Fracture Mechanics of Electrically Passive and Active Composites with Periodic Cracking along the Interface (eBook)

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