2.2 Failure Modes in Unidirectional Fiber-Reinforced Composites
  • 5.3 Tension Damage and Failure of a Unidirectional Composite Ply
  • 5.3.1 Strain-Controlled Tension Failure due to Fracture of the Fibers
  • 5.3.2 Statistical Effects on Unidirectional Composite Strength and Failure
  • 5.3.3 Shear-Lag Load Sharing between Broken Fibers
  • 5.3.4 Fiber Pullout
  • 5.4 Tension Damage and Failure in a Cross-Ply Composite Laminate
  • 5.4.1 Ply Discount Method
  • 5.4.2 Progressive Failure of a Cross-Ply Laminate
  • 5.4.3 Interfacial Stresses at Laminate Edges and Cracks
  • 5.4.4 Effect of Matrix Cracking on Interlaminar Stresses
  • 5.5 Characteristic Damage State (CDS)
  • 5.5.1 Definition of the Characteristic Damage State
  • 5.5.2 Damage Modes That Modify Local Stress Distribution
  • 5.5.3 Stiffness Evolution with Damage Accumulation
  • 5.6 Fatigue Damage in Aerospace Composites
  • 5.6.1 Fatigue of Unidirectional Composites
  • 5.6.2 Fatigue of Cross-Ply Composite Laminate
  • 5.7 Long-Term Fatigue Behavior of Aerospace Composites
  • 5.7.1 Damage Region I-Progression toward Widespread CDS
  • 5.7.2 Damage Region II-Crack Coupling and Delamination
  • 5.7.2.1 Edge Cracks versus Internal Cracks
  • 5.7.2.2 Comparison between Region I and Region II
  • 5.7.2.2.1 Phenomenological Comparison
  • 5.7.2.2.2 Stress-Distribution Comparison
  • 5.7.3 Damage Region III-Damage Acceleration and Final Failure
  • 5.7.3.1 Stiffness-Damage Correlation in Region III toward Composite End of Life
  • 5.7.3.2 Role of Fiber Fracture in Final Failure
  • 5.7.4 Summary of Long-Term Fatigue Behavior of Composites
  • 5.8 Compression Fatigue Damage and Failure in Aerospace Composites
  • 5.8.1 Compression Fatigue Delamination Damage
  • 5.8.2 Compression Fatigue Local Microbuckling Damage
  • 5.8.3 Compression Fatigue Damage under Combined Tension-Compression Loading
  • 5.9 Other Composite Damage Types
  • 5.9.1 Fastener Hole Damage in Composites
  • 5.9.2 Impact Damage in Composites
  • 5.9.3 Composite Sandwich Damage
  • 5.9.3.1 Skin Damage
  • 5.9.3.2 Interface Damage
  • 5.9.3.3 Core Damage
  • 5.9.4 Damage in Adhesive Composite Joints
  • 5.10 Fabrication Defects versus In-service Damage
  • 5.10.1 Fabrication Defects
  • 5.10.2 In-service Damage
  • 5.11 What Could SHM Systems Aim to Detect?
  • 5.12 Summary and Conclusions
  • References
  • 6 Piezoelectric Wafer Active Sensors
  • 6.1 Introduction
  • 6.1.1 SMART LayerT and SMART SuitcaseT
  • 6.1.2 Advantages of PWAS Transducers
  • 6.2 PWAS Construction and Operational Principles
  • 6.3 Coupling Between the PWAS Transducer and the Monitored Structure
  • 6.3.1 1D Analysis of PWAS Coupling
  • 6.3.1.1 Shear-Lag Solution for 1D Coupling
  • 6.3.1.2 Ideal-Bonding Solution: Pin-Force Model
  • 6.3.1.3 Effective Pin-Force Model for Nonideal Bonding
  • 6.3.2 Shear-Layer Analysis for a Circular PWAS
  • 6.3.2.1 Shear-Lag Solution for Circular PWAS
  • 6.3.2.2 Effective Line-Force Model for a Circular PWAS
  • 6.3.2.3 Ideal-Bonding Solution for a Circular PWAS
  • 6.4 Tuning Between PWAS Transducers and Structural Guided Waves
  • 6.4.1 Lamb-Wave Tuning with Linear PWAS Transducers
  • 6.4.1.1 Solution of Lamb-Wave PWAS Tuning with Shear Lag in the Bonding Layer
  • 6.4.1.2 Lamb-Wave PWAS Tuning at Low Frequencies
  • 6.4.1.3 Ideal-Bonding Solution for Lamb-Wave PWAS Tuning
  • 6.4.1.4 Experimental Verification of the Lamb-Wave PWAS-Tuning Phenomenon
  • 6.4.2 Lamb-Wave Tuning with Circular PWAS
  • 6.4.2.1 General Solution for Circular Lamb-Wave Tuning
  • 6.4.2.2 Ideal-Bonding Solution for Circular Lamb-Waves Tuning
  • 6.5 Wave Propagation SHM with PWAS Transducers
  • 6.5.1 Pitch-Catch Guided-Wave Propagation SHM
  • 6.5.2 Pulse-Echo Guided-Wave Propagation SHM
  • 6.5.2.1 Simulation of Axial Waves
  • 6.5.2.2 Simulation of Flexural Waves
  • 6.5.2.3 Comparison between Axial and Flexural Wave Simulation Results
  • 6.5.2.4 The Importance of High-Frequency Excitation
  • 6.5.3 Impact and AE Wave Propagation SHM
  • 6.6 PWAS Phased Arrays and the Embedded Ultrasonics Structural Radar
  • 6.6.1 Phased-Array Processing Concepts
  • 6.6.1.1 Generic Delay-and-Sum Beamforming
  • 6.6.2 Beamforming Formulae for 2D PWAS Phased Arrays
  • 6.6.2.1 Near Field: Exact Traveling Path Analysis (Triangular Algorithm)
  • 6.6.2.2 Far Field: Parallel-Ray Approximation (Parallel Algorithm)
  • 6.6.3 Linear PWAS Phased Arrays
  • 6.6.3.1 Far-Field Parallel-Ray Approximation
  • 6.6.3.2 Firing with Time Delays
  • 6.6.3.3 Transmitter Beamforming
  • 6.6.3.4 Receiver Beamforming
  • 6.6.3.5 Phased-Array Pulse-Echo
  • 6.6.3.6 Damage Detection with Tuned PWAS Phased Arrays
  • 6.6.4 Embedded Ultrasonics Structural Radar
  • 6.6.4.1 The EUSR Concept
  • 6.6.4.2 Practical Implementation of the EUSR Algorithm
  • 6.6.5 EUSR System Design and Experimental Validation
  • 6.6.5.1 Experimental Setup
  • 6.6.5.2 Implementation of the EUSR Data-Processing Algorithm
  • 6.7 PWAS Resonators
  • 6.7.1 Linear PWAS Resonators
  • 6.7.1.1 Resonances and Anti-Resonances of Linear PWAS Resonators
  • 6.7.1.2 Admittance and Impedance Formulae with Damping
  • 6.7.2 Circular PWAS Resonators
  • 6.7.2.1 Resonances and Anti-Resonances of Circular PWAS Resonators
  • 6.7.2.2 Admittance and Impedance Formulae with Damping
  • 6.7.3 Constrained Linear PWAS Resonators
  • 6.7.4 Constrained Circular PWAS Resonators
  • 6.8 High-Frequency Vibration SHM with PWAS Modal Sensors-The Electromechanical (E/M) Impedance Technique
  • 6.8.1 Linear PWAS Modal Sensors
  • 6.8.1.1 E/M Admittance of a PWAS Transducer Attached to a 1D Beam Structure
  • 6.8.1.2 Frequency-Dependent Structural Stiffness of 1D Beam Structure
  • 6.8.1.3 Detection of Structural Resonances from ReZ(?) and ReY(?) of 1D Structures
  • 6.8.2 Circular PWAS Modal Sensors
  • 6.8.2.1 E/M Admittance of a PWAS Transducer Attached to a 2D Circular-Plate Structure
  • 6.8.2.2 Frequency-Dependent Structural Stiffness of 2D Circular-Plate Structure
  • 6.8.2.3 Detection of Structural Resonances from ReZ(?) and ReY(?) of 2D Structures
  • 6.8.3 Damage Detection with PWAS Modal Sensors and the E/M Impedance Technique
  • References
  • 7 Fiber-Optic Sensors
  • 7.1 Introduction
  • 7.1.1 Intensity Modulation Fiber-Optic Sensors
  • 7.1.2 Polarization Modulation Fiber-Optic Sensors
  • 7.1.3 Phase Modulation Fiber-Optic Sensors
  • 7.1.4 Spectral Modulation Fiber-Optic Sensors
  • 7.1.5 Scattering Modulation Fiber-Optic Sensors
  • 7.2 General Principles of Fiber Optic Sensing
  • 7.2.1 Total Internal Reflection
  • 7.2.2 Single-Mode and Multimode Optical Fibers
  • 7.3 Interferometric Fiber-Optic Sensors
  • 7.3.1 Mach-Zehnder and Michelson Interferometers
  • 7.3.2 Intrinsic Fabry-Perot Sensors
  • 7.3.3 Extrinsic Fabry-Perot Interferometric Sensors
  • 7.3.4 Transmission EFPI Fiber-Optic Sensors
  • 7.3.5 In-line Fiber Etalon Sensors
  • 7.4 FBG Optical Sensors
  • 7.4.1 FBG Principles
  • 7.4.1.1 Strain Measuring Principle
  • 7.4.1.2 Refined FBG Patterns
  • 7.4.2 Fabrication of FBG Sensors
  • 7.4.3 Conditioning Equipment for FBG Sensors
  • 7.4.3.1 Optical Spectrum Analyzer Methods for Conditioning FBG Sensors
  • 7.4.3.2 Scanning FP Filter Methods for Conditioning FBG Sensors
  • 7.4.3.3 Interferometric Methods for Conditioning FBG Sensors
  • 7.4.4 FBG Demodulators for Ultrasonic Frequencies
  • 7.4.4.1 Dual (Quasi-Static+Ultrasonic) FBG Sensing
  • 7.4.4.2 Fabry-Perot Tunable Filter for Ultrasonic FBG Demodulation
  • 7.4.4.3 Tunable Narrow-Linewidth Laser Source for Ultrasonic FBG Demodulation
  • 7.4.4.4 Chirped-FBG Filter for Ultrasonic FBG Demodulation
  • 7.4.4.5 Array Waveguide Grating Filter for Ultrasonic FBG Demodulation
  • 7.4.4.6 Two-Wave Mixing Photorefractive Crystal for Ultrasonic FBG Demodulation
  • 7.4.5 FBG Rosettes
  • 7.4.6 Long-Gage FBG Sensors
  • 7.4.7 Temperature Compensation in FBG Sensing
  • 7.4.7.1 Temperature Compensation through Coefficients of Thermal Expansion Difference between Two Materials
  • 7.4.7.2 FBG Temperature Sensor
  • 7.4.7.3 Hybrid FBG/EFPI Sensors
  • 7.5 Intensity-Modulated Fiber-Optic Sensors
  • 7.5.1 Typical Intensity-Modulated Fiber-Optic Sensors
  • 7.5.2 Intensity-Based Optical Fiber Sensors
  • 7.6 Distributed Optical Fiber Sensing
  • 7.6.1 Optical Time Domain Reflectometry
  • 7.6.2 Brillouin Optical Time Domain Reflectometry
  • 7.6.3 Continuous Fiber Sensing Using Rayleigh Backscatter
  • 7.6.4 Fiber-Optic Temperature Laser Radar
  • 7.7 Triboluminescence Fiber-Optic Sensors
  • 7.8 Polarimetric Optical Sensors
  • 7.9 Summary and Conclusions
  • References
  • 8 Other Sensors for SHM of Aerospace Composites
  • 8.1 Introduction
  • 8.2 Conventional Resistance Strain Gages
  • 8.2.1 Resistance Strain Gage Principles
  • 8.2.2 Strain Gage Instrumentation
  • 8.2.3 Aerospace Strain Gage Technology
  • 8.2.4 Strain Gage Usage in Aerospace Composites
  • 8.3 Electrical Property Sensors
  • 8.3.1 Electrical Resistance and Electrical Potential Methods for Composites SHM
  • 8.3.1.1 Electrodes Fabrication on Composite Materials for Electrical SHM Measurements
  • 8.3.1.2 Measurement of the Electrical Resistance
  • 8.3.1.3 Electrical Resistance and Electrical Potential Methods
  • 8.3.1.3.1 Electrical Resistance Method
  • 8.3.1.3.2 Electrical Potential Method
  • 8.3.1.4 Wireless Sensing for Remote Electrical Resistance Monitoring of Aerospace Composites
  • 8.3.1.5 Special-Built Composites for Resistance-Based Self-sensing Electric SHM
  • 8.3.2 Frequency Domain Methods for Electrical SHM of Aerospace Composites
  • 8.3.2.1 Electrochemical Impedance Spectroscopy for Composites SHM
  • 8.3.2.2 Electromagnetic SHM of Composites
  • References
  • 9 Impact and Acoustic Emission Monitoring for Aerospace Composites SHM
  • 9.1 Introduction
  • 9.2 Impact Monitoring-PSD
  • 9.2.1 PSD for Impact Location and Force Identification
  • 9.2.2 Triangulation Example
  • 9.2.3 Model-Based Impact Monitoring
  • 9.2.3.1 Structural Model Approach to Impact Identification
  • 9.2.3.2 System ID Approach to Impact Identification
  • 9.2.3.3 Hybrid System ID-Structural Model Approach to Impact Identification
  • 9.2.4 Data-Driven Impact Monitoring
  • 9.2.5 Directional Sensors Approach to Impact Detection
  • 9.2.6 AE Monitoring
  • 9.2.7 Simultaneous Monitoring of Impact and AE Events
  • 9.3 Impact Damage Detection-ASD and Acousto-ultrasonics
  • 9.3.1 ASD with Piezo Transmitters and Piezo Receivers
  • 9.3.2 ASD with Piezo Transmitters and Fiber-Optic Receivers
  • 9.3.3 Guided-Wave Tomography and Data-Driven ASD
  • 9.3.4 PWAS Pulse-Echo Crack Detection in Composite Beam
  • 9.3.5 Phased Arrays and Directional Transducers
  • 9.4 Other Methods for Impact Damage Detection
  • 9.4.1 Direct Methods for Impact Damage Detection
  • 9.4.2 Strain-Mapping Methods for Damage Detection
  • 9.4.3 Vibration SHM of Composites
  • 9.4.3.1 Model-Based Vibration SHM
  • 9.4.3.2 Model-Free Vibration SHM
  • 9.4.3.3 Statistics-Based Vibration SHM
  • 9.4.3.4 Nonlinear Vibration SHM
  • 9.4.3.5 Combined Vibration-Wave Propagation Methods for Impact Damage Detection
  • 9.4.4 Frequency Transfer Function SHM of Composites
  • 9.4.5 Local-Area Active Sensing with EMIS Method
  • 9.5 Electrical and Electromagnetic Field Methods for Delamination Detection
  • 9.5.1 Delamination Detection with the Electrical Resistance Method
  • 9.5.1.1 Electrical Resistance Change Method for Delamination Detection in Cross-Ply CFRP Laminates
  • 9.5.1.2 Wireless Electrical Resistance Method for Delamination Detection
  • 9.5.1.3 EIT Method for Delamination Detection with the Electrical Resistance Method
  • 9.5.1.4 Delamination Detection in Filament-Wound CFRP Composite Cylinder with the Electrical Resistance Method
  • 9.5.1.5 Multiphysics Simulation of the Electrical Resistance Change Method
  • 9.5.2 Delamination Detection with the Electrical Potential Method
  • 9.5.3 Electromagnetic Damage Detection in Aerospace Composites
  • 9.5.4 Hybrid Electromagnetic SHM of Aerospace Composites
  • 9.5.5 Self-Sensing Electrical Resistance-Based Damage Detection and Localization
  • 9.6 PSD and ASD of Sandwich Composite Structures
  • 9.7 Summary and Conclusions
  • References
  • 10 SHM of Fatigue Degradation and Other In-Service Damage of Aerospace Composites
  • 10.1 Introduction
  • 10.2 Monitoring of Strain, Acoustic Emission, and Operational Loads
  • 10.2.1 Strain Distribution Monitoring
  • 10.2.1.1 Strain Distribution Monitoring in a Composite Patch Repair
  • 10.2.1.2 Conventional Strain-Gage Monitoring for Delamination Detection
  • 10.2.1.3 Combined Fiber Optics and Conventional Strain-Gage Monitoring for Delamination Detection
  • 10.2.1.4 Delamination Occurrence Detection and Growth Monitoring with Specialty FBG Sensors
  • 10.2.2 Composite Panel Buckling Monitoring
  • 10.3 Acoustic Emission Monitoring
  • 10.4 Simultaneous Monitoring of Strain and Acoustic Emission
  • 10.5 Fatigue Damage Monitoring
  • 10.5.1 Fiber-Optic Monitoring of Transverse Cracks in Cross-ply Composites
  • 10.5.2 Pitch-Catch Guided-Wave Detection of Fatigue Microcracking and Delamination
  • 10.5.3 ECIS Monitoring of Composites Fatigue Damage
  • 10.6 Monitoring of In-service Degradation and Fatigue with the Electrical Resistance Method
  • 10.6.1 Fundamentals of the Electrical Resistance Method
  • 10.6.2 Electrical Resistance SHM of CFRP Composites
  • 10.6.3 Electrical Resistance SHM of CNT Doped GFRP Composites
  • 10.6.4 Wireless Sensing Using the Electrical Resistance Method
  • 10.7 Disbonds and Delamination Detection and Monitoring
  • 10.7.1 Disbond and Delamination Detection with Conventional Ultrasonics Guided Waves
  • 10.7.2 Monitoring of Composite Patch Repairs
  • 10.7.3 Monitoring of Composite Adhesive Joints
  • 10.7.4 Dielectrical SHM of Delamination and Water Seapage in GFRP Composites
  • 10.8 Summary, Conclusions, and Suggestions for Further Work
  • References
  • 11 Summary and Conclusions
  • 11.1 Overview
  • 11.2 Composites Behavior and Response
  • 11.3 Damage and Failure of Aerospace Composites
  • 11.4 Sensors for SHM of Aerospace Composites
  • 11.5 Monitoring of Impact Damage Initiation and Growth in Aerospace Composites
  • 11.6 Monitoring of Fatigue Damage Initiation and Growth in Aerospace Composites
  • 11.7 Summary and Conclusions
  • Index
  • Back Cover
Chapter 2

Fundamentals of Aerospace Composite Materials


This chapter is dedicated to the discussion of fundamental aspect of composite materials. The basic principles and notations of anisotropic elasticity theory are reviewed in tensor notations and then converted to Voigt matrix notations. Strain-displacement and stress-strain relations, equation of motion in terms of stresses, and the equation of motion in terms of displacements are introduced. Attention is next focused on the unidirectional composite lamina: formulae for the estimation of lamina elastic properties from the properties of the constituent fiber and matrix were presented in principal axes. The elastic constants in the longitudinal (L), transverse (T), in-plane shear (LT), and transverse shear (23) directions are deduced and the corresponding stiffness and compliance matrices are presented and related to the constitutive fiber and matrix properties. The properties of the rotated unidirectional lamina are considered next, first under the plane-stress (2D) assumption, and then in the fully 3D case. The 2D and 3D rotation matrices are deduced and applied to obtain the rotated 2D and 3D compliance and stiffness matrices. The proof of some of the more intricate steps during this process is also given as separate sections.

Keywords


Composites; aerospace composites; stiffness matrix; compliance matrix; stress tensor; strain tensor; Voigt notations; strain-stress relations; strain-displacement relations; equation of motion; longitudinal modulus; transverse modulus; in-plane shear modulus; transverse-shear modulus; rotation matrix; rotated compliance matrix; rotated stiffness matrix

Outline

2.1 Introduction 26

2.2 Anisotropic Elasticity 27

2.2.1 Basic Notations 28

2.2.2 Stresses-The Stress Tensor 28

2.2.3 Strain-Displacement Relations-The Strain Tensor 29

2.2.4 Stress-Strain Relations 29

2.2.4.1 Stiffness Tensor; Compliance Tensor 29

2.2.4.2 From Tensor Notations to Voigt Matrix Notation 30

2.2.4.3 Stiffness Matrix 32

2.2.4.4 Compliance Matrix 33

2.2.4.5 Stress-Strain Relations for an Isotropic Material 34

2.2.5 Equation of Motion in Terms of Stresses 35

2.2.6 Equation of Motion in Terms of Displacements 35

2.3 Unidirectional Composite Properties 37

2.3.1 Elastic Constants of a Unidirectional Composite 37

2.3.2 Compliance Matrix of a Unidirectional Composite 38

2.3.3 Stiffness Matrix of a Unidirectional Composite 40

2.3.4 Estimation of Elastic Constants from the Constituent Properties 41

2.3.4.1 Estimation of the Longitudinal Modulus EL 41

2.3.4.2 Estimation of the Transverse Modulus ET 42

2.3.4.3 Estimation of Poisson Ratio ?LT 44

2.3.4.4 Estimation of the LT Shear Modulus GLT 45

2.3.4.5 Estimation of Transverse Shear Modulus G23 46

2.3.4.6 Matrix-Dominated Approximations 47

2.4 Plane-Stress 2D Elastic Properties of a Composite Layer 47

2.4.1 Plane-Stress 2D Compliance Matrix 47

2.4.2 Plane-Stress 2D Stiffness Matrix 48

2.4.3 Rotated 2D Stiffness Matrix 49

2.4.4 Rotated 2D Compliance Matrix 52

2.4.5 Proof of RTR-1=T-t 53

2.5 Fully 3D Elastic Properties of a Composite Layer 54

2.5.1 Orthotropic Stiffness Matrix 55

2.5.2 Rotated Stiffness Matrix 56

2.5.3 Equations of Motion for a Monoclinic Composite Layer 61

2.5.4 Rotated Compliance Matrix 62

2.5.5 Note on the Use of Closed-Form Expression in the C and S matrices 63

2.5.6 Proof of RTR-1=T-t in 3D 63

2.6 Problems and Exercises 65

References 65

2.1 Introduction


Aerospace composite materials are made of high-strength fibers embedded in a polymeric matrix. Glass-fiber-reinforced polymer (GFRP), carbon-fiber-reinforced polymer (CFRP), and Kevlar-fiber-reinforced polymer (KFRP) are among the most common aerospace composite materials.

Aerospace composite structures are obtained through the overlapping of several unidirectional layers with various angle orientations as required by the stacking sequence. Thus, we distinguish a stack of laminae (a.k.a. plies) bonded together to act as an integral structural element. Each ply (a.k.a. lamina) may have its own orientation with respect to a global system of axes -y (Figure 1). The information about the orientation of all the plies in the laminate is contained in the stacking sequence. For example, 0/90/45/-45]s signifies a laminate made of °, °, and 45° plies placed in a sequence that is symmetric about the laminate mid-surface, i.e., °, °, 45°, 45°, 45°, 45°, °, °. This laminate has =8 plies and its stacking vector is

?]=[0°90°+45°-45°-45°+45°90°0°]t (1)

(1)
Figure 1 Composite laminates: (a) layup made up of a stack of composite laminae (a.k.a. plies) with various orientations ; (b) longitudinal, transverse, and shear definitions in a lamina (ply) [1].

The plies in the stacking sequence may be of same composite material (e.g., CFRP) or of different materials (e.g., some CFRP, some GFRP, others KFRP, etc.).

The question that composites lamination theory has to answer could be stated as follows: "Given a certain stacking sequence and a set of external loads, what is the structural response of the composite laminate?" In order to address this question, we need to analyze the mechanics of the composite laminate: first we would analyze the local mechanics of an individual layer (a.k.a. lamina) and then apply a stacking analysis (lamination theory) to determine the global properties of the laminated composite and its response under load.

2.2 Anisotropic Elasticity


This section recalls some basic definitions and relations that are essential for the analysis of anisotropic elastic structures such as aerospace composites.

2.2.1 Basic Notations


?x()=(·)´and??t()=(·) (2)

(2)

ij={1ifi=j0otherwise(Kroneckerdelta) (3)

(3)

)ii=()11+()22+()33(Einsteinimpliedsummation) (4)

(4)

)i,j=?()i?xj(differentiationshorthand) (5)

(5)

2.2.2 Stresses-The Stress Tensor


In 1x2x3 notations, the stress tensor is defined as

iji,j=1,2,3(stresstensor) (6)

(6)

where the first index indicates the surface on which the stress acts and the second index indicates the direction of the stress; thus, ij signifies the stress on the surface of normal i acting in the direction j. The strain tensor is symmetric, i.e.,

ji=siji,j=1,2,3(symmetryofstresstensorinx1x2x3notations) (7)

(7)

The stress tensor can be represented in an array form as

sij]=[s11s12s13s13s22s23s13s23s33] (8)

(8)

The array in Eq. (8) was written with the symmetry properties of Eq. (7) already included. In yz notations, Eq. (6) is written as

iji,j=x,y,z (9)

(9)

Hence, Eq. (8) becomes

sij]=[sxxsxysxzsxysyysyzsxzsyzszz] (10)

(10)

The stress symmetry in yz notations is expressed as

yx=sxyszy=syzszx=sxz(symmetryofstresstensorinxyznotations) (11)

(11)

2.2.3 Strain-Displacement Relations-The...


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