| Preface | 6 |
|---|
| Contents | 8 |
|---|
| Acronyms | 10 |
|---|
| Geometry | 10 |
| Material Properties | 10 |
| Electromechanical Fields | 11 |
| Applied Loading | 11 |
| Mathematical Symbols | 12 |
| Functions of Complex Variable | 12 |
| Abbreviations | 12 |
| 1 Literature Review on Cracks Located at the Interface of Dissimilar Materials (Interface Cracks) | 13 |
|---|
| 1.1 Classic Model of the Crack Between Two Materials | 14 |
| 1.2 Contact Model of the Crack Between Two Materials | 15 |
| 1.3 Cracks in Piezoelectric Materials | 16 |
| 1.4 Modeling of Cracks with Friction in the Contact Zone and Other Ways of Modeling of Pre-fracture Zones Near the Crack Tips | 18 |
| 1.5 Periodic Sets of Cracks | 18 |
| References | 19 |
| 2 Set of Cracks with Contact Zones Located at the Interface of Two Isotropic Materials | 24 |
|---|
| 2.1 Periodic Set of Interface Cracks | 24 |
| 2.1.1 Statement of the Problem and Its Reduction to the Periodic Dirichlet-Riemann Boundary Value Problem | 24 |
| 2.1.2 Solution of the Problem for a Periodic Set of Cracks with Contact Zones | 28 |
| 2.1.3 Derivation of the Classical ``Oscillating'' Solution as a Particular Case of the ``Contact'' Model Solution | 37 |
| 2.1.4 Determination of the Contact Zone Length and the Stress Intensity Factors | 38 |
| 2.1.5 Numerical Results | 39 |
| 2.2 Interaction of an Arbitrary Set of Interface Cracks | 43 |
| 2.2.1 Statement and Solution of the Dirichlet-Riemann BVP for a Set of Interface Cracks with Contact Zones | 43 |
| 2.2.2 Investigation of the Interaction of Two Cracks with Contact Zones | 52 |
| 2.3 Analysis of Results and Conclusions | 56 |
| References | 56 |
| 3 Set of Cracks with Contact Zones Located at the Interface of Two Anisotropic Materials | 57 |
|---|
| 3.1 Periodic Set of Interface Cracks | 57 |
| 3.1.1 Statement and Solution of the Problem for a Periodic Set of Cracks with Contact Zones | 57 |
| 3.1.2 Derivation of the Classical ``Oscillating'' Solution as a Particular Case of the ``Contact'' Model Solution | 64 |
| 3.1.3 Determination of the Contact Zone Length and Basic Fracture Parameters | 65 |
| 3.1.4 Assessment of the Obtained Solution and Analysis of the Results | 67 |
| 3.2 Interaction of an Arbitrary Set of Interface Cracks | 71 |
| 3.2.1 Statement and Solution of the Dirichlet-Riemann BVP for a Set of Interface Cracks with Contact Zones | 71 |
| 3.2.2 Investigation of the Interaction of Two Cracks with Contact Zones | 76 |
| 3.3 Analysis of Results and Conclusions | 79 |
| References | 80 |
| 4 Periodic Set of Cracks Located at the Interface of Piezoelectric Materials | 81 |
|---|
| 4.1 Basic Information About Piezoelectric Materials | 81 |
| 4.2 Fundamental Equations for Electromechanical Fields in Piezoelectric Materials | 83 |
| 4.3 Fully Electrically Permeable Cracks | 85 |
| 4.3.1 Solution to the Problem Within the Classical Model | 85 |
| 4.3.2 Solution to the Problem Within the Contact Model | 92 |
| 4.3.3 Fracture Behavior of Periodically Bonded Piezoelectric Interface Under Compressive-Shear Loading | 101 |
| 4.4 Cracks with Finite Electric Permittivity | 105 |
| 4.4.1 Solution for a Homogeneous Piezoelectric Material | 105 |
| 4.4.2 Solution to the Problem Within the Classical Model | 115 |
| 4.4.3 Solution to the Problem Within the Contact Model | 122 |
| 4.5 Conclusions | 133 |
| References | 133 |
| Appendix Conclusions | 134 |