Thermal Barrier Coatings: Failure Theory and Evaluation Technology

Contents
1 Introduction
1.1 TBCs and the Corresponding Preparation Methods
1.1.1 TBC Materials and Structures
1.1.2 TBC Preparation Methods
1.2 TBC Spallation Failure and Its Main Influencing Factors
1.2.1 Service Conditions for TBCs
1.2.2 TBC Spallation Failure and Its Main Influencing Factors
1.3 Solid Mechanics Requirements and Challenges Generated by TBC Failure
1.3.1 Solid Mechanics Requirements Generated by TBC Failure
1.3.2 Solid Mechanics Challenges Presented by TBC Failure
1.4 Content Overview
References
2 Basic Theoretical Frameworks for Thermo–Mechano-Chemical Coupling in TBCs
2.1 Continuum Mechanics
2.2 Theoretical Framework for Thermo–Mechano-Chemical Coupling Based on Small Deformation
2.2.1 Strain and Stress Measures Based on Small Deformation [5, 6]
2.2.2 Stress–Strain Constitutive Relations Based on Small Deformation [5, 6]
2.2.3 Constitutive Theory for Thermomechanical Coupling Based on Small Deformation [11]
2.2.4 Constitutive Theory for Thermo–Mechano-Chemical Coupling Based on Small Deformation [16]
2.3 Theoretical Framework for Thermo–Mechano-Chemical Coupling Based on Large Deformation
2.3.1 Kinematic Description [9]
2.3.2 Stress and Strain Measures
2.3.3 Mass Conservation and Force Equilibrium Equations
2.3.4 Constitutive Theory for Thermomechanical Coupling Based on Large Deformation [18, 25, 26]
2.3.5 Constitutive Theory for Thermo–Mechano-Chemical Coupling Based on Large Deformation
2.4 Summary and Outlook
References
3 Nonlinear FEA of TBCs on Turbine Blades
3.1 FEA Principles
3.1.1 Functional Variational Principle
3.1.2 Weak Form of the Eulerian Formulation
3.1.3 FE Discretization of the Eulerian Formulation
3.1.4 Weak Form of the Lagrangian Formulation
3.1.5 FE Discretization of the Lagrangian Formulation
3.1.6 Weak Form of the Arbitrary Lagrangian–Eulerian Formulation
3.1.7 Initial and Boundary Conditions
3.2 FE Modeling of TBCs on Turbine Blades
3.2.1 Geometric Characteristics of Turbine Blades
3.2.2 Parametric Modeling of Turbine Blades
3.3 Mesh Generation for Turbine Blades
3.3.1 Generation of Unstructured Meshes
3.3.2 Structured Meshes for Turbine Blades
3.4 Image-Based FE Modeling
3.4.1 Image-Based FEM
3.4.2 2D TGO Interface Modeling
3.4.3 Porous Ceramic Layer Modeling
3.4.4 D3 TGO Interface Modeling Method
3.5 Summary and Outlook
References
4 Geometric Nonlinearity Theory for the Interfacial Oxidation of TBCs
4.1 Interfacial Oxidation Phenomenon and Failure
4.1.1 Characteristics and Patterns of Interfacial Oxidation
4.1.2 Stress Field Induced by Interfacial Oxidation
4.1.3 Coating Spallation Induced by Interfacial Oxidation
4.2 TGO Growth Model Based on Diffusion Reaction
4.2.1 Governing Equations
4.2.2 FE Simulation
4.3 Thermo–Chemo–Mechanical Coupling Analytical Model for Interfacial Oxidation of TBCs
4.3.1 Thermo–Chemo–Mechanical Coupling Analytical Growth Model for Interfacial Oxidation
4.3.2 Thermo–Chemo–Mechanical Coupling Growth Constitutive Relations for Interfacial Oxidation
4.3.3 Analysis of the Thermo–Mechano-Chemical Coupling Growth Patterns and Mechanisms During Interfacial Oxidation
References
5 Physically Nonlinear Coupling Growth and Damage Caused by Interfacial Oxidation in TBCs
5.1 Physically Nonlinear Model for Thermo–Mechano–Chemical Coupling Growth Caused by Interfacial Oxidation in TBCs
5.1.1 Model Framework
5.1.2 Numerical Implementation
5.1.3 Results and Discussion
5.1.4 Analytical Coupling Model for Interfacial Oxidation
5.1.5 Comparison with Experimental Results
5.2 Interfacial Oxidation Failure Theory that Integrates the CZM and PFM
5.2.1 Integrated CZM and PFM Framework
5.2.2 Introduction to PFM
5.2.3 Introduction to CZM for Phase-Field Crack Interactions
5.2.4 Numerical Implementation
5.2.5 Results and Discussion
5.3 Summary and Outlook
5.3.1 Summary
5.3.2 Outlook
References
6 Thermo–Mechano–Chemical Coupling During CMAS Corrosion in TBCs
6.1 Correlation Analysis of Molten CMAS Infiltration and Its Key Influencing Factors
6.1.1 Theoretical Model for Molten CMAS Infiltration Depth in EB-PVD TBCs
6.1.2 Experiments on the Molten CMAS Infiltration Depth in an EB-PVD TBC and Its Influencing Factors
6.1.3 CMAS Infiltration Depth in the EB-PVD TBC and Its Influencing Factors
6.1.4 Infiltration of CMAS Melts in an APS TBC
6.2 Microstructural Evolution, Deformation, and Composition Loss of Coatings Due to Corrosion
6.2.1 Microstructural Evolution and Deformation of Coatings
6.2.2 Thermo–Mechano–Chemical Coupling Theory for CMAS Infiltration and Corrosion in TBCs
6.2.3 Quantitative Characterization of the Distribution Pattern of Y in TBCs Subjected to CMAS Corrosion
6.3 Phase-Structure Characterization and Phase-Field Theory for CMAS Corrosion of Coatings
6.3.1 XRD Characterization of the Evolution of the Coating Phase Structure
6.3.2 TEM Characterization of the Microstructural Evolution of Coatings
6.3.3 Thermo–Mechano–Chemical Coupling Phase-Transformation Theory for Corroded Coatings During the Cooling Process
6.4 Summary and Outlook
References
7 Erosion Failure Mechanisms of TBCs
7.1 Erosion Failure Phenomena in TBCs
7.1.1 Failure Phenomena in TBCs
7.1.2 TBC Erosion Rate
7.1.3 Comparison of the Erosion Performance of Various Coatings
7.1.4 General Pattern of the Erosion Performance of TBCs
7.2 Erosion Failure Modes of Typical TBCs
7.2.1 Erosion Failure Modes of EB-PVD TBCs
7.2.2 Erosion Failure Mode of APS TBCs [1, 15, 21]
7.2.3 Erosion Failure Mode of PS-PVD TBCs [15, 26–28, 34, 35]
7.2.4 CMAS Erosion Failure of TBCs
7.2.5 Factors Affecting the Erosion Performance of TBCs
7.3 Numerical Simulation of the Correlations Between the Erosion Parameters of TBCs
7.3.1 Dimensional Analysis Theory
7.3.2 Dimensional Analysis of Erosion in TBCs
7.3.3 Numerical Simulation Analysis of the Correlations Between Erosion Parameters
7.4 Erosion Failure Behavior Analysis Considering Microstructural Effects
7.4.1 Numerical Model of the True Microstructure of an EB-PVD TBC
7.4.2 Yield Conditions Considering the Microstructure
7.4.3 Correlation Analysis of Various Parameters in the Erosion Process
7.4.4 Analysis of Typical Erosion Failure Modes
7.5 Erosion Failure Mechanisms and Resistance Indices of TBCs
7.5.1 Erosion Resistance Index of EB-PVD TBCs
7.5.2 Resistance Index of APS TBCs
7.6 Erosion Failure Mechanism Diagrams of TBCs
7.6.1 Establishment of a Failure Mechanism Diagram from a Theoretical Perspective
7.6.2 Establishment of Failure Mechanism Diagrams for a Certain Failure Mode from a Numerical Simulation Perspective
7.7 Summary and Outlook
7.7.1 Summary
7.7.2 Outlook
References
8 Basic Mechanical Properties of TBCs and Their Characterization
8.1 In Situ Measurement of the Elastic Behavior of EB-PVD TBCs
8.1.1 DIC-Based Microbending Testing
8.1.2 Analysis of the Experimental and Numerical Simulation Results
8.1.3 Factors Affecting the Elastic Modulus Measurement Accuracy
8.2 Temporal and Spatial Correlations Between the Mechanical Properties and Microstructure of TBCs
8.2.1 Principle of the HSNM Technique in the Characterization of Microstructure and Temporal and Spatial Correlations
8.2.2 HSNM and Deconvolution Techniques
8.2.3 Characterization of the Mechanical Properties of BC Layers and Ceramic Coatings by HSNM
8.2.4 Characterization of the Phase Distribution of the Microstructure of the TBC Based on Deconvolution
8.3 Creep Behavior of TBCs
8.3.1 High-Temperature Creep Behavior of EB-PVD TBCs
8.3.2 Creep Behavior of TGOs Under Tensile Stress
8.3.3 Effects of the Creep Behavior of TBCs on Interfacial Stresses
8.4 Summary and Outlook
8.4.1 Summary
8.4.2 Outlook
References
9 Fracture Toughness Characterization of TBCs
9.1 Surface Fracture Toughness KIC Characterization of TBCs
9.1.1 Definition of Fracture Toughness
9.1.2 Surface KIC Characterization of the Pure Ceramic Surface of TBCs Using the SENB Method
9.1.3 Surface KIC Characterization of TBCs Using Three-Point Bending Combined with Acoustic Emission
9.2 Conventional Methods for Characterizing the Interfacial KIC of TBCs
9.2.1 Theoretical Model for the Interfacial KIC Characterization of TBCs
9.2.2 Interfacial KIC Characterization of TBCs Using the Three-Point Bending Method
9.3 Surface and Interfacial KIC Characterization of TBCs Using the Indentation Method
9.3.1 Surface KIC Characterization of TBCs Using the Indentation Method
9.3.2 Interfacial KIC Characterization of TBCs Using the Indentation Method
9.4 Interfacial KIC Characterization of TBCs Using the Buckling Method
9.4.1 Buckling Test for Determining the Interfacial KIC of TBCs
9.4.2 FE Simulation for the Buckling of TBC Interfacial KIC
9.4.3 Theoretical Model for the TBC Interfacial KIC Characterization Based on Buckling Delamination
9.5 Interfacial KIC Characterization of TBCs by the Blister Test
9.6 In Situ KIC Characterization of TBCs at High Temperatures
9.6.1 Surface KIC Characterization of TBCs at High Temperatures by Indentation
9.6.2 KIC Characterization of TBCs at High Temperatures by the Three-Point Bending Test
9.7 Summary and Outlook
9.7.1 Summary
9.7.2 Outlook
References
10 Residual Stresses in TBCs
10.1 Formation of Residual Stresses in TBCs
10.1.1 Causes of Residual Stresses in TBCs
10.1.2 Influencing Factors of the Residual Stresses in TBCs
10.2 Simulation and Prediction of the Residual Stresses in TBCs
10.2.1 Stress Field Evolution and Danger Zone Prediction of a Turbine Blade with a TBC
10.2.2 Analysis of the Stress Field in the Turbine Blade with a TBC Using the Fluid–Solid Coupling Method
10.3 Destructive Characterization of the Residual Stresses in TBCs
10.3.1 Characterization by the Curvature Method
10.3.2 Characterization by the Drilling Method
10.3.3 Characterization by the RCM
10.4 Nondestructive Characterization of the Residual Stresses in TBCs
10.4.1 XRD Characterization
10.4.2 Characterization by Raman Spectroscopy
10.4.3 Characterization of Residual Stresses in the TGO Layer by PLPS
10.5 Summary and Outlook
10.5.1 Summary
10.5.2 Outlook
References
11 Real-Time Acoustic Emission Characterization of Cracks in TBCs
11.1 High-Temperature AE Detection Method
11.1.1 Basic Principle of AE Detection
11.1.2 Waveguide Rod/Wire Transmission Technique for Complex High-Temperature Environments
11.1.3 AE Signal Detection Method Based on Regional Signal Selection
11.2 Analysis of the Key Parameters for Crack Pattern Recognition
11.2.1 Key Failure Modes of TBCs and the Time-Domain Characteristics of the Relevant AE Signals
11.2.2 Pattern Recognition of TBC Failure Modes Based on Characteristic Frequencies
11.2.3 Extraction of the Characteristic Parameters for Pattern Recognition Based on Cluster Analysis
11.3 Intelligent Crack Pattern Recognition Methods Based on Wavelets and Neural Networks
11.3.1 Basic Principle and Method of WT
11.3.2 Wavelet Analysis of AE Signals from TBCs Due to Damage
11.3.3 NN-Based Intelligent Method for Pattern Recognition of AE Signals
11.4 Quantitative Evaluation of the Key Damage in TBCs
11.4.1 Basic Approach for Damage Quantification
11.4.2 Quantitative Analysis of the Surface Crack Density
11.4.3 Quantitative Analysis of the Interface Cracks
11.5 Determination of TBC Failure Mechanisms Based on AE Detection
11.5.1 Failure Mechanisms Under Thermal Cycling
11.5.2 Failure Mechanism Under High-Temperature CMAS Corrosion
11.5.3 Failure Mechanism Under Gas Thermal Shock
11.6 Summary and Outlook
11.6.1 Summary
11.6.2 Outlook
References
12 Characterization of the Microstructural Evolution of TBCs by Complex Impedance Spectroscopy
12.1 Basic Principle of Characterization by CIS
12.1.1 Principle of CIS
12.1.2 Analysis of the Impedance Responses of TBCs
12.2 Numerical Simulation of the Complex Impedance Spectral Characteristics of TBCs
12.2.1 FE Principle of CIS
12.2.2 FE Model for the Complex Impedance Spectrum of a TBC
12.2.3 Complex Impedance Spectral Characteristics of TBCs
12.2.4 Asymmetric Electrode Error Correction Models
12.3 Parametric Optimization of CIS for TBCs
12.3.1 FE Simulation and Impedance Measurement
12.3.2 Optimal AC Voltage Amplitude
12.3.3 Effects of the Test Temperature and Optimal Test Temperature
12.3.4 Effect of the Electrode Size
12.3.5 Summary
12.4 Characterization of Interfacial Oxidation in TBCs by CIS
12.4.1 Equivalent Circuit for Interfacial Oxidation in TBCs
12.4.2 Measurement of the Complex Impedance Spectrum of a TBC
12.4.3 Characterization of Interfacial Oxidation by CIS
12.5 Characterization of CMAS Corrosion in TBCs with CIS
12.5.1 Measurement of the Complex Impedance Spectra of CMAS as Well as Uncorroded and CMAS-Corroded TBCs
12.5.2 Complex Impedance Spectrum Characteristics of CMAS
12.5.3 Complex Impedance Response of the CMAS-Corroded TBC
12.6 Summary and Outlook
12.6.1 Summary
12.6.2 Outlook
References
13 Nondestructive Testing of the Surface and Interfacial Damage and Internal Pores of TBCs
13.1 Characterization of the Strain Fields of TBCs Using DIC
13.1.1 Basic Principle of DIC Characterization of the Strain Field
13.1.2 Preparation of Digital Speckles
13.1.3 DIC/AE-Combined Method for Failure Criterion Analysis
13.1.4 DIC Characterization of the High-Temperature Strain Field in TBCs
13.1.5 DIC Characterization of the High-Temperature CMAS Corrosion-Induced Strain Field in a TBC
13.1.6 Evolution of the Cross-Sectional Strain Field in TBCs Coated with Different Amounts of CMAS
13.1.7 Evolution of the Surface Strain Field in a TBC Subjected to CMAS Corrosion
13.2 X-ray CT Characterization of the Pores in TBCs Under VA Corrosion
13.2.1 Principle of the CT Characterization of the Internal Structure of an Object
13.2.2 Extraction of Pores in TBCs and 3D Reconstruction of CT Images
13.2.3 CT Characterization of the Evolution of Pores in TBCs Under VA Corrosion
13.3 IRT NDT Technique and Its Current Application Status
13.3.1 Principle of IRT
13.3.2 IRT-Based Damage Detection
13.4 Summary and Outlook
13.4.1 Summary
13.4.2 Outlook
References
14 Thermal Insulation Effect of TBCs on Turbine Blades
14.1 Theoretical Analysis of the Thermal Insulation Effect
14.1.1 Heat Transfer Modes of Turbine Blades
14.1.2 Definition of the Thermal Insulation Effect of TBCs on Turbine Blades
14.1.3 Nondimensionalization of the Thermal Insulation Effect
14.2 Numerical Simulation of the Thermal Insulation Effect
14.2.1 Coupled Heat Transfer
14.2.2 Turbulence Models
14.2.3 Numerical Simulation of the Thermal Insulation Effect of TBCs
14.3 Testing Methods for the Thermal Insulation Effect
14.3.1 Setups for Simulating the Service Environment of Turbine Blades
14.3.2 Real-Time Temperature Measurement Techniques for Turbine Blades
14.3.3 An Experimental Investigation of the Thermal Insulation Effect of a TBC on a Turbine Blade
14.4 Factors Influencing the Thermal Insulation Effect
14.4.1 Influential Factors Related to the Material
14.4.2 Influencing Factors Related to the Service Environment
14.4.3 Influencing Factors Related to the Cooling Structure
14.5 Summary and Outlook
References
15 Reliability Assessment of TBCs
15.1 Basic Reliability Theory for TBCs
15.1.1 Randomness and Distribution of Property, Structural, and Environmental Parameters
15.1.2 Definition of Reliability
15.1.3 Reliability Index and Its Geometric Meaning
15.1.4 Reliability Sensitivity
15.2 Reliability Calculation Methods for TBCs
15.2.1 Second-Moment Methods
15.2.2 Monte Carlo Methods
15.2.3 Mean Value Method and Advanced Mean Value Method
15.2.4 Software-Based Numerical Calculation of the Reliability
15.3 Reliability Prediction for TBCs Under Thermal Cycling Stresses
15.3.1 Failure Criterion and Limit State Equation
15.3.2 Distributions of Basic Variables
15.3.3 Prediction of the Spallation Failure Probability of TBCs Under Thermal Cycling, pf, tc
15.3.4 Reliability Sensitivity Analysis
15.4 Reliability Assessment of TBCs Under Interfacial Oxidation
15.4.1 Failure Criterion
15.4.2 Analysis of the Statistical Characteristics of Parameters Influencing Interfacial Oxidation
15.4.3 Reliability and Sensitivity Analysis of TBCs Under Interfacial Oxidation Based on the SOSM Method
15.5 Reliability Assessment of TBCs Against Erosion Failure
15.5.1 Erosion Rate Model and Reliability Analysis Criterion for TBCs on Turbine Blades
15.5.2 Method for Calculating the Erosion Reliability of TBCs on Turbine Blades
15.5.3 Statistical Analysis of Parameters Affecting Erosion Failure
15.5.4 Erosion Failure Probability Prediction and Sensitivity Analysis of TBCs on Turbine Blades
15.6 Summary and Outlook
15.6.1 Summary
15.6.2 Outlook
References
16 Experimental Simulators for the Service Environments of TBCs
16.1 Experimental Simulators for Thermal Loads on TBCs
16.1.1 Experimental Simulator for Automatic High-Temperature Thermal Cycling
16.1.2 Facilities for Measuring the High-Temperature Contact Angle of CMAS During the CMAS Corrosion Process
16.2 Combined Thermomechanical Loading Facility for TBCs and Buckling Failure Mechanism of TBCs Under Thermomechanical Loading
16.2.1 Combined Thermomechanical Loading Testing Facilities
16.2.2 Buckling Failure Modes of TBCs Under Thermomechanical Loading
16.3 Static Thermo–Mechano-Chemical Coupling Simulators for TBCs on Turbine Blades
16.3.1 Overall Design of an Experimental TMCC Simulation and Testing Facility for TBCs on Turbine Blades
16.3.2 Introduction to the Functions of Several Typical Experimental Facilities
16.3.3 Experimental TMCC Simulation and Real-Time Testing Methods
16.4 Dynamic Experimental TMCC Simulation and Testing Facilities for TBCs on Turbine Blades
16.4.1 Overall Design of Dynamic Experimental TMCC Simulation and Testing Facilities for TBCs on Turbine Blades
16.4.2 Main Progress in Dynamic Experimental TMCC Simulation and Testing Facilities
16.4.3 Method and Performance of Dynamic Experimental TMCC Simulation and Testing
16.5 Experimental High-Temperature Vibration Simulators for TBCs on Turbine Blades
16.5.1 High-Temperature Vibration Facilities
16.5.2 Testing of TBCs Under High-Temperature Vibration
16.6 Summary and Outlook
16.6.1 Summary
16.6.2 Outlook
References