2
I. A. Volkov et al.
Keywords Soil · Plate · Paimushin V.nN model · Harmonic wave · Oscillation
frequency · Vibration absorption · Vibrational acceleration
1.1 Introduction
Cyclic properties of structural materials are extremely important for the reliable
assessment of strength and service life of structural elements and supporting units
subjected to alternating combined thermomechanical effects. Evaluation of life of
structural elements using finite element analysis of inelastic strains in hazardous
zones of structural elements requires formulating the constitutive relations of thermoplasticity, which account for real cyclic properties of materials (Mitenkov et al.
2007).
Special attention is currently paid to experimental study of laws of cyclic deformation processes. It has been found that stationary cyclic deformation (if it takes
place) is preceded by a transition stage determined by cyclic hardening, softening
or relaxation of the memory of the material about the preceding cyclic deformation
history. Parameters of a stabilized plastic hysteresis loop do not depend on the place
of its stabilization. In asymmetric cyclic deformation, the material can show onesided accumulation of plastic deformation. During hard cyclic loading with initial
anisotropy of the stress amplitude at half-cycles of tension and compression, average
cycle stresses are observed to relax up to zero in a finite number of loading cycles.
When mechanical loads and temperature act simultaneously but do not change in
phase, processes of cyclic change of stresses, total and plastic strains are multi-axial
and non-proportional, leading to additional effects of cyclic behavior of materials.
The results of experimental studies of these processes show that the behavior of structural materials under cyclic proportional loading differs significantly from that under
monotone deformation processes (the laws of cyclic hardening substantially differ
from those of monotone deformation). In their turn, multi-axial non-proportional
cyclic processes substantially differ from the proportional cyclic ones (Lamba 1978;
Macdowell 1985; Ohasi et al. 1985; Tanaka et al. 1985a, b; Hassan et al. 2008; Huang
et al. 2014; Jiang and Zhang 2008; Taleb et al. 2014).
Equations of state constructed on the basis of monotone loading processes and not
accounting for specific features of cyclic deformation under proportional and nonproportional loading may lead to big errors in determining the main parameters of the
stressed–strained state, which are then used for evaluating service life characteristics
of materials. Formulation of the reliable constitutive equations of thermoplasticity
for the above processes requires, in the first place, experimental studies of the effects
of cyclic behavior of structural materials under proportional and non-proportional
loading (Volkov and Korotkikh 2008; Mitenkov et al. 2015; Bondar and Danshin,
2008; Chaboche 1989; Bodner and Lindholm 1976; Lemaitre 1985).
Classical methods for predicting service life of materials using semiempirical
formulas (rules), based on a stable analysis of the deformation process and connecting
the parameters of plastic hysteresis loops with a number of cycles prior to failure,
I. A. Volkov et al.
Keywords Soil · Plate · Paimushin V.nN model · Harmonic wave · Oscillation
frequency · Vibration absorption · Vibrational acceleration
1.1 Introduction
Cyclic properties of structural materials are extremely important for the reliable
assessment of strength and service life of structural elements and supporting units
subjected to alternating combined thermomechanical effects. Evaluation of life of
structural elements using finite element analysis of inelastic strains in hazardous
zones of structural elements requires formulating the constitutive relations of thermoplasticity, which account for real cyclic properties of materials (Mitenkov et al.
2007).
Special attention is currently paid to experimental study of laws of cyclic deformation processes. It has been found that stationary cyclic deformation (if it takes
place) is preceded by a transition stage determined by cyclic hardening, softening
or relaxation of the memory of the material about the preceding cyclic deformation
history. Parameters of a stabilized plastic hysteresis loop do not depend on the place
of its stabilization. In asymmetric cyclic deformation, the material can show onesided accumulation of plastic deformation. During hard cyclic loading with initial
anisotropy of the stress amplitude at half-cycles of tension and compression, average
cycle stresses are observed to relax up to zero in a finite number of loading cycles.
When mechanical loads and temperature act simultaneously but do not change in
phase, processes of cyclic change of stresses, total and plastic strains are multi-axial
and non-proportional, leading to additional effects of cyclic behavior of materials.
The results of experimental studies of these processes show that the behavior of structural materials under cyclic proportional loading differs significantly from that under
monotone deformation processes (the laws of cyclic hardening substantially differ
from those of monotone deformation). In their turn, multi-axial non-proportional
cyclic processes substantially differ from the proportional cyclic ones (Lamba 1978;
Macdowell 1985; Ohasi et al. 1985; Tanaka et al. 1985a, b; Hassan et al. 2008; Huang
et al. 2014; Jiang and Zhang 2008; Taleb et al. 2014).
Equations of state constructed on the basis of monotone loading processes and not
accounting for specific features of cyclic deformation under proportional and nonproportional loading may lead to big errors in determining the main parameters of the
stressed–strained state, which are then used for evaluating service life characteristics
of materials. Formulation of the reliable constitutive equations of thermoplasticity
for the above processes requires, in the first place, experimental studies of the effects
of cyclic behavior of structural materials under proportional and non-proportional
loading (Volkov and Korotkikh 2008; Mitenkov et al. 2015; Bondar and Danshin,
2008; Chaboche 1989; Bodner and Lindholm 1976; Lemaitre 1985).
Classical methods for predicting service life of materials using semiempirical
formulas (rules), based on a stable analysis of the deformation process and connecting
the parameters of plastic hysteresis loops with a number of cycles prior to failure,