Chapter 1
Modeling Fatigue Life of Structural
Alloys Under Block Asymmetric Loading
Ivan A. Volkov, Leonid Igumnov, Ivan S. Tarasov, Denis N. Shishulin,
and Denis V. Kapitanov
Abstract The processes of plastic deformation and damage accumulation of polycrystalline structural alloys under block-type non-stationary asymmetric cyclic
loading are considered. A mathematical model describing the processes of thermoplastic deformation and fatigue damage accumulation under low-cycle loading has
been developed, based on the viewpoint of mechanics of damaged media (MDM).
The MDM model consists of three interrelated parts: governing equations defining
the cyclic thermoplastic behavior of the material, taking into account its dependence
on the failure process; equations describing the kinetics of damage accumulation;
a strength criterion of the damaged material. A version of the constitutive equations of elastoplasticity is based on the concept of the yield surface and the gradient
principle of the plastic strain rate vector to the yield surface in the loading point.
This version of equations of state reflects the main effects of the cyclic thermoplastic material deformation process for arbitrary complex deformation trajectories.
A version of the kinetic equations of damage accumulation based on the introduction
of a scalar damage parameter has been proposed. Based on the energy principles,
it accounts for the main effects of nucleation, growth and merging of microdefects
under random complex regimes of low-cycle loading. The condition for achieving
the critical damage value is used as the strength criterion of a damaged material.
To assess the reliability and determine the scope of applicability of the constitutive
equations of MDM, the processes of plastic deformation and damage accumulation
in a number of structural steels in low-cycle tests have been numerically analyzed,
and the obtained numerical results have been compared with the data of full-scale
experiments. It is shown that the proposed model of damaged media qualitatively
and quantitatively, with the accuracy required for practical calculations, describes
the main effects of plastic deformation processes and fatigue damage accumulation
in structural alloys under block non-stationary asymmetric low-cycle loading.
I. A. Volkov (B) · L. Igumnov · I. S. Tarasov · D. N. Shishulin · D. V. Kapitanov
Research Institute for Mechanics, National Research Lobachevsky State University of Niznhy
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russian Federation
e-mail: pmptmvgavt@yandex.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_1
1
Modeling Fatigue Life of Structural
Alloys Under Block Asymmetric Loading
Ivan A. Volkov, Leonid Igumnov, Ivan S. Tarasov, Denis N. Shishulin,
and Denis V. Kapitanov
Abstract The processes of plastic deformation and damage accumulation of polycrystalline structural alloys under block-type non-stationary asymmetric cyclic
loading are considered. A mathematical model describing the processes of thermoplastic deformation and fatigue damage accumulation under low-cycle loading has
been developed, based on the viewpoint of mechanics of damaged media (MDM).
The MDM model consists of three interrelated parts: governing equations defining
the cyclic thermoplastic behavior of the material, taking into account its dependence
on the failure process; equations describing the kinetics of damage accumulation;
a strength criterion of the damaged material. A version of the constitutive equations of elastoplasticity is based on the concept of the yield surface and the gradient
principle of the plastic strain rate vector to the yield surface in the loading point.
This version of equations of state reflects the main effects of the cyclic thermoplastic material deformation process for arbitrary complex deformation trajectories.
A version of the kinetic equations of damage accumulation based on the introduction
of a scalar damage parameter has been proposed. Based on the energy principles,
it accounts for the main effects of nucleation, growth and merging of microdefects
under random complex regimes of low-cycle loading. The condition for achieving
the critical damage value is used as the strength criterion of a damaged material.
To assess the reliability and determine the scope of applicability of the constitutive
equations of MDM, the processes of plastic deformation and damage accumulation
in a number of structural steels in low-cycle tests have been numerically analyzed,
and the obtained numerical results have been compared with the data of full-scale
experiments. It is shown that the proposed model of damaged media qualitatively
and quantitatively, with the accuracy required for practical calculations, describes
the main effects of plastic deformation processes and fatigue damage accumulation
in structural alloys under block non-stationary asymmetric low-cycle loading.
I. A. Volkov (B) · L. Igumnov · I. S. Tarasov · D. N. Shishulin · D. V. Kapitanov
Research Institute for Mechanics, National Research Lobachevsky State University of Niznhy
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russian Federation
e-mail: pmptmvgavt@yandex.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_1
1