Austenitic welds and dissimilar welds are extensively used in primary circuit pipes and pressure vessels in nuclear power plants, chemical industries and fossil fuelled power plants because of their high fracture toughness, resistance to corrosion and creep at elevated temperatures. However, cracks may initiate in these weld materials during fabrication process or stress operations in service. Thus, it is very important to evaluate the structural integrity of these materials using highly reliable non-destructive testing (NDT) methods.
Ultrasonic non-destructive inspection of austenitic welds and dissimilar weld components is complicated because of anisotropic columnar grain structure leading to beam splitting and beam deflection. Simulation tools play an important role in developing advanced reliable ultrasonic testing (UT) techniques and optimizing experimental parameters for inspection of austenitic welds and dissimilar weld components.
The main aim of the thesis is to develop a 3D ray tracing model for quantitative evaluation of ultrasonic wave propagation in an inhomogeneous anisotropic austenitic weld material. Inhomogenity in the anisotropic weld material is represented by discretizing into several homogeneous layers. According to ray tracing model, ultrasonic ray paths are traced during its energy propagation through various discretized layers of the material and at each interface the problem of reflection and transmission is solved. The influence of anisotropy on ultrasonic reflection and transmission behaviour in an anisotropic austenitic weld material are quantitatively analyzed in three dimensions. The ultrasonic beam directivity in columnar grained austenitic steel material is determined three dimensionally using Lamb’s reciprocity theorem. The developed ray tracing model evaluates the transducer excited ultrasonic fields accurately by taking into account the directivity of the transducer, divergence of the ray bundle, density of rays and phase relations as well as transmission coefficients. The ray tracing model is able to determine the ultrasonic wave fields generated by a point source as well as finite dimension array transducers.

Acknowledgements IX

Zusammenfassung XI

Abstract XV

1 Introduction: Statement of the Problem and Status of Research 1

1.1 Importance of Austenitic Weld Materials 1

      1.1.1 Microstructure of the Austenitic Weld Material 1

      1.1.2 Symmetry of the Austenitic Weld Material 3

1.2 Non-Destructive Testing and Evaluation of Austenitic Welds 5

      1.2.1 Difficulties in Ultrasonic Inspection of Austenitic Welds 5

1.3 Modeling of Ultrasonic Wave Propagation in Anisotropic Welds: State of the Art 8

      1.3.1 Numerical Approaches 8

      1.3.2 Approximated Approaches 10

      1.3.3 Analytical Approaches 11

1.4 Motivation for the Present Research Work 13

1.5 Outline of the Thesis 14

2 Ultrasonic Wave Propagation in General Anisotropic Media 17

2.1 Introduction 17

2.2 Basic Physics in General Anisotropic Medium 17

      2.2.1 Christoffel Equation for General Anisotropic Solids 17

      2.2.2 Phase Velocity and Slowness Surface 23

      2.2.3 Polarization Vector 29

      2.2.4 Poynting Vector and Energy Density 30

      2.2.5 Energy Velocity Surface 33

2.3 Beam Distortion in Anisotropic Solids 35

      2.3.1 Beam Divergence 35

      2.3.2 Beam Skewing 35

      2.3.3 Beam Spreading Factor 38

3 Ultrasound Energy Reflection and Transmission Coefficients at an Interface between two Anisotropic Materials: Application to Austenitic Welds 41

3.1 Introduction 41

3.2 Reflection and Transmission of Ultrasound at an Interface between two General Anisotropic Materials 42

      3.2.1 Theoretical Procedure 42

      3.2.2 Six - degree Polynomial Equation 44

      3.2.3 Amplitude Coefficients for Reflected and Transmitted Waves 46

      3.2.4 Energy Coefficients for the Reflected and Transmitted Waves 46

      3.2.5 Critical Angle Phenomenon 47

3.3 General Interfaces Occur During Ultrasonic Inspection of Anisotropic Austenitic Welds 47

      3.3.1 Austenitic Weld Material – Isotropic Steel Interface 48

      3.3.2 Austenitic Weld Material – Isotropic Perspex Wedge Interface 52

      3.3.3 Isotropic Ferritic Steel – Austenitic Weld Material Interface 56

      3.3.4 Isotropic Perspex Wedge – Austenitic Weld Material Interface 60

      3.3.5 Austenitic – Austenitic Stainless Steel Interface 63

      3.3.6 Water – Austenitic Weld Interface 65

      3.3.7 Austenitic Weld – Water Interface 68

      3.3.8 Austenitic Weld – Free Surface Interface 72

3.4 Influence of Second Branch of Quasi Shear vertical Waves on Ultrasonic Examination of Austenitic Welds 75

3.5 Frequency Dependence of Energy Reflection and Transmission Coefficients in Anisotropic Austenitic Weld Materials 76

3.6 Validation of Numerical Results Based on Reciprocity Relations for Reflected and Transmitted Plane Elastic Waves 80

4 Analytical Evaluation of 3D Ultrasonic Ray Directivity Factor in Anisotropic Materials: Application to Austenitic Welds 83

4.1 Introduction 83

4.2 Theoretical Procedure: Ray Directivity Evaluation 83

4.3 Numerical Results and Discussion 86

      4.3.1 Amplitude and Energy Reflection Coefficients for the Reflected Waves at a Free Surface Boundary of an Austenitic Steel Material 86

      4.3.2 Point Source Directivity Pattern 88

5 Ray Tracing Model for Ultrasonic Wave Propagation in Inhomogeneous Anisotropic Austenitic Welds 95

5.1 Introduction 95

5.2 Modeling of Austenitic Weld Material Inhomogenity 95

      5.2.1 Comparison between Weld Structure Model and Macrograph of the Reallife Austenitic Weld 98

5.3 Ray Tracing Model for Point Sources 103

      5.3.1 Ray Energy Paths for Point Source Excitation 107

      5.3.2 Ray Incidence from Homogeneous Base Material 109

      5.3.3 Ray Incidence from Inhomogeneous Weld Material 111

      5.3.4 Back wall Reflected Rays from Homogeneous Base Material and Inhomogeneous Weld Material 112

      5.3.5 Back wall Mode Converted Reflected Rays from the Homogeneous-Base Material and Inhomogeneous Weld Material 114

      5.3.6 Ray Tracing of Mode Converted Rays at Weld Boundaries 118

5.4 Ray Tracing Model for Distributed Sources 119

5.5 Ray Tracing Model for Transversal Cracks in Inhomogeneous Anisotropic Austenitic Welds 122

5.6 Comparison of Ultrasonic Energy Ray Paths with Existed Results 124

6 Validation of Ray Tracing Model with 2D Elastodynamic Finite Integration Technique (EFIT) 129

6.1 Introduction 129

6.2 Elastodynamic Finite Integration Technique 129

6.3 Quantitative Evaluation of Ultrasonic Transducer Response (A-scan/C-scan) 130

6.4 Validation of Ray Tracing Model for Point Sources 132

      6.4.1 Application to Homogeneous Isotropic Layered Materials 132

      6.4.2 Application to Homogeneous Austenitic Stainless Steel Materials 134

      6.4.3 Application to Layered Austenitic Clad Materials 140

      6.4.4 Application to Inhomogeneous Austenitic Weld Materials 145

6.5 Validation of Ray Tracing Model for Distributed Sources 148

      6.5.1 Application to Homogeneous Isotropic Materials 148

      6.5.2 Application to Homogeneous Austenitic Steel Materials 150

      6.5.3 Application to Layered Austenitic Steel Materials 153

7 Quantitative Evaluation of Ultrasonic C-scan Image in Homogeneous and Layered Anisotropic Austenitic Steel Materials 157

7.1 Introduction 157

7.2 Quantitative Determination of Ultrasonic C-scan Image in an Anisotropic Austenitic Steel Material 157

      7.2.1 Effect of Columnar Grain Orientation on Ultrasonic C-scan Image 158

      7.2.2 Effect of Layback Orientation on Ultrasonic C-scan Image 161

      7.2.3 Quantitative Determination of Ultrasonic C-scan Image in Layered Anisotropic Austenitic Steel Material 161

7.3 Comparison of Ray Tracing Model Results with CIVA Simulation Tool 165

      7.3.1 Description on CIVA Simulation Tool 165

      7.3.2 Comparison Results on Inhomogeneous Austenitic Weld Material 167

8 Comparison of Ray Tracing Model Results with Experiments on Inhomogeneous Austenitic Welds 171

8.1 Introduction 171

8.2 Experimental Set up and Data Acquisition 171

      8.2.1 Investigated Samples 171

      8.2.2 Experimental Technique 171

      8.2.3 Experiments 174

8.3 Comparison Results 176

      8.3.1 Austenite Base Material 176

      8.3.2 Austenitic Weld Material 179

      8.3.3 Austenitic Clad Material 189

8.4 Discussion on Discrepancies between Ray Tracing and Experiments 191

9 Conclusions 195

9.1 Review of Thesis 195

9.2 Summary of Findings 199

      9.2.1 Ultrasonic Ray Propagation in General Anisotropic Materials 199

      9.2.2 Effect of Columnar Grain Orientation on Energy Reflection and Transmission Behaviour in Anisotropic Austenitic Weld Materials 200

      9.2.3 3D Ray Tracing Method for Quantitative Evaluation of Ultrasound in Inhomogeneous Anisotropic Austenitic Welds 201

      9.2.4 Applications of 3D Ray Tracing Method for Ultrasonic Non-Destructive Inspection of Transversal Defects in Austenitic Welds 202

9.3 Areas of Continued Research and Future Perspectives 203

References 205

Appendix A Transformation Matrices [M], [N] and Elastic Constant Matrix [ c_T ] 221

Appendix B Elements of a_m, b_m and c-m with m=1,2,3,4,5,6 223

Appendix C Coefficients of Six Degree Polynomial Equation 225

Appendix D Analytical Evaluation of Quartic Equation 227

Appendix E Expressions for Reflection and Transmission Coefficients at an Interface between two Transversely Isotropic Materials 231

Nomenclature 235

List of Figures 239

List of Tables 247

List of Publications 249

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