Dynamics, Strength of Materials and Durability in Multiscale Mechanics

410 Pages·2021·18.609 MB·English

by  Francesco dell'Isola, Leonid Igumnov

Advanced Structured Materials
Francesco dell’Isola
Leonid Igumnov   Editors
Dynamics, Strength
of Materials
and Durability
in Multiscale
Mechanics
Advanced Structured Materials
Volume 137
Series Editors
Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of
Applied Sciences, Esslingen, Germany
Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of
Engineering, University of Porto, Porto, Portugal
Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke
University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany
Common engineering materials reach in many applications their limits and new
developments are required to fulfil increasing demands on engineering materials.
The performance ofmaterials can beincreasedby combiningdifferent materials to
achieve better properties than a single constituent or by shaping the material or
constituents in a specific structure. The interaction between material and structure
mayariseondifferentlengthscales,suchasmicro-,meso-ormacroscale,andoffers
possible applications in quite diverse fields.
Thisbookseriesaddressesthefundamentalrelationshipbetweenmaterialsandtheir
structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic
etc.) and applications.
The topics of Advanced Structured Materials include but are not limited to
(cid:129) classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced
plastics)
(cid:129) metal matrix composites (MMCs)
(cid:129) micro porous composites
(cid:129) micro channel materials
(cid:129) multilayered materials
(cid:129) cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere
structures)
(cid:129) porous materials
(cid:129) truss structures
(cid:129) nanocomposite materials
(cid:129) biomaterials
(cid:129) nanoporous metals
(cid:129) concrete
(cid:129) coated materials
(cid:129) smart materials
Advanced Structured Materials is indexed in Google Scholar and Scopus.
More information about this series at http://www.springer.com/series/8611
’
Francesco dell Isola Leonid Igumnov
(cid:129)
Editors
Dynamics, Strength
of Materials and Durability
in Multiscale Mechanics
123
Editors
Francesco dell’Isola LeonidIgumnov
Dipartimento di IngegneriaStrutturale Research Institute for Mechanics
Universitàdegli Studi dell’Aquila National Research LobachevskyState
MEMOCS University of Nizhny Novgorod
L’Aquila, Italy Nizhny Novgorod,Russia
Universitàdi Roma“La Sapienza”
Rome, Italy
ISSN 1869-8433 ISSN 1869-8441 (electronic)
AdvancedStructured Materials
ISBN978-3-030-53754-8 ISBN978-3-030-53755-5 (eBook)
https://doi.org/10.1007/978-3-030-53755-5
©SpringerNatureSwitzerlandAG2021
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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 andSolutiontotheGeneralProblemofWaves
Propagation in Gradient-Elastic Medium . . . . . . . . . . . . . . . . . 19
2.4 The Statement and Solution to the Problem of a Gradient-
Elastic Medium with a Moving Source Generating Surface
Waves.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 The Subsonic Case. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
v
vi Contents
2.4.2 The Supersonic Case . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 On the Spectrum of Relaxation Times in Coupled Diffusion
and Rheological Processes in Metal Alloys . . . . . . . . . . . . . . . . . . . 41
Dmitry Dudin and Ilya Keller
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 The Brassart’s Model Supplemented with Elastic Strains. . . . . . 43
3.2.1 Deformation and Volumetric Expansion . . . . . . . . . . . 43
3.2.2 Free Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.3 Thermodynamic Inequality . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Elastic Relations and Functions of State . . . . . . . . . . . 46
3.2.5 Kinetic Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.6 Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Analysis of Relaxation of Spatial Perturbations . . . . . . . . . . . . 48
3.3.1 Model Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.2 Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.3 Perturbed System and Its Analysis . . . . . . . . . . . . . . . 49
3.3.4 The Relaxation Time of Perturbations
and Their Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Finite Element Method Study of the Protection Damping
Elements Dynamic Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Anastasia V. Demareva, Aleksandr I. Kibets, Maria V. Skobeeva,
Oleg G. Savichin, and Aleksandr F. Lyakhov
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Constitutive System of Equations and Problem
Solution Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 MHS Filler Modeling. . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Results of Computational Experiments. . . . . . . . . . . . . . . . . . . 61
4.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Analyzing the Problem of a Spherical Cavity Expansion
in a Medium with Mohr-Coulomb-Tresca’s Plasticity
Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Vasiliy L. Кotov, Elena Yu. Linnik, and Tatiana A. Sabaeva
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Formulation of an Initial Boundary-Value Problem
for a System of Partial Differential Equations. . . . . . . . . . . . . . 69
Contents vii
5.3 Formulating a Boundary-Value Problem for a System of Two
First-Order Ordinary Differential Equations in the Plastic
Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.4 Formulation and Solution of the Boundary-Value Problem
for Second-Order ODE’s in the Elastic Deformation Region . . . 71
5.5 Determining the Critical Pressure. . . . . . . . . . . . . . . . . . . . . . . 74
5.6 An Analytical Solution of the Cavity Expansion Problem
in a Medium with a Linear Shock Adiabat. . . . . . . . . . . . . . . . 78
5.7 Determining Stresses in a Medium with the Mohr-Coulomb
Yield Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.8 Determining Stress in a Medium with Mohr-Coulomb-
Tresca’s Yield Condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.9 Comparative Analysis of the Results of Analyzing the Cavity
Problem in Media with Tresca’s, Mohr-Coulomb,
and Mohr-Coulomb-Tresca’s Plasticity Conditions . . . . . . . . . . 83
5.10 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Construction of the Solutions of Non-stationary Dynamic
Problems for Linear Viscoelastic Bodies with a Constant
Poisson’s Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Leonid Igumnov, Ekaterina A. Korovaytseva,
and Sergey G. Pshenichnov
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Mathematical Statement of Problem. . . . . . . . . . . . . . . . . . . . . 90
6.3 Representation of the Problem in Transform Domain . . . . . . . . 91
6.4 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.5 Notes and Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7 Features of Subsonic Stage of Contact Interaction of Viscoelastic
Half-Plane and Absolutely Rigid Striker. . . . . . . . . . . . . . . . . . . . . 97
Leonid Igumnov, Ekaterina A. Korovaytseva,
and Dmitrii V. Tarlakovskii
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.3 Green Function Construction. . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4 Contact Problem Solution Algorithm . . . . . . . . . . . . . . . . . . . . 104
7.5 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
viii Contents
8 Interaction of Harmonic Waves of Different Types
with the Three-Layer Plate Placed in the Soil. . . . . . . . . . . . . . . . . 111
Leonid Igumnov, Dmitrii V. Tarlakovskii, Natalia A. Lokteva,
and Nguyen Duong Phung
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.2 ProblemStatementofInteractionofHarmonicSphericalWave
Propagating in Continuum and a Three-Layered Plate. . . . . . . . 112
8.3 Motion Equation of Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.4 Incoming Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.5 The Plate Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.6 Conditions on the Contact Surface. . . . . . . . . . . . . . . . . . . . . . 118
8.7 Fourier Decomposition of Unknown Functions. . . . . . . . . . . . . 119
8.8 Computing of the Fourier Coefficients for the Potentials
in Ambient Media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.9 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.10 Notes and Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9 Computer Simulation of the Process of Loss of Stability
of Composite Cylindrical Shells Under Combined Quasi-static
and Dynamic Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Nikolaii A. Abrosimov, Aleksandr V. Elesin, and Leonid Igumnov
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.2 Problem Formulation and Solution Method . . . . . . . . . . . . . . . 126
9.3 Results of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.3.1 Internal Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9.3.2 External Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
10 The Effect of Preheating on the Thermoelastic Structurally
Inhomogeneous Medium Spectral Properties in the Presence
of an Initial Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Galina Yu. Levi, Leonid Igumnov, and Mikhail O. Levi
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.2 Formulation of the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.3 The 3D Linear Thermoelasticity Equations. . . . . . . . . . . . . . . . 141
10.4 The Plane Surface Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.5 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Contents ix
11 Numerical Evaluation of Integrals in Laplace Domain
Anisotropic Elastic Fundamental Solutions for High
Frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Ivan P. Markov and Marina V. Markina
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.2 Fundamental Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.3 Evaluation of Integrals I ½u;s(cid:2) and I ½u;s(cid:2). . . . . . . . . . . . . . . . 158
1 2
11.4 Numerical Example and Discussions . . . . . . . . . . . . . . . . . . . . 161
11.4.1 Numerical Example Explanation . . . . . . . . . . . . . . . . . 161
11.4.2 Computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
11.4.3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
12 The Dynamics of Eccentric Vibration Mechanism (Part 2). . . . . . . 173
Leonid Igumnov, S. Vladimir Metrikin, V. Irina Nikiforova,
and Lubov N. Fevral’skikh
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
12.2 Problem Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
12.3 The Phase Space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.4 Investigation of Nonlinear Dynamics of the Mechanism
Using the Method of Point Transformations. . . . . . . . . . . . . . . 178
12.5 The Numerical Study of the Dynamics of the Mechanism. . . . . 181
12.5.1 The Region of Existence and Stability of Periodic
Motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
12.5.2 Coordinate Dependencies of Fixed Points
on Frequency Parameter . . . . . . . . . . . . . . . . . . . . . . . 182
12.5.3 Bifurcation Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 183
12.5.4 The Analysis of the Diagrams and Stability
Regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
12.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
13 HighStrainRateTensionExperimentsFeaturesforVisco-Plastic
Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Artem V.Basalin,AnatoliiM. Bragov, Aleksandr Yu. Konstantinov,
Andrey K. Lomunov, and Aleksandr V. Zhidkov
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
13.2 Split Hopkinson bar Technique . . . . . . . . . . . . . . . . . . . . . . . . 192
13.3 High Strain Rate Tension Based on Measuring Bars
Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
13.3.1 Schemes for Dynamic Tension Experiments . . . . . . . . 194
13.3.2 Experimental Setups. . . . . . . . . . . . . . . . . . . . . . . . . . 198
13.3.3 True Stresses and Strains in the Tension
Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198