Contents
1 Modeling Fatigue Life of Structural Alloys Under Block
Asymmetric Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Ivan A. Volkov, Leonid Igumnov, Ivan S. Tarasov,
Denis N. Shishulin, and Denis V. Kapitanov
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 Constitutive Equations of MDM . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.1 Constitutive Equations in Plasticity . . . . . . . . . . . . . . .
3
1.2.2 Evolutionary Equations Describing Fatigue Damage
Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.3 Strength Criterion of Damaged Material . . . . . . . . . . .
7
1.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3.1 Block-Type Asymmetric Soft Cyclic Loading . . . . . . .
8
1.3.2 Multi-axial Proportional and Non-proportional
Regimes of Soft Block-Type Cyclic Loading . . . . . . . .
9
1.3.3 Hard Block-Type Asymmetric Low-Cycle Loading . . . 12
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Excitation of the Waves with a Focused Source, Moving Along
the Border of Gradient-Elastic Half-Space . . . . . . . . . . . . . . . . . . . 17
Artem M. Antonov, Vladimir I. Erofeev, Aleksey O. Malkhanov,
and Nadezhda A. Novoseltseva
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 The Basic Equations of Gradient Theory of Elasticity . . . . . . . . 19
2.3 The Statement and Solution to the General Problem of Waves
Propagation in Gradient-Elastic Medium . . . . . . . . . . . . . . . . . 19
2.4 The Statement and Solution to the Problem of a GradientElastic Medium with a Moving Source Generating Surface
Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 The Subsonic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
v
1 Modeling Fatigue Life of Structural Alloys Under Block
Asymmetric Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Ivan A. Volkov, Leonid Igumnov, Ivan S. Tarasov,
Denis N. Shishulin, and Denis V. Kapitanov
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 Constitutive Equations of MDM . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.1 Constitutive Equations in Plasticity . . . . . . . . . . . . . . .
3
1.2.2 Evolutionary Equations Describing Fatigue Damage
Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.3 Strength Criterion of Damaged Material . . . . . . . . . . .
7
1.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3.1 Block-Type Asymmetric Soft Cyclic Loading . . . . . . .
8
1.3.2 Multi-axial Proportional and Non-proportional
Regimes of Soft Block-Type Cyclic Loading . . . . . . . .
9
1.3.3 Hard Block-Type Asymmetric Low-Cycle Loading . . . 12
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Excitation of the Waves with a Focused Source, Moving Along
the Border of Gradient-Elastic Half-Space . . . . . . . . . . . . . . . . . . . 17
Artem M. Antonov, Vladimir I. Erofeev, Aleksey O. Malkhanov,
and Nadezhda A. Novoseltseva
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 The Basic Equations of Gradient Theory of Elasticity . . . . . . . . 19
2.3 The Statement and Solution to the General Problem of Waves
Propagation in Gradient-Elastic Medium . . . . . . . . . . . . . . . . . 19
2.4 The Statement and Solution to the Problem of a GradientElastic Medium with a Moving Source Generating Surface
Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 The Subsonic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
v